New developments in a strongly coupled cardiac electromechanical model

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Abstract
Aim: The aim of this study is to develop a coupled three-dimensional computational model of cardiac electromechanics to investigate fibre length transients and the role of electrical heterogeneity in determining left ventricular function. Methods: A mathematical model of cellular electromechanics was embedded in a simple geometric model of the cardiac left ventricle. Electrical and mechanical boundary conditions were applied based on Purkinje fibre activation times and ventricular volumes through the heart cycle. The mono-domain reaction diffusion equations and finite deformation elasticity equations were solved simultaneously through the full pump cycle. Simulations were run to assess the importance of cellular electrical heterogeneity on myocardial mechanics. Results: Following electrical activation, mechanical contraction moves out through the wall to the circumferentially oriented mid-wall fibres, producing a progressively longitudinal and twisting deformation. This is followed by a more spherical deformation as the inclined epicardial fibres are activated. Mid-way between base and apex peak tensions and fibre shortening of 40 kPa and 5%, respectively, are generated at the endocardial surface with values of 18 kPa and 12% at the epicardial surface. Embedding an electrically homogeneous cell model for the same simulations produced equivalent values of 36.5 kPa, 4% at the endocardium and 14 kPa, 13.5% at the epicardium. Conclusion: The substantial redistribution of fibre lengths during the early pre-ejection phase of systole may play a significant role in preparing the mid-wall fibres to contract. The inclusion of transmural heterogeneity of action potential duration has a marked effect on reducing sarcomere length transmural dispersion during repolarization.