| Heart disease is one of the major diseases threatening human life and health.With the advancement of science and technology and the continuous advancement of related research,people have realized that tachycardia corresponds to the spiral wave phenomenon,and the instability and breaking of spiral waves are related to fatal ventricular fibrillation.The corresponding mathematical model provides a controllable environment that allows us to simulate the influence of changes in certain parameters on Propagation of electric waves in the myocardium without causing harm to patients or animals.Ischemia or pathological changes in the myocardium can cause changes in local electrophysiological parameters,also known as heterogeneity,which often affects spiral wave dynamics.Anti-arrhythmic drugs or mutations in some gene sites will affect the expression of ion channel proteins in cardiomyocytes.They will affect ion conductivity,The effect of which on the electric wave conduction of the myocardiumwhich can also be described as"A slight move in one part may affect the situation as a whole".Combining these two aspects to carry out research on the elimination and control of spiral waves plays an important theoretical guiding role in the treatment of tachycardia and the prevention of ventricular fibrillation.Therefore,this paper uses the complex Ginzburg-Landau（CGLE）model,the LR model,and the ORD model to study the effects of heterogeneous regions and ion channel conductivity on the dynamics of spiral wave.The main work will proceed from two parts:Part Ⅰ:The complex Ginzburg-Landau equation（CGLE）is used to study the influence of heterogeneous regions on the dynamic behavior of spiral waves.We discovered four different types of dynamic behaviors and plotted their corresponding parameter phase diagrams.A qualitative explanation was given to their formation mechanism,and some laws were discovered.The parameter change in the heterogeneous zone will transform the single-arm spiral wave of the system into four different dynamic behaviors:the state of the regular attractor of the tip of spiral wave moving around the heterogeneous zone,the state in which the target wave formed near the heterogeneous zone drives the spiral wave,The wave arm passing through the heterogeneous zone causes the spiral wave to break and recombine,and the coexistence of different states within and outside the heterogeneous zone.Under the condition of regular attractors,the size of the heterogeneous region and the position have an effect on the tip of helicon wave:When the position of the heterogeneous zone is fixed,as its radius increases,the radius of the attractor that the tip enters will gradually increase and then decrease sharply.When the radius of the heterogeneous zone within a certain range differs by a constant,the tip will enter the same attractor,but the initial drifting direction of the tip is not the same;When the radius of the heterogeneous zone is constant,as the position of the heterogeneous zone gradually moves away from the tip of spiral wave,the radius of the attractor that the tip finally enters will increase sharply,and within a certain range,the tip will enter attractors with the same radius but different positions.If the initial position of the wave head is used as the origin to establish a spatial coordinate system,the angle between the initial drifting direction of the tip and the horizontal direction will show an e-exponential attenuation relationship as the position of the heterogeneous zone gradually moves away from the tip of spiral wave.In the case of the target wave driving the spiral wave away,it is because after the appearance of the heterogeneous zone,when the spiral wave arm passes through the heterogeneous zone,the low-frequency target waves will be formed near the heterogeneous zone and compete with the high-frequency spiral wave.Gradually drive the spiral wave out of the boundary.In the case of wave arm breaking,the wave arm in the passing area is deformed,which affects the wave arm that propagates inward successively behind it.The wavelength changes drastically,which will eventually cause the wave arm in some areas to continue to break and reorganize.Part Ⅱ:The LR model is used to mainly study the influence of the changes in the conductivity of sodium and calcium ions on the traveling wave pulse train in one-dimensional space and the spiral wave dynamics in two-dimensional space.It is given that he action potential regression curve corresponding to different ion conductance in a one-dimensional system.The control of the two-dimensional spiral wave is realized by the assumed change of the conductivity of the ion;At the same time,the ORD model is used to study the influence of some ion conductivity changes on the dynamics of traveling waves.For the LR model,the1S-S2 stimulation protocol was applied,and This article draws the action potential regression curve when the conductivity of the sodium,potassium,and calcium ion channels take different values.The part of the curve with a slope greater than 1 is likely to cause alternating pulses and chaos in the one-dimensional traveling wave pulse train.For a two-dimensional system,first,the conductivity of calcium ions in a circular domain on the right side of the wave head change periodically.Research has found that under some periodic conditions,the wave head will continue to move across domains in and out of this ring,and the trajectory will be petal-shaped.The period will also affect the density of the trajectory.If the calcium ion conductance changes on a line near the wave tip in the same form of change,the wave tip will be guided to the vicinity of this line and move along this straight line in the form of a motion unit.In addition,if a periodic sodium ion conductivity change is applied to the whole area,the wave head will move along the trajectory of a circular rolling line.When the change period is within a certain range,it increases with the period to realize the transition between the inner roll type and the outer roll type of the wave head trajectory.For the ORD ion model,we are limited by computational cost and only studied the effects of changes in calcium ion conductance and delayed potassium ion conductance on the wavelength,perturbation period,action potential duration,and diastolic period of the traveling wave pulse train. |
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