Natural Time Analysis of Electrocardiograms

Abstract

Here, we present the results obtained from the natural time analysis of electrocardiograms. Considering that a general agreement about whether normal heart dynamics are chaotic or not is still lacking, and that a physiological time series may be due to a mixed process, stochastic and deterministic, we use here the concept of entropy which is equally applicable to deterministic as well as stochastic processes. Sudden cardiac death is a frequent cause of death and may occur even if the electrocardiogram seems to be strikingly similar to that of a healthy individual. Upon employing, however, the fluctuations of the entropy in natural time, when a time window of certain length is sliding each time by one ``pulse{''} (heartbeat) through the whole time series, sudden cardiac death individuals (SD) can be clearly distinguished from the truly healthy individuals. Furthermore, by using the complexity measures introduced in 3.6.1 to quantify the change of the natural entropy fluctuations either by changing the time window length scale or by shuffling the ``pulses{''} randomly, we can achieve the classification of individuals into three categories: healthy, heart disease patients and SD. In addition, when considering the entropy change under time reversal, at certain time window length scales (which have a clear physical meaning), not only can the SD risk be identified, but also an estimate of the time of the impending cardiac arrest can be provided. In particular, after the maximization of the amplitude of Delta S at the scale of 13 heartbeats, ventricular fibrillation starts within approximate to 3 hours in 16 out of 18 SD. Finally, an 1/f model is proposed in natural time which leads to results that are consistent with the progressive modification of heart rate variability in healthy children and adolescents. The model results in complexity measures that separate healthy dynamics from heart disease patients as well as from SD.