Mathematical Studies of Excitability in Physiological Systems

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Keener9970086 The investigator develops and uses mathematical models andtools to study a variety of problems in physiology organizedaround the theme of excitability and wave propagation. The threemain interconnected thrusts for this work are: 1) to developmathematical models that can be used to describe specificphysiological phenomena; 2) to develop analytical techniques,numerical algorithms, and computational tools to study the modelequations; 3) to use analytical and numerical tools to understandthe behavior of these systems and to thereby better understandthe underlying physiological processes. The physiologicalproblems are drawn from four specific areas: 1) cardiology andthe problems of fibrillation onset and defibrillation; 2) calciumdynamics and excitation-contraction coupling in cardiac cells; 3)the role of microtubule networks in the transport of chemicalsthroughout a cell; 4) the involvement and spatial spread ofbacteria in chemical reactions, such as mine tailings dumps,water treatment plants, oil spills, etc. The common thread running through this work is that chemicalsignals underlie motion, and this work is directed toward anunderstanding of how chemical signals are generated, controlled,and how they mediate motion. Such an understanding is a crucialfirst step toward solving several important health-related andenvironmentally related problems. Specifically, an improvedunderstanding of the heartbeat and how and why it fails couldgive new clues as to how to prevent or cure some dangerouscardiac disorders. Similarly, an improved understanding of howbacteria (and other living cells) move and regulate their motioncould lead to improved organic control of toxic chemical wastes.