A new approach for the simulation of skeletal muscles using the tool of statistical mechanics

The structure of a skeletal muscle is dominated by its hierarchical architecture in which thousands of muscle fibres are arranged within a connective tissue network. The single muscle fibres consist of many force-producing cells, known as sarcomeres. These micro biological engines are part of a motor unit and contribute to the contraction of the whole muscle. There are a lot of questions concerning the optimisation of muscle strength and agility. Standard experimental investigations are not sufficient to answer these questions because they do not supply enough information. Additionally, these methods are limited because not enough material for testing is accessible. To overcome these problems, numerical testing tools can be an adequate alternative. From the mechanical point of view the material behaviour of muscles is highly non-linear. They undergo large deformations in space, thereby changing their shape significantly, so that geometrical nonlinearity has to be considered. Many authors use continuum-based approaches in combination with the finite element method to describe such material behaviour. However, models of this kind require realistic constitutive relations between stress and strain which are difficult to determine in an inhomogeneous material. Furthermore, biomechanical information cannot be fully exploited in these models. The present approach is crucially based on the use of the finite element method. The material behaviour of the muscle is split into a so-called active and a passive part. To describe the passive part special unit cells consisting of one tetrahedral element and six truss elements have been derived. Embedded into these unit cells are further truss elements which represent bundles of muscle fibres. Depending on the discretisation it is possible to simulate the material behaviour of e.g. artery walls characterised by oriented fibres or soft tissue including only non-oriented fibres. In summary, the present concept has the advantage that a three-dimensional model is developed which allows us take into account many physiological processes at the micro level.