{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T16:22:17Z","timestamp":1783441337463,"version":"3.54.6"},"reference-count":33,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,30]],"date-time":"2023-05-30T00:00:00Z","timestamp":1685404800000},"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 has recently been demonstrated. We studied a model of autonomic nervous system changes to better characterize heart rate variability self-organized criticality. The model included short and long-term autonomic changes associated with body position and physical training, respectively. Twelve professional soccer players took part in a 5-week training session divided into \u201cWarm-up\u201d, \u201cIntensive\u201d, and \u201cTapering\u201d periods. A stand test was carried out at the beginning and end of each period. Heart rate variability was recorded beat by beat (Polar Team 2). Bradycardias, defined as successive heart rates with a decreasing value, were counted according to their length in number of heartbeat intervals. We checked whether bradycardias were distributed according to Zipf\u2019s law, a feature of self-organized criticality. Zipf\u2019s law draws a straight line when the rank of occurrence is plotted against the frequency of occurrence in a log\u2013log graph. Bradycardias were distributed according to Zipf\u2019s law, regardless of body position or training. Bradycardias were much longer in the standing position than the supine position and Zipf\u2019s law was broken after a delay of four heartbeat intervals. Zipf\u2019s law could also be broken in some subjects with curved long bradycardia distributions by training. Zipf\u2019s law confirms the self-organized nature of heart rate variability and is strongly linked to autonomic standing adjustment. However, Zipf\u2019s law could be broken, the significance of which remains unclear.<\/jats:p>","DOI":"10.3390\/e25060880","type":"journal-article","created":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T04:40:51Z","timestamp":1685508051000},"page":"880","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Autonomic Nervous System Influences on Cardiovascular Self-Organized Criticality"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9272-0157","authenticated-orcid":false,"given":"Jacques-Olivier","family":"Fortrat","sequence":"first","affiliation":[{"name":"CHU Angers, M\u00e9decine Vasculaire, INSERM, CNRS, MITOVASC, Equipe CarMe, SFR ICAT, Universit\u00e9 d\u2019Angers, 49933 Angers, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guillaume","family":"Rav\u00e9","sequence":"additional","affiliation":[{"name":"Toulouse Football Club, 1 All\u00e9e Gabriel Bi\u00e9n\u00e8s, 31400 Toulouse, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,30]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"200","DOI":"10.3389\/fphys.2020.00200","article-title":"Homeostasis: The underappreciated and far too often ignored central organizing principle of physiology","volume":"11","author":"Billman","year":"2020","journal-title":"Front. Physiol."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Struzik, Z.R. Is heart rate variability dynamics poised at criticality? In Proceedings of the 8th Conference of the European Study Group on Cardiovascular Oscillations (ESGCO), Trento, Italy, 25\u201328 May 2014; IEEE: Piscataway, NJ, USA, 2014.","DOI":"10.1109\/ESGCO.2014.6847599"},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"012024","DOI":"10.1088\/1742-6596\/1612\/1\/012024","article-title":"Symmetry and Signs of Self-Organized Criticality in Living Organisms","volume":"1612","author":"Frank","year":"2020","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Persson, P.B., and Kirchheim, H.R. (1991). Baroreceptor Reflexes. Integrative Functions and Clinical Aspect, Springer.","DOI":"10.1007\/978-3-642-76366-3"},{"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","unstructured":"Aschwanden, M.J. (2013). Self-Organized Criticality Systems, Open Academic Press."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.physrep.2013.11.002","article-title":"Power laws and self-organized criticality in theory and nature","volume":"536","author":"Gros","year":"2014","journal-title":"Phys. Rep."},{"key":"ref_10","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_11","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_12","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_13","doi-asserted-by":"crossref","unstructured":"Fortrat, J.O. (2020). Zipf\u2019s law of vasovagal heart rate variability sequences. Entropy, 22.","DOI":"10.3390\/e22040413"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Rowell, L.B. (1993). Human Cardiovascular Control, Oxford University Press.","DOI":"10.1249\/00005768-199312000-00021"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"141","DOI":"10.2478\/hukin-2019-0103","article-title":"Heart rate variability is correlated with perceived physical fitness in elite soccer players","volume":"72","author":"Zouhal","year":"2020","journal-title":"J. Hum. Kinet."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1080\/24748668.2018.1460053","article-title":"Heart rate recovery and heart rate variability: Use and relevance in European professional soccer","volume":"18","author":"Fortrat","year":"2018","journal-title":"Int. J. Perform. Anal. Sport"},{"key":"ref_18","unstructured":"Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology (1996). Heart rate variability: Standards of measurement, physiological interpretation and clinical use. Circulation, 93, 1043\u20131065."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1126\/science.6166045","article-title":"Power spectrum analysis of heart rate fluctuation: A quantitative probe of beat-to-beat cardiovascular control","volume":"213","author":"Akselrod","year":"1981","journal-title":"Science"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1109\/TBME.1982.324972","article-title":"1\/f fluctuation of heartbeat period","volume":"29","author":"Kobayashi","year":"1982","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"024003","DOI":"10.1088\/1361-6579\/aaa916","article-title":"Multifractal dynamics of resting-state functional connectivity in the prefrontal cortex","volume":"39","author":"Racz","year":"2018","journal-title":"Physiol. Meas."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"622569","DOI":"10.3389\/fphys.2021.622569","article-title":"Two-tiered response of cardiorespiratory-cerebrovascular network to orthostatic challenge","volume":"12","author":"Mukli","year":"2021","journal-title":"Front. Physiol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1126\/science.3281253","article-title":"Dynamic pattern generation in behavioral and neural systems","volume":"239","author":"Kelso","year":"1988","journal-title":"Science"},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1103\/PhysRevA.38.364","article-title":"Self-organized criticality","volume":"38","author":"Bak","year":"1988","journal-title":"Phys. Rev. A"},{"key":"ref_26","unstructured":"Kalda, J., Sakki, M., Vainu, M., and Laan, M. (2001). Zipf\u2019s law in human heart beat dynamics. arXiv."},{"key":"ref_27","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_28","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_29","doi-asserted-by":"crossref","first-page":"17545","DOI":"10.1073\/pnas.0408242101","article-title":"Common scale-invariant patterns of sleep-wake transitions across mammalian species","volume":"101","author":"Lo","year":"2004","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1137\/070710111","article-title":"Power-law distributions in empirical data","volume":"51","author":"Clauset","year":"2009","journal-title":"SIAM Rev."},{"key":"ref_31","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_32","doi-asserted-by":"crossref","first-page":"6026","DOI":"10.1103\/PhysRevLett.86.6026","article-title":"Behavioral-independent features of complex heartbeat dynamics","volume":"86","author":"Ivanov","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"401","DOI":"10.4103\/apc.apc_235_20","article-title":"Avalanches in cardiology","volume":"14","author":"Subramanyan","year":"2021","journal-title":"Ann. Pediatr. Cardiol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/6\/880\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:45:37Z","timestamp":1760125537000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/6\/880"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,30]]},"references-count":33,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["e25060880"],"URL":"https:\/\/doi.org\/10.3390\/e25060880","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,30]]}}}