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John Cain : Stabilization of Periodic Wavetrains in Excitable Media

Cardiac cells, like toilets, are excitable: Giving a sufficiently strong push to the handle of a quiescent toilet elicits a dramatic response (flush) followed by a gradual return to the resting state. Likewise, supplying a sufficiently strong electrical stimulus to a quiescent cardiac cell elicits a prolonged elevation of the membrane potential (an action potential).

Suppose that one end of an excitable fiber of cardiac cells is paced periodically. If the period is large, the generic response is a stable periodic wave train of the sort associated with normal, coordinated contraction of heart muscle tissue. Reducing the period (think "speeding up the heart rate") can cause the onset of an instability which can have devastating physiological consequences. Echebarria and Karma (Chaos, 2002) argued that if one attempts to stabilize the periodic wave train by using feedback control to perturb the pacing period, success can be achieved only within some small radius of the stimulus site. Those authors used a special case of the ETDAS control method that Dan Gauthier and Josh Socolar devised.

Here, I will offer an explanation as to WHY algorithms like ETDAS, applied locally, cannot achieve global results in this context. Then, I'll argue that it actually IS possible to stabilize the periodic wave train if the perturbations are chosen more carefully. While these findings may seem encouraging from an experimental or clinical standpoint, I will close by describing some recent work of Flavio Fenton which I believe is even more promising.

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