DURHAM, N.C. -- Sensing that irregular heartbeats may be examples of "controllable" chaos, an interdisciplinary team of Duke University researchers is investigating whether the latest ideas in chaos suppression might lead to improved treatments of arrhythmia in heart muscle.
Funded with a Whitaker Foundation grant, assistant physics professor Daniel Gauthier and colleagues at Duke's physics department and School of Engineering will test an alternative to published methods that have briefly stabilized seemingly chaotic oscillations in experimental nerve cell and heart preparations.
The Duke investigators are starting out with comparatively simple studies of frog and earthworm nervous systems, they said in interviews. But their ultimate goal is better devices to correct maladies like "atrial fibrillation," the loss of control in the heart's upper chambers.
While the dictionary defines chaos as complete disorder and randomness, scientists using tools ranging from computers to pencil and paper have learned that chaos can secretly harbor some regularity.
Such embedded order can be revealed, for example, by analyzing chaotic electronic circuits where currents appear to oscillate with total irregularity. Hidden patterns of stability may show up when the circuit's convolutions are plotted out as points on a "state-space" diagram, a kind of graph revealing how a system changes from moment to moment.
If the circuit system were stable, the points would trace out regular orbiting lines that constantly overlap themselves, signifying that an identical cycle is repeating itself over and over. Since the circuit is instead chaotic, its state-space representation forms more convoluted orbits that never exactly overlap each other.
Nevertheless, if those chaotic orbits almost overlap in places, then the system can be said to exhibit nearly regular behavior for short periods of time. And, in 1990, University of Maryland researchers Edward Ott, Celso Grebogi and James Yorke -- sometimes abbreviated "OGY" -- proposed a scheme to exploit that hidden regularity and thus "control" chaos.
The OGY approach is to first cut a cross section through a state-space diagram to better visualize differences in the system's past orbits. By analyzing these previous orbital changes, scientists can select one that looks particularly stable. Then they can nudge the system back onto the targeted orbit and keep it there by applying weak currents or other stimuli.
While most chaos-taming experiments to date have employed this scheme, the OGY method is too time consuming or otherwise demanding to work well with some chaotic systems, said Gauthier and fellow Duke assistant physics professor Joshua Socolar. So they and graduate students David Sukow and Hope Concannon used a technique that departs significantly from OGY in research published in the September 1994 edition of the journal Physical Review E.
That report announced success at stabilizing chaos in an electronic circuit called a fast diode resonator using what Gauthier and Socolar called a "continuous-feedback scheme." They said continuous feedback is superior to OGY in controlling chaos in very high-speed electronic circuitry.
Gauthier and Socolar also suspect their technique can better address the special problems of chaos in biological systems -- their ultimate research goal. Both are participants in Duke's Center for Nonlinear and Complex Systems, an interdisciplinary faculty group that studies chaos and related phenomena.
"In all schemes that adapt OGY, you first have to find the state that you want to stabilize," said Gauthier, the principal investigator for the Whitaker grant. "We realized that if we are going to try to control chaos on a fast-time scale we would be hard pressed to accurately measure the state we're trying to stabilize and hold onto that in computer memory while we do the computations."
In biological systems, the problem is not speed but uncertainty, he added. "It is difficult to uncover regular orbits in the dynamics that can be measured in the heart. In our system, we just assume such orbits exist and try to design a feedback protocol to stabilize the orbits."
Through a process called "time delay autosynchronization," Socolar said, "we use the system's behavior in the recent past as a reference." With small infusions, or "feedbacks" of energy, the system is constantly synchronized with the state it was in approximately one orbital period in the past.
Gauthier hypothesizes their method should also be able to automatically track changing dynamics in the heart when, for instance, a person switches from sitting to jogging.
Socolar, a theoretician, originally helped Gauthier, a laser specialist, devise this control strategy to stabilize the chaos that can erupt in high-speed lasers. Though their work was independent, they also credited Kestutis Pyragus, a Lithuanian researcher, for a 1993 Physical Letters A article on a similar method.
"We were actually considering biological applications almost from the beginning," Socolar stressed. "But we pursued the electronic and laser work first because it allows for cleaner experiments and theories."
Their research into lasers and high-speed circuits continues with funding from the U.S. Army Research Office, the U.S. Air Force's Phillips Laboratory, and the National Science Foundation.
Meanwhile, with the Whitaker grant, Duke researchers have joined other U.S. groups studying the even more difficult problem of chaos control in unstable biological systems.
Experiments at UCLA School of Medicine already have shown that apparent chaos can be controlled in rabbit heart muscle after a drug has caused it to beat erratically. Other studies at the Children's National Medical Center in Washington have produced similar results in rat nerve cell preparations exposed to drugs that produce epileptic-like convulsions.
Each set of experiments used variations on the OGY method. And two well-known chaos control pioneers, William Ditto of Georgia Tech and Mark Spano of the Naval Surface Warfare Center in Maryland, participated in both studies.
In an article in the journal Nature, the rat-nerve-research team's lead author, neurosurgeon Steven Schiff, also acknowledged the "invaluable teaching and advice" of Peter Aitken, a Duke associate research professor of cell biology.
Gauthier concludes that Duke also is excellently placed to study chaos in animals, given the university's high rankings in medical research and biomedical engineering, as well as its expertise in chaos theory.
Controlling chaos in the heart won't be easy, added Patrick Wolf, a Duke assistant biomedical engineering professor who will work with Gauthier and other Whitaker-funded team members. "I would say there's a 20-percent chance this will work, maybe even less than that," he acknowledged.
Working at the Duke-National Science Foundation Engineering Research Center for Emerging Cardiovascular Technologies, Wolf has spent years studying the complex waves of electrical activity that spiral through the arrhythmic hearts of laboratory animals. He maps the waves with the aid of computers and sophisticated monitoring systems.
He said he believes, along with Gauthier and Socolar, that the earlier control work at UCLA did not really duplicate the complexities within an intact dysfunctional heart. Those experiments instead used only tissue samples. Moreover, the study dealt only with "temporal" chaos -- that which expresses itself as change over intervals of time, Gauthier said.
But heart arrhythmias involve bewildering changes over space as well as over time, as irregular currents ripple across the organ's surface. "There are so many parameters that we can't possibly know them all," Wolf said.
So Socolar and his graduate student Michael Bleich have been studying whether continuous feedback can be used to control spatial as well as temporal chaos. They've found some evidence that it can in non-biological systems such as wide-aperture semiconductor lasers -- devices where spatial incoherence limits performance.
But Socolar is still far from certain about its application to biology because their method requires continuous electrical feedbacks to all parts of the system. "That may be impractical for the heart," he acknowledged.
Complicating the problem, after each heart muscle cell fires a burst of energy it must go through a quiet recovery period when "the effects of any stimulus are limited," Socolar added.
So the research has begun with simpler animal systems that Gauthier said he hopes will mimic the heart's electrical activity but lack its spatial complexity. With help from Wanda Krassowska, another Duke assistant professor of biomedical engineering, Gauthier and others have learned how to measure electrical currents in the nerve cells of frogs and earthworms.
Krassowska, who studies electrical stimulation of the heart, said she received additional support for that collaboration from the Lord Foundation. She decided to join the project because "I was in search of new methods, and he (Gauthier) was open for new applications," she added.
Plans are for the experiments to eventually include higher animals and to zero in on the atria, the upper heart chambers that Wolf believes are especially conducive to stabilization. Right now, atrial fibrillation can be controlled by applying large jolts of electricity, he said. There are even implantable devices undergoing approval by the Food and Drug Administration.
But big jolts can also induce fibrillation in the heart's lower chambers -- the ventricles -- and ventricular fibrillation can quickly lead to death. "That's what makes Dan Gauthier's idea attractive," Wolf said.
If atrial fibrillation embodies chaos that can be reversed with small electrical feedbacks, "you'd still have to deliver a shock, but it can be just a little one," Wolf added. "Presumably, it wouldn't be capable of causing ventricular fibrillation. So it would be inherently safer."
A big nagging question is whether the three identified types of atrial fibrillations are really examples of chaos. "I think the jury is still out," Wolf acknowledged. "And, for these different kinds of fibrillation, I think you're going to get different answers."
"If you look at the electrical patterns traversing the atria in a fibrillation, it looks chaotic to me," he said. "Mechanically, if you look at it, it's just sitting there quivering."
But Wolf said he and Duke undergraduate Shawn Spicer are just beginning to do state-space studies to look for classic patterns of chaos. So far, "If they're there, they're hidden," Wolf said.