Abstract.

An algorithm based on Chaos Theory for beat-to-beat time series analysis is here presented. Its application has revealed a continous change in a certain ratio along process of cardiac failures with abrupt changes.

See also Chaos Theory: Applications in Cardiology or Teoria del Caos: Aplicaciones en Cardiologia

Keywords: ventricular and atrial fibrillation, arrhythmia, sudden death, monitoring post-infarction patiens with high risk of cardiac arrest, heart rate patterns, flat pattern, white noise pattern, photoplethysmographic sensor, beat-to-beat interval and relative blood pressure variation, Late Potentials Analysis.

1. INTRODUCTION.

There are several cardiac failures such as ventricular and atrial fibrillation responsive to different aetiology. In order to prevent cardiac arrest and sudden death, it is very interesting the accurate valuation prior to fatal denouement, so rendering possible the preventive monitoring of subjects (e. g. post-infarction patiens with high risk of cardiac arrest). In this sense a research equipment directed by A. L. Goldberger [4] has reported one abnormal heart rate (flat pattern) for which we are found a case described below in which the "flat pattern" changes into "white noise pattern" whereas a "autocorrelation-like ratio" shows a great progessive variation and in great advance in time [1][2][3].

2. BRIEF METHOD DESCRIPTION.

Beat-to-beat time series are obtained by monitoring patients with a spetial photoplethysmographic sensor conected to an interface that sends to PC a time serie containing information at the same time on beat-to-beat interval and relative blood pressure variation. The relativity of blood pressure measuring is untranscendent because Chaos Theory so indicates it with regard to the topologic reconstruction of strange attractors. The time series obtained in this way are processed by an algorithm based on Chaos Theory which first calculates an autocorrelation-like for different temporal increments and then obtains the linear regression and correlation for all the autocorrelations-like values, that are called "logarithmic correlation"[5][6][7][8][9][10].

3. RESULTS.

The last ratio (logarithmic correlation), explained above, for healthy people reveals values within 0.99--0.80 range and a spectrum 1/f-like (fig. 1). This ratio decreases quickly with aging. We have found a case of "flat pattern" (fig. 2) prior to denouement of atrial arrythmia. Five months prior arrythmia, the "logarithmic correlation average" revealed a value of 0.27 (fig. 3). After denouement of atrial arrythmia the spectrum changes abruptly (fig. 4), but in the meantime "logarithmic correlation average" decreases progressively (fig.5).

4. CONCLUSSION.

This method is showing itself very suitable to the exact valuation of risk of cardiac failures, in particular to the post-infarction patiens. In future this method is possible that it could become better than the Late Potential Analysis.

ACKNOWLEDGEMENT.

We wish to thank A. Agudo Catalán for the program implementation and monitor design. We also thank the other people that so kindly did the monitoring test.

REFERENCES.

[1] "L'ordre dans le chaos." ;P. Berge y otros, Hermann, 1.984.

[2] "Chaotic Dinamics of non linear systems." ;Rasband, Jhon Wiley & Sons, 1990.

[3] "El caos en Biologia." ;R.M. May, Mundo Cientifico, vol. 115, 1991

[4] Proceedings ofthe 1st Experimental Chaos Conference. ;October 1-3 ,1991. Arlington, Virginia

[5] "La variabilite sinusale: inter8t en rithmologie." ;J.Y. Le Heuzey. Arch Mal Coeur, 1992:85(IV): 37 - 43

[6] "Patterns of beat - to - beat heart rate variability in advanced heart failure." ;Mary A. Woo y otros. Americal Hearth Journal, March 1992.

[7] Fascinating rhythm: A primer of chaos theory and its application to cardiology. Timothy A. Denton y otros. Americal Hearth Journal, December 1990.

[8] "Cardiac excitability, the Electrophysiologic Matrix and Ellectrically Induced Ventricular Arrhythmias: Order and Reproducibility in Seeming Electrophysiologic Chaos." Morton F. Arnsdorf. JACC Vol. 17 Nø 1, January 1991.

[9] "Low Dimensional Chaos in cardiac tissue." ;Dante R. Chialvo y otros. Nature, Vol. 343, 15 Febrary 1990.

[10] "Controlling Cardiac Chaos.", Alan Grfinkel y otros. Science, Vol. 257, 28 August 1992.