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Applied Math for the Heart; Take a few PDEs and call me in the morning.

The heart is an electro-mechanical system in which, under normal conditions, electrical waves propagate in a coordinated manner to initiate an efficient contraction. In pathologic states, single and multiple rapidly rotating spiral and scroll waves of electrical activity can appear and generate complex spatiotemporal patterns of activation that inhibit contraction and can be lethal if untreated. Despite much study, many questions remain regarding the mechanisms that initiate, perpetuate, and terminate reentrant waves in cardiac tissue.

In this talk, we will discuss how we use a combined experimental, numerical and theoretical approach to better understand the dynamics of cardiac arrhythmias. We will show how mathematical modeling of cardiac cells simulated in tissue using large scale GPU simulations can give insights on the nonlinear behavior that emerges when the heart is paced too fast leading to tachycardia, fibrillation and sudden cardiac death.  Then, how we can use state-of-the-art optical mapping methods with voltage-sensitive fluorescent dyes to actually image the electrical waves and the dynamics from simulations in live explanted animal and human hearts (donated from heart failure patients receiving a new heart).  I will present numerical and experimental data for how period-doubling bifurcations in the heart can arise and lead to complex spatiotemporal patterns and multistability between single and multiple spiral waves in two and three dimensions. Then show how control algorithms tested in computer simulations can be used in experiments to continuously guide the system toward unstable periodic orbits in order to prevent and terminate complex electrical patterns characteristic of arrhythmias.  We will finish by showing how these results can be applied in vitro and in vivo to develop a novel low energy control algorithm that could be used clinically that requires only 10% of the energy currently used by standard methods to defibrillate the heart.

Overall, I will present recent advancements in identifying and quantifying chaotic dynamics in the heart, beginning with mathematical models and extending to experimental validation. This work demonstrates how applied mathematics enables the development of innovative methods to control and terminate arrhythmias, with promising potential for clinical applications.