Study On The Control Of Spiral Waves And Spatiotemporal Chaos In Cardiac Tissues

Spiral waves are observed in many systems. For example, self-organization of viscous mold, calcium waves in frog egg, the electric signal in mammalian cardiac tissue, the BZ systems, etc. Therefore, dynamical behavior and suppression of spiral waves have attracted tremendous interest of scientist. The heart is an important component of the mammalian circulatory system, which function is to maintain the blood circulation of whole body through contraction and relaxation of heart. The occurrence of arrhythmia in heart will affect the blood circulation. Physiological experiments show that the fast heart rate may be related to electrical signal of spiral wave in cardiac tissue, and the fibrillation has been linked with the break up of spiral wave into spatiotemporal chaos. Therefore, how to eliminate the spiral waves and spatiotemporal chaos in cardiac tissues is worth to study. At the present, there are two method of clinical treatment of cardiac arrhythmia: high-voltage defibrillation and drug treatment. On the one hand, high-voltage defibrillation will bring huge pain to the patient, and will possibly leave the hidden danger of the recrudescence of arrhythmia. Therefore, looking for low voltage defibrillation methods causes a lot of attention. On the other hand, suppression of arrhythmia via drug is one of the pop investigations because drugs can directly affect the various ionic currents in myocardial cell. In order to reduce side effect produced by drug, the mechanism of the suppression of arrhythmia via drug should be studiedIn this paper, local feedback control method and different anti-arrhythmic drugs are applied to suppress spiral waves and spatiotemporal chaos in cardiac tissues based on LuoRudy91 model. The numerical results are introduced as follows:Chapter I is the summary part of this paper. It contains six sections. The main characteristics and fundamental nature of chaos are introduced this section. The section II introduces several typical reaction-diffusion systems. The section III introduces the generation, meandering, and instability of spiral wave. The section IV introduces the basic knowledge of the heart and the current method of clinical treatment of fibrillation. The section V introduces some dynamic models of heart. The section VI briefly introduces some control methods of spiral waves and spatiotemporal chaos.Chapter II introduces local feedback control of spiral waves and spatiotemporal chaos in cardiac tissues. We propose local feedback control to suppress spiral waves and spatiotemporal chaos. Two kinds of control strategy are adopted, namely are the static and moving control method. It is found that when related parameters are properly chosen spiral wave can be suppressed by static controller, whereas spatiotemporal chaos cannot be suppressed effectively. However, spiral wave and spatiotemporal chaos can be suppressed effectively by moving controller. The corresponding to control speed depends on the traveling speed of controller. Spiral wave and spatiotemporal chaos can be suppressed in a short time when the control parameters are suitably chosen.Chapter III introduces suppression of spiral waves and spatiotemporal chaos in cardiac tissues via sodium channel blockers. In order to suppress spiral waves and spatiotemporal chaos, we apply drug to reduce the maximum conductivity of sodium current from G Na to G N′a. The results show that spiral waves and spatiotemporal chaos can be effectively suppressed by this method in a short time. The reason is that the control method can effective suppress the depolarization process while the re-polarization process is accelerated, reducing the excitability of myocardial cell, leading to annihilation of spiral waves and spatiotemporal chaos. The feasibility of the control method is discussed briefly.Chapter IV introduces suppression of spiral waves and spatiotemporal chaos in cardiac tissues via calcium channel agonist. In order to suppress spiral waves and spatiotemporal chaos, the control strategy which applies calcium channel agonist to enhance the maximum conductivity of calcium current is proposed. The results show that the method can effectively suppress the spiral waves and spatiotemporal chaos in cardiac tissues even if the distribution of the conductivity of the potassium current is un-uniform. However, when there is a large defect without function of diffusion in the system the method is invalid. The control mechanism has been analyzed briefly.Chapter V introduces the suppression of spiral waves and spatiotemporal chaos in cardiac tissues via controlling the calcium and potassium currents. In order to suppress spiral wave and spatiotemporal chaos, we apply calcium channel agonist to enhance the maximum conductivity of calcium current while apply channel blocker to reduce the maximum conductivity of potassium current G Kand G K1. The results show that the method can effectively suppress the spiral waves and spatiotemporal chaos even if there is the large defect without function of diffusion in medium. The control mechanism has been analyzed.Chapter VI introduces suppression of spiral waves and spatiotemporal chaos in cardiac tissues via amplitude limit of potassium ion current. We propose a control strategy which limits the potassium currents. The effect of limitation of different potassium ion currents on suppression of spiral waves and spatiotemporal chaos has been studied. The results show that when the total potassium ion current is limited the control method can effectively suppress spiral waves and spatiotemporal chaos so long as the threshold value is properly chosen. When only the time-dependent and time-independent potassium currents are controlled respectively the control method works well. However, when the only plateau potassium current is controlled the control method does not work. The control mechanism has been analyzed.