Fully non-linear hyper-viscoelastic modeling of skeletal muscle in compression

Abstract

Understanding the behavior of skeletal muscle is critical to implementing computational methods to study how the body responds to compressive loading. This work presents a novel approach to studying the fully nonlinear response of skeletal muscle in compression. Porcine muscle was compressed in both the longitudinal and transverse directions under five stress relaxation steps. Each step consisted of 5% engineering strain over 1 s followed by a relaxation period until equilibrium was reached at an observed change of 1 g/min. The resulting data were analyzed to identify the peak and equilibrium stresses as well as relaxation time for all samples. Additionally, a fully nonlinear strain energy density-based Prony series constitutive model was implemented and validated with independent constant rate compressive data. A nonlinear least squares optimization approach utilizing the Levenberg-Marquardt algorithm was implemented to fit model behavior to experimental data. The results suggested the time-dependent material response plays a key role in the anisotropy of skeletal muscle as increasing strain showed differences in peak stress and relaxation time (p < 0.05), but changes in equilibrium stress disappeared (p > 0.05). The optimizing procedure produced a single set of hyper-viscoelastic parameters which characterized compressive muscle behavior under stress relaxation conditions. The utilized constitutive model was the first orthotropic, fully nonlinear hyper-viscoelastic model of skeletal muscle in compression while maintaining agreement with constitutive physical boundaries. The model provided an excellent fit to experimental data and agreed well with the independent validation in the transverse direction.

A case for poroelasticity in skeletal muscle finite element analysis: experiment and modeling

“…Fit I was a conservative strain dependent formulation while Fit II was a case of highly nonlinear strain dependence similar to other tissues (Weiss and Maakestad, 2006). Additionally, the “Constant” model was compared against two models incorporating viscoelasticity of the solid phase through a Prony series (Wheatley et al, 2015), one with both poroelasticity and viscoelasticity, and one with viscoelasticity only. The mean Cauchy stress in the direction of compression was compared between models.…”

“…The role which permeability plays in skeletal muscle mechanics, known as poroelasticity, is unclear (Yang and Taber, 1991). In computational models of skeletal muscle, time dependence is often neglected (Van Loocke et al, 2006) or approximated using viscoelastic modeling (Van Loocke et al, 2008; Wheatley et al, 2015). The goals of this work were to 1) characterize skeletal muscle permeability by direct experimental measurement, and 2) identify how various permeability implementations affect skeletal muscle models in compression.…”

An experimental and computational investigation of the effects of volumetric boundary conditions on the compressive mechanics of passive skeletal muscle

“…All samples were taken from muscle midbelly and were kept hydrated by phosphate buffered saline throughout testing [24], [26], [34]. To limit effects of rigor mortis, all testing was completed within eight hours of sacrifice [3]- [5], [17], [29], [35]. Tissue damage was controlled at two points in experimental protocol.…”

“…An Al2O3 porous plunger (diameter = 6.4 mm, length = 25.5 mm) was used along with an impermeable steel well (diameter = 6.9 mm, depth = 8 mm) for CC ( Figure 1B). Two stress relaxation testing conditions were employed for both UC and CC conditions: fast and slow compression stress relaxation [5], [29], [36]. All tests were completed under transverse compression to simulate the most common uniaxial physiological loading orientation [15], [22], [23], [34], [37].…”

“…The time dependent nature of muscle can be observed in significant stress relaxation following compressive deformation [3]- [5], [16], [17]. Stress relaxation tests have been thus used extensively to characterize the stress-strain and stress-time behavior of the tissue, and are typically accompanied by various viscoelastic modelling approaches [3], [4], [17], [27]- [29]. Inverse finite element methods are effective in determining material properties through parameter optimization to experimental data [27], [30]- [32].…”