Activation Models for the Numerical Simulation of Cardiac Electromechanical Interactions
This contribution addresses the mathematical modeling and numerical approximation of the excitation-contraction coupling mechanisms in the heart. The main physiological issues are preliminarily sketched along with an extended overview to the relevant literature. Then we focus on the existing models for the electromechanical interaction, paying special attention to the active strain formulation that provides the link between mechanical response and electrophysiology. We further provide some critical insight on the expected mathematical properties of the model, the ability to provide physiological results, the accuracy and computational cost of the numerical simulations. This chapter ends with a numerical experiment studying the electromechanical coupling on the anisotropic myocardial tissue.
KeywordsActive Strain Ordinary Differential Equation Model Multiplicative Decomposition Force Balance Equation Parallel Finite Element
The support by the European Research Council through the grant ‘Mathcard, Mathematical Modelling and Simulation of the Cardiovascular System’, ERC-2008-AdG 227058 is gratefully acknowledged.
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