Investigating the Role of Meso-scale Structure on the Mechanical Response of Skeletal Muscle Tissues

Abstract

Skeletal muscle tissues are highly hierarchical materials with multifarious fibre bundles embedded in sheaths of extracellular matrix (ECM), which manifests as a honeycomb structure like scaffolding. These tissues are often modelled as transversely isotropic materials with a constitutive form incorporating homogenised (or lumped) material properties of their constituents. The often employed assumption of non-contributing muscle fibres in compression was found wanting by recent observations, wherein the meso-scale hierarchy stabilised by collagen sheaths was hypothesised to play a prominent role. This motivates identifying and incorporating the role of this internal hierarchy and structure in modelling to study the peculiar response of these tissues. In this context, multi-scale models capturing these features as well as inter-component interactions could offer a comprehensive framework to analyse these tissues, and finally predict their response. To this end, this thesis aims at the development and the validation of detailed finite element based models for skeletal muscles. These models were generated using virtually reconstructed three-dimensional tissue volumes from histological sections of muscle samples (obtained from an unloaded state). The spatial disposition of the ECM layers around fibre bundles was estimated by drawing an analogy from steady-state heat transfer analyses. Each constituent (i.e., fibre bundles, and ECM membranes) was then associated with an appropriate continuum material model inspired from physiology and phenomenology, and material symmetry. Individual component material properties were established using recent experimental data on muscle fibres and the ECM in an optimisation based framework. For the ECM in particular, the inverse finite element method based approach was invoked with comprehensive multi-axial experimental data in conjunction with detailed FE models. These resulting FE models with the component level calibration were used to identify, study, and finally predict the peculiar multi-axial response of muscle tissues. Firstly, the significance of 3D microstructure on the mechanical behaviour was revealed by comparing numerical results from the FE models containing varying degrees of 3D details. Secondly, for a wide range of load cases i.e., multi-directional uniaxial, bi-axial, semiconfined compression, computationally predicted mechanical responses were compared to the corresponding experimental data for qualitative and quantitative inferences. Herein, the influence of experimental pre-load on numerical predictions was identified and investigated. Thirdly, the degree of correlation between the experimental results and the numerical simulations, respectively, obtained from specific muscle samples and the FE models developed from their histological information was studied. Finally, in-situ multi-photon microscopy imaging, with improved experimental aids, was employed to perform preliminary investigations towards relating the micro-scale muscle tissue behaviour to the macro-scale stimuli.