Mathematical Studies of the Dynamics of Excitable Systems

研究者使用数学模型和分析来研究几个生理系统的动力学，其中兴奋性是一个共同和基本的特征。要研究的三个广泛的问题领域是：1)心律失常的发生和动态；2)除颤动力学；3)自身免疫性疾病的动态。这些问题的研究涉及复杂的数学模型和工具的开发和使用，包括先进的数值方法，如浸入边界法，分岔理论和动力系统理论，以及渐近分析。这些工具用于对边界区和缺血相关的心律失常、ap不稳定性及其与再入性心律失常的发生和发展的关系、由钙处理系统或交叉桥动力学的稳定性引起的机械交替、除颤的成功或失败、振荡性自身免疫反应等问题提供理论理解。对理论结果和实验结果之间的一致性给予了认真的关注。为此，他与实验学家合作，研究了兔肌细胞的间隙连接偶联，肥大对通过钠钙交换器的兴奋-收缩偶联的影响，导致致命性心律失常倾向增加的延迟钾通道突变的影响，以及模仿在小鼠囊性纤维化振荡动力学中的作用。兴奋性是生理系统中最重要的信号特征之一。它对神经、肌肉、心脏、免疫系统、血液凝固以及许多基因调控网络的运作至关重要。该项目的具体目标是获得对依赖兴奋性的系统的正常功能如何出错，表现出病理行为以及如何控制或预防这些病理行为的改进的理论理解。这里研究的行为是简单行为相互交织的结果，产生了无法通过直觉或简单手段理解的不复杂行为。因此，研究的重点是这些行为的数学模型的发展和分析，相信可以获得实质性的新的和重要的见解，并制定新的假设，而这些假设从现象学描述中是不明显的。虽然该项目主要关注与心脏周期异常有关的几个问题，但它远远超出了涉及共同原理的生理学许多领域。该项目包括对学生的重要培训。

Keener0211366 The investigator uses mathematical models and analysis tostudy the dynamics of several physiological systems in whichexcitability is a common and fundamental feature. The three broadproblem areas to be investigated are 1) The initiation and dynamics of cardiac arrhythmias; 2) The dynamics of defibrillation; 3) The dynamics of autoimmune disease.The study of these problems involves the development and use ofsophisticated mathematical models and tools, including advancednumerical methods such as immersed boundary methods, bifurcationtheory and dynamical systems theory, and asymptotic analysis.These tools are used to give theoretical understanding to problemsof border zone and ischemia related cardiac arrhythmias, APDinstabilities and their relationship to the onset and developmentof reentrant arrhythmias, mechanical alternans deriving frominstabilities of the calcium handling system or crossbridgedynamics, the success or failure of defibrillation, andoscillatory autoimmune responses. Serious attention is given toobtaining agreement between theoretical results and experimentalfindings. To that end collaborations with experimentalistsexamine gap junction coupling of rabbit myocytes, the effect ofhypertrophy on excitation-contraction coupling through thesodium-calcium exchanger, the effect of mutations on the delayedrectifier potassium channel that lead to increased proclivityfor fatal arrhythmias, and the role of mimicry in oscillatorydynamics of cystic fibrosis in mice. Excitability is one of the most important features enablingsignalling in physiological systems. It is crucial to theoperation of nerves, muscle, the heart, the immune system, andblood clotting as well as numerous gene regulatory networks. Thespecific goal of this project is to gain an improved theoreticalunderstanding of how the normal function of systems that rely onexcitability can go awry, exhibiting pathological behaviors, andhow these pathological behaviors might be controlled orprevented. The behaviors that are studied here are the result ofinterwoven interactions of simpler behaviors, resulting incomplex behaviors that defy understanding through intuition orsimple means. The investigation therefore focuses on thedevelopment and analysis of mathematical models of thesebehaviors in the belief that substantial new and importantinsights can be gained, and new hypotheses formulated that arenot apparent from phenomenological descriptions. While thisproject has as its main focus several problems relating toabnormalities of the cardiac cycle, it extends far beyond to manyareas of physiology where common principles are involved. Theproject includes a significant training component for students.