CNCS Graduate Certificate Recipient

G. Martin Hall

Thesis Title: Control of complex behavior in cardiac muscle

Ph.D. Final Defense Date:  November 19, 1999

Ph.D. Dissertation Committee:

Daniel J. Gauthier (Chair)
Robert P. Behringer
Wanda Krassowska
Joshua E.S. Socolar
Roxanne P. Springer

Abstract:

The goal of this research program is to develop experimental methods for suppressing complex behavior in small pieces of cardiac muscle and attempt to generalize these methods to spatio-temporal disorganization in hearts during fibrillation. The general approach is to investigate methods developed by the nonlinear dynamics community for controlling complex behavior using small perturbations. This problem is of broad interest to physicists because the heart is a physical realization of a nonlinear system displaying complex spatio-temporal dynamics.

I explore the dynamics of cardiac muscle using an animal model testbed consisting of small pieces of periodically paced bullfrog. Understanding the behavior of small pieces of tissue is important for developing methods for controlling the observed behaviors as well as complex spatio-temporal dynamics observed in whole hearts. In this testbed I find alternans and bistability are common.

Using this testbed, I demonstrate experimentally feedback control of alternans, a behavior that is believed to be responsible for the genesis of fibrillation in whole hearts. To suppress alternans I use Time Delay Auto-Synchronization, a feedback scheme that compares the current behavior of the system to a previous one and adjusts a parameter to minimize the difference. I also demonstrate control with a restricted version of this protocol that only allows shortening of the pacing intervals.

I also use this simple testbed to demonstrate experimentally that it is possible to induce transitions between bistable dynamical states by injecting a single stimulus between paces. These transitions can be elicited by stimuli applied over a range of timing intervals. I observe both 1:1 to 2:1 transitions as well as two types of 2:1 to 1:1 transitions.

In an effort to understand how feedback control methods effect spatio-temporal disorganization, I apply feedback control to a fibrillating sheep atria in vivo. The controller observes the dynamics of the atria from a single location and occasionally stimulates the tissue at a nearby location. In preliminary experiments, I generally find that at each location on the atria the probability of any inter-activation interval is seemingly unaffected by application of control. However, in one case, I observe that control lengthens the average inter-activation interval.