Force distribution and multi-scale mechanics in smooth muscle tissues

Abstract

The mechanical role of smooth muscle tissue in many physiological processes is vital to their healthy function. In this work, we provide a deeper understanding of the underlying mechanisms that govern the smooth muscle tissue response. Specifically, we model and investigate the distribution and the transmission of passive and active forces throughout the microstructure. Broadly, smooth muscle cells contain a structural network with two types of load carrying structures: (1) contractile units made of actin and myosin filaments, which are capable of generating force, and (2) intermediate filaments. The extracellular matrix comprises elastin and collagen fibers that can sustain stress. We argue that all of the load carrying constituents in the tissue participate in the generation and the transmission of passive and active forces. We begin by modeling the response of the elements in the smooth muscle cell and defining a network of contractile units and intermediate filaments through which forces are transferred. This allows to derive an expression for the stress that develops in the cell. Next, we assume a hyperelastic behavior for the extracellular matrix and determine the stress in the tissue. With appropriate kinematic constraints and equilibrium considerations, we relate the macroscopic deformation to the stretch of the individual load carrying structures. Consequently, the stress on each element in the tissue can be computed. To validate the framework, we consider a simple microstructure of a smooth muscle tissue and fit the model parameters to experimental findings. The framework is also used to delineate experimental evidence which suggests that the suppression of intermediate filaments reduces the active and passive forces in a tissue. We show that the degradation and the reduction of the number of intermediate filaments in the cell fully explains this observation.

Keywords: Cross-bridge cycling; Intermediate filaments; Multi-scale modeling; Smooth muscles.