Study On The Breakup And Spontaneous Generation Of Spiral Wave In Myocardial Tissue With Cellular Automaton

Spiral waves exist widely in nature,therefore,we can observe the spiral waves in various biological systems,physical systems,and chemical systems,such as the self-organization of gummy fungi,the Rayleigh-Bener convection in the fluid,the chemical waves in the reaction diffusion system,the waves of calcium ion in oocyte,and the electrical signal in cardiac.Physiological experiments show that a type of arrhythmia or tachycardia may be caused by the spiral wave of myocardial electrical signal,and the fibrillation which will result in the sudden death is closely related to the breakup of the spiral waves in myocardial tissue.Early afterdepolarization(EAD)plays an important role in the process from ventricular tachycardia to ventricular fibrillation,and the study of how the EAD leads to spiral wave breakup contributes to grasp the mechanism of fatal arrhythmia.On the other hand,it is still unclear how the spontaneous spiral waves in the heart are produced,and whether the coupling of fibroblasts and cardiomyocytes can cause the spontaneous spiral waves and target waves in the heart tissue are still uncertain.The investigating for above topics will give insights for the treatment of heart disease and the controlling of spiral waves and ectopic beats.In this paper,a two-dimensional Greenberg-Hastings(GH)cellular automaton model is used to study the manners of spiral wave breakup induced by EADs and the mechanisms of the generation of spontaneous spiral wave induced by coupling of fibroblasts and cardiomyocytes in myocardial tissue.The main content of this paper is as follows:The first chapter is the summary part,which briefly introduces common models of excitable media,nonlinear waves in excitable media,cardiac structures and its electrophysiological properties,etc.In the second chapter,we explore the manners of spiral wave breakup induced by EADs.The normal cells and aging cells are introduced into the GH cellular automaton model,in which the EAD only occurs in aging cells and can excite the resting cells.In the case of uniform distribution of normal cell and aging cell,the effect of the EAD on the evolution of spiral wave is studied.The manner of spiral wave breakup induced by EADs is mainly discussed.The results of numerical simulation show that: The EAD has no influence on the behavior of spiral wave in a few cases.The ratio of the number of unaffected spiral waves to the number of all tests is about 26.4%.In other cases,there are various effects on spiral waves,including roaming,drifting,deformation of the wave arm and breakup and disappearance of spiral waves,etc.We observe that spiral wave can disappear through the conduction block and transition from spiral wave to target wave.We observe the eight kinds of spiral wave breakups in connection with the excitation of EADs,such as symmetry breaking-induced breakup,nonsymmetry breaking-induced breakup,asymmetric excitation-induced breakup,conduction block-induced breakup,double wave-induced breakup,etc.It is found that the breakup of these spiral waves is all related to the delayed wave produced by the EAD,and the total rate of spiral wave breaking is usually about 13.8%.However,the ratio of spiral wave breakup can reach 32.4% under proper selection of aging cell density and the EAD excitation.The results are basically consistent with the survey results of arrhythmia-induced death rate.In the third chapter,we study the problem that whether the coupling of cardiomyocytes and fibroblasts can lead to spontaneous spiral waves in cardiac tissue.We introduce the cardiomyocyte cells and fibroblast cells in the GH model.The cardiomyocyte cells are randomly covered with fibroblast cells with a given probability.The cardiomyocyte cells are only coupled with the fibroblast cells not exceed one lattice distance.The results of numerical simulations show that: the coexistence of single spiral wave pair,single spiral wave,multi spiral wave pair,single target wave,multiple target wave and spiral wave pair and target wave can occur spontaneously under the proper selection of coupling strength,fibroblast cells density and excitation threshold.Our results will help us to understand the generation mechanism of the spontaneous spiral waves and target waves.The fourth chapter is the summary and prospect.