J. L. Subias.

November 2, 1992.

Keywords: fenotiazines, schizophrenia, tricyclic antidepressants, immune system, leukemia, risk of sudden death, arrhythmia.

See also Evaluating cardiac failures risk

1. INTRODUCTION.

The alive beings possess biorhythms that, in normal conditions of good health, fluctuate in a complex and seemingly random way. Many researchers have dedicated his efforts to elucidate whether in these biorhythms a deterministic chaos underlies or it is simply random noise, understood these concepts in physical mathematical sense. And this way, electroencephalographic waves, electrocardiographic waves, fluctuations of the immunological system have been an object of study and, likewise, other many biorhythms present in the human and animal physiology.

At present, it seems that researchers agree most biorhythms are chaotic, although not exempt from a certain factor of random noise. Precisely, it is this chaos ratio what provides, in case of being quantifiable, a more exact evaluation of the state of health or illness and a diagnosis and prognosis which would not be possible by other means of the traditional Medicine.

In the following work, there is described a method of analysis that allows to detect with large anticipation certain pathological alterations of the cardiac human dynamics.

2. ANALYSIS OF HUMAN HEART AS A DYNAMICAL SYSTEM.

After this brief preamble, it going to exhibit a research line, opened for a concrete application of Chaos theory: the dynamic analysis of human heart (here we use the dynamic term in a physicist - mathematician sense).

Fundamentally, the mathematical analysis method that here is proposed, it considers the human heart as a chaotic dynamic system. Stating this hypothesis was the previous phase, already overcome, in which by means of a semiempirical method, the chaotic dynamics of human heart was established, with a few coefficients of correlation of 0.995 in the most favorable cases and of 0.802 in the most unfavorable.

As soon as this previous phase was overcome, the implications on the classic medicine may be momentous. According to the homeostatic principle [2], doctors have interpreted fluctuations of cardiac rhythm as transitory responses in an attempt of adaptation of this organ to the changeable situations for which the individual crosses in his daily activity. This way it was surmised that the cardiac rhythm will tend to become stable in a constant rule when, in a individual in rest, cessation all kinds of circumstantial perturbation, supporting, in this way, a constant of internal functions.

This theory, initially developed by Walter B. Cannon in Harvard University [2], stays in doubt for realized essays, of which it is deduced, that in entire absence of stimulus, the heart is intrinsically chaotic, his rhythm is always irregular, and it possesses a strange attractor, whose mathematical analysis allows to realize prognoses that are completely away from the scope of classic tests, as the E. K. G.

On this research line, precedents exist in the Harvard University, the Hospital Beth Israel of Boston and Massachusetts Institute of Technology [2].

The following are eloquent examples of this technique.

On the following figures, it will appreciate two different representations of cardiac rhythm from each individual. These two cases have been described by a interdisciplinary research team in the University of Saragossa. Similar results were stated by A. L. Goldberger, teacher of medicine in Harvard University, D. R. Rigney, teacher of medicine in Harvard University and researcher of the M. I. T., B. J. West, president of the physics department of the North of Texas University, [2].

The first case corresponds to a cardiac patient. His cardiac rhythm is represented by time serie (figure1), it charts of spectral analysis (figure 2), and delayed map (phase portrait, figure 3). Five months after this analysis patient suffered a episode of ventricular atrial arrhythmia. It be observed that spectral diagram is "flat", which denotes incapability of heart to answer to a scale of requests excessively diversified, as it happens in the daily life. On the other hand, attractor in phase space is almost a " fixed point ".

The second case corresponds to a healthy individual. There are represented the same three graphs as in the previous case. It be observed that the spectral diagram is bristled of " spikes ", what denotes an enormous wealth of rhythms of different frequency and therefore a great capability of response to the environmental requests. In the phase space, it appreciates a real " strange attractor ", whose fractal dimension, numerically estimable, is foreseeable that would be larger than previous case.

2.1 An important point: instrumentation and data acquisition.

Heart rate frequency is not sufficient for characterizing dynamic state of heart. Also it is necessary a second important variable: blood pressure. Exist a variability as for heart rate as for blood pressure. The problem is that, for detecting the latter, it is needed to measure blood pressure beat-to-beat. This is difficult, if one try to measure blood pressure in concrete units (for example, in mm. of  Hg). But it is more easy, if one measures pressure in relative manner, without calibrate corresponding transducer. Mathematical formulation of Chaos Theory guarantees that phase space reconstruction is possible if one replaces a variable by other depending of that. Therefore phase portrait reconstruction is possible if one replace traditional measure of pressure (in units, for example, mm. of Hg) by a relative estimation of pressure beat-to-beat. In this work, it was used a device specially designed for simultaneously recording heart rate frequency and blood pressure, beat-to-beat.

Fig. 2.1 Heart rate frequency is itself insufficient for characterizing dynamic state of heart.

Also it is necessary blood pressure. Device here schematized, it was specially designed for simultaneously recording heart rate frequency and a estimation of blood pressure, beat-to-beat. For details, click here: High resolution Tensio-ElectroCardiograph

3. OTHER AREAS OF APPLICATION IN MEDICINE.

The chaotic dynamics is, in the nature, much more frequent than could suggest the fact of being CHAOS a strictly physical - mathematical theory.

Continuing in the field of the Medicine, it is necessary to point out that the heart is not the only object of study across the prism of this theory. Also the brain in his activity generates waves with a underlying strange attractor that can characterize certain mental illnesses or the propensity to suffer them, [2], [3]. On the other hand the immune human system is a delicate and complex dynamical system that can oscillate over a " limit cycle " in response to certain "perturbations" as the leukemia, [2]. Also the enzymes and hormones are subject to the chaotic dynamics. Some of them are determinants of the frame of mind. Recent studies demonstrate that the fenotiazines worsen the fundamental mental disorder of the schizophrenia and the antidepressants" increase the speed of cycle of frames of mind, and, in long term, lead to increase number of psychopathologycal relapsing ", [1].

Every day new and surprising works are published in specializing journals in Medicine on chaotic dynamics. Perhaps the most eloquent phrase about this new theory can represent for the Medicine, Ary L. Goldberger expressed in this way: " In 1986, the word "fractal" is not on books of Physiology. Nevertheless I am sure that, in 1996, there will not be one which it did not appear on", [1].

4. CONCLUSIONS.

The conclusions that are deduced of present work are the following:

a) The correlation of the cardiac dynamics with regard to the chaotic dynamics is ideally 0.995 and at the worst 0.802, for healthy individuals.

b) The sensibility of this type of analysis is big, since the results obtained for different persons are notably different.

c) The grade of significance is high and the factor of " random noise " is low, since several tests realized on the same person produce not numerically exact results, but very approximate. Here it is necessary to point out that the principal objection that critiques put to other research works of the same type is, precisely, that the results contain a considerable proportion of " random noise ", which become unreliable by, [3].

BIBLIOGRAPHY AND REFERENCES.

" The Science of Fractal Images", M.F. Barnsley y otros, Springer-Verlag, 1.988.

"Los objetos fractales. Forma, azar y dimensión", B.B. Mandelbrot, Tusquets editores, 1.984.

[1]" CAOS: la creación de una ciencia", J. Gleick, Seix Barral, 1.988.

[2] "Caos y fractales en la Fisiología humana", A.L. Goldberger y otros, Investigación y Ciencia, vol. 163, 1990.

[3] "El caos en Biología", R.M. May, Mundo Científico, vol. 115, 1991