Study For The Effect Of Myocardial Electrical Restitution On Spiral Waves Using Cellular Automaton

The heart realizes it function by the myocardial electrical signal coming from cardiac sinus.Under normal conditions,the cardiac electrical signals pass through the heart in the form of quasi-target waves or quasi-planar waves.If the conduction block or reentrant effect occurs during the conduction process,the spiral wave state of the myocardial electrical signal will be formed,which corresponds to a clinical tachycardia.As soon as the spiral waves are broken,the myocardial electrical signals evolve into the spatiotemporal chaos,it corresponds to the clinically fatal heart fibrillation.The experimental and numerical simulation studies found that the electrical properties of the myocardial electrical signals,including the conduction velocity(CV)restitution,the action potential duration(APD)restitution and its memory effect are important factors in the transition of spiral waves to spatiotemporal chaos,because such transitions are easily observed under the steep CV restitution,APD restitution and its obviously memory effect.For example,patients with Brugada syndrome(Br S)can easily develop from tachycardia to ventricular fibrillation,while experimental data suggest that patients with Br S have the abnormal CV restitution and APD restitution are steeper than healthy people.At present,the connection between the restitution of the electrical properties and the behavior of the spiral wave evolution is not fully clear.Numerical simulation is a useful technique for investigating the subjects of cardiovascular disease such as the Br S,and cellular automaton(CA)is a simple but effective numerical simulation method.In this paper,we study the effect of the CV restitution,APD restitution and its memory of myocardial electrical restitution on the evolution behavior of spiral waves.The paper is arranged as follows:The first chapter introduces the research background and significance of investigation,myocardial cells and their ion channel and transmembrane potential,the electric properties of myocardial electrical signal,the generation and instability of the spiral wave state of myocardial electrical signal,and the CA model.The second chapter introduces our first work.In this work,we explored the effect of CV restitution myocardial electrical signal on the evolution behavior of the spiral waves.We first in considered the CV restitution of myocardial electrical signal in the CA model,then theoretically analyzed the production conditions of conduction block and reentrant effect,and then numerically simulated the evolutionary behavior of spiral waves under CV restitution.The computer simulation results showed that the CV restitution will lead to three types evolution behavior of spiral waves: stable rotation with the shape of concave or diamond,Eckhaus instability and Doppler instability.We investigated the mechanism of the different evolution behaviors by tracking and analyzing the conduction of myocardial electrical signals.The stably rotating spiral wave is concave because the degree of conduction block varies in the system.The spiral waves rotate with diamond shape when the electrical signals along the oblique direction are almost completely blocked.The Eckhaus instability of the spiral wave is due to the breakup of the peripheral wave arms resulting from the strong conduction block and its induced reentrant effect far from the spiral wave tip,while the Doppler instability is originated from the strong conduction block near the tip,which makes the arm squeeze in one direction and stretch along the other direction.The third chapter introduces our second work.In this work,we studied the effect of the CV restitution,APD restitution and its memory effect on the evolution behavior of the spiral waves using cellular automaton,and investigated the relation between the symptoms of the patients with Br S and CV restitution,APD restitution and its memory.In order to solve the difficulty of comparing the simulation results with clinical or experimental data in the first work,we quantified the space and time step of the cellular automaton model by combining the clinical data of action potential duration and conduction velocity in patients with Br S.Given that the electrical properties of cardiomyocytes include not only CV restitution,but also APD restitution and its memory effect,so the CV restitution,APD restitution and its memory effects are considered in the cellular automaton model used here.In numerical simulation,the original stable spiral wave is produced under the condition with no restitution,then the different restitution is applied to the original spiral wave.The results showed that: If just the CV restitution under the 48 sets of parameters that would allow the spiral wave to not break are applied to the original spiral waves,the evolution of the spiral waves include continuous and stable rotation,the stable rotation after meandering,and the continuous meandering.If both the CV restitution under the selected 48 sets of parameters and the no-memory APD restitution are applied to the original spiral waves simultaneously,the spiral waves disappear or break to enter the multiple spiral wave state,and the proportion of the multiple spiral wave state is about 54%,which is higher than the clinical ventricular fibrillation rate of 35% to 48% in clinical Br S patients.If both the CV restitution under the selected 48 sets of parameters and the APD restitution with memory effect are applied to the original spiral waves simultaneously,the spiral waves either rotate stably,or meander,or disappear,or break into multi-spiral waves,which correspond to clinical symptoms such as tachycardia,symptom disappearance and ventricular fibrillation in patients with Br S.The proportion of the multi-spiral waves under these CV restitution and no-memory APD restitution is 35%,which is agree with the clinical data.The no-memory APD restitution promotes the oscillation amplitude of APD,while the APD restitution with memory effect alleviates this oscillatory behavior,so the proportion of breakup of spiral wave is higher under no-memory APD restitution than that under APD restitution with memory effect.This work also focuses on the conduction block caused by CV restitution and APD restitution,and analyzes the reasons of the evolution behavior of the spiral waves under different restitution.The fourth chapter is the summary and outlook.