Mathematical Sciences: Traveling Waves in Excitable Media

行波激发提供了各种生物系统中的通信和空间组织。这个项目的长期目标是从数学上研究心肌、大脑皮层、聚集细胞场和非生物化学混合物中兴奋的行波的起源和性质。一般的方法是首先建立特定系统的真实数学模型，然后用解析方法确定模型的性质，最后将模型的行为与特定系统中观察到的激励波的性质进行比较。该建议强调了波传播的那些特征，这些特征是所有可激发介质的共同特征，因为它们具有相似的数学描述。同时，在模型中建立了当前对具体机制的最好的科学理解，从而可以在理论和实验之间进行详细的定量比较。这些研究具有间接的医学相关性，因为一些生理病理与经典的偏头痛(扩散性抑郁波)有关。

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).