A multiscale sarcomere-to-fiber modeling approach for time-dependent uniaxial skeletal muscle mechanics

A comprehensive understanding of skeletal muscle mechanics requires models that reflect its hierarchical structure and biophysical complexity. This study presents a multiscale continuum model grounded in sarcomere-level mechanisms and extending to the whole-muscle fiber scale under uniaxial loading conditions. Key structural components - including aligned myofibrils, helically oriented collagen fibers, and isotropic matrices such as the proteoglycan-rich extracellular matrix and muscle fiber membrane - are embedded in a composite framework that separates and integrates anisotropic and isotropic mechanical contributions. Based on a network decomposition strategy, myofibrils are divided into actin-myosin weak bindings and titin filaments, each modeled as a distinct macromolecular network. A network alteration framework models both subsystems as dynamic internal variables, with stiffness evolving through stretch-dependent recruitment and rate-sensitive kinetics. A non-affine deformation concept captures the asynchronous engagement of sarcomeric elements, providing a microstructural basis for delayed stiffness development. Though primarily focused on the uniaxial passive response, the model includes a minimal active term to explore how activation modulates stiffness through shared structural pathways. The formulation reproduces key passive features - including nonlinear stiffening, rate sensitivity, and relaxation - using time-dependent internal variables and microstructural recruitment. The model reproduces experimental data from human and animal muscle fibers across various loading protocols, showing strong agreement at both fiber and tissue scales. By linking molecular processes to macroscopic mechanics without relying on phenomenological viscoelastic terms, the model offers a computationally efficient and physiologically grounded tool for exploring skeletal muscle behavior under normal and altered conditions. STATEMENT OF SIGNIFICANCE: Accurately modeling skeletal muscle mechanics remains a major challenge due to the tissue structural complexity, time-dependent behavior, and scale-bridging physiological processes. This study introduces a multiscale continuum model that integrates sarcomere-level macromolecular mechanisms - namely titin unfolding/refolding, passive actin-myosin interactions, and non-affine filament engagement - into a computationally tractable tissue-scale formulation. By combining statistical mechanics-based representations of filament networks with dynamic internal variables, the model captures key experimental phenomena such as stress relaxation, strain-rate sensitivity, and nonlinear stiffening without relying on phenomenological viscoelastic laws. The approach is broadly applicable to musculoskeletal modeling and provides a biophysically interpretable framework for simulating healthy and diseased muscle, with direct relevance for tissue engineering, rehabilitation, and the study of degenerative muscle pathologies.