From single muscle fiber to whole muscle mechanics: a finite element model of a muscle bundle with fast and slow fibers.

Muscles exhibit highly complex, multi-scale architecture with thousands of muscle fibers, each with different properties, interacting with each other and surrounding connective structures. Consequently, the results of single-fiber experiments are scarcely linked to the macroscopic or whole muscle behavior. This is especially true for human muscles where it would be important to understand of how skeletal muscles disorders affect patients' life. In this work, we developed a mathematical model to study how fast and slow muscle fibers, well characterized in single-fiber experiments, work and generate together force and displacement in muscle bundles. We characterized the parameters of a Hill-type model, using experimental data on fast and slow single human muscle fibers, and comparing experimental data with numerical simulations obtained from finite element (FE) models of single fibers. Then, we developed a FE model of a bundle of 19 fibers, based on an immunohistochemically stained cross section of human diaphragm and including the corresponding properties of each slow or fast fiber. Simulations of isotonic contractions of the bundle model allowed the generation of its apparent force-velocity relationship. Although close to the average of the force-velocity curves of fast and slow fibers, the bundle curve deviates substantially toward the fast fibers at low loads. We believe that the present model and the characterization of the force-velocity curve of a fiber bundle represents the starting point to link the single-fiber properties to those of whole muscle with FE application in phenomenological models of human muscles.