Patient-specific acetabular shape modelling: comparison among sphere, ellipsoid and conchoid parameterisations

The shape of the human acetabular cup was commonly represented as a hemisphere, but different geometries and patient-specific shapes have been recently proposed in the literature. Our aim was to test the limits of the sphericity assumption by comparing three different parameterisations, namely the sphere, the ellipsoid and the rotational conchoid. Models of hip surfaces, reconstructed from CT scans taken from Caucasian race cadavers and patients, were automatically processed to extract the acetabular surface. Two separate analyses were carried out on the overall acetabular shape, including both the acetabular fossa and the lunate surface (case A) and acetabular cup represented by the lunate surface only (case B). Nonlinear gradient-based and evolutionary computation approaches were implemented for the fitting process. Minor differences from the three idealised geometries were detected (median values of the fitting errors < 1 mm). Nonetheless, the sphere fitting was found to be statistically different from both the ellipsoid (p < 2.50e - 10) and the conchoid (p < 1.07e - 09), whereas no statistical difference was detected between the ellipsoid and the conchoid for case A. Significance of the difference between ellipsoid and sphere (p < 4.55e - 12) and between conchoid and sphere (p < 1.93e - 11) was found for case B as well. Interestingly, for case B statistical difference was detected between the ellipsoid and the conchoid. In conclusion, we synthesise that the morphology of the overall acetabular cup can be parameterised both with an ellipsoid shape and with a conchoid shape as well with superior quality than the simple sphere. Differently, if one considers just the lunate surface, better fitting results are expected when using the ellipsoid.