Waves of electrical excitation rotating around an obstacle is one of the important mechanisms of dangerous cardiac arrhythmias occurring in the heart damaged by post-infarction scar. Such a scar also has a border zone around it, which has electrophysiological properties different from the rest of normal myocardial tissue. Spatial patterns of wave rotation in the presence of such tissue heterogeneity are poorly studied. In this paper we perform a comprehensive numerical study of various regimes of rotation of a wave in a plane layer of the ventricular tissue around an obstacle surrounded by a gray zone. We use a TP06 cellular ionic model which reproduces the electrophysiological properties cardiomyocytes in the left ventricle of human heart. We vary the extent of obstacle and gray zone and study the pattern of wave rotation and its period. We observed different regimes of wave rotation that can be subdivided into several classes: (1) functional rotation and (2) scar rotation regimes, which were identified in the previous studies, and new (3) gray zone rotation regime: where the wave instead of rotation around the obstacle, rotates around the gray zone (an area of tissue heterogeneity) itself. For each class, the period of rotation is determined by different factors, which we discuss and quantify. We also found that due to regional pathological remodeling of myocardial tissue, we can obtain additional regimes associated with dynamical instabilities of two types which may affect or not affect the period of rotation.

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Waves of electrical excitation rotating around an obstacle is one of the important mechanisms of dangerous cardiac arrhythmias occurring in the heart damaged by a post-infarction scar. Such a scar is also surrounded by the region of heterogeneity called a gray zone. In this paper, we perform the first comprehensive numerical study of various regimes of wave rotation around an obstacle surrounded by a gray zone. We use the TP06 cellular ionic model for human cardiomyocytes and study how the period and the pattern of wave rotation depend on the radius of a circular obstacle and the width of a circular gray zone. Our main conclusions are the following. The wave rotation regimes can be subdivided into three main classes: (1) functional rotation, (2) scar rotation and the newly found (3) gray zone rotation regimes. In the scar rotation regime, the wave rotates around the obstacle, while in the gray zone regime, the wave rotates around the gray zone. As a result, the period of rotation is determined by the perimeter of the scar, or gray zone perimeter correspondingly. The transition from the scar to the gray rotation regimes can be determined from the minimal period principle, formulated in this paper. We have also observed additional regimes associated with two types of dynamical instabilities which may affect or not affect the period of rotation. The results of this study can help to identify the factors determining the period of arrhythmias in post-infarction patients.

Rotating nonlinear waves of excitation in the heart cause dangerous cardiac arrhythmias. Frequently, ventricular arrhythmias occur as a result of myocardial infarction and are associated with rotation of the waves around a post-infarction scar. In this paper, we perform a detailed in silico analysis of scroll waves in an anatomical model of the human ventricles with a generic model of the infarction scar surrounded by the gray zone with modified properties of the myocardial tissue. Our model includes a realistic description of the heart shape, anisotropy of cardiac tissue and a detailed description of the electrical activity in human ventricular cells by a TP06 ionic model. We vary the size of the scar and gray zone and analyze the dependence of the rotation period on the injury dimensions. Two main regimes of wave scrolling are observed: the scar rotation, when the wave rotates around the scar, and the gray zone rotation, when the wave rotates around the boundary of the gray zone and normal tissue. The transition from the gray zone to the scar rotation occurs for the width of gray zone above 10–20 mm, depending on the perimeter of the scar. We compare our results with simulations in 2D and show that 3D anisotropy reduces the period of rotation. We finally use a model with a realistic shape of the scar and show that our approach predicts correctly the period of the arrhythmia.