{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T15:41:17Z","timestamp":1778859677541,"version":"3.51.4"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,6]],"date-time":"2020-04-06T00:00:00Z","timestamp":1586131200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019s 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\u2019s 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 &lt; 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 (\u22120.187 \u00b1 0.004 and \u22120.213 \u00b1 0.006, respectively; p &lt; 0.01). Bradycardias are distributed according to Zipf\u2019s law, providing clear insight into cardiovascular SOC. Bradycardia distribution could provide an interesting diagnosis tool for some cardiovascular diseases.<\/jats:p>","DOI":"10.3390\/e22040413","type":"journal-article","created":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T03:58:39Z","timestamp":1586231919000},"page":"413","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Zipf\u2019s Law of Vasovagal Heart Rate Variability Sequences"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9272-0157","authenticated-orcid":false,"given":"Jacques-Olivier","family":"Fortrat","sequence":"first","affiliation":[{"name":"UMR CNRS 6015 Inserm 1083, Centre Hospitalier Universitaire Angers, 4 Rue Larrey CEDEX 9, 49933 Angers, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Struzik, Z.R. (2014, January 25\u201328). Is heart rate variability dynamics poised at criticality?. Proceedings of the 8th Conference of the European Study Group on Cardiovascular Oscillations (ESGCO), Trento, Italy.","DOI":"10.1109\/ESGCO.2014.6847599"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"031001","DOI":"10.1103\/RevModPhys.90.031001","article-title":"Colloquium: Criticality and dynamical scaling in living systems","volume":"90","year":"2018","journal-title":"Rev. Mod. Phys."},{"key":"ref_3","first-page":"R301","article-title":"How does homeostasis happen? Integrative physiological, systems biological, and evolutionary perspectives","volume":"316","author":"Goldstein","year":"2019","journal-title":"Am. J. Physiol."},{"key":"ref_4","first-page":"113","article-title":"Self-Organization of Blood Pressure Regulation: Clinical Evidence","volume":"7","author":"Fortrat","year":"2016","journal-title":"Front. Physiol."},{"key":"ref_5","first-page":"112","article-title":"Self-Organization of Blood Pressure Regulation: Experimental Evidence","volume":"7","author":"Fortrat","year":"2016","journal-title":"Front. Physiol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2997","DOI":"10.1161\/CIRCULATIONAHA.104.482018","article-title":"Neurocardiogenic syncope and related disorders of orthostatic intolerance","volume":"111","author":"Grubb","year":"2005","journal-title":"Circulation"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bak, P. (1996). How Nature Works: The Science of Self-Organised Criticality, Copernicus Press.","DOI":"10.1007\/978-1-4757-5426-1"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1007\/s10955-011-0229-4","article-title":"Are biological systems poised at criticality?","volume":"144","author":"Mora","year":"2011","journal-title":"J. Stat. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Tria, F., Loreto, V., and Servedio, V.D.P. (2018). Zipf\u2019s, Heaps\u2019 and Taylor\u2019s laws are determined by the expansion into the adjacent possible. Entropy, 20.","DOI":"10.3390\/e20100752"},{"key":"ref_10","unstructured":"Kalda, J., Sakki, M., Vainu, M., and Laan, M. (2001). Zipf\u2019s law in human heart beat dynamics. arXiv."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"108103","DOI":"10.1103\/PhysRevLett.90.108103","article-title":"Linguistic analysis of the human heartbeat using frequency and rank order statistics","volume":"90","author":"Yang","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1881","DOI":"10.4236\/jmp.2015.613193","article-title":"Physical mathematical evaluation of the cardiac dynamic applying the Zipf-Mandelbrot law","volume":"6","author":"Prieto","year":"2015","journal-title":"J. Mod. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Blons, E., Arsac, L.M., Gilfriche, P., and Deschodt-Arsac, V. (2019). Multiscale Entropy of Cardiac and Postural Control Reflects a Flexible Adaptation to a Cognitive Task. Entropy, 21.","DOI":"10.3390\/e21101024"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1007\/s00421-016-3416-9","article-title":"Heart rate variability in the standing position reflects training adaptation in professional soccer players","volume":"116","author":"Fortrat","year":"2016","journal-title":"Eur. J. Appl. Physiol."},{"key":"ref_15","unstructured":"Kitney, R.I., and Rompelman, O. (1986). Accuracy aspects in ECG preprocessing for the study of heart rate variability. The Beat-to-Beat Investigation of Cardiovascular Function, Oxford University Press."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Fortrat, J.O., and Rav\u00e9, G. (2020, January 27\u201329). Autonomic influences on heart rate variability self-organized criticality: Insights of Zipf\u2019s law. Proceedings of the European Study Group on Cardiovascular Oscillations Pisa 2020, Pisa, Italy.","DOI":"10.1109\/ESGCO49734.2020.9158172"},{"key":"ref_17","first-page":"R226","article-title":"Comparison of various techniques used to estimate spontaneous baroreflex sensitivity (the EuroBaVar study)","volume":"286","author":"Laude","year":"2004","journal-title":"Am. J. Physiol."},{"key":"ref_18","first-page":"H261","article-title":"Even slight movements disturb analysis of cardiovascular dynamics","volume":"277","author":"Fortrat","year":"1999","journal-title":"Am. J. Physiol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.amjcard.2010.05.019","article-title":"Holter heart rate variability: Are we measuring physical activity?","volume":"106","author":"Fortrat","year":"2010","journal-title":"Am. J. Cardiol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.3390\/e17031007","article-title":"Entropy Measures in the Assessment of Heart Rate Variability in Patients with Cardiodepressive Vasovagal Syncope","volume":"17","author":"Graff","year":"2015","journal-title":"Entropy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2253","DOI":"10.1007\/s00421-013-2655-2","article-title":"Noisy fluctuation of heart rate indicates cardiovascular system instability","volume":"113","author":"Fortrat","year":"2013","journal-title":"Eur. J. Appl. Physiol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Rowell, L.B. (1993). Passive effect of gravity. Human Cardiovascular Control, Oxford University Press.","DOI":"10.1093\/oso\/9780195073621.001.0001"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/4\/413\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:15:59Z","timestamp":1760174159000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/4\/413"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,6]]},"references-count":22,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["e22040413"],"URL":"https:\/\/doi.org\/10.3390\/e22040413","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,6]]}}}