Structure of heart download2/1/2024 ![]() Omens, Three-dimensional residual strain in midanterior canine left ventricle. ![]() McCulloch, A three-dimensional finite element method for large elastic deformations of ventricular myocardium: Part II-Prolate spherical coordinates. McCulloch, A three-dimensional finite element method for large elastic deformations of ventricular myocardium: Part I-Cylindrical and spherical polar coordinates. Fox, An Introduction to the Theory of Elasticity. We end by offering a critique of the current model of ventricular mechanics and propose new challenges for future modellers. A model of active tissue properties, based on isolated 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. Pressure–volume relations and 3D principal strains predicted by the model are compared with experimental observations. We illustrate the use of high order (cubic Hermite) basis functions in solving the Galerkin finite element stress equilibrium equations based on this orthotropic constitutive law and for incorporating the observed regional distributions of fibre and sheet orientations. These distributions are based on our observations of the fibrous-sheet laminar architecture of myocardial tissue. The orthotropic properties of the passive tissue are described here by a “pole–zero” constitutive law, whose parameters are derived in part from a model of the underlying distributions of collagen fibres. 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.
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