Passive constitutive theory of a single muscle fiber for the potential diagnosis of muscle diseases at the molecular level

Titins are mainly responsible for passive mechanical properties of a single muscle fiber, which, however, can be compromised by the change in molecular structures of titins occurring in some muscle-related diseases. Based on molecular structures of titins within a sarcomere unit, we have developed a constitutive theory for the passive elasticity of a single muscle fiber with the utilization of the virtual work principal. The number density of titins, domain composition of titins, the kinetics of folded domains within titins, the interaction between the water and molecular chains, the sarcomere length, etc., can all be considered in the theory. The predicted stress-strain curves based on the theory are in agreement with experiment. We also demonstrate that abnormal structural parameters of titins from patients with chronic obstructive pulmonary disease or muscle atrophy caused by long-term disuse can be extracted with the theory. We then suggest that this constitutive theory may potentially facilitate the molecular diagnosis of muscle diseases exhibiting abnormality in the passive elasticity.