In cardiac tissue, beat-to-beat alternation of action potential duration (APD) is a warning sign of potentially serious pathologies. When APD alternans is detected, it is desirable to coax the tissue back to a normal rhythm in which APD has little beat-to-beat variation. Mathematically, this is can be accomplished by applying feedback control to stabilize an unstable equilibrium near a periodic (or chaotic) orbit. Clinically, it is accomplished by applying well-timed electrical stimuli via a medical device such as a pacemaker. Such device intervention can be implemented in several ways, two of which are point stimulation and far-field pacing (FFP). In point stimulation, the device applies spatially localized stimuli through the tip of an electrode, whereas in FFP, large plate electrodes apply pulsed electric fields pulses across the entire heart. FFP creates “virtual” electrodes within the tissue by depolarizing or hyperpolarizing cells near the boundaries of non-conducting obstacles (e.g., dead tissue) and, if the field strength is strong enough, propagating action potentials can emanate from these obstacles. Point stimulation has the advantage of straightforward experimental or clinical implementation, but FFP is far more successful in correcting whole-heart dynamics while reducing discomfort to the patient.

In this paper, we present preliminary findings on the use of a particular feedback control algorithm (extended time-delay autosynchronization, ETDAS) for timing the stimuli of both point stimulation and FFP, with the goal of terminating alternans and other abnormal rhythms. ETDAS is more robust than its predecessors, and has an added flexibility that makes it less sensitive to background noise in APD measurements. We begin by analyzing the use of ETDAS to terminate alternans in “zero dimensional” tissue (i.e., a single cell or tiny patch of cells), a useful test case for predicting parameter regimes under which control is most likely to succeed. Next, we report on the use of ETDAS to automate the timing of point stimulation to control alternans in “one-dimensional” fibers of cells joined end-to-end. Past attempts to use point stimulation to terminate alternans in fibers have been met with limited success, but were built upon weaker control algorithms and less realistic models of the action potential. Finally, we report preliminary findings regarding the use of ETDAS to time the intervention of both point stimulation and FFP in simulations of two-dimensional sheets of tissue.

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Copyright © 2012 WSEAS Press. This proceeding first appeared in Mathematical Models and Methods in Applied Sciences.

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