Abstract

Skeletal muscle tissue has a highly complex and heterogeneous structure comprising several physical length scales. In the simplest model of muscle tissue, it can be represented as a one dimensional nonlinear spring in the direction of muscle fibres. However, at the finest level, muscle tissue includes a complex network of collagen fibres, actin and myosin proteins, and other cellular materials. This study shall derive an intermediate physical model which encapsulates the major contributions of the muscle components to the elastic response apart from activation-related along-fibre responses. The micro-mechanical factors in skeletal muscle tissue (eg. connective tissue, fluid, and fibres) can be homogenized into one material aggregate that will capture the behaviour of the combination of material components. In order to do this, the corresponding volume fractions for each type of material need to be determined by comparing the stress-strain relationship for a volume containing each material. This results in a model that accounts for the micro-mechanical features found in muscle and can therefore be used to analyze effects of neuro-muscular diseases such as cerebral palsy or muscular dystrophies. The purpose of this study is to construct a model of muscle tissue that, through choosing the correct material parameters based on experimental data, will accurately capture the mechanical behaviour of whole muscle. This model is then used to look at the impacts of the bulk modulus and material parameters on muscle deformation and strain energy-density distributions.

Highlights

  • Skeletal muscle is a complex heterogeneous structure, and a three dimensional continuum model is required to capture its complete mechanics

  • Comparable material stiffness to healthy muscle occurs for α < 0.10 for sECM = 150 which is a larger range of volume fractions compared to sECM = 250 (< 0.05)

  • As the volume fraction of the extra-cellular matrix (ECM) was increased, there was an increase in stiffness that is expected with fibrotic tissue

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Summary

Introduction

Skeletal muscle is a complex heterogeneous structure, and a three dimensional continuum model is required to capture its complete mechanics. One dimensional models have been developed, often to describe whole body movement or inter-muscular dynamics When examining the mechanics or force production of the muscle these models are not sufficient to understand the complex effects from the heterogeneity or architecture of muscle [2]. Three dimensions are required to fully capture the bulging and deformation seen in skeletal muscle [3]. To capture the complex aspects of muscle tissue, these models are typically built using the theory of continuum mechanics and solved using a finite element method [4,5,6,7,8,9].

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