The solid angle estimation of acetabular coverage of the femoral head using 3D method

입체각 측정을 통한 대퇴골두에 대한 관골구 coverage 측정

We present a method for the estimation of 3D solid angle assessment of the acetabular coverage of the femoral head in 3D space. At first, femoral head and acetabulum is segmented from the original CT scan images. The slice thickness is 1.5mm and the number of slices is usually 30-40 to cover the entire acetabulum. The superior half of the femoral head is modeled as part of a sphere. Thus, the axial cross sections of the upper half of the femoral head are also modeled as circles. A set of points from each outline image of femoral head is fitted recursively into a circle by minimizing root-mean-square (RMS) error. With these fitted circles, a center point of the femoral head model is evaluated. This is a reference point for calculating the solid angle of the acetabular inner surface. Next, the tangent lines connecting from a set of points of the acetabular edge 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, we calculate area and estimate the solid angle. Based on this solid angle, the deformity of the acetabulum is analyzed. In case of normal subject, the solid angle is about 4.3 (rad) and acetabular coverage is 68%.