Investigating Passive Muscle Mechanics With Biaxial Stretch

Figures

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  FIGURE 1. Planar biaxial materials testing overview, with (A) cruciform geometry, (B) representative planar biaxial sample, where the white arrow denotes the longitudinal direction and the white dashed square denotes approximate DIC region of interest (ROI), and (C) experimental stress-relaxation loading protocol schematic (note that axes are not to scale).

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  FIGURE 2. Schematic of passive muscle model for extracellular matrix and muscle fibers. A representative 2D square of muscle tissue shows the longitudinal or muscle fiber direction (red) and two families of collagen fiber dispersion (green) offset from the muscle fiber direction by an angle γ.

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  FIGURE 3. (A) Representative color contour plot of longitudinal (horizontal) stretch from digital image correlation. (B) Deformed symmetric cruciform finite element model with model ROI (black dashed line) symmetric boundary conditions (note that Z-symm is on the bottom, hidden face), and color contour plot of longitudinal stretch. (C) Deformed symmetric cruciform finite element model, showing initial cross-sectional area and reaction force at the model boundary (grip locations) used to determine model nominal stress. (D) Undeformed and deformed single element finite element model. Model Cauchy stress was directly output from the single element.

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  FIGURE 4. (A) Normalized stress relaxation data (shown as dashed mean curves and standard error bars) and a power law fit to the mean data (shown as solid curves). Note that power law fits and experimental data are visually overlapping and thus nearly indistinguishable. (B) Bar graphs for mean power law b coefficient, stress data, and linearized modulus with standard error bars.

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  FIGURE 5. Experimental and model data of passive muscle subject to planar biaxial stretch. (A) Nominal stress relaxation step data (open circles with standard error bars) and model fits (solid curves), with the first 10 s of these data for clarity shown at right, (B) longitudinal constant rate nominal stress-stretch curves for all experimental samples (thin curves) and model (thick curve), (C) longitudinal constant rate ROI stretch-nominal stretch curves, (D) transverse constant rate nominal stress-stretch curves, and (E) transverse constant rate ROI stretch-nominal stretch curves.

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  FIGURE 6. Modeling fits to uniaxial tensile experimental data from the previously published works of (A) Wheatley et al. (2016b), (B) Takaza et al. (2012), and (C) Mohammadkhah et al. (2016). Experimental data are shown as open circles and model data are solid curves.

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  FIGURE 7. Stress-stretch curves for simulated uniaxial stretch (dashed) and biaxial stretch (solid) for optimized parameters from (A) biaxial data presented in this study, (B) Wheatley et al. (2016b), and (C) Mohammadkhah et al. (2016). The increase in stress-stretch curve stiffness with biaxial stretch versus uniaxial stretch is denoted with arrows. Note that some models predict a negligible increase in stiffness (Wheatley) and others a major increase in stiffness (Mohammadkhah).

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  FIGURE 8. Parametric study stress-stretch curves for (A) uniaxial stretch and (B) biaxial stretch. Note that for both models (Aligned – solid curves and Dispersed – dashed curves) they exhibit nearly identical uniaxial behavior for both longitudinal (back curves) and transverse (blue curves), but distinctly different behavior when subject to biaxial stretch, with percentage differences between Aligned and Dispersed shown at λ = 1.3.