Study On Dynamics Behavior Of Spiral Waves In Excitable Media With Cellular Automata Model

Cardiac tissue is a kind of typical excitable media system, and spiral wave is a common nonlinear speckle pattern in excitable media. When the target wave of myocardial electric signal where in cardiac tissue system turn into spiral wave, it may lead to arrhythmia, even cause heart fibrillation and sudden death when spiral wave breake into the spiral wave turbulence. So study on the dynamics of spiral wave has become the hotspot of cardiology. Numerical simulation method is an important auxiliary means to study the spiral wave, and the cellular automaton model is a kind of numerical simulation method which is more mature and efficient. In this paper, we improve the Greenber-Hastings cellular automaton model (G-H model) of the excitable media, and consider the position perturbation, cell gap junction and myocardial cell extraordinary excitation and other factors in the model, men explore the effects of these factors on dynamics of spiral wave. The specific contents of this paper are as follows:Frist of all, position perturbation is introduced to simulate the change of the interaction distance between the excited elements in the excitable media. The results of computer simulation show that the stable spiral wave, generated in a regular grid, is related to the amplitude of position disturbance. Different amplitude of position perturbation leads to stable spiral wave generating two changes:A new stable spiral wave is formed after the rolling line meandering; spiral wave disappeared from the system after meandering. The varying range of cell position perturbation leads to an increase and decrease of the excitation of the system.In the second part, the effect of abnormal gap junction on the stability of spiral wave in the healing area of myocardial infarction was studied by using the improved Greenberg-Hastings cellular automaton model. The connection probability of horizontal, vertical and diagonal directions is introduced in the improved model, which can reflect the distribution of gap junction between cardiac muscle cells. Combined with the existing experimental infarct healing area of gap junction probability data, numerical simulation results show that:(1) gap junction which in infarct healing area as long as the degradation degree is not lower than 53% of normal value, the system also has the ability to maintain the spiral wave; (2) when the abnormal gap connection which in infarct healing area is about 47%～53% of normal value, spiral wave breaking into turbulence, that myocardial infarction healing area is easy to cause new infarction, data of excitation ratio show that the system still has excitability; (3) when the abnormal gap junction which in infarct healing area is lower 47% of normal value, the spiral waves disappear quickly. Data of excitation ratio show that the system lost the ability to inspire completely. It is showed that the infarct healing area in this case is a block, and the signal can not be transmitted. Further numerical simulation results showed that the effect of abnormal gap junction on the dynamic behavior of spiral waves in the cases of ventricular tachycardia and serious arrhythmia was consistent with the situation of the infarct healing zone.In the third part, the occurrence of extraordinary excitation is considered in the model, and the influence of extraordinary excitation on the dynamic behavior of spiral wave is studied. Numerical simulation results show that:(1)When the system is highly excited, the extraordinary excitation of the physiological conditions will not have a significant impact on the spiral wave, include the shape of the spiral wave, and the wavelength, which means that when the system is highly excited, the physiological extraordinary excitation has little effect on the rapid arrhythmia. (2)When the system has a low excitation, the extraordinary excitation of the physiological conditions makes the tip trajectory of the stable spiral wave, the movement cycle of tip, and the wavelength increased. It means that the physiological extraordinary excitation can alleviate the rapid arrhythmia that induced by spiral wave when the system states in low excitation. (3) When the system has a low excitation, pathological extraordinary excitation can not only lead to the formation of new spiral waves, may also lead to spiral turbulence. This conclusion is consistent with the conclusion that the anti arrhythmia drugs in clinical medicine have the effect of promoting the side effects of arrhythmia.