The solid angle estimation of acetabular coverage of the femoral head

Abstract

The center-edge angle (CE angle) and the acetabular angle (AC angle) are generally accepted measurements in diagnosis for the patient with a dysplastic hip. However, the acetabular coverage of the femoral head is a complex three-dimensional (3D) structure. Thus conventional two-dimensional (2D) measurements using anteroposterior (AP) radiograph provide limited information about the contact area between the acetabulum and the femoral head. The authors developed a method for the solid angle estimation of the acetabular coverage of the femoral head in 3D space. The superior half of the femoral head is modeled as part of a sphere, and the tangent lines connecting from a set of points of the acetabular outline to the center of the fitted sphere are obtained. The lines pass through the unit sphere whose center is the same as that of the femoral head. With the points on the unit sphere, the authors calculate the covered area of the femoral head and estimate the solid angle. In this measurement, the solid angle of normal subjects is on an average 4.308 (rad) and the corresponding acetabular coverage is 68.3%. The solid angle is a new concept in comparison with the conventional 2D parameters such as CE and AC angles. Since acetabular coverage itself is 3D structure, solid angle will be more appropriate parameter in evaluating acetabular coverage.