| Rotating spiral wave is a wave pattern formed by the self-organization of nonlinear space-time system far from the thermodynamic equilibrium state.It widely exists in physical,chemical and biological systems.Experiments show that spiral waves in the cerebral cortex are usually associated with certain neurological diseases.For example,spiral waves can be observed in the cerebral cortex during seizures,which can organize and modulate cortical population activity on the mesoscopic scale,thereby affecting the function of the brain.In the cardiac system,the normal rhythm of the heart beat is controlled by the continuous generation of electrical signals in the sinoatrial node that propagate in the form of target waves.Spiral waves may form when the target wave encounters necrotic myocardial tissue or scars during its propagation.Once the spiral wave is unstable,it may break into spatiotemporal chaos,and the spiral wave and the subsequent defective turbulent can cause tachycardia or even ventricular fibrillation,which is life-threatening.Therefore,studying the dynamic behavior of spiral waves in excitable systems such as the heart is of great significance for people to understand the mechanism of medical diseases such as epilepsy and arrhythmia,and to propose effective methods to control spiral waves.Studies have found that both carpal tunnel syndrome and long-term alcoholism can lead to the increase in the relative refractory period of neuronal action potentials,but the effects of relative refractory on the dynamic behavior of spiral waves is less study at present.It is observed in cardiac patients that steep action potential duration(APD)restitution curve can either lead the spiral wave to break up and set up the ventricular fibrillation in certain conditions or result in no breakup of spiral wave in other conditions.However,the relationship between the evolution behavior of spiral wave and steep APD restitution curve is still not completely clear.In order to master the dynamic behavior of spiral wave in excitable medium under complex condition,this paper uses two-dimensional cellular automata model to study the following two problems: The first is the effects of relative refractory state on the dynamic behavior of spiral wave.The second is influence of the dynamic change of cell APD according to different APD restitution curves on evolution behavior of spiral wave.The content of this paper is arranged as follows:The first chapter is the introduction,which mainly introduces the background and significance of investigation,the spiral wave and its control in excitable medium,the cellular automata model and its application,and also introduces the research results of action potential duration restitution curve of cardiomyocytes.The second chapter is our first research work.In this chapter,effect of relative refractory of excited medium on dynamical behavior of spiral waves is investigated in a cellular automata model considering the relative refractoriness.Numerical simulation results show that there is a critical interval in the excitation threshold.Spiral wave period in the critical interval increase suddenly and there is a maximum period.Under the appropriate system size and number of non-resting states,the spiral wave period is not affected by the refractoriness,but only depends on the excitation threshold of the system.When the system size and the number of non-resting states are large,the spiral wave period is unstable in the critical interval of the excitation threshold.Relative refractory state causes the spiral wave tip trajectory to evolve from a single small-scale linear periodic motion without considering the relative refractory state to Z-type meandering,small-scale irregular meandering,petal meandering,jagged meandering,windmill meandering and other complex spiral wave tip motions.Stable spiral wave,meandering spiral wave,and disappearing spiral wave are observed.Mechanisms of these phenomena are briefly analyzed.The third chapter is our second research work.In this chapter,a two-dimensional excitable medium cellular automata model is used to study the influence of the APD restitution curve with different steepness on the evolution behavior of spiral wave.Numerical simulation results show that 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 breakups 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.Two types of disappearance of spiral waves is observed.One type is that spiral wave meanders wildly out of the system boundary and disappeared,and the other type is that spiral wave disappears directly because of conduction obstacles.In addition,we also find that increasing cellular APD is beneficial to preventing spiral wave from breaking up.These results help us to understand the physical mechanism of cardiac arrhythmia and propose effective methods to control the spiral wave.The fourth chapter is a summary and outlook. |
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