Nonlinear Incompressible Finite Element for Simulating Loading of Cardiac Tissue—Part II: Three Dimensional Formulation for Thick Ventricular Wall Segments

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Abstract
A three dimensional incompressible and geometrically as well as materially nonlinear finite element is formulated for future implementation in models of cardiac mechanics. The stress-strain relations in the finite element are derived from a recently proposed constitutive law which is based on the histological composition of the myocardium. The finite element is formulated for large deformations and considers incompressibility by introducing the hydrostatic pressure as an additional variable. The results of passive loading cases simulated by this element allow to analyze the mechanical properties of ventricular wall segments, the main of which are that the circumferential direction is stiffer than the longitudinal one, that its shear stiffness is considerably lower than its tensile and compressive stiffness, and that, due to its mechanically prominent role, the collagenous matrix may affect the myocardial perfusion.