A continuum model for excitation-contraction of smooth muscle under finite deformations

The main focus in most of the continuum based muscle models is the mechanics of muscle contraction while other physiological processes governing muscle contraction, e.g., cell membrane excitation and activation, are ignored. These latter processes are essential to initiate contraction and to determine the amount of generated force, and by excluding them, the developed model cannot replicate the true behavior of the muscle in question. The aim of this study is to establish a thermodynamically and physiologically consistent framework which allows us to model smooth muscle contraction by including cell membrane excitability and kinetics of myosin phosphorylation, along with dynamics of smooth muscle contraction. The model accounts for these processes through a set of coupled dissipative constitutive equations derived by applying first principles. To show the performance of the derived model, it is evaluated for two different cases: a chemo-mechanical study of pig taenia coli cells where the excitation process is excluded, and an electro-chemo-mechanical study of rat myometrium. The results show that the model is able to replicate important aspects of the smooth muscle excitation-contraction process.