A chemo-mechanical model for the single myofibril in striated muscle contraction

Based on the framework of sliding-filament theory and on the cross-bridges dynamics, a mathematical model for the simulation of the force response and length change of individual myofibril is presented. The myofibril is modeled as a group of segments placed in series, each segment represents a half-sarcomere with active and elastic properties. A multiple-state cross-bridge formalism relates the half Sarcomere force to the chemical kinetics of ATP hydrolysis. The corresponding system of nonlinear nonlocal partial differential equations of the model is analyzed. A numerical approach is introduced and some numerical tests are performed. The proposed in-silico model enables the study of biologically relevant process in the muscle contraction process, also in the case of muscular diseases, with reasonable computational effort.