optimización del cálculo de lentes paraxial verónica mateo ... · a mis compañeros y amigos del...

Optimización del cálculo de lentes intraoculares monofocales, acomodativas y multifocales mediante la corrección del error queratométrico empleando óptica paraxial

Verónica Mateo Pérez

http://www.ua.es/

http://www.eltallerdigital.com/

DepartamentodeÓptica,FarmacologíayAnatomía

FacultaddeCiencias

TESISDOCTORAL

OPTIMIZACIÓNDELCÁLCULODELENTES

INTRAOCULARESMONOFOCALES,

ACOMODATIVASYMULTIFOCALES

MEDIANTELACORRECCIÓNDELERROR

QUERATOMÉTRICOEMPLEANDOÓPTICA

PARAXIAL

Doctoranda:VerónicaMateoPérez

TesispresentadaparaaspiraralgradodeDOCTORAPORLAUNIVERSIDADDEALICANTE

DOCTORADOENTECNOLOGÍASPARALASALUDYELBIENESTAR

(VISIÓNYOPTOMETRÍA)

Dirigidapor:D.DavidP.PiñeroLlorensD.VicenteJ.CampsSanchís

Julio2016

D.VICENTEJESÚSCAMPSSANCHÍS,DoctorporlaUniversidaddeAlicanteyD.DAVID

PABLOPIÑEROLLORENS,DoctorporlaUniversidaddeAlicanteyProfesorAsociado

(Acreditado para titular en el área de Óptica) del Departamento de Óptica,

FarmacologíayAnatomíadelaFacultaddeCienciasdelaUniversidaddeAlicante:

CERTIFICA: Quelapresentememoriatitulada“Optimizacióndelcálculodelentes

intraocularesmonofocales,acomodativasymultifocalesmediante

lacorreccióndelerrorqueratométricoempleandoópticaparaxial”

ha sido realizada bajo su dirección por Doña VERÓNICA MATEO

PÉREZenelDepartamentodeÓptica,FarmacologíayAnatomíadela

Facultad de Ciencias de la Universidad de Alicante y constituye su

TesisDoctoralparaoptaralGradodeDoctor.

Y para que conste, y en cumplimiento de la legislación vigente, firman el presente

certificadoenAlicanteaveintisietedejuniodedosmildieciséis.

Fdo.VicenteJCampsSanchís Fdo.DavidPPiñeroLlorens

Agradecimientos: AvosotrosDavidyVicent,tutoresycompañerosdefatigas,portenerestetoque

delocuraalpensarqueseríaunabuenaideatutelarmedespuésdesupervisarmeelTFM

y TFG, dejándome de esta manera continuar aprendiendo de vosotros (espero no

haberosdefraudado…)

Al Hospital Internacional Medimar (Alicante), por darme la oportunidad de

elaborarlasbasesdedatosconsuspacientes.

ADolo,porsuinestimableayudaenlaprogramacióndeMatlab.

A mis compañeros y amigos del máster (Silvia, Esteban, Esther, Eli, Blanca,

Oscar,Vicenta,Maite)quedesdeelprincipiodemiandadurahanestadopreocupándose

pormisavancesyesperanansiososelgrandía.

Amifamilia,porvuestrocariñoysobretodograciasporlaconfianzaquehabéis

depositadosiempreenmí,hacéisquemeatrevaaemprendercualquierproyectoporque

séquesiemprevaisaestarallíparaapoyarme.

MuchasGracias

ÍNDICE Índiceabreviaturas

Capítulo0: Artículosqueconformanlatesis 13

Capítulo1:Introducciónyaspectosgenerales

1.a.Fórmulasdecálculodelentesintraoculares

19

21

1.a.1.Fórmulasde1ªgeneración. 21

1.a.2.Fórmulasde2ªgeneración 23



1.b.FactoresdeerrorenelcálculodelaPIOL 31

1.b.1.Longitudaxial(AL) 32

1.b.2.Posiciónefectivadelalente(ELP) 33

1.b.3.Potenciacorneal(Pc) 35

1.c.Antecedentesyestadoactual 36

1.d.Diseñosdelentesintraoculares 39

1.d.1.Lentesintraocularesacomodativas 40

1.d.2.Lentesintraocularesmultifocales 41

1.d.3.Lentesintraocularesasféricas 44

Capítulo2: Hipótesisyobjetivos 47

2.a.Hipótesis 49

2.b.Objetivos 49

Capítulo3: Materialesymétodos

3.a.Cálculodelapotenciacornealgaussiana(𝑃!!"#$$)y

queratométrica(Pk)

53

53

3.b.Diferenciasentrelapotenciacornealgaussianay

queratométrica(ΔPc) 54

3.c.Obtencióndelíndicequeratométricoexacto(nkexacto)y

ajustado(nkadj) 54

3.d.Obtenciónpotenciadelalenteintraocularqueratométrica

(𝑃!"#! )yGaussiana(𝑃!"#!"#$$) 56

3.e.Obtenciónpotenciadelalenteintraocularajustada

(PIOLadj) 59

3.f.Estimaciónposiciónefectivadelalenteajustada(ELPadj) 61

3.g.Seleccióndepacientes 62

3.h.Protocolodeexamendelospacientes 62

3.i.SistemaPentacam® 62

3.j.Lentesintraocularesutilizadasenlosestudios 64

3.k.Técnicaquirúrgica 66

3.l.Examenpreypostoperatorio

3.m.Análisisestadísticodelosresultados

67

67

Capítulo4: Resultadosydiscusión

4.a.ResultadosenrelaciónconelobjetivoA

69

71

4.b.ResultadosenrelaciónconelobjetivoB 76

4.c.ResultadosenrelaciónconelobjetivoC 86

4.d.ResultadosenrelaciónconelobjetivoD 95

4.e.ResultadosenrelaciónconelobjetivoE 106

Capítulo5: Conclusionesyperspectivasdefuturo 119

5.a.Conclusiones 121

5.b.Perspectivasdefuturo 122

Capítulo6: Referencias 125

Apéndice 143

Trabajo1 145

Clinicalvalidationofanalgorithmtocorrecttheerrorinthekeratometric

estimationofcornealpowerinnormaleyes

Trabajo2 151

MinimizingtheIOLpowererrorinducedbykeratometricpower

Trabajo3 163

Positional accommodative intraocular lens power error induced by the

estimationofthecornealpowerandtheeffectivelensposition

Trabajo4 171

Error induced by estimation of the corneal power and the effective lens

position with a rotationally asymmetric refractive multifocal

intraocularlens

Trabajo5 179

Preliminary evaluation of an algorithm to minimize the power error

selection of an aspheric intraocular lens by optimizing the

estimationofthecornealpowerandtheeffectivelensposition

ÍNDICEDEABREVIATURAS

ΔPc:DiferenciaentrelapotenciacornealqueratométricaylapotenciacornealcalculadaporelmétododeGauss

ΔPIOL: Diferencia entre la potencia de lente intraocular queratométrica y lapotenciadelalenteintraocularcalculadaporelmétododeGauss

ACA: Astigmatismodelacaraanterior

ACP: Astigmatismodelacaraposterior

ACD: Profundidaddelacámaraanterior(AnteriorChamberDepth)

ACDpost: Profundidaddelacámaraanteriorpostoperatoria

ACDpre: Profundidaddelacámaraanteriorpreoperatoria

AEN: Aberraciónesféricanegativa

AEP: Aberraciónesféricapositiva

AL: Longitudaxial(AxialLength)

BCVA: Agudezavisualconlamejorcorrección(BestCorrectionVisualAcuity)

CA: Astigmatismocorneal(cornealastigmatism)

ec: Espesorcorneal

eL: Espesordelcristalino

eLcorr: Espesorcorregidodelcristalino

ELP: Posiciónefectivadelalente(EffectiveLensPosition)

ELPadj: Posiciónefectivadelalenteajustada

ELPHaigis: PosiciónefectivadelalentecalculadamediantelafórmuladeHaigis

ELPHolladay: PosiciónefectivadelalentecalculadamediantelafórmulaHolladay

ELPHofferQ: PosiciónefectivadelalentecalculadamediantelafórmulaHofferQ

ELPSRK/T: PosiciónefectivadelalentecalculadamediantelafórmulaSRK/T

F: PotenciavariableenfuncióndelalongitudaxialenlafórmulaSRKII

factorS: Factor variable debido a la forma de la lente intraocular, fabricación,técnicadelcirujanoydispositivodemedida

FIV: Factorinflacióndelavarianza

H: Alturacorneal(distanciaentreelvérticecorneal-planodeliris)

Hc,H´c: Planosprincipalesdelacórnea

HIOL,H´IOL: Planosprincipalesdelalenteintraocular.

IOL: Lenteintraocular(IntraocularLens)

k: Razónentreradiocaraanterioryposteriorcorneal(𝑟!!/𝑟!!)

L: Grosorretiniano

LoA: Límitesdeacuerdo(LimitsofAgreement)

nc: Índicederefraccióndelacórnea

nha: Índicederefraccióndelhumoracuoso

nhv: Índicederefraccióndelhumorvítreo

nk: Índicederefracciónqueratométrico

nkadj: Índicederefracciónqueratométricoajustado

nkexact: Índicederefracciónqueratométricoexacto

P1c: Potenciacaraanteriordelacórnea

P2c: Potenciacaraposteriordelacórnea

Pc: Potenciacorneal

PcHaigis:PotenciacornealcalculadaparalafórmuladeHaigiscuandoseutilizaunvalordeíndicequeratométrico1.3315

𝑷𝒄𝑮𝒂𝒖𝒔𝒔 PotenciacornealcalculadaporelmétododeGauss

PIOL: Potencialenteintraocular

𝑷𝑰𝑶𝑳𝒌 : Potencialenteintraocularqueratométrica

PIOLadj: Potencialenteintraocularajustada

PIOLadjSRK/T:Potencia lente intraocular ajustada, cuando se usa el valor de ELPobtenidomediantelafórmulaSRK/T

𝑷𝑰𝑶𝑳𝑮𝒂𝒖𝒔𝒔: Potencialenteintraocularqueratométrica

PIOLHaigis: PotencialenteintraocularcalculadamediantelafórmuladeHaigis

PIOLHofferQ: PotencialenteintraocularcalculadamediantelafórmuladeHofferQ

PIOLHolladay: PotencialenteintraocularcalculadamediantelafórmuladeHolladay

PIOLSRK/T: PotencialenteintraocularcalculadamediantelafórmulaSRK/T

PIOLReal: Potencialenteintraocularimplantada

Pk: Potenciacornealqueratométrica

Pk(1.3375):Potencia corneal queratométrica calculada con el índice queratométrico1.3375

Pkadj: Potenciaqueratométricacalculadaconelíndicequeratométricoajustado

r1c: Radiocaraanteriorcorneal

r2c: Radiocaraposteriorcorneal

rc: Radiocorneal

Rdes: Refraccióndeseada

Rpre: Refracciónpreoperatoria

Rpost: Refracciónpostoperatoria

S: Vérticecorneal

SD: Desviaciónestándar(StandardDeviation)

SE: Equivalenteesférico(Sphericalequivalent)

SEpre: Equivalenteesféricopreoperatorio

SEpost: Equivalenteesféricopostoperatorio

WTW: Blancoablanco(WhitetoWhite)

Capítulo0

ARTÍCULOSQUECONFORMANLATESIS

15

ARTÍCULOSQUECONFORMANLATESIS

Lapresentetesis, laconformanuntotalde5artículospublicadosenrevistas

deimpactoanivelinternacional.Dichosartículosseenumeranacontinuaciónsegún

suordendedesarrollodurantelainvestigación:

1. Piñero DP, Camps VJ, Mateo V, Ruiz-Fortes P. Clinical validation of an

algorithm to correct the error in the keratometric estimation of corneal

power in normal eyes. J Cataract Refract Surg. 2012 Aug; 38(8): 1333-

1338.

2. CampsVJ,PiñeroDP,deFezD,MateoV.Minimizing the IOLpowererror

inducedbykeratometricpower.OptomVisSci.2013Jul;90(7):639-49.

3. PiñeroDP,CampsVJ,RamonML,MateoV,Pérez-CambordíRJ.Positional

accommodativeintraocularlenspowererrorinducedbytheestimationof

the corneal power and the effective lens position. Indian J Ophthalmol

2015May;63(5):438-44.

4. Piñero DP, Camps VJ, Ramon ML, Mateo V, Pérez-Cambordí RJ. Error

induced by the estimation of the corneal power and the effective lens

position with a rotationally asymmetric refractive multifocal intraocular

lens.IntJOphthalmol2015Jun18;8(3):501-7.

5. Piñero DP, Camps VJ, Ramon ML, Mateo V, Soto-Negro R. Preliminary

evaluation of an algorithm to minimize the power error selection of an

aspheric intraocular lens by optimizing the estimation of the corneal

powerandtheeffectivelensposition.IntEyeSci2016Jun;16(6):1001-8

15

Capítulo1

INTRODUCCIÓN

19

1.INTRODUCCIÓN

El cristalino en su forma natural es transparente y actúa como una lente

enfocandolaluzqueentraenelojo.Debidoalpasodelosaños,elcristalinopuedeir

perdiendoesa transparencianaturaly convertirseenuna lenteopaca,produciendo

unadisminuciónde la visiónque en casos avanzadospuededar lugar a ceguera.A

este fenómeno de opacificación se le denomina catarata. En estadíos avanzados de

opacificación, es necesario la extracción de la catarata y la sustitución del poder

dióptricodelcristalinoporeldeunalenteintraocular.

Lacatarataeslaprincipalcausadeceguerareversible.Lastécnicasquirúrgicas

para su extracciónhan idoevolucionando conelpasode los años.Hacemásde50

años,noserealizabaningúncálculodelenteintraocular,únicamenteserealizabauna

extracciónintracapsulardelcristalino.Elproblemaquepresentabaestemétodoera

queelpacientequedabaafáquico,precisandounacorrecciónópticahipermetrópica

elevada (fig.1)parapoderdesarrollarunavidanormal.Estemétododecorrección

provocabaaberracionesydebidoalelevadopesodelaslenteshacíaqueestasolución

nofueralaideal.

Figura1:Gafaparaafaquia.(Fuente:www.qvision.es)

La técnica quirúrgica evolucionó hasta poder realizar extracciones

extracapsulares,permitiendoinsertarunalenteintraoculardentrodelojo,conelfin

deproporcionarimágenesretinianassimilaresaltamañofisiológico,consiguiéndose

así una corrección óptica más adecuada. A partir de este momento, comienzan a

Capítulo1

Introducción

20

implantarselentesencirugíadecataratasdeigualpotenciaparatodoslospacientes

(por ejemplo +18 D)(1), lo que provocaba ametropías elevadas, debido a que la

longitudaxialylapotenciacornealnotienenelmismovalorentodoslosojos.

En las últimas décadas, se ha experimentado una enorme evolución en la

cirugíadecataratas,conelfindeconseguirincisionescornealesparalainserciónde

la lente intraocular cada vez más pequeñas, disminuir las complicaciones

postoperatorias, mejorar la recuperación visual del paciente y la realización del

cálculo correcto de la potencia de la lente intraocular (PIOL). En la actualidad, los

estudios van orientados a analizar los posibles parámetros susceptibles de inducir

errorenelcálculodelapotenciadelalenteintraocularparaintentaroptimizarlosy

asíreducirloserroresrefractivosqueaparecenenelpostoperatorio.

Antes de 1975, existía una única fórmula para el cálculo de la potencia de la

lente intraocular basada en la historia clínica(2). Esta fórmula tenía la siguiente

expresión*:

𝑃!"# = 18+ 1.25 ∙ 𝑅!"# [1]

Donde𝑃!"#eslapotenciadelalenteintraocularyRpreeslarefracciónpreoperatoria.

*Nota:Dadoqueensudíanoexistióunconsensoa lahoradeestandarizarparámetrosyesta

circunstanciapuedeinduciraconfusiónendeterminadosmomentos,sehadecididounificartérminosen

todaslasfórmulascitadasenlapresentetesis.

Porlotanto,sielpacienteeraemétropepreviamente(Rpre=0),seutilizabauna

lenteintraocularde18D.Seobservabanerroressuperioresa1.0Denel50%delos

casos,siendoenalgunoscasosestoserrorestanaltosqueseleasignaronelnombre

de “sorpresa refractiva”(3). Estos grandes errores llevaron a muchos autores a

investigar sobre el valor de la potencia de la lente intraocular que se debería

implantarenunpacienteconcataratasydesdeentoncessehanpublicadounaserie

de fórmulas de cálculo de la potencia de la lente intraocular (PIOL). Todas estas

fórmulas tienencomopuntodepartidaelmodelodeojo simplificado, enel cual se

consideraelojocomounsistemaformadoporundioptrioesféricoyunalenteplana

Capítulo1

Introducción

21

correspondientesalacórneayalcristalino,respectivamente,ycuyafocalimagendel

sistemacorrespondealaretina(2,4).

1.a.Fórmulasdecálculodelentesintraoculares

Alolargodelahistoriahanidoapareciendonumerosasfórmulasparaelcálculo

de la potencia de lentes intraoculares. Desde que se comenzó a realizar

intervencionesquirúrgicas,sehanutilizadobásicamentedosconjuntosde fórmulas

decálculo(5); teóricasyempíricas.LasteóricasaplicanlasecuacionesdeGausspara

ópticaparaxialenelmodelodeojoteórico,cuyaimagenfinal focalizaenretina.Las

fórmulas empíricas o de regresión lo que hacen es analizar los resultados de la

refracciónpostoperatoriademúltiplesintervencionesycalculanunoscoeficientesde

ajusteenlafórmuladecálculodela lenteparaobtenerlarefracciónpostoperatoria

deseada.

1.a.1.Fórmulasde1ªgeneración(fórmulasteóricasoriginales)

Estas fórmulas presentan una constante única para cada tipo de lente

intraocular, denominada ACD (profundidad de la cámara anterior) donde su

posicionamientodentrodelojoesconstante.Aestaprimerageneraciónpertenecen

las fórmulas de Fyodorov (1967)(6), Colenbrander (1973)(7), Thijssenn (1975)(8),

Binkhorst(1975)(9)yVanderHeijde(1976)(10)(vertabla1).Aunqueaparentemente

sondiferentes,esfácilcomprobarquetodasestánbasadasenelcálculodelapotencia

deunalenteintraocularenaproximaciónparaxialapartirdelasecuacionesdeGauss.

Fyodorov(6) [ec.2] fue el primer autor enpublicaruna fórmula teóricapara el

cálculodelaPIOLaimplantarenfuncióndelalongitudaxial(AL),lapotenciacorneal

(Pc) y la posición que adopta la lente intraocular al ser insertada en el ojo,

denominadaposiciónefectivadelalente(ELP).

EnlasfórmulasdeprimerageneraciónelvalordelaELPseconsiderabacomo

unaconstanteindependientementedecualquierotroparámetroocular.Enladécada

de los 70, las lentes intraoculares implantadas eran de fijación iridiana, donde la

Capítulo1

Introducción

22

profundidad de la cámara anterior o distancia de vértice corneal al plano del iris

coincidía respecto a la posición efectiva de la lente (ELP). Por esta razón, laELP o

ACDcte (para fórmulas de primera generación) adoptóun valormedio inicial de 4.0

mm,aumentandoalolargodeltiempoamedidaquelaslentesintraocularespasaron

aimplantarseenelsulcus(4.5mm)yposteriormenteenelsacocapsular(5.25mm).

El índice de refracción del humor acuoso y humor vítreo para los cálculos era

consideradosiempreelmismovalor(1.336)[ec.2].

Unosañosdespués,Colenbrander(7) [ec.3]publicóuna fórmulasimilara lade

Fyodorov,con laúnicadiferenciade la incorporacióndeunaconstante0.05mm, la

cual se añadía en losdosdenominadores. Lahipótesisque sebarajaba sobredicha

constanteeraqueelautorconsiderabaestevalorcomoladistanciaentrelosplanos

principalesdelacórneayelvérticecorneal.

Dosañosdespués,en1975,Thijssen(8)presentósufórmula[ec.4],muysimilara

lafórmuladeColenbrander(7).LaúnicadiferenciaconlaecuacióndeFyodorovesque

añadió unas constantes al primer y segundo denominador (Const1 y Const2

respectivamente),quesonconstantespropiasdecadatipode lente.Esemismoaño

Binkhorst(9) [ec.5] introdujoa la fórmuladecálculoun factor4Rcen lugardelradio

corneal,loquesuponíaunadiferenciade0.50Daproximadamenteenrelaciónconlas

demásformulas.VanderHeijde(10)[ec.6]porsupartepublicólamismafórmulaque

ladeFyodorovperoexpresadaendostérminos(verTabla1).

Capítulo1

Introducción

23

Tabla1.Fórmulasde1ªgeneración

𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔 − 𝑨𝑳 ∙ 𝑷𝒄

(𝑨𝑳 − 𝑬𝑳𝑷)(𝟏 − 𝑬𝑳𝑷 ∙ 𝑷𝒄𝟏𝟑𝟑𝟔 ) FórmuladeFyodorov(1967)(6)[2]

𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔

𝑨𝑳 − 𝑬𝑳𝑷 − 𝟎.𝟎𝟓−

𝟏𝟑𝟑𝟔𝟏𝟑𝟑𝟔𝑷𝒄

− 𝑬𝑳𝑷 − 𝟎.𝟎𝟓 FórmuladeColenbrander(1973)(7)[3]


𝑨𝑳 − 𝑬𝑳𝑷 + 𝑪𝒕𝒆𝟏−

𝟏𝟑𝟑𝟔𝟏𝟑𝟑𝟔𝑷𝒄

− 𝑬𝑳𝑷 + 𝑪𝒕𝒆𝟐 FórmuladeThijssen(1975)(8)[4]

𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔(𝟒𝒓𝒄 − 𝑨𝑳)

(𝑨𝑳 − 𝑬𝑳𝑷)(𝟒𝒓𝒄 − 𝑨𝑳) FórmuladeBinkhorst(1975)(9)[5]


𝑨𝑳 − 𝑬𝑳𝑷−

𝟏𝟏𝑷𝒄

− 𝑬𝑳𝑷𝟏𝟑𝟑𝟔

FórmuladeVanderHeijde(1975)(10)[6]

DondePIOL:potenciadelalenteintraocular;AL:longitudaxial;Pc:potenciacorneal;ELP:posiciónefectiva

delalente;Cte1yCte2:constantesdelafórmuladeThijssen;rc:radiocorneal

1.a.2.Fórmulasteóricasyempíricasde2ªgeneración

Dadoque seasumíaque laposiciónefectivade la lenteera igual en todos los

ojos independientemente de su longitud axial, surgieron una gran cantidad de

sorpresasrefractivas,observándoseque losojos largosquedabanhipercorregidosy

los ojos cortos hipocorregidos, de tal manera que se dedujo que el valor de la

profundidaddelacámaraanteriordebíavariardependiendodelalongitudaxial.Por

esta razón, en la década de los 80, se pasó de una ELP constante a una ELP

modificable proporcionalmente en función de la longitud axial. Estas fórmulas se

desarrollaron paralelamente a las fórmulas empíricas basadas en fórmulas de

regresiónmúltiple(vertabla2),lascualesprecisabandeunaconstantepropiadela

lente(A)ademásdelosdatosdelalongitudaxial(AL)ypotenciacorneal(Pc),basadas

enunaecuacióndeltipo:

Capítulo1

Introducción

24

𝑃!"# = 𝐴 − 𝐵 ∙ 𝐴𝐿 − 𝐶 ∙ 𝑃! [7]

EnconcretoSanders,RetzlaffyKraffintrodujeronunosvaloresalasconstantes

B=2.5yC=0.9alaecuación7,denominandoaestafórmulaSRKI(11,12).LaconstanteA

eravariableenfuncióndelaformayfabricacióndelalenteintraocular[ec.8].

Binkhorst,(13)en1981,utilizósupropiafórmulaoriginal[ec.5],peroajustando

la ELP para la posición de la lente dentro del ojo (fijada al iris, en la cápsula, en

sulcus,…)enrelaciónalalongitudaxial[ec.9](13–15).Cuandolalenteestácolocadaen

la cámara posterior, el valor deELPse reduce 0.17mmpor cadamilímetro deAL

inferiora23.45mmyse incrementa0.17mmporcadamilímetrodeAL superiora

23.45mm.LaELPsemodificabaenidénticaproporciónalaAL.

Shammas,(16) en 1982, publicó una fórmula basada en la modificación de la

fórmula de Colenbrander [ec. 3]. Además como sugería Binkhorst, este autor hacía

unavariaciónenel índicederefraccióncornealde1.3375a4/3por loque laPc se

reduceunfactor1.0125,ademásdeintroducirunfactorligadoalaAL[ec.10].

La fórmula de Hoffer(17) [ec.11] está fundamentada en la fórmula de

Colenbrander, al igual que la fórmula anterior. El error postoperatorio esperado

(Rpost)seañadealapotenciacorneal(Pc).Elvalordelaposiciónefectivadelalente

(ELP)seexpresaenfuncióndela longitudaxial(AL)ylaprofundidaddelacámara

anterior(ACD),correspondienteaunaconstantequevaríaenfuncióndelalongitud

axial.

ComparandolafórmulaSRKIderegresiónconlasfórmulasteóricasoriginales

talescomoVanderHeijde(10),Thijssen(8),Binkhorst(9),Colenbrander(7)yFyodorov(6)

,seobservaqueestasfórmulasderegresiónsonválidasenojosdemedidasestándar

yson labasede las fórmulasmodernas(Holladay IyHolladay II,SRK/T,HofferQ).

Sin embargo, debido a los errores que surgían en la medida de la PIOL, Sanders,

Retzlaff y Kraff, en 1988,modificaron su fórmula a la cual denominaron SRK II(18)

[ec.12]. Esta nueva fórmula añade a la potencia calculada con SRK I una cierta

potencia(F),queesvariableenfuncióndelalongitudaxialdelojo,dondeFtomaba

valoresdesde-0.5DparaAL>24.5mmhasta+3.0DparaAL<20.0mm.

Capítulo1

Introducción

25

Olsen,(4) basándose en la fórmula SRK y en un análisis de regresiónmúltiple,

publicóunafórmulautilizandoelmétododelosmínimoscuadrados[ec.13].Usando

estaecuaciónseobservóqueelerrormediocometidoenlarefracciónpostoperatoria

fuede0.00±0.64D.


𝑷𝑰𝑶𝑳 = 𝑨 − 𝟐.𝟓𝑨𝑳 − 𝟎.𝟗𝑷𝒄 FórmuladeSRKI(1980)(12)[8]

𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔(𝟒𝒓𝒄 − 𝑨𝑳)

(𝑨𝑳 − 𝑬𝑳𝑷)(𝟒𝒓𝒄 − 𝑬𝑳𝑷)

• SiAL>26:ELPcorr=ELP·(26/23.45)

• SiAL≤26:ELPcorr=ELP·(AL/23.45)

FórmuladeBinkhorst(1984)(14)[9]


𝑨𝑳 − 𝟎.𝟏 𝑨𝑳 − 𝟐𝟑 − 𝑬𝑳𝑷 − 𝟎.𝟎𝟓−

𝟏𝟏.𝟎𝟏𝟐𝟓𝑷𝒄

− 𝑬𝑳𝑷 + 𝟎.𝟎𝟓𝟏𝟑𝟑𝟔

FórmuladeShammas(1982)(16)[10]


𝑨𝑳 − 𝑬𝑳𝑷 − 𝟎.𝟎𝟓−

𝟏𝟑𝟑𝟔𝟏𝟑𝟑𝟔

𝑷𝒄 + 𝑹𝒑𝒐𝒔𝒕− 𝑬𝑳𝑷 + 𝟎.𝟎𝟓𝟏𝟎𝟎𝟎

FórmuladeHoffer(1981)(19)[11]

𝑷𝑰𝑶𝑳 = 𝑷𝑰𝑶𝑳 𝑺𝑹𝑲 𝑰 + 𝑭FórmuladeSRKII(1988)(18)[12]

𝑷𝑰𝑶𝑳 = 𝟏𝟓𝟏.𝟑 − 𝟏.𝟐𝑷𝒄 − 𝟑.𝟑 ∙ 𝑨𝑳FórmuladeOlsen(2007)(4)[13]

DondePIOL:potenciadelalenteintraocular;A:constatedelalenteintraocular;AL:longitudaxial;Pc:

potencia corneal; rc: radio corneal;ELP:posiciónefectivade la lente;ELPcorr: posiciónefectivade la

lente corregida ; Rpost: refracción postoperatoria; PIOL(SRK I): Potencia lente intraocular calculada

mediantelafórmulaSRKI;F:potenciavariableenfuncióndelalongitudaxialparalafórmulaSRKII

Capítulo1

Introducción

26

1.a.3.Fórmulasde3ªgeneración

EstageneracióndefórmulassurgióalobservarquelaELPnosecorrelacionaba

con laACD preoperatoria, considerandoque laELP se incrementaba en ojos largos

(mayor AL) y decrecía en ojos cortos (menor AL). Como se ha comentado

anteriormente, este incrementonoeraproporcional a laAL comoconsideraban las

ecuaciones de segunda generación y laELP se correlacionaba con la posición de la

lente intraocular,yaseaencámaraanterior, sulcusosacocapsular.Poresta razón,

surgieronlasfórmulasdetercerageneración,lascualestratandepredecirlaposición

efectiva de la lente a implantar en el ojo (ELP) en función de dos parámetros, la

longitudaxialylaqueratometría(atendiendoacurvaturayespesorcorneal).Aesta

generaciónpertenecenlafórmuladeHolladayI(1988)(20),SRK/T(1990)(21)yHoffer

Q(1993)(17)(vertabla3).

Holladay (20) en 1988 desarrolló una fórmula empírica [ec.21] a partir de la

modificacióndelasecuacionesdeFyodorov[ec.2]yVanderHeijde[ec.6],queincluía

criterios de selección para identificarmedidas improbables de queratometría y de

longitudaxial,unamayorprecisiónenlaestimacióndelaprofundidadqueadquiere

lacámaraanteriorcuandoseintroducíaunalenteintraocular(ACDpost)equivalentea

ELP[ec.14],quenoeramásquelasumadelaprofundidaddelacámaraanteriordel

ojo(ACD)yladistanciaexistenteentreelplanoanteriordelirisyelplanoópticodela

lenteintraocular(Ꮪ).

𝐸𝐿𝑃 = 𝐴𝐶𝐷 + 𝑆 [14]

Aunque el factor Ꮪ es un valor medible definido como la distancia entre el

vérticecornealyelplanodeliris,realmentesecalculaapartirderesolverdemanera

inversaunafórmulaqueutilizacomovariableslalongitudaxial(AL),elpropiovalor

de la lente intraocular implantada (PIOL) y el valor de la refracción postoperatoria

(Rpost)(22).ElfactorᏚesvariabledebidoalaformadelalente,lafabricación,latécnica

del cirujano y de los dispositivos de medida. Esta distancia se predice con mayor

precisiónmediante el uso de una fórmulamatemática donde suma el valormedio

empleadoparaelgrosorcorneal(0.56mm)ylaalturacorneal(H).

Capítulo1

Introducción

27

LarelaciónquedioHolladayentreelfactorᏚylaconstanteAqueaparecíaenla

fórmulaSRKfue:

𝑆!"#$%& = 𝐴 − 𝐶𝑡𝑒 ∙ 0.5663 − 65.60 [15]

OenfuncióndelvalordelaACD:

𝑆!"#$%& = 𝐴𝐶𝐷 ∙ 0.9704 − 3.595 [16]

PorlaestrecharelaciónexistenteentreelfactorᏚyELP(casi1:1),uncambiode

una unidad en el factorᏚ es idéntico al cambio de 1.0mm en el valor deELP y la

refracciónpostoperatoriasemodificaalrededorde1.5D.

LafórmulaSRK/T(21)[ec.22],alcontrarioquelasfórmulasSRKI[ec.8]ySRKII

[ec.12], era una fórmula teórica basada en la fórmula de Fyodorov(6) [ec.2], que

utilizabalametodologíaderegresiónparalaoptimizacióndelaprediccióndelaELP,

delespesordelaretinaydelacorreccióndelíndicederefraccióncorneal.Elcálculo

estimadodelaACDpostoperatoriaveníadadopor:

𝐸𝐿𝑃 = 𝐻 + 𝑑𝑒𝑠𝑝𝑙𝑎𝑧𝑎𝑚𝑖𝑒𝑛𝑡𝑜 [17]

𝑑𝑒𝑠𝑝𝑙𝑎𝑧𝑎𝑚𝑖𝑒𝑛𝑡𝑜 = 𝐴𝐶𝐷 𝑐𝑡𝑒 − 3.336 [18]

Donde: H es la distancia entre la córnea y el plano del iris y ACD(cte) puede ser

medidaapartirdelacontanteA:

𝐴𝐶𝐷 𝑐𝑡𝑒 = 0.62467 ∙ 𝐴 − 68.747 [19]

LafórmulaSRK/TutilizabalamismaconstanteAdiseñadaoriginalmentepara

laecuaciónSRK.LaconstanteAabarcamúltiplesvariablesdel fabricante,elestiloy

colocación del implante dentro del ojo, la técnica del cirujano y los equipos de

medición.

Hoffer Q(17) después de publicar su fórmula [ec.11], continuó estudiando la

relaciónexistenteentreELPyAL,encontrandounarelaciónnolineal,loqueresultaba

contradictorioconlopublicadoporélmismoen1984,porloquemodificósupropia

fórmulaconunanuevaprediccióndeELP[ec.23].Hofferestudiólarelaciónexistente

entreELPyAL,encontrandoquesurelaciónseajustabaaunacurvatangenteenlugar

de a una recta. Hizo muchas variaciones de la fórmula en función de la AL y el

promedio de lecturas queratométricas hasta que encontró una fórmula que se

ajustabaalacurvadeseada.Lafórmulaconsistíaen:

Capítulo1

Introducción

28

• UnvalorpersonalizadodeELP (quedenominópACD)desarrolladoapartirde

cualquieradelasseriesdelestilodeunalenteintraocular.

• UnfactorqueaumentaELPcuandoaumentaAL.

• UnfactorqueaumentaELPcuandoaumentalacurvaturacorneal.

• UnfactorquemoderaloscambiosenelvalordeELPparaojosextremadamente

largos(>26mm)oextremadamentecortos(<22mm).

• UnaconstanteañadidaaELP.

ELP = pACD + 0.3 AL − 23.5 + (tan𝑃!)! + (0.1M(23.5 − A)!(tan 0.1 G − A)! − 0.99166

[20]

• SiAL≤23 M=1 G=28

AL>23 M=-1 G=23.5• SiELP>6.5 ELP=6.5

ELP<2.5 ELP=2.5


𝑷𝑰𝑶𝑳 =𝟏𝟎𝟎𝟎𝒏𝒉𝒂 𝒏𝒉𝒂𝒓𝟏𝒄 − 𝒏𝒌 − 𝟏 𝑨𝑳 − 𝟎.𝟎𝟎𝟏𝑹𝒑𝒐𝒔𝒕(𝜹𝒗(𝒏𝒉𝒂𝒓𝟏𝒄 − 𝒏𝒌 − 𝟏 𝑨𝑳 + 𝑨𝑳 ∙ 𝒓𝟏𝒄

(𝑨𝑳 − 𝑬𝑳𝑷)(𝒏𝒉𝒂𝒓𝟏𝒄 − 𝒏𝒌 − 𝟏 𝑬𝑳𝑷 − 𝟎.𝟎𝟎𝟏𝑹𝒑𝒐𝒔𝒕(𝜹𝒗 𝒏𝒉𝒂𝒓𝟏𝒄 − 𝒏𝒌 − 𝟏 𝑬𝑳𝑷 + 𝑬𝑳𝑷 ∙ 𝒓𝟏𝒄

FórmuladeHolladay(1988)(20)[21]

𝑷𝑰𝑶𝑳 =𝟏𝟎𝟎𝟎𝒏𝒉𝒂(𝒏𝒉𝒂𝒓𝒄 − 𝒏𝒄 − 𝟏 𝑨𝑳)

(𝑨𝑳 − 𝑬𝑳𝑷)(𝒏𝒉𝒂𝒓𝒄 − 𝒏𝒄 − 𝟏 𝑬𝑳𝑷) FórmuladeSRK/T(1990)(21)[22]


(𝑨𝑳 − 𝑬𝑳𝑷 − 𝟎.𝟎𝟓)−

𝟏𝟑𝟑𝟔𝟏𝟑𝟑𝟔

𝑷𝒄 + 𝑹𝒅𝒆𝒔− 𝑬𝑳𝑷 + 𝟎.𝟎𝟓

𝟏𝟎𝟎𝟎

FórmuladeHofferQ(1993)(17)[23]

DondePIOL:potenciadelalenteintraocular;nha:índicehumoracuoso;;r1c:radiocornealanterior;nk:

índicequeratométrico;AL:longitudaxial;Rpost:refracciónpostoperatoria;δv:distanciaalvértice;ELP:

posiciónefectivadelalente;rc:radiocorneal;nc:índicecorneal;Pc:potenciacorneal;Rdes:refracción

deseada

Capítulo1

Introducción

29

1.a.4.Fórmulasde4ªgeneración

Apesardequeactualmentenoesunacategoríauniversalmenteaceptada,en

losúltimosañossehanpropuestonuevasfórmulas quesepodríanincluirdentrode

unanuevageneración.Estasfórmulasempleanmásdedosfactoresparapredecirla

ELP,teniendoencuentaademásdelaALylapotenciacorneal(Pc),variablescomoel

grosordelcristalino(eL),larefracciónpostoperatoria(Rpost),etc.(vertabla4).

LafórmuladeOlsen(23–25)[ec.25]fuedesarrolladaen1980enunaépocaenla

que las fórmulas de regresión fuerondominantes y las fórmulas ópticasno estaban

bien consideradas, por lo que esta fórmula no se publicó hasta añosmás tarde. El

objetivoeradesarrollaruna fórmula conelmenornúmerodesuposicionesposibles

en el ámbito de la óptica Gaussiana para intentar hacer elmodelo aplicable al ojo

pseudofáquico.En1990,decidió incluirhastacuatro factoresmásde los tenidosen

cuentaanteriormente: longitudaxial(AL),profundidaddelacámaraanterior(ACD),

potenciacorneal(Pc)ygrosorretiniano(L).LafórmulaquedeterminalaELPesuna

ecuaciónderegresiónque incluyeelparámetroH, el cualesobtenidomediante las

ecuaciones ya utilizadas para las fórmulas Holladay I [ec.21] o SRK/T [ec.22], el

espesor del cristalino y el valor ACDcte determinado para cada tipo de lente

intraocularunavezestudiadoretrospectivamenteunnúmerodecasosutilizandoun

índicequeratométricode1.3315.

La fórmuladeHolladay II fuedesarrolladaen1996paramejorar lacapacidad

predictivadelaELPenojosmuycortos(AL<22.0mm).Loquepretendeespredecir

de una forma más precisa la posición efectiva de la lente (ELP) mediante la

incorporación de la medida blanco-blanco (WTW), la ACD fáquica, el espesor del

cristalino(eL),laedaddelpacienteyelsexo.Estafórmulanohasidopublicadapero

seencuentradisponiblecomopartedelsoftwareHolladayIOLConsultant(26,27).

Haigis(28)demostróqueparacaracterizarlaslentes,enlugardeunaconstante,

eramásconvenienteutilizarunaexpresiónquerelacionaralalongitudaxial(AL)con

laprofundidaddelacámaraanterior(ACD).LafórmuladeHaigis[ec.26]noempleala

potencia corneal para la predicción de ELP, sino que utiliza tres constantes para

ajustarlaposiciónylaformadelacurvadeprediccióndelapotencia.

Capítulo1

Introducción

30

𝐸𝐿𝑃 = 𝑎! + 𝑎!𝐴𝐶𝐷 + (𝑎!𝐴𝐿) [24]

Lasconstantesa0,a1ya2seobtienenapartirdelosdatosderegresióndeunos

200casos.Laconstantea0variadelamismamaneraqueelfactorᏚolaconstanteA

enlasfórmulasdeHolladayySRK/T,respectivamente.


𝑷𝑰𝑶𝑳 =𝒏!𝑷𝒄𝑳𝒄𝒐𝒓

𝑳𝒄𝒐𝒓!𝑬𝑳𝑷 𝟏!𝑬𝑳𝑷∙𝑷𝒄𝒏

donde:FórmuladeOlsen(2004)(23–25)[25]

𝑬𝑳𝑷 = 𝑨𝑪𝑫𝒄𝒕𝒆 − 𝟒.𝟎𝟑 + 𝟎.𝟏𝟗𝑨𝑳 + 𝟎.𝟒𝟗𝑨𝑪𝑫𝒑𝒓𝒆 + 𝟎.𝟐𝟖𝑳 − 𝟎.𝟒𝟏𝒓𝒄 + 𝟎.𝟎𝟐𝟖𝑹𝒑𝒓𝒆

𝑷𝑰𝑶𝑳 =𝒏

𝑨𝑳 − 𝑬𝑳𝑷−

𝒏𝟏.𝟑𝟑𝟔𝒁 − 𝑬𝑳𝑷

donde: 𝒛 = 𝑷𝒄 +𝑹𝒅𝒆𝒔

𝟏 − 𝑹𝒅𝒆𝒔δ𝒗

FórmuladeHaigis(2003)(28)[26]

DondePIOL:potenciadelalenteintraocular;n:índicequeratométrico;Pc:potenciacorneal;Lcorr:espesor

del cristalino corregido; ELP: posición efectiva de la lente; ACDcte: profundidad de la cámara anterior

constante; AL: longitud axial; ACDpre: profundidad de la cámara anterior preoperatoria; L: espesor

cristalino; rc: radio corneal, Rpre: refracción preoperatoria; Rdes: refracción deseada;δ𝒗: distancia del

planodelagafaalvérticecorneal

Sehademostradoque las fórmulasmodernasofrecenmejores resultadosque

lasfórmulasteóricasoriginales(Colenbrander(7)yBinkhorst(9))yquelasfórmulasde

regresión (SRK y SRK II). En ojos con valores promedio, no existen diferencias

significativas entre las fórmulas de Holladay, SRK/T y Hoffer Q. No obstante, la

fórmula de Holladay II mejora la precisión en ojos cortos, con un error absoluto

menor que en la fórmula de Holladay (21,27). La desventaja que presentaban las

fórmulasderegresiónesquesólofuncionabanparaelconjuntodedatosdelcualse

derivaba.Porejemplo,silalongitudaxialsemideportécnicasdiferentes,laconstante

(ytalvezloscoeficientesderegresión)cambiarían.

Capítulo1

Introducción

31

Acontinuaciónsevaaanalizarlaimportanciadeesteyotrosfactoresclave,que

son necesarios para el cálculo preciso tanto de la potencia como de la posición

efectivadelalente,asícomosuniveldeinfluenciaenelcálculodelaPIOL.

1.b.Factoresdeerrorenelcálculodelapotenciadelalenteintraocular

Estudios clínicos han demostrado que el uso de una única potencia de lente

intraocular (PIOL) dejaría a un 5% de los pacientes con errores refractivos no

coincidentes con su refracción en más de 5.0 D(4). Estudios más recientes(29,30)

demuestran los errores cometidos en el cálculo de la PIOL a pesar de los avances

tecnológicos y las nuevas fórmulas. Estos errores alcanzan hasta 3.0 D en algunos

casos. En concreto, en el estudio realizado porNarváez et al.(29)se comparó cuatro

fórmulasdecálculodePIOL,HolladayI,HolladayII,HofferQySRK/Tparaobtenery

comparar los erroresque se cometían con cadaunade estas fórmulas.Observaron

quetodaslasfórmulascomprendíanunoserroresdesdeaproximadamente0Dhasta

másde3.0D.LafórmuladeHofferQeralaqueobteníaelrangodeerrorinferiorcon

unosvaloresde0,02Da3,03D.Enotroestudio realizadoporTerzietal.(30)donde

también se compararon las predicciones de errores cometidas mediante cuatro

fórmulasmodernas, talescomoHofferQ,SRK/T,HaigisyHolladay IIenojos largos

conlongitudesaxiales>26,0mmyenojoscortos<22,0mmobservaronqueenojos

miópicos existía una tendencia a la hipermetropización. Zaldivar et al.(31) en su

estudio con 50 ojos utilizando las mismas fórmulas que Terzi et al.(30) también

concluyeronquecontodaslasfórmulasseobteníaunvalorinferiordePIOLrespectoa

lacorrecta.

En el artículo publicado por Olsen(4) se indica que la precisión que se puede

lograr en la predicción de la refracción promedio con lametodologíamoderna, es

decir, en condiciones óptimas y con los algoritmos de última generación de

predicciónenelcálculodeACD,es<±0.5D,conunadesviaciónestándar<0,6D.Aún

contodoesto,alrededordel10%deloscasossiguenestandofueradelrangode±1.0

D,por loque todavía sigue siendo importanteencontraruna fórmula con laque se

puedanminimizarestoserrores.Olsenconcluyóqueestaprediccióneramásprecisa

Capítulo1

Introducción

32

enojoslargosqueenojoscortos.

Sepuedededucirportantoqueelerrorenlaprediccióndelcálculototaldela

PIOL es la suma de los errores asociados con las variables principales. Tal y como

hemoscomentadoanteriormentesepuedecomprobarenla literaturaexistenteque

losparámetrosquepresentanunamayorinfluenciaenelerrordelcálculodelalente

intraocularson:

1. Medidadelalongitudaxial(AL)

2. Medidadelaposiciónefectivadelalente(ELP)

3. Medidadelapotenciacorneal(Pc)

1.b.1.Longitudaxial

Entre los factores que pueden influir en el error del cálculo de la PIOL, la

medicióndelalongitudaxialsiguesiendounodelosfactoresmásrelevantes,puesto

queunerrorde0.1mmdeALesequivalenteaunerrorde0.27Denelplanodelas

gafas(enelsupuestodeojosnormales).

Antiguamente, a la hora de decidir qué fórmula o fórmulas eran las más

adecuadas en funcióndeAL, no existíaun criterio general. Enun estudio realizado

porNarváezetal(29)seutilizócomoreferencialafórmulaHolladayIIconunfactorde

cirujano personalizado. Para un mejor análisis, la muestra de ojos del estudio fue

divididaengruposdependiendodelalongitudaxial:ojoscortos(<22.0mm),medios

(entre22.0y24.5mm),medianamentelargos(entre24.5y26.0mm)ymuylargos(>

26.0mm).En losresultadosnoseobtuvierondiferenciassignificativasdeprecisión

respecto a la predicción del error refractivo postoperatoriomedido con las cuatro

fórmulasdeestudioytampocoseobtuvierondiferenciasconlalongitudaxial,porlo

que concluyeron que las cuatro fórmulas de estudio eran igualmente válidas

independientemente de la longitud total del ojo. Sin embargo, Donoso et al(32)

evaluaron en212 ojos la precisión alcanzada con las fórmulas SRK II, Binkhorst II,

Hoffer Q, Holladay II y SRK/T y concluyeron que las fórmulas de Binkhorst II y la

HofferQeranlasqueproporcionabanmejoresresultadosenlaprediccióndelaPIOL

enojospequeños(<22.0mm),mientrasquelaSRK/Teramásprecisaenojoslargos

Capítulo1

Introducción

33

(> 28.0 mm). En un estudio realizado por Tsang et al(33) con longitudes axiales

grandes (>25.0mm), sepudodemostrarque la fórmuladeHofferQ siempredaba

mejorresultadoenlaprediccióndelaPIOL,mientrasquelaHolladayIySRK/Tdaban

resultadoscomparablesentreellas,peropeoresquelaHofferQ.Hoffer(27)examinóel

errorabsolutomedioen317ojosusandolasfórmulasSRKII,BinkhorstII,HofferQ,

Holladay IIySRK/T.Elerrorenvalorabsoluto tendíaaser inferiorenojosmedios

(entre22.0y24.5mm)conlas fórmulasdeHolladayIyHofferQ.Enojoscortos(<

22.0 mm), las fórmulas Hoffer Q y Holladay II proporcionaban un error absoluto

medioinferior.LafórmulaSRK/Tmostrabaunatendenciamásbajadelamediapara

elerrorabsolutoenojosmedianamentelargos(entre24.5y26.0mm)ymuylargos

(>26.0mm).

1.b.2.Posiciónefectivadelalente.

Eltérminodeposiciónefectivadelalente(ELP)fuerecomendadoporlaFDAen

1995 para describir la posición que adoptaba la lente intraocular cuando era

insertada en el ojo(34) (ya sea en cámara anterior, iris, sulcus o en la cápsula del

cristalino). EstaELPeraequivalentealaACDpostdefinidapordiversosautoresenla

bibliografíayvienedeterminadaporladistanciaexistenteentreelvérticecornealyla

caraanteriordelalenteintraocular.(verfig.2)

Figura2.Distanciasusadasenlaprediccióndelaposiciónefectivadelalente

(ELP)oACDpostoperatoria(ACDpost)(4)

LpreACDpre

ELP

AL

H Ojo Fáquico

Ojo Pseudofáquico

Capítulo1

Introducción

34

LaELPpara lentes intraoculares antes de 1980 era una constante de 4.0mm

paratodoslostiposdelentesyentodoslospacientes(fórmulasde1ªgeneración).La

mayoríadelaslentesimplantadaseranfijadasaliris,dondeladistanciapromediode

suplanoprincipalposterioralvérticecornealeradeaproximadamente4.0mm.En

1981, Binkhorst mejoró la predicción de la ELP utilizando un factor variable de

predicción,lalongitudaxial,comounfactordeescalaparaELP(fórmulasteóricasde

2ªgeneración)(13).Enlospacientesconunalongitudaxial10%superioralanormal

(>23.45mm),aumentaba laELPenun10%.Posteriormente, el valorpromediode

ELPfueaumentadoa4.5mmporqueel implantede la lente intraocularseprefería

hacer en el sulcus, aproximadamente 0.5mmmás que el plano del iris, y además

había que tener en cuenta que muchas lentes eran convexo-planas, con formas

similares a la de las lentes de apoyo iridiano. El promedio de ELP en 1996 se

incrementóa5.25mm.Esteaumentodedistanciasediopordosrazones:lamayoría

delosimplantesdelentesintraoculareseranbiconvexos,desplazándosemáselplano

principaldelalentedentrodelojo,ylalocalizacióndeseadadelalenteenlacápsula

era0.25mmmayorqueensulcus(35).

Actualmente,hayfuertesindiciosdequelaACDpostoperatoriasecorrelaciona

positivamenteconlalongitudaxial(4).Cuandoenunmodelodecálculodepotenciade

lenteintraocularsedejabafijoelvalordelaACD,seobservabaquelamedidadeACD

era demasiado corta cuando semedía en ojos largos ymuy grandes comparado a

cuandose tratabadeojoscortos.Comoconsecuencia,seproducíaunerrormiópico

en ojos cortos y un error hipermetrópico en ojos largos. Para evitar este efecto, la

predicción de la ACD postoperatoria debía de alguna manera corregir la longitud

axial.

Hoyendía,laestimacióndelaposiciónefectivadelalenteELPestábasadaen

las observaciones de las asociaciones estadísticas entre varias medidas

preoperatoriasdelojoydelaposiciónefectivadeACD.Porlotanto,laestimaciónde

laELPsiguesiendoelverdaderocontenidoempíricodecadafórmuladecálculodela

lenteintraocularylosmodelosdiferentesqueseutilizanpararealizarelcálculodela

PIOLsonlacausadeladiferenciaenlaprecisión.

Capítulo1

Introducción

35

1.b.3.Potenciacorneal.

Elcálculodelvalorexactodelapotenciacornealesunparámetroclaveparala

obtencióndelaPIOL,además,talycomosehacomentadoanteriormente,lasfórmulas

de3ªy4ªgeneraciónutilizanlaPcparapredecirlaposiciónefectivadelalente(ELP).

Hoyendía, todavía seutiliza lapotenciade la córneamedidaapartirdeun índice

queratométrico,denominadapotenciacornealqueratométrica(Pk).Sinembargo,son

numerosos losautoresquehandemostrado loserroresqueseproducencuandose

utilizalamedidadelapotenciacornealqueratométrica(4,34,36–51).

Lascarasanterioryposteriordelacórneacontribuyenalapotenciatotaldela

córnea. Sin embargo, en el cálculo de la potencia corneal utilizando un índice

queratométrico,tansóloseconsideraelradiodelacaraanteriordelacórnea(r1c).El

índice queratométrico (nk) proviene de la adopción de unmodelo simple, con una

sola superficie de refracción y omitiendo la caraposterior de la córnea, y su valor

varía dependiendo del queratómetro(36,50). Los más comunes son: 1.3375, (Haag-

Streit,Bausch&Lomb),1.336(AmericanOptical),1.333y1.332(Zeiss).

Enel cálculode laPIOL, las razonesque llevaronaseleccionarunnkparticular

fueronvarias.Olsen(37)optóporelvalor1.3315,yaqueobtuvolosmejoresresultados

paraelcálculodelaPIOL.BinkhorstyHolladayeligieronelvalorde4/3(1.333)como

elnk normalizado en sus fórmulas de cálculo dePIOL (fórmula de Binkhorst II y la

fórmula Holladay I)(34,36). La fórmula SRK/T utiliza 1.333 como el índice

queratométrico estandarizado(21). La fórmula Hoffer Q(17) no designó un índice

queratométrico específico si no que utilizaba el valor de Pk medido por el

queratómetro, por tanto, el índice real queratométrico utilizado depende del

queratómetro que utilizara el clínico. Actualmente se dispone de nuevos

instrumentos como el sistema Pentacam® (Pentacam system, Oculus Optikgeräte),

Sirius(CSO)yOrbscanII(Orbscamsystem,Bausch&Lomb), loscualespuedenmedir

losradiosanterioresyposterioresdelacórneay,portanto,puedenaportarunvalor

de la potencia corneal basada en sus dos superficies. De todos modos, también

ofrecenlaposibilidaddeutilizarunapotenciacornealqueratométricacalculadacon

elíndicequeratométrico1.3375,lacualsiguesiendomuyutilizadaenlasfórmulasde

Capítulo1

Introducción

36

cálculodelaspotenciasdelaslentesintraoculares.

1.c.Antecedentesyestadoactualdeltema

Alolargodelahistoria,sehaobservadounaclaratendenciaasobrestimarla

potenciacorneal(Pc)cuandoseusaelvalordeuníndicequeratométrico(nk)parasu

cálculo(37,39–46),peroestatendenciavaríaentreindividuoseinclusoenlamayoríade

losestudiosquecomparan lapotenciacornealobtenidamedianteunqueratómetro

(Pk) y la potencia obtenida teniendo en cuenta las dos superficies corneales

considerando la óptica gaussiana (𝑃!!"#$$). Muchos de estos estudios comparativos

utilizanelmodelodeojodeGullstrandpararealizarestoscálculos.Porejemplo,Hoet

al.(44) comparando ojos derechos de 114 hombres y 107 mujeres calcularon la

potenciacornealGaussiana(denominadaPactual)basadaenelmodelodeojo teórico

de Gullstrand, la potencia corneal usando el índice queratométrico de 1.3315

(denominado PGullstrand) y la potencia corneal con índice queratométrico de 1.3375

(quedenominaronPconv).Encontraronqueladiferenciadepotenciacornealentrela

PactualylaPGullstrandvariabademedia0.43±0.23D,fluctuandoentre-0.64y+1.27D,y

ladiferenciaentrelaPactualylaPconvvariabademedia1.21±0.24D,oscilandoentre

+0.17y+1.99D.Enotroestudiosimilar,Shammasetal(45)con32ojosnormales(con

una media de r1c = 7.76 mm) y usando solamente nk = 1.3375, encontraron una

sobrestimación de la potencia corneal queratométrica en comparación con la

𝑃!!"#$$ basadaenelmodelodeojodeGullstrand,conunadiferenciamediade-1.17±

0.71 D (rango de -2.95 a +0.03 D). Fam et al(39) realizaron el mismo estudio que

Shammas et al(45) pero con una población distinta, obteniendo un rango de

diferenciasquevariabaentre-1.29y+0.49D.

Unfactorqueexplicaestavariabilidadentreautoreseslasuposiciónerrónea

dequelasuperficieanterioryposteriordelacórneatieneunarelaciónlineal(39,40).La

relaciónentreelradiodelacaraanterior(r1c)yposterior(r2c)delacórnea(k=r1c/r2c)

no es constante para el rango de curvatura de un ojo sano. De hecho, se ha

encontrado que el valor de k en población normal puede variar entre 1.157 y

1.295(47–50).

Capítulo1

Introducción

37

Conelfindeminimizarloserroresdecálculodelapotenciacornealdebidoal

uso de índices queratométricos, varios autores con diferentes técnicas han

recalculadoelvalordel índicequeratométrico. En1992,Dunneetal(51)observando

80 ojos sanos propusieron un valor de nk de 1.3283, con un rango asociado entre

1.3251 y 1.3305. Gobbi et al(43) hallaron un valor de nk de 1.3241 a partir de 20

córneas humanas normales. Dubbelman et al(52) con el estudio de 114 ojos

propusieronunvalormediodenkde1.329±0.001,Tangetal.(46)evaluando32ojos

obtuvieronunvalorde1.3278,FamyLim(39)en2429sujetosdescribieronunvalor

de nk= 1.3273 ± 0.0013, en un rango comprendido entre 1.3248 y 1.3298. Mas

recientementeHoetal.(44)enunestudiocon221ojosnormalesrealizadoenelaño

2008 obtuvieron una media calculada de nk de 1.328 ± 0.0018, con un rango de

1.3209a1.3363.Estosautoresdeterminaronquelosdiferentesvaloresdenkquese

obteníanvariabanenfuncióndeláreadecórneaanalizada:1.3278±0.0027,1.3284±

0.0021,1.3284±0.0031,1.3280±0.0038y1.3277±0.0042paraunamedidacentral

delacórneade3.0,5.0,6.0,7.0,y7.5mmrespectivamente.Shammasetal.(45)enun

artículopublicadoenelaño2009,sugirieronqueenrealidadelíndicederefracción

efectivoestabamascercade1.329quede1.3315usadoenalgunosqueratómetros.

Por tanto, sehandescritodiferentes enfoquesdenk condiscrepancias importantes

entre ellos. Estas discrepancias pueden deberse a los diferentes estudios entre los

aparatos utilizados en la medición del radio anterior corneal, del área de córnea

analizada,delmodelodeojousadoparaloscálculosydelapoblaciónevaluada(edad

yrefracción).

Elprimertrabajopublicadoenlalíneadeinvestigaciónalacualperteneceesta

tesis,Campsetal.(53)determinaronlasdiferenciasexistentesentrelapotenciacorneal

medida conun índicequeratométrico (Pk) y laque seobtendría apartirde lasdos

superficiescornealespormediodelasecuacionesdeGauss(𝑃!!"#$$),demaneraque

cuando se calculaba la diferencia entre ambas potencias corneales (∆𝑃! = 𝑃! −

𝑃!!"#$$) se consideraban las posibles variaciones de k en la población normal, sin

ningúntipodepatologíanicirugíaprevia.Observandoestasdiferenciasencontraron

quelaestimaciónqueratométricaPksobrestimabaosubestimabaelpodercornealdel

modelodeGauss𝑃!!"#$$ entre-0.75Dy+1.79DparaelmodelodeojodeGullstrandy

Capítulo1

Introducción

38

enelmodelodeojodeLeGrand,entre-1.12Dy+1.47D,dependiendodelosvalores

deradioscornealestantoanteriorcomoposterior(r1cyr2c,respectivamente).Cuando

elpoderqueratométricosecalculóutilizandounnkde1.3375,elvalordeΔPcresultó

sersiemprepositivo(hasta2.50DenelmodelodeojoGullstrandyhasta2.30Denel

modelodeLeGrand),revelandolapresenciadeunasobreestimaciónsistemáticaen

elcálculodelapotenciacorneal.TambiéndemostraronqueesasdiferenciasdeΔPcse

ajustabanperfectamenteaecuacioneslinealesdependientesdelarelaciónkoauna

expresióncuadráticadependienteder2C,conloqueresultamuysencillopredecirel

valor del error cometido. Estas ecuaciones se utilizaron para calcular el error

asociado con el uso de la potencia corneal queratométrica cuando se consideraba

únicamente la primera superficie corneal. Todos estos hallazgos revelaron la

necesidaddeunmodeloprecisoparadeterminarelíndicequeratométricoapropiado

paraelcálculodelapotenciacornealqueratométricasinasumirunerrorimportante.

Dehechoencontraronquelosvaloresdenk=1.3315delmodelodeojodeGullstrand,

nk= 1.3304 del modelo de ojo de Le Grand y el valor de nk =1.3375 no eran los

adecuados para el cálculo de la potencia corneal correspondiente a una población

normalyaqueloserrorescometidos(∆Pc)eransuperioresa0.5Denlamayoríade

loscasosanalizados.

Debido a todas las discrepancias encontradas entre los diversos autores(39,43–

46,51,52), Camps et al.(53) propusieron dos opciones para la selección del nk más

apropiadoparacadacaso.Laprimeraopcióneraobtenerelvalorexactodel índice

queratométrico(nkexacto)conelcualseigualabaelvalordelapotenciaqueratométrica

(Pk)yelvalordelapotenciacornealGaussiana(𝑃!!"#$$),esdecirseobteníantodoslos

posiblesvaloresdenkquecumplíanque∆𝑃! = 𝑃! − 𝑃!!"#$$=0,enfuncióndetodoslos

posiblesvaloresquepudierantomarr1cyr2c.Sinembargo,estemétodonosepodría

aplicar clínicamente si no se conocía el valor exacto de los radios de las dos

superficies corneales. La segunda opción era obtener el valor de un índice

queratométricoajustado (nkadj).Estemétodoeramás rápidoy fácildeaplicaren la

práctica clínica porque solo era necesario conocer el valor de r1c para realizar su

cálculo.Paracalcularelvalordenkadjsedesarrollóunalgoritmoparaelmodelodeojo

teóricodeGullstrandyLeGrand,válidoparaunrangodevaloresdecaraanteriory

Capítulo1

Introducción

39

posterior pertenecientes a una población normal sin ninguna patología ni cirugía

previa.

A lo largo de la historia han existido una gran variedad de autores que han

determinado el radio anterior corneal en ojos normales, no patológicos(39,44,45,47,50,51,54–72).Analizandotodosestosestudiosseestablecieronunrangonormal

para la cara anterior de la córnea entre 7.00 y 8.50 mm, siendo este rango

independiente del instrumento demedida, la edad, la refracción y el sexo. Para la

medida de la curvatura de la cara posterior se analizaron diferentes estudios

realizados por el sistema Pentacam® (Pentacam system, Oculus Optikgeräte)(57)

puesto que la repetibilidad de las medidas era mayor que con otros aparatos de

medida (57). Se estableció como rango normal para el radio de la cara posterior de

córneaelintervaloentre5.5y7.00mm(53).

Con este algoritmo, se obtuvo unos valores variables denkadj entre 1.32224 y

1.33188paraelmodelodeGullstrandyentre1.32383y1.33334paraelmodelode

Le Grand. Con este valor ajustado del índice queratométrico se estimó de forma

teóricaun errormáximode0.7D en el cálculode∆Pc tomando como referencia la

potenciacornealobtenidamedianteópticagaussianaapartirde lasdossuperficies.

Además esta condición de error máximo se observó en los valores máximos y

mínimosder2cenunrangodepoblaciónnormal(5.5,5.6,6.9y7.0mm),siendopara

el resto de los casos el error inferior a 0.5 D lo cual no representa un valor

clínicamentesignificativo.Estasdosopcionesconfirmaronqueunvalorparticularde

nknoeraválidoparatodosloscasosenlosquesequieracalcularlapotenciacorneal

yportantoningunodelosvaloresaportadosenlabibliografíapodríaserválidopara

elcálculodelapotenciacornealenpoblaciónnormalcomonormageneral.

1.d.Diseñosdelentesintraocularesafáquicas

Con el avance de las nuevas tecnologías, han surgido una gran variedad de

dispositivos tales como tabletas, libros electrónicos, teléfonos inteligentes, etc, que

precisan de una visión óptima en media y corta distancia. Por esta razón, los

Capítulo1

Introducción

40

pacientesprésbitasestándemandandosolucionesque lepermitancontinuarconsu

actividaddiariaenelmanejodeestosdispositivos.

Ademásde la correcciónmediante lentes oftálmicas y lentes de contacto, se

han desarrollado diferentes opciones quirúrgicas para la corrección de la

presbicia(73), como la sustitución del cristalino por una lente intraocular. Cuando

optamos por la inserción de una lente intraocular, el ojo pasa a denominarse

pseudofáquico,elcualestácompuestopordossuperficiesrefractivas(córneaylente

intraocular), cinco medios con sus respectivos índices de refracción (aire, córnea,

humos acuoso, lente intraocular y humor vítreo) y la distancia entre las diferentes

superficies refractivas (espesor corneal, cámara anterior pseudofáquica, espesor

lenteintraocularycámaravítreapseudofáquica).

Dentrodelosdiferentestiposdelentesintraocularesafáquicasquesepueden

implantarnosvamosacentrarenelestudiode3tiposdelentesintraoculares:

1. Lentesintraocularesacomodativas

2. Lentesintraocularesmultifocalesasimétricas

3. Lentesintraocularesasféricas

1.d.1.Lenteintraocularacomodativa

Laslentesintraocularesacomodativassonlentesmonofocalesdiseñadaspara

corregir el defecto refractivo de lejos. Estas lentes pretenden imitar la acción

fisiológicadel cristalinomediante la contracciónmusculardel cuerpo ciliar,poseen

unas pequeñas bisagras oscilantes dentro del saco capsular simulando la

acomodación natural del ojo. Al cambiar de posición, la lente hace que los rayos

enfoquen a una distancia más cercana de la posición original, aunque tiene un

movimiento limitado (fig. 3). Por lo que este tipo de lente intraocular intenta

proporcionarunavisióncercana funcional,dandounavisión lejanae intermediade

alta calidad sin distorsión óptica debido a la formación de una sola imagen en

retina(74).Sonvarioslosmodelosdelentesintraocularesacomodativasdesarrolladas

como la Crystalens AT-45 (Eyeonics)(75,76), 1CU (HumanOptic)(77–80) o la Tetraflex

Capítulo1

Introducción

41

(Lenstec)(75,81).Dadoqueestosmodelospreliminaresmostrabanunavisióndecerca

limitada(75,81),sedesarrollaronnuevosmodelos,deópticadual(82)enlacuallalentese

basaenelprincipiodecontraccióndelmúsculociliarpermitiendoquelasdosópticas

se separen incrementando así el poder total de la lente intraocular, permitiendo al

pacienteenfocardecercayotrasposicionesacomodativas(83)estetipodelentesson

rígidasdepotenciafijaconunmovimientohaciadelanteyhaciaatrásconsiguiendo

asíuncambioenelplanofocaldelalente.

Figura3.MecanismodeacciónCrystalensHDTM(Bausch&Lomb)

(Fuente:www.nuevocristalino.es)

Para nuestro estudio utilizamos la lente intraocular acomodativa Crystalens

HDTM (Bausch&Lomb). Estudios relativamente recientes(84) en los que se compara

con unamonofocal estándar, concluyeron que la CrystalensHD proporcionaba una

visión aceptable en lejos, con una mejoría significativa en cerca siendo la calidad

óptica similar a la monofocal convencional. Sin embargo, también se observaron

erroresrefractivospostoperatoriosinesperados.

1.d.2.Lenteintraocularmultifocal

Este tipo de lentes son capaces de recuperar la capacidad de enfocar a

distintasdistancias(85–87).

Las lentes intraocularesmultifocalessedividenendostiposbásicossegúnel

modoconelqueconsiguenlamultifocalidad:endifractivasyrefractivas.

LEJOS INTERMEDIO CERCA

Capítulo1

Introducción

42

1. Lentes intraoculares multifocales difractivas, consiguen su capacidad

multifocal a través de una serie de anillos concéntricos que forman una red de

difracción.Esta característicaóptica tiene la capacidaddedirigir los rayosde luz a

dosfocosdistintosalmismotiempocreandodospuntosfocalesseparados,unopara

lejosyotroparacerca(fig.4.a).Estetipodelentesofrecenbuenaagudezavisualde

cerca y lejos, además de experimentar menos problemas de visión nocturna(88,89).

Variosmodeloscomerciales sehayandentrodeestegrupocomosonTecnisZM900

(AMO)yAcrySofReSTOR(AlconLab.).

2. Lentes intraocularesmultifocales refractivas, emplean un método refractivo

multizonal,esdecir, sedefinendospotencias incorporadasdentrodeanillosozonas

refractivas circulares condiferente índice de refracción (fig. 4.b). Este tipode lentes

ofrecen muy buena visión intermedia y una mayor transmisión de la luz(90) pero

puedenprovocarsíntomasdisfotópsicosrelacionadoscon lavisiónnocturna,además

deunaagudezavisualinferioralaqueofrecenlaslentesintraocularesdifractivas(91–93).

Dentro este tipo de lentes se encuentran las rotacionales simétricas compuestas de

círculosozonasconcéntricasquepermitenunavisiónde lejosydecercademanera

alternativa y las rotacionales asimétricas, compuesta de una superficie asférica y

asimétrica para visión lejana junto a una superficie de visión cercana. Una de las

característicasmásimportantesdeestaslentesesquesonlentespupilodependientesy

necesitanundiámetrodepupilamínimoparaquelaluzpuedaatravesarlasdiversas

zonasdelalente(94).Dentrodeestetipodelentesintraocularessonvarioslosmodelos

comerciales desarrollados como son Array (AMO),ReZoom NXG (AMO), LentisMplus

LS-312(OculentisGmbH).

Capítulo1

Introducción

43

Figura4a.Lenteintraocularmultifocaldifractiva


Figura4b.Lenteintraocularmultifocalrefractiva

(Fuente:www.oculentis.com)

Sehademostradoquetantoconlaslentesintraocularesmultifocalesdifractivas

como refractivas se obtiene una visión de cerca eficaz, con un rendimiento visual

cercano a J3 entre el 92% y 99% de los pacientes(86,95–98). Sin embargo, existen

autores(89) que afirman que las lentes multifocales difractivas proporcionan mejor

visióncercanaencomparaciónconmodelosdelentesmultifocalesrefractivas,siendo

la distribución de potencias de lejos y cerca en las lentes multifocales difractivas

cuestionadaporalgunosexpertos(99).

Otros estudios indican una mejora en el rendimiento visual después de la

implantaciónunalentemultifocaldifractivaconbajaonuladisminucióndelacalidad

visualencomparaciónconunalenteintraocularmonofocal(5,100–103).

El tipode lente intraocularquevamosautilizarparanuestroestudioesuna

lentemultifocal refractiva de rotación asimétrica. En concreto se realizó el estudio

con la Lentis Mplus LS-312 (Oculentis GmbH), la cual presenta una zona de visión

lejanaasféricacombinadaconunazonaenformadesectorenlazonainferiordela

lenteparalavisióndecerca(fig.5).

Capítulo1

Introducción

44

Fig.5.GeometríadelalenteMplusLS-312,dondeseobservaelaumentode

curvaturadelsegmentoinferior.(Fuente:www.windsoreyeclinic.zendesk.com)

Los estudios sobre esta lente demuestran buenos resultados visuales en

visióndelejosycerca,conunasensibilidadalcontrastepostoperatoriadentrodelos

rangos fisiológicos, obteniendo además un impacto positivo en la calidad de

vida(84,85,104–110). Algunos estudios también han reportado unos buenos niveles de

visiónintermediaconestetipodelente(84,104).Sinembargo,apesardeestosestudios,

se ha demostrado un cierto nivel de variabilidad en la corrección

refractiva(84,104,105,108–110).

1.d.3.Lenteintraocularasférica

El ojo humano está compuesto de dos lentes asféricas (córnea y cristalino),

quesonlosquedeterminanengranmedidalacalidaddeimagenópticaquellegaala

retina.Lacórneacompuestapordossuperficiesprolatas,inducenaberraciónesférica

positiva (AEP) que aumenta con la edad(111). El cristalino compuesto por dos

superficiesasféricasproducenaberraciónesféricanegativa(AEN)(112).Conlaedad,la

diferencia entre la aberración esférica de la córnea y el cristalino disminuye

progresivamente,reduciendoasíelniveldecalidaddeimagenretiniana(96–98,113).Las

Capítulo1

Introducción

45

lentes intraoculares asféricas tratan de imitar el cristalino joven, con el fin de

minimizarlasaberraciones,enlaquealmenosunasuperficieópticaesasféricapara

asímejorarelcontrastedelaimagenylacalidadvisual(114,115).Laslentesasféricasse

basan en una superficie prolata (más curva en el centro y plana en la periferia)

modificada(fig.6).Estediseñoprolatopuedeincorporarseenlacaraanterior,como

eselcasodelaAMOTecnisoposteriordelalentecomoenlaAlconSN60WF.

Figura6.ComparacióndeRayosdeluzcruzandoópticasEsféricayAsférica

(Fuente:https://www.syscom.com.m)

Son numerosos los autores(114,116–124) que compararon la agudeza visual

obtenida con una lente intraocular asférica con una esférica, los cuales o no

encontrarondiferenciasentreambostiposde lentesó lascondicionesen lasquese

realizaronesasmedicionesnoeranlosuficientementeprecisasparadetectarcambios

visualesdebidoalareduccióndeaberraciónesféricaaconsecuenciadelareducción

de la asfericidad.Otros, sin embargo, observaron unamenor aberración esférica al

implantarunalenteintraocularasféricaencomparaciónconunaesférica(122,125,126).

Encuantoasensibilidadalcontrasteserefiere,existenestudios(116–118,124,127–

129) en los cuales muestran una mejoría en los resultados al utilizar una lente

intraocular asférica en comparación con una esférica. Sin embargo, otros

autores(114,121,123) no encontraron diferencias significativas entre ambos tipos de

Capítulo1

Introducción

46

lentes.Estasdiscrepanciaspuedenserdebidasalasdiferenciasenmaterialydiseño

delenteexistenteentreestudios.

El tipo de lente escogida para este estudio fue la lente monofocal asférica

LentisL-313(OculentisGmbH).

Capítulo2

HIPÓTESISYOBJETIVOS

49

2.HIPÓTESISYOBJETIVOS

2.aHipótesis

La hipótesis de trabajo de la presente tesis doctoral es la siguiente: La

optimizacióndelcálculodelapotenciadelalenteintraocular,dependiendodeltipode

lenteintraocularaimplantar,yaseamonofocal,acomodativaomultifocalmediantela

minimizacióndelerrorenelcálculodelapotenciacorneal.

2.b.Objetivos

Losobjetivosdeltrabajoparacorroborarlahipótesisplanteadayquesehan

tratadodeconseguirconlosartículossonlossiguientes:

A. Validar clínicamente en una población sana el algoritmo diseñado

paraminimizar el error cometido en la estimación de la potencia

cornealbasándonosenelusodeuníndicequeratométricoajustado

(nkadj).

B. Evaluardeformateóricaenojosnormaleslainfluenciadelerroren

el cálculode la potencia corneal en el cálculode laPIOL cuando se

utiliza un valor queratométrico nk y analizar y validar de forma

preliminarelusodeuníndicequeratométricoajustado(nkadj)enel

cálculodelapotenciadelalenteintraocular(PIOLadj).

C. Evaluar la predictibilidad de diferentes fórmulas comerciales de

cálculodelapotenciadeunalenteintraocularydelaPIOLadjenuna

lenteacomodativa.

D. Evaluar la predictibilidad de diferentes fórmulas comerciales de


lentemultifocalrefractivaderotaciónasimétrica.

E. Evaluar la predictibilidad de diferentes fórmulas comerciales de


lenteasférica.

Capítulo2

HipótesisyObjetivos

50

Acontinuaciónsedetallanlaspublicacionesincluidasenlapresentetesis,en

relaciónconcadaunodelosobjetivospropuestos:

ObjetivoA:

Clinical validation of an algorithm to correct the error in the

keratometricestimationofcornealpowerinnormaleyes.(JCataractRefractSurg)

ObjetivoB:

MinimizingtheIOLpowererrorinducedbykeratometricpower.(Optom

VisSci)

ObjetivoC:

Positional accommodative intraocular lens power error induced by the

estimationofthecornealpowerandtheeffectivelensposition.(IndianJOphthalmol)

ObjetivoD:

Error induced by the estimation of the corneal power and the effective

lenspositionwitharotationallyasymmetricrefractivemultifocalintraocularlens.(IntJ

Ophthalmol)

ObjetivoE:

Preliminary evaluation of an algorithm to minimize the power error

selection of an aspheric intraocular lens by optimizing the estimation of the corneal

powerandtheeffectivelensposition.(IntEyeSci)

Capítulo3

MATERIALYMÉTODOS

53

3.MATERIALYMÉTODOS

3.a.CálculodelaPotenciacornealGaussiana(𝑷𝒄𝑮𝒂𝒖𝒔𝒔)yqueratométrica(Pk)

La córnea es un tejido que permite que la luz se refracte y se transmita. Su

formaconsistebásicamenteenunalentecóncavo-convexaconunacaraanterior,en

contactoíntimoconlapelículalagrimalprecornealyotracaraposterior,bañadapor

elhumoracuoso.Elpoderdióptricototaldelacórneasesitúaentre42.0y42.5Dy

representa aproximadamente el 70% del poder dióptrico del ojo por lo que es un

elementoesencialparaelcálculodelapotenciadelalenteintraocular.Elpoderdela

córneasepuedecalcularmedianteópticagaussiana,enlaaproximaciónparaxialdela

siguientemanera:

𝑃!!"#$$ = 𝑃!! + 𝑃!! − 𝛿𝑃!!𝑃!! =!!!!!!!!

+ !!!!!!!!!

− !!!!∙ !!!!!

!!!∙ !!!!!!

!!![27]

donde𝑃!!"#$$eslapotenciatotaldelacórneaobtenidaporelmétododeGauss,

P1ceslapotenciadelacaraanteriordelacórnea,P2clapotenciadelacaraposterior

delacórnea,r1celradioanteriorcorneal,r2celradioposteriorcorneal,naelíndicede

refraccióndelaire,ncel índicederefraccióndelacórnea,nhael índicederefracción

delhumoracuosoyecelespesorcorneal.

Para nuestros estudios siempre hemos considerado los parámetros

correspondientesalmodelodeojoteóricodeGullstrandydeLeGrand(vertabla5).

Tabla5.ParámetrosocularesparalosmodelosdeojosteóricosdeLeGrandyGullstrand

na nc nha nhv

ec

(mm)

r1c

(mm)

r2c

(mm)k nk

AL

(mm)

ACD

(mm)

LeGrand 1 1.3771 1.3374 1.336 0.55 7.80 6.50 1.20 1.3304 24.197 3.05

Gullstrand 1 1.376 1.336 1.366 0.50 7.70 6.80 1.132 1.3315 24.385 3.10

Capítulo3

MaterialyMétodos

54

La medida de la potencia queratométrica (Pk) nos viene definida por la

siguienteecuación:

𝑃! =!!!!!!!

[28]

Dondenkeselvalordelíndicequeratométricoyr1celradiodelacaraanterior

delacórnea.

Elvalordekvienedefinidocomoelcocienteorazóndadaentreelradiodela

caraanterioryposteriordelacórnea:

𝑘 = !!!!!![29]

3.b.Diferenciasentrelapotenciacornealgaussianayqueratométrica(ΔPc)

Usandolasecuaciones[27]y[28],podemoscalcularladiferencia(ΔPc)quese

obtieneentrelamedidadelapotenciacornealmedidaconelqueratómetro(Pk)yla

Gaussiana(𝑃!!"#$$)mediantelaexpresión:

Δ𝑃! = 𝑃! − 𝑃!!"#$$ =!!!!!!!

− !!!!!!!!

+ !!!!!!!!!

− !!!!∙ !!!!!

!!!∙ !!!!!!

!!![30]

Siusamoslaecuación[29],podemosmodificarlaecuación[30]delasiguiente

manera:

Δ𝑃! = 𝑃! − 𝑃!!"#$$ =!!!!!!!

− !!!!!!!!

∙ !!!!!!!!!!

− !!!!∙ !!!!!

!!!∙ !!!!!!!!!

![31]

3.c. Obtención del índice queratométrico exacto (nkexacto) y del índice

queratométricoajustado(nkadj)

Paraelcálculodelíndicequeratométricoexactocorrespondienteaunmodelo

deojoteórico(nkexacto),sedebenigualarlasecuaciones[30]o[31]acero,conloque

obtenemoslassiguientesexpresiones:

Capítulo3

MaterialyMétodos

55

𝑛!"#$%&' =!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!![32]

o

𝑛!"#$%&' =!!!!"!!!!!!!!!!!!"!!!!!!"!!!!!!!!!!!!!"!!!!!!!!!!!!!!!

!!!!![33]

Como se ha mencionado anteriormente, nuestro grupo de investigación ha

propuestorecientementeelusodeuníndicequeratométricovariable(nkadj)(53).Este

valorseobtuvoalconsiderarparacadavalorder1cymodelodeojoteórico,elvalor

que igualaba ΔPc con los valores extremos de r2c(53). Una vez obtenidos todos los

valores de nkadj, se comprobó que todos los valores de nkadj se ajustaban

perfectamenteaunaecuaciónlineal(R2:0.99)

ModeloGullstrand:𝑛!"#$ = −0.0064286𝑟!! + 1.37688[34]

ModeloLeGrand:𝑛!"#$ = −0.0063804𝑟!! + 1.37806[35]

Donder1cestáexpresadoenmm.

Medianteestealgoritmo,definimosunanuevapotenciacornealqueratométrica,

denominada potencia corneal queratométrica ajustada (Pkadj), la cual puede ser

calculadaapartirdelaecuación28utilizandocomoíndicequeratométricoelvalorde

nkadjobtenidomediantelasecuaciones[34]y[35].

Los datos clínicos del valor de los parámetros relacionados con la córnea se

obtuvieronconelsistemaPentacam®.Además,seutilizólaTrueNetPower(explicada

endetalleenelapartado3.h)quenosproporcionaelvalorde lapotenciacorneala

partir del valor de los radios corneales de la primera y segunda cara de la córnea,

despreciandoelespesorcornealytomandoparaelcálculodelaspotenciascorneales

decadacaralosvaloresproporcionadosporelmodelodeojoteóricodeGullstrand.

Portanto,paranuestroestudioclínicoseutilizólaecuacióndenkadjcorrespondiente

almodelodeojoteóricodeGullstrand[ec.34].

Capítulo3

MaterialyMétodos

56

3.d. Obtención de la potencia de la lente intraocular queratométrica (𝑷𝑰𝑶𝑳𝒌 ) y

Gaussiana(𝑷𝑰𝑶𝑳𝑮𝒂𝒖𝒔𝒔)

Comosehamencionadoanteriormente, lagranmayoríadefórmulasteóricas

existentes para el cálculo de la potencia de una lente intraocular, se basan en el

modelodeojosimplificadoenel cual seconsideraelojocomounsistema formado

porundioptrioesféricoyunalenteplanacorrespondientesalacórneayalcristalino

respectivamenteycuyafocalimagendelsistemacorrespondealaretina(2,4).

Siguiendo el esquema de la figura 7, se puede calcular fácilmente el valor

correspondiente a la potencia de la lente intraocular que sustituye al cristalino

mediantelaecuacióndeGaussparaópticaparaxialsuponiendoquesequieredejaral

paciente con una refracción deseada (Rdes). Este esquema presenta una serie de

limitaciones claras, puesto que realmente la córnea y el cristalino tienen espesor y

ademáslaópticaparaxialsoloesválidaparaángulospequeños.

Figura7.Modelodeojosimplificado

Enelesquemadelafigura,ACDeslaprofundidaddelacámaraanterior,AL

longitudtotaldelojo,O1objetosituadoenelpuntoremotodeseado(prdes),Selvértice

Córnea IOL

Retina

O´1=O2

prdes

Hc = H´c HIOL = H´IOL

O´2

ACD

AL

nhv

S

nha

O1

Capítulo3

MaterialyMétodos

57

delacórnea,Hc=H´closplanosprincipalesdelacórnea,nhaelíndicedelhumor

acuoso,IOLlalenteintraocular,nhvelíndicedelhumorvítreoyHIOL=H´IOLlosplanos

principalesdelalenteintraocular,O´1=O2imagendadaporlacórnea,O´2imagen

finalformadaenretina.

BasándonosenesteesquemasepuedeobtenermedianteelmétododeGauss,la

fórmulaquedeterminalapotenciadelalenteintraocular:

𝑃!"# =!!!

!"!!"#− !!!

!!!!!"#!!!

!!"# [36]

Donde:PIOLeslapotenciadelalenteintraocular,nhvelíndicederefraccióndelhumor

vítreo, nha el índice de refracción del humor acuoso, AL la longitud axial, Rdes la

refracción deseada, Pc la potencia corneal y ELP la posición efectiva de la lente

(ELP=ACD).

Estafórmulaestáexpresadaenfuncióndelaposiciónefectivadelalente(ELP)

en lugar de la profundidad de la cámara anterior (ACD), esto es debido a que es

preferiblehablarde laposiciónqueadopta la lentecuandose implantaenelojoen

lugar de hablar de profundidad de cámara anterior (ya que dependiendo del lugar

dondeseimplantelalenteintraocular,elvalordeELPserádiferente).

Comosehamencionadoenelapartado3.a,vamosaconsiderarquelapotencia

cornealpuedemedirsea travésdeunqueratómetro (Pk)oporelmétododeGauss

(𝑃!!"#$$). Es por esta razónquepara realizar el cálculo de la potencia de una lente

intraocular teniendo en cuenta la ec. 36, se han definido dos fórmulas de cálculo

diferentesdependiendodelapotenciacornealescogida(Pk)o(𝑃!!"#$$).

Si para la medida de la potencia corneal se utiliza Pk, la ecuación

correspondientealcálculodePIOLserá:

𝑃!"#! = !!!!"!!"#

− !!!!!!

!!"#!!!!!!!!

!!"# [37]

ysipararealizarelcálculodelapotenciacornealseutiliza𝑃!!"#$$,laecuaciónparael

cálculodelaPIOLserá:

Capítulo3

MaterialyMétodos

58

𝑃!"#!"#$$ =!!!

!"!!"#− !!!

!!!!!"#!

!!!!!!!!!

!!!!!!!!!!

!!!!!∙!!!!!!!!

∙!!!!!!!!!

!!"#[38]

Donde:nhvíndicedelhumorvítreo,ALlongitudaxial,ELPposiciónefectivadelalente,

nha índice refracción del humor acuoso, Rdes refracción deseada, nk es el índice

queratométrico, r1c radio corneal anterior, r2c radio corneal posterior, na índice

refraccióndelaire,ncíndicerefraccióndelacórneayecelespesordelacórnea.

Esimportanteseñalarqueenlasecuaciones[37]y[38]lapotenciacornealestá

referenciada desde diferentes planos debido al modelo de córnea considerado (de

unasolasuperficie[ec.37]ydedossuperficies[ec.38]).

Siutilizamoslaecuación29podemosvolverareescribirlaecuación[38]comosigue:

𝑃!"#!"#$$ =!!!

!"!!"#− !!!

!!!

!!"#!!!!!!!!!!

!!!!!!!!!!!

!!!!!∙!!!!!!!!

∙!!!!!!!!!!

!!"#[39]

La diferencia que existe entre realizar el cálculo de la PIOL con el valor de la

potencia corneal queratométrica (Pk) [ec.37] oGaussiana (𝑃!!"#$$) [ec.38]nosda la

siguienteexpresión:

Δ𝑃!"# = 𝑃!"#! − 𝑃!"#! = !!!!!!

!!"#!!!!!!!!

!!"#− !!!

!!!!!"#!

!!!!!!!!!

!!!!!!!!!!

!!!!!∙!!!!!!!!

∙!!!!!!!!!

!!"#[40]

Siintroducimoslavariablekenla[ec.40],obtenemoslasiguienteexpresión:

Δ𝑃!"# =!!!

!!!!!"#!

!!!!!!!

!!"#− !!!

!!!

!!"#!!!!!!!!!!

!!!!!!!!!!!

!!!!!∙!!!!!!!!

∙!!!!!!!!!!

!!"#[41]

ElvalordeΔPIOLsecalculóparaunrangodecurvaturacornealpertenecientea

una población normal, que corresponde a un rango de curvatura corneal anterior

entre 7.0 y 8.5mm(39,44,45,52,53,64,130,131) y de cara posterior entre 5.6 y 7.0mm. Por

tanto,ennuestrosestudiosteóricos,seasumieronunosvaloresdekvariabledesde1

hasta 1.51. Además, se consideró una ELP variable entre 2 y 6 mm, acorde a la

bibliografíaencontrada(4,13,20).TambiénseoptóporunosvaloresdeRdesvariablesde

Capítulo3

MaterialyMétodos

59

0,-1.0y+1.0D.

Mediante la ecuación 36 podemos explicar y entender las primeras fórmulas

que aparecieron para el cálculo de potencia de lentes intraoculares denominadas

fórmulas de primera generación. Por ejemplo, Van der Heijde(10) introdujo esta

fórmulaparalarealizacióndelcálculodelapotenciadelalenteintraocularenelcaso

de cataratas y suponiendo que el paciente quedaba emetropizado. La fórmula era

idéntica a la ecuación 36, donde sustituyó nha=nhv=1.336, las multiplicó por 1000,

consideróquelaRdes=0ylaACDpasóallamarseACDpost.Enelcasodelasfórmulasde

segunda generación, realmente son desarrollos en serie de Taylor de la ecuación

teórica 36 hasta el primer orden en función de AL y Pc, entorno a valores

determinados de AL y Pc. Por lo tanto derivan realmente de la expresión teórica

obtenidaanteriormente.

3.e.Obtencióndelapotenciadelalenteintraocularajustada(PIOLadj)

Siparaelcálculode lapotenciade la lente intraocular introducimoselvalorde

Pkadjobtenidomedianteelcálculodenkadjpertenecientesalosmodelosdeojoteórico

deGullstrandoLeGrand[ec.34yec.35,respectivamente]enla[ec.36],obtenemosla

siguienteexpresión:

𝑃!"#$%& =!!!

!"!!"#− !!!

!!!!!"#!!!"#$

!!"#[42]

Elvalorteóricodelapotenciadelalenteintraocularajustada(PIOLadj)secalculó

paralosdiferentestiposdelentesintraocularesestudiadasmediantelaecuación36,

usandoelvalordenkadjparalaestimacióndelapotenciacorneal(Pkadj),asícomolos

valores de nha y nhv correspondientes al modelo de ojo teórico de Gullstrand y Le

Grand(vertabla5).Paraelvalordelarefraccióndeseadaesprácticahabitualquese

pretenda dejar al paciente con una refracción determinada (Rdes) después de

implantar la lente intraocular,por loqueesmuy importantequeel clínicoconozca

bien las necesidades de su paciente. Debe saber si su paciente prefiere quedarse

miopepara así poder leer sin gafas o si por el contrario desea ser emétrope y por

Capítulo3

MaterialyMétodos

60

tanto, deberá usar gafas de cerca. En algunos casos se opta por una distancia

intermedia (-1.00 D)(35) para un mejor compromiso. Para nuestro estudio,

seleccionamoselequivalenteesféricopostoperatoriomedidodesdeelvérticecorneal

(Rdes=SEpost).EstacondiciónfueelegidaparapodercomprobarsielvalordelaPIOLadj

eraintercambiableconlalenteimplantada(PIOLReal),paraelloseasumióqueelclínico

realmente quería dejar al paciente con una cierta refracción residual [ec.42]. Este

valordepotenciadelenteintraocular(PIOLadj)secomparóconelvalorrealdelalente

intraocularimplantada(PIOLReal)encadacaso.

En primer lugar, se realizó una prevalidación clínica de la PIOLadj en la cual se

obtuvo una relación de ΔPIOL con ΔPc para el rango de curvatura corneal

pertenecienteaunapoblaciónnormalsincirugíaprevia(r1crangoentre7.0y8.5mm,

r2centre5.6y7.0mm).PararealizarestacomparativaseconsideróRdes=0,siendoel

valor del índice queratométrico el propuesto para cada modelo (1.3304 y 1.3315,

paraelmodelodeLeGrandyGullstrandrespectivamente)ademásde incorporarel

valor queratométrico de 1.3375. El valor de ELP considerado en este primer

momentofueeldescritoparacadamodelo(3.05mmparaelmodelodeLeGrandy

3.10 mm para el modelo de Gullstrand, ver Tabla 5), así como un valor de ELP

variable entre 2.0 y 6.0mm, puesto que dependiendo del tipo de lente intraocular

implantadasuposiciónpuedevariar.

Acontinuación,seprocedióarealizarunavalidaciónclínicaprevia.Enestecaso,

se comparó la PIOLadj con la PIOL obtenida mediante el cálculo de cuatro fórmulas

comerciales como la fórmula de Haigis (PIOLHaigis) [ec. 26], fórmula de Hoffer Q

(PIOLHofferQ) [ec. 23], fórmula SRK/T (PIOLSRK/T) [ec. 22] y fórmula de Holladay I

(PIOLHolladay) [ec.21], en las que se consideró para cada paciente el valor de ELP

definidoparacadafórmulayRdes=SEpost.

En los estudios donde se utilizaron datos de lentes reales, para realizar las

comparativas entre la potencia real implanta (PIOLReal) en cada tipo de lente

intraocular analizada y la potencia ajustada (PIOLadj) obtenida mediante nuestro

algoritmo, se procedió a calcular el valor de laPIOLadj utilizando el valor de laELP

siguiendo las directrices de la fórmula SRK/T (a la que se le denominóPIOLadjSRK/T),

Capítulo3

MaterialyMétodos

61

debido a la elección en todos los casos por parte del clínico del valor de la PIOL

obtenidamedianteelIOLMaster®correspondientealaobtenidamediantelafórmula

SRK/T. También se desarrolló un nuevo método de cálculo de ELP usando una

expresiónmatemáticaobtenidamedianteregresiónmúltiple(alaqueseledenominó

ELPadj)enlaqueseexplicarádetalladamenteenelsiguienteapartado.Estosvalores

dePIOLsecompararonconlasfórmulascomercialesdeHofferQ,HaigisyHolladayI,

en las cuales se consideró el valor de ELP definido para cada fórmula, siendo

Rdes=SEpost.

3.f.EstimaciónELPadj

Sondiversas lasposibles fuentesdeerrorpara la realizacióndel cálculode la

potencia deuna lente intraocular, como son la potencia corneal, longitud axial y la

posiciónefectivadelalente.Lapotenciacornealseanalizómedianteelusodelvalor

de nkadj para minimizar el error cometido en la estimación de la potencia de la

córnea(53,132).Dadoqueestevalorsehaminimizado,otraposiblefuentedeerrorera

la obtención de la longitud axial. Puesto que la exactitud del IOLMaster® para el

cálculo de la longitud axial ha sido ampliamente demostrada(133), se consideró el

cálculodeELPcomofactorcríticoporlapresenciadeunalimitadapredictibilidaden

elcálculodeunalenteintraocular.Enlosestudiosrealizadosconlentescomerciales

setratódecalcularcuáldeberíaserelvalordelaELPexacto.Paraello,seconsideróla

ecuación 36, PIOLReal, Pkadj y la Rdes=SEpost y se obtuvo el valor de la ELP para cada

paciente. Una vez obtenidos los valores de ELP para cada paciente se realizó un

análisis de regresión múltiple de pasos hacia atrás (backwards) para obtener una

expresión matemática que relacionara la variable ELP a partir de diferentes

parámetros anatómicos y clínicos preoperatorios. Una vez obtenida la ecuación, el

valor que se obtenía para cada paciente se denominó posición efectiva de la lente

ajustada(ELPadj).EstevalordeELPadjsecomparóconotrosvaloresdeELPobtenido

conotrasfórmulasconvencionalesdecálculodeELP.

Capítulo3

MaterialyMétodos

62

3.g.Seleccióndepacientes

El criterio de inclusión en todos los estudios fueron pacientes con catarata

significativa o présbitas/pre-présbitas candidatos para la implantación de lentes

intraocularesqueexigíanunavisiónóptimaa todas lasdistancias.Comocriteriode

exclusiónseconsiderólapresenciadepatologíaocularactiva,elanalfabetismo,ojos

quehubieransidosometidosacualquierprocedimientoquirúrgicoprevio,asícomo

la presencia de astigmatismos superiores a 1.5 D. Todos los voluntarios leyeron y

firmaronpreviamenteunconsentimiento informadoacordecon loestablecidoen la

DeclaracióndeHelsinki,quefueaprobadoporelcomitédeéticalocal.

3.h.Protocolodeexamendelospacientes

Entodosloscasosserealizóunexamenoftalmológicocompletoenlosquese

incluíanlarefracción,lamejoragudezavisualcorregida(BCVA),biomicroscopíacon

lámpara, tonometría de Goldman, evaluación del fondo de ojo y un análisis de la

estructura corneal por medio de una fotografía basada en la tomografía de

Scheimpflug, conel sistemaOculusPentacam®(OculusOptikgeräteGmbH,Germany).

Enconcreto,losdatosdelosparámetrosrecogidosyanalizadosfueron:radiocorneal

delacaraanterior(r1c)yposterior(r2c)pertenecientealos3mmdeáreacentraldela

córnea,elastigmatismocornealanterior(ACA)yposterior(ACP)enlos3mmdeárea

central de la córnea, la potencia corneal real calculada teniendo en cuenta la cara

posterior de la córnea denominada “true net power”, la profundidad de la cámara

anterior(ACD)yelespesorcorneal(ec).

3.i.SistemaPentacam

ElOculusPentacam® esunsistemano invasivopara lamedidaycaracterización

delsegmentoanteriorutilizandounacámararotatoriadeScheimpflug(64,134)figura(8).

Capítulo3

MaterialyMétodos

63

A

B

C

Figura8.SistemadetopografíacornealPentacam®.A:Pantallavisualizacióndedatos.B.BasedelfuncionamientodelsistemaPentacam®medianteproyección/reflexiónencórnea.C.Montajedispositivo

Pentacam®(Fuente:www.pentacam.com)

El procedimiento de examen rotatorio genera imágenes Scheimpflug

tridimensionalesatiemporealdelsegmentoanteriorocular,conunamatrizdepunto

demallafinaenelcentrodebidoalarotación.Serecogenuntotalde100imágenes

con500puntos demedidade la cara anterior y posterior de la córnea durante un

movimientorotatoriode360º.Losdatosdeelevaciónobtenidosdecada imagense

combinan con el fin de generar una reconstrucción tridimensional de la estructura

corneal(135). Este sistema necesita unmáximo de 2 segundos en tomar una imagen

completadelacaraanteriordelojo.Cualquiermovimientodelojoserácaptadopor

una segunda cámara y se corregirá durante el proceso de examen. El Oculus

Pentacam® calcula un modelo tridimensional de la cara anterior del ojo con un

examenrealdehasta25.000puntosdeelevación.LasimágenesScheimpflugtomadas

durante el examen son digitalizadas en una unidad y todas esas imágenes son

transferidasalordenador.Elsoftwarenosproporcionaunagrancantidaddemapas

de códigos de colores, una variedad de parámetros geométricos de la superficie

Capítulo3

MaterialyMétodos

64

anterior y posterior, un análisis aberrométrico así comomedidas volumétricas de

espesores.ElOculusPentacam®mide lasdos superficiesde la córneayusa losdos

mapas de curvatura para calcular el mapa de potencia real (true net power). Los

valores refractivosde la caraanteriorde la córnease calculanusando ladiferencia

entreelíndicederefraccióndelaire(n=1),elíndicederefraccióndeltejidocorneal

(n=1.376) y el índice de refracción del humor acuoso (n=1.336). Los valores

refractivosmostrados en elmapa de la true net power se obtienen a partir de las

potenciascornealesdelaprimeraysegundacaradespreciandoelespesorcorneal.La

expresiónutilizadaeslasiguiente(135):

𝑇𝑟𝑢𝑒𝑁𝑒𝑡𝑃𝑜𝑤𝑒𝑟 = !.!"#!!!!!

×1000+ !.!!"!!.!"#!!!

𝑥1000 [43]

Para la toma demedidas en todos los casos se ha utilizado el software del

OculusPentacam®versión1.14r01.

3.j.Lentesintraocularesutilizadasenlosestudios

Para laelaboracióndelArtículo3, seutilizó la lenteCrystalensHD(Bausch&

Lomb)(fig.9),unalentecondiseñobiconvexo.Estalenteesdesiliconabiocompatible

de tercera generación (Biosil) con un índice de refracción de 1.427. Tiene una

modificaciónbi-asféricaenlazonacentralparaaumentarlaprofundidaddefocoyasí

proporcionarunamejorvisiónenlazonaintermediaycerca.Estádisponibleendos

tamañosdependiendodelapotencianecesaria,elmodelode12.0mm(HD520)para

potenciascomprendidasentre10.00y16.75Dyelmodelode11.5mm(HD500)para

potenciascomprendidasentre17.00y33.00D.Segúnlasindicacionesdelfabricante,

lalenteintraoculartieneundoblemecanismoparamejorarlafunciónvisualdecerca:

movimiento axial como consecuencia del musculo ciliar y variación del radio de

curvaturadelasuperficieanteriordelalenteintraocular(arqueamientoóptico)(136).

Capítulo3

MaterialyMétodos

65

Figura9.CrystalensHD500(Bausch&Lomb)

(Fuente:www.eyepress.ru)

ParaelArtículo4,seutilizólaLentisMplusLS-312(OculentisGmbH)lacuales

una lente multifocal refractiva de rotación asimétrica compuesta por una zona de

visiónde lejosasféricacombinadaconunazonade3.00D(quesecorrespondecon

+2.50Denelplanodegafa)(109)enformadesectorparavisióndecercaparapermitir

latransiciónentrezonas.Compuestadeuncopolímeroacrílicoconcomponentesde

filtrado UV y con una superficie hidrofóbica. Tiene un diseño biconvexo con una

ópticade6.0mm, conuna longitud totalde11.0mmyundiseñodehápticosde0

grados.Disponibleenunrangodepotenciasde-10.00a-1.00D(enpasosde1.0D)y

entre0.00y+36.00D(enpasosde0.5D).

Figura10.LentisMplusLS-312(OculentisGmbH)


Capítulo3

MaterialyMétodos

66

EnelArticulo5,seestudiólaLentisL-313(OculentisGmbH).Unalentedeuna

solapiezaacrílica(copolímerodeHydroSmart)conunasuperficiehidrofóbicayfiltro

ultravioleta.Tieneundiseñobiconvexoconunaópticade6.0mm,unalongitudtotal

de11.0mmyundiseñodehápticosde0grados.Lasuperficieposteriorde lalente

intraoculares asférica y proporciona un nivel negativo de aberración esférica para

compensarlaaberraciónesféricapositivadelacórnea.Estádisponibleenpotencias

de -10.00a+35.00Denpasosde1.00Dyde+10.50a+29.50Denpasosde0.50

D(137).

Figura1.LentisL-313(OculentisGmbH)


3.k.Técnicaquirúrgica

Todaslascirugíasfueronrealizadasporunacirujanaexperimentada(MLR).En

todaslasintervencionesseusóunatécnicaestándardefacoemulsificación,enlosque

seadministróanestesiatópicaydilataciónpupilarinducidaconunacombinaciónde

tropicamida y fenilefrina al 10% cada 15 minutos, media hora antes de la

intervención.Diezminutosantesdelaoperaciónseinstiló5%desoluciónyodada.Se

realizóunaclaraincisiónde2.75mmconunacuchilladediamanteenelmeridiano

mayorparaminimizar el astigmatismopostquirúrgico. Se creóunaparacentesis en

sentido horario de 60-90º desde la incisión principal y donde el compartimiento

anteriorestaballenodematerialviscoelástico.Despuésdelaextraccióndelcristalino

lalenteintraocularseimplantóatravésdelaincisiónenelsacocapsularutilizando

Capítulo3

MaterialyMétodos

67

un inyector específico para cada tipo de lente. Finalmente la cirujana procedió a

recuperarelmaterialviscoelásticoutilizandoelsistemade irrigacióndeaspiración.

Se prescribieron una combinación de esteroides tópicos y antibióticos (Tobradex,

Alcon, Fort Worth, TX, USA) así como un antiinflamatorio no esteroideo en gotas

(Dicloabak, Laboratorios Thea, Barcelona, España) para aplicar cuatro veces al día

duranteunasemanadespuésde lacirugíay tresvecesaldíaen lasegundasemana

postoperatoria. Además, las gotas antiinflamatorias no esteroideas también fueron

prescritasparaaplicartresvecesaldíadurante2semanasmásdespuésdelacirugía.

3.l.Examenpreypostoperatorio

Previamente,serealizóunexamenoftalmológicocompletoenelqueseincluía

unaevaluacióndelestadorefractivo,tomadeagudezasvisualestantodelejoscomo

de cerca, un examen con lámpara de hendidura, biometría óptica (IOL-Master,Carl

ZeissMeditec, Jena,Alemania), tonometría deGoldman y fundoscopia. Las agudezas

visualesenvisióndelejos(a4m)yvisióncercana(a40cm)seevaluaronmediante

lascartasETDRS.Postoperatoriamente,lospacientesfueronevaluadosdespuésde1

día,1semana,1mesy3mesesdelacirugía.Entodaslasvisitas,seevaluólaagudeza

visual,larefracciónylaintegridaddelsegmentoanterior.Lafundoscopiatambiénse

realizóenlarevisiónpostoperatoriadelos3meses.

3.m.Análisisestadístico

El análisis estadísticoen los artículos1 a3 se realizómedianteelprograma

SPSSversión19.0paraWindows(IBM,Amonk,NY,USA),enelcasodelosartículos4y

5 se utilizó el programa SPSS versión 21.0.0.0 paraMac (IBM, Amonk, NY, USA). La

normalidad de las variables fue evaluadamediante el testKolmogorov-Smirnov, se

utilizóunniveldeconfianzadel95%yniveldesignificancia(α)del5%.Seconsideró

quelosdatosseguíanunadistribuciónnormalenaquelloscasosenlosqueelp-valor

erasuperiora0.05.

Para comparar los distintos valores de las PIOL obtenidos se utilizó el test

estadístico t-Student para datos pareados en el supuesto de que se cumpliera la

Capítulo3

MaterialyMétodos

68

condición de normalidad, en caso contrario se utilizó el test de los rangos de

Wilcoxon. En cualquiera de losmétodos utilizados para contrastar las variables se

aceptóquenoexistíandiferenciasestadísticamente significativasentre lasmedidas

cuandoseobtuvounp-valor>0.05.

Para evaluar la intercambiabilidad entre métodos analizados se realizó un

análisis Bland Altman, en el que se muestran las diferencias entre los métodos

evaluados frente a la media de los mismos. Los límites de acuerdo (LoA) vienen

definidoscomolamedia±1.96ladesviaciónestándar(SD)delasdiferencias.

Se valoró la presencia de correlaciones entre distintos tipos de variables

mediantes los coeficientes de Pearson o Spearman, dependiendo si la condición de

normalidadsecumplíaonorespectivamente.

También se realizó un análisis de regresión múltiple de pasos hacia atrás

(backwards) para obtener una expresión matemática que relacionara la variable

ELPadj a partir de diferentes parámetros anatómicos y clínicos preoperativos. Para

evaluarlaslimitacionesdelmodelomatemáticoobtenido,seanalizólanormalidadde

los residuosnoestandarizados (homoscedasticidad)y lasdistanciasdeCookconel

fin de detectar outliers. Además, se comprobó la ausencia de correlación entre

errores con el test de Durbin-Watson y la presencia de multicolinealidad con la

toleranciadecolinealidadyelfactordeinflacióndelavarianza(FIV).

Capítulo4

RESULTADOSYDISCUSION

71

4.RESULTADOSYDISCUSIÓN

4.a.ResultadosdelostrabajosenrelaciónconelobjetivoA

Validaciónclínicadeunalgoritmoparalacorreccióndelaestimacióndel

error queratométrico de la potencia corneal en ojos normales. [Piñero DP,

CampsVJ,MateoV,Ruiz-FortesP. Clinical validationof an algorithm to correct the

errorinthekeratometricestimationofcornealpowerinnormaleyes.JCataractSurg

2012;38:1333-1338]

EnesteestudiosevalidódeformaclínicaelalgoritmodefinidoporCampset

al.(53) para la corrección del error en la estimación queratométrica de la potencia

corneal en personas con ojos sanos sin cirugía previa, basándonos en el uso de un

índice queratométrico variable (nkadj). Para ello, de acuerdo con la literatura

revisada(39,44,45,52,53,64,130,131), se consideró un rango de radio corneal anterior

pertenecienteaojossanosvariableentre7.0y8.5mm,siendoelrangoparalacara

posteriordelacórneaentre5.6y7.0mm.

Elalgoritmoutilizadoparaelestudiosecorrespondeconelmodelodeojoteóricode

Gullstrand[ec.34],conunrangodevaloresdesuperficieanterioryposteriorcorneal

pertenecientesapoblaciónnormal(53).

𝑛!"#$ = −0.0064286𝑟!! + 1.37688[34]

Este valor de nkadj se ha utilizado para realizar el cálculo de la Pkadj y así poder

comparar este valor con el obtenido por el método de Gauss(𝑃!!"#$$) . A las

diferenciasentreambasmedidasselehadesignadocomoΔPc.

Sevaloraronun totalde92ojosde92pacientes conunaedadmediade36.7

años (rango de 15 a 64 años) de los cuales 47 (51.1%) eranmujeres. Lamuestra

estabacompuestapor49ojosderechos(53.3%).Latabla6muestralosparámetrosde

losojosevaluados.

Capítulo4

ResultadosyDiscusión

72

Tabla6.Parámetrosocularesevaluados

Parámetro Media±SD Rango

SE(D) -2.80±3.89 -15.75a+4.00

r1c(mm) 7.67±0.01 7.19a8.43

r2c(mm) 6.30±0.21 5.87a6.82

ACA(D) 1.13±0.98 0.00a5.80

ACP(D) 0.36±0.24 0.00a1.60

𝑷𝒄𝑮𝒂𝒖𝒔𝒔 (𝑫) 42.76±1.30 38.80a45.50

Pkadj(D) 42.74±1.47 38.28a45.99

ΔPc(D) -0.02±0.22 -0.55a+0.52

ACD(mm) 3.08±0.38 2.21a4.96

ec(ìm) 559.0±33.8 485.0a665.0

Donde: SE= equivalente esférico; r1c= radio caraanterior de la córnea; r2c= radio cara

posterior de la córnea; ACA= astigmatismo anterior corneal; ACP= astigmatismo

posteriorcorneal;=potenciacornealcalculadaporelmétododeGaussparaelmodelo

de ojo de Gullstrand; Pkadj= potencia corneal queratométrica calculada con el índice

queratométricoajustado;ÄPc=diferenciaentrelapotenciacornealqueratométricayla

potencia corneal calculada por el método de Gauss; ACD=profundidad de la cámara

anterior;ec=espesorcorneal

Losprincipaleshallazgosyconsideracionessobrelosresultadosobtenidosse

exponenacontinuación:

Capítulo4


73

1. No se encontraron diferencias estadísticamente significativas entre la

potencia queratométrica ajustada (Pkadj) y la potencia corneal gaussiana

(𝑃!!"#$$) (P=.43, t-Student).Comoseobservaen la figura12, se encontró

unafuertecorrelaciónentreambasmedidasdepotenciacorneal(r=0.994,

P<.01)

Figura12.Diagramadispersióndondesemuestralarelaciónentre𝑃!!"#$$yPkadj

2. En el análisis de Band-Altman (fig.13) se obtuvo que la media de las

diferencias entre ambas medidas fue de -0.02 D, con unos límites de

concordanciainferiorde–0.46Dysuperiorde+0.42D, loscualesnoson

clínicamenterelevantes.Seaprecióunapequeña tendenciaasobrestimar

elvalordePcconelusodenkadjencórneascurvasyasubestimarsuvalor

encórneasplanas.

38,0

40,0

42,0

44,0

46,0

38,0 40,0 42,0 44,0 46,0

P kadj(D)

PcGauss(D)

Capítulo4


74

Figura13.DiagramadepuntosBlandAltmancorrespondientealasdiferenciasentrelaPkadjyla𝑃!!"#$$frentealamediadelasdiferencias

3. No se encontraron correlaciones significativas entre laΔPc (Pkadj-𝑃!!"#$$)

conlaedad(r=0.13;P=.21),equivalenteesférico(SE)(r=-0.045;P=.67),

agudeza visual con la mejor corrección (BCVA)(r = 0.04; P =.73),

profundidad de la cámara anterior (ACD) (r = -0.05; P =.64), espesor

corneal (ec) (r = -0.09; P =.41), astigmatismo corneal anterior (ACA) (r =

0.07;P=.52)yastigmatismocornealposterior(ACP)(r=0.08;P=.43).Por

contra, se observó una fuerte correlación estadísticamente significativa

entre ΔPc y el radio corneal posterior (r2c) (r = -0.96; P <.01) (fig. 14).

También se encontró una correlación estadísticamente significativa,

aunqueenmenorgrado,entrelaΔPcyelradiocornealanterior(r1c)(r=-

0.79;P<.01).

+0,42D

-0,46D-0,02D

-2,5

-1,5

-0,5

0,5

1,5

2,5

38,0 39,0 40,0 41,0 42,0 43,0 44,0 45,0 46,0 47,0

DiferenciasP

kadj-P

cGauss (D)

MediaPkadj-PcGauss(D)

Capítulo4


75

Figura14.Diagramadedispersióndondesemuestralarelacióndeladiferencia(ΔPc)entrelapotenciacornealqueratométricaajustada(Pkadj)ylapotenciacornealgaussiana(PcGauss)conelvalordelradiodelacaraposteriordelacornea(r2c)

En un estudio de simulación previo(53) realizado por nuestro grupo de

investigación, al analizar losmodelosdeojosdeGullstrandyLeGrandseencontró

quelaestimaciónqueratométricasubestimabaosobrestimabaelvalordelapotencia

corneal gaussiana, siendo este error dependiente de ambos radios corneales y por

consiguiente del cociente k(53). La sobrestimación de la potencia corneal estuvo

siemprepresenteenambosmodeloscuandoseempleóelvalordenk=1.3375.Estos

resultados(53) junto con los estudios previos(39,44,45) muestran la necesidad de un

modeloprecisoparadeterminarelvalormásapropiadodenkparacalcularelvalorde

lapotenciacornealqueratométrica.Porestarazóndesarrollamosunmétodorápido,

fácil y clínicamente aplicable para la determinación del nk más adecuado para la

estimaciónqueratométricaencadacasoconcreto(53).Paraelloseutilizóunaecuación

linealparadeterminarelvalordenk (nkadj)dependienteúnicamenteder1c.Elerror

máximocalculadoasociadoaesteenfoque(ΔPc) fuede0.70D, correspondientesa

losdosvaloresdecadaextremoder2cdefinidosparaunapoblaciónnormalysana(

5.5,5.6mmy6.9,7.0mm)paraelrestodevaloresder2c,elerrorasociadoconeluso

de nkadj se situó por debajo de 0.5 D independiente del valor r1c. Como cabía de

esperar se encontró una fuerte correlación entre Pkadj y𝑃!!"#$$(true net power),

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

5,8 6,0 6,2 6,4 6,6 6,8 7,0

ΔPc(D)

r2c(mm)

Capítulo4


76

apreciándosediferenciasnosignificativasestadísticamente(-0,02±0.22D,rangode-

0,55a0,52D),confirmándosedeestemodolaintercambiabilidaddeambosmétodos

demedidadepotenciacornealobtenidosenlosresultadosteóricosprevios(53).Enla

práctica clínica, se consideran aceptables diferencias de hasta 0,50 D entre Pkadj y

𝑃!!"#$$portanto,lasdiferenciasqueseobtuvieronnofueronclínicamenterelevantes.

ElanálisisdeBlandyAltman(138)confirmólavalidezclínicadelalgoritmodenkadj,se

apreció una pequeña tendencia a sobrestimar el valor dePc con el uso delnkadj en

córneascurvasyasubestimarsuvalorencórneasplanas,siendoelrangodeacuerdo

entre ambas medidas de potencia corneal de 0,44 D. Es decir, el 95% de las

diferenciasentrelapotenciagaussianayloscálculosqueratométricosteníanunvalor

≤0,44D.

4.2.ResultadosdelostrabajosenrelaciónconelobjetivoB

Minimizacióndelerrordelapotenciadeunalenteintraocularinducida

por la potencia queratométrica. [Camps VJ, Piñero DP, de Fez D, Mateo V.

MinimizingtheIOLpowererrorinducedbykeratometricpower.OptomVisSci.2013

Jul;90(7):639-49.]

Enesteestudioseevaluódeformateóricaenunapoblacióndeojossanosla

influencia del error en el cálculo de la potencia corneal debido al uso de un índice

queratométrico(nk)enelcálculodelapotenciadelalenteintraocular(PIOL).Además

seanalizóyvalidódeformapreliminarelusodeuníndicequeratométricoajustado

(nkadj)enelcálculodelapotenciadelalenteintraocular(PIOLadj).

Lapotencia corneal se calculó, al igualqueenel estudioanterior,paraunos

rangosdecaraanterioryposteriorcornealcorrespondientesacórneassanas,rango

deradiocornealanteriorentre7.0y8.5mm,siendoelrangoparalacaraposteriorde

lacórneaentre5.6y7.0mm[ec.37y38].Paraelvalordenkseeligieronlosvalores

correspondientes al modelo de ojo de Gullstrand(139) y Le Grand(140,141) (1.3315 y

1.3304,respectivamente)yelvalorclásicode1.3375.SeconsideróRdes=0yelvalor

deELPteóricoqueseintrodujoparaelcálculodelapotenciadelalenteintraocular

Capítulo4


77

correspondió al valor de la profundidad de cámara anterior teórica proporcionada

por los dosmodelos de ojo teórico utilizados (3.05 y 3.10 para losmodelos de Le

GrandyGullstrandrespectivamente)así comounvalordeELP variableentre2.0y

6.0mm,parasimularlasdistintasposicionesquepuedeadoptarlalenteintraocular

alserinsertada.Conlosvaloresdepotenciadelenteintraoculargaussiana(𝑃!"#!"#$$)y

queratométrica(𝑃!"#! )obtenidas,seprocedióaanalizarlarelacióndeΔPIOLrespectoa

ΔPc.

Acontinuación,seprocedióarealizarunavalidaciónclínicaprevia.Enestecaso,

se analizó en primer lugar la intercambiabilidad existente entre PIOLadj [ec 42] y

𝑃!"#!"#$$[ec 38]. Al confirmar su intercambiabilidad se procedió a comparar nuestra

PIOLadjconlaPIOLobtenidamedianteelcálculodecuatrofórmulascomercialescomo

son la fórmuladeHaigis (PIOLHaigis) [ec.26], fórmuladeHofferQ(PIOLHofferQ) [ec.23],

fórmulaSRK/T(PIOLSRK/T)[ec.22]y fórmuladeHolladayI(PIOLHolladay)[ec.21],en las

que se consideró para cada paciente el valor deELP definido para cada fórmula y

Rdes=SEpost

Los algoritmos de nkadj utilizados para este estudio clínico previo, son los

correspondientesalmodelodeGullstrandyalmodelodeLeGrandpropuestospor

nuestro grupo de investigación(53) dependientes únicamente del radio anterior

corneal[ec.34y35]

ModeloojodeGullstrand:nkadj=-0.0064286r1c+1.37688 [34]

ModeloojodeLeGrand:nkadj=-0.0063804r1c+1.37806 [35]

Estos algoritmos, se utilizaron para calcular la potencia corneal queratométrica

ajustada (Pkadj) mediante el uso de la fórmula clásica de la potencia corneal

queratométrica[ec.28].

Para la validación preliminar de la PIOL con el algoritmo propuesto en este

estudio se consideró unamuestra de ojos normales conAL entre 22.0 y 26.0mm.

Específicamenteseescogióunamuestrade81ojoscorrespondientesa81pacientes

candidatos a cirugía refractiva que fueron examinados en elHospital Internacional

Capítulo4


78

Medimar (Alicante). Únicamente se escogió un ojo por paciente para realizar el

estudio.

Los principales hallazgos y consideraciones sobre los resultados obtenidos se


1. Secompararonlasdiferenciasteóricas(ΔPIOL)encontradasentrelamedidade

lapotenciadelalenteintraocularqueratométrica(𝑃!"#! )obtenidaapartirdela

potenciacornealqueratométrica(Pk)y lagaussiana(𝑃!"#!"#$$) obtenidapartir

delapotenciacornealgaussiana(𝑃!!"#$$).Estasdiferenciasfueronanalizadas

en función de las diferencias entre la potencia corneal queratométrica y la

gausiana (ΔPc) para un rango normal de r1c (valores de 7.0 a 8.5mm) en el

modelo de ojo de Le Grand y Gullstrand y distintos valores de nk (1.3304,

1.3315y1.3375).Comosepuedeapreciarenlatabla7,existeunatendenciaa

subestimarelvalordelaPIOLcuandoseutilizaPkenelcálculo(𝑃!"#! )enlugar

de𝑃!"#!"#$$ (ΔPIOL<0). Esta tendencia proviene de la sobreestimación de Pk

respecto a𝑃!!"#$$ en el cálculo de la potencia corneal (ΔPc>0). La mayor

sobrestimaciónhalladaseencontróenlacombinaciónder1c=7.0mmyr2c=

7.0mm con unos valores de +1.41 y +0.95D para elmodelo de LeGrand y

Gullstrand respectivamente. La mayor subestimación se situó en la

combinaciónder1c=8.5mmyr2c=5.60mm,conunosvaloresde-1.76y-2.16

DparaelmodelodeojodeLeGrandyGullstrandrespectivamente.Cuandose

usónk= 1.3375para losdosmodelos, se observóuna subestimaciónde𝑃!"#!

respecto a𝑃!"#!"#$$ . El valor máximo de subestimación se encontró en la

combinaciónder1c=8.5mmyr2c=5.60mm,conunosvaloresde-3.01y-2.77

DparaelmodelodeGullstrandyLeGrand,respectivamente.

Capítulo4


79

Tabla 7. Resumen de las diferencias obtenidas entre la potencia de la lente intraocularqueratométrica y gaussiana (ΔPIOL) obtenidos dentro de un rango de curvatura de radioanteriornormal(r1cde7.0a8.5mm)paralosmodelosdeojodeLeGrandyGullstrand,asícomoparalosdiferentesvaloresdenkutilizados(1.3304,1.3315y1.3375)

LeGrand Gullstrand

nk:1.3304 nk:1.3375 nk:1.3315 nk:1.3375

r1c(mm) ΔPc(D) ΔPIOL(D) ΔPc(D) ΔPIOL(D) ΔPc(D) ΔPIOL(D) ΔPc(D) ΔPIOL(D)

7.00 0.26;-1.12 -0.33;1.41 1.28;-0.11 -1.61;0.14 0.65;-0.75 -0.81;0.95 1.50;0.10 -1.90;-0.13

7.10 0.36;-1.03 -0.45;1.29 1.36;-0.03 -1.71;0.03 0.74;-0.66 -0.93;0.84 1.58;0.18 -1.99;-0.23

7.20 0.45;-0.93 -0.57;1.17 1.44;0.05 -1.80;-0.07 0.83;-0.57 -1.03;0.72 1.66;0.26 -2.08;-0.32

7.30 0.55;-0.84 -0.68;1.05 1.52;0.13 -1.89;-0.16 0.91;-0.49 -1.14;0.61 1.73;0.33 -2.17;-0.42

7.40 0.63;-0.75 -0.78;0.94 1.59;0.20 -1.98;-0.25 1.00;-0.40 -1.24;0.50 1.81;0.41 -2.25;-0.51

7.50 0.72;-0.67 -0.89;0.83 1.67;0.28 -2.06;-0.34 1.08;-0.32 -1.34;0.40 1.88;0.48 -2.33;-0.59

7.60 0.80;-0.59 -0.99;0.72 1.74;0.35 -2.14;-0.43 1.16;-0.24 -1.43;0.30 1.95;0.55 -2.41;-0.68

7.70 0.89;-0.50 -1.09;0.62 1.81;0.42 -2.22;-0.51 1.24;-0.17 -1.52;0.20 2.02;0.61 -2.49;-0.76

7.80 0.96;-0.42 -1.18;0.52 1.87;0.48 -2.30;-0.60 1.31;-0.09 -1.61;0.11 2.08;0.68 -2.56;-0.84

7.90 1.04;-0.35 -1.27;0.43 1.94;0.55 -2.37;-0.67 1.39;-0.02 -1.70;0.02 2.15;0.74 -2.63;-0.91

8.00 1.12;-0.27 -1.36;0.33 2.01;0.61 -2.44;-0.75 1.46;0.05 -1.78;-0.07 2.21;0.80 -2.70;-0.99

8.10 1.19;-0.20 -1.44;0.24 2.07;0.68 -2.51;-0.82 1.53;0.12 -1.86;-0.15 2.27;0.86 -2.76;-1.06

8.20 1.26;-0.13 -1.53;0.15 2.13;0.74 -2.58;-0.90 1.60;0.19 -1.94;-0.23 2.33;0.92 -2.83;-1.13

8.30 1.33;-0.06 -1.61;0.07 2.19;0.80 -2.64;-0.97 1.66;0.26 -2.01;-0.31 2.39;0.98 -2.89;-1.19

8.40 1.40;0.01 -1.69;-0.01 2.25;0.85 -2.71;-1.03 1.73;0.32 -2.09;-0.39 2.44;1.04 -2.95;-1.26

8.50 1.47;0.08 -1.76;-0.09 2.30;0.91 -2.77;-1.10 1.79;0.39 -2.16;-0.47 2.50;1.09 -3.01;-1.32

2. Seencontróque ladiferenciaΔPIOL conk(r1c/r2c),seajustabaaunaecuación

linealenfunciónder1c(vertabla8).

Capítulo4


80

Tabla8.Ecuacioneslineales(R2=0.99)deΔPIOLenrelaciónakenfunciónder1cenpasosde0.1

mmparalosmodelosdeojoteóricodeGullstrandydeLeGrand

Gullstrand LeGrand

nk=1.3315 nk=1.3375 nk=1.3304 nk=1.3375

r1c(mm) ΔPIOL(D)=ak+b ΔPIOL(D)=ak+b ΔPIOL(D)=ak+b ΔPIOL(D)=ak+b

7.00 ΔPIOL=-7.07k+8.03 ΔPIOL=-7.07k+6.94 ΔPIOL=-6.99k+8.40 ΔPIOL=-6.99k+7.12
















3. Se analizó la dependencia deΔPIOLcon variaciones deELP. Los distintos

valores de ELP que se utilizaron para el estudio son: el valor de ACD

anatómica (ACDa) la cual corresponde aunos valoresde3.05 y3.10mm

paralosmodelosdeojoteóricodeLeGrandyGullstrand,respectivamente,

además de un rango de variación entre 2.0 y 6.0 mm. Con todo esto se

observó que en términos generales este valor de ELP no influyó

clínicamente en el error cometido en el cálculo de la lente intraocular,

siendo el valormáximode variaciónΔPIOL encontrado correspondiente a

un valor de ELP= 6.0 mm, no superando en ningún caso 0.48 D en

comparaciónconelvalorobtenidodeACDaparacadamodelodeojo.

4. AlcompararlosvaloresdeΔPIOLconsiderandounrangodeRdesentre-1.0y

+1.0D,siendolosdemásparámetrosconstantes,seobservóquelaRdesno

Capítulo4


81

eraun factor influyenteen laobtencióndelerrordecálculode laPIOL,ya

que las diferencias máximas que se encontraron respecto a considerar

Rdes=0fueronde0.02D.

5. Utilizandoelvalordenkadjcalculadoapartirdelasecuaciones34y35para

laobtencióndelapotenciacornealqueratométricaycalculandoelvalorde

PIOLadj, el error máximo teórico de ΔPIOL que se obtuvo fue de ± 0.9 D

medido desde el vértice corneal, independientemente delmodelo de ojo

analizado. Si consideramos que 1.0 D de variación de PIOL induce una

variacióndeaproximadamentede0.9Dmedidodesdeelvérticecorneal,se

observóqueelerrorcometidoparaelcálculodePIOLqueseobtuvoconel

valordenkadj,noexcedióde±0.6Dmedidodesdeelplanodelalenteó±

0.5 D desde el vértice corneal para un rango de r2c de 5.8 y 6.7mm. Al

utilizarlavariacióndeELP,seobservóqueparavaloresdeELP>4.0mm,

el error en el cálculo de la PIOL no excedió de ± 0.5 D medido desde el

vérticecornealenningunodeloscasos.

6. Lavalidaciónpreliminarclínica,serealizó(talycomosehacomentadoenelapartado3.e)mediantelacomparativadediferentesfórmulasdecálculo

dePIOL,talescomoSRK/T(PIOLSRK/T),Haigis(PIOLHaigis),HofferQ(PIOLHofferQ)y

Holladay (PIOLHolladay) con la obtenida con nuestro algoritmo para una

población normal (PIOLadj), siendoRdes=SEpost y ELP el definido para cada

fórmula. Se observaron diferencias clínicamente relevantes y

estadísticamentesignificativas(tabla9).SiendolafórmulaPIOLHaigislaque

presentómenosdiferenciasalcompararlaconnuestraPIOLadj (0.39±0.33

SD) y la fórmulaPIOLHofferQ la quemostró lasmayores diferencias (1.92±

0.58 SD) llegando a alcanzar diferencias de hasta 3.07 D. En todas las

comparativasseobtuvounafuertecorrelacióndeladiferenciaencontrada

conelvalordePIOLadjcalculadaconnkadj.

Capítulo4


82

Tabla 9. Resumen comparativa de análisis de PIOL obtenida con diferentes fórmulascomercialesynuestroalgoritmo

SRK/T HAIGIS HOFFER-Q HOLLADAY

Diferenciademedias conPIOLcalculadaconnkadj(SD)

1.01(0.26) 0.39(0.33) 1.92(0.58) 1.04(0.77)

p-valor <0.01 <0.01 <0.01 <0.01

CoeficientedecorrelaciónconPIOLcalculadaconnkadj

0.997 0.996 0.993 0.977

Límites de acuerdo con PIOLcalculadaconnkadj

0.50a1.52 -0.27a1.04 0.78a3.07 -0.50a2.50

7. El análisis Bland-Altmanmuestra las diferencias clínicamente relevanteshalladas (fig. 15 A a D), las cuales fueron positivas en lamayoría de los

casos,porloqueelvalordePIOLobtenidomediantenuestroalgoritmofue

mayor que el encontrado con otras fórmulas estándar de cálculo dePIOL.

Además se observaron diferencias clínicamente significativas entre las

fórmulas de cálculo comerciales analizadas en este estudio. Se encontró

quelasdiferenciasentrePIOLadjyPIOLSRK/Tsecorrelacionabaconlapotencia

cornealgaussiana(𝑃!!"#$$)(r=-0.81,p<0.01),radioposteriordelacórnea

(r2c) (r = -0.81, p < 0.01), con la diferencia entre la potencia corneal

obtenida mediante índice queratométrico ajustado y la potencia

queratométrica(nk=1.3375)(r=-0.81,p<0.01), posiciónefectivade la

lente(ELP)(r=-0.46,p<0.01)yradioanteriorcorneal(r1c)(r=-0.81,p<

0.01).UnatendenciasimilarseobservóentrePIOLadjyPIOLHaigis,siendoestas

diferenciascorrelacionadasconlapotenciacornealgaussiana(𝑃!!"#$$)(r=

-0.75,p<0.01),radioposteriorcorneal(r2c)(r=0.54,p<0.01),diferencia

entre la potencia corneal obtenida mediante índice queratométrico

ajustadoy lapotenciaqueratométrica (nk=1.3375)(r=0.75,p<0.01)y

radioanteriordelacórnear1c(r=0.75,p<0.01).

Capítulo4


83

A

B

1,04D

-0,27D0,39D

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

5,0 10,0 15,0 20,0 25,0 30,0

DiferenciasP

IOLadj-P

IOLHaigis(D)

MediaPIOLadj-PIOLHaigis(D)

1,52D

0,50D

1,01D

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

5,0 10,0 15,0 20,0 25,0 30,0

DiferenciasP

IOLadj-P

IOLSRK/T(D)

MediaPIOLadj-PIOLSRK/T(D)

Capítulo4


84

C

D

Figura15.ComparativaB-AentrelaPIOLobtenidausandolaPkadjylaobtenidautilizandolasdistintasfórmulasdecálculo.(A)diferenciasentrePIOLadjyPIOLobtenidamediantelafórmulaSRK/T(PIOLSRK/T).(B)diferenciasentrePIOLadjyPIOLobtenidamediantelafórmulaHaigis(PIOLHaigis).(C)diferenciasentrePIOLadjyPIOLobtenidamediantelafórmulaHofferQ(PIOLHofferQ).(D)diferenciasentrePIOLadjyPIOLobtenidamediantelafórmula

Holladay(PIOLHolladay)

Con los resultados obtenidos, se observó que en una simulación teórica

considerandoun rangonormalde curvatura cornealperteneciente aunapoblación

2,50D

-0,50D

1,04D

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

5,0 10,0 15,0 20,0 25,0 30,0DiferenciasP

IOLadJ-P

IOLHolladay(D)

MediaPIOLadj-PIOLHolladay(D)

3,07D

0,78D

1,92D

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

5,0 10,0 15,0 20,0 25,0

DiferenciasP

IOLadj-P

IOLHofferQ(D)

MediaPIOLadj-PIOLHofferQ(D)

Capítulo4


85

sana, optimizando el valor denk para el cálculo de la potencia corneal, éste puede

conducir a errores clínicamente relevantes en el cálculo de la PIOL en cirugía de

cataratas(hastade3Dsink=1.3375).Sisobrestimamoselpodercornealconelusode

un valor único de nk, esta sobrestimación nos conducirá a una subestimación del

correspondiente valor queratométrico de la potencia de la lente intraocular y

viceversa. Se encontró una ecuación cuadrática dependiente del valor de r2c y una

lineal dependiente de k para la predicción del valor de ΔPIOL. Para minimizar los

errores cometidos en las estimacionesde laPIOL debido al error en el cálculode la

potencia cornealqueratométrica, sepropusounanueva fórmulapara la estimación

de la potencia de la lente intraocular usando óptica paraxial y aproximación

queratométricateniendoencuentaunnkvariable(nkadj)deacuerdoconelalgoritmo

desarrollado(53)yvalidadoclínicamente(143)pornuestrogrupodeinvestigaciónyque

denominamospotenciade la lente intraocularajustada(PIOLadj).En lassimulaciones

teóricas, la diferencia entre la PIOLadj y la𝑃!"#!"#$$ (ΔPIOL) nunca superó las 0.90 D

medidodesdeelvérticecorneal,independientementedelmodelodeojoutilizado,del

valorder1cydelaRdes.Estemargendeerrornoresultóserclínicamentesignificativo

en la mayoría de las posibles combinaciones r1c – r2c para ojos normales y sanos.

Además,seobservóquelavariacióndeELPteníaunainfluencia,aunquemínima,en

laΔPIOL.EspecíficamentesielvalordeELPerainferioralaprofundidaddelacámara

anterior anatómica (ACDa), las diferencias entre PIOLadj y𝑃!"#!"#$$ disminuyeron y

viceversa,siendoestasdiferenciasentodos loscasos inferiora0.50D locualnoes

clínicamentesignificativo.

En la prevalidación clínica se encontraron diferencias estadísticamente

significativas entre nuestra fórmula de cálculo y otras fórmulas comerciales, tales

comoHaigis,HofferQ,HolladayySRK/T.LamáximadiferenciarespectoalaPIOLadjse

obtuvo al compararla con la fórmula de Hoffer Q (PIOLHofferQ) (1.92 ± 0.58 SD) y la

menordiferenciaconlafórmuladeHaigis(PIOLHaigis)(0.39±0.33SD).Aunqueeneste

últimocasolos intervalosdeconfianzaresultabanclínicamentesignificativos[-0.27,

1.04]D.

Capítulo4


86

4.3.ResultadosdelostrabajosenrelaciónconelobjetivoC

Error inducido en la estimación de la potencia corneal y la posición

efectivaenlapotenciadeunalenteintraocularacomodativa.[PiñeroDP,Camps

VJ, RamónML, Mateo V, Pérez-Cambordi RJ. Positional accommodative intraocular

lens power error inducedby the estimation of the corneal power and the effective

lensposition.IndJOphthal2015May;63(5):438-44]

En este estudio se evaluó la predictibilidad de la PIOLadj y de las diferentes

fórmulas de cálculo comerciales de PIOL para el cálculo de la lente acomodativa

CrystalensHD (B&L), desarrollando una fórmula predictiva de cálculo de ELP para

minimizar los errores asociados a la estimación queratométrica de la potencia

corneal.

Para la obtención de la potencia de la lente intraocular (PIOLadj) se calculó

medianteelusodelaecuacióndeGaussparaópticaparaxial(132)[ec.36].Delosdos

algoritmos para el cálculo de nk propuestos recientemente por nuestro grupo de

investigación(53), se escogió para este estudio el correspondiente al modelo de

Gullstrand[ec.34],puestoqueparalaobtencióndelapotenciadelalenteintraocular

implantada,elclínicosebasóenelvalordePcproporcionadoporelPentacam,elcual

sebasaenelmodelodeojoteóricodeGullstrandpararealizarloscálculos.

nkadj=-0.0064286r1c+1.37688 [34]

Con el uso de este algoritmo se calculó el valor de la potencia corneal

queratométrica (Pkadj) [ec. 28], con el uso de nkadj y los valores de nha y nhv

correspondientesalmodelodeojodeGullstrand(1.336paraambosíndices).Parael

equivalenteesférico, sepensóqueel clínicoqueríadejar alpaciente conuna cierta

refracción residual, por lo cual se consideró el equivalente esférico postoperatorio

igual a la refracción deseada (SEpost= Rdes). Este valor de PIOLadj se comparó con la

PIOLReal implantada, siendo el valor de PIOLadj calculada mediante dos métodos

diferentesdecálculodeELP.EnprimerlugarsecalculóelvalordeELPmediantelas

directricesdecálculodelafórmulaSRK/T(PIOLadjSRK/T)puestoqueparalaobtención

de la lente implantada por parte del clínico, se basó en la obtenida mediante la

Capítulo4


87

fórmula SRK/T. En segundo lugar se calculó el valor de ELP mediante el uso del

algoritmoobtenidoporregresiónmúltiple(ELPadj).Talycomosehaexplicadoenel

apartadodemétodos,pararealizarestecálculo,enprimerlugarsecalculóelvalorde

ELPexactoparacadapacienteapartirdeigualarlaexpresióndelaPIOLadjalvalorde

la lente implantada (PIOLadj=PIOLReal). Con todos los valores obtenidos para cada

paciente se realizó un análisis de regresión múltiple teniendo en cuenta todas las

variables preoperatorias medidas. De todas las ecuaciones obtenidas se escogió

aquellaquepresentóausenciadecorrelaciónentreerroresmedianteeltestDurbin-

Watsonypresentóunamulticolinealidadconlatoleranciadecolinealidadyfactorde

inflación de la varianza (FIV), teniendo presente también, cual es la ecuación que

presentó mejores resultados al analizar la normalidad de los residuos no

estandarizados (homocesdasticidad) y distancias de Cook. A la ecuación que se

obtuvo se le denominóELPadj y se utilizó para calcular denuevo el valor dePIOLadj.

Este valor de potencia de lente intraocular se comparó con el valor obtenido por

diversasfórmulascomercialesdecálculo,comoHaigis,HofferQyHolladay,siendoel

valordeELPeldefinidoparacadafórmulaylaRdes=SEpost..

Sevaloraronuntotalde25ojosde14pacientesconunaedadmediade65.9

años (rango de 52 a 79 años) de los cuales 16 (64%) eran hombres. La muestra

estabacompuestapor13ojosizquierdos(52%).Latabla10muestralosparámetros

evaluados

Capítulo4


88

Tabla10.Medidasvisuales,refractivas,biométricasydatosdecálculodelaPIOL

Parámetros Media±SD RangoSEpre(D) 0.81±2.77 -5.50a5.38SEpost(D) -0.36±0.76 -3.13a1.14r1c(mm 7.80±0.26 7.35a8.25ACD(mm) 3.27±0.30 2.63a3.84AL(mm) 23.21±0.89 21.65a25.04ELPSRK/T(mm) 5.21±0.34 4.78a6.17ELPadj(mm) 4.18±0.27 3.70a4.83ELPHaigis(mm) 5.41±0.18 5.12a5.82ELPHofferQ(mm) 5.25±0.23 4.88a5.83ELPHolladay(mm) 4.95±0.30 4.31a5.52nkadj 1.327±0.02 1.324a1.330Pk(1.3375)(D) 43.29±1.44 40.91a45.89PcHaigis(1.3315)(D) 42.52±1.42 40.18a45.07Pkadj(D) 41.91±1.61 39.25a44.82PIOLReal(D) 22.53±2.70 16.00a28.00PIOLadjSRK/T(D) 24.51±2.91 17.69a32.09PIOLadj(D) 22.53±2.79 15.86a29.07PIOLHofferQ(D) 22.94±3.14 15.43a30.89PIOLHolladay(D) 23.03±2.98 16.00a30.80PIOLHaigis(D) 24.33±3.36 16.53a33.25Donde:SEpre=equivalenteesféricopreoperatorio; SEpost= equivalenteesféricopostoperatorio; r1c= radiocara anterior de la córnea; ACD=profundidad de la cámara anterior; AL= longitud axial; ELPSRK/T=posiciónefectivade la lentecalculadamediante la fórmulaSRK/T;ELPadj=posiciónefectivade la lenteajustada; ELPHaigis= posición efectiva de la lente calculada mediante la fórmula de Haigis; ELPHofferQ=posiciónefectivadelalentecalculadamediantelafórmuladeHofferQ;ELPHolladay=posiciónefectivadelalente calculadamediante la fórmula de Holladay; nkadj= índice de refracción queratométrico ajustado;Pk(1.3375)= potencia corneal queratométrica calculada con el índice queratométrico 1.3375; PcHaigis=potenciacornealcalculadaparalafórmuladeHaigisconunvalordeíndicequeratométrico1.3315;Pkadj=potencia queratométrica calculada con el índice queratométrico ajustado; PIOLReal= potencia lenteintraocularimplantada;PIOLadjSRK/T=potencialenteintraocularcalculadaparalafórmulaSRK/T;PIOLadj=potencia lente intraocularajustada;PIOLHofferQ=potencia lente intraocularcalculadapara la fórmuladeHofferQ;PIOLHolladay=potencialenteintraocularcalculadaparalafórmuladeHolladay;PIOLHaigis=potencialenteintraocularcalculadaparalafórmuladeHaigis

Losprincipaleshallazgosyconsideracionessobrelosresultadosobtenidosseexponenacontinuación:

1. SeencontrarondiferenciasestadísticamentesignificativasentrePIOLadjSRK/T

y PIOLReal cuando se usó el valor de ELP calculado mediante la fórmula

Capítulo4


89

SRK/T(p<0.01,t-Student).Comoseobservaenlafigura16,seencontró

una fuerte correlación entre ambas medidas de potencia de lente

intraocular(r=0.960,P<.01)

Figura16.DiagramadedispersióndondesemuestralarelaciónentrelaPIOLadjSRK/TylaPIOLReal

2. EnelanálisisdeBand-Altman(fig.17)seobservóunasobrestimacióndel

valordePIOLSRK/TrespectoalvalordePIOLReal(r=0.960;P<0.01).Lamedia

delasdiferenciasentreambasmedidasfuede1.97D,conunoslímitesde

concordancia inferior de 0.36 D y superior de 3.39 D, los cuales fueron

clínicamenterelevantes.

15

20

25

30

35

15 20 25 30 35

P IOLadjSRK/T(D)

PIOLReal(D)

Capítulo4


90

Figura17.DiagramadepuntosdeBlandAltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/TylaPIOLRealfrentealamediadelasdiferencias

3. Medianteunanálisisderegresiónmúltiple,seobtuvoqueelvalordeELPadj

estabacorrelacionadoconlalongitudaxial(AL),profundidaddelacámara

anterior (ACD), lapotenciaqueratométrica ajustada (Pkadj) y la edad (p<

0.001):

𝐸𝐿𝑃!"# = −9.549+ 0.422 ∙ 𝐴𝐿 + 0.164 ∙ 𝑃!"#$ − 1.612 ∙ 𝐴𝐶𝐷 − 0.014 ∙ 𝐸𝑑𝑎𝑑

[44]

Lahomocedasticidaddelmodeloseconfirmóal realizarelanálisisde los

residuos no estandarizados (p=0.20) y la ausencia de valores atípicos

(distanciadeCook:0.049±0.081).Conestemodelo,el72%delosresiduos

tuvieron un valor ≤ 0.30 y el 80% se encontraron por debajo de 0.40.

También se confirmó la pobre correlación existente entre residuos (test

Durbin-Watson: 2.165) y la falta demulticolinealidad (tolerancia0.486 a

0.992,FIV2.056a1.008).

4. Cuando se comparó este valor de ELPadj con el valor de ELP obtenido

mediante la fórmula SRK/T (ELPSRK/T), se observaron diferencias

estadísticamente significativas entre ambas medidas (p < 0.01, test T-

3,39D

0,36D

1,97D

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

10,0 15,0 20,0 25,0 30,0 35,0

DiferenciasP

IOLadjSRK/T-P IOLReal(D)

MediaPIOLadjSRK/T-PIOLReal(D)

Capítulo4


91

Student), siendoELPadj el demenor valor (4.18± 0.27mm, rango3.70 a

4.83)(vertabla10).

5. Al comparar la PIOLReal con PIOLadj cuando se utilizó el valor de ELPadj

calculada mediante la ecuación 39, no se observaron diferencias

estadísticamentesignificativas(p=0.10,t-Student).Seencontróunafuerte

correlación estadísticamente significativa entre ambas medidas de PIOL

(r=0.97,p<0.01)(figura18).

Figura18.DiagramadedispersióndondesemuestralarelaciónentrelaPIOLadjyla

PIOLReal

6. De acuerdo con en el análisis de Band Altman (fig.19), la media de las

diferencias entre ambas medidas fue de 0.002 D, con unos límites de

concordancia inferior de -1.225 D y superior de 1.229 D, valores

clínicamentesignificativos.

15

20

25

30

35

15 20 25 30 35

P IOLadj(D)

PIOLReal(D)

Capítulo4


92

1,229D

-1,225D

0,002D

-4

-2

0

2

4

10 15 20 25 30 35

DiferenciaPIOLadj-P

IOLReal(D)

MediaPIOLadj-PIOLReal(D)

Figura19.DiagramadepuntosBlandAltmancorrespondientealasdiferenciasentrelaPIOLadjylaPIOLRealfrentealamediadelasdiferencias

7. Se comparó el valor de PIOLadj con las distintas fórmulas de cálculo másusadasenlaactualidad,comosonlafórmuladeHaigis(PIOLHaigis),HofferQ

(PIOLHofferQ) y Holladay (PIOLHolladay). Se encontraron diferencias

estadísticamente significativas con cada una de las fórmulas (p<0.01, t-

Student).Seencontróunafuertecorrelaciónestadísticamentesignificativa

entrePIOLHaigisyPIOLadj (r=0.983, p<0.01), entrePIOLHofferQyPIOLadj (r=0.992,

p<0.01) y entre PIOLHolladay y PIOLadj (r=0.987, p<0.01). En la tabla 11 se

muestran los análisis Bland-Altman correspondientes, donde se observa

que todas las diferencias son clínicamente significativas y que la mayor

diferenciasedioentrePIOLHaigisyPIOLadj.

Tabla11.AnálisisBland-AltmanentrePIOLadjyPIOLobtenidoconfórmulascomerciales

ΔPIOL±SD(D) LoA(D) p-valor

Haigis 1.77±0.79 3.33a0.21 <0.01

HofferQ 0.40±0.52 1.40a-0.64 <0.01

HolladayI -0.47±0.50 1.44a-0.50 <0.01

Capítulo4


93

8. Comosepuedeapreciarenlatabla10,elvalordeELPadj(4.18±0.27mm,

rango3.70a4.83)essignificativamentemenorqueelvalordeELPquese

obtuvo con cualquiera de las fórmulas comerciales usadas (p<0.01, t-

Student).

Enelpresenteestudio,setratódeminimizarelerrordecálculodelapotencia

de la lente intraocular a implantar para el modelo específico de lente intraocular

acomodativaCrystalensHD(Bausch&Lomb). Para ello, por una parte de utilizó el

algoritmo de cálculo del índice queratométrico ajustado (nkadj) para minimizar el

errorenelcálculodelapotenciacornealqueratométricayporotraparteseoptimizó

elcálculode laELPen funcióndevalorespreoperatorioscomolaAL,Pkadj,ACDy la

edad.

En este estudio los pacientes presentaban en algunos casos un error

postoperatorio miópico o hipermetrópico inesperado. Este error postoperatorio

(SEpost)presentóunrangode-3.13a+1.14D,confirmándoseunatendenciamiópica

significativa, lo cual inducía a pensar en la necesidad de la realización de algunas

optimizaciones en el cálculo de la potencia de la lente intraocular acomodativa a

implantar.

Lasposibles fuentesdeerrorparaelcálculode lapotenciadeestetipode lente

intraocularacomodativa,podíanserdebidoalasumirerroresenlapotenciacorneal,

enlaobtencióndelalongitudaxialoenlainexactitudenlaestimacióndelaposición

efectivadelalenteparaestalenteintraocularespecífica.Enprimerlugar,elimpacto

del error queratométrico se analizó mediante el cálculo de la potencia corneal

mediante el valor denkadj paraminimizar el error cometido en la estimación de la

potencia de la córnea(53,132,144). Sin embargo, aún seguían apreciándose diferencias

estadísticamente significativas y clínicamente relevantes entre el cálculo de la

potencia de la lente intraocular ajustada y la real (obtenida de acuerdo con los

resultados de la fórmula SRK/T). Puesto que la exactitud del IOLMaster® para el

cálculodela longitudaxial fueampliamentedemostrada(143),seconsideróelcálculo

deELP comounfactorcríticopara lapresenciadeunaprevisibilidadrelativamente

limitadade la lente intraocularacomodativaevaluada.Porestarazón,sedesarrolló

unaexpresiónmatemáticaparalaestimaciónyoptimizacióndeELPdeacuerdocon

Capítulo4


94

parámetrospreoperatorios (ELPadj),obtenidamedianteregresión linear.Elvalorde

PIOLadjobtenidoconelusodeesteELPadjsecomparóconlosobtenidosmedianteotros

algoritmosdeprediccióndeELP(17,20,21,145,146). Revelando este análisis queELPadj es

significativamente menor comparado con los valores obtenidos con las fórmulas

comerciales.

Respecto a la intercambiabilidad entre PIOLReal y PIOLadj, no se encontraron

diferenciassignificativasentre lasmedias (media0.002±0.67D),aunquepresentó

unos límites de acuerdo clínicamente relevantes (LoA 1.229 a -1.225D), lo cual es

clínicamente significativo, siendoestevalor limitado si tenemosen cuentaqueeste

tipode lente intraocularestádisponibleenpasosdemediadioptría. Estoconfirma

queaunsiendolaposicióndelalenteintraocularmásanterior,éstapuedecontribuir

a errores de ELP en el cálculo de la lente intraocular acomodativa, así como la

inestabilidad posicional que puede aparecer en este tipo de lente cuando se sitúa

dentro de la bolsa capsular. Estos resultados concuerdan con los obtenidos por

algunosestudiosquerevelanlapresenciadeposicionesinesperadasconestetipode

lenteintraocularacomodativa(147–149).Posteriormente,sepasóacomprobarsiexistía

intercambiabilidad entre PIOLadj y las distintas fórmulas de cálculo comerciales. Se

obtuvierondiferenciasestadísticamentesignificativasentrelosparesPIOLadj-PIOLHaigis,

PIOLadj-PIOLHofferQyPIOLadj-PIOLHolladay(p<0.01,testT-Student),siendoestasdiferencias

máximasparalacombinaciónPIOLadjyPIOLHaigis(rangoacuerdo1.77±0.79D,LoA3.33

a-0.21D).Enlatabla10semuestranlosvaloresBlandAltmancorrespondientes.Con

estosdatosseobservóquelaparejaPIOLReal-PIOLadjeralaqueproporcionóelmenor

intervalorespectoalasdemásfórmulasdecálculoanalizadas,indicandoqueseríala

fórmulamásadecuadaparatratardereproducirlosvaloresdelaPIOLReal.

Se obtuvo una relación entreELP y algunos factores preoperativos como laAL,

Pkadj,ACDy laedad.Enojoslargos,elvalormáselevadosecorrespondióalvalorde

ELPadj, lo cual concuerda con los resultados anteriormente obtenidos por otros

autores como Olsen et al.(25), quienes observaron una tendencia en ojos cortos a

presentarunacámaraanteriormenorqueenojoslargos.Comoyareportaronotros

autoresdemanerasimilarenotromodelodelenteintraocularacomodativa,laedad

también resultó ser un factor influyente(150). Uno de los principales factores que

Capítulo4


95

pueden explicar estos hallazgos es la posición más anterior que adopta la lente

acomodativaCrystalensHDdebidoasushápticosflexibles.

Elpresenteestudiopresentaunaseriede limitaciones,comoel tamañolimitado

de la muestra o el seguimiento de corta duración realizado. Otra limitación es la

determinacióndelarefracciónconestalenteacomodativa.LalenteCrystalensHDes

una lente con una óptica central bi-asférica modificada, generando una ligera

aberración esférica negativa la cual contribuye al aumento de la profundidad de

foco(151,152). Se han reportado pequeños niveles de aberración esférica primaria en

este tipo de lentes intraoculares acomodativas(152) y de signo positivo en algunos

casos(151). Errores refractivos residualesdemasde -0.50Dno sepuedenatribuir a

estosniveleslimitadosdeaberraciónesférica,ademásdeencontrarcasosconerrores

refractivos residuales hipermetrópicos clínicamente significativos. Otro factor que

puedehaber contribuido a la variabilidad en la estimaciónde la refracción sería la

presenciadeunalenteintraocularmalposicionada,yaseainclinadaodescentrada,la

cual conduciría a una degradación de la calidad visual y por tanto limitaría la

exactitud de refracción manifiesta. Algunos autores han reportado casos de lentes

malposicionadasobasculantes(153).Ennuestroestudionoseobservóenelexamen

conlámparadehendiduraningunadesalineaciónniinclinación.

4.4.ResultadosdelostrabajosenrelaciónconelobjetivoD


efectiva en la potencia de una lente intraocular multifocal rotacional

asimétrica. [Piñero DP, Camps VJ, RamónML, Mateo V, Pérez-Cambordí RJ. Error

inducedbytheestimationofthecornealpowerandtheeffectivelenspositionwitha

rotationallyasymmetricrefractivemultifocalintraocularlens.IntJOphthalmol2015

Jun18;8(3):501-7]

En este estudio seha evaluado lapredictibilidadde lasdiferencias entre las

fórmulas de cálculo de la potencia de la lente intraocular multifocal refractiva de

rotaciónasimétricaMplusLS-312(OculentisGmbH,Germany)y laPIOLadj, así comoel

Capítulo4


96

impactodelerrorcometidoenlaestimaciónqueratométricadelapotenciacornealy

lafórmulapredictivadecálculodelaELP.

Paralaobtencióndelapotenciadelalenteintraocular(PIOL),aligualquecon

el objetivo C, se calculó mediante el uso de la ecuación de Gauss para óptica

paraxial(132)[ec.36].Escogiendoparaelcálculodenkelcorrespondientealmodelode

Gullstrand[ec.34],propuestopornuestrogrupodeinvestigación(53),porlasrazones

quesehanexpuestoanteriormente.


queratométricaajustada(Pkadj),conelusodenkadjparalaestimacióndelaPkadjylos

valores de nha y nhv correspondientes al modelo de ojo de Gullstrand (1.336 para

ambos índices). Para el equivalente esférico, se consideró igual a la refracción

deseada (SEpost= Rdes). Este valor de PIOLadj se comparó con la PIOLReal implantada,

siendo el valor de PIOLadj calculada mediante los dos métodos de cálculo de ELP,

detalladosanteriormente.Estevalordepotenciadelenteintraocularsecomparócon

elvalorobtenidopordiversasfórmulascomercialesdecálculo,comoHaigis,HofferQ

yHolladay,siendoelvalordeELPeldefinidoparacadafórmula.

Sevaloraronuntotalde25ojosde13pacientesconunaedadmediade65.6

años(rangode50a83años)deloscuales7(53.8%)eranmujeres.Lamuestraestaba

compuestapor13ojosizquierdos(52%).Latabla12muestralosparámetrosdelos

ojosevaluados.

Capítulo4


97

Tabla11.Medidasvisuales,refractivas,biométricasydatosdecálculodelaPIOL

Parámetros Media±SD Rango SEpre(D) -1.27±2.87 -7.50a3.00 SEpost(D) -0.11±0.56 -1.83a0.76 r1c(mm) 7.61±0.25 7.19a8.01 ACD(mm) 3.31±0.28 2.61a3.79 AL(mm) 23.52±1.04 22.02a27.36 ELPSRK/T(mm) 5.12±0.45 4.60a6.83 ELPadj(mm) 4.31±0.50 3.39a5.34 ELPHaigis(mm) 5.01±0.16 4.77a5.46 ELPHofferQ(mm) 5.00±0.27 4.63a6.01 ELPHolladay(mm) 4.59±0.27 3.89a5.07 nkadj 1.328±0.02 1.325a1.331 Pk(1.3375)(D) 44.37±1.44 42.14a46.95 PcHaigis(D) 43.57±1.41 41.39a46.11 Pkadj(D) 43.11±1.61 40.62a45.99 PIOLReal(D) 19.78±2.32 12.50a23.50 PIOLadjSRK/T(D) 21.18±2.74 12.51a25.46 PIOLadj(D) 19.71±2.55 11.02a23.53 PIOLHaigis(D) 20.40±3.15 10.16a24.99 PIOLHofferQ(D) 19.30±3.04 9.50a23.90 PIOLHolladay(D) 19.57±2.99 9.40a23.90 Donde:SEpre=equivalenteesféricopreoperatorio; SEpost= equivalenteesféricopostoperatorio; r1c= radiocara anterior de la córnea; ACD=profundidad de la cámara anterior; AL= longitud axial; ELPSRK/T=posiciónefectivade la lentecalculadamediante la fórmulaSRK/T;ELPadj=posiciónefectivade la lenteajustada; ELPHaigis= posición efectiva de la lente calculada mediante la formula de Haigis; ELPHofferQ=posiciónefectivadelalentecalculadaconlafórmuladeHofferQ;ELPHolladay=posiciónefectivadelalentecalculada con la fórmula de Holladay; nkadj= índice de refracción queratométrico ajustado; Pk(1.3375)=potenciacornealqueratométricacalculadaconelíndicequeratométrico1.3375;PcHaigis=potenciacornealcalculadapara la fórmuladeHaigis cuando seutilizaunvalorde índicequeratométrico1.3315;Pkadj=potencia queratométrica calculada con el índice queratométrico ajustado; PIOLReal= potencia lenteintraocular implantada;PIOLadjSRK/T=potencia lente intraocularcalculadacon la fórmulaSRK/T;PIOLadj=potencia lente intraocular ajustada; PIOLHofferQ= potencia lente intraocular calculada con la fórmula deHofferQ;PIOLHolladay=potencialenteintraocularcalculadaconlafórmuladeHolladay;PIOLHaigis=potencialenteintraocularcalculadaconlafórmuladeHaigis



1. Se encontraron diferencias estadísticamente significativas entre PIOLadjSRK/T y

PIOLRealcuandoseusóelvalordeELPcalculadomediantelafórmulaSRK/T(p<

0.01,Wilcoxontest).Comoseobservaenlafigura20,seencontróunafuerte

Capítulo4


98

correlaciónentreambasmedidasdepotenciadelenteintraocular(r=0.860,P

<.01)

Figura20.Diagramadedispersióndondesemuestralarelaciónentrela

PIOLadjSRK/TylaPIOLReal

2. EnelanálisisdeBand-Altman(fig.21)seobservóunatendenciaasobrestimar

elvalordePIOLSRK/TrespectoalvalordePIOLReal(r=0.960;P<0.01).Lamedia

de las diferencias entre ambas medidas fue de 1.41 D, con unos límites de

concordancia inferior de -0.48 D y superior de 3.29 D, los cuales son

clínicamenterelevantes.

5

10

15

20

25

5 10 15 20 25

P IOLadjSRK/T(D)

PIOLReal(D)

Capítulo4


99

Figura21.DiagramadepuntosBlandAltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/TylaPIOLRealfrentealamediadelasdiferencias

3. Mediante un análisis de regresiónmúltiple, se obtuvoque el valor deELPadj

estaba correlacionado con la longitud axial (AL), profundidad de la cámara

anterior(ACD),ypotenciaqueratométricaajustada(Pkadj)(p<0.01):

𝐸𝐿𝑃!"# = −17.333+ 0.612 ∙ 𝐴𝐶𝐷 + 0.360 ∙ 𝐴𝐿 + 0.268 ∙ 𝑃!"#$ [45]

La homocedasticidad del modelo se confirmó al realizar el análisis de los


(distancia deCook: 0.155±0.528). Con estemodelo, el 56%de los residuos

tuvieron un valor de ≤ 0.20 y el 76% se encontraron por debajo de 0.50.

También se confirmó la pobre correlación existente entre residuos (test

Durbin-Watson: 1.629) y la falta de multicolinealidad (tolerancia 0.805 a

0.560,FIV1.785a1.243).

4. Seencontrarondiferenciasestadísticamentesignificativasalcompararelvalor

de ELPadj con el valor de ELP obtenido con cualquiera de las fórmulas

comercialesanalizadas(p<0.01,Wilcoxontest).Comoseapreciaenlatabla12,

el valormínimodeELPcorrespondeaELPadj (4.31± 0.50mm, rango3.39 a

5.34).

3,29D

-0,48D

1,41D

-5

-3

-1

1

3

5

10 15 20 25

DiferenciasP

IOLadjSRK/T-P IOLReal(D)


Capítulo4


100

5. Al comparar laPIOLadjcuandoseutilizóel valor calculadodeELPadj, obtenida

mediante la ec. 40, con el valor de PIOLReal no se encontraron diferencias

estadísticamente significativas (p=0.65, test t-Student). Además se encontró

una fuerte correlación estadísticamente significativa entre ambas medidas

(r=0.95,p<0.01)(figura22).

Figura22.RelaciónentrelaPIOLadjylaPIOLReal

6. En el análisis de Bland Altman (fig.23) se observó que la media de las

diferencias entre ambas medidas fue de -0.07 D, con unos límites de

concordancia inferior de -1.61 D y superior de 1.47 D, los cuales son

clínicamentesignificativos.

5

10

15

20

25

5 9 13 17 21 25

P IOLadj(D)

PIOLReal(D)

Capítulo4


101

Figura23.DiagramadepuntosBlandAltmancorrespondientealasdiferencias

entrelaPIOLadjylaPIOLRealfrentealamediadelasdiferencias

7. Posteriormente se comprobaron las diferencias entre PIOLadj y las distintas

fórmulas de cálculo comerciales, obteniéndose diferencias estadísticamente

significativas entre PIOLadj y PIOLHaigis y entre PIOLadj y PIOLHofferQ (p<0.01, test

Wilcoxon),peronoentrePIOLadjyPIOLHolladay(p=0.20,testWilcoxon).Enlatabla

13semuestranlosvaloresBlandAltmancorrespondientes.

Tabla12.AnálisisBland-AltmanentrePIOLadjyPIOLobtenidaconfórmulascomerciales

ΔPIOL± SD(D) LoA(D) p-valor

Haigis 0.68±0.72 2.09a-0.73 <0.01

HofferQ -0.43±0.75 1.05a-1.90 <0.01

Holladay1 -0.13±0.67 1.01a-1.28 0.20

8. Como se aprecia en la figura 24 se obtuvo una fuerte correlación

estadísticamentesignificativaentrePIOLadjyPIOLHolladay(r=0.96,p<0.01).

1,47D

-1,61D

-0,07D

-5

-3

-1

1

3

5

10 15 20 25

DiferenciasP

IOLadj-P

IOLReal(D)


Capítulo4


102

Figura24.RelaciónentrelaPIOLHolladayylaPIOLadj

9. En el análisis de Band-Altman (fig.25) se observó que la media de las

diferencias entre la potencia de la lente intraocular ajustada (PIOLadj) y la

obtenidamediantelafórmuladeHolladay(PIOLHolladay)fuede-0.13D,conunos

límitesdeconcordanciainferiorde-1.28Dysuperiorde1.01D.

Figura25.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLHolladayylaPIOLadjfrentealamediadelasdiferencias

5791113151719212325

5 7 9 11 13 15 17 19 21 23 25

P IOLHolladay(D)

PIOLadj(D)

1,01D

-1,28D

-0,13D

-5

-3

-1

1

3

5

10 15 20 25

DiferenciasP

IOLHolladay-P

IOLadj(D)

MediaPIOLHolladay-PIOLadj(D)

Capítulo4


103

10. Al comprobar la intercambiabilidad entre nuestra PIOLadj y PIOLHolladay , se

decidió comprobar, la posible intercambiabilidad entrePIOLRealy las distintas

fórmulas de cálculo comerciales. En este caso, se obtuvieron diferencias

estadísticamentesignificativasentrePIOLRealyPIOLHaigisyentrePIOLRealyPIOLHofferQ

(p<0.05 test Wilcoxon), pero no entre PIOLReal y PIOLHolladay (p=0.29, test

Wilcoxon)(vertabla14).

Tabla13.AnálisisBland-AltmanentrePIOLRealyPIOLobtenidaconfórmulascomerciales

ΔPIOL± SD(D) LoA(D) p-valor

Haigis 0.62±1.15 2.88a-1.64 0.01

HofferQ -0.43±1.13 1.73a-2.69 0.03

Holladay1 -0.21±1.10 1.96a-2.37 0.29

11. En el análisis de Band-Altman (fig.26) al comparar PIOLReal y PIOLHolladay se

observaquelamediadelasdiferenciasenestecasofuede-0.21D,conunos

límitesdeconcordanciainferiorde-2.37Dysuperiorde1.96D,siendoestos

límitessuperioresalosobtenidosentrePIOLRealyPIOLHolladay.

Figura26.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLHolladayylaPIOLRealfrentealamediadelasdiferencias

1,96D

-2,37D

-0,21D

-5

-3

-1

1

3

5

10 12 14 16 18 20 22 24 26 28DiferenciaPIOLHolladay-P

IOLReal(D)

MediaPIOLHolladay-PIOLReal(D)

Capítulo4


104

Ennuestroestudio,setratódeminimizarelerrordecálculodelapotenciade

la lente intraocular a implantar para el modelo específico de lente intraocular

multifocalderotaciónasimétricaMplusLS-312(OculentisGmbH,Germany).Paraello,

por unaparte deutilizó el algoritmode cálculo del índice queratométrico ajustado

(nkadj)paraminimizarelerrorenelcálculode lapotenciacornealqueratométricay

porotraparteseoptimizóelcálculode laELPen funciónde lapotenciade la lente

intraocular.

A partir de este estudio, se observó en los pacientes una significantiva

variabilidadenelvalordelequivalenteesféricopostoperatorio(-0.11±0.56D,rango

-1.83 a 0.76D), con una ligera tendenciamiópica tal y como ya indicaban algunos

estudiospreviosdelmismotipodelenteintraocularmultifocal(84,85,110).Estoconfirmó

la necesidad de optimizar un algoritmo para el cálculo de la potencia de la lente

intraocular con el fin de afinar los resultados refractivos y visuales de este tipode

lenteintraocularmultifocalpremium.Lalimitaciónrelativaenlaprevisibilidaddela

correcciónrefractivaenalgunoscasosimplantadosconla lenteMplusLS-312puede

ser atribuible al sesgo asociado del uso de la potencia corneal queratométrica, los

erroresenladeterminacióndelalongitudaxialoenlainexactituddelaestimaciónde

laELP.Lapotenciacornealqueratométricafueanalizadaycalculadaconelusodeun

índicequeratométricoajustadoconelfindeminimizarelerrorenlaestimacióndela

potenciacorneal(Pkadj)(53,132).EstaPkadj seutilizópara laobtenciónde laestimación

de la potencia lente intraocular considerando la longitud axial y la ELP calculada

segúnlasdirectricesdelafórmulaSRK/T(PIOLadjSRK/T)(21).Alanalizarlosresultadosse

encontraron diferencias estadísticamente significativas y clínicamente relevantes

entreestamedidadepotenciadelenteintraocularylarealdelalenteimplantada.La

ELPesunafactorcríticoporlapresenciadela limitadapredictibilidadenelcálculo

deestetipodelenteintraocular.ElcálculodelvalordeELPoptimizada,conseguido

mediante regresión lineal, sedenominó comoposición efectivade la lente ajustada

(ELPadj). Se obtuvo que este valor de ELP estaba relacionado con algunos factores

anatómicos,comolaAL,PkadjylaACD.AlcompararlaintercambiabilidadentrePIOLadj

y PIOLReal, no se encontraron diferencias entre las medias (p<0.05) sin embargo el

Capítulo4


105

intervalodeconfianzasiresultóserclínicamentesignificativo(rangoacuerdo-0.07D,

conunosLoAinferiorysuperior-1.61y1.47D,respectivamente).

El valor deELPadj se comparó con otros obtenidosmediante otras fórmulas de

cálculo de ELP(21,146,154). Se encontró un valor significativamente menor de ELPadj

comparadoconlosvaloresestimadosdelasfórmulasdeHaigis,HofferQyHolladay

(ELPHaigis,ELPHofferQyELPHolladay, respectivamente)(146,154).Ladiferenciamáspequeña

correspondióa laencontradaentreELPadjyELPHolladay,estopuedeserlarazóndela

ausenciadediferenciasestadísticamentesignificativasentrePIOLHolladayyPIOLadj(rango

de acuerdo 0.13± 0.67D, LoA -1.28 a 1.01D). Aún sin la presencia de diferencias

significativasentreambasmedidas,seobtuvounintervalodeconfianzaclínicamente

relevante.Porelcontrario,seencontrarondiferenciasestadísticamentesignificativas

y clínicamente relevantes al comparar nuestro valor calculado de lente intraocular

(PIOLadj)conlasfórmulasdeHaigisyHofferQ(PIOLHaigisyPIOLHofferQ,respectivamente).

DadalafaltadediferenciaentrelasmediasdelosparesPIOLReal-PIOLadjyPIOLHolladay-

PIOLadj, se analizó la intercambiabilidad entre PIOLReal y PIOLHolladay, sin apreciarse

diferencias significativas entre ambas medidas aunque el intervalo de confianza

resultóserclínicamentesignificativo(rangodeacuerdo-0.13D,LoA1.96a-2.37D).

Con estos datos se observó que la parejaPIOLReal -PIOLadj era la que proporcionó el

menorintervalorespectoalasdemásfórmulasdecálculoanalizadas, indicandoque

seríalafórmulamásadecuadaparatratardereproducirlosvaloresdelaPIOLReal.

Elpresenteestudiopresentaunaseriede limitaciones,comoel tamañolimitado

de la muestra o el seguimiento de corta duración realizado. Otra limitación es la

determinacióndelarefracciónconestalentemultifocal.Ciertasdificultadeshansido

descritasenlaobtencióndelarefraccióndespuésdelaimplantacióndelosdiferentes

modelosdelenteintraocular,conunatendenciaclaraalasobrestimaciónesféricacon

signo positivo(155). La refracción manifiesta se obtuvo mediante el mismo

procedimiento descrito para la obtención de la refracción en lentes intraoculares

multifocales(156) y sin el uso del autorrefractómetro como base, dado que se ha

demostradoel falloqueapareceenojos implantadoscon la lente intraocularMplus

LS-312(157).

Capítulo4


106

4.5.ResultadosdelostrabajosenrelaciónconelobjetivoE


efectiva en lapotenciadeuna lente intraocular asférica. [PiñeroDP,CampsVJ,

Ramon ML, Mateo V, Soto-Negro R. Preliminary evaluation of an algorithm to

minimizethepowererrorselectionofanasphericintraocularlensbyoptimizingthe

estimationofthecornealpowerandtheeffectivelensposition.IntEyeSci2016Jun;

16(6):1001-8]

Enesteestudioseevaluó lapredictibilidaddediferentes fórmulasdecálculo

delapotenciadelalenteintraocularasféricaLentisL-313ydelaPIOLadjdesarrollando

unafórmulapredictivadecálculodelaELP.

El cálculode lapotenciade la lente intraocular (PIOL) secalculóde lamisma

manera que en los artículos anteriores, escogiendo para el cálculo de nk el

correspondientealmodelodeGullstrand,elmotivodeestaelecciónhasidodetallado

anteriormente.


queratométricaajustada(Pkadj),conelusodenkadjparalaestimacióndelaPkadjylos

valores de nha y nhv correspondientes al modelo de ojo de Gullstrand (1.336 para

ambos índices). Se consideró el equivalente esférico igual a la refracción deseada

(SEpost=Rdes).SecomparóelvalordePIOLadjconlaPIOLReal implantada,siendoelvalor

de PIOLadj calculada mediante los dos métodos de cálculo de ELP detallados

anteriormente. Este valor depotencia de lente intraocular se comparó con el valor

obtenido por diversas fórmulas comerciales de cálculo, como Haigis, Hoffer Q y

Holladay,siendoelvalordeELPeldefinidoparacadafórmula.

Enprincipioseoptóporhacerunestudiocontodoslospacientessometidosa

estudio.Dadolosmalosresultadosobtenidosydebidoalbeneficiomáslimitadoque

presentanlaslentesintraocularesasféricasenojosmáslargos(158)seoptópordividir

a lamuestraanalizadaen funciónde lapotenciade la lente intraocular implantada,

conelfindeoptimizarelvalordeELPmásadecuadoparacadapaciente.

Capítulo4


107

Lamuestrasedividióportantoendosgruposdeacuerdoconlapotenciadela

lenteintraocularimplantada.EnelgrupoA(PIOL≥23.0D),sevaloraronuntotalde12

ojosde8pacientesconunaedadmediade68.2años(rangode56.0a80.0años)de

loscuales11(91.7%)erandehombres.EnelgrupoB(PIOL<23.0D),sevaloraronun

totalde53ojosde35pacientesconunaedadmediade72.2años(rangode57.0a

92.0 años) de los cuales 29 (54.7%) eran de mujeres. La tabla 15 muestra los

parámetrosdelosojosevaluados.

Tabla14.Medidasvisuales,refractivas,biométricasydatosdecálculodelaPIOL Parámetro PIOLReal>23.0D PIOLReal<23.0D

Media±SD Rango Media±SD Rango SEpre(D) 1.04±1.64 -2.38a2.75 -0.84±3.05 -12.38a3.38 SEpost(D) -0.02±0.40 -0.75a0.75 -0.25±0.44 -1.38a0.75 r1c(mm) 7.54±0.24 7.13a7.86 7.61±0.23 7.14a8.21 ACD(mm) 2.95±0.33 2.41a3.35 3.32±0.34 2.48a4.15 AL(mm) 22.33±0.55 21.30a23.09 23.70±1.13 22.20a28.33 ELPadjSRK/T(mm) 4.60±0.13 4.37a4.86 5.17±0.78 4.65a9.24 ELPadj(mm) 4.44±0.31 3.93a5.01 4.61±0.53 3.82a6.24 ELPHaigis(mm) 4.75±0.14 4.54a4.90 5.04±0.21 4.66a5.65 ELPHofferQ(mm) 4.68±0.08 4.59a4.88 5.06±0.33 4.74a6.42 ELPHolladay(mm) 3.77±0.42 3.08a4.29 4.24±0.43 3.17a5.31 nkadj 1.328±0.002 1.326a1.331 1.328±0.002 1.324a1.331 Pk(1.3375)(D) 44.79±1.44 42.92a47.34 44.37±1.35 41.09a47.28 PcHaigis(D) 43.99±1.41 42.16a46.50 43.58±1.33 40.35a46.43 Pkadj(D) 43.58±1.61 41.50a46.44 43.12±1.51 39.45a46.36 PIOLReal(D) 23.75±0.69 23.00a25.00 19.72±3.10 7.50a22.50 PIOLadjSRK/T(D) 24.18±0.98 21.85a25.87 20.69±3.00 9.81a24.31 PIOLadj(D) 23.82±1.02 22.16a25.76 19.74±3.11 728a22.91 PIOLHaigis(D) 23.95±1.16 21.25a26.14 19.95±3.58 6.35a24.05 PIOLHofferQ(D) 22.68±1.47 20.24a25.07 17.94±4.15 4.55a22.47 PIOLHolladay(D) 22.90±1.00 20.51a24.61 19.19±3.37 5.58a23.01 Donde:SEpre=equivalenteesféricopreoperatorio;SEpost=equivalenteesféricopostoperatorio;r1c=radiocara anterior corneal; ACD=profundidad cámara anterior; AL= longitud axial; ELPSRK/T= posiciónefectivadelalentecalculadamediantefórmulaSRK/T;ELPadj=posiciónefectivadelalenteajustada;ELPHaigis= posición efectiva de la lente calculada mediante fórmula de Haigis; ELPHofferQ= posiciónefectivade la lentecalculadamediante fórmuladeHofferQ;ELPHolladay=posiciónefectivade la lentecalculadamediantefórmuladeHolladay;nkadj=índicederefracciónqueratométricoajustado;Pk(1.3375)=potencia corneal queratométrica calculada con índice queratométrico 1.3375; PcHaigis= potenciacorneal calculada para la fórmula de Haigis cuando se utiliza un valor de índice queratométrico1.3315; Pkadj= potencia queratométrica calculada con índice queratométrico ajustado; PIOLReal=potencia lente intraocular implantada; PIOLadjSRK/T= potencia lente intraocular calculada mediantefórmula SRK/T; PIOLadj= potencia lente intraocular ajustada; PIOLHofferQ= potencia lente intraocularcalculadamediante fórmula de Hoffer Q; PIOLHolladay= potencia lente intraocular calculadamediantefórmuladeHolladay;PIOLHaigis=potencialenteintraocularcalculadamediantefórmuladeHaigis

Capítulo4


108



1. En el grupo A, no se encontraron diferencias estadísticamente significativas

(aunque por poco) entre PIOLadjSRK/T y PIOLReal cuando se usó el valor deELP

calculado mediante la fórmula SRK/T (p = 0.06, test t-Student). Como se

apreciaen la figura27a,existeunacorrelaciónestadísticamentesignificativa

entreambasmedidas(r=0.680,p<0.01).

EnelgrupoB,seencontrarondiferenciasestadísticamentesignificativasentre

PIOLadjSRK/T y PIOLReal cuando se usó el valor de ELP calculado mediante la

fórmula SRK/T (p < 0.01, testWilcoxon). Como se aprecia en la figura 27b,

existe una fuerte correlación estadísticamente significativa entre ambas

medidas(r=0.898,p<0.01).

Fig.27a.(GrupoA)RelaciónentrelaPIOLadjSRK/TylaPIOLReal.

20

22

24

26

28

20 21 22 23 24 25 26 27

P IOLadjSRK/T(D)

PIOLReal(D)

Capítulo4


109

Fig27b.(GrupoB)RelaciónentrelaPIOLadjSRK/TylaPIOLReal

2. AlrealizarelanálisisdeBland-AltmanenelgrupoA(fig.28a)seobtuvoquela

mediadelasdiferenciasentreambasmedidasfuede0.43D,conunoslímites

de concordancia inferior de -0.98 D y superior de +1.84 D, lo cual resulta

clínicamente significativo. En el análisis de Bland-Altman en el grupo B

(fig.28b)seobtuvoquelamediadelasdiferenciasentreambasmedidasfuede

0.97 D, con unos límites de concordancia inferior de -0.30 D y superior de

+2.24D.

Fig.28a.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/TylaPIOLReal

frentealamediadelasdiferenciasenelGrupoA

5

10

15

20

25

30

5 10 15 20 25 30

P IOLadjSRK/T(D)

PIOLReal(D)

1,84D

-0,98D

0,43D

-5

-3

-1

1

3

5

22 23 24 25 26 27

DiferenciaPIOLadjSRK/T-P IOLReal(D)


Capítulo4


110

Fig.28b.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/TylaPIOLRealfrentealamediadelasdiferenciasenelGrupoB

3. Mediante un análisis de regresiónmúltiple, se obtuvoque el valor deELPadj

paraelgrupoA,estabacorrelacionadoconlaedadyelastigmatismocorneal

(AC)(p<0.01):

𝐸𝐿𝑃!"#!!" = 5.983− 0.015 ∙ 𝐸𝑑𝑎𝑑 − 0.460 ∙ 𝐶𝐴 [46]



(distanciadeCook:0.146±0.259).Conestemodelo,el58.33%delosresiduos

no estandarizados tenían un valor ≤ 0.20. También se confirmó la pobre

correlaciónexistenteentreresiduos(testDurbin-Watson:2.320)ylafaltade

multicolinealidad(tolerancia0.971a0.971,FIV1.029a1.029).

No se encontraron diferencias estadísticamente significativas entre ELP

calculadamediantelafórmulaSRK/TylaELPadj(p=0.07,testt-Student).

En el grupo B, se descubrió que el valor de ELPadj en este caso estaba

correlacionado con la edad, la profundidad de la cámara anterior (ACD),

longitudaxial(AL)yradiocornealanterior(r1c)(p<0.01):

2,24D

-0,30D

0,97D

-5

-3

-1

1

3

5

7 11 15 19 23

DiferenciaPIOLadjSRK/T-P IOLReal(D)


Capítulo4


111

𝐸𝐿𝑃!"#!!" = 5.327 + 0.015 ∙ 𝐸𝑑𝑎𝑑 + 0.346 ∙ 𝐴𝐶𝐷 + 0.334 ∙ 𝐴𝐿 − 1.430 ∙ 𝑟!! [47]



(distanciadeCook:0.04±0.13).Conestemodelo, el84.91%de los residuos

teníanunvalorde≤0.50.Lapobrecorrelaciónexistenteentreresiduos(test

Durbin-Watson: 2.208) y la falta de multicolinealidad (tolerancia 0.733 a

0.926,FIV1.080a1.364)fueconfirmada.

Para este grupo, se encontraron diferencias estadísticamente significativas

entre ELP calculada mediante la fórmula SRK/T y la ELPadj (p < 0.01, test

Wilcoxon),siendoelvalormenorelcorrespondienteaELPadj(vertabla15).

4. Enambosgrupos,seencontrarondiferenciasestadísticamentesignificativasal

compararelvalordeELPadjconelvalordeELPobtenidoconcualquieradelas

fórmulas comerciales analizadas (p<0.01, test T-Student para el grupo A y

p<0.01,testWilcoxonparaelgrupoB).Comoseapreciaenlatabla15,elvalor

mínimodeELPcorrespondeaELPHolladayparaambosgrupos(3.77±0.42mm,

rango3.08a4.29mmy4.24±0.43mm,rango3.17a5.31mm,pertenecientes

alosgruposAyB,respectivamente).

5. Noseencontrarondiferenciasentrelasmediasestadísticamentesignificativas

entrePIOLadjyPIOLRealalanalizarlaintercambiabilidadentreambasmedidasen

losdosgruposdeestudios(GrupoA:p=0.64,testt-Student;GrupoB:p=0.82,

test Wilcoxon). Se encontró una fuerte correlación estadísticamente

significativaentrePIOLadjyPIOLRealtantoparaelGrupoA(r=0.88,p<0.01)como

paraelGrupoB(r=0.91,p<0.01)(Figura29ay29b,respectivamente).

Capítulo4


112

Fig.29a.(GrupoA)RelaciónentrelaPIOLadjylaPIOLReal

Fig.29b.(GrupoB)RelaciónentrelaPIOLadjylaPIOLReal

6. AlrealizarelanálisisBland-Altman,paraelGrupoA(figura30a)seobtuvoun

valorde0.08Ddelamediadelasdiferenciasentreambasmedidas,conunos

límitesdeconcordanciainferiorde-0.96Dysuperiorde+1.11D.EnelGrupo

B, el valorde lamediade lasdiferencias fuede -0.02D conunos límitesde

concordancia inferiory superiorde -1.18y+1.14D, respectivamente (figura

30b).

0

5

10

15

20

25

0 5 10 15 20 25

P IOLadj(D)

PIOLReal(D)

21

22

23

24

25

26

21 22 23 24 25 26

P IOLadj(D)

PIOLReal(D)

Capítulo4


113

Fig.30a.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/Ty

laPIOLRealfrentealamediadelasdiferenciasenelGrupoA

Fig.30b.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/T

ylaPIOLRealfrentealamediadelasdiferenciasenelGrupoB

1,14D

-1,18D

-0,02D

-5

-3

-1

1

3

5

7 11 15 19 23

DiferenciasP

IOLadj-P

IOLReal(D)

MediaPIOLReal-PIOLadj(D)

1,11D

-0,96D0,08D

-5

-3

-1

1

3

5

22 23 24 25 26 27

DiferenciasP

IOLadj-P

IOLReal(D)


Capítulo4


114

7. Al comprobar la intercambiabilidad existente entre PIOLadj y las distintas

fórmulas de cálculo comerciales, se obtuvo en el Grupo A, diferencias

estadísticamente significativasentre todas las combinaciones (p<0.01, test t-

Student), excepto para la combinación de PIOLadj y PIOLHaigis (p=0.53, test t-

Student),conunamediade0.13±0.69yunintervalodeconfianzade1.47a-

1.22D.LamáximadiferenciaseobtuvoentrePIOLadjyPIOLHofferQ(-1.14±1.15D,

rangode+1.11a-3.40D).Seencontróunafuertecorrelaciónestadísticamente

significativa entrePIOLadjyPIOLHaigis(r=0.81, p<0.01) y entrePIOLHolladayyPIOLadj

(r=0.82, p<0.01). Además de una moderada correlación estadísticamente

significativaentrePIOLHofferQyPIOLadj(r=0.63,p=0.03).

Al analizar el Grupo B, se encontraron diferencias estadísticamente

significativas entre PIOLadj y todas las fórmulas analizadas (p<0.01, test

Wilcoxon). Coincidiendo estas diferencias máximas, como en el grupo A, al

comparar PIOLadj con PIOLHofferQ (-1.76 ± 1.84 D, rango de +1.84 a -5.36 D).

AparecióunafuertecorrelaciónestadísticamentesignificativaentrePIOLHaigisy

PIOLadj (r=0.99, p<0.01), entrePIOLHolladayyPIOLadj (r=0.98, p<0.01), siendo esa

correlaciónmasmoderadaentrePIOLHofferQyPIOLadj(r=0.66,p<0.01).Enlatabla

16semuestraunresumendelosvaloresBlandAltmancorrespondientes.

Tabla15.AnálisisBland-AltmanentrePIOLadjyPIOLobtenidoconfórmulascomerciales

GRUPOA GRUPOB

ΔPIOL± SD(D) LoA(D) p-value ΔPIOL± SD(D) LoA(D) p-value

Haigis 0.13±0.69 1.47to-1.22 <0.01 0.25±0.50 1.24to-0.73 <0.01

HofferQ -1.14±1.15 1.11to-3.40 <0.01 -1.76±1.84 1.84to-5.36 <0.01

HolladayI -0.93±0.61 0.26to-2.12 0.53 -0.50±0.36 0.20to-1.20 <0.01

Ennuestroestudio,setratódeminimizarelerrordecálculodelapotenciade

lalenteintraocularaimplantarparaelmodeloespecíficodelenteintraocularasférica

Capítulo4


115

Lentis L-313. Para ello, por una parte de utilizó el algoritmo de cálculo del índice

queratométricoajustado (nkadj)paraminimizarel errorenel cálculode lapotencia

cornealqueratométricayporotraparteseoptimizóelcálculodelaELPenfunciónde

lapotenciade la lente intraocular,hechoquehastaahoranohabíamosrealizadoen

losanterioresartículos.

Los pacientes presentaban un rango de valores de esfera equivalente

postoperatoriaentre-0.75y+0.75DenojosconPIOL≥23Dyentre-1.38y+0.75Den

ojos conPIOL<23D.Observándoseuna ligera tendenciaa lamiopíaen los casosde

ojosconpotenciadelenteintraocularmenoryenconsecuenciaenojoslargos.Estoes

coherente con los estudiosdonde sehan reportadouna tendencia a lamiopización

con lentes intraoculares asféricas, especialmente en casos de extrema miopía

preoperatoria(159).

Seevaluólaslimitacionesenlapredictibilidaddelerrorrefractivoenestetipo

de lente. Dado que los errores en la estimación de la AL eran mínimos y de bajo

impacto en la predicción del error(133), se evaluó la influencia del error

queratométrico mediante el cálculo de la potencia corneal con el valor de índice

queratométricoajustado(nkadj)conelfindeminimizarelerrorcorneal(53,132,143).Este

valor dePkadj se utilizó para obtener el valor de la potencia de la lente intraocular

considerandoAL,Rdes=SEpost yELP calculadomediante las directrices de la fórmula

SRK/T(PIOLadjSRK/T)(21).Paralosdosgruposdeestudio(ojosimplantadosconPIOL≥23

DyPIOL<23D)seobservarondiferenciasclínicamenterelevantesentrelaPIOLadjSRK/T

yPIOLReal siendomayores lasdiferenciasenojos implantadosconpotenciasbajasde

lente intraocular. De acuerdo con los resultados obtenidos, se observó que la

estimación de la ELP parecía ser el factor más crítico para la presencia de una

previsibilidad relativamente limitadaen la lente intraocular asférica, especialmente

enojos cortos. Conel finde confirmar esto, seobtuvopormediodeunanálisisde

regresión múltiple, una expresión para la estimación del valor de ELP optimizado

(ELPadj)deacuerdo conalgunosparámetrospreoperatorios.EstevalordeELPadj se

utilizó para calcular la potencia de la lente intraocular (PIOLadj) considerandoRdes =

SEpost,conelobjetivodecomprobarsiestanuevaestimacióneracapazdereproducir

el resultado clínico real. Con este enfoque, no se encontraron diferencias

Capítulo4


116

estadísticamentesignificativasyclínicamenteaceptablesentrePIOLadjyPIOLRealenlos

dosgrupos.

Ennuestroanálisis,seencontróqueELPadjestabarelacionadocondiferentes

factores en los grupos A y B. La edad es el único factor que compartían ambos

modelos.Estopuedeserdebidoalarelaciónexistenteconladependenciadelaedad

del comportamiento capsular después de la cirugía de cataratas. Un estudio reveló

que la edad podría estar asociada con el síndrome de distensión de la bolsa

capsular(160). En el grupo B, que incluyó los ojos con mayor AL, los factores

anatómicos fueron cruciales en el cálculo de la ELP para el cálculo de la lente

intraocularevaluada.ElvalordeELPadj fuemayorenojosconmayorALyACD,que

resulta ser consistente con la dependencia lineal de la posición final de la lente

intraocular en elAL reportado por diversos autores(161–163). También se incluyó un

factorcornealentérminosdemagnituddeastigmatismocornealenelgrupoAyde

radiodecurvaturade laprimerasuperficiecornealenelgrupoB.Siendoenambos

grupos nuestro valor de ELPadj< ELPadjSRK/T (ELPadj 4.44 ± 0.31 mm y 4.61 ± 0.53,

correspondientesalgrupoAyB,respectivamente)

Por último, se comparó la PIOLadj con las diversas fórmulas de cálculo de

potencia de lente intraocular. En ambos grupos, se encontraron diferencias

clínicamente relevantes entre PIOLadj y los valores de potencia de lente intraocular

obtenidos con la fórmula de Haigis, Hoffer Q y Holladay. Estas diferencias fueron

estadísticamente significativas, salvo la diferencia entre PIOLadj y PIOLHaigis que no

alcanzó una significación estadística, posiblemente debido a la limitación en el

tamaño de la muestra de este grupo. Estas diferencias entre las fórmulas parecen

estarenrelaciónconlasdiferentesestimacionesdeELPproporcionadosporcadauno

deellos,conelresultadomásprecisoparaELPadj.AlcompararnuestraELPadjconel

restodeELPcalculadas,seencontróquelafórmuladeHolladay(ELPHolladay)fuelaque

dioelvalormásbajodeELPpara losdosgrupos(3.77±0.42,rangode3.08a4.29

mmy4.24± 0.43, rangode3.17a5.31,parael grupoAyB, respectivamente). Sin

embargo,nuestraPIOLadjfuecapazdereproducirconmásprecisiónelvalorrealdela

potenciadelalenteintraocularimplantada.Estosugierequenuestroenfoquepuede

Capítulo4


117

ser un método útil para el cálculo de potencia de la lente intraocular asférica

evaluada.

Existenvariaslimitacionesenelestudioactual,talescomoeltamañolimitado

delamuestraoelcortoseguimientorealizado.Debetenerseencuenta,aunqueson

poco frecuentes, los cambios en la posición de la lente intraocular descritos en

pacientes de más de tres meses después de la cirugía, sobre todo después de la

capsulotomíaposteriorconlaserYAG(164).Otraposiblelimitaciónpuedeserdebidoa

que la fórmula Holladay II no se utilizó en nuestra comparación ya que no era

disponibleennuestraclínica.Posiblemente,nuestroenfoquepudierasermássimilar

a losresultadosde la fórmulaHolladayIIyaqueambostiposdecálculoutilizanun

algoritmo optimizado para la estimación de laELP, que deberá ser confirmado en

estudiosfuturos.

Capítulo5

CONCLUSIONESYPERSPECTIVASDEFUTURO

121

5.CONCLUSIONESYPERSPECTIVASDEFUTURO

5.a.Conclusiones

Con estos resultados, se deduce que la imprecisión en el cálculo de Pc,

pertenecientes a una población sana sin cirugía previa, con la estimación

queratométrica puede serminimizada en la práctica clínicamediante el uso de un

índicequeratométricovariabledependientede r1c,al cualhemosdenominadonkadj.

Siendo esta estimación válida únicamente cuando sea inviable la obtención de r2c,

dado que la mejor opción para la realización del cálculo es obtener el valor de la

potenciacornealgaussianaconsiderandoambassuperficiescorneales.Por loquese

concluyequeelusodeunúnicovalordenkparaelcálculodePIOLpuededarlugara

imprecisiones las cuales pueden ser minimizadas mediante el uso de un valor

variabledenkdependientedelasuperficieanteriorcorneal.

Los resultados refractivos obtenidos después de la cirugía de cataratas

mediante el implante de la lente intraocular acomodativa Crystalens HD, pueden

optimizarsemedianteunalgoritmodecálculodenkadjparaminimizarelerrorenel

cálculodelapotenciacornealqueratométrica,ademásdeunaoptimizacióndelvalor

de ELP, dependiente de AL, Pkadj, ACD y la Edad. Siendo nuestro valor de ELPadj

significativamente menor comparado con los valores obtenidos con el resto de

fórmulas comerciales analizadas. No se obtuvieron errores clínicamente

significativos,aunquesifueronclínicamenterelevantesloslímitesdeacuerdo,entre

nuestra PIOLadj y la PIOLReal, pero sí entre nuestra PIOLadj y el resto de fórmulas

comerciales. Concluyendo que la PIOLadj es la que mejor reproduce los valores de

PIOLReal.

Los resultados refractivos obtenidos en el caso de implante de la lente

intraocularmultifocalLentisMplusLS-312despuésdecirugíadecatarata,aligualque

enel estudioanterior,puedeoptimizarsemedianteunalgoritmodecálculodenkadj

paraminimizarelerrorenelcálculodelapotenciacornealqueratométrica,además

Capítulo5

ConclusionesyPerspectivasdefuturo

122

de una optimizacióndel valor deELP, en este casodependiente deAL,Pkadj yACD.

Siendo en este caso también significativamente menor nuestro valor de ELPadj

comparadoconlosvaloresobtenidosconelrestodefórmulascomercialesanalizadas,

siendo estas diferencias mínimas para la pareja ELPadj – ELPHolladay. En este caso,

tampoco se obtuvieron errores clínicamente significativos, aunque si fueron los

límitesdeacuerdoentrenuestraPIOLadjy laPIOLRealyentrePIOLadjyPIOLHolladay.Siendo

para la pareja PIOLadj - PIOLReal la que proporcionó un menor intervalo de acuerdo

respectoalrestodefórmulascomercialesanalizadas,indicandoqueseríalafórmula

másadecuadaparareproducirlosvaloresdePIOLReal.

Los resultados refractivos obtenidos en el caso de implante de la lente

intraocular asféricaLentisL-313después de cirugía de catarata, al igual que en los

estudiosanteriores,tambiénpuedeoptimizarsemedianteunalgoritmodecálculode

nkadj para minimizar el error en el cálculo de la potencia corneal queratométrica,

ademásdeunaoptimizacióndelvalordeELP.Sinembargo,enestaocasiónsedividió

lamuestraendosgruposenfuncióndelvalorde lapotenciade la lente intraocular

implantada, siendo el valor de ELPadj dependiente de la Edad y el astigmatismo

corneal,paralamuestraPIOLadj>23DydependientedelaEdad,ACD,ALyr1cparala

muestraPIOLadj<23D.SiendoelvalordeELPadjmayorenojosconmayorALyACD.

Sin embargo, el valor más bajo de ELP para ambos grupos, se correspondió con

ELPHolladay. Al igual que en los estudios anteriores, no se obtuvieron errores

clínicamente significativos entre nuestra PIOLadj y PIOLReal, en ninguno de los dos

grupos. Al comparar PIOLadj con el resto de fórmulas comerciales, se encontraron

diferencias significativas excepto cuando se comparó con PIOLHaigis, posiblemente

debidoallimitadotamañodelamuestra.NuestraPIOLadjfuecapazdereproducircon

más precisión el valor de la indicando de este modo que sería la fórmula más

adecuadaparareproducirlosvaloresdePIOLReal.

5.bPerspectivasdefuturo

Variossonlosobjetivosplanteadosparafuturosestudios,comoson:

Evaluarelimpactodelaestimaciónqueratométricaenpacientessometidosa

cirugíapreviaparaconfirmarel inadecuadousodeunúnico índicequeratométrico,

Capítulo5

ConclusionesyPerspectivasdefuturo

123

ademásdecomprobarelbeneficiodeestealgoritmoparaoptimizarelcálculode la

potenciadelalenteintraocular.

Es necesario confirmar todos los resultados obtenidos teóricamente en el

cálculo de la potencia de la lente intraocular con diferentes tipos de lentes

intraocularesyporconsiguientecondiferentesconstantesA.

Sedebeanalizar la influenciade lapotenciaqueratométricaajustadaparael

cálculodelapotenciadecadalenteintraocularanalizada,comosonlaacomodativa,

multifocalyasférica,sobreunamuestramásgrandeincluyendocasosextremos(ojos

largosycortos).

Capítulo6

BIBLIOGRAFÍA

127

BIBLIOGRAFIA

1. Binkhorst R. Selection of intraocular lens power. Contemp Ophthalmol.1980;1:1–8.

2. ShammasHJ.Atlasofopthalmicultrasonographyandbiometry. St. LouisMO,editor.CVMosbyCO;1984.

3. ShammasHJ.Historicoverview.SlackInco.Intraocularlenspowercalculation.UnitedStatesofAmerica;2004.

4. Olsen T. Calculation of intraocular lens power: a review. Acta OphthalmolScand.2007;85(5):472–85.

5. SouzaCE,MuccioliC,SorianoES,ChalitaMR,OliveiraF,FreitasLL,etal.Visualperformance of AcrySof ReSTOR apodized diffractive IOL: a prospectivecomparativetrial.AmJOphthalmol.2006;141(5):827–32.

6. FyodorovSN,GalinMA,LinkszA.Calculationoftheopticalpowerofintraocularlenses.InvestOphthalmol.1975;14(8):625–8.

7. ColenbranderMC.Calculationofthepowerofaniriscliplensfordistantvision.BrJOphthalmol.1973;57(10):735–40.

8. Thijssen JM. The emmetropic and the iseikonic implant lens: computercalculation of the refractive power and its accuracy. Ophthalmologica.1975;171(6):467–86.

9. BinkhorstRD.Theopticaldesignofintraocularlensimplants.OphthalmicSurg.1975;6(3):17–31.

10. Van der Heijde GL. The optical correction of unilateral aphakia. Trans SectOphthalmolAmAcadOphthalmolOtolaryngol.1976;81(1):OP80–8.

11. Sanders DR, Retzlaff J, Kraff MC. Comparison of empirically derived andtheoreticalaphakicrefractionformulas.ArchOphthalmol.1983;101(6):965–7.

12. SandersDR,KraffMC.Improvementofintraocularlenspowercalculationusingempiricaldata.JAmIntraoculImplantSoc.1980;6(3):263–7.

13. Binkhorst RD. Intraocular lens power calculation manual. A guide to theauthor´sTI58/59IOLpowermodule.2nded.NewYork;1981.

Capítulo6

Referencias

128

14. Binkhorst RD. biometric A-scan ultrasonography and intraocular lens powercalculation. InEmery JE, (Ed):CurrentConcepts inCataractSurgery:SelectedProceedings of the Fifth Biennial Cataract Surgical Congress, St. Louis, MO,MosbyCV;1987.p.175–82.

15. Camellin M. Proposed formula for the dioptric power evaluation of theposteriorcornealsurface.RefractCornealSurg.1990;6(4):261–4.

16. ShammasHJ.Thefudgedformulaforintraocularlenspowercalculations.JAmIntraoculImplantSoc.1982;8(4):350–2.

17. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regressionformulas.JCataractRefractSurg.1993;19(6):700–12.

18. SandersDR,Retzlaff J,KraffMC.Comparisonof theSRK II formulaandothersecondgenerationformulas.JCataractRefractSurg.1988;14(2):136–41.

19. HofferKJ.Intraocularlenscalculation:theproblemoftheshorteye.OphthalmicSurg.1981;12(4):269–72.

20. HolladayJT,PragerTC,ChandlerTY,MusgroveKH,LewisJW,RuizRS.Athree-partsystemforrefiningintraocularlenspowercalculations.JCataractRefractSurg.1988;14(1):17–24.

21. Retzlaff JA,SandersDR,KraffMC.Developmentof theSRK/T intraocular lensimplantpowercalculationformula.JCataractRefractSurg.1990;16(3):333–40.

22. ShammasH.Intraocularlenspowercalculations.SlackInco.Thorofare,NJ,USA;2004.

23. OlsenT,OlesenH,ThimK,CorydonL.Predictionofpostoperative intraocularlenschamberdepth.JCataractRefractSurg.1990;16(5):587–90.

24. Olsen T. Theoretical approach to intraocular lens calculation using Gaussianoptics.JCataractRefractSurg.1987;13(2):141–5.

25. Olsen T, Corydon L, Gimbel H. Intraocular lens power calculation with animprovedanteriorchamberdepthpredictionalgorithm.JCataractRefractSurg.1995;21(3):313–9.

26. Shammas H. Modern formulas for intraocular lens power calculation. SlackInco.UnitedStatesofAmerica;2004.15-24p.

Capítulo6

Referencias

129

27. HofferKJ.ClinicalresultsusingtheHolladay2intraocularlenspowerformula.JCataractRefractSurg.2000;26(8):1233–7.

28. Haigis W. Intraocular lens calculation after refractive surgery for myopia:Haigis-Lformula.JCataractRefractSurg.2008;34(10):1658–63.

29. Narvaez J,ZimmermanG,StultingRD,ChangDH.Accuracyof intraocular lenspower prediction using the Hoffer Q, Holladay 1, Holladay 2, and SRK/Tformulas.JCataractRefractSurg.2006;32(12):2050–3.

30. Terzi E, Wang L, Kohnen T. Accuracy of modern intraocular lens powercalculation formulas in refractive lens exchange for high myopia and highhyperopia.JCataractRefractSurg.2009;35(7):1181–9.

31. Zaldivar R, Shultz MC, Davidorf JM, Holladay JT. Intraocular lens powercalculations in patients with extreme myopia. J Cataract Refract Surg.2000;26(5):668–74.

32. Donoso R, Mura JJ, Lopez M, Papic A. [Emmetropization at cataract surgery.Looking for the best IOL power calculation formula according to the eyelength].ArchSocEspOftalmol.2003;78(9):477–80.

33. TsangCS,ChongGS,YiuEP,HoCK.Intraocularlenspowercalculationformulasin Chinese eyes with high axial myopia. J Cataract Refract Surg.2003;29(7):1358–64.

34. HolladayJT.Standardizingconstantsforultrasonicbiometry,keratometry,andintraocularlenspowercalculations.JCataractRefractSurg.1997;23(9):1356–70.

35. Holladay JT. Intraocular lenspower calculation. InFineHI,PacerM,HoffmanRS,RefractiveLenssurgery.SpringerB.EugenOregon,USA;2005.

36. HolladayJT,GillsJP,LeidleinJ,CherchioM.Achievingemmetropiainextremelyshort eyes with two piggyback posterior chamber intraocular lenses.Ophthalmology.1996;103(7):1118–23.

37. Olsen T. On the calculation of power from curvature of the cornea. Br JOphthalmol.1986;70(2):152–4.

38. Goss DA, West RW. Introduction to the optics of the eye. Oxford, UK,Butterwoerth-Heinemann;2002.

Capítulo6

Referencias

130

39. Fam HB, Lim KL. Validity of the keratometric index: large population-basedstudy.JCataractRefractSurg.2007;33(4):686–91.

40. Borasio E, Stevens J, Smith GT. Estimation of true corneal power afterkeratorefractive surgery in eyes requiring cataract surgery: BESSt formula. JCataractRefractSurg.2006;32(12):2004–14.

41. CanarimdeOliveira EC, Arce CG, CamposM, Schor PO. Calculo do poder daslentesIntra-OculareseoOrbscan-II.Parte1:Opoderopticodacorneanormal.ArqBrasOftalmol.2003;567–74.

42. EspinosaJ,RouarchJ,PerezJ,IlluecaC,MasD.Geometricalapproximationsforaccureevaluationofrefractioninhumancornea.Optik(Stuttg).2007;209–15.

43. GobbiPG,CaronesF,BrancatoR.Keratometric index,videokeratography,andrefractivesurgery.JCataractRefractSurg.1998;24(2):202–11.

44. Ho JD,TsaiCY,TsaiRJ,KuoLL,Tsai IL,LiouSW.Validityof thekeratometricindex: evaluation by the Pentacam rotating Scheimpflug camera. J CataractRefractSurg.2008;34(1):137–45.

45. ShammasHJ,Hoffer KJ, ShammasMC. Scheimpflug photography keratometryreadingsforroutineintraocularlenspowercalculation.JCataractRefractSurg.2009;35(2):330–4.

46. TangM,LiY,AvilaM,HuangD.Measuringtotalcornealpowerbeforeandafterlaser in situ keratomileusiswith high-speed optical coherence tomography. JCataractRefractSurg.2006;32(11):1843–50.

47. Lowe RF, Clark BA. Posterior corneal curvature. Correlations in normal eyesand in eyes involvedwith primary angle-closure glaucoma. Br J Ophthalmol.1973;57(7):464–70.

48. RoystonJM,DunneMC,BarnesDA.Measurementofposteriorcornealsurfacetoricity.OptomVisSci.1990;67(10):757–63.

49. Royston JM, Dunne MC, Barnes DA. Measurement of the posterior cornealradiususingslitlampandPurkinjeimagetechniques.OphthalmicPhysiolOpt.1990;10(4):385–8.

50. Edmund C. Posterior corneal curvature and its influence on corneal dioptricpower.ActaOphthalmol.1994;72(6):715–20.

Capítulo6

Referencias

131

51. DunneMC,RoystonJM,BarnesDA.Normalvariationsoftheposteriorcornealsurface.ActaOphthalmol.1992;70(2):255–61.

52. Dubbelman M, Sicam VA, Van der Heijde GL. The shape of the anterior andposteriorsurfaceoftheaginghumancornea.VisRes.2006;46(6-7):993–1001.

53. CampsVJ,PineroLlorensDP,deFezD,ColomaP,CaballeroMT,GarciaC,etal.Algorithm for correcting the keratometric estimation error in normal eyes.OptomVisSci.2012;89(2):221–8.

54. GarnerLF,OwensH,YapMK,FrithMJ,KinnearRF.Radiusofcurvatureoftheposteriorsurfaceofthecornea.OptomVisSci.1997;74(7):496–8.

55. Lam A, Douthwaite WA. The ageing effect on the central posterior cornealradius.OphthalmicPhysiolOpt.2000;(20):63–9.

56. Cairns G, McGhee CN. Orbscan computerized topography: attributes,applications,andlimitations.JCataractRefractSurg.2005;31(1):205–20.

57. Maldonado MJ, Nieto JC, Diez-Cuenca M, Pinero DP. Repeatability andreproducibility of posterior corneal curvature measurements by combinedscanning-slit and placido-disc topography after LASIK. Ophthalmology.2006;113(11):1918–26.

58. NilforoushanMR,SpeakerM,MarmorM,AbramsonJ,TulloW,MorschauserD,et al. Comparative evaluation of refractive surgery candidates with Placidotopography, Orbscan II, Pentacam, andwavefront analysis. J Cataract RefractSurg.2008;34(4):623–31.

59. NishimuraR,Negishi K, SaikiM, AraiH, Shimizu S, Toda I, et al. No forwardshiftingofposteriorcornealsurfaceineyesundergoingLASIK.Ophthalmology.2007;114(6):1104–10.

60. Chakrabarti HS, Craig JP, Brahma A, Malik TY, McGhee CN. Comparison ofcorneal thickness measurements using ultrasound and Orbscan slit-scanningtopography in normal and post-LASIK eyes. J Cataract Refract Surg.2001;27(11):1823–8.

61. Iskander NG, Anderson Penno E, Peters NT, Gimbel H V, Ferensowicz M.Accuracy of Orbscan pachymetry measurements and DHG ultrasoundpachymetry in primary laser in situ keratomileusis and LASIK enhancementprocedures.JCataractRefractSurg.2001;27(5):681–5.

Capítulo6

Referencias

132

62. GiesslerS,DunckerGI.OrbscanpachymetryafterLASIKisnotreliable.JRefractSurg.2001;17(3):385–7.

63. Prisant O, Calderon N, Chastang P, Gatinel D, Hoang-Xuan T. Reliability ofpachymetric measurements using orbscan after excimer refractive surgery.Ophthalmology.2003;110(3):511–5.

64. Pinero DP, Saenz Gonzalez C, Alio JL. Intraobserver and interobserverrepeatability of curvature and aberrometric measurements of the posteriorcorneal surface in normal eyes using Scheimpflug photography. J CataractRefractSurg.2009;35(1):113–20.

65. Cheng AC, Rao SK, Lam DS. Accuracy of Orbscan II in the assessment ofposterior curvature in patients with myopic LASIK. J Refract Surg.2007;23(7):677–80.

66. Ueda T, Nawa Y,Masuda K, Ishibashi H, Hara Y, Uozato H. Posterior cornealsurfacechangesafterhyperopiclaserinsitukeratomileusis.JCataractRefractSurg.2005;31(11):2084–7.

67. NawaY,MasudaK,UedaT,HaraY,UozatoH.Evaluationofapparentectasiaofthe posterior surface of the cornea after keratorefractive surgery. J CataractRefractSurg.2005;31(3):571–3.

68. GrzybowskiDM,RobertsCJ,MahmoudAM,Chang Jr. JS.Model fornonectaticincrease in posterior corneal elevation after ablative procedures. J CataractRefractSurg.2005;31(1):72–81.

69. Twa MD, Roberts C, Mahmoud AM, Chang Jr. JS. Response of the posteriorcorneal surface to laser in situ keratomileusis formyopia. J Cataract RefractSurg.2005;31(1):61–71.

70. TouzeauO, Allouch C, Borderie V, Kopito R, Laroche L. [Correlation betweenrefractionandocularbiometry].JFrOphtalmol.2003;26(4):355–63.

71. Hernandez-QuintelaE,SamapunphongS,KhanBF,GonzalezB,LuPC,FarahSG,et al. Posterior corneal surface changes after refractive surgery.Ophthalmology.2001;108(8):1415–22.

72. Carney LG, Mainstone JC, Henderson BA. Corneal topography andmyopia. Across-sectionalstudy.InvestOphthalmolVisSci.1997;38(2):311–20.

Capítulo6

Referencias

133

73. WaringGOth,BerryDE.Advancesinthesurgicalcorrectionofpresbyopia.IntOphthalmolClin.2013;53(1):129–52.

74. AlioJL,TavolatoM,DelaHozF,ClaramonteP,Rodriguez-PratsJL,GalalA.Nearvision restoration with refractive lens exchange and pseudoaccommodatingandmultifocalrefractiveanddiffractiveintraocularlenses:comparativeclinicalstudy.JCataractRefractSurg.2004;30(12):2494–503.

75. BrownD,DoughertyP,GillsJP,HunkelerJ,SandersDR,SandersML.Functionalreadingacuityandperformance:Comparisonof2accommodating intraocularlenses.JCataractRefractSurg.2009;35(10):1711–4.

76. Patel S, Alio JL, Feinbaum C. Comparison of Acri. Smart multifocal IOL,crystalens AT-45 accommodative IOL, and Technovision presbyLASIK forcorrectingpresbyopia.JRefractSurg.2008;24(3):294–9.

77. HarmanFE,MalingS,KampougerisG,LanganL,KhanI,LeeN,etal.Comparingthe 1CU accommodative, multifocal, and monofocal intraocular lenses: arandomizedtrial.Ophthalmology.2008;115(6):993–1001e2.

78. Uthoff D, Gulati A, Hepper D, Holland D. Potentially accommodating 1CUintraocularlens:1-yearresultsin553eyesandliteraturereview.JRefractSurg.2007;23(2):159–71.

79. DogruM, Honda R, OmotoM, Toda I, FujishimaH, Arai H, et al. Early visualresultswith the1CUaccommodating intraocular lens. JCataractRefractSurg.2005;31(5):895–902.

80. MastropasquaL,TotoL,NubileM,FalconioG,BalloneE.Clinical studyof the1CU accommodating intraocular lens. J Cataract Refract Surg.2003;29(7):1307–12.

81. Wolffsohn JS, Naroo SA, Motwani NK, Shah S, Hunt OA, Mantry S, et al.Subjective and objective performance of the Lenstec KH-3500“accommodative”intraocularlens.BrJOphthalmol.2006;90(6):693–6.

82. Ossma IL, Galvis A, Vargas LG, TragerMJ, VagefiMR,McLeod SD. Synchronydual-optic accommodating intraocular lens. Part 2: pilot clinical evaluation. JCataractRefractSurg.2007;33(1):47–52.

83. Alio JL, Ben-nun J, Rodriguez-Prats JL, Plaza AB. Visual and accommodativeoutcomes 1 year after implantation of an accommodating intraocular lensbasedonanewconcept.JCataractRefractSurg.2009;35(10):1671–8.

Capítulo6

Referencias

134

84. Alio JL, Pinero DP, Plaza-Puche AB, Chan MJ. Visual outcomes and opticalperformanceofamonofocal intraocular lensandanew-generationmultifocalintraocularlens.JCataractRefractSurg.2011;37(2):241–50.

85. AlioJL,Plaza-PucheAB,JavaloyJ,AyalaMJ,MorenoLJ,PineroDP.Comparisonofanewrefractivemultifocalintraocularlenswithaninferiorsegmentalnearadd and a diffractive multifocal intraocular lens. Ophthalmology.2012;119(3):555–63.

86. Javitt JC, Steinert RF. Cataract extraction with multifocal intraocular lensimplantation: a multinational clinical trial evaluating clinical, functional, andquality-of-lifeoutcomes.Ophthalmology.2000;107(11):2040–8.

87. AlfonsoJF,Fernandez-VegaL,PuchadesC,Montes-MicoR.Intermediatevisualfunction with different multifocal intraocular lens models. J Cataract RefractSurg.2010;36(5):733–9.

88. Alfonso JF,Fernandez-VegaL,SenarisA,Montes-MicoR.Prospectivestudyofthe Acri.LISA bifocal intraocular lens. J Cataract Refract Surg.2007;33(11):1930–5.

89. Kohnen T, Nuijts R, Levy P, Haefliger E, Alfonso JF. Visual function afterbilateral implantation of apodized diffractive aspheric multifocal intraocularlenseswitha+3.0Daddition.JCataractRefractSurg.2009;35(12):2062–9.

90. KawamoritaT,UozatoH,AizawaD,KamiyaK,ShimizuK.Opticalperformancein rezoom and array multifocal intraocular lenses in vitro. J Refract Surg.2009;25(5):467–9.

91. ChangDF.Prospective functionalandclinicalcomparisonofbilateralReZoomand ReSTOR intraocular lenses in patients 70 years or younger. J CataractRefractSurg.2008;34(6):934–41.

92. Chiam PJT, Chan JH, Haider SI, Karia N, Kasaby H, Aggarwal RK. Functionalvision with bilateral ReZoom and ReSTOR intraocular lenses 6months aftercataractsurgery.JCataractRefractSurg.2007;33(12):2057–61.

93. Pepose JS,QaziMA,Davies J, Doane JF, Loden JC, SivalinghamV, et al. VisualPerformanceofPatientswithBilateralvsCombinationCrystalens,ReZoom,andReSTORIntraocularLensImplants.AmJOphthalmol.2007;144(3).

Capítulo6

Referencias

135

94. Kawamorita T, Uozato H. Modulation transfer function and pupil size inmultifocal andmonofocal intraocular lenses in vitro. J Cataract Refract Surg.2005;31(12):2379–85.

95. Steinert RF, Aker BL, Trentacost DJ, Smith PJ, Tarantino N. A prospectivecomparative study of the AMO ARRAY zonal-progressive multifocal siliconeintraocular lens and a monofocal intraocular lens. Ophthalmology.1999;106(7):1243–55.

96. Claoue C, Parmar D. Multifocal intraocular lenses. Dev Ophthalmol.2002;34:217–37.

97. Allen ED, Burton RL, Webber SK, Haaskjold E, Sandvig K, Jyrkkio H, et al.Comparisonofadiffractivebifocalandamonofocalintraocularlens.JCataractRefractSurg.1996;22(4):446–51.

98. AvitabileT,MaranoF,CaninoEG,BiondiS,ReibaldiA.Long-termvisualresultsof bifocal intraocular lens implantation. J Cataract Refract Surg.1999;25(9):1263–9.

99. Vega F, Alba-Bueno F, Millan MS. Energy distribution between distance andnear images in apodized diffractive multifocal intraocular lenses. InvestOphthalmolVisSci.2011;52(8):5695–701.

100. Chiam PJ, Chan JH, Aggarwal RK, Kasaby S. ReSTOR intraocular lensimplantation in cataract surgery: quality of vision. J Cataract Refract Surg.2006;32(9):1459–63.

101. OliveiraF,MuccioliC, SilvaLM, SorianoES, SouzaCE,Belfort Jr.R. [Contrastsensitivityandstereopsisinpseudophakicpatientswithmultifocalintraocularlens].ArqBrasOftalmol.2005;68(4):439–43.

102. SouzaCE,GerenteVM,ChalitaMR,SorianoES,FreitasLL,Belfort Jr.R.Visualacuity, contrast sensitivity, reading speed, and wavefront analysis:pseudophakic eye withmultifocal IOL (ReSTOR) versus fellow phakic eye innon-presbyopicpatients.JRefractSurg.2006;22(3):303–5.

103. Rocha KM, Chalita MR, Souza CE, Soriano ES, Freitas LL, Muccioli C, et al.Postoperative wavefront analysis and contrast sensitivity of a multifocalapodized diffractive IOL (ReSTOR) and threemonofocal IOLs. J Refract Surg.2005;21(6):S808–12.

Capítulo6

Referencias

136

104. RamonML, PineroDP, Perez-CambrodiRJ. Correlation of visual performancewithqualityof lifeand intraocularaberrometricprofile inpatients implantedwithrotationallyasymmetricmultifocalIOLs.JRefractSurg.2012;28(2):93–9.

105. VenterJA,PelouskovaM,CollinsBM,SchallhornSC,HannanSJ.Visualoutcomesandpatient satisfaction in9366eyesusing a refractive segmentedmultifocalintraocularlens.JCataractRefractSurg.2013;39(10):1477–84.

106. VanderLindenJW,vanVelthovenM,vanderMeulenI,NieuwendaalC,MouritsM, Lapid-Gortzak R. Comparison of a new-generation sectorial additionmultifocal intraocular lens and a diffractive apodized multifocal intraocularlens.JCataractRefractSurg.2012;38(1):68–73.

107. Alfonso JF, Fernandez-Vega L, Blazquez JI, Montes-Mico R. Visual functioncomparisonof2asphericmultifocalintraocularlenses.JCataractRefractSurg.2012;38(2):242–8.

108. MunozG,Albarran-DiegoC,Ferrer-BlascoT,SaklaHF,Garcia-LazaroS.Visualfunction after bilateral implantation of a new zonal refractive asphericmultifocalintraocularlens.JCataractRefractSurg.2011;37(11):2043–52.

109. McAlinden C, Moore JE. Multifocal intraocular lens with a surface-embeddednear section: Short-term clinical outcomes. J Cataract Refract Surg.2011;37(3):441–5.

110. AlioJL,Plaza-PucheAB,PineroDP,JavaloyJ,AyalaMJ.Comparativeanalysisoftheclinicaloutcomeswith2multifocalintraocularlensmodelswithrotationalasymmetry.JCataractRefractSurg.2011;37(9):1605–14.

111. Alio JL, Schimchak P, Negri HP, Montes-Mico R. Crystalline lens opticaldysfunctionthroughaging.Ophthalmology.2005;112(11):2022–9.

112. WangL, SantaellaRM,BoothM,KochDD.Higher-order aberrations from theinternalopticsoftheeye.JCataractRefractSurg.2005;31(8):1512–9.

113. Glasser A, Campbell MC. Presbyopia and the optical changes in the humancrystallinelenswithage.VisRes.1998;38(2):209–29.

114. KasperT,BuhrenJ,KohnenT.Visualperformanceofasphericalandsphericalintraocular lenses: intraindividual comparison of visual acuity, contrastsensitivity, and higher-order aberrations. J Cataract Refract Surg.2006;32(12):2022–9.

Capítulo6

Referencias

137

115. MencucciR,PonchiettiC.Nuove IOLequalitàdellavisione lenti asferiche.LaVoce.AICCER.:16–8.

116. KershnerRM.Retinal image contrast and functional visual performancewithaspheric, silicone, and acrylic intraocular lenses: Prospective evaluation. JCataractRefractSurg.2003;29(9):1684–94.

117. Packer M, Fine H, Hoffman R, Piers P. Prospective randomized trial of ananteriorsurfacemodifiedprolateintraocularlens.JRefractSurg.2002;18:692–6.

118. Packer M, Fine IH, Hoffman RS, Piers PA. Improved functional vision with amodifiedprolateintraocularlens.JCataractRefractSurg.2004;30(5):986–92.

119. BellucciR,MorselliS,PiersP.Comparisonofwavefrontaberrationsandopticalquallityofeyesimplantedwitthfivedifferentintraocularlenses.JRefractSurg.2004;20:297–306.

120. Kasper T, Bühren J, Kohnen T. Intraindividual comparison of higher-orderaberrationsafterimplantationofasphericalandsphericalintraocularlensesasafunctionofpupildiameter.JCataractRefractSurg.2006;32(1):78–84.

121. Muñoz G, Albarrán-Diego C, Montés-Micó R, Rodríguez-Galietero A, Alió JL.Spherical aberration and contrast sensitivity after cataract surgery with theTecnisZ9000intraocularlens.JCataractRefractSurg.2006;32(8):1320–7.

122. Rocha KM, Soriano ES, Chalita MR, Yamada AC, Bottós K, Bottós J, et al.Wavefront Analysis and Contrast Sensitivity of Aspheric and SphericalIntraocular Lenses: A Randomized Prospective Study. Am J Ophthalmol.2006;142(5).

123. Denoyer A, Le Lez ML, Majzoub S, Pisella PJ. Quality of vision after cataractsurgery after Tecnis Z9000 intraocular lens implantation. Effect of contrastsensitivity and wavefront aberration improvements on the quality of dailyvision.JCataractRefractSurg.2007;33(2):210–6.

124. Tzelikis PF, Akaishi L, Trindade FC, Boteon JE. Spherical Aberration andContrastSensitivityinEyesImplantedwithAsphericandSphericalIntraocularLenses:AComparativeStudy.AmJOphthalmol.2008;145(5).

125. Van Gaalen KW, Koopmans SA, Jansonius NM, Kooijman AC. Clinicalcomparison of the optical performance ofaspheric and spherical intraocularlenses.JCataractRefractSurg.2010;36(1):34–43.

Capítulo6

Referencias

138

126. AssafA,KotbA.Ocular aberrations and visual performancewith an asphericsingle-piece intraocular lens: Contralateral comparative study. J CataractRefractSurg.2010;36(9):1536–42.

127. MesterU,DillingerP,AnteristN. Impact of amodified optic designon visualfunction:Clinicalcomparativestudy. JCataractRefractSurg.2003;29(4):652–60.

128. Bellucci R, Scialdone A, Buratto L, Morselli S, Chierego C, Criscuoli A, et al.VisualacuityandcontrastsensitivitycomparisonbetweenTecnisandAcrySofSA60ATintraocularlenses:Amulticenterrandomizedstudy.JCataractRefractSurg.2005;31(4):712–7.

129. CaporossiA,MartoneG,CaspriniF,RapisardaL.Prospectiverandomizedstudyofclinicalperformanceof3asphericand2sphericalintraocularlensesin250eyes.JRefractSurg.2007;23(7):639–48.

130. WangL,MahmoudAM,AndersonBL,KochDD,RobertsCJ.Totalcornealpowerestimation: Ray tracing method versus Gaussian optics formula. InvestigOphthalmolVisSci.2011;52(3):1716–22.

131. OlsenT,ArnarssonA,SasakiH,SasakiK, JonassonF.On theocular refractivecomponents: The Reykjavik Eye Study. Acta Ophthalmol Scand.2007;85(4):361–6.

132. Camps VJ, Pinero DP, de Fez D, Mateo V. Minimizing the IOL Power ErrorInducedbyKeratometricPower.OptomVisSci.2013;90(7):639–49.

133. Faria-RibeiroM,Lopes-FerreiraD,L??pez-GilN,JorgeJ,Gonz??lez-M??ijomeJM.Errors Associatedwith IOLMaster Biometry as a Function of Internal OcularDimensions.JournalofOptometry.2014;

134. Shankar H, Taranath D, Santhirathelagan CT, Pesudovs K. Anterior segmentbiometry with the Pentacam: Comprehensive assessment of repeatability ofautomatedmeasurements.JCataractRefractSurg.2008;34(1):103–13.

135. ThePentacamTheGoldStandardinAnteriorSegmentTomography[Internet].2011. Available from: Optigërate GmbH. Available inhttp://www.pentacam.com/sites/calc_corneal_power.php#ptop

136. Bausch & Lomb Incorporated. Crystalens HD [online]. 2010. Disponible en:http://www.bausch.nl/ecp/-/m/BL/BaseSite/Files/Downloads/ECP/Surgical/Crystalens-AO-Brochure.pdf

Capítulo6

Referencias

139

137. CristalinoN. Lentis L-313.Disponible en: http://www.nuevocristalino.es/wp-content/uploads/sources/oculentis/LENTIS-L-313-EN.pdf?812a88

138. BlandJM,AltmanDG.Statisticalmethodsforassessingagreementbetweentwomethodsofclinicalmeasurement.Lancet.1986.

139. PedrottiL,PedrottiF.OpticsandVision.UpperSadd.Prentice-Hall;1998.

140. Y LG, El Hage S. Physiological Optics (El Hage SG, trans.). Springer-V. Berlin,Germany;1980.

141. TunnacliffeA.IntroductiontoVisualOptics.London,UK:AssociationofBritishDispensingOpticians;1997.

142. SandersD,Retzlaff J,KraffM,GimbelH,RaananM.Comparisonof theSRK/Tformulaandothertheoreticalandregressionformulas.JCataractRefractSurg.1990;16:341–6.

143. PiñeroDP,CampsVJ,MateoV,Ruiz-FortesP.Clinicalvalidationofanalgorithmtocorrecttheerrorinthekeratometricestimationofcornealpowerinnormaleyes.JCataractRefractSurg.2012;38(8):1333–8.

144. Zamora-Alejo K V, Moore SP, Parker DGA, Ullrich K, Esterman A, Goggin M.Objective accommodation measurement of the Crystalens HD compared tomonofocalintraocularlenses.JRefractSurg.2013;29(2):133–9.

145. Shammas HJ, Chan S. Precision of biometry, keratometry, and refractivemeasurementswith a partial coherence interferometry-keratometry device. JCataractRefractSurg.2010;36(9):1474–8.

146. HaigisW. TheHaigis formula. In: ShammasH, editor. Intraocular lens powercalculation.Slack.Thorofare,NJ;2004.p.41–57.

147. Stachs O, Schneider H, Stave J, Guthoff R. Potentially accommodatingintraocularlenses-Aninvitroandinvivostudyusingthree-dimensionalhigh-frequencyultrasound.JRefractSurg.2005;21:37–45.

148. Marchini G, Pedrotti E, Sartori P, Tosi R. Ultrasound biomicroscopic changesduring accommodation in eyeswith accommodating intraocular lenses: Pilotstudyandhypothesisforthemechanismofaccommodation.JCataractRefractSurg.2004;30(12):2476–82.

Capítulo6

Referencias

140

149. Koeppl C, Findl O, Menapace R, Kriechbaum K, Wirtitsch M, Buehl W, et al.Pilocarpine-induced shift of an accommodating intraocular lens: AT-45Crystalens.JCataractRefractSurg.2005;31(7):1290–7.

150. LiX-M,WangW.ToobserveclinicaleffectofaccommodativeIOLondifferentagepatients.ZhonghuaYanKeZaZhi.2008;44(1):30–2.

151. Ramón ML, Piñero DP, Blanes-Mompó FJ, Pérez-Cambrodí RJ. Clinical andquality of lifedata correlationwith a single-optic accommodating intraocularlens.JOptom.2013;6(1):25–35.

152. Alio JL, PineroDP,Plaza-PucheAB.Visual outcomes andoptical performancewith a monofocal intraocular lens and a new-generation single-opticaccommodating intraocular lens. J Cataract Refract Surg. 2010;36(10):1656–64.

153. Yuen L, Trattler W, Boxer Wachler BS. Two cases of Z syndrome with theCrystalens after uneventful cataract surgery. J Cataract Refract Surg.2008;34(11):1986–9.

154. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regressionformulas.JCataractRefractSurg.1993;19(6):700–12.

155. PiñeroDR,AyalaEspinosaMJ,AlióJL.LASIKoutcomesfollowingmultifocalandmonofocalintraocularlensimplantation.JRefractSurg.2010;26(8):569–77.

156. PiñeroD,AyalaEspinosaMJ,Alio JL.Reply: subjectiverefraction ineyeswithmultifocalIOLs.JRefractSurg.2011;27:161–2.

157. Van der Linden JW, Vrijman V, El-Saady R, van der Meulen IJ, Mourits MP,Lapid-Gortzak R. Autorefraction versus subjective refraction in a radiallyasymmetricmultifocalintraocularlens.ActaOphthalmologica.2014;

158. Langenbucher A, Janunts E, Seitz B, Kannengießer M, Eppig T. TheoreticalimageperformancewithcustomizedasphericandsphericalIOLs-whendoweget a benefit from customized aspheric design? ZMed Phys. 2014;24(2):94–103.

159. Fang Y, Lu Y, Miao A, Luo Y. Aspheric intraocular lenses implantation forcataractpatientswithextrememyopia.ISRNOpthalmol.2014;2014:403432.

160. Gonzalez-Martin-Moro J, Gonzalez-sanz F, Zarallo-Gallardo J, Cobo-Soriano R.Posterior capsule opacification, capsular bag distension syndrome, and

Capítulo6

Referencias

141

anterior capsular phimosis: A retrospective cohort study. Arch Soc EspOftalmol.2015;90:69–75.

161. EngrenAL,BehndigA.Anteriorchamberdepth, intraocular lensposition,andrefractive outcomes after cataract surgery. J Cataract Refract Surg.2013;39(4):572–7.

162. Norrby S. Sources of error in intraocular lens power calculation. J CataractRefractSurg.2008;34(3):368–76.

163. PreussnerPR,WahlJ,WeitzelD,BertholdS,KriechbaumK,FindlO.Predictingpostoperativeintraocular lenspositionandrefraction. JCataractRefractSurg.2004;30(10):2077–83.

164. FindlO,DrexlerW,MenapaceR,GeorgopoulosM,RainerG,HitzenbergerCK,etal.Changes in intraocular lenspositionafterneodymium:YAGcapsulotomy. JCataractRefractSurg.1999;25(5):659–62.

165. Jin H, Rabsilber T, Ehmer A, Borkenstein AF, Limberger IJ, Guo H, et al.Comparison of ray-tracing method and thin-lens formula in intraocular lenspowercalculations.JCataractRefractSurg.2009;35(4):650–62.

APÉNDICE

ARTICLE

Clinical validation of
an algorithm to correctthe error in the keratometric estimation
of corneal power in normal eyesDavid P. Pi~nero, PhD, Vicente J. Camps, PhD, Ver�onica Mateo, MSc, Pedro Ruiz-Fortes, OD

Q 2012 A

Published

SCRS an

by Elsev

PURPOSE: To validate clinically in a normal healthy population an algorithm to correct the error inthe keratometric estimation of corneal power based on the use of a variable keratometric index ofrefraction (nk).

SETTING: Medimar International Hospital (Oftalmar) and University of Alicante, Alicante, Spain.

DESIGN: Case series.

METHODS: Corneal power was measured with a Scheimpflug photography–based system (Penta-cam software version 1.14r01) in healthy eyes with no previous ocular surgery. In all cases,keratometric corneal power was also estimated using an adjusted value of nk that is dependenton the anterior corneal radius (r1c) as follows: nkadj Z �0.0064286 r1c C1.37688. Agreementbetween the Gaussian (Pc

Gauss) and adjusted keratometric (Pkadj) corneal power values wasevaluated.

RESULTS: The study evaluated 92 eyes (92 patients; age range 15 to 64 years). The mean differencebetween Pc

Gauss and Pkadj was �0.02 diopter (D)G 0.22 (SD) (PZ.43). A very strong, statisticallysignificant correlation was found between both corneal powers (r Z .994, P<.01). The rangeof agreement between Pc

Gauss and Pkadj was 0.44 D, with limits of agreement of �0.46 andC0.42 D. In addition, a very strong, statistically significant correlation of the difference betweenPc

Gauss and Pkadj and the posterior corneal radius was found (r Z 0.96, P<.01).

CONCLUSION: The imprecision in the calculation of corneal power using keratometric estimationcan be minimized in clinical practice by using a variable keratometric index that depends on theradius of the anterior corneal surface.

Financial Disclosure: No author has a financial or proprietary interest in any material or methodmentioned.

J Cataract Refract Surg 2012; 38:1333–1338 Q 2012 ASCRS and ESCRS

Accuratemeasurement of corneal power (Pc) in clinicalpractice is crucial because this parameter is used forseveral purposes, such as intraocular lens (IOL) powercalculation, contact lens management, and keratoco-nus diagnosis. However, the total Pc is usually calcu-lated considering only the radius of curvature of theanterior corneal surface measured using a keratometeror a topography system.1 This simplification arisesbecause in the past, it has been difficult to measurethe posterior corneal surface because of technologicallimitations. In addition, there was an assumptionthat this surface contributes little to the ocular refrac-tive power because of the small difference in therefractive index at this surface.1 In an attempt to mini-mize the error caused by this simplification, the

d ESCRS

ier Inc.145

keratometric index of refraction (nk) was defined.Themost commonly used approach in a clinical settingis to estimate Pc by considering only the radius ofcurvature of the anterior corneal surface and the nkvalue of 1.3375, which is used by most commerciallyavailable keratometers and topography systems. Aclear trend toward Pc overestimation has been re-ported with the estimation obtained with this specificvalue of nk.2–10 Several recalculations of nk have beenproposed to compensate for the keratometric Pc esti-mation error.2,3,5,6,9,11 However, differences betweenkeratometric and Gaussian corneal powers in normalhealthy populations have been reported even withthe use of some of these recalculations (Ho et al.,3 range�1.10 to 0.87 D; Fam and Lim,4 range�1.29 to 0.49 D).

0886-3350/$ - see front matter 1333doi:10.1016/j.jcrs.2012.03.026

http://dx.doi.org/10.1016/j.jcrs.2012.03.026

1334 ALGORITHM TO CORRECT KERATOMETRIC ERROR IN NORMAL EYES

Today, new advanced devices, such as the Scheimp-flug photography–based tomographers,12,13 are avail-able that allow clinicians to measure the anterior andposterior corneal surfaces simultaneously and reliably.These devices normally provide the true net power,which considers the real optical conditions of thecornea. Specifically, the true net power is calculatedusing the Gaussian equation and therefore consideringthe measured values of the anterior corneal radius ofcurvature (r1c), posterior corneal radius of curvature(r2c), central corneal thickness (ec), and conditionsof the Gullstrand eye model (corneal refractiveindex nc Z 1.376; aqueous humor refractive indexnha Z 1.336). Despite the adequacy of this approachfor Pc calculation, these devices are not alwaysavailable in clinical practice. For this reason, Pc estima-tions based on r1c only are commonly used. Ourresearch group recently proposed the use of a variablenk (nkadj) that depends on the radius of curvature ofthe anterior corneal surface.1 Specifically, the mostappropriate value of nk to use in each specific case isderived from a simple linear equation that requiresonly the r1c value in millimeters. This approachprovides Pc estimations differing from the Gaussiancalculation a maximum of 0.70 diopter (D) and lessthan 0.50 D in most of the probable combinations ofr1c and r2c.1

The aim of the current study was to clinicallyvalidate this algorithm based on the use of a variablenk developed to correct the error in the keratometricestimation of Pc in a normal healthy population.

PATIENTS AND METHODS

This study comprised candidates for corneal refractive sur-gery who were screened at the Department of Ophthalmol-ogy (Oftalmar) of the Medimar International Hospital,Alicante, Spain. For the study, 1 eye of each patient waschosen according to a random-number sequence (dichoto-mic sequence, 0 and 1). Eyes with active ocular pathologyor previous ocular surgery were excluded from the study.All patients were informed about the study and signed an

Submitted: December 19, 2011.Final revision submitted: February 15, 2012.Accepted: March 5, 2012.

From Grupo de �Optica y Percepci�on Visual (Pi~nero, Camps, Mateo),the Department of Optics, Pharmacology and Anatomy, Universityof Alicante, the Department of Ophthalmology, Oftalmar (Pi~nero,Ruiz-Fortes), Medimar International Hospital, and the Foundationfor the Visual Quality (Pi~nero), Alicante, Spain.

Corresponding author: David P. Pi~nero, PhD, Department of Optics,Pharmacology and Anatomy, University of Alicante, Carretera SanVicente del Raspeig s/n, 03690 San Vicente del Raspeig, Alicante,Spain. E-mail: [email protected].

J CATARACT REFRACT SURG -

146

informed consent document in accordance with the Declara-tion of Helsinki.

Clinical Evaluation

A comprehensive ophthalmologic examination was per-formed in all cases. It included refraction, corrected distancevisual acuity (CDVA), slitlamp biomicroscopy, Goldmanntonometry, fundus evaluation, and analysis of the cornealstructure using a Scheimpflug photography–based tomogra-pher (Pentacam system, software version 1.14r01, OculusOptikger€ate GmbH). Specifically, the following parameterswere recorded and analyzed: anterior corneal radius (r1c)and posterior corneal radius (r2c) in the central 3.0 mm cor-neal area; anterior corneal astigmatism (ACA) and posteriorcorneal astigmatism (PCA) in the central 3.0 mm cornealarea; the true net power, which is the Pc calculated usingthe Gaussian equation with the Gullstrand eye model(Pc

Gauss); anterior chamber depth (ACD), defined as the dis-tance from corneal epithelium to lens surface; and centralcorneal thickness (ec).

Scheimpflug System

The Pentacam is a noninvasive system for measuring andcharacterizing the anterior segment using a rotatingScheimpflug camera.12,13 The rotational measuring proce-dure generates Scheimpflug images in 3 dimensions, withthe dot matrix fine-meshed in the center due to the rotation.It takes a maximum of 2 seconds to generate a completeimage of the anterior eye segment. Any eye movement isdetected by a second camera and corrected for in the process.The system calculates a 3-dimensional model of the anterioreye segment from as many as 25 000 true elevation points.The Scheimpflug images taken during the examination aredigitized in the main unit, and all image data are transferredto a computer.

Correction of Keratometric Estimation Error

As previously stated, the use of a variable keratometricindex (nkadj) has been proposed for Pc calculation; the vari-able is dependent on the radius of the anterior corneal sur-face (r1c).1 Specifically, the following expression wasdefined assuming the ocular conditions of the Gullstrandeye model and the range of anterior and posterior curvaturefor the normal healthy population1:

nkadjZ � 0:0064286 r1c þ 1:37688 (1)

The Pc valuewas calculated considering nkadj to determinewhether it minimizes the error associated to the keratometricestimation of Pc (DPc) as follows:

PkadjZnkadj � 1

r1c(2)

The difference between Pkadj and the true net powerprovided directly by the Scheimpflug photography–basedsystem, which is the Pc derived from the Gaussian equation(Pc

Gauss), was calculated (DPc). The agreement between Pkadjand PGauss

c was carefully evaluated.

Statistical Analysis

Statistical analysis was performed using the SPSS forWindows software (version 19.0, SPSS, Inc.). Normality of

VOL 38, AUGUST 2012

mailto:[email protected]

1335ALGORITHM TO CORRECT KERATOMETRIC ERROR IN NORMAL EYES

data distributions was first evaluated using theKolmogorov-Smirnov test. Only the variables Pc

Gauss, Pkadj,DPc, and ec followed a normal distribution. Thus, parametricstatistics were applied for statistical analysis involving thesevariables. Specifically, the unpaired Student t test was usedfor comparing the 2 approaches for Pc calculation. Bland-Altman analysis14 was used to evaluate the interchangeabil-ity of the 2 methods used for obtaining Pc, the Gaussiancalculation (true net power), and the adjusted keratometricestimation. Specifically, Bland-Altman plots show the differ-ences between the methods evaluated plotted against themean of the 2 methods. The limits of agreement are definedas the mean G1.96 standard deviation (SD) of the differ-ences. Pearson or Spearman correlation coefficients, depend-ing on whether the normality condition could be assumed,were used to assess the correlation between DPc and allanalyzed parameters.

Figure 1. Relationship between the Gaussian corneal power (PcGauss)

and the adjusted keratometric corneal power (Pkadj).
RESULTS
This study comprised 92 eyes of 92 patients (47women[51.1%]) with a mean age was 36.7 years G 10.3 (SD)(range 15 to 64 years). The sample comprised 49 righteyes (53.3%). Table 1 shows the mean ocular featuresof the eyes evaluated.

Agreement of Pkadj and PGaussc

No statistically significant differences were foundbetween Pkadj and Pc

Gauss (true net power) (PZ.43,unpaired Student t test). A very strong, statisticallysignificant correlation was found between Pkadj andPc

Gauss (r Z 0.994, P!.01) (Figure 1). According tothe Bland and Altmanmethod, the range of agreementbetween Pkadj and Pc

Gauss was 0.44 D, with limits ofagreement of �0.46 and C0.42 D. Figure 2 shows theBland and Altman plot corresponding to this

Table 1. Mean ocular features.

Parameter Mean G SD Range

SE (D) �2.80 G 3.89 �15.75, C4.00r1c (mm) 7.67 G 0.01 7.19, 8.43r2c (mm) 6.30 G 0.21 5.87, 6.82ACA (D) 1.13 G 0.98 0.00, 5.80PCA (D) 0.36 G 0.24 0.00, 1.60PGaussC ðDÞ 42.76 G 1.30 38.80, 45.50Pkadj (D) 42.74 G 1.47 38.28, 45.99DPc (D) �0.02 G 0.22 �0.55, C0.52ACD (mm) 3.08 G 0.38 2.21, 4.96ec (mm) 559.0 G 33.8 485, 665

DPc Z difference between Pkadj and PGaussc ; ACAZ anterior corneal astig-matism; ACD Z anterior chamber depth; ec Z central corneal thickness;PCA Z posterior corneal astigmatism; PGaussc Z true net or Gaussianpower; Pkadj Z corneal power obtained using the adjusted keratometricindex; r1c Z radius of the anterior corneal surface; r2c Z radius of theposterior corneal surface; SE Z spherical equivalent


147

agreement analysis. There was a trend toward Pc over-estimation with the use of nkadj for steep corneas,whereas the opposite trend was present for flatcorneas; the trends were not clinically relevant.

Correlation of DPc with Other Clinical Variables

The correlations of DPc with several variables werepoor and not significant; the variables included age(r Z 0.13, PZ.21), spherical equivalent (r Z �0.045,PZ.67), CDVA (r Z 0.04, PZ.73), ACD (r Z �0.05,PZ.64), ec (r Z �0.09, PZ.41), ACA (r Z 0.07,

Figure 2. Differences between the adjusted keratometric cornealpower (Pkadj) and the Gaussian corneal power (Pc

Gauss) plottedagainst the mean value of both. The upper and the lower linesrepresent the limits of agreement calculated as mean of differencesG1.96 SD.

VOL 38, AUGUST 2012

Figure 3. Relationship of the difference (DPc) between the Gaussiancorneal power (Pc

Gauss) and the adjusted keratometric corneal power(Pkadj) with the radius of the posterior corneal surface (r2c). Theadjusting line to the data obtained by means of the least-squares fitis shown in the 2 graphs as follows:DPcZ 6.46� 1.03 r2c (R2Z 0.92).


PZ.52), and PCA (r Z 0.08, PZ.43). However, a verystrong, statistically significant correlation was foundbetween DPc and r2c (r Z �0.96, P!.01) (Figure 3).Furthermore, a statistically significant correlationwas found between DPc and r1c (r Z �0.79, P!.01),although the correlation was of less magnitude.

DISCUSSION

Numerous approaches for defining a keratometric in-dex (nk) have been developed, allowing the clinician toobtain an estimation of Pc by considering the cornea asa single refractive surface.2–4,9,11 The classic nk value of1.3375 was proposed for convenience rather than foroptical significance because it provided an agreementbetween a specific value of the anterior radius of cur-vature and the total Pc (7.5 mm and 45.0 D).10 Othernk values have been derived from schematic eyemodels, such as the value of 1.3315, whichwas derivedfrom the Gullstrand schematic eye and recommendedby Olsen.10 Several authors have provided other nkvalues obtained from normal and healthy populations.For example, Shammas et al.2 defined an effectiveindex of refraction closer to 1.329. Ho et al.3 obtaineda mean calculated nk of 1.328 G 0.0018 (range 1.3209to 1.3363) and propose using different nk valuesdepending on the corneal area analyzed (1.3278G 0.0027, 1.3284 G 0.0021, 1.3284 G 0.0031, 1.3280G 0.0038, and 1.3277 G 0.0042 for the central3.0 mm, 5.0 mm, 6.0 mm, 7.0 mm, and 7.5 mm zones,respectively). All these approaches attempted to


148

minimize the difference between the keratometricand Gaussian corneal power (DPc) using a single nkvalue with the SD or range as a general solution. How-ever, differences between keratometric and Gaussianpowers have been reported despite the use of someof the proposed nk values; some differences werehigher than 1.0 D.3,4 One factor accounting for this isthe incorrect assumption of a constant and linearrelationship1,4,5 between the curvature of the anteriorand the posterior corneal surface. The k ratio, whichis defined as the ratio of r1c to r2c, is not constant inthe range of curvatures of the normal healthy cornea,which range from 1.157 to 1.295.15–17

In a previous simulation study performed by ourresearch group using the Gullstrand and Le Grandeye models,1 we found that keratometric estimationcan significantly overestimate or underestimate theGaussian corneal power. This error (DPc) was foundto be dependent on both r1c and r2c, and therefore onthe k ratio.1 Corneal power overestimation wasalways found in both eye models when an nk valueof 1.3375 was used. These findings1 and those in previ-ous studies2–4 show there is a need for a precise modelto determine the most appropriate nk value forcalculating Pc with the keratometric approach. We de-veloped and reported a fast, easy, and clinicallyapplicable method for determining the most appropri-ate nk for the keratometric estimation in each specificcase.1 It uses a linear equation to determine nk (nkadj),which is dependent only on r1c, a parameter easilymeasurable in the clinical setting with a variety of de-vices. The maximum calculated error associated withthis approach (DPc) was 0.70 D, corresponding to the2 highest and 2 lowest r2c values of the range definedfor the normal and healthy population (5.5 mm,5.6 mm, 6.9 mm, and 7.0 mm). For the remaining r2cvalues, the error associated with the use of nkadj wasbelow 0.50 D, independent of the r1c value. The aimof the current study was to validate clinically the nkadjalgorithm developed to correct the error in thekeratometric estimation of Pc in a normal healthypopulation.

As expected, the corneal powers Pkadj and PcGauss

(true net power)were strongly correlated.Mean differ-ence between Pkadj and Pc

Gauss in the analyzed samplewas�0.02 D (range�0.55 toC0.52 D), confirming ourprevious theoretical results. This difference did notreach statistical significance, confirming the similarityof both Pc calculation methods. Differences up to0.50 D between Pkadj and Pc

Gauss might be consideredacceptable in clinical practice and thus not clinicallyrelevant. A variation of 0.50 D is equivalent to mini-mum differences in r1c (!0.1 mm), which are equiva-lent to or slightly higher than the curvature steps ofcurrently available contact lenses. In addition, an error

VOL 38, AUGUST 2012

1337ALGORITHM TO CORRECT KERATOMETRIC ERROR IN NORMAL EYES

of 0.50 D in Pc estimation induces errors in IOL powerestimation by only as much as 0.50 D at the cornealvertex according to optical simulations,1 which isthe minimum IOL power step provided by mostmanufacturers. Bland and Altman analysis14 con-firmed the clinical validity of the nkadj algorithm,with a range of agreement between Pkadj and Pc

Gauss

of 0.44 D. Therefore, 95% of differences between theGaussian and adjusted keratometric calculationswere 0.44 D or less. This excellent outcome confirmsthe interchangeability of the 2 approaches for calculat-ing Pc for clinical purposes.

The linear equation defining nkadj was obtained byconsidering the magnitude of DPc for all the combina-tions of r1c and r2c in the range of Pc in the normalhealthy population, including combinations of flatanterior and steep posterior corneal curvatures andvice versa. This is the reason for the trend observedin the Bland and Altman plot toward Pc overestima-tion by using nkadj for steep corneas and the oppositetrend for flat corneas. The curvature of both cornealsurfaces is correlated in normal eyes18,19; therefore, ifthe anterior corneal surface is steep, the posterior isalso expected to be steep. This potential correlationwas not considered in the definition of the nkadjalgorithm. In concordance with this, DPc was foundto be strongly correlated with r2c (r Z 0.96). In anycase, these trends toward Pc overestimation for steepcorneas and underestimation for flat corneas werenot clinically relevant. Indeed, the range of agreementbetween Pkadj and Pc

Gauss was 0.44 D. All these find-ings confirm the relevance of the curvature of theposterior corneal surface in the error of the keratomet-ric estimation, even minimizing it by consideringa variable nk (nkadj).

In summary, the imprecision in the calculation ofPc with keratometric estimation can be minimizedin clinical practice by using a variable keratometricindex that depends on the radius of the anteriorcorneal surface. This approach is valid only whenthe curvature of the posterior corneal surface is notavailable clinically because the best option is to calcu-late the Gaussian corneal power considering thecurvature of both corneal surfaces. The potentialimprovement of our algorithm, including the profileof correlation between anterior and posterior cornealcurvature, should be evaluated. In addition, futurestudies evaluating the impact of posterior corneal sur-face changes after different types of corneal surgeryon the keratometric estimation should be evaluatedto confirm the inadequacy of using such simplifica-tion in these cases. In addition, the potential benefitof using this algorithm in IOL power calculationto optimize the refractive outcomes should beevaluated.

J CATARACT REFRACT SURG - V

149

WHAT WAS KNOWN

� A clear trend toward corneal power overestimation hasbeen reported with the estimation obtained with thekeratometric refractive index of 1.3375.

� Theoretical simulations have demonstrated that this over-estimation can be minimized by using a linear adjustmentbased on the curvature of the anterior corneal surface.

WHAT THIS PAPER ADDS

� The imprecision in the calculation of corneal power usingthe keratometric estimation in normal healthy eyes can beminimized in the clinical practice by using a variablekeratometric index that depends on the radius of theanterior corneal surface, with a level of agreement withthe Gaussian corneal power below 0.50 D.

REFERENCES1. Camps V, Pi~nero Llorens DP, de Fez D, Coloma P,

Caballero MT, Garc�ıa C, Miret JJ. Algorithm for correcting the

keratometric estimation error in normal eyes. Optom Vis Sci

2012; 89:221–228

2. ShammasHJ, Hoffer KJ, ShammasMC. Scheimpflug photogra-

phy keratometry readings for routine intraocular lens power

calculation. J Cataract Refract Surg 2009; 35:330–334

3. Ho J-D, Tsai C-Y, Tsai RJ-F, Kuo L-L, Tsai I-L, Liou S-W.

Validity of the keratometric index: evaluation by the Pentacam

rotating Scheimpflug camera. J Cataract Refract Surg 2008;

34:137–145

4. Fam H-B, Lim K-L. Validity of the keratometric index: large

population-based study. J Cataract Refract Surg 2007;

33:686–691

5. Borasio E, Stevens J, Smith GT. Estimation of true corneal

power after keratorefractive surgery in eyes requiring cataract

surgery: BESSt formula. J Cataract Refract Surg 2006;

32:2004–2014

6. Tang M, Li Y, Avila M, Huang D. Measuring total corneal power

before and after laser in situ keratomileusis with high-speed

optical coherence tomography. J Cataract Refract Surg 2006;

32:1843–1850

7. Canarim de Oliveira �EC, Arce CG, Campos M, Schor PO.

O c�alculo do poder das lentes intra-oculares e o Orbscan-II.

Parte 1: o poder �optico da c�ornea normal [Power calculation of

intraocular lenses and the Orbscan-II. Part 1: The power of the

normal cornea]. Arq Br�as Oftalmol 2003; 66:567–574. Available

at: http://www.scielo.br/pdf/abo/v66n5/18141.pdf. Accessed

April 14, 2012

8. Espinosa J, Rouarch J, P�erez J, Illueca C, Mas D. Geometrical

approximations for accurate evaluation of refraction in the

human cornea. Optik 2007; 118:209–215

9. Gobbi PG, Carones F, Brancato R. Keratometric index, video-

keratography, and refractive surgery. J Cataract Refract Surg

1998; 24:202–211

10. OlsenT.On the calculation of power fromcurvature of the cornea.

Br JOphthalmol 1986; 70:152–154. Available at: http://www.ncbi.

nlm.nih.gov/pmc/articles/PMC1040942/pdf/brjopthal00624-0073.

pdf. Accessed April 14, 2012

OL 38, AUGUST 2012

http://www.scielo.br/pdf/abo/v66n5/18141.pdf

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1040942/pdf/brjopthal00624-0073.pdf




11. Dunne MCM, Royston JM, Barnes DA. Normal variations of the

posterior corneal surface. Acta Ophthalmol (Copenh) 1992;

70:255–261

12. Shankar H, Taranath D, Santhirathelagan CT, Pesudovs K.

Anterior segment biometry with the Pentacam: comprehensive

assessment of repeatability of automated measurements.

J Cataract Refract Surg 2008; 34:103–113

13. Pi~nero DP, Saenz Gonz�alez C, Ali�o JL. Intraobserver and

interobserver repeatability of curvature and aberrometric

measurements of the posterior corneal surface in normal eyes

using Scheimpflug photography. J Cataract Refract Surg

2009; 35:113–120

14. Bland JM, Altman DG. Statistical methods for assessing

agreement between two methods of clinical measurement.

Lancet 1986; 1:307–310. Available at: http://www-users.york.

ac.uk/wmb55/meas/ba.pdf. Accessed April 14, 2012

15. Edmund C. Posterior corneal curvature and its influence on

corneal dioptric power. Acta Ophthalmol (Copenh) 1994;

72:715–720

16. Royston JM, Dunne MCM, Barnes DA. Measurement of

posterior corneal surface toricity. Optom Vis Sci 1990;

67:757–763


150

17. Royston JM, Dunne MCM, Barnes DA. Measurement of the

posterior corneal radius using slit lamp and Purkinje image

techniques. Ophthalmic Physiol Opt 1990; 10:385–388

18. Pi~nero DP, Ali�o JL, Ales�on A, Escaf Vergara M, Miranda M.

Corneal volume, pachymetry, and correlation of anterior and

posterior corneal shape in subclinical and different stages of

clinical keratoconus. J Cataract Refract Surg 2010; 36:814–825

19. Mas D, Espinosa J, Domenech B, Perez J, Kasprzak H,

Illueca C. Correlation between the dioptric power, astigmatism

and surface shape of the anterior and posterior corneal surfaces.

Ophthalmic Physiol Opt 2009; 29:219–226

VOL
38, AUGUST 2012
First author:David P. Pi~nero, PhD

Department of Optics, Pharmacologyand Anatomy, University of Alicante,Alicante, Spain

http://www-users.york.ac.uk/%7Emb55/meas/ba.pdf

http://www-users.york.ac.uk/%7Emb55/meas/ba.pdf

Minimizing the IOL Power Error Induced byKeratometric Power

Vicente J. Camps*, David P. Pinero*, Dolores de Fez*, and Veronica Mateo†

ABSTRACTPurpose. To evaluate theoretically in normal eyes the influence on IOL power (PIOL) calculation of the use of a keratometricindex (nk) and to analyze and validate preliminarily the use of an adjusted keratometric index (nkadj) in the IOL powercalculation (PIOLadj).Methods. A model of variable keratometric index (nkadj) for corneal power calculation (Pc) was used for IOL power cal-culation (named PIOLadj). Theoretical differences ($PIOL) between the new proposed formula (PIOLadj) and which is obtainedthrough Gaussian optics (PIOL

Gauss) were determined using Gullstrand and Le Grand eye models. The proposed new formula for IOLpower calculation (PIOLadj) was prevalidated clinically in 81 eyes of 81 candidates for corneal refractive surgery and compared withHaigis, HofferQ, Holladay, and SRK/T formulas.Results. A theoretical PIOL underestimation greater than 0.5 diopters was present in most of the cases when nk = 1.3375 wasused. If nkadj was used for Pc calculation, a maximal calculated error in $PIOL of T0.5 diopters at corneal vertex in most caseswas observed independently from the eye model, r1c, and the desired postoperative refraction. The use of nkadj in IOL powercalculation (PIOLadj) could be valid with effective lens position optimization nondependent of the corneal power.Conclusions. The use of a single value of nk for Pc calculation can lead to significant errors in PIOL calculation that mayexplain some IOL power overestimations with conventional formulas. These inaccuracies can be minimized by using thenew PIOLadj based on the algorithm of nkadj.(Optom Vis Sci 2013;90:639Y649)

Key Words: intraocular lens, IOL power, IOL power calculation, HofferQ, Holladay, Haigis, SRK-T

Unsatisfactory visual outcomes after cataract surgery as aresult of a residual refractive error can be obtained be-cause of inaccuracies in biometric analysis,1 inadequate

calculation and selection of the intraocular lens (IOL) power,1 orlongitudinal IOL positional errors.2 Some studies have evidencedthat some errors are still possible in the calculation of the IOLpower (PIOL) for a normal eye (no pathology or previous ocularsurgeries) despite the technological diagnostic advances and thelatest formulas developed for PIOL calculation.3 The most im-portant sources of these errors are the axial length (AL), the ef-fective lens position (ELP), and the corneal power (Pc).

3

An accurate calculation of the corneal optical power is crucialfor an optimized IOL power calculation. It is even relevant for theprediction of the ELP in some of the third- and fourth-generationformulas.3 In clinical practice, total corneal power is still calcu-lated only considering the radius of curvature of the anteriorcorneal surface measured by means of a keratometer or a topog-raphy system. Specifically, the cornea is assumed to have a singlespherical surface with the radius of curvature of the epithelialsurface and an adjusted index of refraction, the keratometric in-dex (nk), providing a correction for such simplification. Severalauthors have analyzed such simplification, some of them reveal-ing that the keratometric corneal power (Pk) can lead to an over-estimation of the corneal optical power.4Y6

Different values of nk have been defined as useful for PIOL

calculations, such as the value of 1.3315 described by Olsen,7

the value of 4/3 described by Holladay,8 or the value of 1.333used in the SRK/T formula.9 Other authors have also performedrecalculations of the nk with the aim of defining a more accu-rate approach to overcome the errors introduced by the cor-neal keratometric power.6,10,11 Our research group has recently

1040-5488/13/9007-0639/0 VOL. 90, NO. 7, PP. 639Y649

OPTOMETRY AND VISION SCIENCE

Copyright * 2013 American Academy of Optometry

ORIGINAL ARTICLE

Optometry and Vision Science, Vol. 90, No. 7, July 2013

*PhD†MSc

Grupo de Optica y Percepcion Visual, Department of Optics, Pharmacology

and Anatomy, University of Alicante, Alicante, Spain (VJC, DPP, DdF, VM); and

Foundation for the Visual Quality (Fundacion para la Calidad Visual-FUNCAVIS),

Alicante, Spain (DPP).

151

proposed the use of a variable nk for normal and nonpathologicalpopulations, depending on the radius of curvature of the anteriorcorneal surface.4,5 Specifically, the most appropriate value of nk touse in each specific case is derived from a simple linear equationonly requiring the anterior corneal radius (r1c) in millimeters andwith a maximal associated error in the calculation of the cornealpower of 0.5 diopters (D).4 These theoretical results were vali-dated clinically.5

The aim of the current study was to evaluate in a normalpopulation (no pathology and previous ocular surgeries) thetheoretical influence on IOL power (PIOL) calculation of the errorin the calculation of corneal power ($Pc) caused by the use of thekeratometric index (nk) and to develop and validate preliminarilyan algorithm to avoid this influence.

METHODS

Corneal power was calculated for the range of anterior andposterior curvatures of the healthy cornea according to the peer-reviewed literature by using nk and also by using the Gaussianequation that considers the contribution of two corneal surfaces.The nk values corresponding to the Gullstrand12 and Le Grandeye13,14 models (1.3315 and 1.3304, respectively) and the clas-sical value of 1.3375 were used. Differences in the IOL powercalculation obtained with a simplified formula using the ker-atometric and Gaussian corneal power were determined andmodeled by regression analysis. All calculations and simula-tions were performed by Matlab software (MathWorks Inc.,Natick, MA).

Calculation of the Gaussian and Keratometric IOLPower

The starting point of almost all theoretical formulas for IOLpower calculation is the classical vergence equation based on theuse of a simplified eye model, with thin cornea and lens models.3

According to such scheme, the power of the IOL (PIOL) thatreplaces the lens can be easily calculated using the Gauss equationsin paraxial optics:

PIOL ¼ nhvðALjELPÞj

nhanha

Rdes þ PcjELP

� � ð1Þ

The first term after the equal sign is an expression for the vergencethat must leave the effective lens position (ELP) to focus on theretina. The second term is the vergence arriving at the ELP, sothe difference between those two yields is the required power ofthe IOL. In this equation, Pc represents the total corneal power,ELP, the effective lens position, AL, the axial length, nha, theaqueous humor refractive index, nhv, the vitreous humor refractiveindex, and Rdes represents the postoperative desired refraction cal-culated at corneal vertex.

The IOL power when a keratometric corneal power (Pk) wasused for its estimation was defined as Pk

IOL and the IOL powerwhen a Gaussian corneal power P c

Gauss was used as defined asP IOL

Gauss. The calculation of Pk and P cGauss was described in detail in

a previous article of our research group.4 The calculation of P kIOL

and P IOLGauss was performed as follows:

PkIOL ¼

nhvALjELF

jnha

nha

Rdes þ nkj1

r1c

jELPð2Þ

PGaussIOL ¼

nhvALjELP

� nhanha

Rdes þ ncjna

r1cþ nhajnc

r2cj

ec

ncqncjna

r1cqnhajnc

r2c

� �jELPð3Þ

It is important to note here that in equations 2 and 3, thecorneal power is referenced from different planes because of theone-surface and two-surface corneal models considered. However,the secondary principle plane for corneas in the normal range isonly around a fraction of millimeter from the corneal vertex.Therefore, the use of these relatively different reference planes inequations 2 and 3 could not introduce any significant bias in thecalculations proposed. For example, in the complete Le Grand eyemodel, a distance of only 0.06 mm is present between the sec-ondary principle plane and the corneal vertex.13

We defined the k ratio as the relation between the anteriorcorneal radius and the posterior corneal radius (k = r1c/r2c). Whenthis parameter was used in equation 3, we obtained the followingexpression:

PGaussIOL ¼

nhvALjELP

jnha

Rdes þ ncjna

r1cþ nhajnc

r1ck

jec

ncqncjna

r1cqnhajnc

r1ck

0@

1A

jELP ð4Þ

In all these expressions, nk is the keratometric index, r1c, theanterior corneal surface radius, r2c, the posterior corneal radius, na

is the refractive index of air, nc, the refractive index of the cornea,nha, the refractive index of the aqueous humor, and ec is the centralcorneal thickness.

Difference between the Gaussian and KeratometricIOL Power

The difference between the keratometric and Gaussian IOLpower calculation ($PIOL) was obtained by using equations 2 and4 as follows:

$PIOL ¼ PkIOLjPGauss

IOL ¼nha

nha

Rdes þ ncjna

r1cþ nhajnc

r2cj

ec

ncqncjna

r1cqnhajnc

r2c

� �jELP

jnha

nha

Rdes þ nkj1

r1c

jELPð5Þ

If the k ratio was used in equation 5, we obtained the followingexpression:

$PIOL ¼ nhanha

Rdes þ ncjna

r1cþ nhajnc

r1c

k

jec

ncqncjna

r1cqnhajnc

r1c

k

0BBB@

1CCCA

jELPj

nhanha

Rdesþnkj1

r1c

jELPð6Þ

As can be seen in equations 5 and 6, $PIOL was not depen-dent on AL.

640 Minimizing IOL Power Error Induced by Keratometric PowerVCamps et al.


152

The $PIOL was calculated for the range of corneal curvatureof the normal population. According to the peer-reviewedliterature,4,6,10,15Y19 we considered that the anterior corneal ra-dius in the healthy normal population ranged between 7 and8.5 mm, whereas the posterior corneal radius ranged between 5.6and 7 mm. Therefore, we assumed k ratio values ranging from 1 to1.51 in our theoretical calculations. In addition, we considered inthe calculations performed in the current study that ELP could varybetween 2 and 6 mm according to previous authors dealing with thisissue.3,20,21 The desired postoperative refraction was also varied inthe calculations, performing an analysis of $PIOL for values of Rdes

of 0, +1, and j1 D.

Difference between the Gaussian and KeratometricIOL Power Using the Adjusted Keratometric Index

As previously commented, our research group recently pro-posed the use of a variable keratometric index (nkadj) depending onthe radius of the anterior corneal surface (r1c) expressed in mil-limeters for corneal power calculations.4 Specifically, two differentexpressions were defined depending on the eye model used:

Gullstrand eye model; nkadj ¼ j0:0064286 r1c

þ 1:37688ð7Þ

Le Grand eye model; nkadj ¼ j0:0063804 r1cþ1:37806

ð8Þ

Using these algorithms, a new keratometric corneal power(named adjusted keratometric corneal power, Pkadj) can be cal-culated using the classical keratometric corneal power formula.4

Therefore, PIOLadj was defined as the IOL power calculated fromequation 2 using the nkadj value for the estimation of the cornealpower (Pkadj). After that, $PIOL was also calculated consideringthe adjusted IOL power (PIOLadj) and the Gaussian IOL powerðPGauss

IOL ).

Preliminary Clinical Validation

A preliminary validation of the IOL power calculation with thealgorithm proposed in this study was performed in a sample ofnormal eyes with AL between 22 and 26 mm to avoid in thispreliminary study the inclusion of highly myopic or hyperopiceyes. Specifically, 81 eyes of 81 candidates for corneal refractivesurgery who were screened at the Department of Ophthalmology(Oftalmar) of the Medimar International Hospital (Alicante,Spain) were included. Only one eye from each subject was chosenrandomly for the study according to a random number sequence(dichotomic sequence, 0 and 1). Eyes with active ocular pathol-ogies or previous ocular surgeries were excluded from the study.This clinical study was approved by the local ethics committee andhas therefore been performed in accordance with the ethicalstandards laid down in the 1964 Declaration of Helsinki. Writteninformed consent was obtained after explaining the nature of theprocedure before surgery in all cases.

A comprehensive ophthalmologic examination was performedin all cases, which included optical biometry (IOLMaster, Carl ZeissMeditec) and analysis of the corneal structure by means of aScheimpflug photographyYbased tomographer, the Pentacam system(software version 1.14r01, Oculus Optikgerate GmbH, Germany).

Intraocular lens power calculation was performed with the IOL-Master software using the SRK/T, Haigis, HofferQ, and Holladayformulas and also with our paraxial approximation using the nkadj

(PIOLadj). All calculations in all formulas were performed for only onesimulated IOL type with an A-constant of 118.0. A comparativeanalysis of our estimations with those obtained with the otherestablished formulas was performed by using the statistical softwareSPSS version 19.0 for Windows (IBM, Armonk, NY). Normality ofdata distributions was first evaluated by means of the Kolmogorov-Smirnov test. The unpaired Student t test was used for analyzingthe statistical significance of differences between IOL power calcu-lations, whereas the Bland-Altman method was used for evaluatingthe interchangeability of such calculations. In the Bland-Altmananalysis, differences between the different formulas evaluated in theIOL power to implant were considered as clinically relevant forvalues of more than 0.5 D because this value is the IOL power stepprovided currently by most manufacturers and has been shown to bethe optical neutralization tolerance since many years ago.13 Besidesall these analyses, Pearson correlation coefficients were used to assessthe correlation between differences among calculations and differentclinical parameters. Finally, it should be considered that the calcu-lations with our algorithm were performed using the values of ELPobtained with the estimation equations defined by the authors de-veloping each of the formulas used (Haigis, HofferQ, SRK/T, andHolladay).20,22,23

RESULTS

Relationship between $PIOL and $Pc

Table 1 summarizes the $PIOL outcomes obtained within thenormal range of anterior corneal curvature (r1c, from 7 to 8.5 mm)for each eye model and for the different nk values used. The in-terval shown for each value of $PIOL and $Pc corresponded to thevalues associated to the extreme values of the normality rangedefined for r2c, from 5.6 to 7 mm.

As shown in Table 1, there was an underestimation of the IOLpower by P k

IOL with respect to P GaussIOL ($PIOL 90) provided that

an overestimation of the corneal power was present and vice versa. Inboth theoretical eyes models, overestimations and underestimationsof IOL power were possible depending on the multiple combina-tions of r1c and r2c, although more underestimations were presentwith the Gullstrand eye model. Overestimations of IOL power byP k

IOL with respect to P GaussIOL higher than 0.5 D were present in

the Le Grand eye model (nk = 1.3304) from r1c =7 mm combinedwith r2c Z[6.2, 7] mm to r1c = 7.8 mm with r2c = 7 mm and in theGullstrand eye model (nk = 1.3315) from r1c = 7 mm combined withr2c Z[6.6, 7] mm to r1c = 7.40 mm with r2c = 7 mm. The highestoverestimation value was always found for the combination ofr1c = 7 mm with r2c = 7 mm (unlikely corneal curvature combi-nation), with values of +1.41 and +0.95 D for the Le Grand andGullstrand eye models, respectively. The higher underestimationswere found for r1c = 8.5 mm combined with r2c Z[5.60, 6.60] mmand for r1c = 8.5 mm combined with r2cZ[5.60, 6.90] for Le Grandand Gullstrand eye models, respectively. The highest underesti-mation value was found for the combination of r1c = 8.5 mm andr2c = 5.6 mm for both eye models, with values ofj1.76 andj2.16 Dfor the Le Grand and Gullstrand eye models, respectively.

Minimizing IOL Power Error Induced by Keratometric PowerVCamps et al. 641


153

When nk = 1.3375 was used in both models, an underestimationof IOL power by P k

IOL with respect to P GaussIOL was almost always

observed. The magnitude of this underestimation was higher than0.5 D in almost all possible combinations of r1c and r2c. Themaximum underestimation was again found for the combination ofr1c = 8.5 mm with r2c = 5.6 mm, with values ofj3.01 andj2.77 Dfor Gullstrand and Le Grand eye models, respectively. It should beremarked that differences in $PIOL values between the two eyemodels used in the current study were below or equal to 0.27 D ifnk = 1.3375 was used and below or equal to 0.48 D if the theoreticalnk values (1.3304 and 1.3315) were used.

All these trends for $PIOL were modeled by means of linear re-gression analysis. Specifically, predictive linear equations (R2 = 0.99)relating $PIOL and k ratio as a function of r1c in 0.1-mm steps werefound for the two eye models used in this study (Tables 2, 3).Likewise, $PIOL data could also be adjusted by a quadratic ex-pression (R2 = 0.99) dependent on r2c (Fig. 1). As example, $PIOL

data corresponding to r1c = 8.5 mm using the Gullstrand eye modelwith nk = 1.3375 could be adjusted to the quadratic expression$PIOL = j0.188464 r 2

2c + 3.577053r2c + 17.130125, where r2c

is expressed in millimeters (Fig. 1). The equivalent equation de-pending on k was $PIOL = j5.566861Ik + 5.436452 (Table 2).

Relationship between $PIOL and ELP

A comparative analysis of $PIOL variation with the value of$PIOL obtained for the ELP values coincident with the anatomicalACD (ACDa) of the two eye models used in this study (3.05 and3.10 mm for Le Grand and Gullstrand eye models) was performed

considering a range of variation of ELP between 2 and 6 mm aswell as no variation in the rest of parameters. Differences in $PIOL

calculation did not become clinically significant because of ELP

TABLE 1.

Summary of the differences between the keratometric andGaussian IOL ($PIOL) obtainedwithin the normal range of anteriorcorneal curvature (r1c, from 7 to 8.5 mm) for the Le Grand and Gullstrand eye models as well as for the different nk valuesused (1.3304, 1.3315, and 1.3375)

Comparative $PIOL and $Pc

Le Grand Gullstrand

nk: 1.3304 nk: 1.3375 nk: 1.3315 nk: 1.3375

r1c, mm $Pc, D $PIOL, D $Pc, D $PIOL, D $Pc, D $PIOL, D $Pc, D $PIOL, D

7.00 0.26; j1.12 j0.33; 1.41 1.28; j0.11 j1.61; 0.14 0.65; j0.75 j0.81; 0.95 1.50; 0.10 j1.90; j0.137.10 0.36; j1.03 j0.45; 1.29 1.36; j0.03 j1.71; 0.03 0.74; j0.66 j0.93; 0.84 1.58; 0.18 j1.99; j0.237.20 0.45; j0.93 j0.57; 1.17 1.44; 0.05 j1.80; j0.07 0.83; j0.57 j1.03; 0.72 1.66; 0.26 j2.08; j0.327.30 0.55; j0.84 j0.68; 1.05 1.52; 0.13 j1.89; j0.16 0.91; j0.49 j1.14; 0.61 1.73; 0.33 j2.17; j0.427.40 0.63; j0.75 j0.78; 0.94 1.59; 0.20 j1.98; j0.25 1.00; j0.40 j1.24; 0.50 1.81; 0.41 j2.25; j0.517.50 0.72; j0.67 j0.89; 0.83 1.67; 0.28 j2.06; j0.34 1.08; j0.32 j1.34; 0.40 1.88; 0.48 j2.33; j0.597.60 0.80; j0.59 j0.99; 0.72 1.74; 0.35 j2.14; j0.43 1.16; j0.24 j1.43; 0.30 1.95; 0.55 j2.41; j0.687.70 0.89; j0.50 j1.09; 0.62 1.81; 0.42 j2.22; j0.51 1.24; j0.17 j1.52; 0.20 2.02; 0.61 j2.49; j0.767.80 0.96; j0.42 j1.18; 0.52 1.87; 0.48 j2.30; j0.60 1.31; j0.09 j1.61; 0.11 2.08; 0.68 j2.56; j0.847.90 1.04; j0.35 j1.27; 0.43 1.94; 0.55 j2.37; j0.67 1.39; j0.02 j1.70; 0.02 2.15; 0.74 j2.63; j0.918.00 1.12; j0.27 j1.36; 0.33 2.01; 0.61 j2.44; j0.75 1.46; 0.05 j1.78; j0.07 2.21; 0.80 j2.70; j0.998.10 1.19; j0.20 j1.44; 0.24 2.07; 0.68 j2.51; j0.82 1.53; 0.12 j1.86; j0.15 2.27; 0.86 j2.76; j1.068.20 1.26; j0.13 j1.53; 0.15 2.13; 0.74 j2.58; j0.90 1.60; 0.19 j1.94; j0.23 2.33; 0.92 j2.83; j1.138.30 1.33; j0.06 j1.61; 0.07 2.19; 0.80 j2.64; j0.97 1.66; 0.26 j2.01; j0.31 2.39; 0.98 j2.89; j1.198.40 1.40; 0.01 j1.69; j0.01 2.25; 0.85 j2.71; j1.03 1.73; 0 .32 j2.09; j0.39 2.44; 1.04 j2.95; j1.268.50 1.47; 0.08 j1.76; j0.09 2.30; 0.91 j2.77; j1.10 1.79; 0.39 j2.16; j0.47 2.50; 1.09 j3.01; j1.32

The interval shown for each value of r1c is the maximum and minimum values of $Pc and $PIOL corresponded to the values associatedwith the extreme values of the normality range defined for r2c, from 5.6 to 7 mm are also shown.

TABLE 2.

Linear equations (all R2 = 0.99) relating $PIOL and k ratioas a function of r1c in 0.1-mm steps using the Gullstrandeye model

nk = 1.3315 nk = 1.3375

r1c, mm $PIOL, D = a k + b $PIOL, D = a k + b

7.00 $PIOL = j7.07 k + 8.03 $PIOL = j7.07 k + 6.947.10 $PIOL = j6.95 k + 7.88 $PIOL = j6.95 k + 6.827.20 $PIOL = j6.83 k + 7.74 $PIOL = j6.83 k + 6.707.30 $PIOL = j6.71 k + 7.61 $PIOL = j6.71 k + 6.587.40 $PIOL = j6.60 k + 7.48 $PIOL = j6.60 k + 6.477.50 $PIOL = j6.49 k + 7.35 $PIOL = j6.49 k + 6.367.60 $PIOL = j6.38 k+ 7.23 $PIOL = j6.38 k + 6.257.70 $PIOL = j6.28 k + 7.11 $PIOL = j6.28 k + 6.157.80 $PIOL = j6.18 k + 7.00 $PIOL = j6.18 k + 6.057.90 $PIOL = j6.09 k + 6.89 $PIOL = j6.09 k + 5.958.00 $PIOL = j5.99 k + 6.78 $PIOL = j5.99 k + 5.868.10 $PIOL = j5.90 k + 6.68 $PIOL = j5.90 k + 5.778.20 $PIOL = j5.81 k + 6.58 $PIOL = j5.81 k + 5.688.30 $PIOL = j5.73 k + 6.48 $PIOL = j5.73 k + 5.608.40 $PIOL = j5.65 k + 6.38 $PIOL = j5.65 k + 5.528.50 $PIOL = j5.57 k + 6.29 $PIOL = j5.57 k + 5.44

The linear adjustment for the keratometric indexes of 1.3315 and1.3375 and for the range of normality defined for r1c is shown.



154

changes in such conditions. The highest variation was found forELP = 6 mm, and it did not exceed more than 0.48 D in com-parison with the value obtained with the eye model ACDa.

Relationship between $PIOL and Rdes

For a range of Rdes between j1 and +1 D and considering theother parameters constant, the variation of $PIOL was not of morethan 0.02 D in comparison with the values obtained for Rdes = 0 Din any of the conditions simulated.

$PIOL Using nkadj for Minimizing $PC

If nkadj derived from equations 7 and 8 was used for the cal-culation of keratometric corneal power and then PIOLadj wascalculated, a maximal error of T0.9 D in $PIOL was observedindependently from the eye model used, r1c and Rdes (Fig. 2A, B).Considering that 1 D of variation of PIOL induced approximately0.9 D of change in subjects’ refraction at the corneal vertex,$PIOL obtained with the nkadj simulations did not exceed T0.60or T0.50 D at the corneal vertex for a range of r2c between 5.8 and6.7 mm (almost all the normality range for this parameter). Theanalysis of the effect on PIOL calculation when the nkadj was usedon the variation of ELP was also performed. For ELP values

higher than 4 mm, the range of r2c associated with $PIOL notexceeding T0.5 D at the corneal vertex was somewhat more re-duced, including the values between 5.9 and 6.6 mm.

Preliminary Clinical Validation

Table 4 summarizes the results of the comparative analysis ofthe IOL power obtained with different standard formulas andwith our optimized algorithm in a clinical population. As shown,clinically relevant and statistically significant differences betweenthe result obtained with our formula (PIOLadj) and the IOL powervalues obtained with the SRK/T (PIOLSRK/T), Haigis (PIOLHaigis),Holladay (PIOLHolladay), and HofferQ (PIOLHofferQ) formulas werefound. The Bland-Altman plots show these clinically relevantdifferences in Fig. 3A to D. These differences were positive inmost cases and, therefore, the PIOL obtained with our formula washigher than that obtained with the other standard IOL powercalculation formulas. In addition, clinically relevant differenceswere found between most of the standard formulas used for thecurrent comparative analysis, as shown in Bland-Altman plots ofFig. 4A to F.

The difference between PIOLadj and PIOLSRK/T was found tocorrelate significantly with the Gaussian corneal power (r = j0.81,p G 0.01), r2c (r = 0.81, p G 0.01), the difference between the

FIGURE 1.$PIOL data using the Gullstrand eye model with nk=1.3375 corresponding to three values of r1c (7, 7.70, and 8.5 mm) adjusted to quadratic expressionsdependent on r2c (R

2 = 0.99).



155

corneal power obtained with the adjusted keratometric indexand the keratometric power (nk = 1.3375) (r = 0.81, p G 0.01), ELP(r =j0.46, p G 0.01), and r1c (r = 0.81, p G 0.01). A similar trend wasobserved for the difference between PIOLadj and PIOLHaigis thatcorrelated significantly with the Gaussian corneal power (r =0.j75, p G 0.01), r2c (r = 0.54, p G 0.01), the difference betweenthe corneal power obtained with the adjusted keratometric indexand the keratometric power (nk = 1.3375) (r = 0.75, p G 0.01), andr1c (r = 0.75, p G 0.01). In contrast, the difference between PIOLadj

and PIOLHofferQ correlated significantly with AL (r = 0.97, pG0.01)and ELP (r = 0.99, p G 0.01). Regarding the difference betweenPIOLadj and PIOLHolladay, it correlated significantly with the Gaussiancorneal power (r = j0.25, p = 0.02), the difference between thecorneal power obtained with the adjusted keratometric index andthe keratometric power (nk = 1.3375) (r = 0.25, p = 0.02),ELP (r = 0.64, p G 0.01), and r1c (r = 0.26, p = 0.02).

DISCUSSION

In the current study, we have observed in a theoretical simu-lation considering the range of corneal curvature of the normalhealthy population that the use of a nonoptimized nk for corneal

FIGURE 2.Comparison ofPIOL fornk = 1.3375andnkadj with P Gauss

IOL in the range of normality corresponding to r2c and for a) r1c = 7 mm and b) r1c = 8.5 mm.

TABLE 3.

Linear equations (all R2 = 0.99) relating $PIOL and k ratio as afunction of r1c in 0.1-mm steps using the Le Grand eye model

nk = 1.3304 nk = 1.3375

r1c, mm $PIOL, D = a k + b $PIOL, D = a k + b

7.00 $PIOL = j6.98 k + 8.40 $PIOL = j6.98 k + 7.127.10 $PIOL = j6.86 k + 8.25 $PIOL = j6.86 k + 6.997.20 $PIOL = j6.74 k + 8.10 $PIOL = j6.74 k + 6.877.30 $PIOL = j6.63 k + 7.96 $PIOL = j6.63 k + 6.757.40 $PIOL = j6.52 k + 7.83 $PIOL = j6.52 k + 6.637.50 $PIOL = j6.41 k + 7.69 $PIOL = j6.41 k + 6.527.60 $PIOL = j6.31 k + 7.57 $PIOL = j6.31 k + 6.417.70 $PIOL = j6.20 k + 7.45 $PIOL = j6.20 k + 6.317.80 $PIOL = j6.11 k + 7.33 $PIOL = j6.11 k + 6.217.90 $PIOL = j6.01 k + 7.21 $PIOL = j6.01 k + 6.118.00 $PIOL = j5.92 k + 7.10 $PIOL = j5.92 k + 6.028.10 $PIOL = j5.83 k + 6.99 $PIOL = j5.83 k + 5.928.20 $PIOL = j5.75 k + 6.89 $PIOL = j5.75 k + 5.838.30 $PIOL = j5.66 k + 6.78 $PIOL = j5.66 k + 5.758.40 $PIOL = j5.58 k + 6.68 $PIOL = j5.58 k + 5.668.50 $PIOL = j5.50 k + 6.59 $PIOL = j5.50 k + 5.58

The linear adjustment for the keratometric indexes of 1.3304 and1.3375 and for the range of normality defined for r1c is shown.

TABLE 4.

Summary of the comparative analysis of the IOL powerobtained with different standard formulas and with ouroptimized algorithm in a clinical population

SRKT Haigis HofferQ Holladay

Mean differencewith PIOL

calculatedwith nkadj (SD)

1.01 (0.26) 0.39 (0.33) 1.92 (0.58) 1.04 (0.77)

p G0.01 G0.01 G0.01 G0.01

Coefficient ofcorrelation withPIOL calculatedwith nkadj

0.997 0.996 0.993 0.977

Limits ofagreement withPIOL calculatedwith nkadj

0.50Y1.52 j0.27 to 1.04 0.78Y3.07j0.5 to 2.5



156

power calculation can lead to relevant clinically errors in PIOL

calculation if cataract surgery is needed and consequently theimplantation of an IOL. We observed that if the corneal powerwas overestimated when a single nk was used, there was an un-derestimation of the corresponding value of P k

IOL and vice versa.Specifically, the higher the nk used, the higher was the level ofunderestimation observed, with a maximum value of 3.01 D whenthe Gullstrand model was used with nk = 1.3375. Several authorshave adjusted the keratometric index on the basis of posterior

corneal curvature for improving the IOL outcomes,6,10,11,17 butusing in most cases a single value of nk. Our results suggest that theuse of a single keratometric index for calculating Pc when it is usedfor PIOL calculations would not be adequate and it would lead tosignificant postoperative residual refractive errors (refractive sur-prise) after cataract surgery.

A quadratic equation dependent on r2c was found to be pre-dictive of the $PIOL value (Tables 2, 3). These equations may beuseful to calculate the magnitude of the error associated with IOL

FIGURE 3.Bland-Altman plots for the comparison between the PIOL obtained using our formula considering the potential influence of the keratometric error (PIOLadj)and that obtained with other calculation formulas. (A) Differences between PIOLadj and PIOL obtained with the SRK-T formula (PIOLSrk/t). (B) Differencesbetween PIOLadj and PIOL obtained with the Haigis formula (PIOLHaigis). (C) Differences between PIOLadj and PIOL obtained with the HofferQ formula(PIOLHofferQ). (D) Differences between PIOLadj and PIOL obtained with the Holladay formula (PIOLHolladay). Upper and lower lines represent the limits ofagreement calculated as mean of differences T1.96 SD.



157

FIGURE 4.Bland-Altman plots for the comparison between the PIOL obtained with different calculation formulas. (A) Differences between the PIOL obtained with theHaigis formula (PIOLHaigis) and that obtained with the HofferQ formula (PIOLHofferQ). (B) Differences between the PIOL obtained with the Haigis formula(PIOLHaigis) and that obtained with the Holladay formula (PIOLHolladay). (C) Differences between the PIOL obtained with the Haigis formula (PIOLHaigis) and thatobtained with the SRK/T formula (PIOLSRK/T). (D) Differences between the PIOL obtained with the HofferQ formula (PIOLHofferQ) and that obtained with theHolladay formula (PIOLHolladay). (E) Differences between the PIOL obtained with the HofferQ formula (PIOLHofferQ) and that obtained with the SRK/T formula(PIOLSRK/T). (F) Differences between the PIOL obtained with the Holladay formula (PIOLHolladay) and that obtained with the SRK/T formula (PIOLSRK/T). Upperand lower lines represent the limits of agreement calculated as mean of differences T1.96 SD.



158

power calculation when it is calculated using P kIOL or using

P GaussIOL . The group of equations obtained for predicting $PIOL

with the two eye models used in the study was practicallyequivalent, with minimal differences between models. Effectivelens position was found to have an influence on $PIOL, although itwas minimal. Specifically, if the ELP was lower than the ana-tomical chamber depth (ACDa), the differences between P k

IOL

and P GaussIOL decreased and vice versa. These variations were al-

ways found to be lower than 0.5 D. It should be considered that, inour simulations, the exact value of ELP was considered as mea-surable preoperatively and therefore totally predictable. However,it should be considered that the behavior of the IOL within thecapsular bag is not the same in each case in clinical practice and theELP value used in the IOL power calculations is obtained usingprediction formulas that are, in most of cases (except Haigisformula), dependent on corneal power.8,20,23

In an attempt of defining an algorithm minimizing the errors inIOL power estimations and with potential use in clinical practice, anew formula was proposed for IOL power estimation (PIOLadj) usingparaxial optics and the keratometric approximation but consideringa variable nk according to the algorithm developed4 and validatedclinically5 by our research group. In theoretical simulations, dif-ferences between PIOLadj and P Gauss

IOL never exceeded 0.9 D, inde-pendently from the theoretical eye model used, r1c and Rdes. Thiserror range did not result clinically significant in most of the po-tential combinations of r1c and r2c in the healthy normal eye atcorneal vertex plane and did not vary significantly with ELP vari-ations. When the formula was validated in a clinical population,statistically significant and clinically relevant differences were foundbetween our formula for IOL power estimation and other com-monly used (Haigis, HofferQ, Holladay, and SRK/T). Specifically,our formula always provided higher IOL power values, although itwas less evident when compared with those of the Haigis formula.Therefore, our formula cannot be used interchangeably with any ofthe formulas used in this comparative analysis. However, the in-terchangeability between the four formulas used currently in clinicalsetting was not possible either (Fig. 4A to E and D). This is con-sistent with previous studies performed by other authors.24Y26

Several factors may have accounted for the clinically relevantdifference between our formula and those evaluated and usedcommonly in clinical practice. Among them, the correction of thekeratometric error with our approach seems to be crucial. Indeed,differences between our PIOLadj and the SRK-T, Haigis, andHolladay formulas correlated significantly with the difference be-tween the corneal power obtained with the adjusted keratometricindex and the keratometric power. The higher the overestimation ofthe keratometric approach, the higher was the underestimation ofthe IOL power, as observed in the theoretical simulations. Thisconfirms the relationship between the keratometric overestimationand the presence of errors in IOL power calculation that may resultin very significant postoperative refractive errors. McEwan andcolleagues24 found in a previous study that inaccuracy in axial lengthmeasurements and keratometer readings were first-order determi-nants of postoperative spherical refractive error after cataract withIOL implantation. Specifically, measurement errors of 0.2 mmin axial length and 0.50 D in corneal curvature lead to IOL powererrors of T1.17 D using the modified Binkhorst, modifiedColenbrander, Holladay, Hoffer, and SRK II formulas.

Another factor influencing the postoperative refractive outcomeafter cataract surgery and leading to errors in IOL power calcu-lations is the postoperative position of the IOL,3,27 which can beassumed to be equivalent to ELP using the thin lens approxi-mation. In our clinical validation, a strong and significant cor-relation of ELP with the difference between the IOL powerobtained with our formula and those obtained with the HofferQand Holladay formulas was obtained. The higher the ELP, thehigher was the difference between formulas. With the SRK/Tformula, this correlation of ELP with the difference in IOL powercompared with our formula was also found, but it was weaker.One factor accounting for this finding may be that the calcula-tion of ELP with these three formulas requires the use of thekeratometric reading8,20,23 and therefore the overestimation as-sociated with the keratometric approach interferes with the cal-culation of IOL power. Shammas et al.6 and Savini et al.28Y30

groups performed an optimization of ELP depending on thecorneal power measurement and the IOL formula. With theseoptimizations, the mean refractive error outcome was 0 D,demonstrating that a compensation of errors introduced by cor-neal power measurements can be achieved by optimizing ELP.Indeed, the lower the corneal power, the lower was the A-constantvalue required.6,28Y30 This suggests that errors caused by theoverestimation of the keratometric cornea are minimized andcorrected with some formulas with the selection of the A-constant.In our study, the lower the A-constant value used for ELP cal-culation to estimate PIOLadj, the lower were differences betweenour formula and standard formulas evaluated. Specifically, clini-cally tolerable and not statistically significant differences werefound between PIOLadj obtained with an A-constant of 117 andPIOLSRK/T obtained with an A-constant of 118 (limits of agree-ment = j0.59 to 0.56 D, p = 0.66) as well as between PIOLadj

obtained with an A-constant of 117.6 and PIOLHaigis obtainedwith an A-constant of 118 (limits of agreement = j0.69 to 0.62 D,p = 0.3). Therefore, our formula for IOL power estimation (PIOLadj)can be used clinically after an appropriate estimation of the ELPand A-constant associated to each specific type of IOL, with theadvantage of a less dependence of this estimation on cornealpower. The selection of the A-constant to use for different designsof IOL should be investigated further in future studies.

Finally, it should be noted that there are some potentialweaknesses in the formula developed for IOL power calculationusing our adjusted keratometric approach for corneal power es-timation. Our formula is based on paraxial optics, not consideringthe effect of asphericity. Future studies evaluating the validity ofour model for nonparaxial optics as well as if there is an im-provement with clinical relevance when using a more complexoptical estimation are required. In any case, Einighammer et al.31

found that there was an agreement between the IOL power esti-mations obtained by ray tracing and Gaussian optics in normaleyes. Likewise, Jin et al.32 found that theoretical thin-lens for-mulas were as accurate as the ray-tracing method in IOL powercalculations in normal eyes. Besides the paraxial approximation,corneal thickness is not considered in our formula, which can beconsidered as a limitation. However, differences in PIOLadj weredemonstrated to be always below 0.036 D for the potential rangeof corneal thickness in the normal healthy population (centralcorneal thickness from 450 to 600 Km).33 Finally, the eye model



159

selected can be considered as an additional limitation. We used inour study two theoretical eye models, Gullstrand and Le Grandmodels, both providing very similar results. Therefore, the choiceof one model or another is therefore not decisive and with smallclinical relevance for normal eyes.

Regarding the clinical study, the main limitation was the rangeof cases considered, including only eyes with AL between 22 and26 mm. It should be considered that Narvaez et al.34 found errorsin the postoperative manifest refraction higher to 2.00 D using theHofferQ, the SRK/T, and the Holladay 1 and 2 formulas in thistype of eyes. We have demonstrated that the correction of theerror associated with the keratometric approach in this AL range isable to minimize potential refractive surprises because of this fac-tor. Future studies should elucidate if the trends found here are alsoobserved in very short and long eyes or in eyes with previous lasercorneal refractive surgery. Furthermore, IOL power calculationswere performed in a large sample of eyes with a variety of formulas,but these eyes did not undergo cataract surgery, and therefore wewere not able to analyze the postoperative outcomes, which can besignificantly affected by the postoperative position of the IOLwithin the capsular bag and consequently by differences in ELPwith respect to the predicted. In our study, we assumed a pre-dictable ELP and an accurate AL measurement, being the error incorneal power the main source of error.

In conclusion, we have shown that the use of a single value of nk

for the calculation of IOL power can lead to inaccuracies that mayexplain some IOL power overestimations with conventionalformulas after cataract surgery in eyes with AL between 22 and26 mm. These inaccuracies in PIOL calculations can be minimizedtheoretically by using a variable nk depending on the radius ofcurvature of the anterior corneal surface. Future studies would benecessary to confirm all these outcomes in eyes undergoing cat-aract surgery and implanted with different types of IOL andtherefore having different A-constants. It should be consideredthat the algorithm proposed for the minimization of the impactof the keratometric error on IOL power calculation is under-standable and accessible for the clinician, uses a model that re-quires minimal computation time in comparison with morecomplex models or approaches such as ray tracing, and does notrequire the measurement of the radius of the posterior cornealsurface and, therefore, without the necessity of acquiring expen-sive systems, such as Scheimpflug photographyYbased systems oroptical coherence tomographers, which cannot be available in allclinical settings.

ACKNOWLEDGMENTS

The authors have no financial or proprietary interest in a product, method, ormaterial described herein.

All the authors have full control of all primary data, and they agree to allowOptometry and Vision Science to review the data of the current study ifrequested.

Received December 29, 2012; accepted April 4, 2013.

REFERENCES

1. Raman S, Redmond R. Reasons for secondary surgical interventionafter phacoemulsification with posterior chamber lens implantation.J Cataract Refract Surg 2003;29:513Y7.

2. Erickson P. Effects of intraocular lens position errors on postoper-

ative refractive error. J Cataract Refract Surg 1990;16:305Y11.

3. Olsen T. Calculation of intraocular lens power: a review. Acta

Ophthalmol Scand 2007;85:472Y85.

4. Camps VJ, Pinero DP, de Fez D, Coloma P, Caballero MT, Garcia

C, Miret JJ. Algorithm for correcting the keratometric estimation

error in normal eyes. Optom Vis Sci 2012;89:221Y8.

5. Pinero DP, Camps VJ, Mateo V, Ruiz-Fortes P. Clinical validation of

an algorithm to correct the error in the keratometric estimation of

corneal power in normal eyes. J Cataract Refract Surg 2012;38:1333Y8.

6. Shammas HJ, Hoffer KJ, Shammas MC. Scheimpflug photography

keratometry readings for routine intraocular lens power calculation. J

Cataract Refract Surg 2009;35:330Y4.

7. Olsen T. On the calculation of power from curvature of the cornea.

Br J Ophthalmol 1986;70:152Y4.

8. Holladay JT. Standardizing constants for ultrasonic biometry, kera-

tometry, and intraocular lens power calculations. J Cataract Refract

Surg 1997;23:1356Y70.

9. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T

intraocular lens implant power calculation formula. J Cataract Re-

fract Surg 1990;16:333Y40.

10. Ho JD, Tsai CY, Tsai RJ, Kuo LL, Tsai IL, Liou SW. Validity of the

keratometric index: evaluation by the Pentacam rotating Scheimpflug

camera. J Cataract Refract Surg 2008;34:137Y45.

11. Gobbi PG, Carones F, Brancato R. Keratometric index, video-

keratography, and refractive surgery. J Cataract Refract Surg 1998;24:

202Y11.

12. Pedrotti LS, Pedrotti FL. Optics and Vision. Upper Saddle River,

NJ: Prentice-Hall; 1998.

13. Le Grand Y, El Hage SG. Physiological Optics (El Hage SG, trans.).

Berlin, Germany: Springer-Verlag; 1980.

14. Tunnacliffe AH. Introduction to Visual Optics. London, UK: As-

sociation of British Dispensing Opticians; 1997.

15. Wang L, Mahmoud AM, Anderson BL, Koch DD, Roberts CJ.

Total corneal power estimation: ray tracing method versus Gaussian

optics formula. Invest Ophthalmol Vis Sci 2011;52:1716Y22.

16. Pinero DP, Saenz Gonzalez C, Alio JL. Intraobserver and interobserver

repeatability of curvature and aberrometric measurements of the pos-

terior corneal surface in normal eyes using Scheimpflug photography. J

Cataract Refract Surg 2009;35:113Y20.

17. Fam HB, Lim KL. Validity of the keratometric index: large population-

based study. J Cataract Refract Surg 2007;33:686Y91.

18. Olsen T, Arnarsson A, Sasaki H, Sasaki K, Jonasson F. On the ocular

refractive components: the Reykjavik Eye Study. Acta Ophthalmol

Scand 2007;85:361Y6.

19. Dubbelman M, Sicam VA, van der Heijde GL. The shape of the

anterior and posterior surface of the aging human cornea. Vision Res

2006;46:993Y1001.

20. Holladay JT, Prager TC, Chandler TY, Musgrove KH, Lewis JW,

Ruiz RS. A three-part system for refining intraocular lens power

calculations. J Cataract Refract Surg 1988;14:17Y24.

21. Binkhorst R. Intraocular Lens Power Calculation Manual. A Guide

to the Author’s TI 58/59 IOL Power Module, 2nd ed. New York,

NY: R. D. Binkhorst; 1981.

22. Haigis W. Biometrie. In: Kampik A, ed. Optik und Refraktion.

Zulpich: Biermann-Verlag; 1995:123Y40.

23. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and

regression formulas. J Cataract Refract Surg 1993;19:700Y12.

24. McEwan JR, Massengill RK, Friedel SD. Effect of keratometer and

axial length measurement errors on primary implant power calcu-

lations. J Cataract Refract Surg 1990;16:61Y70.



160

25. Sanders DR, Retzlaff JA, Kraff MC, Gimbel HV, Raanan MG.Comparison of the SRK/T formula and other theoretical and re-gression formulas. J Cataract Refract Surg 1990;16:341Y6.

26. Richards SC, Olson RJ, Richards WL, Brodstein RS, Hale PN.Clinical evaluation of six intraocular lens calculation formulas. J Am

Intraocul Implant Soc 1985;11:153Y8.

27. Lee AC, Qazi MA, Pepose JS. Biometry and intraocular lens powercalculation. Curr Opin Ophthalmol 2008;19:13Y7.

28. Savini G, Barboni P, Carbonelli M, Hoffer KJ. Accuracy of Scheimpflugcorneal power measurements for intraocular lens power calculation.J Cataract Refract Surg 2009;35:1193Y7.

29. Savini G, Barboni P, Carbonelli M, Hoffer KJ. Accuracy of a dual

Scheimpflug analyzer and a corneal topography system for intraoc-ular lens power calculation in unoperated eyes. J Cataract RefractSurg 2011;37:72Y6.

30. Savini G, Barboni P, Carbonelli M, Hoffer KJ. Accuracy of cornealpower measurements by a new Scheimpflug camera combined with

Placido-disk corneal topography for intraocular lens power calcula-tion in unoperated eyes. J Cataract Refract Surg 2012;38:787Y92.

31. Einighammer J, Oltrup T, Bende T, Jean B. Calculating intraocularlens geometry by real ray tracing. J Refract Surg 2007;23:393Y404.

32. Jin H, Rabsilber T, Ehmer A, Borkenstein AF, Limberger IJ, Guo H,

Auffarth GU. Comparison of ray-tracing method and thin-lens

formula in intraocular lens power calculations. J Cataract Refract

Surg 2009;35:650Y62.

33. Amano S, Honda N, Amano Y, Yamagami S, Miyai T, Samejima T,

Ogata M, Miyata K. Comparison of central corneal thickness mea-

surements by rotating Scheimpflug camera, ultrasonic pachymetry, and

scanning-slit corneal topography. Ophthalmology 2006;113:937Y41.

34. Narvaez J, Zimmerman G, Stulting RD, Chang DH. Accuracy of in-

traocular lens power prediction using the Hoffer Q, Holladay 1, Holladay

2, and SRK/T formulas. J Cataract Refract Surg 2006;32:2050Y3.

David P. PineroDepartamento de Optica Farmacologıa y Anatomıa

Universidad de AlicanteCrta San Vicente del Raspeig s/n

03690 San Vicente del RaspeigAlicante, Spain

e-mail: [email protected]



161

Original Article

Positional accommodative intraocular lens power error induced by the estimation of the corneal power and the effective lens position

David P Piñero1,2,3, Vicente J Camps1, María L Ramón2, Verónica Mateo1, Rafael J Pérez‑Cambrodí2,3

Purpose: To evaluate the predictability of the refractive correction achieved with a positional accommodating intraocular lenses (IOL) and to develop a potential optimization of it by minimizing the error associated with the keratometric estimation of the corneal power and by developing a predictive formula for the effective lens position (ELP). Materials and Methods: Clinical data from 25 eyes of 14 patients (age range, 52–77 years) and undergoing cataract surgery with implantation of the accommodating IOL Crystalens HD (Bausch and Lomb) were retrospectively reviewed. In all cases, the calculation of an adjusted IOL power (PIOLadj) based on Gaussian optics considering the residual refractive error was done using a variable keratometric index value (nkadj) for corneal power estimation with and without using an estimation algorithm for ELP obtained by multiple regression analysis (ELPadj). PIOLadj was compared to the real IOL power implanted (PIOLReal, calculated with the SRK‑T formula) and also to the values estimated by the Haigis, HofferQ, and Holladay I formulas. Results: No statistically significant differences were found between PIOLReal and PIOLadj when ELPadj was used (P = 0.10), with a range of agreement between calculations of 1.23 D. In contrast, PIOLReal was significantly higher when compared to PIOLadj without using ELPadj and also compared to the values estimated by the other formulas. Conclusions: Predictable refractive outcomes can be obtained with the accommodating IOL Crystalens HD using a variable keratometric index for corneal power estimation and by estimating ELP with an algorithm dependent on anatomical factors and age.

Key words: Accommodating intraocular lenses, Crystalens HD, effective lens position, intraocular lenses power, keratometry

1Department of Optics, Pharmacology and Anatomy, Group of Optics and Visual Perception, University of Alicante, 2Department of Ophthalmology, Medimar International Hospital, 3Foundation for the Visual Quality (FUNCAVIS), Alicante, Spain

Correspondence to: Dr. David P Piñero, Department of Ophthalmology (OFTALMAR), 1st Floor, Medimar International Hospital, C/Padre Arrupe, 20, 03016 Alicante, Spain. E‑mail: [email protected]

Manuscript received: 17.05.14; Revision accepted: 24.05.15

With the advancement of new technologies, a great variety of devices have emerged requiring exigent demands at near and intermediate vision, such as tablets, E‑books, smartphones. For this reason, presbyopic patients and younger patients with cataract currently demand solutions allowing them to continue their daily activities with these devices. Besides spectacles glasses and contact lenses, different surgical options for the correction of presbyopia have been developed.[1] One of the surgical options that have gained popularity in the last decade is the implantation of accommodative intraocular lenses (IOLs) after cataract surgery. An accommodating IOL tries to provide a functional near vision, giving a high‑quality intermediate and distance vision without optical distortion because only one image at a time is formed on the retina.[2] Different single‑optic models were developed and marketed, such as the Crystalens AT‑45 (Eyeonics),[3,4] the 1CU (HumanOptic)[5‑8] or the Tetraflex (Lenstec).[3,9] However, these preliminary models of accommodating IOLs were shown to provide very limited near visual outcomes.[3,9] This was the main reason for the development of new models of accommodating IOLs, such as the dual‑optic[10] and other nonpositional accommodating models.[11]

Recently, Bausch and Lomb released the IOL Crystalens HD™ which theoretically overcomes the limitations of its predecessor, the Crystalens AT‑45. Specifically, a central bi‑aspheric optical modification has been added to increase depth of focus and some changes in the design and material of the IOL has been included that allow the variation of the radius of curvature of the anterior IOL surface (arching optic) with the contraction of the ciliary muscle.[12] A relatively recent study[12] comparing this IOL with a standard monofocal IOL concluded that the Crystalens HD provided a restoration of the distance visual function and a significant improvement of near vision, with an optical quality similar to that corresponding to the conventional monofocal IOL. However, in spite of these acceptable visual outcomes, the refractive predictability was observed to be limited in some cases showing an unexpected postoperative myopic or hyperopic postoperative refractive error. This may be due to an inappropriate IOL power calculation, mainly biased by an inaccurate estimation of the corneal power and ELP.[13]

The hypothesis of the current research is that an improvement of the refractive precision after cataract surgery with implantation of the Crystalens HD IOL may be achievable with a formula for IOL power calculation controlling the error induced by the keratometric approach for the estimation of the corneal power and the error associated with an inaccurate estimation of ELP. For testing such hypothesis, two main objectives were set up. The first objective was to evaluate the predictability of the refractive correction achieved with this positional accommodating IOL and consequently the range of error. The second objective was to develop an optimization of the predictability error by minimizing the error associated with the keratometric estimation of the corneal power and

Access this article onlineWebsite: www.ijo.inDOI: 10.4103/0301-4738.159882PMID: *****

Quick Response Code:

163

May 2015 Piñero, et al.: Errors in accommodative IOL power calculations 439

by developing a predictive formula of the effective lens position (ELP) for accommodating IOL evaluated.

Materials and MethodsPatientsThis retrospective study included a total of 25 eyes of 14 patients with ages ranging between 52 and 77 years old. All these eyes underwent cataract surgery with implantation of the accommodating IOL Crystalens HD (Bausch and Lomb). The inclusion criteria of this study were patients with visually significant cataract or presbyopic/pre presbyopic patients suitable for refractive lens exchange and demanding complete spectacle‑independence. The exclusion criteria were patients with active ocular diseases, ruptured posterior capsule, zonulodialysis, scotopic pupil size of more than 6.0 mm, illiteracy and topographic astigmatisms higher than 1.25 D. All volunteers were adequately informed and signed a consent form. The study adhered to the tenets of the declaration of Helsinki and was approved by the Local Ethical Committee.

Intraocular lensThe accommodating IOL used in this study was the Crystalens HD (Bausch and Lomb), which has a biconvex single‑optic design. The IOL is of a biocompatible third‑generation silicone (Biosil) with a refractive index of 1.428. It has a central bi‑aspheric modification (around 1.5‑mm diameter) to increase depth of focus and thus provide better intermediate and near foci. Two sizes are available depending on the required power, the 12.0 mm model (HD520) for powers between 10.00 and 16.50 D, and the 11.5 mm model (HD500) for powers between 17.00 and 33.00 D. According to the manufacturer, the IOL has a double mechanism to improve the near visual function: Axial movement of the optic as a consequence of the ciliary muscle changes and variation of the radius of curvature of the anterior IOL surface (arching optic). In the current study, the SRK/T formula and the IOL Master software (Carl Zeiss Meditec, Jena, Germany) were used in all cases for the IOL power calculation, with an A‑constant value of 118.8.

Surgical techniqueAll surgeries were performed by one of the experienced surgeons (MLR) us ing a s tandard technique of phacoemulsification. In all cases, topical anesthesia was administered, and pupillary dilation was induced with a combination of tropicamide and phenylephrine 10% every 15 min ½ h prior to the procedure. Povidone iodine solution 5% was instilled on the eye 10 min before the operation. A 2.75‑mm clear incision was made with a diamond knife on the steepest meridian to minimize post‑surgical astigmatism. A paracentesis was made 60–90° clockwise from the main incision and the anterior chamber was filled with viscoelastic material. A continuous curvilinear capsulorhexis between 5.5 and 6.0 mm was performed. After the crystalline lens removal, the IOLs were implanted through the incision into the capsular bag using a specific injector developed by the manufacturer for such purpose. Finally, the surgeon proceeded to retrieve the viscoelastic material using the irrigation‑aspiration system. A combination of topical steroid and antibiotic (Tobradex, Alcon, Fort Worth, TX, USA) as well as a nonsteroidal anti‑inflammatory drops (Dicloabak, Laboratorios Thea, Barcelona, Spain) were prescribed to be applied four times daily for a week after the surgery and

3 times daily the second postoperative week. In addition, the nonsteroidal anti‑inflammatory drops were also prescribed to be applying three times daily during 2 weeks more after surgery.

Calculation of the adjusted IOL power to minimize the keratometric errorAlmost all theoretical formulas for IOL power calculation are based on the use of a simplified eye model, with a thin cornea and crystalline lens model.[13] According to such approach, the power of the IOL (PIOL) can be easily calculated using the Gauss equation in paraxial optics:[14]

( )

hahv

IOL ha

des c

P = ELPAL ELP R + P

(1)

Where Pc is the total corneal power, ELP the effective lens plane, AL the axial length (AL), nha the aqueous humor refractive index, nhv the vitreous humor refractive index and Rdes is the postoperative desired refraction calculated at corneal vertex.

Our research group has recently proposed the use of a variable keratometric index (nkadj) depending on the radius of the anterior corneal surface (r1c) expressed in millimeters for minimizing the error associated to the keratometric approach for corneal power calculation.[15] Specifically, the following expression was defined according to the Gullstrand eye model:

nkadj = −0.0064286r1c + 1.37688 (2)

Using this algorithm, a new keratometric corneal power, named adjusted keratometric corneal power (Pkadj), can be calculated using the classical keratometric corneal power formula.[15] In the current study, the adjusted IOL power (PIOLadj) was calculated, defined as the IOL power calculated from the equation 1 using the nkadj value for the estimation of the corneal power (Pkadj), the nha and nhv values corresponding to the Gullstrand eye model (1.336 for both index). In such calculation, the postoperative spherical equivalent (SE) at corneal vertex was considered as the desired refraction (Rdes = SEpost). Afterward, this IOL power (PIOLadj) was compared with the real power of the IOL implanted (PIOLReal). The PIOLadj calculation was performed after estimating the ELP using two different approaches: ELP calculation following the SRK/T formula guidelines (named PIOLadjSRK/T) and ELP calculation using a mathematical expression obtained by multiple regression analysis (named PIOLadj), as explained carefully in the next section.

Furthermore, the PIOL was also calculated using three conventional formulae (Haigis, HofferQ and Holladay I) considering the ELP defined for each formula and that Rdes = SEpost. A comparative analysis was done between these values of PIOL and PIOLadj.

Estimation of adjusted ELPConsidering equation 1, PIOLreal, Pkadj and Rdes = SEpost in each case, ELP was obtained and named adjusted ELPadj. A multiple regression analysis was performed with the aim of obtaining a mathematic expression for predicting the ELPadj from different anatomical and clinical parameters.

164

440 Indian Journal of Ophthalmology Vol. 63 No. 5

Preoperative and postoperative examinationsPreoperatively, all patients had a full ophthalmologic examination including the evaluation of the refractive status, the distance and near visual acuities, slit lamp examination, optical biometry (IOL‑Master, Carl Zeiss Meditec, Jena, Germany), Goldman tonometry and funduscopy. Distance (4 m) and near (40 cm) visual acuities were evaluated with ETDRS charts. Postoperatively, patients were evaluated at 1‑day, 1‑week, 1‑month, and 3 months after surgery. At all visits, visual acuity, refraction and the integrity of the anterior segment were evaluated. Funduscopy was also performed in the postoperative revision at 3 months.

Statistical analysisThe statistical analysis was performed using the SPSS statistics software package version 19.0 for Windows (IBM, Armonk, NY, USA). Normality of data samples was evaluated by means of the Kolmogorov‑Smirnov test. When parametric analysis was possible, the Student’s t‑test for paired data was used for comparing the different approaches for PIOL calculation and also for comparing preoperative and postoperative data. When parametric analysis was not possible, the Wilcoxon rank sum test was applied to assess the significance of such comparisons. Differences were considered to be statistically significant when the associated P < 0.05. Correlation coefficients (Pearson or Spearman depending if normality condition could be assumed) were used to assess the correlation between different variables. Regarding the interchangeability between pairs of methods used for obtaining PIOL, the Bland‑Altman analysis was used.[16] This is a graphical method for assessing if there is an agreement between two clinical procedures.[16] Specifically, Bland‑Altman plots show the differences between the methods plotted against the mean of the 2 methods. The limits of agreement (LoA) are defined as the mean ± 1.96 standard deviation (SD) of the differences.[16] If the limits are clinically relevant, the 2 methods cannot be used interchangeably. In the current study, differences in IOL power between the different formulas evaluated was considered as clinically relevant for values of more than 0.5 D because this value is the IOL power step provided currently by most of manufacturers and has been shown to be the optical neutralization tolerance since many years ago.[17]

A multiple regression analysis was used for predicting the ELPadj from different preoperative anatomical and clinical parameters. Model assumptions were evaluated by analyzing residuals, the normality of nonstandardized residuals (homoscedasticity), and the Cook distance to detect influential points or outliers. In addition, the lack of correlation between errors and multicollinearity was assessed using the Durbin–Watson test, the calculation of the colinearity tolerance, and the variance inflation factor.

ResultsThis study evaluated 25 eyes of 14 patients (16 men [64%]), with a mean age of 65.9 years ± 8.9 (SD) (range, 52–79 years). The sample comprised 13 left eyes (52%). Mean preoperative keratometry, AL and anterior chamber depth (ACD) were 43.29 D ± 1.45 (range, 40.91–45.89 D), 23.21 mm ± 0.89 mm (range, 21.65–25.04 mm), and 3.27 mm ± 0.30 mm (range, 2.63–3.84 mm), respectively. According to all these data and using the SRK‑T formula, mean IOL power implanted

was 22.53 D ± 2.70 (SD) (range, 16–28 D). Table 1 summarizes the preoperative and postoperative visual and refractive data, and Table 2 displays the biometric and IOL power calculation data of the eyes evaluated.

Agreement of PIOLReal and PIOLadj‑SRK/T

Statistically significant differences were found between PIOLadjSRK/T and PIOLReal when ELP was calculated with the SRK/T formula guidelines and Rdes = EEpost (P < 0.01, paired Student’s t‑test). A very strong and statistically significant correlation was found between PIOLadj‑SRK/T and PIOLReal (r = 0.960, P < 0.01) [Fig. 1]. According to the Bland and Altman method, the PIOLadj‑SRK/T was higher than PIOLReal (mean of differences 1.97 D), with clinically relevant LoA (3.39 and 0.36 D). Fig. 2 shows the Bland and Altman plot corresponding to this agreement analysis.

Estimation of ELPadj

The multiple regression analysis revealed that the ELPadj was significantly correlated with AL, ACD, Pkadj and age (P < 0.001):

= 9.549 + 0.422 × + 0.164 × 1.612 ×

0.014 ×

− −

−adj kadjELP LA P

ACD Age (3)

The homoscedasticity of the model was confirmed by the normality of the nonstandardized residuals distribution (P = 0.20) and the absence of influential points or outliers (mean Cook’s distance: 0.049 ± 0.081). With this model, 72% of nonstandardized residuals were 0.30 or lower and 80% were lower than 0.40. The poor correlation between residuals (Durbin‑Watson test: 2.165) and the lack of

Table 1: Comparative table showing the preoperative and postoperative visual and refractive outcomes. The corresponding P values for the comparison between the preoperative and postoperative data are shown for each parameter evaluated

Mean (SD)Median (range)

Preoperative Postoperative (3 months)

P

LogMAR UDVA ‑ 0.21 (0.24)0.15 (0.00 ‑ 0.80)

‑

Sphere (D) +1.09 (2.76)+2.25 (−5.25 - +6.00)

+0.03 (0.79)0.00 (−2.50 - +2.00)

0.06

Cylinder (D) −0.57 (0.54)−0.50 (−2.00-0.00)

−0.80 (0.56)−1.00 (−1.75 - 0.00)

0.04

SE (D) +0.81 (2.77)+2.00 (−5.50 - +5.38)

−0.37 (0.78)−0.25 (−3.25 - +1.13)

0.35

LogMAR CDVA 0.18 (0.21)0.10 (0.00 ‑ 0.80)

0.06 (0.07)0.05 (0.00 ‑ 0.22)

0.02

LogMAR UNVA ‑ 0.44 (0.23)0.30 (0.22 ‑ 1.00)

‑

LogMAR DCNVA ‑ 0.53 (0.18)0.52 (0.30 ‑ 1.00)

‑

Near addition (D) 2.55 (0.37)2.50 (2.00 ‑ 3.00)

1.68 (0.70)1.50 (0.00 ‑ 3.00)

0.03

LogMAR CNVA 0.11 (0.14)0.10 (0.00 ‑ 0.40)

0.10 (0.07)0.10 (0.00–0.30)

0.55

SD: Standard deviation, D: Diopters, UDVA: Uncorrected distance visual acuity, SE: Spherical equivalent, CDVA: Corrected distance visual acuity, UNVA: Uncorrected near visual acuity, DCNVA: Distance‑corrected near visual acuity, CNVA: Corrected near visual acuity

165


multicollinearity (tolerance 0.486–0.992; variance inflation factors 2.056–1.008) was also confirmed.

A statistically significant difference was found between ELP calculated with the SRK/T formula guidelines and the

ELPadj (P < 0.01, paired Student’s t‑test), with the lowest value for the adjusted calculation [Table 1].

Agreement between PIOLReal and PIOLadj

No statistically significant differences were found between PIOLadj and PIOLReal when ELPadj was used and Rdes = SEpost were considered for PIOLadj calculation (P = 0.10, paired Student’s t‑test). A very strong and statistically significant correlation was found between PIOLadj and PIOLReal (r = 0.97, P < 0.01) [Fig. 3]. According to the Bland and Altman method, the mean difference between both PIOLadj and PIOLReal was 0.002 D, with LoA of 1.229 and −1.225 D. Fig. 4 shows the Bland and Altman plot corresponding to this agreement analysis.

Agreement of PIOLadj and other formulasStatistically significant differences were found between PIOLadj and each of the formulas studied (P < 0.01, paired Student’s t‑test). A very strong and statistically significant correlation was found between PIOLHaigis and PIOLadj (r = 0.983, P < 0.01), between PIOLHofferQ and PIOLadj (r = 0.992, P < 0.01) and between PIOLHolladay and PIOLadj (r = 0.987, P < 0.01). Table 3 shows the Bland and Altman analysis outcomes corresponding to all comparisons done. Furthermore, the ELPadj (mean ± SD: 4.18 ± 0.27 mm, range 3.70–4.83 mm) was significantly lower than the ELP obtained following the guidelines proposed by each of the formulas used (paired Student’s t‑test, P < 0.01) [Table 1].

DiscussionCurrently, a great variety of options are available for the correction of presbyopia, such as the replacement of the transparent crystalline lens by an accommodating IOL that theoretically provide a restoration of the visual function not only at distance, but also at intermediate and near. However, the various preliminary models of accommodating IOLs were found to provide limited near visual outcomes and the results with the new generation of accommodating IOLs are not completely successful. Beiko[17] concluded from a comparative study that the single‑optic accommodating IOLs, such as Crystalens HD and Tetraflex, did not offer a significant

Table 2: Mean biometric and IOL power calculation data

Parameter Mean±SD Range

SEpre (D) 0.81±2.77 −5.50-5.38

SEpost (D) −0.36±0.76 −3.13-1.14

r1c (mm) 7.80±0.26 7.35‑8.25

ACD (mm) 3.27±0.30 2.63‑3.84

AL (mm) 23.21±0.89 21.65‑25.04

ELPSRK/T (mm) 5.21±0.34 4.78‑6.17

ELPadj (mm) 4.18±0.27 3.70‑4.83

ELPHaigis (mm) 5.41±0.18 5.12‑5.82

ELPHoffer Q (mm) 5.25±0.23 4.88‑5.83

ELPHolladay (mm) 4.95±0.30 4.31‑5.52

nkadj 1.327±0.02 1.324‑1.330

Pk(1.3375) (D) 43.29±1.44 40.91‑45.89

PcHaigis(1.3315) (D) 42.52±1.42 40.18‑45.07

Pkadj (D) 41.91±1.61 39.25‑44.82

PIOLReal (D) 22.53±2.70 16.00‑28.00

PIOLadjSRK/T (D) 24.51±2.91 17.69‑32.09

PIOLadj (D) 22.53±2.79 15.86‑29.07

PIOLHoffer Q (D) 22.94±3.14 15.43‑30.89

PIOLHolladay (D) 23.03±2.98 16.00‑30.80PIOLHaigis (D) 24.33±3.36 16.53‑33.25

SEpre: Preoperative spherical equivalent, SEpost: Postoperative spherical equivalent, r1c: Radius of curvature of the anterior corneal surface, ACD: Anterior chamber depth, AL: Axial length, ELPSRK/T: Effective lens position for the SRK/T formula, ELPadj: Effective lens position for the adjusted formula, ELPHaigis: Effective lens position for the Haigis formula, ELPHoffer Q: Effective lens position for the Hoffer Q formula, ELPHolladay: Effective lens position for the Holladay formula, nkadj: Adjusted keratometric index, Pk(1.3375): Corneal power obtained using the IOL‑Master or keratometric power, PcHaigis(1.3315): Corneal power obtained for the Haigis formula, Pkadj: Corneal power obtained using the adjusted keratometric index, PIOLReal: Power of the intraocular lens implanted which was calculated using the SRK/T formula, PIOLadj: Intraocular lens power obtained using the adjusted formula, PIOLHofferQ: Intraocular lens power obtained using the Hoffer Q formula, PIOLHolladay: Intraocular lens power obtained using the Holladay formula, PIOLHaigis: Intraocular lens power obtained using the Haigis formula, IOL: Intraocular lens, SD: Standard deviation, D: Diopters

Table 3: Bland and Altman analysis outcomes of the comparison between PIOLadj and the IOL power obtained with other commonly used formulas

∆PIOL±SD (D) LoA (D) P

Haigis 1.77±0.795 3.33‑0.21 <0.01

Hoffer Q 0.40±0.52 1.40-−0.64 <0.01Holladay 1 −0.47±0.50 1.44-−0.50 <0.01

IOL: Intraocular lens, SD: Standard deviation, D: Diopters, PIOL: Power of the intraocular lens, LoA: Limits of agreement, PIOLadj: Intraocular lens power obtained using the adjusted formula

Figure 1: Scattergram showing the relationship between the adjusted intraocular lenses (IOL) power using the effective lens position estimated using the SRK‑T formula guidelines (PIOLadj‑SRK/T) and the real power of the IOL implanted (PIOLReal)

166


advantage in near visual acuity over mini‑monovision with a monofocal IOL. Zamora‑Alejo et al.[18] concluded in another comparative study that the Crystalens HD was able to provide some benefit for intermediate visual function compared to a monofocal IOL. Likewise, Alió et al.[12] compared this IOL with a standard monofocal IOL and concluded that the intraocular optical quality achieved with this IOL was similar to that obtained with a conventional monofocal IOL. However, the refractive predictability was observed to be limited in some cases showing an unexpected postoperative myopic or hyperopic postoperative refractive error. In our study, the postoperative SE ranged from −3.13 to +1.14 D, which confirms the presence of a significant variability with a trend to postoperative myopia. According to all this evidence, some optimizations seem to be necessary in the calculation of the power required to be implanted with this accommodating IOL.

Possible sources of error in the calculation of this accommodation IOL might be the bias introduced by considering the corneal power assuming the keratometric error, errors in the determination of the AL or inaccuracy in the estimation of the ELP for this specific IOL. First, the potential impact of the keratometric error was analyzed by calculating the corneal power using an adjusted keratometric index aimed at minimizing the clinical error in the estimation of the corneal power.[14,15,19] However, we still obtained statistically significant and clinically relevant differences between the adjusted calculation, and the real power of the IOL implanted that was selected according to the SRK‑T formula outcomes. As the accuracy of the IOL‑Master for obtaining AL measurements has been widely demonstrated,[20] the ELP was thought to be a critical factor for the presence of a relatively limited predictability with the accommodating IOL evaluated. For such purpose, an expression for estimating an optimized ELP according to some preoperative parameters, designated as adjusted ELP, was obtained by means of multiple linear regression. The IOL power calculation was performed considering this adjusted ELP and the results were compared to those obtained with other predicting algorithms of ELP.[21‑25] This analysis revealed that the ELPadj was significantly lower compared to the values

estimated with the commonly used formulas. One of the main factors that may account for this finding is the potentially more anterior position of the optic of the evaluated accommodating IOL due to the flexible haptics. Indeed, considering equation 1, a longer ELP would lead to the calculation of a higher value of IOL power that may potentially lead to the presence of postoperative myopia. This may explain in part the trend to myopia observed in our sample. Indeed, when the calculation of IOL power was done correcting the keratometric power and also assuming the ELPadj value, no statistically significant differences were found between the implanted and the estimated IOL power. In contrast, significant differences in IOL power were observed with the other commonly used formulas, Haigis, HofferQ and Holladay, which used significantly higher values of ELP.

Regarding the clinical interchangeability of PIOLReal and PIOLadj, a range of agreement of 1.23 D was found which is limited considering that the evaluated IOL is available in half diopter steps. This confirms that although a potential more anterior position of the IOL may contribute to ELP errors with the accommodating IOL evaluated, some positional instability of this IOL within the capsular bag could also influence on them. This is consistent with the results of some ultrasonographic studies revealing the presence of unexpected positions with this type of accommodating IOL.[26‑28]

Finally, ELPadj was found to be related to some factors, such as the AL, the adjusted keratometric corneal power (Pkadj), the ACD and age. Specifically, the longer the eye, the higher was the ELPadj. This is consistent with previous outcomes reported by other authors such as Olsen et al.[29] who found that short eyes tended to have a shallow anterior chamber postoperatively and vice versa. These authors also found that myopic eyes with a large capsular bag showed less IOL movement postoperatively.[29] However, not only anatomical parameters influenced on ELP; age was also found to be an influencing factor. Similarly, other authors have reported a similar finding for another model of accommodating IOL.[30] The interaction between capsular bag fusion and the fibrotic reaction following IOL implantation that leads to capsular bag shrinkage seems to be the main factor accounting for this.

Figure 2: Bland–Altman plots for the comparison between the adjusted intraocular lenses (IOL) power using the effective lens position estimated using the SRK‑T formula guidelines (PIOLadj‑SRK/T) and the real power of the IOL implanted (PIOLReal). The dotted lines show the limits of agreement (±1.96 SD)

Figure 3: Scattergram showing the relationship between the adjusted intraocular lenses (IOL) power using the regression analysis adjusted effective lens position (PIOLadj) and the real power of the IOL implanted (PIOLReal)

167


There are several limitations in the current research, such as the limited sample size or the short follow‑up. It should be considered that, although rare, changes in IOL position has been described more than 3 months after surgery, especially after Nd: YAG capsulotomy.[31] This requires further analysis and investigation in future studies. Another potential limitation is the determination of refraction with this accommodating IOL. As previously mentioned, the Crystalens HD IOL has a central bi‑aspheric optical modification generating theoretically some level of negative spherical aberration and therefore contributing to the increase of the depth of focus.[12,32] This may have led to some degree of myopia under pupillary constriction and therefore to some bias in the estimation of the refraction. However, it should be considered that small levels of intraocular primary spherical aberration have been reported with this accommodating IOL,[12] and of positive sign in some cases.[32] Residual myopic refractive errors of more than 0.50 D cannot be attributed to these limited levels of spherical aberration. Furthermore, there were several cases with clinically significant hyperopic residual refractive errors, not only myopic. Another factor that may have contributed to some variability and bias in the estimation of refraction would be the presence of IOL tilts or decentration leading to a degradation of the visual quality and therefore limiting the accuracy of manifest refraction. Some authors have reported cases of misalignment, tilting or bad positioning with previous models of the evaluated accommodating IOL leading to significant levels of visual deterioration.[33‑35] In our sample, IOL misalignment and tilt were not observed in the slitlamp examination, but a more detailed analysis with advanced imaging techniques, such as optical coherence tomography or ultrasonography would be recommendable. Future studies should be conducted to evaluate the position adopted by this IOL into the capsular bag and how it is relation to limitation in the precision of the refractive correction. Finally, it must be acknowledged as an additional limitation that intermediate visual acuity was not recorded in the current series.

ConclusionRefractive outcomes after cataract surgery with implantation of the accommodating IOL Crystalens HD can be optimized by

minimizing the keratometric error using a variable keratometric index for corneal power estimation and by estimating ELP using a mathematical expression dependent on anatomical factors and age. The correction only of the error associated with the keratometric estimation of the corneal power using a variable refractive index does not improve significantly the refractive precision achieved with the accommodating IOL evaluated. The optimization of the estimation of ELP is also necessary. Future studies should be performed to validate this model of IOL power calculation for the Crystalens HD IOL with larger sample of sizes including more extreme cases (long and short).

References1. Waring GO 4th, Berry DE. Advances in the surgical correction of

presbyopia. Int Ophthalmol Clin 2013;53:129‑52.2. Alió JL, Tavolato M, De la Hoz F, Claramonte P, Rodríguez‑Prats JL,

Galal A. Near vision restoration with refractive lens exchange and pseudoaccommodating and multifocal refractive and diffractive intraocular lenses: Comparative clinical study. J Cataract Refract Surg 2004;30:2494‑503.

3. Brown D, Dougherty P, Gills JP, Hunkeler J, Sanders DR, Sanders ML. Functional reading acuity and performance: Comparison of 2 accommodating intraocular lenses. J Cataract Refract Surg 2009;35:1711‑4.

4. Patel S, Alió JL, Feinbaum C. Comparison of Acri. Smart multifocal IOL, crystalens AT‑45 accommodative IOL, and Technovision presbyLASIK for correcting presbyopia. J Refract Surg 2008;24:294‑9.

5. Harman FE, Maling S, Kampougeris G, Langan L, Khan I, Lee N, et al. Comparing the 1CU accommodative, multifocal, and monofocal intraocular lenses: A randomized trial. Ophthalmology 2008;115:993‑1001.e2.

6. Uthoff D, Gulati A, Hepper D, Holland D. Potentially accommodating 1CU intraocular lens: 1‑year results in 553 eyes and literature review. J Refract Surg 2007;23:159‑71.

7. Dogru M, Honda R, Omoto M, Toda I, Fujishima H, Arai H, et al. Early visual results with the 1CU accommodating intraocular lens. J Cataract Refract Surg 2005;31:895‑902.

8. Mastropasqua L, Toto L, Nubile M, Falconio G, Ballone E. Clinical study of the 1CU accommodating intraocular lens. J Cataract Refract Surg 2003;29:1307‑12.

9. Wolffsohn JS, Naroo SA, Motwani NK, Shah S, Hunt OA, Mantry S, et al. Subjective and objective performance of the Lenstec KH‑3500 “accommodative” intraocular lens. Br J Ophthalmol 2006;90:693‑6.

10. Ossma IL, Galvis A, Vargas LG, Trager MJ, Vagefi MR, McLeod SD. Synchrony dual‑optic accommodating intraocular lens. Part 2: Pilot clinical evaluation. J Cataract Refract Surg 2007;33:47‑52.

11. Alió JL, Ben‑nun J, Rodríguez‑Prats JL, Plaza AB. Visual and accommodative outcomes 1 year after implantation of an accommodating intraocular lens based on a new concept. J Cataract Refract Surg 2009;35:1671‑8.

12. Alió JL, Piñero DP, Plaza‑Puche AB. Visual outcomes and optical performance with a monofocal intraocular lens and a new‑generation single‑optic accommodating intraocular lens. J Cataract Refract Surg 2010;36:1656‑64.

13. Olsen T. Calculation of intraocular lens power: A review. Acta Ophthalmol Scand 2007;85:472‑85.

14. Camps VJ, Piñero DP, de Fez D, Mateo V. Minimizing the IOL power error induced by keratometric power. Optom Vis Sci 2013;90:639‑49.

Figure 4: Bland–Altman plots for the comparison between the adjusted intraocular lenses (IOL) power using the regression analysis adjusted effective lens position (PIOLadj) and the real power of the IOL implanted (PIOLReal). The dotted lines show the limits of agreement (±1.96 SD)

168


15. Camps VJ, Pinero Llorens DP, de Fez D, Coloma P, Caballero MT, Garcia C, et al. Algorithm for correcting the keratometric estimation error in normal eyes. Optom Vis Sci 2012;89:221‑8.

16. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986;1:307‑10.

17. Le Grand Y, El Hage SG. Physiological Optics. Berlin: Springer‑Verlag; 1980.

18. Beiko GH. Comparison of visual results with accommodating intraocular lenses versus mini‑monovision with a monofocal intraocular lens. J Cataract Refract Surg 2013;39:48‑55.

19. Zamora‑Alejo KV, Moore SP, Parker DG, Ullrich K, Esterman A, Goggin M. Objective accommodation measurement of the Crystalens HD compared to monofocal intraocular lenses. J Refract Surg 2013;29:133‑9.

20. Piñero DP, Camps VJ, Mateo V, Ruiz‑Fortes P. Clinical validation of an algorithm to correct the error in the keratometric estimation of corneal power in normal eyes. J Cataract Refract Surg 2012;38:1333‑8.

21. Shammas HJ, Chan S. Precision of biometry, keratometry, and refractive measurements with a partial coherence interferometry‑keratometry device. J Cataract Refract Surg 2010;36:1474‑8.

22. Haigis W. The Haigis formula. In: Shammas HJ, editor. Intraocular Lens Power Calculations. Thorofare, NJ: Slack; 2004. p. 41‑57.

23. Hoffer KJ. The Hoffer Q formula: A comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19:700‑12.

24. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16:333‑40.

25. Holladay JT, Prager TC, Chandler TY, Musgrove KH, Lewis JW, Ruiz RS. A three‑part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17‑24.

26. Stachs O, Schneider H, Stave J, Guthoff R. Potentially accommodating intraocular lenses – An in vitro and in vivo study

using three‑dimensional high‑frequency ultrasound. J Refract Surg 2005;21:37‑45.

27. Marchini G, Pedrotti E, Sartori P, Tosi R. Ultrasound biomicroscopic changes during accommodation in eyes with accommodating intraocular lenses: Pilot study and hypothesis for the mechanism of accommodation. J Cataract Refract Surg 2004;30:2476‑82.

28. Koeppl C, Findl O, Menapace R, Kriechbaum K, Wirtitsch M, Buehl W, et al. Pilocarpine‑induced shift of an accommodating intraocular lens: AT‑45 Crystalens. J Cataract Refract Surg 2005;31:1290‑7.

29. Olsen T, Corydon L, Gimbel H. Intraocular lens power calculation with an improved anterior chamber depth prediction algorithm. J Cataract Refract Surg 1995;21:313‑9.

30. Li XM, Wang W. To observe clinical effect of accommodative IOL on different age patients. Zhonghua Yan Ke Za Zhi 2008;44:30‑2.

31. Findl O, Drexler W, Menapace R, Georgopoulos M, Rainer G, Hitzenberger CK, et al. Changes in intraocular lens position after neodymium: YAG capsulotomy. J Cataract Refract Surg 1999;25:659‑62.

32. Ramón ML, Piñero DP, Blanes‑Mompó FJ, Pérez‑Cambrodí RJ. Clinical and quality of life data correlation with a single‑optic accommodating intraocular lens. J Optom 2013;6:25‑35.

33. Yuen L, Trattler W, Boxer Wachler BS. Two cases of Z syndrome with the Crystalens after uneventful cataract surgery. J Cataract Refract Surg 2008;34:1986‑9.

34. Jardim D, Soloway B, Starr C. Asymmetric vault of an accommodating intraocular lens. J Cataract Refract Surg 2006;32:347‑50.

35. Cazal J, Lavin‑Dapena C, Marín J, Vergés C. Accommodative intraocular lens tilting. Am J Ophthalmol 2005;140:341‑4.

Cite this article as: Piñero DP, Camps VJ, Ramón ML, Mateo V, Pérez-Cambrodí RJ. Positional accommodative intraocular lens power error induced by the estimation of the corneal power and the effective lens position. Indian J Ophthalmol 2015;63:438-44.

Source of Support: Nil. Conflict of Interest: None declared.

169

陨灶贼允韵责澡贼澡葬造皂燥造熏灾燥造援 8熏晕燥援 3熏 Jun.18, 圆园15 www. IJO. cn栽藻造押8629原愿圆圆源缘员苑圆 8629-82210956 耘皂葬蚤造押ijopress岳员远猿援糟燥皂

Error induced by the estimation of the corneal powerand the effective lens position with a rotationallyasymmetric refractive multifocal intraocular lens

窑Clinical Research窑

1Grupo de 魷ptica y Percepci佼n Visual (GOPV). Departmentof Optics, Pharmacology and Anatomy, University ofAlicante, San Vicente del Raspeig, Alicante 03690, Spain2Department of Ophthalmology (Oftalmar), Vithas MedimarInternational Hospital, Alicante 03016, Spain3Foundation for the Visual Quality (FUNCAVIS: Fundaci佼npara la Calidad Visual), Alicante 03016, SpainCorrespondence to: David P. Pi觡ero. Department ofOphthalmology (OFTALMAR), 1st floor, MedimarInternational Hospital, C/Padre Arrupe 20, Alicante 03016,Spain. [email protected]: 2014-09-02 Accepted: 2014-12-01

Abstract·AIM : To evaluate the prediction error in intraocular lens(IOL) power calculation for a rotationally asymmetricrefractive multifocal IOL and the impact on this error ofthe optimization of the keratometric estimation of thecorneal power and the prediction of the effective lensposition (ELP).

·METHODS: Retrospective study including a total of 25eyes of 13 patients (age, 50 to 83y) with previous cataractsurgery with implantation of the Lentis Mplus LS-312 IOL(Oculentis GmbH, Germany). In all cases, an adjusted IOLpower (PIOLadj) was calculated based on Gaussian opticsusing a variable keratometric index value (nkadj) for theestimation of the corneal power (Pkadj) and on a new valuefor ELP (ELPadj) obtained by multiple regression analysis.This PIOLadj was compared with the IOL power implanted(PIOLReal) and the value proposed by three conventionalformulas (Haigis, Hoffer Q and Holladay 玉).

·RESULTS: PIOLReal was not significantly different thanPIOLadj and Holladay IOL power ( >0.05). In the Bland andAltman analysis , PIOLadj showed lower mean difference(-0.07 D) and limits of agreement (of 1.47 and -1.61 D)when compared to PIOLReal than the IOL power valueobtained with the Holladay formula. Furthermore, ELPadj

was significantly lower than ELP calculated with otherconventional formulas ( <0.01) and was found to bedependent on axial length, anterior chamber depth and Pkadj.

· CONCLUSION: Refractive outcomes after cataractsurgery with implantation of the multifocal IOL LentisMplus LS -312 can be optimized by minimizing the

keratometric error and by estimating ELP using amathematical expression dependent on anatomicalfactors.

·KEYWORDS: Mplus;multifocal intraocularlens;keratometry;effective lens position; intraocular lens powerDOI:10.3980/j.issn.2222-3959.2015.03.12

Pi觡ero DP, Camps VJ, Ram佼n ML, Mateo V, P佴rez-Cambrod侏 RJ.

Error induced by the estimation of the corneal power and the effective

lens position with a rotationally asymmetric refractive multifocal

intraocular lens. 2015;8(3):501-507

INTRODUCTION

S everal studies[1-8] have confirmed the ability of multifocalintraocular lenses (IOLs) of providing a good near and

distance functional vision without the use of corrective lensesafter cataract surgery. One modality of IOL multifocality isthe use of a rotationally asymmetric refractive profilecontaining an aspheric distance-vision zone combined with asector-shaped near-vision zone in the inferior area of the IOL.This concept of multifocality is the basis of the multifocalIOL Lentis Mplus LS-312 (Oculentis GmbH). Studies on thisIOL have shown good near and distance visual outcomes,combined with postoperative contrast sensitivity withinphysiological ranges and positive impact on patient's qualityof life [1,2,9-15]. Even some studies have reported good levels ofintermediate visual acuity with this type of IOL[1,2].Despite the good visual outcomes reported with this IOL[1,2,9-15],some studies have shown some level of variability in therefractive correction achieved[1,2,9,13-15]. Ali佼 [15] found in aprospective comparative study evaluating a group of 21 eyesimplanted with the Mplus IOL a mean 3mo postoperativesphere of -0.34依0.93 D, ranging from -3.00 to +1.25 D. Inanother sample of 9366 eyes implanted with this type of IOL,Venter [9] found that 91.8% of eyes had a postoperativespherical equivalent (SE) within 依1.00 D. In the same line,Mu觡oz [13] found that 6 eyes (9.4%) from a sample of 64eyes had a postoperative myopic SE of more than 0.50 D(mean residual SE: -0.75依0.15 D). McAlinden and Moore [14]

reported in another series of cases a percentage of 86.4% ofeyes with an SE within 依0.50 D. Several factors may be inrelation to this variable level of predictability, such as some

501171

inaccuracies in IOL power calculation due to the use of notfully optimized formulae for this specific type of IOL.The aim of the current study was to evaluate thepredictability of the refractive correction achieved with thisrefractive multifocal IOL and to develop an optimization ofthe predictability error by minimizing the error associated tothe keratometric estimation of the corneal power and bydeveloping a predictive formula of the effective lens positionfor this specific type of IOL.SUBJECTS AND METHODSSubjects This retrospective study included a total of 25 eyesof 13 patients. All eyes underwent cataract surgery withimplantation of the rotationally asymmetric multifocal IOLLentis Mplus LS-312 (Oculentis GmbH). Inclusion criteriafor this study were patients with visually significant cataractor presbyopic/pre-presbyopic patients suitable for refractivelens exchange and demanding complete spectacleindependence. Exclusion criteria were patients with activeocular diseases, illiteracy and topographic astigmatismshigher than 1.5 D. All volunteers were adequately informedabout the surgery and signed a consent form. The studyadhered to the tenets of the Declaration of Helsinki and wasapproved by the Local Ethical Committee.MethodsIntraocular lens The Lentis Mplus LS-312 (OculentisGmbH, Germany) is a rotationally asymmetric multifocalIOL that contains an aspheric distance-vision zone combinedwith a 3.00 D posterior sector-shaped near-vision zone toallow good transition between the zones. It has biconvexdesign with a 6.0 mm optic, a 12.0 mm overall length, and aC-loop haptic design with 0-degree angulation. The IOL ismade of an acrylic copolymer comprising acrylates with ahydrophobic surface and ultraviolet-filtering components.Surgical technique All surgeries were performed by thesame experienced surgeon (Ram佼n ML) using a standardtechnique of phacoemulsification. In all cases, topicalanesthesia was administered and pupillary dilation wasinduced with a combination of tropicamide andphenylephrine 10% every 15min half an hour previous to theprocedure. Iodine solution 5% was instilled on the eye 10minbefore the operation. A 2.75-mm clear incision was madewith a diamond knife on the steepest meridian to minimizepost-surgical astigmatism. A paracentesis was made 60毅-90毅clockwise from the main incision and the anterior chamberwas filled with viscoelastic material. After the crystalline lensremoval, the IOLs were implanted through the incision intothe capsular bag using a specific injector developed by themanufacturer for such purpose. Finally, the surgeonproceeded to retrieve the viscoelastic material using theirrigation-aspiration system. A combination of topical steroidand antibiotic (Tobradex, Alcon, Fort Worth, TX, USA) as

well as a non-steroidal anti-inflammatory drops (Dicloabak,Laboratorios Thea, Barcelona, Spain) were prescribed to beapplied four times daily for a week after the surgery and threetimes daily the second postoperative week. In addition,non-steroidal anti-inflammatory drops were also prescribed tobe applied three times daily during 2 additional weeks aftersurgery.Calculation of an adjusted intraocular lens powerAlmost all theoretical formulas for IOL power (PIOL)calculation are based on the use of a simplified eye model,with thin cornea and lens models [16]. According to suchapproach, PIOL can be easily calculated using the Gaussequations in paraxial optics:[17]

(1)where, Pc is the total corneal power, ELP the effective lensplane, AL the axial length, nha the aqueous humour refractiveindex, nhv the vitreous humour refractive index, and Rdes thepostoperative desired refraction calculated at corneal vertex.Our research group proposed the use of a variablekeratometric index (nkadj) depending on the radius of theanterior corneal surface (r1c) expressed in millimetres forminimizing the error associated to the keratometric approachfor corneal power calculation [18]. Specifically, the followingexpression was defined according to the Gullstrand eyemodel:nkadj = -0.0064286r1c + 1.37688 (2)Using these algorithm, a new keratometric corneal power,named adjusted keratometric corneal power (Pkadj), can becalculated using the classical keratometric corneal powerformula [18]. In the current study, the adjusted IOL power(PIOLadj) was calculated, which was defined as the IOL powercalculated from the equation 1 using the nkadj value for theestimation of the corneal power (Pkadj), and the nha and nhv

values corresponding to the Gullstrand eye model (1.336 forboth indexes). In this IOL power calculation, thepostoperative SE at corneal vertex was considered as thedesired refraction (Rdes=SEpost). The PIOLadj calculation wasperformed by estimating the ELP using two differentapproaches: ELP calculation following the SRK/T formulaguidelines (named PIOLadjSRK/T) [19] and ELP calculation using amathematical expression obtained by multiple regressionanalysis (named PIOLadj), following a procedure described inthe next section. These values of IOL power (PIOLadj) werecompared with the real power of the IOL implanted (PIOLReal).An PIOL calculation was also performed using threeconventional formulae (Haigis [20], Hoffer Q [21] and Holladay

( )

−

+

−

−

=

ELPcPdesR

hanhan

ELPALhvn

IOLP

Optimization of lentis mplus IOL power calculation

502172


Ⅰ [22]) considering the ELP defined for each formula andRdes=SEpost. All these values of PIOL were also compared toPIOLadj. The calculation with the conventional IOL powerformulas was performed by implementing them in an Excelsoftware sheet version 14.0.0 for Mac.Estimation of adjusted effective lens positionConsidering the equation 1, PIOLreal, Pkadj and Rdes=SEpost, anestimation of ELP was obtained in each case. By means ofmultiple regression analysis, a mathematic expression wasobtained for predicting the ELP in each specific case. ThisELP was named as adjusted effective lens position (ELPadj).Preoperative and postoperative examinationsPreoperatively, all patients had a full ophthalmologicexamination including the evaluation of the refractive status,distance and near visual acuities, slit lamp examination,optical biometry (IOL-Master, Zeiss), applanation tonometryand funduscopy. Distance (4 m) and near (40 cm) visualacuities were evaluated with ETDRS charts. Postoperatively,patients were evaluated at 1d, 1wk, 1mo and 3mo aftersurgery. In all visits, visual acuity, refraction and the integrityof the anterior segment were evaluated. Funduscopy was alsoperformed in the postoperative revision at 3mo.Statistical Analysis The statistical analysis was performedusing the SPSS statistics software package version 21.0.0.0for Mac (IBM, Armonk, NY, USA). Normality of datasamples was evaluated by means of the Kolmogorov-Smirnov test. When parametric analysis was possible, theStudent test for paired data was used for comparing thedifferent approaches for PIOL calculation. When parametricanalysis was not possible, the Wilcoxon rank sum test wasapplied to assess the significance of such comparisons.Differences were considered to be statistically significantwhen the associated -value was of less than 0.05.Regarding the interchangeability between pairs of methodsfor obtaining PIOL, the Bland-Altman analysis was used[23].A multiple regression analysis was performed by using thebackward elimination method for obtaining a mathematicalexpression allowing the prediction of ELPadj from differentpreoperative anatomical and clinical parameters. Modelassumptions were evaluated by analysing residuals, thenormality of non-standardized residuals (homoscedasticity),and the Cook distance to detect influential points or outliers.In addition, the lack of correlation between errors andmulticolinearity was assessed using the Durbin-Watson test,the calculation of the colinearity tolerance, and the varianceinflation factor.RESULTSThis study evaluated 25 eyes of 13 patients [6 men (46.2%)and 7 women (53.8%)], with a mean age of 65.6y依7.6 SD(range, 50 to 83y). The sample comprised 12 (48%) and 13(52%) right and left eyes, respectively. Table 1 summarizessome preoperative visual, refractive and anatomical data of

the eyes evaluated as well as all the estimation performed forELP and IOL power. According to axial length (AL), anteriorchamber depth (ACD) and corneal power, and using theSRK-T formula, the mean power of the IOL implanted was19.78 D依2.32 SD (range, 12.50 to 23.50 D).Agreement of PIOLReal and PIOLadjSRK/T Statistically significantdifferences were found between PIOLadjSRK/T and PIOLReal,considering that ELP was calculated following the SRK/Tformula guidelines and considering Rdes=SEpost ( <0.01,Wilcoxon test). A very strong and statistically significantcorrelation was found between PIOLadj and PIOLReal ( =0.86,

<0.01, Figure 1). According to the Bland and Altmananalysis of interchangeability, the PIOLadjSRK/T was higher thanPIOLReal (mean difference: 1.41 D) and the limits of agreement

Table 1 Summary of several parameters involved in the study: mean preoperative anatomical and corneal power (calculated with the conventional keratometric index 1.3375, the Haigis approach[20] and the approach developed by our research group[18]) parameters, mean preoperative and postoperative SE, mean nkadj (calculated with our approach[18]), and mean ELP and IOL power calculated with different formulas

Parameters sx ± Range SEpre (D) -1.27± 2.87 -7.50 to 3.00 SEpost (D) -0.11±0.56 -1.83 to 0.76 r1c

[24] 7.61 ± 0.25 7.19 to 8.01 ACD[24] 3.31 ± 0.28 2.61 to 3.79 AL[24] 23.52 ± 1.04 22.02 to 27.36 ELPSRK/T

[24] 5.12 ± 0.45 4.60 to 6.83 ELPadj

[24] 4.31 ± 0.50 3.39 to 5.34 ELPHaigis

[24] 5.01 ± 0.16 4.77 to 5.46 ELPHofferQ

[24] 5.00 ± 0.27 4.63 to 6.01 ELPHolladay

[24] 4.59 ± 0.27 3.89 to 5.07 nkadj 1.328 ± 0.002 1.325 to 1.331 Pk(1.3375) (D) 44.37 ± 1.44 42.14 to 46.95 PcHaigis (D) 43.57 ± 1.41 41.39 to 46.11 Pkadj (D) 43.11 ± 1.61 40.62 to 45.99 PIOLReal (D) 19.78 ± 2.32 12.50 to 23.50 PIOLadjSRK/T (D) 21.18 ± 2.74 12.51 to 25.46 PIOLadj (D) 19.71 ± 2.55 11.02 to 23.53 PIOLHaigis (D) 20.40 ± 3.15 10.16 to 24.99 PIOLHofferQ (D) 19.30 ± 3.04 9.50 to 23.90 PIOLHolladay (D) 19.57 ± 2.99 9.40 to 23.90

SEpre: Preoperative spherical equivalent; SEpost: Postoperative spherical equivalent; r1c: Radius of curvature of the anterior corneal surface; ACD: Anterior chamber depth; AL: Axial length; ELPSRK/T: Effective lens position for the SRK/T formula; ELPadj: Effective lens position for the adjusted formula; ELPHaigis: Effective lens position for the Haigis formula; ELPHofferQ: Effective lens position for the Hoffer Q formula; ELPHolladay: Effective lens position for the Holladay formula; nkadj: Adjusted keratometric index; Pk(1.3375): Corneal power obtained using IOL-Master or keratometric power; PcHaigis: Corneal power obtained for the Haigis formula; Pkadj: Corneal power obtained using the adjusted keratometric index; PIOLReal: Power of the intraocular lens implanted which was calculated using the SRK/T formula; PIOLadjSRK/T: Power of the intraocular lens obtained using adjusted formula and ELP calculated with the SRK/T formula; PIOLadj: Intraocular lens power obtained using the adjusted formula and ELPadj; PIOLHaigis: Intraocular lens power obtained using the Haigis formula; PIOLHofferQ: Intraocular lens power obtained using the Hoffer Q formula; PIOLHolladay: Intraocular lens power obtained using the Holladay formula.

503173

were clinically relevant (3.29 and -0.48 D). Figure 2 showsthe Bland and Altman plot corresponding to this agreementanalysis.Estimation of ELPadj The multiple regression analysisrevealed that the ELPadj was significantly correlated with AL,ACD and Pkadj ( <0.01):ELPadj=-17.333+0.612伊ACD+0.360伊AL+0.268伊Pkadj（3）

The homoscedasticity of the model was confirmed by thenormality of the non-standardized residuals distribution( =0.20) and the absence of influential points or outliers(mean Cook's distance: 0.155依0.528). With this model, 56%of non-standardized residuals were 0.20 or lower and 76%were lower than 0.50. The poor correlation between residuals(Durbin-Watson test: 1.629) and the lack of multicolinearity(tolerance 0.805 to 0.560; variance inflation factors 1.785 to1.243) was also confirmed.A statistically significant difference was found between

ELPadj and the rest of ELP values obtained following theguidelines proposed by each of the formulas used ( <0.01,unpaired Wilcoxon test). ELPadj was the lowest ELP value(Table 1) among all values of ELP calculated (4.31依0.50 mm,range 3.39 to 5.34 mm).Agreement between PIOLReal and PIOLadj No statisticallysignificant differences were found between PIOLadj and PIOLReal

when ELPadj and Rdes=SEpost were considered for PIOLadj

calculation ( =0.65, unpaired Student's -test). A verystrong and statistically significant correlation was foundbetween PIOLadj and PIOLReal ( =0.95, <0.01) (Figure 3).According to the Bland and Altman [23] analysis, the meandifference between both PIOLadj and PIOLReal was -0.07 D, withlimits of agreement of 1.47 and -1.61 D. Figure 4 shows theBland and Altman plot corresponding to this agreementanalysis.Agreement of PIOLadj with other formulas Statisticallysignificant differences were found between PIOLadj and PIOLHaigis,

and between PIOLadj and PIOLHofferQ ( <0.01, Wilcoxon test), butnot between PIOLadj and PIOLHolladay ( =0.20, Wilcoxon test).

Figure 1 Relationship between the adjusted IOL power usingthe ELP estimated using the SRK/T formula guidelines(PIOLadjSRK/T) and the real power of the IOL implanted (PIOLReal).

Figure 2 Bland-Altman plots for the comparison between theadjusted IOL power using the ELP estimated using the SRK/Tformula guidelines (PIOLadjSRK/T) and the real power of the IOLimplanted (PIOLReal) The dotted lines show the limits of agreement(依1.96SD).

Figure 4 Bland-Altman plots for the comparison between theadjusted IOL power using the regression analysis adjustedELP (PIOLadj) and the real power of the IOL implanted (PIOLReal)The dotted lines show the limits of agreement (依1.96SD).

Figure 3 Relationship between the adjusted IOL power usingthe regression analysis adjusted ELP (PIOLadj) and the realpower of the IOL implanted (PIOLReal).


504174


Table 2 shows the Bland and Altman analysis outcomescorresponding to all comparisons done. A very strong andstatistically significant correlation was found between PIOLadj

and PIOLHolladay ( = 0.96, <0.01, Figure 5). According to theBland and Altman [23] analysis, the mean difference betweenboth PIOLadj and PIOLHolladay was -0.13 D, with limits of agreementof 1.01 and -1.28 D. Figure 6 shows the Bland and Altmanplot corresponding to this agreement analysis.Agreement of PIOLreal with other formulas Statisticallysignificant differences were found between PIOLreal and PIOLHaigis,

and between PIOLreal and PIOLHofferQ ( <0.05, Wilcoxon test), butnot between PIOLreal and PIOLHolladay ( =0.29, Wilcoxon test).Table 3 shows the Bland and Altman analysis outcomescorresponding to all comparisons done. According to theBland and Altman method, the mean difference betweenPIOLHolladay and PIOLreal was -0.21 D, with limits of agreement of1.96 and -2.37 D (Figure 7).DISCUSSIONThe refractive results obtained after cataract surgery withimplantation of a multifocal IOL based on the concept ofrefractive rotationally asymmetry, the Lentis LS-312 IOL,have been evaluated in the current series. A significantvariability in the postoperative SE was observed in theanalyzed sample, with a mean value of -0.11 依0.56 D.Specifically, the SE at 3mo after surgery ranged from -1.83 to+0.76 D, with a slight trend to some level of residual myopia,as in some previous series evaluating the results of the same

type of multifocal IOL [2,11,15]. This confirms that anoptimization in the algorithm of IOL power calculation isnecessary in order to refine the refractive and visualoutcomes with this premium multifocal IOL. The relativelimitation of the predictability of the refractive correction insome cases implanted with the Mplus IOL may beattributable to the bias associated to the use of thekeratometric approach for the calculation of the cornealpower, errors in the determination of the axial length orinaccuracy in the estimation of the ELP for this specific IOL.However, the errors in the estimation of axial length with thetechnology used have been shown to be minimal and with avery limited impact on the refractive predictability [24].Therefore, in the current study, the potential contribution ofthe corneal power and ELP factors to the limitation of the

Table 2 Bland and Altman analysis outcomes of the comparison between PIOLadj and the IOL power obtained with other commonly used formulas

Comparison ∆PIOL ±SD (D) LoA (D) P PIOLHaigis - PIOLadj 0.68 ± 0.72 2.09 to -0.73 <0.01 PIOLHofferQ - PIOLadj -0.43 ± 0.75 1.05 to -1.90 <0.01 PIOLHolladay - PIOLadj -0.13 ± 0.67 1.01 to -1.28 0.20

Figure 6 Bland-Altman plots for the comparison between theadjusted IOL power using the regression analysis adjustedELP (PIOLadj) and the IOL power when using the Holladayformula (PIOLHolladay) The dotted lines show the limits of agreement

(依1.96 SD).

Figure 7 Bland-Altman plots for the comparison between theIOL power when using the Holladay formula (PIOLHolladay) andthe real power of the IOL implanted (PIOLHolladay) The dotted lines

show the limits of agreement (依1.96SD).

Table 3 Bland and Altman analysis outcomes of the comparison between PIOLreal and the IOL power obtained with other commonly used formulas

Comparison ∆PIOL ±SD (D) LoA (D) P PIOLHaigis - PIOLreal 0.62 ± 1.15 2.88 to -1.64 0.01 PIOLHofferQ - PIOLreal -0.43 ± 1.13 1.73 to -2.69 0.03 PIOLHolladay - PIOLreal -0.13 ± 1.10 1.96 to -2.37 0.29

Figure 5 Relationship between the adjusted IOL power usingthe regression analysis adjusted ELP (PIOLadj) and the IOLpower when using the Holladay formula (PIOLHolladay).

505175

refractive predictability with the multifocal IOL evaluatedhave been investigated.First, the potential impact of the keratometric error wasanalysed by calculating the corneal power using an adjustedkeratometric index aimed at minimizing the clinical error inthe estimation of the corneal power[17,18]. This adjusted cornealpower was used to obtain an estimation of the IOL powerconsidering the axial length and an ELP estimated followingthe algorithm established for the SRK-T formula [19]. With thisapproach, statistically significant and clinically relevantdifferences were found between the adjusted calculation(PIOLadjSRK/T) and the real power of the IOL implanted that wasselected according to the SRK-T formula (PIOLReal) [19].Therefore, the correction of this factor seems to have aminimal effect on the outcomes achievable with themultifocal IOL evaluated. Then, ELP was thought to be acritical factor for the presence of a relatively limitedpredictability with the IOL evaluated. For such purpose, anexpression for estimating an optimized ELP according tosome preoperative parameters was obtained by means ofmultiple linear regression. This new ELP estimation wasnamed adjusted ELP (ELPadj). The ELPadj were compared tothose ELP values obtained with other predicting algorithmsof ELP [19-21]. This analysis revealed that the ELPadj wassignificantly lower compared to the values estimated with theHaigis, Hoffer Q and Holladay Ⅰ formulas (ELPHaigis,ELPHofferQ and ELPHolladay respectively) [20,21]. In any case,differences between ELPadj and ELPHolladay were found to be thelowest in magnitude and this may be the reason for theabsence of statistically significant differences between PIOLadj

and PIOLHolladay. In contrast, the difference was statisticallysignificant and clinically relevant when our IOL power(PIOLadj) was compared to Haigis or Hoffer Q formulas (PIOLHaigis

and PIOLHofferQ, respectively). One factor attributable to thelower value of ELPadj compared to those ELP values obtainedwith conventional formulas is a more anterior position of theoptic of the multifocal IOL evaluated due to the flexibility ofthe haptics. This more anterior position was better predictedwith the Holladay formula and with our ELPadj calculationalgorithm (see equation 3). This may explain in part the trendtoward myopia observed in our sample, in which the IOLpower calculation was performed with the SRK-T formulathat uses higher estimated values of ELP. Indeed, consideringequation 1, a longer ELP would lead to the calculation of ahigher value of IOL power that may potentially lead to thepresence of postoperative myopia. Future studies shouldevaluate the real position of the IOL within the capsular bagby means of imaging techniques in order to confirm ourhypotheses, as has been done for other types of IOLs[25].In our linear regression analysis, ELPadj was found to berelated to some factors, such as the AL, Pkadj and the ACD.

The anatomical factors were crucial determinants of the finalposition of the IOL evaluated within the eye. ELPadj washigher in those eyes with longer AL and ACD, as happens inmoderate to high myopic eyes. This finding was consistentwith those reported by previous authors, reporting a lineardependence of the final position of the IOL on the AL [26-28].Considering that ELPadj and ELPHolladay were not significantlydifferent, this formula seems to be the most recommendableapproach for IOL power calculation with the multifocal IOLevaluated. More studies with larger samples sizes should beperformed to confirm all these outcomes.Finally, it should be mentioned that when all IOL powerformulas were compared with PIOLreal, PIOLadj and PIOLHolladay didnot differ significantly with PIOLreal. The Bland-Altman plotsshowed less clinically relevant level of agreement of PIOLreal

with PIOLadj than with PIOLHolladay (Figures 4, 7). Therefore, PIOLadj

was able to reproduce more accurately PIOLReal and therefore ofthe refractive outcome. This suggests that our approach maybe a useful method for IOL power calculation with themultifocal IOL evaluated. This should be corroborated infuture prospective studies.There are several limitations in the current research, such asthe limited sample size or the short follow-up. It should beconsidered that, although rare, changes in IOL position hasbeen described more than 3mo after surgery, especially afterNd:YAG capsulotomy [29]. This requires further analysis andinvestigation in future studies with the Mplus IOL. Anotherpotential limitation is the determination of refraction with thismultifocal IOL. Some difficulties have been described forobtaining an accurate refraction after implantation ofdifferent models of IOL, with a clear trend to overestimationof the sphere with positive sign [30]. In any case, the manifestrefraction was obtained using the same procedure describedfor refracting eyes with multifocal IOLs [31] and without usingthe autorrefraction as the basis because it has been shown tofail in eyes implanted with the Mplus IOL [32]. Finally, itshould be mentioned that the Holladay II formula was notused in our comparison as it was not available in our clinic.Possibly, our approach may be more similar to the results ofthe Holladay II formula as both types of calculation use anoptimized algorithm for the estimation of ELP, but thisshould be confirmed in future studies.In conclusion, refractive outcomes after cataract surgery withimplantation of refractive rotationally asymmetric IOL LentisMplus LS-312 may be optimized by minimizing thekeratometric error using a variable keratometric index forcorneal power estimation and by estimating ELP using amathematical expression dependent on anatomical factors.Future studies should be performed to validate this model ofIOL power calculation for the Lentis Mplus IOL with larger


506176


sample of sizes including more extreme cases (long andshort AL).ACKNOWLEDGEMENTSConflicts of Interest: Pi觡ero DP, None; Camps VJ, None;Ram佼n ML, None; Mateo V, None; P佴rez-Cambrod侏 RJ,None.REFERENCES1 Ram佼n ML, Pi觡ero DP, P佴rez-Cambrod侏 RJ. Correlation of visual

performance with quality of life and intraocular aberrometric profile in

patients implanted with rotationally asymmetric multifocal IOLs.

2012;28(2):93-99

2 Ali佼 JL, Pi觡ero DP, Plaza-Puche AB, Chan MJ. Visual outcomes and

optical performance of a monofocal intraocular lens and a new-generation

multifocal intraocular lens. 2011;37(2):241-250

3 Ali佼 JL, Plaza-Puche AB, Pi觡ero DP, Amparo F, Jim佴nez R,

Rodr侏guez-Prats JL, Javaloy J, Pongo V. Optical analysis, reading

performance, and quality-of-life evaluation after implantation of a

diffractive multifocal intraocular lens. 2011;37(1):

27-37

4 Alfonso JF, Fern觃ndez-Vega L, Puchades C, Mont佴s-Mic佼 R.

Intermediate visual function with different multifocal intraocular lens

models. 2010;36(5):733-739

5 Kohnen T, Nuijts R, Levy P, Haefliger E, Alfonso JF. Visual function

after bilateral implantation of apodized diffractive aspheric multifocal

intraocular lenses with a +3.0 D addition. 2009;35

(12): 2062-2069

6 Alfonso JF, Puchades C, Fern觃ndez-Vega L, Mont佴s-Mic佼 R, Valc觃rcel

B, Ferrer-Blasco T. Visual acuity comparison of 2 models of bifocal

aspheric intraocular lenses. 2009;35(4):672-676

7 Alfonso JF, Fern觃ndez-Vega L, Se觡aris A, Mont佴s-Mic佼 R. Prospective

study of the Acri.LISA bifocal intraocular lens.

2007;33(11):1930-1935

8 Alfonso JF, Fern觃ndez-Vega L, Baamonde MB, Mont佴s-Mic佼.Prospective visual evaluation of apodized diffractive intraocular lenses.

2007;33(7):1235-1243

9 Venter JA, Pelouskova M, Collins BM, Schallhorn SC, Hannan SJ. Visual

outcomes and patient satisfaction in 9366 eyes using a refractive segmented

multifocal intraocular lens. 2013;39(10): 1477-1484

10 van der Linden JW, van Velthoven M, van der Meulen I, Nieuwendaal

C, Mourits M, Lapid-Gortzak R. Comparison of a new-generation sectorial

addition multifocal intraocular lens and a diffractive apodized multifocal

intraocular lens. 2012;38(1): 68-73

11 Ali佼 JL, Plaza-Puche AB, Javaloy J, Ayala MJ, Moreno LJ, Pi觡ero DP.

Comparison of a new refractive multifocal intraocular lens with an inferior

segmental near add and a diffractive multifocal intraocular lens.

2012;119(3): 555-563

12 Alfonso JF, Fern觃ndez-Vega L, Bl觃zquez JI, Mont佴s-Mic佼 R. Visual

function comparison of 2 aspheric multifocal intraocular lenses.

2012;38(2):242-248

13 Mu觡oz G, Albarr觃n-Diego C, Ferrer-Blasco T, Sakla HF,

Garc侏a-L觃zaro S. Visual function after bilateral implantation of a new zonal

refractive aspheric multifocal intraocular lens.

2011;37(11):2043-2052

14 McAlinden C, Moore JE. Multifocal intraocular lens with a

surface-embedded near section: short-term clinical outcomes.

2011;37(3): 441-445

15 Ali佼 JL, Plaza-Puche AB, Pi觡ero DP, Javaloy J, Ayala MJ. Comparative

analysis of the clinical outcomes with 2 multifocal intraocular lens models

with rotational asymmetry. 2011;37(9):1605-1614

16 Olsen T. Calculation of intraocular lens power: a review.

2007;85(5): 472-485

17 Camps VJ, Pi觡ero DP, de Fez D, Mateo V. Minimizing the IOL power

error induced by keratometric power. Optom Vis Sci 2013;90(7): 639-649

18 Camps VJ, Pi觡ero DP, de Fez D, Coloma P, Caballero MT, Garcia C,

Miret JJ. Algorithm for correcting the keratometric estimation error in

normal eyes. 2012;89(2): 221-228

19 Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T

intraocular lens implant power calculation formula.

1990;16(3):333-340

20 Haigis W. The Haigis formula. In Shammas HJ, ed.

. Thorofare, NJ: Slack; 2004:41-57

21 Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and

regression formulas. 1993;19(6):700-712

22 Holladay JT, Prager TC, Chandler TY, Musgrove KH, Lewis JW, Ruiz

RS. A three-part system for refining intraocular lens power calculations.

1988;14(1):17-24

23 Bland JM, Altman DG. Statistical methods for assessing agreement

between two methods of clinical measurement. 1986;1 (8476):

307-310

24 Faria-Ribeiro M, Lopes-Ferreira D, L佼pez-Gil N, Jorge J,

Gonz佗lez-M佴ijome JM. Errors associated with IOL Master biometry as a

function of internal ocular dimensions. 2014;7(2):75-78

25 Ho JD, Liou SW, Tsai RJ, Tsai CY. Estimation of the effective lens

position using a rotating Scheimpflug camera.

2008;34(12):2119-2127

26 Engren AL, Behndig A. Anterior chamber depth, intraocular lens

position, and refractive outcomes after cataract surgery.

2013;39(4):572-577

27 Norrby S. Sources of error in intraocular lens power calculation.

2008;34(3):368-376

28 Preussner PR, Wahl J, Weitzel D, Berthold S, Kriechbaum K, Findl O.

Predicting postoperative intraocular lens position and refraction.

2004;30(10):2077-2083

29 Findl O, Drexler W, Menapace R, Georgopoulos M, Rainer G,

Hitzenberg CK, Fercher AF. Changes in intraocular lens position after

neodymium: YAG capsulotomy. 1999;25: 659-662

30 Pi觡ero DP, Ayala Espinosa MJ, Ali佼 JL. LASIK outcomes following

multifocal and monofocal intraocular lens implantation.

2010;26(8):569-577

31 Mohammadi SF, Rahman-A N, Mazouri A. Subjective refraction in eyes

with multifocal IOLs. 2011;27(3):16; author replay 162

32 van der Linden JW, Vrijman V, El-Saady R, van der Meulen IJ, Mourits

MP, Lapid-Gortzak R. Autorefraction versus subjective refraction in a

radially asymmetric multifocal intraocular lens. 2014;92

(8):764-768

507177

·Original article·

Preliminary evaluation of an algorithm to minimize thepower error selection of an aspheric intraocular lens byoptimizing the estimation of the corneal power and theeffective lens positionDavid P. Pi觡ero1,2, Vicente J. Camps1, Mar侏a L. Ram仵n2, Ver佼nica Mateo1, RobertoSoto-Negro2

1Group of Optical and Visual Perception, Department ofOptics, Pharmacology and Anatomy, University of Alicante,San Vicente del Raspeig, Alicante 03690, Spain2Department of Ophthalmology, Vithas Medimar InternationalHospital, Alicante 03016, SpainCorrespondence to: David P. Pi觡ero. Department ofOphthalmology, Vithas Medimar International Hospital,Alicante 03016, Spain. dpinero@ oftalmar. esReceived: 2015-07-23摇摇 Accepted: 2016-03-17

非球面人工晶状体度数计算的最优化David P. Pi觡ero1,2, Vicente J. Camps1, Mar侏a L. Ram仵n2,Ver佼nica Mateo1, Roberto Soto-Negro2

(作者单位:1西班牙,阿利坎特 03690,圣维森特-德埃拉斯佩

奇,阿利坎特大学,视光学、药理学和解剖学系,光学和视觉知觉

组;2西班牙,阿利坎特 03016,Vithas Medimar 国际医院,眼科)通讯作者:David P. Pi觡ero. dpinero@ oftalmar. es

摘要目的:通过评价非球面人工晶状体( intraocular lens, IOL)屈光度的可预测性,初步开发一种计算屈光度(PIOL)的优

化算法。方法:本研究纳入植入非球面 IOL ( LENTIS L - 313,Oculentis GmbH)65 眼,并分为 2 组:A 组 8 例 12 眼,PIOL逸23. 0D;B 组 35 例 53 眼,PIOL<23. 0D。术后 3mo 进行屈光

度可预测性评价。参考角膜屈光力估计所致的可变性屈

光指数计算出校正的 IOL 度数(PIOLadj)及屈光结果,根据

年龄和解剖学因素得出校正的有效晶状体位置( adjustedeffective lens position, ELPadj)。结果:术后 A、B 两组等效球镜度数分别为-0. 75 ~ +0郾 75D、-1. 38 ~ +0. 75D。 A、B 两组的 PIOLadj和实际晶状体屈光度

(PIOLReal)之间无统计学差异 ( P = 0. 64、0. 82)。 Bland -Altman 分析显示 A、B 两组 PIOLadj和 PIOLReal之间的一致性区

间分别为+1. 11 ~ -0. 96D 和+1. 14 ~ -1. 18D。 Hoffer Q公式和 Holladay I 公式计算 PIOLadj和 PIOL之间存在临床和

统计学上的显著差异(P<0. 01)。结论:植入非球面 IOL 白内障手术的屈光可预测性可通过

平行轴光学联合线性法则使角膜屈光力及晶状体位置相

关误差最小化。

关键词:非球面人工晶状体;人工晶状体屈光度计算;有效

晶状体位置

引用:Pi觡ero DP, Camps VJ, Ram仵n ML, Mateo V, Soto-NegroR. 非球面人工晶状体度数计算的最优化. 国际眼科杂志 2016;16(6):1001-1008

Abstract誗AIM: To evaluate the refractive predictability achievedwith an aspheric intraocular lens ( IOL) and to develop apreliminary optimized algorithm for the calculation of itspower (PIOL) .誗METHODS: This study included 65 eyes implanted withthe aspheric IOL LENTIS L - 313 (Oculentis GmbH) thatwere divided into 2 groups: 12 eyes (8 patients) with PIOL

逸23. 0 D (group A), and 53 eyes (35 patients) with PIOL<23. 0 D ( group B ) . The refractive predictability wasevaluated at 3mo postoperatively. An adjusted IOL power(PIOLadj ) was calculated considering a variable refractiveindex for corneal power estimation, the refractiveoutcome obtained, and an adjusted effective lens position(ELPadj) according to age and anatomical factors.誗 RESULTS: Postoperative spherical equivalent rangedfrom - 0. 75 to + 0. 75 D and from - 1. 38 to + 0. 75 D ingroups A and B, respectively. No statistically significantdifferences were found in groups A (P = 0. 64) and B (P =0. 82 ) between PIOLadj and the IOL power implanted(PIOLReal) . The Bland and Altman analysis showed rangesof agreement between PIOLadj and PIOLReal of +1. 11 to -0. 96D and +1. 14 to -1. 18 D in groups A and B, respectively.Clinically and statistically significant differences werefound between PIOLadj and PIOL obtained with Hoffer Q andHolladay I formulas (P<0. 01) .誗CONCLUSION: The refractive predictability of cataractsurgery with implantation of an aspheric IOL can beoptimized using paraxial optics combined with linearalgorithms to minimize the error associated to theestimation of corneal power and ELP.誗KEYWORDS:aspheric intraocular lens; intraocular lenspower calculation; effective lens positionDOI:10. 3980 / j. issn. 1672-5123. 2016. 6. 01

1001

Int Eye Sci, Vol. 16, No. 6, Jun. 2016摇摇 http: / / ies. ijo. cnTel:029鄄82245172摇 82210956摇摇 Email:IJO. 2000@163. com

179

Citation:Pi觡ero DP, Camps VJ,Ram佼n ML, Mateo V, Soto-NegroR. Preliminary evaluation of an algorithm to minimize the powererror selection of an aspheric intraocular lens by optimizing theestimation of the corneal power and the effective lens position. GuojiYanke Zazhi( Int Eye Sci) 2016;16(6):1001-1008

INTRODUCTION

T he human eye is composed of two aspheric lenses, corneaand crystalline lens, which are the main ocular optical

elements accounting for the final quality of the retinal image.The cornea is comprised of two prolate surfaces that inducepositive spherical aberration that increases with age[1] . Thecrystalline lens is comprised of two aspheric surfaces thatinduce negative spherical aberration[2] . With age, thebalance between the spherical aberration of the cornea andcrystalline lens is progressively lost, leading to a reduction inthe level of quality of the retinal image[3-6] . Asphericintraocular lenses ( IOLs) were developed with the aim ofproviding a compensation for the corneal positive sphericalaberration and therefore to maintain the balance in terms ofspherical aberration between cornea and IOL after cataractsurgery[7] . An aspheric IOL may lead then to the achievementof better contrast sensitivity compared to a spherical IOL,especially under dim light conditions[7] .According to some optical simulations, a real benefit can beobtained with aspheric IOLs in corneas of a moderate prolateaspheric shape with a negative asphericity ( Q) value of-0. 22 or below[8] . In spite of the potential benefit of asphericIOLs over conventional spherical IOLs, it should bementioned that the outcomes obtained with aspheric IOLs aremore susceptible to misalignments or decentrations[9] as wellas to residual optical errors[10] . Furthermore, the potentialbenefit of aspheric IOLs has been suggested to be more limitedin longer eyes than in short eyes[8] . This may be due to someinaccuracies in IOL power calculations in such cases.Hoffmann and Lindeman[11] demonstrated that ray tracingbased on biometry data improved IOL prediction accuracy overconventional formulas in normal eyes implanted with asphericIOLs. The aim of the current study was to evaluate thepredictability of the refractive correction achieved with aspecific model of aspheric IOL and to develop a preliminaryalgorithm for IOL power calculation to optimize the refractivepredictability with this IOL by minimizing the error associatedto the keratometric estimation of the corneal power and bydeveloping a predictive formula for the estimation of theeffective lens position. This study was planned as apreliminary evaluation of the possibility of a furtheroptimization of IOL power calculation using paraxial optics.SUBJECTS AND METHODSPatients摇 A total of 65 eyes of 43 patients ranging in agefrom 56 to 92 years old were included retrospectively in thisstudy. All these eyes underwent cataract surgery withimplantation of the aspheric IOL LENTIS L-313 (OculentisGmbH, Berlin, Germany). As will be explained later, twogroups of eyes were differentiated according to the power of the

IOL implanted: group A, including 12 eyes of 8 patientsimplanted with an IOL 逸23. 0 D, and group B, including 53eyes of 35 patients with an IOL < 23. 0 D of power. Theinclusion criteria of this study were patients with visuallysignificant cataract or presbyopic / pre - presbyopic patientssuitable for refractive lens exchange. The exclusion criteriawere patients with active ocular diseases, illiteracy andtopographic astigmatisms > 1. 5 D. All volunteers wereadequately informed and signed a consent form. The studyadhered to the tenets of the Declaration of Helsinki and wasapproved by the ethics committee of the University of Alicante(Alicante, Spain) .Intraocular Lens 摇 The LENTIS L-313 is an acrylic one -piece IOL with a hydrophobic surface and ultraviolet-filteringcomponents. It has biconvex design with a 6. 0-mm optic, anoverall length of 11. 0 mm, and a C-loop haptic design with 0- degree angulation. The posterior surface of the IOL isaspheric and provides some level of negative sphericalaberration aimed at compensating for the positive sphericalaberration of the cornea. It is available in powers from 10 to30 D in 0. 5-D steps and from 0 to 10 D and from 30 to 35 Din 1. 0-D steps.Surgical Technique 摇 All surgeries were performed by oneexperienced surgeon (Ram佼n ML) using a standard techniqueof phacoemulsification. In all cases, topical anesthesia wasadministered and pupillary dilation was induced with acombination of tropicamide and phenylephrine 10% every15min half an hour previous to the procedure. Iodine solution5% was instilled on the eye 10min before the operation. A2郾 75-mm clear incision was made with a diamond knife onthe steepest meridian to minimize post-surgical astigmatism.A paracentesis was made 60毅 -90毅 clockwise from the mainincision and the anterior chamber was filled with viscoelasticmaterial. After the crystalline lens removal, the IOL wasimplanted through the incision into the capsular bag using aspecific injector developed by the manufacturer for suchpurpose. Finally, the surgeon proceeded to retrieve theviscoelastic material using the irrigation-aspiration system. Acombination of topical steroid and antibiotic ( Tobradex,Alcon, Fort Worth, TX, USA) as well as a non - steroidalanti - inflammatory drops ( Dicloabak, Laboratorios Thea,Barcelona, Spain) were prescribed to be applied 4 times dailyfor 1wk after the surgery and 3 times daily the secondpostoperative week. In addition, the non - steroidal anti -inflammatory drops were also prescribed to be applied 3 timesdaily during 2wk more after surgery.Preoperative and Postoperative Examinations 摇Preoperatively, all patients had a full ophthalmologicexamination including the evaluation of the refractive status,distance and near visual acuities, slit lamp examination,optical biometry ( IOL -Master, Carl Zeiss Meditec, Jena,Germany ), tonometry and funduscopy. Postoperatively,patients were evaluated at 1d, 1wk, 1 and 3mo after surgery.In all visits, visual acuity, refraction and the integrity of theanterior segment were evaluated. Funduscopy was alsoperformed in the postoperative revision at 3mo.

2001

国际眼科杂志摇 2016 年 6 月摇第 16 卷摇第 6 期摇摇 http: / / ies. ijo. cn电话:029鄄82245172摇摇 82210956摇摇电子信箱:IJO. 2000@ 163. com

180

Calculation of the Adjusted IOL Power 摇 Almost alltheoretical formulas for IOL power calculation are based on theuse of a simplified eye model, with thin cornea and lensmodels[12] . According to such approach, the power of the IOL(PIOL) can be easily calculated using the Gauss equations inparaxial optics[13]:

where Pc is the total corneal power, ELP is the effective lensplane, AL is the axial length of the eye, nha is the aqueoushumour refractive index, nhv is the vitreous humour refractiveindex and Rdes represents the postoperative desired refractioncalculated at corneal vertex.Our research group proposed in 2012 the use of a variablekeratometric index ( nkadj ) depending on the radius of theanterior corneal surface ( r1c ) expressed in millimetres forminimizing the error associated to the keratometric approachfor corneal power calculation[14] . Specifically, the followingexpression was defined according to the Gullstrand eye model:

nkadj = -0. 0064286r1c+ 1. 37688摇摇摇摇摇摇摇摇摇 (2)

Using this algorithm, a new keratometric corneal power,named adjusted keratometric corneal power ( Pkadj ), can becalculated using the classical keratometric approach forcorneal power estimation without clinically relevant error[15] .In the current study, an adjusted IOL power ( PIOLadj ) wascalculated, which was defined as the IOL power calculatedfrom the equation 1 using the nkadj value for the estimation ofthe corneal power ( Pkadj), as well as the nha and nhv valuescorresponding to the Gullstrand eye model (1. 336). In suchcalculation, the postoperative spherical equivalent at cornealvertex was considered as the desired refraction (Rdes =SEpost).This adjusted IOL power (PIOLadj) was compared with the realpower of the IOL implanted (PIOLReal). The PIOLadj calculationwas performed after estimating the ELP(effective lens plane)using two different approaches: ELP calculation following theSRK / T formula guidelines ( named PIOLadjSRK / T ) and ELPcalculation using a mathematical expression obtained bymultiple regression analysis ( named ELPadj ), as explainedcarefully in the next section.Furthermore, the PIOL was also calculated using threeconventional formulas ( Haigis, Hoffer Q and Holladay I )considering the ELP defined by each formula and that Rdes =SEpost . A comparative analysis was done between these valuesof PIOL and PIOLadj and PIOLReal . All the formulas wereimplemented in Excel version 14. 0. 0 for Mac ( Microsoft,Irvine, CA, USA).Estimation of Adjusted ELP by Multiple RegressionAnalysis 摇 Considering in each case the equation 1, thevalues of PIOLreal and Pkadj , and that Rdes = SEpost, the real ELP

was obtained. A multiple regression analysis was thenperformed to obtain a mathematical expression predicting thebest as possible the real ELP corresponding to each case. ThisELP was named adjusted effective lens position (ELPadj). Aninitial estimation of ELPadj was obtained considering the wholesample of 65 eyes, but the results were inconsistent leading toclinically relevant errors in the calculation of the PIOL adj . Aswe realized that the calculation of ELPadj was dependent on theIOL power implanted and consequently of the IOL geometry,two groups were differentiated according to this parameter,groups A and B, as previously mentioned. In group A, thiseffective lens position was named ELPadj 逸23, whereas in groupB it was named ELPadj<23 .Statistical Analysis 摇 The statistical analysis was performedusing the SPSS statistics software package version 21. 0 forMac (IBM, Armonk, NY, USA). Normality of data sampleswas evaluated by means of the Kolmogorov - Smirnov test.When parametric analysis was possible, the Student蒺s t- testfor paired data was used for comparing the differentapproaches for PIOL calculation. When parametric analysis wasnot possible, the Wilcoxon rank sum test was applied to assessthe significance of such comparisons. Differences wereconsidered to be statistically significant when the associated P-value was less than 0. 05. Regarding the interchangeabilitybetween pairs of methods used for obtaining PIOL, the Bland-Altman analysis was used[16] .A multiple regression analysis was used for predicting the realELP from different preoperative anatomical and clinicalparameters ( ELPadj ). Model assumptions were evaluated byanalysing residuals, the normality of non - standardizedresiduals ( homoscedasticity ), and the Cook蒺s distance todetect influential points or outliers. In addition, the lack ofcorrelation between errors and multicolinearity was assessedusing the Durbin - Watson test, the calculation of thecolinearity tolerance, and the variance inflation factor.RESULTSGroup A included 12 eyes of 8 patients [11 eyes in males(91. 7% )], with a mean age of 68. 2依9. 4y (range: 56. 0 to80. 0y ) . In this group, mean preoperative keratometry( Pk1. 3375 ), axial length ( AL) and anterior chamber depth(ACD) were 44. 79依1. 44 D ( range: 42. 92 to 47. 34 D),22. 33依0. 55 mm (range: 21. 30 to 23. 09 mm), and 2. 95依0. 33 mm ( range: 2. 41 to 3. 35 mm ), respectively.According to all these data and using the SRK-T formula,mean IOL power implanted ( PIOLReal ) was 23. 75 依 0. 69 D( range: 23. 00 to 25. 00 D). Group B included 53 eyes of 35patients [24 eyes in males (45郾 3% )], with a mean age of72. 2依7郾 1y (range: 57. 0 to 92. 0y) . Mean Pk1. 3375, AL andACD were 44. 37依1. 35 D (range: 41. 09 to 47. 28 D), 23.70依1. 13 mm (range: 22郾 20 to 28. 33 mm), and 3. 32依0. 34mm (range: 2. 48 to 4. 15 mm), respectively. According toall these data and using the SRK-T formula, mean IOL powerimplanted was 19. 72依3. 10 D ( range: 7. 50 to 22. 50 D).All these data are summarized in Table 1.

3001


181

Table 1摇 Mean visual, refractive, biometric and IOL power calculation data

ParameterPIOLReal逸23. 0D

Mean依SD RangePIOLReal<23. 0D

Mean依SD RangeSEpre(D) 1. 04依1. 64 -2. 38 to 2. 75 -0. 84依3. 05 -12. 38 to 3. 38SEpost(D) -0. 20依0. 40 -0. 75 to 0. 75 -0. 25依0. 44 -1. 38 to 0. 75r1c(mm) 7. 54依0. 24 7. 13 to 7. 86 7. 61依1. 13 7. 14 to 8. 21ACD (mm) 2. 95依0. 33 2. 41 to 3. 35 3. 32依0. 34 2. 48 to 4. 15AL (mm) 22. 33依0. 55 21. 30 to 23. 09 23. 70依1. 13 22. 20 to 28. 33ELPadjSRK / T(mm) 4. 60依0. 13 4. 37 to 4. 86 5. 17依0. 78 4. 65 to 9. 24ELPadj(mm) 4. 44依0. 31 3. 93 to 5. 01 4. 59依0. 50 3. 90 to 6. 16ELPHaigis(mm) 4. 75依0. 14 4. 54 to 4. 90 5. 04依0. 21 4. 66 to 5. 65ELPHofferQ(mm) 4. 68依0. 08 4. 59 to 4. 88 5. 06依0. 33 4. 74 to 6. 42ELPHolladay(mm) 3. 77依0. 42 3. 08 to 4. 29 4. 24依0. 43 3. 17 to 5. 31nkadj 1. 328依0. 002 1. 326 to 1. 331 1. 328依0. 002 1. 324 to 1. 331Pk 1. 3375(D) 44. 79依1. 44 42. 92 to 47. 34 44. 37依1. 35 41. 09 to 47. 28PcHaigis(D) 43. 99依1. 41 42. 16 to 46. 50 43. 58依1. 33 40. 35 to 46. 43Pkadj(D) 43. 58依1. 61 41. 50 to 46. 44 43. 11依1. 51 39. 45 to 46. 36PIOLReal(D) 23. 75依0. 69 23. 00 to 25. 00 19. 72依3. 10 7. 50 to 22. 50PIOLadjSRK / T(D) 24. 18依0. 99 21. 85 to 25. 87 20. 69依3. 00 9. 81 to 24. 31PIOLadj(D) 23. 82依1. 02 22. 16 to 25. 76 19. 70依3. 13 7. 41 to 23. 08PIOLHaigis(D) 23. 95依1. 16 21. 25 to 26. 14 19. 95依3. 58 6. 35 to 24. 05PIOLHofferQ(D) 22. 68依1. 47 20. 24 to 25. 07 17. 93依4. 15 4. 55 to 22. 47PIOLHolladay(D) 22. 90依1. 00 20. 51 to 24. 61 19. 19依3. 37 5. 58 to 23. 01

SEpre: Preoperative spherical equivalent; SEpost: Postoperative spherical equivalent; r1c: Radius of curvature of the anterior corneal surface;ACD: Anterior chamber depth; AL: Axial length; ELPSRK / T: Effective lens position for the SRK / T formula; ELPadj: Effective lens position forthe adjusted formula; ELPHaigis: Effective lens position for the Haigis formula; ELPHofferQ: Effective lens position for the Hoffer Q formula;ELPHolladay: Effective lens position for the Holladay formula; nkadj: Adjusted keratometric index; Pk1. 3375: Corneal power obtained using IOL-Master or keratometric power; PcHaigis: Corneal power obtained for the Haigis formula; Pkadj: Corneal power obtained using the adjustedkeratometric index; PIOLReal: Power of the intraocular lens implanted which was calculated using the SRK / T formula; PIOladj-SRK / T: Power of theintraocular lens obtained using adjusted formula and ELP calculated with the SRK / T formula; PIOLadj: Intraocular lens power obtained using theadjusted formula and ELPadj; PIOLHaigis: Intraocular lens power obtained using the Haigis formula; PIOLHofferQ: Intraocular lens power obtainedusing the Hoffer Q formula; PIOLHolladay: Intraocular lens power obtained using the Holladay formula.

Agreement of PIOLReal and PIOLadj-SRK / T 摇 In group A, nostatistically significant differences were found betweenPIOLadj-SRK / T and PIOLReal when ELP was calculated with the SRK /T formula guidelines and Rdes = SEpost ( P = 0. 06, pairedStudent蒺s t - test ) . The correlation between PIOLadj-SRK / T andPIOLReal was statistically significant ( r = 0. 680, P < 0. 01 )(Figure 1A). According to the Bland and Altman analysis,mean difference between PIOLadj-SRK / T and PIOLReal was 0. 43 D,with limits of agreement of +1. 84 and - 0. 98 D. Figure 2Ashows the Bland and Altman plot corresponding to thisagreement analysis.In group B, statistically significant differences were foundbetween PIOLadj-SRK / T and PIOLReal when ELP was calculated withthe SRK / T formula guidelines and Rdes = SEpost ( P < 0. 01,Wilcoxon test ) . A very strong and statistically significantcorrelation was found between PIOLadj-SRK / T and PIOLReal ( r =0郾 898, P < 0. 01 ) ( Figure 1B). The Bland and Altmananalysis showed a mean difference between PIOLadj-SRK / T andP IOLReal of 0 . 97 D, with limits of agreement of +2 . 24 and-0. 30 D (Figure 2B).Estimation of ELPadj 摇 The multiple regression analysisrevealed that the ELPadj was significantly correlated with age

and corneal astigmatism (CA) (P<0. 01) in group A:

ELPadj 逸23 =5. 983-0. 015Age-0. 460CA摇摇摇摇摇摇 (3)

The homoscedasticity of the model was confirmed by thenormality of the non-standardized residuals distribution (P =0. 20) and the absence of influential points or outliers (meanCook蒺s distance: 0. 146依0. 259). With this model, 58. 33%of non-standardized residuals were 0. 20 or lower. The poorcorrelation between residuals (Durbin-Watson test: 2. 320)and the lack of multicolinearity ( tolerance 0. 971 to 0. 971;variance inflation factors 1. 029 to 1. 029 ) was alsoconfirmed.No statistically significant differences were found between ELPcalculated with the SRK / T formula guidelines and theELPadj 逸23(P=0. 07, Student蒺s t-test) .In group B, the ELPadj <23 was found to be significantlycorrelated with age, ACD, AL and r1c(P<0. 01):

ELPadj<23 =5. 327+0. 015Age+0. 346ACD+0. 334AL-1. 430r1c摇摇摇摇摇摇摇摇摇摇摇摇摇摇摇摇摇摇摇摇摇摇 (4)

4001


182

Figure 1 摇 Scattergram showing the relation between theadjusted IOL power using the ELP estimated using the SRK-Tformula guidelines (PIOLadj-SRK/ T) and the real power of the IOLimplanted (PIOLReal)摇 A: Results in group A; B: Results in group B.

Figure 2摇 Bland-Altman plots for the comparison between theadjusted IOL power using the ELP estimated using the SRK-Tformula guidelines (PIOLadj-SRK/ T) and the real power of the IOLimplanted ( PIOLReal ) 摇 The dotted lines show the limits ofagreement ( 依 1. 96SD). A: Results in group A; B: Results ingroup B.

The homoscedasticity of the model was also confirmed by thenormality of the non-standardized residuals distribution (P =0. 20) and the absence of influential points or outliers (meanCook蒺s distance: 0. 04依0. 13). With this model, 84. 91% ofnon-standardized residuals were 0. 50. The poor correlationbetween residuals (Durbin-Watson test: 2. 208) and the lack

Figure 3 摇 Scattergram showing the relation between theadjusted IOL power using the regression analysis adjusted ELP(PIOLadj) and the real power of the IOL implanted (PIOLReal) 摇A: Results in group A; B: Results in group B.

of multicolinearity ( tolerance 0. 733 to 0. 926; varianceinflation factors 1. 080 to 1. 364) was also confirmed.A statistically significant difference was found between ELPcalculated with the SRK / T formula guidelines and theELPadj <23(P<0. 01, Wilcoxon test), with a lower value withour adjustment (Table 1) .Agreement between PIOLReal and PIOLadj 摇 No statisticallysignificant differences were found in any group between PIOLadj

and PIOLReal when ELPadj and Rdes = SEpost were considered forPIOLadj calculation (Group A: P=0. 64, unpaired Student蒺s t-test; Group B: P = 0. 82, Wilcoxon test ) . A strong andstatistically significant correlation was found between PIOLadj

and PIOLReal in both groups ( Group A: r = 0. 88, P <0. 01;Group B: r= 0. 91, P<0. 01) (Figure 3) . In group A, theBland and Altman analysis showed a mean difference betweenPIOLadj and PIOLReal of 0. 08 D, with limits of agreement of +1郾 11 and - 0. 96 D ( Figure 4A). In group B, the meandifference between PIOLadj and PIOLReal was -0. 02 D, with limitsof agreement of +1. 14 and -1. 18 D (Figure 4B).Agreement of PIOLadj and PIOL with Other Formulas 摇 TheELP values corresponding to different available IOL powerformulas were calculated and afterwards an estimation of PIOL

was performed with each of these formulas ( Table 1 ) . Ingroup A, statistically significant differences were found in allcomparisons (P<0. 01, paired Student蒺s t-test) except for the

5001


183

摇摇 Table 2摇 Bland & Altman analysis outcomes of the comparison between PIOLadj and the IOL power obtained with other摇摇 commonly used formulas

FormulasGroup A

DPIOL依SD (D) LoA (D) PGroup B

DPIOL依SD (D) LoA (D) PHaigis 0. 13依0. 69 1. 47 to -1. 22 =0. 53 0. 25依0. 50 1. 24 to -0. 73 <0. 01Hoffer Q -1. 14依1. 15 1. 11 to -3. 40 <0. 01 -1. 76依1. 84 1. 84 to -5. 36 <0. 01Holladay 1 -0. 93依0. 61 0. 26 to -2. 12 <0. 01 -0. 50依0. 36 0. 20 to -1. 20 <0. 01

摇摇 DPIOL: Difference in intraocular lens power; LoA: Limits of agreement; SD: Standard deviation.

Figure 4摇 Bland-Altman plots for the comparison between theadjusted IOL power using the regression analysis adjusted ELP(PIOLadj) and the real power of the IOL implanted (PIOLReal) 摇The dotted lines show the limits of agreement ( 依 1. 96SD); A:Results in group A; B: Results in group B.

comparison of PIOLadj and PIOLHaigi s(P=0. 53 paired Student蒺s t-test) . A strong and statistically significant correlation wasfound between PIOLHaigis and PIOLadj( r = 0. 81, P<0. 01), andbetween PIOLHolladay and PIOLadj( r = 0. 82, P <0. 01). Also, astatistically significant correlation but of moderate strength wasfound between PIOLHofferQ and PIOLadj( r = 0. 63, P = 0. 03). Ingroup B, statistically significant differences were foundbetween PIOLadj and all formulas analysed (P<0. 01, Wilcoxontest) . A strong and statistically significant correlation wasfound between PIOLHaigis and PIOLadj ( r = 0. 99, P < 0. 01 ),between PIOLHofferQ and PIOLadj( r=0. 66, P<0. 01) and betweenPIOLHolladay and PIOLadj( r=0. 98, P<0. 01). Table 2 summarizesthe outcomes of the Bland and Altman analysis whencomparing PIOLadj with the rest of formulas.DISCUSSIONThe selection of the IOL power to implant in cataract surgeryis a critical step for obtaining an optimized outcome[17-18] .This power is determined by using mathematical formulasbased most of them on paraxial optics[17-18] . In theseformulas, some ocular parameters are required as well as theintended target refraction[17-18] . The AL and corneal power arealways necessary for IOL power calculation and the accuracyof the measurement of these parameters is considered as thefirst potential source of inaccuracy in the determination of theIOL power to implant. Another source of potential bias is theestimation of the IOL position that is required for the opticalcalculations. Specifically, the “ effective lens position 冶

(ELP) is estimated which is defined as the effective distancefrom the anterior surface of the cornea to the lens plane as ifthe lens was of infinite thinness[19] . This parameter is formula-dependent and do not need to reflect the true postoperativeACD in the anatomical sense[19] . Indeed, each formula forIOL power calculation has its own algorithm to estimate theELP that is based on different anatomical parameters, such ascorneal power, preoperative ACD[19] or the horizontal cornealdiameter or white - to - white distance (WTW) [20] . In thecurrent study, a preliminary algorithm based on paraxialoptics was developed to calculate the power to implant of aspecific model of aspheric IOL. This algorithm was optimizedby minimizing the error associated to the keratometricestimation of the corneal power as well as by obtaining aconsistent predictive formula for the estimation of the ELP. Aspreviously commented, the visual outcomes obtained withaspheric IOLs are especially worsened when refractive residualerrors are present due to inaccurate IOL powercalculations[10] .In our series, the refractive outcomes obtained with theaspheric IOL evaluated were less predictable for those eyesimplanted with IOLs of powers of less than 23 D. Specifically,the postoperative SE ranged from -0. 75 to +0. 75 D in eyesimplanted with PIOL逸23 D and from -1. 38 to +0. 75 D ineyes implanted with PIOL<23 D. Therefore, there was a slighttrend to residual myopia in those eyes implanted with lowerIOL power values and consequently longer AL. This isconsistent with the results of previous studies reporting myopicresidual refractive errors in myopic eyes implanted withaspheric IOLs, especially in those with extreme preoperativemyopia[21] . The results of the study of Eldaly and Mansour[22]

suggested that AL -adjusted A-constants might be used forIOL power calculations. Indeed, these authors found differenttrends for a personal A-constant with different aspheric IOLseven for the same range of axial length[22] . In our series, inspite of the acceptable predictability achieved with the specificmodel of aspheric IOL evaluated, an attempt of optimizationhas been done by using an optimized model for corneal powercalculation and an equation to estimate ELP based on aretrospective regression analysis of the postoperative outcomesobtained. As the behaviour of this regression model was verydependent on the IOL power, two groups were differentiated,as previously mentioned.A limitation of the predictability of the refractive correctionwith the evaluated aspheric IOL may be attributable to the bias

6001


184

associated to the use of the keratometric approach for thecalculation of the corneal power, errors in the determination ofthe axial length or inaccuracy in the estimation of the ELP forthis specific IOL. However, the errors in the estimation of ALwith optical biometry have been shown to be minimal and witha very limited impact on the refractive predictability[23] . Forthis reason, the current study was aimed at analysing thepotential contribution of the corneal power and ELP factors tothe limitation of the refractive predictability with the asphericIOL evaluated. The potential impact of the keratometric errorwas first evaluated by calculating the corneal power using anadjusted keratometric index aimed at minimizing the clinicalerror in the estimation of the corneal power[13-15] . Thisadjusted corneal power was used to obtain an estimation of theIOL power considering the AL, Rdes = SEpost and an ELPestimated with the algorithm established for the SRK - Tformula (PIOLadj-SRK / T)

[24] . Thus, the ability of this approachto reproduce the real clinical outcome was evaluated. In thetwo groups of our study, eyes implanted with PIOL逸23 D andeyes implanted with PIOL<23 D, clinically relevant differenceswere found between PIOLadjSRK / T and PIOLReal which demonstratedthat the correction of this factor had a minimal effect on theoutcomes achievable with the aspheric IOL evaluated.Likewise, statistically significant differences were foundbetween PIOLadjSRK / T and PIOLReal in those eyes implanted withlower IOL powers. The reason for not finding statisticallysignificant differences in group A may be the smaller numberof patients included in this group.According to these first outcomes, the estimation of ELPseemed to be the most critical factor accounting for thepresence of a relatively limited predictability with the asphericIOL, especially in eyes with shorter AL. In order to confirmthis, an analysis was performed to obtain an expression forestimating an optimized ELP ( ELPadj ). As a result, twodifferent expressions were obtained by means of multiple linearregression analysis according to the power of the IOLimplanted, one expression for PIOL < 23 D ( ELPadj<23 ) andanother for PIOL 逸 23 D ( ELPadj 逸23 ). This confirms therelevance of the geometric factor of the IOL in the estimationof ELP. The adjusted ELP was used to recalculate the IOLpower considering that Rdes = SEpost( PIOLadj ) with the aim ofchecking if this new estimation was able to reproduce the realclinical outcome. An initial expression for ELPadj consideringthe whole sample of 65 eyes was obtained, but the ELPadj

values obtained led to inconsistent values of PIOL adj . However,when the two differentiated groups of eyes were considered,and two different expressions for ELPadj were obtained(ELPadj<23D and ELPadj 逸23D ), no statistically significant andclinically acceptable differences between PIOLadjand PIOLReal werefound. Indeed, mean differences between simulated andclinical outcomes were practically zero in groups A and B,with limits of agreement around 1 D, which is themanufacturer tolerance for extreme IOL powers ( IOLs withpowers from 0 to 10 D and from 30 to 35 D).

In our linear regression analyses, ELPadj was found to berelated to different factors in groups A and B. Age is the onlyfactor shared by both models. This may be in relation with theage - dependence of the capsular behaviour after cataractsurgery. A retrospective cohort study conducted on 801patients in a Spanish hospital revealed that age could beassociated with capsular bag distension syndrome[25] . Vass etal[26] confirmed that the capsular bag diameter was correlatedwith age, among other factors such as AL, corneal power orlens thickness. In group B that included eyes with longer AL,the anatomical factors were crucial determinants of the ELP ofthe IOL evaluated. Specifically, ELPadj was higher in thoseeyes with longer AL and ACD, which is consistent with thelinear dependence of the final position of the IOL on the ALreported by previous authors[27] . Besides the AL and ACDanatomical factors in group B, a corneal factor was included inthe ELP models obtained in groups A and B in terms ofcorneal astigmatism magnitude and radius of curvature of thefirst corneal surface, respectively. This may be expected assome level of anatomical correlation between the cornealgeometry and intraocular dimensions has been described in thehuman eye[28] .Finally, commonly used IOL power formulas were comparedwith our PIOLadj . In both groups, according to the Bland andAltman analysis, clinically relevant differences were foundbetween PIOLadj and the IOL power values obtained with theHaigis, Hoffer Q, and Holladay I formulas. Likewise, thesedifferences were also statistically significant. Only thedifference between PIOLadj and the IOL power calculated withthe Haigis formula in group A did not reach statisticalsignificance possibly due to the limitation in the sample size ofthis group. These differences between formulas seem to be inrelation with the different estimations of ELP provided by eachof them, with the most accurate outcome for ELPadj . PIOLadj wasable to reproduce more accurately the real value of the powerof the IOL implanted and therefore the refractive outcome.This suggests that our approach may be a useful method forIOL power calculation with the aspheric IOL evaluated. Thisshould be corroborated in future prospective studies.There are several limitations in the currentstudy, such as thelimited sample size, the use in some cases of both eyes of thesame subject or the short follow-up. It should be consideredthat, although rare, changes in IOL position has beendescribed more than 3mo after surgery, especially after Nd:YAG capsulotomy[29] . Another potential limitation is that theHolladay II formula was not used in our comparison as it wasnot available in our clinic. Possibly, our approach may bemore similar to the results of the Holladay II formula as bothtypes of calculation use an optimized algorithm for theestimation of ELP, but this should be confirmed in futurestudies. This study was planned as a preliminary experience toevaluate the possibility of optimizing further the widely usedapproaches for IOL power calculation based on paraxialoptics. For this reason, a retrospective study with a limitedsample size was conducted. According to the positive findings

7001


185

obtained, a prospective study with a large sample size is beingconducted currently, including eyes implanted with differenttypes of IOL. Finally, it should be mentioned that only onesurgeon performed all the surgeries and therefore the algorithmdeveloped could be somewhat imprecise for some surgeons. Infuture studies, this algorithm will be validated for differentsurgeons and the clinical relevance of differences will beevaluated. Furthermore, an analysis similar to that performedin the current study could be used to define a personalizedalgorithm for IOL power calculation for each specific surgeon.In conclusion, the refractive outcomes after cataract surgerywith implantation of aspheric IOLs can be optimized byminimizing the keratometric error using a variable keratometricindex for corneal power estimation and by estimating ELPusing a mathematical expression dependent on the geometricfactor of the IOL, age and anatomical factors. Therefore,optimizations of paraxial models for IOL power calculationscan be performed to improve the clinical outcomes obtainedwith currently available IOL models without the need for raytracing simulations. Jin et al[30] confirmed in a simulationstudy that theoretical thin-lens formulas were as accurate asthe ray-tracing method in IOL power calculations in normaleyes and even in eyes after refractive surgery. Futureprospective studies should be performed to validate this modelof IOL power calculation for the evaluated aspheric IOL andother models with larger sample of sizes including moreextreme cases ( long and short AL).REFERENCES1 Ali佼 JL, Schimchak P, Negri HP, Mont佴s-Mic佼 R. Crystalline lensoptical dysfunction through aging. Ophthalmology 2005;112(11):2022-20292 Philip K, Martinez A, Ho A, Conrad F, Ale J, Mitchell P,Sankaridurg P. Total ocular, anterior corneal and lenticular higher orderaberrations in hyperopic, myopic and emmetropic eyes. Vision Res 2012;52(1):31-373 Lyall DA, Srinivasan S, Gray LS. Changes in ocular monochromatichigher-order aberrations in the aging eye. Optom Vis Sci 2013;90(9):996-10034 Fujikado T, Kuroda T, Ninomiya S, Maeda N, Tano Y, Oshika T,Hirohara Y, Mihashi T. Age - related changes in ocular and cornealaberrations. Am J Ophthalmol 2004;138(1):143-1465 Amano S, Amano Y, Yamagami S, Miyai T, Miyata K, Samejima T,Oshika T. Age - related changes in corneal and ocular higher - orderwavefront aberrations. Am J Ophthalmol 2004;137(6):988-9926 Glasser A, Campbell MC. Presbyopia and the optical changes in thehuman crystalline lens with age. Vision Res 1998;38(2):209-2297 Schuster AK, Tesarz J, Vossmerbaeumer U. The impact on vision ofaspheric to spherical monofocal intraocular lenses in cataract surgery: asystematic review with meta - analysis. Ophthalmology 2013;120 (11):2166-21758 Langenbucher A, Janunts E, Seitz B, Kannengie茁er M, Eppig T.Theoretical image performance with customized aspheric and sphericalIOLs - when do we get a benefit from customized aspheric design? Z MedPhys 2014;24(2):94-1039 Guo H, Goncharov A, Dainty C. Intraocular lens implantation positionsensitivity as a function of refractive error. Ophthalmic Physiol Opt 2012;32(2):117-124

10 Dick HB. Recent developments in aspheric intraocular lenses. CurrOpin Ophthalmol 2009;20(1):25-3211 Hoffmann PC, Lindemann CR. Intraocular lens calculation foraspheric intraocular lenses. J Cataract Refract Surg 2013;39(6):867-87212 Olsen T. Calculation of intraocular lens power: a review. ActaOphthalmol Scand 2007;85(5):472-48513 Camps VJ, Pi觡ero DP, de Fez D, Mateo V. Minimizing the IOLpower error induced by keratometric power. Optom Vis Sci 2013;90(7):639-64914 Camps VJ, Pinero-Llorens DP, de Fez D, Coloma P, Caballero MT,Garcia C, Miret JJ. Algorithm for correcting the keratometric estimationerror in normal eyes. Optom Vis Sci 2012;89(2): 221-22815 Camps VJ, Pi觡ero DP, Mateo V, Ribera D, de Fez D, Blanes -Momp佼 FJ, Alzamora - Rodr侏guez A. Algorithm for correcting thekeratometric error in the estimation of the corneal power in eyes withprevious myopic laser refractive surgery. Cornea 2013; 32(11):1454-145916 Bland JM, Altman DG. Statistical methods for assessing agreementbetween two methods of clinical measurement. Lancet 1986;1 (8476):307-31017 Hoffer KJ. IOL power. Thorofare, NJ, USA: Slack Incorporated, 201118 Shammas HJ. Intraocular lens power calculations. Thorofare, NJ,USA: Slack Incorporated, 200419 Olsen T. Prediction of the effective postoperative ( intraocular lens)anterior chamber depth. J Cataract Refract Surg 2006;32(3):419-42420 Fenzl RE, Gills JP, Cherchio M. Refractive and visual outcome ofhyperopic cataract cases operated on before and after implementation ofthe Holladay II formula. Ophthalmology 1998;105(9):1759-176421 Fang Y, Lu Y, Miao A, Luo Y. Aspheric intraocular lensesimplantation for cataract patients with extreme myopia. ISRN Ophthalmol2014;2014:40343222 Eldaly MA, Mansour KA. Personal A-constant in relation to axiallength with various intraocular lenses. Indian J Ophthalmol 2014;62(7):788-79123 Faria-Ribeiro M, Lopes-Ferreira D, L仵pez-Gil N, Jorge J, Gonz仳lez-M伢ijome JM. Errors associated with IOLMaster biometry as a function ofinternal ocular dimensions. J Optom 2014;7(2):75-7824 Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK / Tintraocular lens implant power calculation formula. J Cataract RefractSurg 1990;16(3):333-34025 Gonz仳lez - Mart侏n - Moro J, Gonz仳lez - L仵pez JJ, G仵mez - Sanz F,Zarallo -Gallardo J, Cobo - Soriano R. Posterior capsule opacification,capsular bag distension syndrome, and anterior capsular phimosis: Aretrospective cohort study. Arch Soc Esp Oftalmol 2015;90(2):69-7526 Vass C, Menapace R, Schmetterer K, Findl O, Rainer G, SteineckI. Prediction of pseudophakic capsular bag diameter based on biometricvariables. J Cataract Refract Surg 1999;25(10):1376-138127 Engren AL, Behndig A. Anterior chamber depth, intraocular lensposition, and refractive outcomes after cataract surgery. J CataractRefract Surg 2013;39(4):572-57728 Park SH, Park KH, Kim JM, Choi CY. Relation between axial lengthand ocular parameters. Ophthalmologica 2010;224(3):188-19329 Ale JB. Intraocular lens tilt and decentration: a concern forcontemporary IOL designs. Nepal J Ophthalmol 2011;3(1):68-7730 Jin H, Rabsilber T, Ehmer A, Borkenstein AF, Limberger IJ, GuoH, Auffarth GU. Comparison of ray - tracing method and thin - lensformula in intraocular lens power calculations. J Cataract Refract Surg2009;35(4):650-662

8001


186

optimización del cálculo de lentes paraxial verónica mateo ... · a mis compañeros y amigos del...

Documents