The Multi-level Angular Deformity Determination in 3D Space with Total Curvature Analysis for Long Bones

Determination of angular deformity apex and plane for long bone is one of the tasks in our preoperative surgery planning system. Long bone angular deformity of the upper and lower extremities, in general, is three-dimensional. In our computerized planning system, the simplified long bone is represented by two components. One is the three-dimensional curve of its central axis, which as indicated in our previous study, is obtained from both frontal and lateral X-ray image outlines. Another component is represented by a series of ellipses in the horizontal planes centralized with this central axis. The central axis can be described by total curvature, which contains both the curvature and the torsion of this 3D curve of the central axis. The curvature measures how sharply a curve is turning and the torsion measures its twist in 3D space. In our previous study, the assumption was made that the angular deformity planes determined by the central axis always bisected the coronal and sagittal plane, i.e. these planes are perpendicular to the horizontal plane. However, this is not true for multi-level angular deformity and the deformity planes should be arbitrary in 3D space. The improved method we are using is to apply the total curvature to the central axis of the long bone. The curvature and torsion could completely define the shape of this 3D curve of central axis. By analyzing the central axis of the long bone with the total curvature, the severity and the level as well as the plane of the deformity of the long bone in 3D can be determined automatically