A micromechanical model of skeletal muscle to explore the effects of fiber and fascicle geometry

Abstract

Computational models of muscle generally lump the material properties of connective tissue, muscle fibers, and muscle fascicles together into one constitutive relationship that assumes a transversely isotropic microstructure. These models do not take into account how variations in the microstructure of muscle affect its macroscopic material properties. The goal of this work was to develop micromechanical models of muscle to determine the effects of variations in muscle microstructure on the macroscopic constitutive behavior. We created micromechanical models at the fiber and fascicle levels based on histological cross-sections of two rabbit muscles, the rectus femoris (RF) and the soleus, to determine the effects of microstructure geometry (fiber and fascicle shapes) on the along-fiber shear modulus of muscle. The two fiber-level models predicted similar macroscopic shear moduli (within 13.5% difference); however, the two fascicle-level models predicted very different macroscopic shear moduli (up to 161% difference). We also used the micromechanical models to test the assumption that the macroscopic properties of muscle are transversely isotropic about the fiber (or fascicle) direction. The fiber-level models exhibited behavior consistent with the transverse isotropy assumption; however, the fascicle-level models exhibited transversely anisotropic behavior. Micromechanical models, combined with fiber and fiber bundle mechanical experiments, are needed to understand how normal or pathological variations in microstructure give rise to the observed macroscopic behavior of muscle.

A structural model of passive skeletal muscle shows two reinforcement processes in resisting deformation

“…In future, finite element modelling of whole muscle including fascicles similar to the work of Blemker's group (eg , Sharafi and Blemker, 2010, Blemker et al, 2005) will be necessary to further understand the collagen fibre pressure terms considered in the present work. These works have shown that the finite element approach is effective, for example in confirming the role of muscle force transmission through shear in the connective tissue in the case of terminating fibres and this approach could help to confirm the pressure/hoop-stress hypothesis for passive muscle resistance to external deformation reported in this paper.…”

Multiscale models of skeletal muscle reveal the complex effects of muscular dystrophy on tissue mechanics and damage susceptibility

“…To initially validate the approach for defining geometries and boundary conditions, we performed simulations with a muscle to ECM shear modulus ratio ranging from 0.01 to 500 for a healthy muscle fascicle; the results replicated those found by Sharafi & Blemker [26]. The micromechanical model was then used in a parameter analysis to test the individual effect of a number of variations in microstructures prevalent in musculoskeletal disease.…”

“…As muscle fibre force is known to be transmitted laterally through shearing of the endomysium, we were interested in analysing the muscle in shear [4,26]. We assigned the boundary conditions to prescribe simple shear deformation, representing the shear displacement of muscle fibres and fascicles relative to each other.…”

“…Fat infiltration was modelled as a simple incompressible, hyperelastic, neo-Hookean material with a single material parameter representing Young's modulus of the material. Currently, there are no known measurements for the along-fibre shear modulus of muscle and ECM, G is the critical factor in determining the contribution of structural variation on tissue-level properties [26]. Furthermore, there remains a debate in the literature as to whether muscle fibres are more or less stiff than the ECM [2][3][4].…”

“…The agent-based model was used to generate new fascicle cross sections for each simulation so that all analyses were completed with a unique geometry, accounting for typical variability seen in muscle fibres. Because there is debate in the literature on whether muscle fibres are stiffer than the ECM or the ECM is stiffer than muscle fibres, all parameter analyses were repeated at two ratios of G : one in which the muscle is 75 times stiffer than the ECM [26], and one in which the ECM is 25 times stiffer than the muscle [3]. Total finite-element simulation time was 8 min on a 32 GB eight-processor IBM Linux workstation.…”