Mechanotransduction in Ischemic Cardiac Tissue: A Mechanical Bidomain Approach under Plane Stress

Abstract

Mechanotransduction is the process by which biological tissue translates mechanical forces and signals, such as those produced by strains or membrane forces, into biological reactions including cell remodeling, growth, and differentiation. While some analyses assume strain (the derivative of either the intracellular or extracellular displacement) as the cause of mechanotransduction, this paper assumes that differences between the intracellular and extracellular displacements, known as membrane force, result in mechanical forces acting on integrin proteins, causing mechanotransduction. The mechanical bidomain model is a two-dimensional mathematical representation that describes this behavior. Previous analyses describe mechanotransduction using plane strain, which assumes zero displacement in the z-direction. This analysis uses plane stress, which assumes zero stress in the z-direction, to describe where mechanotransduction occurs in comparison to plane strain models. A sample of healthy tissue with a circular ischemic region with no active tension in the center is analyzed using numerical methods. Fixed and free boundary conditions are implemented. Under fixed conditions, the membrane force was largest in the ischemic border zone and zero everywhere else. However, the strain was found to be largest in the ischemic region. Under free conditions, the membrane force was largest on the vertical edges and in the ischemic border zone. The strain was found to be nearly zero in the ischemic region and ranged up to 10% throughout the tissue. In conclusion, this paper found that both plane strain and plane stress predict a membrane force in the ischemic border zone, but the distribution of individual displacements and strain vary according to each model. These results are significant in determining which model is most appropriate to use in predicting how mechanical forces affect cellular remodeling when analyzing thin monolayers of tissue.