{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T11:44:49Z","timestamp":1792669489933,"version":"4.5.0"},"reference-count":85,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T00:00:00Z","timestamp":1792627200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"},{"start":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T00:00:00Z","timestamp":1792627200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["physoc.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["The Journal of Physiology"],"abstract":"\n Abstract<\/jats:title>\n \n The three\u2010element Windkessel model of the systemic circulation comprises terms that represent the resistance of peripheral vessels (\n \n R\n p<\/jats:sub>\n <\/jats:italic>\n ), compliance of the arteries (\n C<\/jats:italic>\n ) and characteristic impedance (\n \n Z\n c<\/jats:sub>\n <\/jats:italic>\n ) of the aorta. It is widely used to represent the biophysics of the arterial system, and can be used to model the vascular load that can be experimentally presented to isolated hearts or muscles. Reported values of the three Windkessel parameters span several orders of magnitude. By collecting literature data across species, we found empirical relationships that are naturally preserved among the three Windkessel parameters. We applied these empirical relationships in our experiments when prescribing loads to isolated cardiac muscles, and compared the results with loading protocols that do not preserve these empirical relationships. Thus, in our loading protocols,\n \n R\n p<\/jats:sub>\n <\/jats:italic>\n was varied, whereas\n C<\/jats:italic>\n and\n \n Z\n c<\/jats:sub>\n <\/jats:italic>\n were either held constant or varied according to their empirical relationship with\n \n R\n p<\/jats:sub>\n <\/jats:italic>\n . Muscles responded to the prescribed loads and generated force\u2013length work\u2010loops that were unique to the various loading protocols. The differences in work\u2010loops were most evident during muscle shortening in terms of the force achieved to commence shortening, the dynamics of the force during shortening and the force reached at the completion of shortening. With these loading protocol\u2010specific shortening, muscles liberated distinct amounts of shortening heat and performed different amounts of work, resulting in different levels of mechanical efficiency. In conclusion, the three\u2010element Windkessel parameters have empirical relationships that uniquely define the load and mechanoenergetics of cardiac muscle shortening.\n \n \n image<\/jats:alt-text>\n <\/jats:graphic>\n <\/jats:boxed-text>\n <\/jats:p>\n <\/jats:sec>\n \n Key points<\/jats:title>\n \n \n \n The heart pumps blood into the aorta against the arterial load imposed by the systemic vasculature. The biophysical properties of the vasculature are characterised by resistance, compliance and impedance.<\/jats:p>\n <\/jats:list-item>\n \n By compiling literature data across multiple species, we identified a relation that is rather \u2018universal\u2019 linking resistance and compliance, and another linking resistance and impedance.<\/jats:p>\n <\/jats:list-item>\n \n We conducted experiments on isolated cardiac muscles subjected to contract against loads that either conformed to or departed from the relations.<\/jats:p>\n <\/jats:list-item>\n \n We found that when the loads conformed to the relations, the mechanics, kinetics and energetics of muscle contraction and shortening were distinct from those loads that deviated from the relations.<\/jats:p>\n <\/jats:list-item>\n \n These findings establish a fundamental link between arterial load and cardiac muscle mechanoenergetics, demonstrating that presenting isolated muscles with loading conditions that conform to the empirical relations is essential for understanding the physiological mechanics of cardiac contraction.<\/jats:p>\n <\/jats:list-item>\n <\/jats:list>\n <\/jats:p>\n <\/jats:sec>","DOI":"10.1113\/jp291772","type":"journal-article","created":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T11:30:04Z","timestamp":1792668604000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The three\u2010element Windkessel parameters have empirical relations that uniquely define the mechanoenergetics of cardiac muscle shortening"],"prefix":"10.1113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4314-7769","authenticated-orcid":false,"given":"Chamal","family":"Kohombakadawala","sequence":"first","affiliation":[{"name":"Auckland Bioengineering Institute University of Auckland Auckland New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6323-9217","authenticated-orcid":false,"given":"Toan","family":"Pham","sequence":"additional","affiliation":[{"name":"Auckland Bioengineering Institute University of Auckland Auckland New Zealand"},{"name":"Department of Engineering Science and Biomedical Engineering University of Auckland Auckland New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8651-3557","authenticated-orcid":false,"given":"Kenneth","family":"Tran","sequence":"additional","affiliation":[{"name":"Auckland Bioengineering Institute University of Auckland Auckland New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0452-0308","authenticated-orcid":false,"given":"Andrew","family":"Taberner","sequence":"additional","affiliation":[{"name":"Auckland Bioengineering Institute University of Auckland Auckland New Zealand"},{"name":"Department of Engineering Science and Biomedical Engineering University of Auckland Auckland New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6396-7628","authenticated-orcid":false,"given":"June\u2010Chiew","family":"Han","sequence":"additional","affiliation":[{"name":"Auckland Bioengineering Institute University of Auckland Auckland New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,22]]},"reference":[{"issue":"103","key":"e_1_2_6_2_1","article-title":"Cardiac pressure\u2010volume loop analysis using conductance catheters in mice","author":"Abraham D.","year":"2015","journal-title":"Journal of Visualized Experiments: JoVE"},{"key":"e_1_2_6_3_1","first-page":"H969","article-title":"Influence of mean pressure on aortic impedance and reflections in the systemic arterial system","volume":"257","author":"Alexander J.","year":"1989","journal-title":"The American Journal of Physiology"},{"issue":"2","key":"e_1_2_6_4_1","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1161\/01.RES.19.2.230","article-title":"Pressure\u2010flow relations in dog arteries","volume":"19","author":"Attinger E. 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