{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T06:50:40Z","timestamp":1791960640483,"version":"4.3.4"},"reference-count":13,"publisher":"Wiley","issue":"19","license":[{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"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":["Physiological Reports"],"published-print":{"date-parts":[[2026,10]]},"abstract":"Abstract<\/jats:title>\n \n Effective arterial elastance (\n E<\/jats:italic>\n a<\/jats:sub>\n ) is a lumped descriptor of arterial load. The contributions of arterial characteristics to\n E<\/jats:italic>\n a<\/jats:sub>\n , and their interactions with cardiac timing parameters, have not been fully elaborated. Previous studies have shown that\n E<\/jats:italic>\n a<\/jats:sub>\n can be approximated by equations of the form\n E<\/jats:italic>\n a<\/jats:sub>\n \u2009\u2248\u2009\n R<\/jats:italic>\n \/\n T<\/jats:italic>\n \u2009+\u2009\n k<\/jats:italic>\n \/\n C<\/jats:italic>\n , where\n R<\/jats:italic>\n is either total or peripheral resistance,\n T<\/jats:italic>\n is cardiac cycle time, and\n C<\/jats:italic>\n is arterial compliance, but reported values for the coefficient\n k<\/jats:italic>\n vary substantially, and some analyses suggest that compliance contributes little to\n E<\/jats:italic>\n a<\/jats:sub>\n . Here, an analytical approximation is derived from Sunagawa's Windkessel expression for\n E<\/jats:italic>\n a<\/jats:sub>\n by replacing the exponential term with a truncated Taylor expansion. The resulting approximation predicts that\n k<\/jats:italic>\n is not constant but varies with cardiac timing, such that\n k<\/jats:italic>\n \u2009\u2248\u20090.5 (\n t<\/jats:italic>\n d<\/jats:sub>\n \/\n T<\/jats:italic>\n )\n 2<\/jats:sup>\n , where\n t<\/jats:italic>\n d<\/jats:sub>\n is diastolic time. Approximation accuracy was assessed across 693 combinations of resistance, compliance, and heart rate and in a virtual population of 4374 adults derived from a published one\u2010dimensional vascular model. The linear approximation for\n E<\/jats:italic>\n a<\/jats:sub>\n closely tracked the Windkessel expression across the full parameter space (\n R<\/jats:italic>\n 2<\/jats:sup>\n \u2009>\u20090.9999, mean absolute percentage error 0.51%). In the virtual population, the approximation showed good agreement with the\u00a0\n E<\/jats:italic>\n surrogate\n P<\/jats:italic>\n ES<\/jats:sub>\n \/SV (end\u2010systolic pressure\/stroke volume), surpassing previous approximations. These findings show that the contribution of compliance to\n E<\/jats:italic>\n a<\/jats:sub>\n is modulated by cardiac timing and provide a mechanistic explanation for previously reported values of\n k<\/jats:italic>\n .\n <\/jats:p>","DOI":"10.14814\/phy2.71112","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T02:32:07Z","timestamp":1790735527000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cardiac timing modulates the contribution of compliance to effective arterial elastance"],"prefix":"10.14814","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-7630-0005","authenticated-orcid":false,"given":"Thomas","family":"Murchie","sequence":"first","affiliation":[{"name":"Te Puna Wai Ora, Southern Critical Care Dunedin Hospital Dunedin New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.14814\/phy2.13195"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1152\/ajpheart.00218.2019"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1152\/ajpheart.00823.2002"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1161\/HYPERTENSIONAHA.114.03696"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1161\/01.cir.86.2.513"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.4137\/CMC.S18742"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMoa2026845"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/clc.4960040106"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00134\u2010015\u20103898\u20107"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1445\u20105994.1976.tb03323.x"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1152\/ajpheart.00764.2001"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1152\/ajpheart.1983.245.5.H773"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11517\u2010008\u20100359\u20102"}],"container-title":["Physiological Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/physoc.onlinelibrary.wiley.com\/doi\/pdf\/10.14814\/phy2.71112","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/physoc.onlinelibrary.wiley.com\/doi\/full-xml\/10.14814\/phy2.71112","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/physoc.onlinelibrary.wiley.com\/doi\/pdf\/10.14814\/phy2.71112","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T06:40:48Z","timestamp":1791960048000},"score":1,"resource":{"primary":{"URL":"https:\/\/physoc.onlinelibrary.wiley.com\/doi\/10.14814\/phy2.71112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,29]]},"references-count":13,"journal-issue":{"issue":"19","published-print":{"date-parts":[[2026,10]]}},"alternative-id":["10.14814\/phy2.71112"],"URL":"https:\/\/doi.org\/10.14814\/phy2.71112","archive":["Portico"],"relation":{},"ISSN":["2051-817X","2051-817X"],"issn-type":[{"value":"2051-817X","type":"print"},{"value":"2051-817X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,29]]},"assertion":[{"value":"2026-06-22","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-09","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e71112"}}