Mathematical Sciences: Traveling Waves in Excitable Media

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Traveling waves of excitation provide for communication and spatial organization in a variety of biological systems. The long term goal of this project is to study mathematically the origin and properties of travelling waves of excitation in heart muscle, cerebral cortex, fields of aggregating cells, and in nonliving chemical mixtures. The general method is first to build a realistic mathematical model of the specific system, then to determine the properties of the model by analytical methods, and finally to compare the behavior of the model with observed properties of excitation waves in the specific system. The proposal emphasizes those features of wave propagation that are common to all excitable media because of their similar mathematical description. At the same time, the best current scientific understanding of specific mechanisms is built into the models, so that a detailed quantitative comparison between theory and experiment can be sought. These studies have indirect medical relevance because some physiological pathologies are associated with classical migraine (waves of spreading depression).