Modelling cardiac mechanical properties in three dimensions

Abstract
The central problem in modelling the multi–dimensional mechanics of the heart is in identifying functional forms and parameters of the constitutive equations, which describe the material properties of the resting and active, normal and diseased myocardium. The constitutive properties of myocardium are three dimensional, anisotropic, nonlinear and time dependent. Formulating useful constitutive laws requires a combination of multi–axial tissue testing in vitro, microstructural modelling based on quantitative morphology, statistical parameter estimation, and validation with measurements from intact hearts. Recent models capture some important properties of healthy and diseased myocardium including: the nonlinear interactions between the responses to different loading patterns; the influence of the laminar myofibre sheet architecture; the effects of transverse stresses developed by the myocytes; and the relationship between collagen fibre architecture and mechanical properties in healing scar tissue after myocardial infarction.