Brian C.

I decided to research the applications of chaos in the healthcare field. As of yet, there is little actual usage of chaos in the field (but there is some), although there is much research currently being conducted. I plan on focusing most of the research on heartcare (as the majority of available information pertains to the heart), but will also discuss briefly other applications.
Tentative Outline
Title: Under the Care of Your… Chaostician?
I. Traditional Medicine vs. Chaotic Medicine
1. Controversy
2. Conflicting Generations of Doctors
II. Overview of Various Uses of Chaos in Healthcare
1. Brain Treatments
2. Treatments of other Various Diseases such
as Epilepsy
3. Heart Treatments
III. Present and Potential Uses of Chaos for the Heart
1. Heart Arythmia
2. Heart Disease
3. Possible Display of Heart Rates before and
after Chaotic Therapy
IV. Conclusion, What's to Come


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Brian Concannon
Dr. DiDio
Honors Chaos and Fractals
December 2007
Under the Care of your… Chaostician?
I. Traditional Medicine vs. Chaotic Medicine
Amidst a time in the medical realm when new research augments the pool of information almost daily, doctors are finding themselves in a position where it’s sometimes hard to stay afloat—especially when medical practices they have previously learned and accepted are being challenged by new discoveries. Presently, over 400,000 biological science research papers are being produced each year; or, in other words, over 1,000 new papers each day. Perhaps, then, it is for this reason that the integration of non-linear dynamics (chaos theory) and medicine has not come to the attention of millions of doctors until recently (if at all)—despite the fact that articles on the subject began being produced nearly twenty years ago! Back in 1988, Ary L. Goldberger and David R. Rigney wrote an article entitled “Sudden Death Is Not Chaos” that offered counterintuitive insight about the sinus-rhythm heart-rate patterns of healthy individuals and those whom cardiac arrest imminently awaits. In recent years, it is their exact findings that have surfaced in the medical industry—this time leading to applicable results in healthcare.
When Stuart Davidson, a renowned medical journalist, was asked what he felt chaos had to do with healthcare, he responded with a single word: “everything.” Traditionally, chaos, which can be described as “locally unpredictable order existing in a deterministic system that obeys simple equations,” has been thought of as a collection of mathematical theories used for mathematical purposes—a self-contained subject. However, the scope of non-linear dynamics has moved beyond pure mathematics and into various fields including that of biological science. As a result of the research by a select few specialists (and the research papers they have published), chaos theory is now beginning to be recognized as a “real phenomenon”, and not simply ‘mathematics for the sake of mathematics’.
Despite the increasing amount of recognition given to chaos theory, the application of the research into healthcare is ultimately dependent upon the nation’s doctors. Those who begin to assess the relevance of non-linear dynamics in biomedicine must overcome a series of mathematical jargon, such as “non-linearity, fractals, periodic oscillations, bifurcations, and complexity.” There is presently great potential in treating heart and brain diseases utilizing the available research, but before this can be done, the jargon must be understood. Recognizing the dilemma, Ary Goldberger, Harvard’s noted professor of cardiology, wrote an article entitled “Non-linear dynamics for clinicians: Chaos theory, fractals, and complexity at the bedside” that ‘decoded’ some of the mathematical language in an attempt to promote awareness and understanding of the possible applications of chaos in medical practice.
Before understanding the applications, perhaps the most important thing to realize is that chaotic systems differ greatly from linear ones. Linear systems are completely predictable. The magnitude of the output of a linear system is directly proportionate to the magnitude of the input. Furthermore, linear systems can be viewed as individual sub-units which each contribute a predictable part to the whole. In contrast, non-linear systems follow a different set of rules—rules which can be taken advantage of within medicine since the human body is non-linear. The input into the system certainly does not yield proportionate output. In fact, small changes can lead to astronomically disproportionate results. As would be expected then, it offers no insight to analyze non-linear systems by their individual components due to the fact these individual components interrelate. Such examples would be the interaction between pacemaker cells in the heart or the communication of neurons within the brain. Modeling a single neuron or pacemaker cell reveals insignificant results about the whole. It is the collective relationship which yields results and these cannot be modeled using linear techniques. As Goldberger puts it, “non-linear coupling generates behaviors that defy explanation by traditional (linear) models such as self-sustained, periodic waves (eg. ventricular tachycardia); abrupt changes (eg. sudden onset of a seizure); and, possibly, chaos.” The utilization of non-linear dynamics offers possible solutions.
Now, before delving into the analysis of the “self-sustained periodic waves” and “abrupt changes” to understand how non-linear dynamics can be used to treat heart conditions and epilepsy respectively, it is first a must to understand bifurcations and fractals. Bifurcations make up a specific class of abrupt non-linear transitions. They can be witnessed in systems which change suddenly from one type of behavior to another. The rapid development of periodicity (such as oscillations that alternate between two values) is a frequent type of bifurcation. Up until the late 1980s, it was thought that the sinus rhythm of the heart exhibited such characteristics as periodicity, and that chaotic fluctuations were the result of “pathological systems such as cardiac electrical activity during atrial or ventricular fibrillation.”
…to be continued

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