Mathematical Sciences: Wave Propagation in Excitable Media

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9303502 Keener The investigator studies propagation of waves in one, two and three dimensional excitable media, with a special emphasis on cardiac tissue. The goal of this study is to understand the dynamics of spatial patterns, especially the formation and evolution of spiral and scroll waves, taking into account specific features of cardiac tissue such as discreteness, anisotropy, inhomogeneity, geometry, and ionic kinetics. The study involves the construction of mathematical models for the dynamics of wave patterns, the mathematical analysis of model equations, development and implementation of suitable numerical algorithms for their simulation in large scale contexts, including but not limited to eikonal-curvature methods, and comparison of results with available experimental results. While there are many complementary and supplementary problems to address, the overriding goal of this research is to develop a quantitatively reliable whole heart model with which to vizualize the heartbeat. While this is an achievable goal, it is impossible with present day computers and mathematical models. The emphasis of this research is to develop improved mathematical models, rather than await the development of machines of sufficient size and speed. Such a model would be of great value in extending the diagnostic usefulness of the EKG, or in understanding the role of infarctions and clinical procedures in inducing life threatening cardiac arrhythmias. ***