A Continuum Model of Skeletal Muscle Tissue with Loss of Activation

Abstract

We present a continuum model for the mechanical behavior of the skeletal muscle tissue when its functionality is reduced due to aging. The loss of ability of activating is typical of the geriatric syndrome called sarcopenia. The material is described by a hyperelastic, polyconvex, transverse isotropic strain energy function. The three material parameters appearing in the energy are fitted by least square optimization on experimental data, while incompressibility is assumed through a Lagrange multiplier representing the hydrostatic pressure. The activation of the muscle fibers, which is related to the contraction of the sarcomere, is modeled by the so called active strain approach. The loss of performance of an elder muscle is then obtained by lowering of some percentage the active part of the stress. The model is implemented numerically and the obtained results are discussed and graphically represented. arXiv:1701.07823v1 [q-bio.TO]

A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials

“…where S is a scalar function. One may notice that, according to (6), the non-null components of P act are all along Fm ⊗ m while in the active strain approach all the components are involved. Denoting by W act a primitive function of S, one has that…”

“…Indeed one can see that a constant active strain cannot fit at all the experimental data. To address this problem we will assume that F a depends on the deformation gradient F, see also [4,6,7,5,25]. Such an approach, which is a generalization of the active strain, is crucial in the applications to skeletal muscle: it allows to capture the physics of a muscle, in which the stress produced when the tissue is activated depends on strain.…”

Loss of mass and performance in skeletal muscle tissue: a continuum model

“…Therefore it is desirable to build a mathematical model of muscle tissue affected by sarcopenia. As far as we know, the first elastic model of sarcopenic skeletal muscle has been proposed in [2]; however, that paper focuses only on the loss of performance.…”

Strain-dependent internal parameters in hyperelastic biological materials

“…The previous calculation has often been overlooked in the literature, especially in the modeling of active biological tissues, and the simpler expression P = ∂W ∂F (F, γ) has been used instead of the former (see for instance [5,6,7,8,9]). In this paper we want to emphasize the correct expression of the stress when the internal parameter depends on the strain and one persists in the context of hyperelasticity.…”

“…Moreover, we propose two reliable models for the tetanized skeletal muscle tissue. The issue has been widely studied in the recent literature [6,10,7,8,11,9]; the new approaches here proposed use the same passive strain energy function, which has been introduced in [6], while the activation is described in two different ways. Notice that the proposed models consider the behavior of a muscle when the activation is at its maximum: the amount of activation cannot be voluntarily controlled, but it is an experimental datum which depends only on the strain.…”