Mathematical representation of the normal proximal human femur: Application in planning of cam hip surgery

Abstract

Precise modelling of the proximal femur can be used for detecting and planning corrective surgery for subjects with deformed femurs using robotic technology or navigation systems. In this study, the proximal femoral geometry has been modelled mathematically. It is hypothesised that it is possible to fit a quadratic surface or combinations of them onto different bone surfaces with a relatively good fit. Forty-six computed tomography datasets of normal proximal femora were segmented. A least-squares fitting algorithm was used to fit a quadratic surface on the femoral head and neck such that the sum of distances between a set of points on the femoral neck and the quadratic surface was minimised. Furthermore, the position of the head-neck articular margin was also measured. The femoral neck was found to be represented as a good fit to a hyperboloid with an average root mean-squared error of 1.0 ± 0.13 mm while the shape of the femoral articular margin was a reproducible sinusoidal wave form with two peaks. The mathematical description in this study can be used for planning corrective surgery for subjects with cam-type femoroacetabular impingement.