Mathematical Sciences: Traveling Waves in Excitable Media

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9525766 Tyson Traveling waves of excitation provide a mechanism for communication and spatial organization in a variety of biological systems, such as waves of membrane depolarization in neuromuscular tissue, waves of mitosis in fruit fly embryos, waves of cyclic AMP during slime mold aggregation, and waves of infection spreading through susceptible populations. These and other examples of excitability share many common features that can be expressed in generic mathematical models of excitable media. The investigator and his colleague study wave propagation in such models using established theoretical tools and new computational approaches, focusing primarily on rotating scroll waves in three-dimensional excitable media. As a scroll waves rotates around its central "filament," the filament moves slowly through space according to certain laws of motion that are still poorly understood. The investigators develop efficient and accurate computational tools, based on a cellular automaton model of excitable media, in order to simulate the motion of scroll filaments in large domains over long periods of time. The thick-walled ventricle of the mammalian heart is a three-dimensional excitable medium that propagates waves of electrochemical activity. By modulating intracellular calcium levels, these waves control the beating of the heart. During a normal heartbeat the wave induces the muscle fibers of the left ventricle to contract synchronously and blood is efficiently expelled from the chamber. But under pathological conditions (flutter and fibrillation), the heartbeat degenerates into a rotating scroll wave of the sort studied in this project. The rotating scroll wave causes the muscle fibers to contract asynchronously, so that part of the chamber is relaxed when other parts are contracting. As a result the blood within the chamber is not pumped efficiently and the heart must be "defibrillated" to save the victim's life. To understand the fundamental causes of ventricular fibrillation and its effective treatment, one needs a better understanding of the onset, development and annihilation of rotating scroll waves in three-dimensional excitable media, which is the basic goal of this project.