Zipf's Law of Vasovagal Heart Rate Variability Sequences.

Jacques-Olivier Fortrat

doi:10.3390/e22040413

Abstract

Cardiovascular self-organized criticality (SOC) has recently been demonstrated by studying vasovagal sequences. These sequences combine bradycardia and a decrease in blood pressure. Observing enough of these sparse events is a barrier that prevents a better understanding of cardiovascular SOC. Our primary aim was to verify whether SOC could be studied by solely observing bradycardias and by showing their distribution according to Zipf’s law. We studied patients with vasovagal syncope. Twenty-four of them had a positive outcome to the head-up tilt table test, while matched patients had a negative outcome. Bradycardias were distributed according to Zipf’s law in all of the patients. The slope of the distribution of vasovagal sequences and bradycardia are slightly but significantly correlated, but only in cases of bradycardias shorter than five beats, highlighting the link between the two methods (r = 0.32; p < 0.05). These two slopes did not differ in patients with positive and negative outcomes, whereas the distribution slopes of bradycardias longer than five beats were different between these two groups (−0.187 ± 0.004 and −0.213 ± 0.006, respectively; p < 0.01). Bradycardias are distributed according to Zipf’s law, providing clear insight into cardiovascular SOC. Bradycardia distribution could provide an interesting diagnosis tool for some cardiovascular diseases.

Highlights

Complexity, the final frontier of the cardiovascular system, has emerged as a major topic over the last decade
The slope of the distribution of vasovagal sequences and bradycardia are slightly but significantly correlated, but only in cases of bradycardias shorter than five beats, highlighting the link between the two methods (r = 0.32; p < 0.05). These two slopes did not differ in patients with positive and negative outcomes, whereas the distribution slopes of bradycardias longer than five beats were different between these two groups (−0.187 ± 0.004 and −0.213 ± 0.006, respectively; p < 0.01)
The blood pressure decrease is not compensated by an increase of the heart rate as expected due to blood pressure homeostatic regulatory mechanisms

Summary

Introduction

Complexity, the final frontier of the cardiovascular system, has emerged as a major topic over the last decade. It became more and more difficult to integrate it into the current view of cardiovascular physiology that is largely dominated by the deterministic homeostatic principle According to this principle, physiological variables are regulated and maintained at their normal values thanks to negative feedback regulatory loops. We showed that occurrences of spontaneous vasovagal events are distributed according to Gutenberg Richter’s law This law has been initially described in earthquakes occurrences: the magnitude plotted against the total number of earthquakes of at least this magnitude draws a straight line on a log-log graph. This finding explained how vasovagal reaction may occur.

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