Anisotropic Viscoelastic Characterization of In Vitro Muscle During Passive Stretching

Passive stretching is commonly used in exercise rehabilitation, and the aim of this study was to quantitatively characterize the effect of passive stretching force on the anisotropic viscoelastic properties of bovine muscle tissues in vitro, so as to clarify the effects of different stretching modes and intensities on the muscles. Graded stretching forces (0-30 N) were applied along the fiber direction of three bovine tenderloin samples (N = 3). Multi-frequency shear waves (100-300 $\mathrm{Hz}$) were generated using an external mechanical vibration, and the resulting shear wave velocity dispersion was measured in directions parallel and perpendicular to the fibers. To ensure measurement stability, three acquisitions were performed for each experimental condition and the results were averaged for analysis (n = 3). The dispersion data were fitted to the Kelvin-Voigt model to estimate the shear elastic modulus and shear viscous coefficient. With applied stretching force, both the shear elastic modulus and shear viscous coefficient exhibited significant, non-linear increases in both measurement directions. This enhancement was particularly pronounced in the parallel fiber direction: as stretching force increased from 0 to 30$N$, the shear elastic modulus increased from $4.67\pm 0.33kPa$ to $10.07\pm 0.59kPa$ (an increase of $116\%\pm 15\%$), and the shear viscous coefficient increased from $5.28\pm 0.38Pa·s$ to $10.82\pm 0.47Pa·s$ (an increase of $105\%\pm 12\%$), thereby amplifying the tissue's mechanical anisotropy. A two-way repeated measures ANOVA confirmed that the effects of stretching force, measurement direction, and their interaction were all highly significant ($p<0.005$). Passive stretching is a primary modulator of the anisotropic viscoelasticity in muscle tissue. This study systematically reveals the direction-specific, force-dependent evolutionary patterns of both elastic and viscous parameters, providing a critical experimental foundation for advancing the understanding of passive muscle mechanics and for the validation and refinement of biomechanical constitutive models. Furthermore, in the field of sports rehabilitation, these findings can inform the development of more scientific muscle rehabilitation protocols.