On a "Columbus' Egg": Modeling the shape of asymptomatic, dysplastic and impinged hip joints

Understanding morphological features that characterize normal hip joint is critical and necessary for a more comprehensive definition of pathological presentations, such as femoroacetabular impingement and hip dysplasia. Based on anatomical observations that articular surfaces of synovial joints are better represented by ovoidal shapes than by spheres, the aim of this study is to computationally test this morphological classification for the femoral head and acetabular cavity of asymptomatic, dysplastic and impinged hips by comparing spherical, ellipsoidal and ovoidal shapes. An image-based surface fitting framework was used to assess the goodness-of-fit of spherical, ellipsoidal and tapered ellipsoidal (i.e., egg-like) shapes. The framework involved image segmentation with active contour methods, mesh smoothing and decimation, and surface fitting to point clouds performed with genetic algorithms. Image data of the hip region was obtained from computed tomography and magnetic resonance imaging scans. Shape analyses were performed upon image data from 20 asymptomatic, 20 dysplastic and 20 impinged (cam, pincer, and mixed) hips of patients with ages ranging between 18 and 45 years old (28 male and 32 women). Tapered ellipsoids presented the lowest fitting errors (i.e., more oval), followed by ellipsoids and spheres which had the worst goodness-of-fit. Ovoidal geometries are also more representative of cam, pincer, mixed impinged hips when compared to spherical or ellipsoidal shapes. The statistical analysis of the surface fitting errors reveal that ovoidal shapes better represent both articular surfaces of the hip joint, revealing a greater approximation to the overall features of asymptomatic, dysplastic and impinged cases.