Predicting the compression mechanical properties of muscle from microscale indentation mechanics using multiscale mechanical models

The texture properties of muscles are determined by the organization and interactions of their hierarchical structures. This study aims to establish a mechanical model from micro-to macro-scales to predict and explain the compressive mechanical properties of muscles. The nanomechanical properties of myofibrils, endomysium, and perimysium of different meats were first measured by atomic force microscopy (AFM). Using these data as input, a two-level analytical model from the myofibril-endomysial scale to the fiber-perimysium scale, adopting a simplified multi-component series model (Reuss model), was constructed to predict the transverse compression modulus of a single muscle fiber and that of a muscle fiber bundle. On the macroscale, two constitutive models (a combined logarithmic-polynomial model and a novel logistic model) were used to fit the stress-strain curves of muscle samples from transverse compression measurements. The correlation between the predicted modulus from the analytical model and the compression mechanical parameters obtained by the constitutive models were analyzed, revealing the relationship between macroscopic muscle mechanics and the mechanical properties of microscopic components. The results indicate that the linear mechanical properties of macroscopic muscles are primarily associated with the transverse modulus of myofibrils, and that the transition from linear to nonlinear mechanics is jointly influenced by myofibrils and connective tissues (endomysium and perimysium), while the nonlinear response is mainly associated with the incremental strain-stiffening behavior of the connective tissue. This study provides a quantitative mechanical basis for understanding the microstructural origins of muscle tissue texture.