To describe the mechanical behaviour of biological tissues and transport processes in biological tissues, conservation laws such as conservation of mass, momentum and energy play a central role. Mathematically these are cast into the form of partial differential equations. Because of nonlinear material behaviour, inhomogeneous properties and usually a complex geometry, it is impossible to find closed-form analytical solutions for these sets of equations. The objective of the finite element method is to find approximate solutions for these problems.
The concepts of the finite element method are explained on a finite element continuum model of skeletal muscle. In this case, the momentum equations have to be solved with an extra constraint, because the material behaves as nearly incompressible. The material behaviour consists of a highly nonlinear passive part and an active part. The latter is described with a two-state Huxley model. This means that an extra nonlinear partial differential equation has to be solved. The problems and solutions involved with this procedure are explained. The model is used to describe the mechanical behaviour of a tibialis anterior of a rat. The results have been compared with experimentally determined strains at the surface of the muscle. Qualitatively there is good agreement between measured and calculated strains, but the measured strains were higher.
Finite element modelling of contracting skeletal muscle
