Comparison of Data-Driven and Physics-Informed Neural Networks for Surrogate Modelling of the Huxley Muscle Model

Biophysical muscle models based on sliding filament and cross-bridge theory are called Huxley-type muscle models. The method of characteristics is typically used to solve Huxley’s muscle contraction equation, which describes the distribution of attached myosin heads to the actin-binding sites, called cross-bridges. Once this equation is solved, we can determine the generated force and the stiffness of the muscle fibers, which can then be used at the macro level during finite element analysis. In our paper, we present alternative approaches to finding an approximate solution of Huxley’s muscle contraction equation using neural networks. In one approach, we collect the data from simulations and train multilayer perceptrons to predict probabilities of cross-bridge formation based on the available actin site positions, time, activation, current and previous stretch. In another approach, besides using the data, we also inform the neural network with Huxley’s equation, thus improving the generalization of the neural network’s predictions.