Micromechanical modelling of skeletal muscles: from the single fibre to the whole muscle

Abstract

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 fibre consists of many force-producing cells, known as sarcomeres, which contribute to the contraction of the whole muscle. There are a lot of questions concerning the optimisation of muscle strength and agility. To answer these questions, numerical testing tools, e.g. in the form of finite element models can be an adequate alternative to standard experimental investigations. The present approach is crucially based on the use of the finite element method. The material behaviour of the muscle is additively 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 non-linear truss elements which represent bundles of muscle fibres. Besides the representation of the material model, this contribution focuses on the application to anatomically based 3D problems, as the animal soleus muscle of the rat.

A continuum model for skeletal muscle contraction at homogeneous finite deformations

“…(20) is given by ∂Ψ p /∂λ and its contribution is generally small in this region for skeletal muscle (Böl 2010;Ehret et al 2011;Gordon et al 1966;Davis et al 2003); an observation which holds here too. The passive part may, therefore, be neglected.…”

A new approach for the validation of skeletal muscle modelling using MRI data

“…Based on our previous work on skeletal muscle modelling [7][8][9] as well as on contributions to cardiac repair [10] a brief review on the general approach is given.…”

In Vitro/in Silico Characterization of Active and Passive Stresses in Cardiac Muscle

“…In contrast to the recently proposed phenomenological models for passive cardiac tissue (Göktepe et al, 2011;Holzapfel and Ogden, 2009;Schmid et al, 2006Schmid et al, , 2009, we pursue an approach in which the passive material response is characterized by means of discrete representative volume elements in the form of tetrahedra. These elements have originally been developed for rubberlike materials (Böl and Reese, 2006), and are now modified for networks of biopolymers in muscular tissue (Böl andReese, 2007, 2008). The characteristic microstructure of the polymeric tissue network is incorporated through the statistical mechanics of long chain molecules (Flory, 1969;Treloar, 1975) represented discretely at the six edges of each tetrahedral element.…”

“…Here, we model the individual chains as wormlike chains with an initial stiffness characterized through the persistence length (Bustamante et al, 1994;Kratky and Porod, 1949;Kuhl et al, 2005Kuhl et al, , 2006Kuhl and Holzapfel, 2007). In addition to the energy of the six wormlike chain bundles on the tetrahedral edges, each tetrahedral energy accounts for an incompressible ground substance through a phenomenological volumetric free energy term (Böl and Reese, 2007;Böl, 2012).…”