| Spiral wave is a self-sustained wave which does not depend on any external periodic signal source. The spiral wave patterns have been observed in excitable media and oscillatory media. Physiological experiments show that a class of arrhythmia or tachycardia phenomena observed in patients with heart disease may be caused by the spiral wave in cardiac tissue, and the cardiac death caused by fibrillation is closely related with the instability of spiral wave. How to effectively eliminate spiral waves and irregular waves (i.e., spatiotemporal chaos generated by the breakup of spiral wave) in cardiac tissues is a scientific and technical issue that must be resolved. So the investigation of the dynamic behaviors and suppression of spiral waves has attracted much attention of scientists in nonlinear science.Because spiral wave in cardiac tissues is harmful, a variety of methods which are applied to eliminate spiral waves and spatiotemporal chaos have been proposed, such as periodically pacing control, spatial gradient field perturbation, feedback control and so on. The anti-arrhythmic drug therapy and defibrillators for are commonly used in clinical treatment. However, the treatments have drawbacks or side effects because drugs can destroy the balance of ions in the myocardial tissue, and defibrillators may damage myocardial cells and brings great suffering to the patient. Therefore, to find new methods of eliminating spiral waves and spatiotemporal chaos in cardiac tissues is necessary and meaningful.Since above control methods have some drawbacks, we propose two new methods to control spiral waves and spatiotemporal chaos in two-dimensional cardiac tissues, based on Luo-Rudy phase I model. This paper will be divided into three parts to introduce our work.Chapter1is the comprehensive introduction of this paper. It contains4sections. In order to describe spiral wave, section1briefly introduces chaotic phenomena and dynamics of spatiotemporal pattern. Section2describes the dynamical behavior of spiral wave, including the movement of the spiral tip, the breakup of spiral wave into spatiotemporal chaos, and some control methods of spiral waves. Section3introduces some necessary basic knowledge of electrophysiology and cardiac models. Section4introduces some methods that can be applied to treat arrhythmia and fibrillation. In chapter2, suppression of spiral waves and spatiotemporal chaos in cardiac tissue is investigated. Two control methods are proposed.(1) A planar wave is generated by alternately changing the extracellular potassium ion concentration, and then a weak external electric field is used to help plane wave to suppress spiral waves and spatiotemporal chaos.(2) The extracellular potassium ion concentration is first enhanced. Planar waves are then generated by wave emission induced by external electric field. We apply the planar waves to suppress spiral waves and spatiotemporal chaos. The results show that the control methods can effectively suppress spiral waves and spatiotemporal chaos when related parameters are properly chosen. When regional myocardial ischemia occurs, high extracellular potassium ion concentration will appear in where myocardial ischemia occurs. The methods of wave emission can be used to suppress spiral waves and spatiotemporal chaos in heart under this case. The advantages and mechanism of the control methods are explained.In chapter3, cardiac memory effect, which exhibits the time-delayed coupling of membrane voltage, is introduced into Luo-Rudy phase I cardiac model. The effect of the cardiac memory on spiral waves is investigated. The numerical results show that the cardiac memory can lead to irregular meandering of spiral waves. When the delay-time is properly chosen, the increase of memory strength causes the decrease of spiral wave frequency. If memory strength exceeds the critical value, the cardiac memory results in the disappearance of spiral waves and spatiotemporal chaos in system because the time-dependent potassium ion current is excessively suppressed by cardiac memory. |
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