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、聚集细胞、分裂细胞和非生物化学混合物中兴奋的行波的起源和性质。研究人员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，因为它们有相似的数学描述。同时，目前对特定机制的最好科学理解被构建到模型中，以便在理论和实验之间进行详细的定量比较。用解析数学方法和数值模拟方法对模型进行了研究。在现代工业化国家，两种最常见的死亡原因是心脏病和癌症。每一种疾病都是一系列复杂的疾病，有许多不同的病因和治疗方法。尽管如此，从根本上说，心脏衰竭是因为心脏肌肉收缩的电刺激出现了问题，癌症的扩散是因为对细胞生长和分裂的正常控制是短路的。要制定合理的策略来治疗或治愈这些疾病，人们必须了解控制心肌收缩和身体细胞分裂的基本生物机制。研究人员和其他数学生物学家正在使用强大的数学工具来解开跳动的心脏和分裂细胞的内部工作原理。他们的模型揭示了之前隐藏的秘密。例如，心脏衰竭时的快速无组织的扑动是由微小的旋转收缩波引起的，这种旋转波使心脏肌肉失去控制。数学模型被用来揭示支配这些旋转的波的规律，这些规律决定了它们的开始和消亡，并掌握着它们治疗的关键。同样，控制细胞分裂的法则，决定了哪些细胞应该分裂以及何时分裂，最终都可以用数学精度来表达。随着这些规律变得清晰，通过实验和理论研究，智能地使用它们来控制叛变的癌细胞将是可能的。

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.