Part IIInternational audienceIn this work, a modified coupling Lattice Boltzmann Model (LBM) in simulation of cardiac electrophysiology is developed in order to capture the detailed activities of macro- to micro-scale transport processes. The propagation of electrical activity in the human heart is mathematically modelled by bidomain type systems. As transmembrane potential evolves, we take into account domain anisotropical properties using intracellular and extracellular conductivity, such as in a pacemaker or an electrocardiogram, in both parallel and perpendicular directions to the fibers. The bidomain system represents multi-scale, stiff and strongly nonlinear coupled reaction-diffusion models that consists of a set of ordinary differential equations coupled with a set of partial differential equations. Due to dynamic and geometry complexity, numerical simulation and implementation of bidomain type systems are extremely challenging conceptual and computational problems but are very important in many real-life and biomedical applications. This paper suggests a modified LBM scheme, reliable, efficient, stable and easy to implement in the context of such bidomain systems. The numerical results demonstrate the effectiveness and accuracy of our approach using general methods for bidomain type systems and show good agreement with analytical solutions and numerical results reported in the literature

In this work, a modied coupling Lattice Boltzmann Model (LBM) in simulation of cardiac electrophysiology is developed in order to capture the detailed activities of macro-to micro-scale transport processes. The propagation of electrical activity in the human heart through torso is mathematically modeled by bidomain type systems. As transmembrane potential evolves, we take into account domain anisotropical properties using intracellular and extracellular conductivity, such as in a pacemaker or an electrocardiogram, in both parallel and perpendicular directions to the bers. The bidomain system represents multi-scale, sti and strongly nonlinear coupled reaction-diusion models that consist of a set of ordinary dierential equations coupled with a set of partial dierential equations. Due to dynamic and geometry complexity, numerical simulation and implementation of bidomain type systems are extremely challenging conceptual and computational problems but are very important in many real-life and biomedical applications. This paper suggests a modied LBM scheme, reliable, ecient, stable and easy to implement in the context of such bidomain systems. Numerical tests to conrm eectiveness and accuracy of our approach are provided and the propagation of electrophysiological waves in the heart is analyzed.

In this work, we propose a mathematical model of the cardiac electrophysiology which take into account time delays in signal transmission, in order to capture the whole activities of macro- to micro-scale transport processes, and use this model to analyze the propagation of electrophysiological waves in the heart by using a developed coupling Lattice Boltzmann Method (LBM). The propagation of electrical activity in the heart is mathematically modeled by a modified bidomain system. As transmembrane potential evolves, the domain has anisotropical properties which are transposed into intracellular and extracellular conductivity. The new bidomain system is a multi-scale, stiff and strongly nonlinear coupled reaction-diffusion model in the shape of a set of ordinary differential equations coupled with a set of partial differential equations with multiple time delays. Due to delays, dynamic and geometry complexity, numerical simulation and implementation of this type of coupled systems are very ambitious mathematical and computational problems but are crucial in several biomedical applications. We introduce a modified LBM scheme, reliable, efficient, stable and easy to implement in the context of such bidomain systems with multiple time delays. Numerical tests to confirm effectiveness and accuracy of our approach are provided and, the influence and impact of delays to restore normal heart rhythm are analyzed.

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