Skeletal muscle tensile strain dependence: Hyperviscoelastic nonlinearity

Abstract

Introduction Computational modeling of skeletal muscle requires characterization at the tissue level. While most skeletal muscle studies focus on hyperelasticity, the goal of this study was to examine and model the nonlinear behavior of both time-independent and time-dependent properties of skeletal muscle as a function of strain. Materials and Methods Nine tibialis anterior muscles from New Zealand White rabbits were subject to five consecutive stress relaxation cycles of roughly 3% strain. Individual relaxation steps were fit with a three-term linear Prony series. Prony series coefficients and relaxation ratio were assessed for strain dependence using a general linear statistical model. A fully nonlinear constitutive model was employed to capture the strain dependence of both the viscoelastic and instantaneous components. Results Instantaneous modulus (p<0.0005) and mid-range relaxation (p<0.0005) increased significantly with strain level, while relaxation at longer time periods decreased with strain (p<0.0005). Time constants and overall relaxation ratio did not change with strain level (p>0.1). Additionally, the fully nonlinear hyperviscoelastic constitutive model provided an excellent fit to experimental data, while other models which included linear components failed to capture muscle function as accurately. Conclusions Material properties of skeletal muscle are strain-dependent at the tissue level. This strain dependence can be included in computational models of skeletal muscle performance with a fully nonlinear hyperviscoelastic model.

How does tissue preparation affect skeletal muscle transverse isotropy?

“…While skeletal muscle tensile studies are common (Abraham et al, 2012; Calvo et al, 2010; Gras et al, 2012; Morrow et al, 2010; Takaza et al, 2012; Wheatley et al, 2016), separate investigations have determined the tissue to be stiffer in the longitudinal direction (Morrow et al, 2010) or the transverse direction (Takaza et al, 2012). Our data for fresh samples agree well with Takaza et al for both transverse isotropy (transverse stiffer than longitudinal) and in terms of general stress-strain shape (longitudinal is nonlinear, transverse appears linear).…”

Current Understanding of the Biomechanics of Ventricular Tissues in Heart Failure

“…In the constitutive models of ventricular viscoelasticity, a finite element analysis with orthotropic viscoelastic model has been used to describe the passive myocardium viscoelastic behavior [93]. Another option to represent the viscoelastic behavior is by the hereditary (or convolution) integral with a strain-dependent Prony series, which has been found to successfully capture the strain-and time-dependent behavior in non-cardiovascular tissues [51,[94][95][96]. A nice review of constitutive models of cardiac tissue viscoelasticity can be found in the literature [93,97,98].…”

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.…”

“…Computational modeling of passive skeletal muscle is thus essential to simulations of impact biomechanics [2]- [8], rehabilitation engineering [9], [10], surgical planning [11], [12], and bed sore development [9], [13]. These models rely on accurate material properties for skeletal muscle, which have been shown to be anisotropic [14], [15], time dependent [3]- [5], [16], [17], non-linear [3], [17], and asymmetric in regards to tension and compression [18], [19]. However, the compressive behavior of skeletal muscle is not fully understood, particularly regarding the differences in muscle response to in vivo loading conditions [3]- [5], [20].…”

“…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].…”