Abstract
Skeletal muscle is an anisotropic soft biological tissue composed of muscle fibres embedded in a structurally complex, hierarchically organised extracellular matrix. In a recent work (Kuravi et al., 2021) we have developed 3D finite element models from series of histological sections. Moreover, based on decellularisation of fresh tissue samples, a novel set of experimental data on the direction dependent mechanical properties of collagenous ECM was established (Kohn et al., 2021). Together with existing information on the material properties of single muscle fibres, the combination of these techniques allows computing predictions of the composite tissue response. To this end, an inverse finite element procedure is proposed in the present work to calibrate a constitutive model of the extracellular matrix, and supplementary biaxial tensile tests on fresh and decellularised tissues are performed for model validation. The results of this rigorously predictive and thus unforgiving strategy suggest that the prediction of the tissue response from the individual characteristics of muscle cells and decellularised tissue is only possible within clear limits. While orders of magnitude are well matched, and the qualitative behaviour in a wide range of load cases is largely captured, the existing deviations point at potentially missing components of the model and highlight the incomplete experimental information in bottom-up multiscale approaches to model skeletal muscle tissue.
Highlights
Mathematical and computational modelling of skeletal muscle tissues poses a special challenge due to the composition, complex spatial distribution and orientation of its constituents, and their respective internal hierarchical structure, which altogether contribute to the overall motion, force generation and gait stabilising characteristics of skeletal muscle
Thereafter, we present the results of the numerical simulations for 90% pre-compressed extracellular matrix (ECM) samples, for 300 μm cubic muscle samples and for 900 μm extruded muscle samples with and without an intermediate layer between muscle fibres and ECM
While clear differences are noticeable between the stresses predicted by the small and large samples in uniaxial extension with lateral contraction (UAE)/uniaxial compression with lateral expansion (UAC) along 0◦ and 90◦ directions (Figs. 15a, b) as well as mode I and II semi-confined compression (SCC), and even a very strong effect in mode III SCC (Fig. 15c), these results indicate that the size of
Summary
Mathematical and computational modelling of skeletal muscle tissues poses a special challenge due to the composition, complex spatial distribution and orientation of its constituents, and their respective internal hierarchical structure, which altogether contribute to the overall motion, force generation and gait stabilising characteristics of skeletal muscle. The tissue is predominantly comprised of long, multi-nucleated excitable muscle fibres grouped into fascicles to form muscles (Barrett et al, 2016; Lieber, 2002) This hierarchy is established by collagenous layers referred to as endomysium, perimysium and epimysium that wrap fibres, fascicles and muscles, respectively (Barrett et al, 2016; Lieber, 2002). These layers form a substantial part of the extracellular matrix (ECM) and constitute 1%–10% (Kjær, 2004) of the muscle dry weight. Experimental evidence suggests a strong relation between this complex internal microstructure and the mechanical behaviour observed at tissue scale, such as a pronounced tension–compression asymmetry (Mohammadkhah et al, 2016; Gindre et al, 2013), local deformation mechanisms (Mohammadkhah et al, 2018; Takaza et al, 2014), and complex material symmetry (Böl et al, 2014)
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