Oomens, Maenhout, van Oijen, Drost, Baaijens, 2003

Model Status

This model can not currently be represented in valid CellML 1.0 or 1.1 and as such is not solvable by existing CellML tools.

Model Structure

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. These laws, together with constitutive laws which describe the material properties of the tissue, and boundary and initial conditions make it possible to mathematically solve a wide range of functional, biological problems. Mathematically, these equations are presented as partial differential equations.

Many soft biological materials undergo large deformations, and the relationship between stress and the applied strain is nonlinear, anisotropic and inhomogeneous. Add the complex geometry of biological structures and it becomes impossible to find closed-form solutions for these equations. Instead the finite element method is used to find good approximate solutions to these equations. The finite element method transforms the partial differential equations into a finite set of algebraic equations.

In the Oomens et al. 2003 publication described here, the authors aim to explain the concepts of a finite element model of contracting skeletal muscle. The material behaviour of contracting skeletal muscle consists of a highly nonlinear passive part and an active part. The later is described with a two state Huxley model. The model incorporates a stimulation function chi, which is used to control the active stress in the muscle. This stimulation function is derived from another paper by Zahalak and Ma, 1990 (full reference below).

The complete original paper reference is cited below:

Finite element modelling of contracting skeletal muscle, C.W.J. Oomens, M. Maenhout, C.H. van Oijen, M.R. Drost, and F.P. Baaijens, 2003, Phil. Trans. R. Soc. Lond. B , 358, 1453-1460. (A PDF version of the article is available to subscribers on the Phil. Trans. R. Soc. Lond. B website.) PubMed ID: 14561336

Muscle Activation and Contraction: Constitutive Relations Based Directly on Cross-Bridge Kinetics, George I. Zahalak and Shi-Ping Ma, 1990, Journal of Biomedical Engineering , 122, 52-62. PubMed ID: 2308304 Please note that this article is not available in an electronic format.