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Research aims to separate noise from chaos in subtle heart rhythms

The subtle rhythms of the heart are being studied closely by MIT scientists, who are applying techniques used in mathematics and physics to prevent heart arrhythmia and sudden cardiac death.

Research led by Dr. Chi-Sang Poon, principal research scientist in the Harvard-MIT Division of Health Sciences and Technology (HST), investigates the seemingly indistinguishable rhythms of healthy and diseased hearts to identify people at risk for cardiac disease. In their most recent findings, Poon and his colleague, former graduate student and postdoctoral associate Mauricio P. Barahona (Ph.D. 1996), now at Stanford University's Ginzton Laboratory, further demonstrate that subtle heart-rate variabilities are not simply random fluctuations, but are complex yet deterministic patterns that are probably chaotic.

In a paper published in the June 19 issue of the Proceedings of the National Academy of Science, Poon confirmed his previous finding that a weakly chaotic signal might be more susceptible to noise than a strongly chaotic signal and that it would be more likely to indicate congestive heart failure.

In earlier studies published in 1997, Poon and Christopher K. Merrill (S.B. 1996) discovered that heart disease actually makes the heart beat less chaotically. Paradoxically, that means an orderly and regular heartbeat might indicate heart disease. Instead of looking for correlations in beat patterns, they analyzed the long sequence of beat-to-beat intervals with a sophisticated mathematical procedure used to detect the signatures of chaotic signals. Poon and Merrill proposed the use of these analytical methods in nonlinear dynamics to detect and diagnose congestive heart failure.

These techniques contributed to Poon and Barahona's latest findings, which show that the intensity of chaos can be measured by its so-called titration strength against added noise. An analysis technique commonly used in chemistry, titration determines a reaction's end point and the precise quantity or concentration of an unknown reagent--a substance used in chemical reactions to detect, measure, examine or produce other substances. Titration is achieved using a standard concentration of a known reagent that reacts with the unknown reagent.

Typically, we experience noise as unwanted static on electronic devices, but in this case, noise refers to the random, purposeless fluctuations in signal patterns. Although noise is not a chemical reagent, in Poon's investigations, it is used as a reagent to achieve numerical titration.

According to Poon, measuring titration strength against added noise is analogous to measuring the strength of an acid by how well it can be titrated against a strong alkaline. His latest research verifies this "litmus test" analogy, and confirms his earlier work that the decrease of heart-rate variability in patients with congestive heart failure is due to a decrease of cardiac chaos.

Poon believes that the numerical titration method detailed in the recent article can be applied to problems in almost any physical, biomedical and socioeconomic system that exhibits chaos--including the identification and control of cardiac arrhythmia, epileptic seizures or other biomedical variables; the analysis and forecasting of geological, astrophysical or economic data; and even unmasking chaotically encrypted communications signals.

"The numerical titration procedure is a simple yet powerful procedure to track the changes of chaotic dynamics in any signal," he said. "When applied to the analysis of heart-rate variability, it provides an inexpensive and noninvasive means to detect and assess cardiac chaos in heart diseases such as congestive heart failure. The available data suggest that a decrease in heart-rate chaos might indicate a poor prognosis."

Poon also pointed out another important feature of the titration method. "When one fails to detect chaos, or even nonlinear dynamics, in experimental data, it doesn't necessarily mean that the system isn't chaotic. The background noise might be so high that chaos in the signal is totally covered by the noise. Our research clarifies this issue and explains why chaos might be obscured by noise. It solves the longstanding issue of separating chaos from additive noise.

"Although many methods are available to distinguish purely chaotic signals from purely random signals, until now there was no method to reliably detect chaos contaminated by noise. This is a severe limitation because virtually all empirical data suffers from some degree of noise corruption. The titration method is the only method that can identify chaotic dynamics in noisy data. It not only goes further than simply giving sufficient proof of whether or not chaos is present, but it also quantifies the strength of the chaos. Thus, it is a quantitative method rather than just a qualitative one."

Poon acknowledged that the most challenging part of this research was conceiving the idea and then communicating it to others. "This is the kind of research where either you see it or you don't. It's like an apple falling to the ground. You see it happen all the time, but it never occurs to you that it could mean something big, if anything at all. When we tell people about our results, their first reaction is often, 'Is that it? What's new? Hasn't that been said before?'"

Looking to the future, he said, "The next big issue is the phenomenon of stochastic chaos--high-order complexities that arise when noise and nonlinear dynamics interact nonlinearly, not just additively."

This research is supported by the National Science Foundation and the National Institutes of Health.

A version of this article appeared in MIT Tech Talk on August 29, 2001.

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