Numerical Simulation of Propagation of Electric Excitation in the Heart Wall Taking into Account Its Fibrous-Laminar Structure
The propagation of excitation wave in the inhomogeneous anisotropic finite element model of cardiac muscle is investigated. In this model, the inhomogeneity stands for the rotation of anisotropy axes through the wall thickness and results from a fibrous-laminar structure of the cardiac muscle tissue. Conductivity of the cardiac muscle is described using a monodomain model and the Aliev-Panfilov equations are used as the relationships between the transmembrane current and transmembrane potential. Numerical simulation is performed by applying the splitting algorithm, in which the partial differential solution to the nonlinear boundary value problem is reduced to a sequence of simple ordinary differential equations and linear partial differential equations. The simulation is carried out for a rectangular block of the cardiac tissue, the minimal size of which is considered to be the thickness of the heart wall. Two types of distribution of the fiber orientation angle are discussed. The first case corresponds to the left ventricle of a dog. The endocardium and epicardium fibers are generally oriented in the meridional direction. The angle of fiber orientation varies smoothly through the wall thickness making a half-turn. A circular layer, in which the fibers are oriented in the circumferential direction locates deep in the cardiac wall. The results of calculations show that for this case the wave form strongly depends on a place of initial excitation. For the endocardial and epicardial initial excitation one can see the earlier wave front propagation in the endocardium and epicardium, respectively. At the intramural initial excitation the simultaneous wave front propagation in the endocardium and epicardium occurs, but there is a wave front lag in the middle of the wall. The second case refers to the right ventricle of a swine, in which the endocardium and epicardium fibers are typically oriented in the circumferential direction, whereas the subepicardium fibers undergo an abrupt change in the angle of orientation. For this case the dependence of the wave front on the location of initial excitation is weak. One can see the earlier wave front propagation in the middle of the wall. However, the wave front formation rate is different: with highest velocity for intramural initial excitation and with lowest one during excitation on the endocardial surface.