The Control Of Two-Dimensional Spiral Wave And Spatiotemporal Chaos Based On L-R Phase ? Heart Model

Cardiac tissue is mainly composed of cardiomyocytes and fibroblasts.Aging as well as pathological states such as ischemia and heart failure can cause cell death,fibroblasts proliferation and myocyte-fibroblast electrical coupling(i.e.M-F coupling).Both the M-F coupling and the appearance of spiral wave in the electrical activity of the heart can result in arrhythmias.When spiral wave breaks up into spatiotemporal chaos,it also leads to ventricular fibrillation.This is a life threatening arrhythmias.How to effectively control arrhythmia as well as spiral waves and spatiotemporal chaos in cardiac tissues has attracted much attention of scientists.In this thesis,both Luo-Rudy phase I heart model and the passive model of fibroblast were used to study the control of spiral wave and spatiotemporal chaos in cardiac tissues as well as the effect of M-F coupling on the formation of spiral wave.The obtained results can provide a new idea for antiarrhythmic therapy.The thesis is organized as follows.The first chapter is the literature review.The chapter introduces the universality of spiral waves,several reaction-diffusion systems,two heart models,the control methods of spiral wave and spatiotemporal chaos,and so on.The second chapter introduces our first research work.We used the Luo-Rudy phase I model to study how to regulate the change of sodium current in cardiomyocytes to control spiral wave and spatiotemporal chaos in a two-dimensional cardiac tissues.We propose such a sodium current control scheme: when the cell is excited,the regulation of sodium current begins.If the absolute value of sodium current obtained from the model equation is less than the absolute value of sodium current control threshold,the sodium current is simply equal to the control threshold of sodium current.In other cases,the absolute value of sodium current cannot exceed the maximum value without control.When the membrane potential rises over-5 mV,the sodium current evolves naturally.This method of regulating sodium current ensures that all cells have almost the same amplitude of sodium current,while without obviously changing the excitation-time.All cells thus have the same excitability under the control of sodium current,so that the excitation of cell is less affected by spiral wave tip.The numerical simulation results show that as long as the control threshold of sodium current reaches a critical value,the rotation of spiral wave tip is effectively suppressed,causing spiral wave to move out of the system boundary and spatiotemporal chaos to disappear after it has evolved into a spiral wave.If the absolute value of sodium current control threshold is large enough,the spiral wave and spatiotemporal chaos would also disappear through conductive block.The third chapter introduces our second research work.We used the heart Luo-Rudy phase I model and the passive model of fibroblast to study the effects of the M-F coupling on the formation of spiral wave and the control of spiral wave and spatiotemporal chaos in a two-layer composite medium composed of cardiomyocytes and fibroblasts.We propose a control scheme to control spiral waves and spatiotemporal chaos by increasing the coupling strength between cells.The numerical results show that as the density of fibroblasts increases,M-F coupling may result in spiral wave meander and breakup of spiral wave into spatiotemporal chaos,and even induce transitions from spatiotemporal chaos(or spiral wave)to no wave.The reason is that M-F coupling can reduce the excitability of the medium.The eliminating spiral wave and spatiotemporal chaos in the composite medium by increasing the coupling strength between cells is only effective in most cases.It depends on the role played by fibroblasts.Furthermore,there are the abnormal effects of control,i.e.,the control effects are very different for two adjacent initial states.When fibroblasts act as current sinks for the cardiomyocyte,spiral wave and spatiotemporal chaos cannot be eliminated in some cases by increasing the coupling strength between cells.Although in most cases increasing the coupling strength between cells can terminate spiral wave and spatiotemporal chaos when the coupling strength exceeds a critical value,but controlled area is small.Increasing the coupling strength between cardiomyocytes is the key factor controlled spiral waves and spatiotemporal chaos.When fibroblasts act as a current source for the cardiomyocyte,increasing the coupling strength between cells beyond a critical value can effectively terminate spiral wave and spatiotemporal chaos,and the controllable area is greatly increased compared with the former.Spiral wave and spatiotemporal chaos disappear in two ways.One is directly disappearance through conductive block.The other is the disappearance about the transition from initial state to target wave or new spiral wave.The forth chapter is a summary and outlook.