An inverse problem approach to identify the internal force of a mechanosensation process in a cardiac myocyte

Mechanosensation and mechanotransduction are fundamental processes in understanding the link between physical stimuli and biological responses which currently still remain not well understood. The precise molecular mechanism involved in stress and strain detection in cells is unclear. Sarcomeres are the contractile machines of a cardiac myocyte and two main sarcomeric components that are directly involved in the sensation and transmission of mechanical stimuli are titin and filaments (thin and thick). Titin is known as the largest protein in biology with a mass of up to 4.2 MDa. Its flexible region (I-band region) may function as a length sensor (ε=l/l0) while its Z-disc domain may be involved in the sensation of tension and stress (σ=F/A). Filaments act as contractile machineries by converting biochemical signals into mechanical work which in response cells either shorten or relax. Based on these considerations and a qualitative understanding of the maladaptation contribution to the development of heart failure, an inverse problem approach is taken to evaluate the contractile force in a mathematical model that describes mechanosensation in normal heart cells. Different functional forms to describe the contractile force are presented and for each of them we study the computational efficiency and accuracy of two numerical techniques.