Computational mechanics of the heart - From tissue structure to ventricular function

Finite elasticity theory combined with finite element analysis provides the framework for analysing ventricular mechanics during the filling phase of the cardiac cycle, when cardiac cells are not actively contracting. The ort hotropic properties of the passive tissue are described here by a "pole-zer o" constitutive law, whose parameters are derived in part from a model of t he underlying distributions of collagen fibres. These distributions are bas ed on our observations of the fibrous-sheet laminar architecture of myocard ial tissue. We illustrate the use of high order (cubic Hermite) basis funct ions in solving the Galerkin finite element stress equilibrium equations ba sed on this orthotropic constitutive law and for incorporating the observed regional distributions of fibre and sheet orientations. Pressure-volume re lations and 3D principal strains predicted by the model are compared with e xperimental observations. A model of active tissue properties, based on iso lated muscle experiments, is also introduced in order to predict transmural distributions of 3D principal strains at the end of the contraction phase of the cardiac cycle. We end by offering a critique of the current model of ventricular mechanics and propose new challenges for future modellers.