Indentation of Anisotropic Tissue Using a Three-Dimensional Mechanical Bidomain Model

Abstract

Computation-based mathematical models of tissue indentation are capable of predicting the distribution of forces and mechanical properties of soft tissues. This paper presents a three-dimensional mathematical model of anisotropic tissue indentation developed using the mechanical bidomain model. The mechanical bidomain model hypothesizes that the relative displacement between intra- and extracellular spaces triggers a force on the mechanosensitive proteins in the membrane: integrins. Some soft tissues, such as cardiac muscle, are anisotropic, a property which arises from the fibrous structure of the tissue. The degree of anisotropy in intra- and extracellular spaces can be different. Tissue indentation for different anisotropy ratios that indicate isotropy, equal anisotropy and unequal anisotropy, were tested using the model. Results of the tissue indentation analysis compared the spatial distribution of the magnitude of bidomain displacement for different anisotropy conditions between monodomain and bidomain models. The proposed mathematical model predicted unexpected spatial patterns of cardiac mechanotransduction for unequal anisotropy ratios of mechanical modulus.