It is observed in cardiac patients that the steepness of action potential duration (APD) restitution curve of cardiomyocytes in different regions of the ventricle was significantly different. However, the steep APD restitution curve can either lead to the breakup of spiral wave and ventricular fibrillation in certain conditions or may not result in the breakup of spiral wave in other conditions. The relationship between the dynamic behavior of spiral wave and steep APD restitution curve is

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... not completely clear. Therefore, further research is needed. In this paper, a two-dimensional excitable medium cellular automata model is used to study the influence of the APD restitution curve with different steepness on the dynamic behavior of spiral wave. Numerical simulation results show that the steep APD restitution curve can stabilize the meandering spiral wave, causing the stable spiral wave to roam or break, and even to disappear. When the total average slope of APD restitution curve is greater than 1, it is observed that spiral wave may be still stable or meandering. When the total average slope of APD restitution curve is much smaller than 1, the breakup of spiral waves may occur. Three types of spiral wave breakup are observed. They are the Doppler instability, Eckhaus instability and APD alternation. The Doppler instability and Eckhaus instability are related to the total average slope of APD restitution curve greater than 1, and the spiral wave breakup caused by APD alternans may occur when the total average slope of APD restitution curve is much smaller than 1. When the total average slope of APD restitution curve is greater than 1, the phenomena that spiral wave disappears by meandering out of the system boundary and conduction barriers are observed. In addition, we also found that increasing cellular APD is beneficial to prevent spiral wave breaking up. The physical mechanisms underlying those phenomena are heuristically analyzed.