Modeling and Visualization of Inter-Bone Distances in Joints

We demonstrate a method for visualizing inter-bone distances in articular joints. Visualization of inter-bone distances has the potential to characterize 3D structures and spatial relations non-invasively in complex joints. Our method uses both implicit and parametric representations of bones. The two types of representation have complementary strengths for different types of calculations. The implicit representation, the distance field, is a scalar field sampled on a regular grid. It specifies the signed distance from a point in the field to the nearest point on the bone. We calculate distance fields from the parametric representations which are smooth, locally controllable manifold surface models [1] of the bones. These models are approximated from segmented CT scans of the bones [2]. We calculate inter-bone distances in a simple and efficient way with the help of the distance fields. We visually represent calculated inter-bone distances using color mapping and iso-contouring. We have found animations of these visualizations particularly helpful for understanding changes in relationships among bones. We applied our technique separately to three related joint structures of the hand – the distal radioulnar joint, the carpal bones of the wrist, and the scapholunate joint. Although studies on structure and kinematics of joints have been done mostly in vitro using techniques such as soft tissue sectioning, electro-magnetic motion tracking and cadaveric CT scanning,studies using 3-D techniques have recently been introduced [3, 4, 5, 6]. To our knowledge, there has been no previous work using distance fields to represent bones, however distance fields have been used for other purposes in robotics [7] and computer graphics [8, 9]. The two scalar data visualization techniques we used, color mapping and iso-contouring, are well known scientific visualization techniques [10].