Contemporary Materials, XIV-1 (2023) 43 1. INTRODUCTION To analyze muscle behavior via in silico anal- ysis we model biophysical processes on multiple spatial and temporal scales. We perform multi-scale simulation in which continuum muscle mechanics is modeled using the finite element method and materi- al characteristics of muscle at the microscopic scale are defined by Huxley’s muscle contraction model [1]. During transient finite element simulation, we use Huxley’s model to calculate stress and instanta- neous stiffness, given the muscle activation, stretch, and other material parameters and properties. These finite element simulations can be quite computa- tionally intensive. The most time-consuming part of these simulations are calculations carried out at the microscale. To lower the computational require- ments of the simulations, we create a computational- ly more efficient surrogate model to replace the real Huxley muscle model. We solved the Huxley equa- tion, using physics-informed neural networks, to ac- quire the distribution of attached myosin heads to the actin-binding sites. 2. METHODS Huxley considered the dynamics of the fila- ments within muscle and the probability of establish- ing connections (cross-bridges) of myosin heads to actin filaments inside sarcomeres. The n(x,t) func- tion describes the rate of connections between myo- sin heads and actin filaments, as a function of the po- sition of the nearest available actin-binding site rela- tive to the equilibrium position of the myosin head x: (1) where f(x,a) and g(x) represent the attachment and detachment rates of cross-bridges respectively, v is Original scientific paper UDK 517.938:004.738.5 DOI 10.7251/COMEN2301043M NEURAL NETWORKS FOR SOLVING HUXLEY’S EQUATION Bogdan Milićević 1,2* , Miloš Ivanović 2,3 , Boban Stojanović 2,3 , Nenad Filipović 1,2 1 Faculty of Engineering Sciences, University of Kragujevac, Kragujevac, Serbia 2 Research and Development Center for Bioengineering, Kragujevac, Serbia 3 Faculty of Science and Mathematics, University of Kragujevac, Kragujevac, Serbia * Corresponding author: bogdan.milicevic@uni.kg.ac.rs Abstract: Biophysical muscle models, also known as Huxley-type models, are appropriate for simulating non-uniform and unsteady contractions. Large-scale simulations can be more challenging to use because this type of model can be computationally intensive. The method of characteristics is typically used to solve Huxley’s muscle equation, which describes the distribution of connected myosin heads to the actin-binding sites. Once this equation is solved, we can determine the generated force and the stiffness of the muscle fibers, which may then be employed in the macro-level simulations of finite element analysis. In our paper, we developed a physics-informed surrogate model that functions similarly to the original Huxley muscle model but uses a lot less computational resources in order to enable more effective use of the Huxley mus- cle model. Keywords: physics-informed neural networks, numerical analysis, machine learning, Huxley’s muscle model.