Multi-scale striated muscle contraction model linking sarcomere length-dependent cross-bridge kinetics to macroscopic deformation

Abstract

© 2019 The investigation of healthy and diseased muscle behavior via in silico analysis requires the modeling of biophysical processes on multiple spatial and temporal scales. Owing to the complexity of the phenomena in question, simultaneous simulations of all the processes across different scales are extremely computationally expensive. Therefore, many multi-scale models utilize simplified phenomenological models at the micro level. However, such models may not be able to predict transient contractile behavior accurately when the deformation is unsteady or non-uniform. To overcome these deficiencies of phenomenological models, we propose a novel multi-scale muscle model in which continuum muscle mechanics are modeled utilizing the finite element method, and the material characteristics of muscle tissues at the microscopic scale are defined by Huxley's model of muscle contraction. Owing to the specific application of the sliding-filament theory coupled with the kinetic formulation of Gordon's length-tension relationship, the proposed model can provide more precise simulations of muscle behavior under both isotonic and transient conditions. The proposed model is verified using both benchmark data and real-world examples, and the results are compared to corresponding predictions obtained using the FE-Hill model. Specific implementations of biophysical components at the muscle fiber scale are validated by comparing them to predictions obtained using a spatially explicit molecular model implemented on the MUSICO platform. To enable the execution of two-scale simulations in a reasonable timeframe, we utilize a custom-tailored parallelization platform called Mexie. The ability of the proposed model to describe tissue-scale motor system behavior and the efficiency of its parallel execution are demonstrated through simulations of tongue movement during the propulsive phase of human swallowing. In these simulations the tissue's complex muscular structure is represented by a 2D finite element mesh. The proposed model provides tools for the scientific investigation of musculoskeletal disorders and facilitates the prospective development of clinical applications for characterizing neuromuscular disorders and monitoring disease progression during therapy.