A Geometric Model for Cylinder-Cylinder Impact with Application to Vertebrae Motion Simulation

Abstract

The reconstruction of inter-vertebral motion of the human cer- vical spine, although basically understood, still poses many open problems. This is so because pairs of vertebrae undergo in general six-dimensional mo- tion relative to one another, but display a high degree of coupling between gross translational and rotational degrees-of-freedom due to restraints im- posed by ligaments and muscles and the compliant nature of the inter- vertebral discs (White and Panjabi, 1990). Described in this paper is the mathematical modeling of a vertebrae pair using multibody methods and impact analysis techniques with elementary contact geometry for the facet joints. The results are compared with existing approaches and with exper- imental data, showing a good agreement with the latter and an efficiency boost compared to existing approaches by a factor of 350. The investiga- tions are focused on the vertebrae pair C5–C6 but can be easily extended to other vertebrae.