Lattice Boltzmann method based feedback control approach for pinned spiral waves

Abstract

Spiral waves are common in nature and have received a lot of attention. Spiral wave is the source of ventricular tachycardia and fibrillation, and pinned spiral wave is less likely to be eliminated than free spiral wave. Therefore, it is important to find an effective method to control the pinned spiral wave. In this work, we investigate the feedback control approach to eliminating pinned spiral wave based on the lattice Boltzmann method, by using the FitzHugh-Nagumo model as an object. The numerical results show that the feedback control method has a good control effect on the pinned spiral wave no matter whether it is pinned on a circular or rectangular obstacle. In addition, the excitability coefficient, amplitude of feedback control, recording feedback signal time and obstacle size are systematically investigated by numerical simulation. The study shows that there are three cases of pinned spiral wave cancellation. Firstly, the amplitude of feedback control and excitability coefficient are related to the time required to eliminate the pinned spiral wave, and the larger the amplitude of feedback control signal or the smaller the excitability coefficient, the faster the cancellation of the pinned spiral waveis. Secondly, the size of the obstacle and the excitability coefficient affect the time interval between the time of recording the feedback signal and the time of adding the feedback control that can successfully control the pinned spiral wave. Finally, the recorded feedback signal time affects the minimum amplitude of feedback control required to successfully eliminate the pinned spiral wave, while the added feedback control time is constant. According to the discussion in this paper, it can be seen that the feedback control method has a good control effect on the pinned spiral wave.