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

Control of spiral wave and spatiotemporal chaos in reaction-diffusion systems has attracted much attention of scientists and technologists. The research interest is that spiral wave has been observed in living cardiac tissue. It is confirmed that arrhythmia relates to spiral wave of electrical activity in cardiac muscle. Spiral wave breaking into spatiotemporal chaos will lead to life-threatening fibrillation. It is very important for cardiac disease treatment to propose the methods of suppressing arrhythmia by studying numerically and experimentally spiral wave dynamics. Up to present, many control methods have been suggested to control spiral wave and spatiotemporal chaos based on the characteristic of spiral wave, such as spatial gradient field perturbation, parameter perturbation, chaos signal control, feedback control,periodically pacing control and so on. Because many control methods do not come from specific cardiac model, some control methods do not work or are not suitable for the control of spiral wave and spatiotemporal chaos in cardiac tissue. In addition, many pharmacological control methods have proposed, based on electrophysiological properties of the cardiac tissue. Although these pharmacological control methods make good effect on the therapy in arrhythmia, the long-term use of anti-arrhythmia agents can destroy the ionic equilibrium of cardiac tissues, leading to fibrillation. Therefore, it is interesting to explore new technique of arrhythmia treatment.The control of spiral waves and spatiotemporal chaos is studied in the present paper based on a two-dimensional cardiac model. The paper is organized as follows:Chapter 1 is the summary part of this paper. It contains seven sections. The section 1 briefly introduces nonlinear systems and chaos. The section 2 introduces several typical reaction-diffusion systems. The section 3 introduces the dynamical behavior of spiral wave, such as the generation, meandering and breaking up of spiral waves. The section 4 introduces the basic structure of the heart and membrane potential formation. The section 5 introduces some dynamical models of the heart. The section 6 introduces some control methods of arrhythmia based on nonlinear dynamics. The section 7 briefly introduces the types of fibrillation and the clinical control method of fibrillation.In chapter 2, we use calcium channel blockade to suppress spiral waves and spatiotemporal in cardiac. It is generally accepted that spiral waves and spatiotemporal chaos can't b suppressed by calcium channel-blocking drug when the maximum conductivity of calciur current is monotonously reduced by the drug. So we propose a control strategy which applie blockade to modulate the maximum conductivity of calcium current and lead to change of th conductivity in the form of traveling-wave. The numerical results show that the control metho can quickly eliminate the spiral waves and spatiotemporal chaos in cardiac tissue when th related parameters are properly chosen. The system return to the rest state after transient dru controls. The phenomenon that the modulated calcium conductivity transforms spatiotempora chaos into spiral wave is observed. The control mechanism is briefly discussed.In chapter 3, we develop a control method of enhancing diffusion coefficient to suppres spiral waves and spatiotemporal chaos. We apply non-alternate and alternate ways to alter th diffusion coefficient. The numerical results show that when the related parameters are properl chosen the non-alternate control method can effectively suppress spiral wave. But it can nc effectively suppress spatiotemporal chaos because the control effect depends on the contrc opportunity. However, the alternate control method can effectively suppress spatiotempora chaos. It is found that the appearance of conduction block in homogeneous medium leads to th suppression of spiral wave and spatiotemporal chaos.In chapter 4, we study the suppression of spiral waves and spatiotemporal chaos in cardia tissue by elevating potassium ion concentration. We propose two strategies of suppressing spin wave and spatiotemporal chaos. One is to elevate the extracellular potassium ion concentratio suddenly. This method can effectively suppress spiral waves and spatiotemporal chaos when th elevated extracellular potassium ion concentration reaches a critical value. Especially,the spin wave pinned to defects also can be suppressed. The other is to let the extracellular potassium io concentration varies periodically while the amplitude of concentration is limited. We find that th method can effectively suppress spiral waves and spatiotemporal chaos when the relate parameters are properly chosen. But it can not suppress the pinned spiral waves. The contrc mechanism is discussed.