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

Abstract

Computational modeling, such as finite element analysis, is employed in a range of biomechanics specialties, including impact biomechanics and surgical planning. These models rely on accurate material properties for skeletal muscle, which comprises roughly 40% of the human body. Due to surrounding tissues, compressed skeletal muscle in vivo likely experiences a semi-confined state. Nearly all previous studies investigating passively compressed muscle at the tissue level have focused on muscle in unconfined compression. The goals of this study were to (1) examine the stiffness and time-dependent material properties of skeletal muscle subjected to both confined and unconfined compression (2) develop a model that captures passive muscle mechanics under both conditions and (3) determine the extent to which different assumptions of volumetric behavior affect model results. Muscle in confined compression exhibited stiffer behavior, agreeing with previous assumptions of near-incompressibility. Stress relaxation was found to be faster under unconfined compression, suggesting there may be different mechanisms that support load these two conditions. Finite element calibration was achieved through nonlinear optimization (normalized root mean square error <6%) and model validation was strong (normalized root mean square error <17%). Comparisons to commonly employed assumptions of bulk behavior showed that a simple one parameter approach does not accurately simulate confined compression. We thus recommend the use of a properly calibrated, nonlinear bulk constitutive model for modeling of skeletal muscle in vivo. Future work to determine mechanisms of passive muscle stiffness would enhance the efforts presented here.

Anisotropic and viscoelastic tensile mechanical properties of aponeurosis: Experimentation, modeling, and tissue microstructure

“…Parameter determination was performed in two steps: a Monte Carlo simulation followed by a nonlinear least-squares deterministic optimization (lsqnonlin in MATLAB) (Vaidya and Wheatley, 2019). In the Monte Carlo simulation, the six parameters ( 1−3 and 1−3 ) were randomly varied for 100,000 simulations, ensuring 0 < 1 + 2 + 3 < 1.…”

Investigating Passive Muscle Mechanics With Biaxial Stretch

“…16) enables the use of viscoelastic coefficients g i and associated time constants τ i that characterize the amount and rate of relaxation, respectively. For this study, we fixed τ i terms as spaced parameters to ensure a broad range of relaxation rates (Table 1) and varied g i terms (Vaidya and Wheatley, 2019).…”

“…Parameter optimization was completed in two steps -first the viscoelastic Prony series parameters were fit to normalized stress-relaxation data for both the longitudinal and transverse directions, then hyperelastic parameters were fit to the full set of longitudinal and transverse stress data. This approach has the advantage of reducing the overall number of parameters needed to be optimized at any given step in the process by first determining stress relaxation behavior and then hyperelastic stiffness (Vaidya and Wheatley, 2019). All optimization was performed in MATLAB using constrained nonlinear optimization (lsqnonlin) by varying model parameters and minimizing the sum of squared residuals between model (σ m ) and experimental (σ e ) stresses as an objective function obj across all experimental data points (total number npts) (Eq.…”

“…Model fits to experimental data were evaluated with an average percent error for each experimental data point, normalized root mean square error (NRMSE, where 1 is a perfect fit and −∞ is the worst possible fit), and root mean square error (RMSE, in kPa) (Vaidya and Wheatley, 2019).…”

“…The advantage of this approach is a relatively low number of parameters while still enabling model robustness. The use of a Prony series viscoelastic model may increase the overall number of parameters of the model, but as we have shown in this and previous works (Vaidya and Wheatley, 2019), those parameters can be optimized with a two-step fitting procedure. Based on stress-stretch data alone, it would be unclear how load is shared between the ECM and muscle fibers.…”