geometria e meccanica leardini

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Thesis summary

Geometry and mechanics of the human ankle complex and ankleprosthesis design

Alberto Leardini

Movement Analysis Laboratory, Istituti Ortopedici Rizzoli, Via di Barbiano 1/10, 40136 Bologna, Italy

Received 12 December 2000; accepted 7 March 2001

Abstract

The main objective of the study was to develop a model of the intact human ankle complex. It was also aimed at designing total

ankle replacement which would better reproduce the physiological function of the joint. Passive exion was analysed in seven lower-leg preparations with a stereophotogrammetric system. The articular surfaces and bres within the calcaneobular and tibio-

calcaneal ligaments prescribed the changing positions of the axis of rotation. Joint motion included rolling as well as sliding. A

computer-based model elucidated the observed kinematics at the intact joint. The experimental evidence and the geometrical model

gave the basis for the design of models of replaced ankle in the sagittal plane. A three-component, convex-tibia prosthesis was

eventually selected with articular surface shapes compatible with the geometry of the ligaments. It was demonstrated that in intact

ankle joint, the geometry of the articular surfaces is strictly related to that of the ligaments and that current prosthesis designs do not

restore physiological pattern of ligament tensioning. Careful reconstruction of the ligaments is recommended in any ankle surgery

for maintenance of the normal kinematics and mechanics. A proposed novel design based on ligament/shape compatibility may

improve total ankle replacement results. 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Ankle complex; Ligaments; Articular surfaces; Centre rotation; Lever arm; Joint replacement

1. Introduction

After early encouraging results, ankle arthroplasty

has acquired a bad reputation based on many clinical

studies [1]. These poor results are causing surgeons to

abandon arthroplasty and to return to fusion again. The

frequent failure has been primarily related to inadequate

restoration of the original mobility and stability of the

ankle complex, and to the poor knowledge of the cor-

responding guiding and stabilising role of the ligaments

involved.

Despite the deep understanding of the knee joint,there is considerable lack of knowledge for the human

ankle complex [2,3]. The principal aim of this project

was to develop a mathematical model of this complex.

The project also aimed at the development of a new total

ankle prosthesis, designed to better reproduce the

physiological function of the entire complex.

2. Methods for human joint modelling

Mathematical models of human joints serve to

predict quantities which are dicult to measure experi-

mentally, and to simulate changes from the physio-

logical conditions [2]. A sequential geometrical plus

mechanical approach has been utilised. Geometrical

models show rst how the ligament orientations and the

shapes of the articular surfaces can guide the movements

of the bones upon each other within their allowable

range of movement. Mechanicalmodels then show how

the ligaments can act together with the muscles and thearticular surfaces to transmit load from one bone to

the other and how they combine to dene that range.

The knowledge of the geometrical conguration of the

joint structures at any exion angle is fundamental be-

fore carrying out mechanical analysis. By providing the

lines of action of the muscles, ligaments and contact

normals and the locations of the instantaneous axis of

rotation, a geometric model reduces the number of un-

knowns in the equilibrium equations of the subsequent

mechanical analysis in which the structures are also al-

lowed to deform.

Clinical Biomechanics 16 (2001) 706709

www.elsevier.com/locate/clinbiomech

E-mail address: [email protected] (A. Leardini).

0268-0033/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.

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3. Review of the literature

The role played by the passive structures of the ankle

joint complex in mobility and stability was initially

investigated from the literature [3]. Although there is

still controversy on several issues, important ndings

seem to be consistently observed. A more isometric

pattern of rotation for the calcaneobular (CaFi) and

the tibiocalcaneal (TiCa) ligaments has been reported.

Many recent studies have found changing positions of

the instantaneous axis of rotation, suggesting that the

hinge joint concept is an oversimplication for the ankle

kinematics. A few recent works have also claimed shift

of the contact area at the tibial mortise. Many ndings

from the literature support the view of a close interac-

tion between the geometry of the ligaments and the

shapes of the articular surfaces in guiding and stabilising

joint motion.

4. Kinematics at the human ankle complex in passive

conditions

The experimental part of the work investigated whe-ther or not a preferred path of joint motion is prescribed

by the ligaments and articular surfaces during passive

exion. A rig was built to move the ankle complex

through its range of exion while applying a minimum

load [46]. Joint motion was constrained only by the

articular surfaces and the ligaments. The movements of

the calcaneus, talus and bula relative to the stationary

tibia in seven lower-leg preparations were tracked with a

stereophotogrammetric system. It was shown that the

calcaneus follows a unique path of unresisted coupled

motion relative to the tibia and that most of this motion

occurred at the ankle, with little motion at the subtalar

level. The CaFi and the TiCa ligaments showed near-

isometric pattern of rotations. All specimens showed

motion of the axis of rotation relative to the bones.

Axial deviations from the unique path involved mostly

subtalar motion and were resisted. The ankle complex

exhibits one degree of unresisted freedom, the subtalar

behaving as a exible structure. A further experiment

[4], combining roentgen-stereophotogrammetry and 3D

digitisation, showed which single bres within the CaFi

and TiCa rotate most isometrically and an anteriorly

translation of the articular contact on the tibial mortise

during dorsiexion. It was deduced that the ankle is a

single degree-of-freedom mechanism where mobility isallowed by the sliding of the articular surfaces upon

each other and the isometric rotation of two ligament

bres about their origins and insertions, without tissue

deformation.

5. Geometrical and mechanical modelling of the ankle

joint

A computer-based geometrical model [7,8] elucidated

this mechanism in the sagittal plane. The geometrical

Fig. 1. Diagrammatic sketches of the single-d.o.f. mechanism in the

sagittal plane as predicted by the geometrical models: at the intact (a)

and replaced (b) ankle complex. For both conditions, geometrical ar-

rangement of the passive structures are superimposed in two joint

positions: at 20 plantarexion (solid) and 10 dorsiexion (dashed).

The kinematics is guided by the isometric rotation of the CaFi and

TiCa ligaments (thicker segments). The buckling of the other ankle

ligaments (buckled segments), the articular surfaces (bold arcs), the

instantaneous centre of rotation IC (grey circle), the course of the three

main muscle-tendon units and the pulleys (empty circles) representing

the extensor retinaculum bands are all depicted. In the replaced ankle,

bone-anchored prosthesis components (grey) and meniscal bearing

(dotted) are also depicted in the two joint positions. The physiological

pattern of ligament slackening/tightening and the muscle force leverage

is maintained.

A. Leardini / Clinical Biomechanics 16 (2001) 706709 707


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arrangement of ligaments, articular surfaces, and centre

of rotation in two joint positions are depicted in Fig. 1(a)

as taken from the computer animation during a com-

plete cycle of dorsiexion.

Fibres within the CaFi and TiCa ligaments rotate

isometrically about their origins and insertions, while all

other ligament bres located more anteriorly slacken

during dorsiexion, those located posteriorly slacken

during plantarexion. The instantaneous centre of ro-

tation (IC, grey circle), the point at which the two lig-

ament bres cross, moves from a postero-distal to an

antero-proximal position during dorsiexion. The ar-

ticular contact moves from the posterior part of the

tibial mortise in maximal plantarexion to the anterior

part in maximal dorsiexion: the talus rolls forward on

the tibial mortise during dorsiexion, backward during

plantarexion.

The shapes of the articular surfaces are compatible

with this ligament rotation, i.e. articular surfaces move

in contact with one another while maintaining these -bres just tight at constant length. The deduced shape of

the complementary surface of the talus, compatible with

a mortise shape taken as an arc of a circle, is a poly-

centric and polyradial curve as in the intact talus.

The model was then extended by including the me-

chanical eect of the extensor retinacula to predict the

changing lever arm lengths of the main exor and ex-

tensor muscles [7]. Each of the three extensor retinacu-

lum bands was modelled as a frictionless pulley (empty

circles in Fig. 1), around which the tibialis anterior

tendon wraps. The changing positions of both muscle

lines of action and IC produce a lever arm of the exor

muscles maximised in dorsiexion, that of the extensor

muscle maximised in plantarexion. The joint positions

in which these two muscle groups re during gait are

exactly those in which they were predicted to be me-

chanically advantaged.

6. Toward the design of a new ankle prosthesis

The experiments and the relevant computer-based

model demonstrated the close relationship between the

geometry of the ligaments and the shapes of the articular

surfaces at the ankle joint. For the art of joint replace-ment, these observations suggest a further fundamental

design criterion: the shapes of the prosthetic articular

surfaces must be compatible with the geometry of the

ligamentous structures retained.

The general type of a new articulation was devised

[9,10] by means of sagittal plane models of the replaced

ankle based on the previously validated model. The ki-

nematics of the ankle when replaced by non-conforming

two-component and by fully conforming three-compo-

nent designs with either at, concave or convex tibial

surfaces were analysed. The degree of congruity, the

resulting possible ligament anisometricity, the level of

entrapment of the meniscal bearing and the thickness of

the bone removed were analysed to select the most ap-

propriate shapes of the prosthetic articular surfaces. A

ligament-compatible convex-tibia fully congruent three-

component prosthesis (Fig. 1(b)) gave the most entrap-

ment. As in the intact joint, the talar component slides

backward while rolling forward during dorsiexion and

vice versa during plantarexion. These movements are

accommodated by the forward and backward displace-

ment of the meniscal bearing on the tibial surface under

the control of the ligaments. The circular surfaces pro-

vide complete congruence over the entire range of ex-

ion. The new design allows replication of almost exactly

the original pattern of ligament bre slackening/tight-

ening, motion of the IC of rotation and muscle leverage.

This simulation work also revealed that the talar surface

which is compatible with ligament isometry and a at

tibial surface has a larger radius of curvature than the

natural talus, so that most of prior art designs cannot becompatible with physiological ligament function.

A 3D design of a new total ankle prosthesis was

eventually devised [11,12]. The tibial component has a

spherical convex articulatory surface. The talar com-

ponent has a convex shape in the frontal plane, a con-

cave sulcus in the frontal plane. A meniscal bearing is

located in between and has complementary articulating

surfaces. The device can move under natural ligamen-

tous control, closely restoring that of a natural joint.

The meniscal bearing prosthesis provides complete

congruence over the entire range of joint exion to-

gether with minimally constrained components to en-

able the soft tissues to control the physiologic motion at

the joint.

Trial implantation with stainless-steel/polyethylene

prosthesis prototypes were carried out in three below-

knee amputation specimens to assess experimentally a

successful restoration of the original mechanism at the

replaced joint. The meniscal bearing was observed to

move anteriorly during plantarexion, posteriorly dur-

ing dorsiexion, conrming the computer model pre-

dictions.

7. Clinical relevance

It has been learnt that in the intact ankle the geom-

etry of the articular surfaces is intimately related to that

of the ligaments. A careful reconstruction of the original

geometry of the ligaments, both in terms of natural at-

tachment areas and natural bre mapping, is necessary

after injury or during ligament reconstruction.

This mechanism ought to be restored also in total

ankle replacement. The experimental and modelling

evidence suggests that the outcome of ankle replacement

may be improved by a careful restoration of the com-

708 A. Leardini / Clinical Biomechanics 16 (2001) 706709


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patibility between prosthetic surface shapes and liga-

ment geometrical arrangement.

Acknowledgements

The author wishes to thank Prof. John J. O'Connor

(Oxford Orthopaedic Engineering Centre, University of

Oxford, UK) for the precious inspirations and the active

support in his role of supervisor. The work was sup-

ported economically by the Italian Ministry of Health

Care, the joint action British Council Conferenza dei

Rettori delle Universita Italiane, and the Arthritis Re-

search Campaign of Great Britain.

References

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