Simulation of a computational winding filament model with an exponential spring to represent titin

The goal of developing high fidelity simulation of muscle force is of considerable interest for the biomedical community. Traditionally Hill models have been incorporated. However, feasible scope of the Hill model is inherently limited, especially in light of the growing relevance of muscle history dependence. History dependence is considered to be significant for motor control and stability. Attempts have been made to augment the Hill model to emulate history dependence. The titin winding filament model best elucidates history dependence of muscle force including force enhancement. The recent version of the titin winding filament model accounts for the functionality of titin through a pulley linked with the contractile element and a linear spring to represent the elastic properties of titin. A new and more realistic amendment to the winding filament model is incorporation of an exponential spring to characterize the elastic properties of titin. A sensitivity study as a function of the titin exponential spring constant is presented. Overall the amalgamation of the titin exponential spring to the winding filament model improves the respective force enhancement characteristics with a relatively more optimal exponential spring constant that provides a maximal averaged coefficient of determination.