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Measurements of the geometry and fibrous-sheet structure of the left and right ventricles of the pig heart are fitted with a finite element model. Mechanical changes during the heart cycle are computed by solving the equations of motion under specified ventricular boundary conditions and using experimentally defined constitutive laws for the active and passive material properties of myocardial tissue. The resulting patterns of deformation, such as axial torsion and changes in wall thickness and base-apex length, are consistent with experimental observations. The model can therefore be used to predict sarcomere length changes and other strain patterns throughout the myocardium and throughout the cardiac cycle. Here we present sarcomere length changes at a limited number of material points within the wall. Sarcomere length typically varies by 10% above and below the unloaded length; although under the boundary conditions imposed in the current model the midwall circumferentially oriented sarcomere lengths increased by up to 20% at end diastole. We provide web-access details for a downloadable software program designed to provide more extensive information on mechanical deformation, such as the principal strains and muscle fibre cross-sectional area changes during the cardiac cycle.

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The system of equations, material constitutive laws, and boundary conditions required to construct an anatomically and biophysically based model of ventricular mechanics is reviewed. The models use high-order field descriptions to represent the geometry and embedded microstructural information relevant to whole organ function. Constitutive laws are presented which characterize the nonlinear passive elasticity of cardiac tissue and model the active development of tension produced by myocyte contraction. Finally, the integration of metabolic energetics with organ-scale mechanical simulations is discussed and future research directions are proposed.

Calculation of mechanical stresses and strains in the left ventricular (LV) myocardium by the finite element (FE) method relies on adequate knowledge of the material properties of myocardial tissue. In this paper we present a model-based estimation procedure to characterize the stress-strain relationship in passive LV myocardium. A 3D FE model of the LV myocardium was used, which included morphological fiber and sheet structure and a nonlinear orthotropic constitutive law with different stiffness in the fiber, sheet and sheet-normal directions. The estimation method was based on measured wall strains. We analyzed the method's ability to estimate the material parameters by generating a set of synthetic strain data by simulating the LV inflation phase with known material parameters. In this way we were able to verify the correctness of the solution and to analyze the effects of measurement and model error on the solution accuracy and stability. A sensitivity analysis was performed to investigate the observability of the material parameters and to determine which parameters to estimate. The results showed a high degree of coupling between the parameters governing the stiffness in each direction. Thus, only one parameter in each of the three directions was estimated. For the tested magnitudes of added noise and introduced model errors, the resulting estimated stress-strain characteristics in the fiber and sheet directions converged with good accuracy to the known relationship. The sheet-normal stress-strain relationship had a higher degree of uncertainty as more noise was added and model error was introduced