Mathematical Sciences: Traveling Waves in Excitable Media

激励的行波提供通信， 各种生物系统中的空间组织。 的 该项目的长期目标是从数学上研究 心脏兴奋行波的起源和性质 肌肉，大脑皮层，聚集细胞的区域，以及 无生命的化学混合物 一般的方法是首先 建立具体系统的现实数学模型，然后 为了通过分析方法确定模型的性质， 最后，将模型的行为与观察到的行为进行比较 特定系统中激发波的性质。 的 该提案强调了波传播的这些特征， 所有可兴奋介质的共同点是， 数学描述 与此同时，最好的电流 对具体机制的科学理解是建立在 模型，使理论之间的详细定量比较 可以进行实验。 这些研究间接 医学相关性，因为一些生理病理学 与典型的偏头痛相关（扩散波 抑郁症）。

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).