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，在领域的聚集细胞，在领域的分裂 细胞和无生命的化学混合物中。 研究者 强调波传播的那些特征， 所有令人兴奋的媒体，因为它们具有相似的数学特性 说明. 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，因此，理论之间的详细定量比较 可以进行实验。 这些模型的研究， 分析数学方法和数值模拟。 在现代工业化国家， 心脏病和癌症。 每个是一个 一系列复杂的疾病，有许多不同的原因， 治疗。尽管如此，从根本上说， 因为心脏肌肉收缩的电刺激 癌症扩散是因为正常的控制 细胞的生长和分裂被阻断。 发展 治疗或治愈这些疾病的合理策略，必须 了解控制生物的基本生物机制， 心肌收缩和体细胞分裂。 的 研究人员和其他数学生物学家正在使用强大的 用数学工具来解释 心脏和分裂细胞。 他们的模型显示 以前隐藏的秘密 例如，快速无组织 衰竭的心脏颤动是由微小的旋转波引起的， 心脏肌肉的旋转失控。 数学模型被用来揭示 这些旋转的波浪决定了它们的开始和消亡，并且 是治疗的关键 同样， 控制细胞分裂，决定哪些细胞应该分裂， 最终可以用数学精确表达。 作为 通过实验和理论，这些定律变得清晰起来， 调查，将有可能明智地使用它们， 使复发的癌细胞重新得到控制。

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 traveling waves of excitation in heart muscle, in fields of aggregating cells, in fields of dividing cells, and in nonliving chemical mixtures. The investigator 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 detailed quantitative comparisons between theory and experiment can be sought. The models are studied by analytical mathematical methods and by numerical simulations. In modern industrialized nations, the two most common causes of death are heart disease and cancer. Each is a complicated suite of diseases with many different causes and treatments. Nonetheless, at a fundamental level, hearts fail because the electrical stimulation of heart muscle contraction goes awry, and cancers spread because the normal controls over cell growth and division are short-circuited. To develop rational strategies to treat or cure these diseases, one must understand the basic biological machinery that controls the contraction of heart muscle and the division of body cells. The investigator and other mathematical biologists are using powerful mathematical tools to unravel the inner workings of the beating heart and the dividing cell. Their models have revealed previously hidden secrets. For instance, the rapid disorganized fluttering of a failing heart is caused by tiny rotating waves of contraction the spin out of control in the heart muscle. Mathematical models are used to uncover the laws that govern these spinning waves, that dictate their onset and demise, and that hold the key to their treatment. Similarly, the laws that govern cell division, that determine which cells shall divide and when, are ultimately expressible with mathematical precision. As these laws become clear, through experimental and theoretical investigations, it will be possible to use them intelligently to bring renegade cancer cells back under control.