Study On The Effects Of Potassium Diffusive Coupling And Delayed Recovery Of Potassium On The Dynamics Of Spiral Wave

Spiral waves have been observed in many natural systems.11is found that spiral wave obsevered in the cardiac electric activity is generally connected with tachycardia, and the breakup of spiral wave will lead to ventricular fibrillation, threatening life. So for a long time, many scholars study the control and dynamics of spiral waves and spatiotemporal chaos in different reaction diffusion systems,and propose many control methods, such as global control, local control,gr adient field control,band so on. The clinical defibrillation method generally is the electrical defibrillation shocks with high energy, which can bring a lot of pain to patients with ventricular fibrillation when the high-energy current contacts with the human body, and may cause harm to the myocardial tissue at the same time. Therefore, we need to look for some low energy defibrillation methods to replace the high energy control method of spiral waves and spatiotemporal chaos in the heart.H ow to terminate ventricular fibrillation by using the characteristics of spiral wave,spatiotemporal chaos and the dynamics of the heart needs to delve into the dynamics of spiral wave in cardiac tissues.In theis article,we studied the effect on the dynamic changes of the potassium ion concentration on the dynamics of spiral wave and spatiotemporal chaos by using Luo-Rudy phase1cardiac model. The investigation results have the certain enlightenment for the design of low-power defibrillator. In this paper, the contents are arranged as following:The first chapter is the overview. We fistly introduce some basic knowledge of the nonlinear and pattern dynamics,and then introduce the process of cardiac electrophysiology and some cardiac models. Finally we introduce some existing defibrillation methods and the control method of the spiral wave and spatiotemporal chaos proposed by simulation.In the second chapter, we apply the Luo-Rudy phase I cardiac model to study the effect of potassium diffusive coupling on spiral wave is investigated. The numerical results show that when the strength of potassium diffusive coupling is relatively strong, the potassium diffusive coupling makes extracellular potassium ion concentration rise first and then causes it to regularly oscillate, leading to the irregular meandering of spiral wave. It is observed that the width of spiral arm and the frequency of spiral wave decrease with the strength of potassium diffusive coupling increases. Thus, when the strength of the potassium diffusive coupling is strong enough, the potassium diffusive coupling can eliminate spiral wave and spatiotemporal chaos.In the third chapter, we study the influence of the delayed restoration of extracellular potassium ion concentration on spiral wave based on the work of the second chapter. The numerical simulation results show that under the state of spiral wave, the delayed restoration of the extracellular potassium ion concentration leads to the periodic oscillation of extracellular potassium concentration, and the period and amplitude of oscillation increases with the increase of delayed recovery time, resulting in the emergence of arious phenomena, such as the breathing spiral wave, the coexistence of multiple spiral waves, the meandering of spiral waves in the manner of Levy flight, spiral wave meandering or drifting out of the boundary of the medium and spiral wave disappearing at the system. Some phenomena are observed in the related experiment.The results in the second and third chapters are discussed in the fourth chapter, and the idea of further research is given.