Title: Micro-Macro Modelling:From Sarcomere to Muscles Contraction

Abstract:
The main purpose of the present study is the development of an efficient three-dimensional modelling concept for the mathematical description and simulation of the physiological behaviour of skeletal muscles.

An elementary concept of the study is the fragmentation of the Helmholtz free energy function into active and passive parts. The proposed concept is based on the idea of representing the passive part by means of an assembly of non-linear truss elements. In each truss element the micromechanical force-stretch behaviour of a certain group of collagen fibres is implemented. The truss elements are arranged in such a way that one of them lies on each edge of one finite tetrahedral element. In this way a so-called tetrahedral unit cell is formed. An ensemble of these cells lets us simulate the behaviour of the soft tissue alone. To incorporate muscle activation, bundles of muscle fibres in form of nonlinear truss elements are embedded in the before mentioned assembly of unit cells. These trusses contain a mathematical description of the activation at the fibre level. In this way we are able to simulate complex muscle structures with arbitrary muscle fibre distributions.

In conclusion, the present study has the advantage that a three-dimensional model is available which allows us to take into account many physiological processes at the micro level.