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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.

Rotational Activity around an Obstacle in 2D Cardiac Tissue in Presence of Cellular Heterogeneity