The Effect Of Ion Channel Controlling Parameters On Dynamics Of Traveling Wave In Human Myocardial Tissue

Heart disease is a major killer which has been a threat to human health. Survey data shows that every year about 600 thousand people die of cardiac sudden cardiac death in China. To treat and prevent the heart disease effectively, we have traced to understand the propagation of electrical signals in the heart of myocardial tissue on level of the ion channel. In this paper, we study the effects of ion channel conductivity of the dynamical behavior of the traveling wave pulses by using the ORd ion model with the diffusion. The main work is divided into three parts:Firstly, we study the effect of ion channel conductivity on the dynamical behavior of the single traveling wave pulse by using the ORd ion model with the diffusion. We give data range of ion channel conductivity when the traveling wave pulses steadily propagate and variation of propagation velocity of traveling wave pulses with ion channel conductivity(introduced in Chapter 2). Taking into account the actual situation, we let the value of the ion channel conductivity change in the vicinity of the reference. Studies have shown that: for the maximal inward rectifier K+ current and the maximal transient outward K+ current, when their conductance GK1 and toG are at low value area, the system supports a stable traveling wave pulse; while maximal Na+ Current conductance at high value area, the system supports a stable traveling wave pulse. In NaG-K1 G andNaG-toG parameter space, the value of NaG on the dividing line of steady traveling wave pulses and damped wave pulses is an increasing function of K1 G and toG respectively. In the case of stable propagation of a traveling wave pulse, various in kinds of ion channel conductance have different effects on the propagation velocity of traveling wave pulses. With maximal background current conductanceKbG, the maximal Na+/Ca2+ exchange current conductancencxG, K1 G and toG increasing, propagation velocity of traveling wave pulses reduces in different ways. Propagation velocity of traveling wave pulses increase with NaG increasing. In addition, some ion channels parameter has no effect on the propagation velocity of traveling wave pulses, such as maximal Slow Delayed Rectifier K+ Current conductance, maximal Rapid Delayed Rectifier K+ Current conductance and stimulation current amplitude.Secondly, we study the effects of ion channel conductivity on the dynamical behavior of traveling wave pulse strings by using the ORd ion model with the diffusion. We give the relation between excitation periods and perturbation periods of traveling wave pulse strings and the dispersion relation of traveling wave pulse strings(introduced in Chapter 3). When the perturbation period within the scope of some value, the relationship between excitation periods eT and perturbation periods pT was a linear relationship and the slope is rational. The linear relationships of 1:4, 1:2, 1:1 are very obvious. While the value of NaG increasing within a certain range, the positions of linear relationships of 1:4 and 1:2 move toward the direction of perturbation periods reducing. The corresponding perturbation period range reduces and the minimal perturbation periods that can generate traveling wave pulse train reduce. While the value of K1 G increasing within a certain range, the positions of linear relationships of 1:4 and 1:2 move toward the direction of perturbation periods reducing. The corresponding perturbation period range reduces and the minimal perturbation periods that can generate traveling wave pulse train reduce. We give the relationship between wave length λ and perturbation period pT and the dispersion relation of traveling wave pulse train. The velocity of traveling wave pulse train is monotone increasing function of perturbation period and the slope of the curve is decreasing. When pT is very little, the system does not produce traveling wave pulse train; while pT is very large, the traveling wave pulse train is equivalent to a plurality of independent traveling wave pulses.Finally, we study the effects of ion channel conductivity on the region in vulnerable period in excitable system by using the ORd ion model with the diffusion. We give the change rule of region in vulnerable period when ion channel conductance varies(introduced in Chapter 4). The region that condition waves pass through, can be successively divided into the region in bidirectional propagation period, the region in vulnerable period and the region in refractory period from away from the condition waves to close to the condition waves. The impact of NaG,K1 G andtoG on the region in vulnerable period in the system are different: With the gradual increasing of toG, the region of vulnerable period move towards the direction close to the condition wave and the width of the region of vulnerable period gradually increases. But the region in bidirectional propagation period in system becomes large. With the gradual increasing of NaG andK1 G, the region of vulnerable period move towards the direction close to the condition wave and the width of the region of vulnerable period gradually decreases. But the region in bidirectional propagation period in system becomes large. We also explain the relationship between that the linear relation between excitation periods and perturbation periods of traveling wave pulse strings and that the region in vulnerable period in the system.