A unified structure-based constitutive model for both tension and shear of passive myocardium

Abstract

This paper presents a hyperelastic model for replicating the passive response of ventricular myocardium and pericardium using fourth-order structural tensors. Models that can accurately predict mechanical response of cardiac samples are useful in understanding diseased tissues or postulating potential biomaterials for the replacement of damaged tissue in surgical applications. An orthotropic model is postulated here and is demonstrated to perform well in recreating experimental results in a variety of planar biaxial testing protocols and six modes of simple shear. The work outlines the fourth-order structural tensor (FOST) approach to representations of hyperelasticity for prescribing individual microstructural components (or interaction between them) that contribute to the overall elastic response of a biological tissue, through selection of specific FOSTs and constructing fourth-order material tensors possessing the constitutive properties and directional biases of that constituent. A fourth-order scalar product is then performed between this and an appropriately chosen fourth-order finite strain measure that returns a physically meaningful contribution to the strain energy density function for the overall tissue. A structure-based model for ventricular myocardium and pericardium is presented in this work using this approach. In the case of human myocardium, a consistent set of seven material constants simultaneously replicates five planar biaxial tension protocols and six modes of simple shear response.