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704 Acta Orthop Scand 1988;59(6):704-707

Femoral shaft fracture in 265 childrenLog-normal correlation with age of speed of healingSsren Valdemar Skak and Tim Toftghrd Jensen

After exclusion of delayed unions and pseudoarthroses in teenagers, the timerequired for union of 275 consecutive fractures of th e femoral diaphysis inchildren followed a log-normal pattern with a constant 10 percent coefficientof variation and a geometric mean increasing uniformly by 0.7 weeks per year.Multiple injuries increased, and operative treatment reduced the geometricmean time for fracture healing.

Investigations on the sp eed of fracture union havealmost exclusively been carried out on tibialfractures in adults (Watson-Jones 1943, Ellis1958, Nicoll 1964, Edwards 1965, Hoaglund andStater 1967, Allum and Mowbray 1979, Austin1981, Hamm er e t al. 1984), and we could not findany study dealing with fracture healing in chil-dren.

Edwards and Nilsson (1965) found that thetimes of healing of tibial fractures in adultsconformed to a log-normal pattern, whereas Aus-tin (1977) advocated a reciprocal transformationof data. We assessed the pattern and variationwith age of the healing times in a large series offractures of the fem oral shaft in children.

Patients and methodsDuring the period 1970-1981,278 nonpathologicfractures of the fem oral diaphysis in children weretreated at th e orthopedic departme nts at Esbjerg,Frederiksberg, and Son derborg Hospitals in Den-mark. Included were fractures between the lessertrochanter and the distal quarter of the femur.Because the radiographs and records of threepatients were lost, 275 fractures in 265 children(197 boys, 68 girls) were studied. Twelve fracture swere open. Multiple injuries, including other

severe fractures, injuries to the trunk or head,were found in 57 patients.The treatment was usually nonoperative, but

the teenagers often had open reduction andinternal fixation (Table 1). In only a few cases,internal fixation with th e R ush pin was carried outafter closed reduction. In 9 fractures, anotherreduction or internal fixation was performed aftermore than 2 weeks owing to a malposition. Fou rfractures were treated with internal fixation be-cause of delayed healing. In 3 patients a newtraum a before clinical union led to bending at thefracture site, and in another 2 patients radio-graphs revealed new fracture lines. Eight frac-tures healed with a distance between the boneends of more than 1 cm. There were two deepinfections.

The fractures were considered healed at thetime of full unsupported weight bearing for babiesand toddlers when all kinds of treatment orrestrictions were discontinued. When weightbearing was not allowed or possible because ofother injuries, the assessment was based on th eradiographic appearance. Delayed un ion was de-fined as union occurring after more than 5 monthsand pseud oarthrosis as union following a second-Table 1. Treatment of 275 femoral fractures in children

Departments of Orthopedics at Sonderborg, Esbjerg,and Fredriksberg Hospitals, DenmarkCorrespondence: D r. S.V. Skak, Fenrisgade 1,3T.V.,DK-2200 Copenhagen, Denmark

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Acta Orthop Scand 1988;59(6):704-707 705

I

OBLIOUETRANSVERSE

1rnax.s BILONGITUDINAL

"2B1 I IFigure 1. The lengthof the projec-tion of the fracture on the longi-tudinal axis of the bone (A) wasused to separate transverse, ob-lique, and longitudinal fractures.

ary operation carried out after more than 6months. Th ere were 14 cases of delayed union and5 pseudoarthroses. The youngest patients withdelayed union or pseudoarthrosis w ere 13 and 15years of age, respectively. There was no case ofrefracture following final union.

Th e accidents were classified as high- or low-energy trauma according to Bauer et al. (1962).The fractures were classified as transverse,oblique, and longitudinal. (Figure 1 ). Fractureswith fragments of more than half the diameter ofthe shaft and segm ental fractures were classifiedas comminuted.

StatisticsTh e preliminary assessment of th e approximationof data to various patterns of distributions wasaccomplished by plotting the data in a probitdiagram and using the chi-square test for go odnessof fit. The geo metn cm ean was used as an estimateof the mean time for union. Bartlett's test wasused to compare variances and the F -test to assessmeans. Calculations of the increment of the meantime of union with age was accomplished bysimple regression analysis after exclusion of de-layed unions and pseudoarthroses. The multiva-riate regression analysis was used to assess theinfluence of side, sex, type of fracture, type oftrauma, type of treatment, and multiple injuries(Tab le 2) complemented w ith the values of log H(H = time required for union in weeks). B ecausethe ages of 0 and 1 year fell outside a rectilinearconnection between age and log H, these ageswere excluded from this part of the study. Toavoid random factors with a potential for interfe r-ence with fracture union, grade I11 open fractures(Gustilo and Anderson 1976), infected fractu res,fractures w ith a gap > 1cm, refractures, and casesof late rereduction w ere excluded as well.Resu sTh e time required for union va ned from 3 weekst o 2 years (Table 3) and followed a log-normaldistribution; for the teenagers, however, onlyafte r exclusion of patients with delayed union andpseudoarthrosis (Figure 2). Dealing with yearsrather than the broad age groups in Figure 2wouldincrease the inclination ( i.e. reduce th e variation)

Table 2. Data subjected to multivariate regression analysis. Figures are number of fractures. Grade 11 1 open fractures, infectedfractures, refractures, and fractures healed with more than 1 cm of lengthening have been excluded

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Acta Orthop Scand 1988;59(6):704-707 707

lihood of union. T he healing times of these series,as those of the teenagers in ou r study, tend to betoo dispersed to conform to the log-normal pat-tern , some fitting bette r, although not very accu-rately, to the reciprocal-normal patter n proposedby Austin (1977).

The re might be two explanations for the obser-vation that delayed unions and pseudoarthrosesin the teen-age group had to be excluded toprovide an acceptable fit to th e log-normal distri-bution. One is that the potential for healing inadult persons is less reliable than in children.Another is that the more liberal use of opentreatment caused more complications.

As bone healing like growth is likely to be alog-normally distributed process, statistical para-meters should be based on the logarithms ratherthan calculated directly from the times observed.

ReferencesAllum R L, Mowbray M A. A retrospective review ofthe healing of fractures of the shaft of the tibia with

special reference to the mechanism of injury. Injury1980;11(4):3O4-8.Austin R T . Fractures of the tibial shaft: is medical auditpossible? Injury 1977;9(2):93-101.

Austin R T. Th e Sarmiento tibial plaster: a prospectivestudy of 145 fractures. Injury 1981;13( ):lO-22.Bauer G C H, Edwards P , Widmark P H. Shaft fracturesof the tibia. Etiology of poor results in a consecutiveseries of 173 fractures. Acta Chir Scand 1962;44:386-95.

Christensen J, Greiff J, Rosendahl S. Fractures of theshaft of the tibia treated with A 0 compressionosteosynthesis. Injury 1982;13(4):307-14.Edwards P. Fracture of the shaft of the tibia: 492consecutive cases in adults. Importance of soft tissueinjury. Acta Orth op Scand 1965;36(Suppl 76).

Edwards P , Nilsson B E R. Graphic representation ofhealing time in fractu res of the s haft of the tibia. A ctaOrthop Scand 1965;36:104-11.

Ellis H. The speed of healing after fracture of the tibialshaft. J Bone Joint Surg (Br) 1958;40:42-6.Gustilo R B, Anderson J T. Prevention of infection in

the treatment of one thousand and twenty-five openfractures of long bones: retrospective and prospectiveanalyses. J Bone Joint Surg (Am) 1976;58(4):453-8.Jensen J S, Hansen F W, Johansen J. Tibial shaftfractures. A comparison of conservative treatmentand internal fixation with conventional plates or A 0compression plates. Acta Orthop Scand 1977;48(2):204-12.

Th e skewed shape of the log-normal distributionwhen plotted into diagrams with linear scalesshould be taken in to consideration when estimat-ing cases of slow healing. Such cases should not,as pointed ou t by Hamm er et al. (1984), indiscri-minately be regarded as therape utic failures. Th emean values of the log-normal distributions arefairly insensitive to an increment in the numberof observations to the far right of the mean, asseen in series which tend to identify slow healers.Interpretation of differences of means betweengroups should thus be drawn guardedly, particu-larly when they occur simultaneously with differ-ences of variances. Such differences may merelyindicate trends towards segregation of series ofobservations less compatible with the log-normalpresumption than any systemic effect exertedupon the basic fracture healing times.

Hammer R, Edholm P, Lindholm B. Stability of unionafter tibial shaft fracture. Analysis by a non-invasivetechnique. J Bone Joint Surg (Br) 1984;66(4):529-34.

Harley J M, Campbell M Ji Jackson R K . A comparisonof plating an d traction in the trea tmen t of tibial shaftfractures. Injury 1986;17(2):91-4.

Hoaglund F T, States J D . Factors influencing the rateof healing in tibial shaft fractures. Surg GynecolObstet 1967;124(1):71-6.Kristensen K D. ibial shaft fractures. The frequencyof local complications in tibial shaft fractures treatedby internal compression osteosynthesis. Acta OrthopScand 1979;50(5):593-8.Nicoll E A. Fractures of the tibial shaft. A survey of 705cases. J Bone Joint Surg (Br) 1964;46:373-87.

Watson-Jones R , Coltart W D. Slow union of fractureswith a study of 804 ractures of the shafts of the tibiaand femur. Br J Surg 1943;30:260-76.

AcknowledgementsThis study was supported by grants from Fonden forkgevidenskabelig forskning m.v. ved sygehusene iRingkobing, Ribe og Soderjyllands amter. Statens 19-gevidenskabelige Forskningsrld, and S . A. Skaks Fa-milie Fond.We are indebted to Cand. Polit. Severin Olesen-Larsen, Department of Biostatistics, Statens Serum-institut, Copenhagen, for the accomplishment of themultivariate regression analysis.

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