Border-collision bifurcations in cardiac muscle

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The purpose of this research program is to understand the origins of bifurcations that occur in the electrical response of small pieces of cardiac muscle. It is generally believed that bifurcations occurring in spatially-localized tissue can destabilize spatial-temporal waves of electrical activity in the whole heart, leading to tachycardia or even fibrillation. Thus, it is important to characterize the bifurcations and develop methods for their control. The researchers hypothesize that the transition to alternans is mediated by a border-collision bifurcation. Using a simple test-bed, consisting of a piece of periodically-paced frog myocardium, they are using several techniques to test their hypotheses. They are using new pacing protocols and simultaneous measurement of the transmembrane voltage and intracellular calcium to investigate the stability of the induced responses in the vicinity of the bifurcation. They are also developing mathematical models of the cardiac membrane that incorporates short-term memory and intracellular ionic concentrations. The models are simple enough that the parameters of the model can be adjusted on an animal-by- animal basis, which allows for a detailed comparison with the experiments. The enumeration of the available long-time solutions of the model and close comparison to the experimental results is lending coherence to the experimental data, paving the way for a complete understanding of the cardiac tissue response and providing a test of the models. The researchers are also investigating close-loop feedback suppression of the observed bifurcation and are especially focusing on using knowledge of the intracellular calcium concentration in the control algorithm.The program will train undergraduate and graduate students, and post-doctoral associates within a horizontally and vertically integrated environment. In addition, they will be trained to work in teams where the unique background and expertise of each team member is needed to effectively tackle the research question, combining both experimental and theoretical approaches to quantitative science and engineering. The researchers are also involved with outreach to local middle schools to showcase the research to students and to work with teachers to develop related curricular materials.