Collaborative Research: Hybrid Bifurcation With Applications In Cardiac Dynamics

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The objective of this collaborative research is to explore the full potential and limitations of border-collision models in describing cardiac alternans. The project will develop a theoretical understanding of nonsmooth bifurcations as unfoldings of piecewise smooth problems, which will allow a more complete comprehension of the relation between a piecewise smooth bifurcation problem and the original smooth one. The theory developed in the present project will be applied to existing and new cardiac models to examine hybrid smooth/nonsmooth bifurcation to alternans. Theoretical and numerical predictions will be validated experimentally using isolated cardiac myocytes as well as whole isolated rabbit hearts to explore physiological mechanisms accounting for hybrid phenomena in cardiac dynamics.Cardiac alternans is a marker of ventricular fibrillation, a fatal heart rhythm that is one of the leading causes of mortality in the Western world. Mathematical analyses combined with experimental studies of this research may lead to new insights on the physiological mechanism of alternans and therefore will impact the diagnosis and treatment of cardiac arrhythmias. The developed bifurcation techniques will provide new approaches to other nonsmooth problems in engineering and biology such as vibro-impacting systems, systems with friction, and switching in electrical circuits. The research program will train graduate and undergraduate students in a multidisciplinary environment giving them the ability to use nonlinear analyses to understand complexities in engineering and biological systems. The outreach activities will expose high school students to mathematical biology and nonlinear ways of thinking.