Enhancing rheological muscle models with stochastic processes

Abstract

Purpose Biological musculoskeletal systems operate under variable conditions. Muscle stiffness, activation signals, and loads change during each movement. The presence of noise and different harmonic components in force production significantly influences the behaviour of the muscular system. Therefore, it is essential to consider these factors in numerical simulations. Methods This study aims to develop a rheological mathematical model that accurately represents the behaviour of the actual muscular system, taking into account the phenomena described by the stochastic model in the form of stationary processes. Stochastic disturbances were applied to simulate variable conditions, in which musculo-skeletal system operates. Numerical simulations were conducted for two dynamic tasks, where we calculated the internal force generated by the system (task 1), and its displacement (task 2). These simulations were performed using two different datasets sourced from the literature. In the next step, simulation results were compared with our own experiment. Results The considered mathematical model was successfully tuned and compared with both the literature data and our own experimental results. During the analysis of muscle model behavior, depending on the data source for model tuning, we observed distinct frequencies characterized by a sine-type pattern and a higher frequency marked by stochastic perturbations. Conclusions The proposed model can be customized to simulate systems of varying sizes, levels of maximum voluntary contraction, and the effects of perturbations, closely resembling real-world data. The presented approach can be applied to simulate the behaviour of the musculoskeletal system as well as of individual muscles.