Surface instability of sheared active skeletal muscle tissue with loss of muscle mass

Abstract

In the present work, we study the surface instability of the wrinkling kind for the active-elastic skeletal muscle tissue subject to shear when the tissues are modeled by the mixture active strain approach. We consider two different models for the strain energy density functions, one as a sum of an incompressible neo-Hookean for the isotropic tissue constituents with the shear modulus μ and the anisotropic standard reinforcing model with the fiber stiffness E, and the other as a sum of the Gent material as an isotropic part and a function of the anisotropic variant I4 to model the anisotropic part. In both models, we introduce the activation parameter γ which describes the microstructural degree of contraction of the muscle. With the help of incremental deformation over the equations of equilibrium and incremental boundary conditions in the form of sinusoidal perturbations, we investigate the solutions for the surface instabilities of the wrinkling kind. First, we show that the critical amount of shear for instability, Kcr, decreases with an increasing E/μ ratio for the first model and the surface loses its stability with an increase in γ for a given E/μ ratio up to that angle Φ between the fibers and the direction of shear at which Kcr abruptly drops to a very low value for γ=0. For the second model, we find that Kcr increases with an increase in limiting chain extensibility of the Gent model and it either increases or almost remains constant with an increase in γ. Then we also introduce a decay deformation tensor involving a dimensionless parameter g into the multiplicative decomposition of the deformation gradient tensor, which helps model the loss of muscle mass during sarcopenia. We find that Kcr is almost independent with an increase in g for the first model but decreases with the increase in g for the second model for most Φ’s. Based on our results, we suggest that the second model is more compatible with the intuitive reasoning that the stability of the skeletal muscle surface should decrease with an increase in the loss of muscle mass.