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.
