Anil Bhave , John E . Herzenberg and J . Richard Bowen Multiplier Method for Predicting Limb - Length Discrepancy

Background: In patients with a congenital or developmental limb-length discrepancy, the short limb grows at a rate proportional to that of the normal, long limb. This is the basis of predicting limb-length discrepancy with existing methods, which are complicated and require multiple data points. The purpose of our study was to derive a simple arithmetic formula that can easily and accurately predict limb-length discrepancy at skeletal maturity. Methods: Using available databases, we divided the femoral and tibial lengths at skeletal maturity by the femoral and tibial lengths at each age for each percentile group. The resultant number was called the multiplier. Using the multiplier, we derived formulae to predict the limb-length discrepancy and the amount of growth remaining. We verified the accuracy of these formulae by evaluating two groups of patients with congenital shortening who were managed with epiphysiodesis or limblengthening. We also calculated and compared the multipliers for other databases according to radiographic, clinical, and anthropological lower-limb measurements. Results: The multipliers for the femur and tibia were equivalent in all percentile groups, varying only by age and gender. Because congenital limb-length discrepancy increases at a rate proportional to growth, the discrepancy at maturity can be calculated as the current discrepancy times the multiplier for the current age and the gender. This calculation can be performed with use of a single measurement of limb-length discrepancy. For progressive developmental (noncongenital) discrepancies, the discrepancy at skeletal maturity can be calculated as the current discrepancy plus the growth inhibition times the amount of growth remaining. The timing of the epiphysiodesis can also be calculated with the multiplier. The predictions made with use of the multiplier method correlated well with those made with use of the Moseley method as well as with the actual limb-length discrepancy in both the limb-lengthening and epiphysiodesis groups. The multipliers derived from the radiographic, clinical, and anthropological measurements of femora and tibiae were all similar to each other despite differences in race, ethnicity, and generation. Conclusions: The multiplier method allows for a quick calculation of the predicted limb-length discrepancy at skeletal maturity, without the need to plot graphs, and is based on as few as one or two measurements. This method is independent of percentile groups and is the same for the prediction of femoral, tibial, and total-limb lengths. The multiplier values are also independent of generation, height, socioeconomic class, ethnicity, and race. We verified the accuracy of this method clinically by evaluating patients who had been managed with limblengthening or epiphysiodesis. The method was also comparable with or more accurate than the Moseley method of limb-length prediction. Limb-length discrepancy in children is generally progressive until skeletal maturity. Treatment decisions depend on the predicted limb-length discrepancy at skeletal maturity. Accurate prediction of the discrepancy is therefore important. We present a quick, convenient, accurate method for predicting limb-length discrepancy at skeletal maturity. Shapiro identified five patterns of progression of limb-length discrepancy in children. The current methods of predicting limb-length discrepancy at skeletal maturity are applicable only to the Shapiro type-I proportionate progression pattern. Limb-length discrepancies associated with other types of progression (Shapiro types II through V) have periods of acceleration or deceleration and therefore cannot be predicted accurately. Because most lower-limb-length discrepancies with congenital causes (such as congenital short femur, fibular hemimelia, hemiatrophy, and hemihypertrophy) and developmental causes (such as enchondromatosis [Ollier disease], poliomyelitis, and growth arrest) follow a type-I proportionate progression pattern, they can be predicted. The current methods of predicting limb-length discrepancy at skeletal maturity for patients who have the Shapiro type-I progression pattern are based on the longitudinal data presented by Anderson et al.. These data include the lengths of the femur and tibia from the age of one year to skeletal maturity for boys and girls, within one or two standard deviations from the mean. For lower-limb-length discrepancies that are present *No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article. No funds were received in support of this study. †Maryland Center for Limb Lengthening and Reconstruction, The James Lawrence Kernan Hospital, 2200 Kernan Drive, Baltimore, Maryland 21207. E-mail address for D. Paley: drorpaley@ hotmail.com. E-mail address for A. Bhave: [email protected]. Email address for J. E. Herzenberg: [email protected]. ‡The Alfred I. duPont Institute, 1600 Rockland Road, Wilmington, Delaware 19899. E-mail address: [email protected]. Copyright © 2000 by The Journal of Bone and Joint Surgery, Incorporated MULTIPLIER METHOD FOR PREDICTING LIMB-LENGTH DISCREPANCY 1433 VOL. 82-A, NO. 10, OCTOBER 2000 at birth, the predicted length of the short lower limb can be determined on the basis of the observation that the percentage of growth inhibition remains the same until skeletal maturity. To predict the limb-length discrepancy at skeletal maturity, Amstutz and Hootnick et al. recommended multiplying the ratio of the current length of the short limb to the current length of the long limb by the predicted length of the long limb at skeletal maturity to calculate the predicted length of the short limb at skeletal maturity. Subtracting the predicted length of the short limb from the predicted length of the long limb yields the predicted limb-length discrepancy at skeletal maturity. To determine the predicted length of the long limb at skeletal maturity, the current femoral and tibial lengths of the long limb are compared with the measurements collected by Anderson et al. for the current age and the gender of the child to determine the correct percentile group. The predicted length of the normal femur and tibia at skeletal maturity for that percentile group is recorded from the Anderson table or graph. Perhaps the most popular tool for predicting limblength discrepancy at skeletal maturity is the Moseley straight-line graph. Moseley converted the Anderson growth curve of the normal limb into a straight line with a 45-degree slope by shifting the data points along the x axis and altering the distance between the age scale on the x axis by a comparable amount. This is why, in the Moseley straight-line graph, the age scale is not linear but is similar to a semilogarithmic scale. The Moseley straight-line method requires serial follow-up (with at least three data points) to accurately predict limb-length discrepancy. It allows for refinement of the prediction because the growth percentile of the patient is based on more than one measurement. The Moseley graph can also be used to predict limb-length discrepancy with only one data point by incorporating the Amstutz method graphically. The Amstutz method requires the availability of tables, and the Moseley method requires the availability of graphs. Neither method can be used for children younger than one year, so prediction during the first year of life is not possible with these methods. The greatest difficulty associated with these methods is determining the percentile of the patient within the skeletal age range. This determination is improved somewhat by taking skeletal rather than chronological age into account in children who are older than nine years. All of these methods of prediction can be cumbersome, confusing, and time-consuming. Therefore, the purpose of the present study was to simplify the method of predicting limb-length discrepancy at skeletal maturity. Materials and Methods Development of the Multiplier The data collected by Anderson et al. are divided into the mean, mean plus one standard deviation, mean plus two standard deviations, mean minus one standard deviation, and mean minus two standard deviations of the femoral and tibial lengths at different chronological ages for boys and girls. These values correspond to the fifth, thirtythird, fiftieth, sixty-seventh, and ninety-fifth percentiles, respectively. For each percentile group, we divided the length of the femur and tibia for boys and girls at skeletal maturity (Lm) by the corresponding length of the femur or tibia at each year of age from one year to skeletal maturity (L). This converted every data point from the Anderson tables to a multiplier for length at skeletal maturity (M): M = Lm/L. Conversely, the current length of the femur or tibia can be multiplied by the age-specific multiplier to calculate the length of that bone at skeletal maturity: LM = Lm. The data of Anderson et al. begin at the age of one year. Maresh presented data on femoral and tibial lengths that were measured radiographically between birth and skeletal maturity. We incorporated the data presented by Maresh to include the period between birth and the age of one year. Development and Clinical Testing of the Formulae To predict the limb-length discrepancy and the amount of growth remaining, we developed formulae using the multipliers that had been calculated. We chose the Moseley method as the so-called gold standard for limb-length prediction. We compared the predictions that were made with use of the Moseley method with the predictions that were made with use of the multiplier formulae for two groups of patients who had reached skeletal maturity: a group managed with epiphysiodesis and a group managed with limb-lengthening. The epiphysiodesis group consisted of sixteen patients who were managed and followed at the Alfred I. duPont Institute in Wilmington, Delaware, by one of the authors (J. R. B.). The only treatment administered to fifteen of the sixteen patients was epiphysiodesis. The procedure was performed in the distal aspect of the femur in ten of these fifteen patients, in the proximal aspect of the tibia in one, and in both the distal aspect of the femur and the proximal aspect of the tibia in four. In the remaining patient, distal femoral and proximal tibial epiphysiodesis (6.5 centimeters) was performed with simultaneous femoral and tibial lengthening (7.5 and five centimeters, respectively). The predictions were made preoperatively with use of the Moseley and multiplier methods and were compared with use of the system presented by Little et al.. The accuracy of the predictions made with use of each method was then checked postoperatively. The effect of epiphysiodesis was factored in with use of Moseley’s method for the Moseley predictions and with use of the calculation of the amount of growth remaining for the multiplier predictions. With both the Moseley method and the multiplier method, we used the Anderson approximation that 71 percent of the total amount of femoral growth occurs at the distal aspect of the femur and 57 percent of the total amount of tibial growth occurs at the proximal aspect of the tibia. The limb-lengthening group consisted of fourteen patients who were managed with equalization of limb length by means of femoral and/or tibial lengthening at the Maryland Center for Limb Lengthening and Reconstruction in Baltimore, Maryland. For this group, the prediction of final limb-length discrepancy included the contribution of the lengthening process itself, assuming that no inhibition or stimulation of growth occurred as a result of the lengthening. The total actual limb-length difference was compared with the predicted limblength difference with use of both the Moseley method and the multiplier method. Comparison of Available Growth Databases In addition to the two databases presented by Anderson et al., eighteen other databases of femoral, tibial, and/or limb-length measurements in children were identified. We used the same methods to calculate the age and gender-related multipliers from these databases. In total, we analyzed and compared twenty databases: