{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T23:56:10Z","timestamp":1790898970341,"version":"4.1.0"},"reference-count":36,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T00:00:00Z","timestamp":1789603200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Respiratory heart rate variability (RespHRV), also known as respiratory sinus arrhythmia, is a healthy variation of heart rate (HR) whereby HR increases during inhalation and decreases during exhalation. Although RespHRV has long been used as a prognostic indicator of heart health, several hypotheses have been suggested for its physiological benefits. The aim of this study was to test the hypothesis that RespHRV minimizes the work done by the left ventricle of the heart while maintaining physiological levels of carbon dioxide in the blood. To do this, we coupled a previously published mathematical model of HR control, which includes a model of the lungs and gas exchange, with two different mechanical models of blood circulation. This allowed us to calculate the work done by the left ventricle of the heart from its pressure and volume and study the effects of different models of heart contraction, which could not have been done previously. We found that although the central respiratory modulation of HR is the main source of RespHRV in our model, changes in the intrathoracic pressure also have a sizeable effect on RespHRV. The two models of heart contraction led to different responses when the effect of the intrathoracic pressure on blood flow was removed from the models, providing a potential way to test the models experimentally. We calculated the work done by the left ventricle of the heart over a whole interval or beat-by-beat and although the two work calculation methods gave a value of RespHRV for which a minimum work exists, the beat-by-beat calculations gave lower values, closer to physiological values.<\/jats:p>","DOI":"10.1093\/imammb\/dqag011","type":"journal-article","created":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T07:33:52Z","timestamp":1789630432000},"source":"Crossref","is-referenced-by-count":0,"title":["The role and source of respiratory heart rate variability: exploration using mathematical models of heart rate regulation and blood circulation"],"prefix":"10.1093","author":[{"given":"Weiwei","family":"Ai","sequence":"first","affiliation":[{"name":"Auckland Bioengineering Institute , The University of Auckland, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Gibbs","sequence":"additional","affiliation":[{"name":"School of Natural and Computational Sciences , Massey University, Auckland, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julian F R","family":"Paton","sequence":"additional","affiliation":[{"name":"Manaaki Manawa \u2013 the Centre of Heart Research , Department of Physiology, The University of Auckland, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alona","family":"Ben-Tal","sequence":"additional","affiliation":[{"name":"Insightful Modelling , Auckland, New Zealand"},{"name":"Manaaki Manawa \u2013 the Centre of Heart Research , Department of Physiology, The University of Auckland, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,9,17]]},"reference":[{"key":"2026100119361564300_ref1","doi-asserted-by":"crossref","DOI":"10.1016\/j.compbiomed.2021.105136","article-title":"Development of closed-loop modelling framework for adaptive respiratory pacemakers","volume":"141","author":"Ai","year":"2022","journal-title":"Comput. Biol. Med."},{"key":"2026100119361564300_ref2","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1098\/rspb.1936.0006","article-title":"Respiratory variations of the heart rate II: the central mechanism of the respiratory arrhythmia and the inter-relations between the central and the reflex mechanisms","volume":"119","author":"Anrep","year":"1936","journal-title":"Proc. R. Soc. Lond. Ser. B"},{"key":"2026100119361564300_ref3","doi-asserted-by":"crossref","first-page":"1989","DOI":"10.1113\/jphysiol.2011.222422","article-title":"Evaluating the physiological significance of respiratory sinus arrhythmia: Looking beyond ventilation\u2013perfusion efficiency","volume":"590","author":"Ben-Tal","year":"2012","journal-title":"J. Physiol."},{"key":"2026100119361564300_ref4","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.jtbi.2005.06.005","article-title":"Simplified models for gas exchange in the human lungs","volume":"238","author":"Ben-Tal","year":"2006","journal-title":"J. Theor. Biol."},{"key":"2026100119361564300_ref5","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.mbs.2014.06.015","article-title":"Central regulation of heart rate and the appearance of respiratory sinus arrhythmia: New insights from mathematical modeling","volume":"255","author":"Ben-Tal","year":"2014","journal-title":"Math. Biosci."},{"key":"2026100119361564300_ref6","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1016\/j.jtbi.2007.12.018","article-title":"A model for control of breathing in mammals: Coupling neural dynamics to peripheral gas exchange and transport","volume":"251","author":"Ben-Tal","year":"2008","journal-title":"J. Theor. Biol."},{"key":"2026100119361564300_ref7","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1113\/jphysiol.1977.sp012067","article-title":"Respiratory modulation of baroreceptor and chemoreceptor reflexes affecting heart rate through the sympathetic nervous system","volume":"272","author":"Davis","year":"1977","journal-title":"J. Physiol."},{"key":"2026100119361564300_ref8","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1002\/j.1552-4604.1995.tb04054.x","article-title":"The effect of atropine on parasympathetic control of respiratory sinus arrhythmia in two ethnic groups","volume":"35","author":"du Plooy","year":"1995","journal-title":"J. Clin. Pharmacol."},{"key":"2026100119361564300_ref9","doi-asserted-by":"crossref","first-page":"1740","DOI":"10.1152\/japplphysiol.91107.2008","article-title":"Point: Counterpoint: Respiratory sinus arrhythmia is due to a central mechanism vs. respiratory sinus arrhythmia is due to the baroreflex mechanism","volume":"106","author":"Eckberg","year":"2009","journal-title":"J. Appl. Physiol."},{"key":"2026100119361564300_ref10","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1172\/JCI108699","article-title":"Respiratory and baroreceptor reflex interactions in man","volume":"59","author":"Eckberg","year":"1977","journal-title":"J. Clin. Investi."},{"key":"2026100119361564300_ref11","first-page":"H6","article-title":"Cardiorespiratory interactions in humans and animals: Rhythms for life","volume":"315","author":"Elstad","year":"2018","journal-title":"Amer. J. Physiol."},{"key":"2026100119361564300_ref12","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/B978-0-323-91534-2.00006-0","article-title":"Respiratory\u2013cardiovascular interactions","volume":"188","author":"Fisher","year":"2022","journal-title":"Handb. Clin. Neurol."},{"key":"2026100119361564300_ref13","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1113\/jphysiol.1978.sp012240","article-title":"Inhibition of baroreceptor and chemoreceptor reflexes on heart rate by afferents from the lungs","volume":"276","author":"Gandevia","year":"1978","journal-title":"J. Physiol."},{"key":"2026100119361564300_ref14","doi-asserted-by":"crossref","first-page":"108739","DOI":"10.1016\/j.biopsycho.2023.108739","article-title":"Respiratory sinus arrhythmia (RSA), vagal tone and biobehavioral integration: Beyond parasympathetic function","volume":"186","author":"Grossman","year":"2023","journal-title":"Biol. Psychol."},{"key":"2026100119361564300_ref15","volume-title":"Text Book of Medical Physiology","author":"Guyton","year":"2000"},{"key":"2026100119361564300_ref16","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1161\/01.CIR.94.4.842","article-title":"Respiratory sinus arrhythmia: A phenomenon improving pulmonary gas exchange and circulatory efficiency","volume":"94","author":"Hayano","year":"1996","journal-title":"Circulation"},{"key":"2026100119361564300_ref17","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1152\/japplphysiol.00241.2001","article-title":"Computational modeling of cardiovascular response to orthostatic stress","volume":"92","author":"Heldt","year":"2002","journal-title":"J. Appl.. Physiol."},{"key":"2026100119361564300_ref18","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195138467.001.0001","volume-title":"Physiology of Respiration","author":"Hlastala","year":"2001"},{"key":"2026100119361564300_ref19","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1152\/japplphysiol.00196.2009","article-title":"Comments on point: Counterpoint: Respiratory sinus arrhythmia is due to a central mechanism vs. respiratory sinus arrhythmia is due to the baroreflex mechanism","volume":"106","author":"Julien","year":"2009","journal-title":"J. Appl. Physiol."},{"key":"2026100119361564300_ref20","doi-asserted-by":"crossref","first-page":"1742","DOI":"10.1152\/japplphysiol.91107.2008a","article-title":"Counterpoint: Respiratory sinus arrhythmia is due to the baroreflex mechanism","volume":"106","author":"Karemaker","year":"2009","journal-title":"J. Appl. Physiol."},{"key":"2026100119361564300_ref21","doi-asserted-by":"crossref","first-page":"1750","DOI":"10.1152\/japplphysiol.00225.2009","article-title":"Last word on point: Counterpoint: Respiratory sinus arrhythmia is due to a central mechanism vs. respiratory sinus arrhythmia is due to the baroreflex mechanism","volume":"106","author":"Karemaker","year":"2009","journal-title":"J. Appl. Physiol."},{"key":"2026100119361564300_ref22","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1016\/j.jbiomech.2005.06.016","article-title":"Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves","volume":"39","author":"Korakianitis","year":"2006","journal-title":"J. Biomech."},{"key":"2026100119361564300_ref23","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1016\/S0140-6736(97)11144-8","article-title":"Baroreflex sensitivity and heart-rate variability in prediction of total cardiac mortality after myocardial infarction","volume":"351","author":"La Rovere","year":"1998","journal-title":"The Lancet"},{"key":"2026100119361564300_ref24","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1111\/j.1540-8167.1993.tb01222.x","article-title":"Assessment of beat-by-beat control of heart rate by the autonomic nervous system: Molecular biology techniques are necessary, but not sufficient","volume":"4","author":"Levy","year":"1993","journal-title":"J. Cardiovasc. Electrophysiol."},{"key":"2026100119361564300_ref25","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1038\/s41569-025-01160-z","article-title":"Redefining respiratory sinus arrhythmia as respiratory heart rate variability: An international expert recommendation for terminological clarity","volume":"22","author":"Menuet","year":"2025","journal-title":"Nat. Rev. Cardiol."},{"key":"2026100119361564300_ref26","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1113\/jphysiol.2014.282723","article-title":"Silicon central pattern generators for cardiac diseases","volume":"593","author":"Nogaret","year":"2015","journal-title":"J. Physiol."},{"key":"2026100119361564300_ref27","volume-title":"Mathematical modelling of the cardiovascular system to study the effects of respiratory sinus arrhythmia and heart failure","author":"Noreen","year":"2021"},{"key":"2026100119361564300_ref28","doi-asserted-by":"crossref","DOI":"10.1016\/j.mbs.2021.108766","article-title":"Mathematical modelling of atrial and ventricular pressure\u2013volume dynamics and their change with heart rate","volume":"344","author":"Noreen","year":"2022","journal-title":"Math. Biosci."},{"key":"2026100119361564300_ref29","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1113\/JP277293","article-title":"Enhancing respiratory sinus arrhythmia increases cardiac output in rats with left ventricular dysfunction","volume":"598","author":"O\u2019Callaghan","year":"2020","journal-title":"J. Physiol."},{"key":"2026100119361564300_ref30","doi-asserted-by":"crossref","first-page":"108728","DOI":"10.1016\/j.biopsycho.2023.108728","article-title":"Putting back respiration into respiratory sinus arrhythmia or high-frequency heart rate variability: Implications for interpretation, respiratory rhythmicity, and health","volume":"185","author":"Ritz","year":"2024","journal-title":"Biol. Psychol."},{"key":"2026100119361564300_ref31","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/s00395-022-00911-0","article-title":"Reverse re-modelling chronic heart failure by reinstating heart rate variability","volume":"117","author":"Shanks","year":"2022","journal-title":"Basic Res. Cardiol."},{"key":"2026100119361564300_ref32","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s00395-025-01110-3","article-title":"Reinstating respiratory heart rate variability improves hemodynamic responses during exercise in heart failure with reduced ejection fraction","volume":"120","author":"Shanks","year":"2025","journal-title":"Basic Res. Cardiol."},{"key":"2026100119361564300_ref33","doi-asserted-by":"crossref","DOI":"10.3389\/fphys.2022.768465","article-title":"Respiratory sinus arrhythmia is mainly driven by central feedforward mechanisms in healthy humans","volume":"13","author":"Skytioti","year":"2022","journal-title":"Front. Physiol."},{"key":"2026100119361564300_ref34","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1093\/eurheartj\/6.suppl_C.43","article-title":"Chapter 9: Pulmonary blood volume","volume":"6","author":"Tarazi","year":"1985","journal-title":"Eur. Heart. J."},{"key":"2026100119361564300_ref35","doi-asserted-by":"crossref","DOI":"10.1016\/j.biopsycho.2022.108382","article-title":"An overview of the phylogeny of cardiorespiratory control in vertebrates with some reflections on the \u2018polyvagal theory\u2019","volume":"172","author":"Taylor","year":"2022","journal-title":"Biol. Psychol."},{"key":"2026100119361564300_ref36","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1093\/imammb\/dqt004","article-title":"Patient-specific modelling of head-up tilt","volume":"31","author":"Williams","year":"2014","journal-title":"Math. Med. Biol."}],"container-title":["Mathematical Medicine and Biology: A Journal of the IMA"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/imammb\/advance-article-pdf\/doi\/10.1093\/imammb\/dqag011\/71179374\/dqag011.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/imammb\/advance-article-pdf\/doi\/10.1093\/imammb\/dqag011\/71179374\/dqag011.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T23:36:29Z","timestamp":1790897789000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imammb\/advance-article\/doi\/10.1093\/imammb\/dqag011\/8810646"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,17]]},"references-count":36,"URL":"https:\/\/doi.org\/10.1093\/imammb\/dqag011","relation":{},"ISSN":["1477-8599","1477-8602"],"issn-type":[{"value":"1477-8599","type":"print"},{"value":"1477-8602","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,17]]},"article-number":"dqag011"}}