A mathematical model for predicting postoperative leg shortening after curved intertrochanteric varus osteotomy for osteonecrosis of the femoral head

Despite good clinical outcomes associated with curved intertrochanteric varus osteotomy for the treatment of osteonecrosis of the femoral head, post-operative leg-length discrepancy is frequently reported and might reduce patient satisfaction. Although previous report showed that varus angulation affected post-operative leg-length discrepancy, sufficient varus angulation is the most important factor for obtaining a lateral intact portion. Therefore, to ensure better postoperative outcomes, detection of other parameters associated with leg shortening may prove useful. This study aimed to detect other factors influencing post-operative leg-length discrepancy and to develop a theory for pre-operative planning. The study included 42 hips of 36 patients with osteonecrosis of the femoral head [25 men and 11 women; mean age at the time of surgery, 33.8 years (range, 17 to 53 years)]. Patients were assessed their clinical and radiological results bofore and after surgery. Additionally, a mathematical model was developed to predict leg shortening after curved intertrochanteric varus osteotomy based on the degree of varus angulation and the distance between the femoral head and osteotomy arc centers. Predicted and actual leg shortening in patients were compared to verify the accuracy of our model. Post-operatively, mean varus angle was 21.7° (range, 15 to 38°) and mean leg shortening was 1.7 mm (range, -5.1 to 11.4 mm). Univariate analysis showed that varus angulation and lateral shift of the osteotomy arc might influence the degree of leg shortening. Furthermore, mathematically predicted leg shortening significantly correlated with actual leg shortening (r = 0.905, p < 0.001), suggesting the usefulness of our model for predicting complications of curved intertrochanteric varus osteotomy. This study indicates the importance of not positioning the center of the osteotomy arc lateral from the center of the femoral head to minimize leg shortening after curved intertrochanteric osteotomy.