Mathematical Sciences: Traveling Waves in Excitable Media

激发的行波在各种生物系统中提供通信和空间组织。该项目的长期目标是用数学方法研究心肌、聚集细胞、分裂细胞和非活性化学混合物中兴奋行波的起源和性质。研究者强调了所有可激介质所共有的波传播特征，因为它们具有相似的数学描述。同时，将当前对具体机制的最佳科学理解构建到模型中，以便在理论和实验之间寻求详细的定量比较。通过解析数学方法和数值模拟对模型进行了研究。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。每一种疾病都是一套复杂的疾病，有许多不同的病因和治疗方法。然而，从根本上说，心脏衰竭是因为对心肌收缩的电刺激出错，癌症扩散是因为对细胞生长和分裂的正常控制短路。为了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。研究者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的细胞的内部工作原理。他们的模型揭示了以前隐藏的秘密。例如，衰竭的心脏快速无组织的跳动是由心肌中失去控制的微小旋转收缩波引起的。数学模型被用来揭示控制这些自旋波的规律，这些规律决定了它们的发生和消亡，并掌握了治疗它们的关键。同样，支配细胞分裂的规律，决定哪些细胞何时分裂，最终也能用精确的数学表达出来。随着这些规律通过实验和理论研究变得清晰，将有可能巧妙地利用它们来控制叛逆的癌细胞。

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.