The shape of the acetabular cartilage surface: a geometric morphometric study using three-dimensional scanning

The acetabular cartilage surface plays an important role in hip joint biomechanics, locomotion and lubrication, but few studies has focused on its geometric morphometry. The aim of this study was to present a novel, accurate mathematical representation of the acetabular cartilage surface based on a new method, combined with a reverse engineering technique, surface-fitting algorithms and mathematical curve surface theory. By using a three-dimensional (3D) laser scanner, a 3D triangulated mesh surface approximation of acetabular cartilage was created. Using surface-fitting algorithms and mathematical curve surface theory, two main curvature parameters, Gaussian curvature and mean curvature at each point on the surface of the acetabular cartilage, were calculated. The distribution patterns of both parameters over the curved surface were elucidated and the eigenvalues of the surface were calculated to determine the shape of the acetabular cartilage surface. By statistically analyzing 25 specimens, it was found that the shape of the acetabular cartilage surface was not theoretically spherical but rotational ellipsoidal, which is a novel mathematical description. The surface-fitting error of a rotational ellipsoid shape was significantly smaller than that of a spherical shape for representing the acetabular cartilage surface (p<0.001). The highest surface-fitting error for a spherical shape was seen in the roof area of the acetabular cartilage, where a rotational ellipsoid surface presented a better anatomical fit. The results will not only be helpful in gaining a new anatomical understanding of the acetabular cartilage surface, but will also be usable in the construction of a precise 3D numerical model in simulation studies of the hip joint.