Vortex Filaments in 3 Dimensional Excitable Media

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The principal investigator will study three dimensional excitable media, both in terms of chemical reactions but also are related to the electrophysiology of the heart. The key ideas of the project are 1) the normal heart muscle is an excitable medium; 2) some aspects of the dynamics of excitable media are generic, notably their vortex excitations; 3) these aspects are inherently 3-dimensional; 4) in heart muscle these vortex excitations are responsible for the most pernicious arrhythmias, but are almost impossible to study 3-dimensionally in living heart muscle; 5) they can be studied computationally and in chemically excitable media, both of which support action-potential-like propagation in three dimensions; 6) the utility of this comparison has been validated in two dimensional studies; 7) the pure computation for equations of mechanism should be complemented by experiments; 8) such experiments can be implemented by adapting existing computational procedures in optical tomography to existing computational procedures for analysis and display of the data that are currently obtained by supercomputer solution of the mechanistic equations of cardiac electrophysiology and of the analogous chemical kinetics. The investigator will solve the "three- dimensional" for the mechanisms and use computer-assisted optical tomography to observe three dimensional activation wavefronts in the chemical medium during the analog to these arrhythmias. The current project is being supported by four programs at the National Science Foundation: Theoretical and Computational Chemistry, Applied & Computational Mathematics, Physiology, and Computational Biology Activities.