{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T07:14:08Z","timestamp":1776323648703,"version":"3.50.1"},"reference-count":65,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,10]],"date-time":"2018-12-10T00:00:00Z","timestamp":1544400000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100012352","name":"University of Milan","doi-asserted-by":"publisher","award":["Piano di Sostegno alla Ricerca 2018"],"award-info":[{"award-number":["Piano di Sostegno alla Ricerca 2018"]}],"id":[{"id":"10.13039\/100012352","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Italian Ministry of Health","award":["Ricerca Corrente of the IRCCS Policlinico San Donato"],"award-info":[{"award-number":["Ricerca Corrente of the IRCCS Policlinico San Donato"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Synergy and redundancy are concepts that suggest, respectively, adaptability and fault tolerance of systems with complex behavior. This study computes redundancy\/synergy in bivariate systems formed by a target X and a driver Y according to the predictive information decomposition approach and partial information decomposition framework based on the minimal mutual information principle. The two approaches assess the redundancy\/synergy of past of X and Y in reducing the uncertainty of the current state of X. The methods were applied to evaluate the interactions between heart and respiration in healthy young subjects (n = 19) during controlled breathing at 10, 15 and 20 breaths\/minute and in two groups of chronic heart failure patients during paced respiration at 6 (n = 9) and 15 (n = 20) breaths\/minutes from spontaneous beat-to-beat fluctuations of heart period and respiratory signal. Both methods suggested that slowing respiratory rate below the spontaneous frequency increases redundancy of cardiorespiratory control in both healthy and pathological groups, thus possibly improving fault tolerance of the cardiorespiratory control. The two methods provide markers complementary to respiratory sinus arrhythmia and the strength of the linear coupling between heart period variability and respiration in describing the physiology of the cardiorespiratory reflex suitable to be exploited in various pathophysiological settings.<\/jats:p>","DOI":"10.3390\/e20120949","type":"journal-article","created":{"date-parts":[[2018,12,10]],"date-time":"2018-12-10T11:31:16Z","timestamp":1544441476000},"page":"949","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Paced Breathing Increases the Redundancy of Cardiorespiratory Control in Healthy Individuals and Chronic Heart Failure Patients"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6720-9824","authenticated-orcid":false,"given":"Alberto","family":"Porta","sequence":"first","affiliation":[{"name":"Department of Biomedical Sciences for Health, University of Milan, 20097 Milan, Italy"},{"name":"Department of Cardiothoracic, Vascular Anesthesia and Intensive Care, IRCCS Policlinico San Donato, San Donato Milanese, 20097 Milan, Italy"}]},{"given":"Roberto","family":"Maestri","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, IRCCS Istituti Clinici Scientifici Maugeri, 27040 Montescano, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5346-2677","authenticated-orcid":false,"given":"Vlasta","family":"Bari","sequence":"additional","affiliation":[{"name":"Department of Cardiothoracic, Vascular Anesthesia and Intensive Care, IRCCS Policlinico San Donato, San Donato Milanese, 20097 Milan, Italy"}]},{"given":"Beatrice","family":"De Maria","sequence":"additional","affiliation":[{"name":"IRCCS Istituti Clinici Scientifici Maugeri, 20097 Milan, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3396-6883","authenticated-orcid":false,"given":"Beatrice","family":"Cairo","sequence":"additional","affiliation":[{"name":"Department of Biomedical Sciences for Health, University of Milan, 20097 Milan, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5873-6609","authenticated-orcid":false,"given":"Emanuele","family":"Vaini","sequence":"additional","affiliation":[{"name":"Department of Cardiothoracic, Vascular Anesthesia and Intensive Care, IRCCS Policlinico San Donato, San Donato Milanese, 20097 Milan, Italy"}]},{"given":"Maria Teresa","family":"La Rovere","sequence":"additional","affiliation":[{"name":"Department of Cardiological Rehabilitation, IRCCS Istituti Clinici Scientifici Maugeri, 27040 Montescano, Italy"}]},{"given":"Gian Domenico","family":"Pinna","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, IRCCS Istituti Clinici Scientifici Maugeri, 27040 Montescano, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1002\/cplx.20249","article-title":"An information-theoretic primer on complexity, self-Organization, and emergence","volume":"15","author":"Prokopenko","year":"2008","journal-title":"Complexity"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"037201","DOI":"10.1103\/PhysRevE.81.037201","article-title":"Redundant variables and Granger causality","volume":"81","author":"Angelini","year":"2010","journal-title":"Phys. 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