Numerical simulation of the propagation of electrical excitation in the heart wall taking its fibrous laminar structure into account

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The propagation of an excitation wave in an inhomogeneous anisotropic finite-element model of cardiac muscle was studied. In this model, the inhomogeneity consists in the rotation of anisotropy axes across the wall thickness and results from the fibrous laminar structure of the cardiac-muscle tissue. The conductivity of the cardiac muscle was described using a monodomain model and the Aliev–Panfilov equations were used to relate the transmembrane current and transmembrane potential. Numerical simulation was performed by applying the splitting algorithm, in which the partial differential solution to a nonlinear boundaryvalue problem is reduced to a sequence of simple ordinary differential equations and linear partial differential equations. The simulation region is a rectangular block of cardiac tissue with a minimal size that matches the thickness of the heart wall. The anisotropy of the cardiac tissue, which is determined by its fibrous laminar structure, has a considerable effect on the shape of the electrical excitation wave front. Two types of distribution of the fiber orientation angle are discussed. The first type corresponds to the canine left ventricle. The endocardium and epicardium fibers are generally oriented in the meridional direction. The angle of the fiber orientation gradually changes across the wall thickness, making a half turn. The circular layer, in which the fibers are circumferentially oriented, lies deep in the heart wall. The computation results show that the wave shape for this case strongly depends on the site of initial excitation. If the initial excitation is in the endocardium and epicardium, the wave front propagates faster in the endocardium and epicardium, respectively. An intramural initial excitation induces simultaneous wave-front propagation in the endocardium and epicardium with a wave-front lag within the wall. The second type corresponds to the porcine right ventricle, where endocardium and epicardium fibers are circumferentially oriented but the angle drastically changes in the subepicardium. In this case, the wave front weakly depends on the site of the initial excitation, while the wave front propagates faster within the wall. However, the wave-front formation rates are different; they are highest for intramural initial excitation and the lowest for the excitation on the endocardium surface.