Controlling Spiral Wave And Spatiotemporal Chaos In Cardiac Tissues Using The Methods Of Low Pass Filtering And Regulating The Gate Of Sodium Current

Spiral wave is the most common pattern in nonlinear reaction diffusion systems. It have been observed in diverse systems, such as biologic, physical, chemical systems. So it is very important to study the dynamics of spiral wave. The dynamics of spiral waves in reaction-diffusion systems have extensively been studied by scientists in recent decades. And many research results have been obtained. Research shows that some tachycardia are associated with the presence of spiral waves in the heart, The breakup of electrical spiral wave into spatiotemporal chaos can lead to ventricular fibrillation and sudden cardiac death. Therefore, it is of great value of application to explore how to eliminate spiral waves and spatiotemporal chaos in cardiac tissues. So far, the control of spiral wave and spatiotemporal chaos has been studied by using a variety of models. Many control methods have proposed. However the most common method of clinical defibrillation is extracorporeal shock method, which success rate of defibrillation is not high. Sometimes it needs to shock for many times. And each electric shock will bring great pain to the patient and produce other side effects. Therefore it is need to explore low energy defibrillation method. In this paper, we use the Luo-Rudy phase I heart model to investigate how to control the spiral waves and spatiotemporal chaos in cardiac tissues by regulating the gate variable of sodium current of myocardial cell. We find that regulating the gate variable of current can change the behavior of the medium so that the medium has a low pass filtering effect, leading to the change of behavior of spiral wave and spatiotemporal chaos. So it can effectively control spiral wave and spatiotemporal chaos. The contents of the paper are arranged as follows:The first chapter is the overview. We briefly introduces the basic knowledge of pattern dynamics and the cardiac electrophysiology, some heart model, the generation of spiral wave and spatiotemporal chaos, some control methods of spiral wave and spatiotemporal chaos, and so on.The second chapter is the introduction of terminating spiral wave and spatiotemporal chaos in cardiac tissue using the low-pass filtering scheme. To cause the sodium ion activation gate of cardiomyocyte delay to open, the ability of excitation delay should be given to the medium. The time of excitation delay of the medium increases as the control voltage and frequency of stimulation increase. When the control voltage exceeds a threshold value, the medium with excitation delay has the property of low-pass filtering:low-frequency waves can continuously pass through the medium, whereas high-frequency wave does not pass consecutively. In this paper, the effect of excitation delay of the medium on spiral wave and spatiotemporal chaos is investigated by using Luo-Rudy phase I model. The numerical simulation results show that when the control voltage exceeds the threshold value, the excitation delay of the medium can effectively eliminate spiral wave and spatiotemporal chaos. When the control voltage gradually increases from a small wave, at a small maximal conductance of calcium channel, the excitation delay could reduce the excitability of medium, making the amplitude of spiral wave meander increase until conduction failure results in the disappearance of spiral wave. Under large maximal conductance of calcium channel, the excitation delay can reduce the unstability of spiral wave so that spatiotemporal chaos evolves into meandering spiral wave when the control voltage is large enough. The phenomenon that the spiral wave with a large meandering motion of its tip moves out of the system is observed when the control voltage is properly chosen. The further increase of the control voltage leads to the disappearance of spatiotemporal chaos.The third chapter is the introduction of regulating gate variable of sodium current to control spiral wave and spatiotemporal chaos in cardiac tissues. To control the rate at which sodium current increase and disappear, we let the relaxation time constant of the sodium ion activation gate increases p times while letting its slow inactivation gate is not closed. Numerical simulation results show that a gradual increasing of p will cause the sodium ion activation gate to reach maximum more slowly, and its amplitude is gradually reduced, so that the amplitude and duration of the action potential of cardiomyocyte are gradually reduced. When the control parameter p is large enough, the spiral wave and spatiotemporal chaos can not propagate in the medium, but the planar wave can propagate in the medium. The reason is that the excitability of medium and wave speed significantly decreases..Therefore, the spiral waves and spatiotemporal chaos can be effectively eliminated when the control time is properly selected and the control parameter p is large enough. Spiral wave and spatiotemporal chaos disappear mainly through conduction obstacle. Other ways of disappearing are also observed. For example, spiral wave disappears through the transition from spiral wave to target wave or tip retraction. Spatiotemporal chaos disappears after spatiotemporal chaos evolves into meandering spiral wave. When the parameters are chosen properly, it is also observed that spiral wave evolves into self-sustained target wave. The corresponding target wave source is the pair of spiral waves with opposite rotation directions.The fourth chapter is the summary of our results and research outlook.