Abstract
A new, anatomically accurate, mathematical model of the right and left porcine ventricular myocardium is described based on measurements of the geometry and fibrous-sheet structure. Passive and active properties of the myocardium are calculated using an orthotropic constitutive law based on the fibrous-sheet structure and a biophysical cellular based model of cardiac contraction. Using Galerkin finite element techniques, the equations of finite deformation are solved to determine deformation and regional wall stress through the heart cycle. The mechanics model is coupled via myocardial wall stress, to a one-dimensional coronary blood flow model embedded in the myocardium. Bidomain electrical activation of the myocardium is also modeled, with ionic current based electrophysiological equations and reaction–diffusion equations based on orthotropic conductivity tensors referred to the fibrous-sheet material axes. Metabolic models are used to couple energy supply to contraction and excitation in the heart, and at the body surface, a framework for quantifying the effect of ischemic heart disease is developed.
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