Chapter 14 - Mathematical and Finite Element Modeling

Abstract

Mathematical modeling and finite element analysis have been widely used for the investigation of the biomechanics of the spine, and are considered to be one of the pillars of spine research together with in vitro testing and in vivo studies. Hundreds of finite element models aimed at predicting the biomechanical response of the spine under both healthy and pathological conditions as well as after the implantation of surgical devices have been discussed in the literature. In this chapter, after providing a historical perspective on how mathematical and numerical modeling became an integral part of biomechanics research, the basic principles of finite element modeling are described. Then a selection of the most relevant finite element models of the spine, which had a major influence on contemporary studies, is briefly illustrated.