{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T01:02:31Z","timestamp":1781658151519,"version":"3.54.5"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T00:00:00Z","timestamp":1557360000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Ischemic mitral regurgitation (IMR) occurs as an adverse consequence of left ventricle remodeling post-myocardial infarction. A change in mitral valve configuration with an imbalance between closing and tethering forces underlie this pathological condition. These abnormalities lead to impaired leaflet coaptation and a variable degree of mitral regurgitation, which can in turn influence the ventricular filling status, the heart rhythm and the afterload regardless of the residual ischemic insult. The IMR correction can be pursued through under-sizing mitral annuloplasty and papillary muscle approximation to restore the mitral valve and left ventricle physiological geometry to, consequently, achieve normalization of the engaged physical forces. Because the structures involved undergo extremely large deformations, a biomechanics model based on the Euler\u2019s Elastica \u2013the mitral leaflet\u2013 interlaced with nonlinear chordae tendineae anchored on papillary muscles has been constructed to elucidate the interactions between closing and tethering forces. The model takes into account the actual updated geometrical and mechanical features of the valvular and subvalvular apparatuses in physiological and IMR conditions, as well as in case of papillary muscle approximation, finally furnishing ad hoc geometry-based mathematical relations that could be utilised to support\u2014and optimize\u2014the relevant choices in cardiac surgery.<\/jats:p>","DOI":"10.3390\/ma12091518","type":"journal-article","created":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T08:19:59Z","timestamp":1557389999000},"page":"1518","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Euler\u2019s Elastica-Based Biomechanics of the Papillary Muscle Approximation in Ischemic Mitral Valve Regurgitation: A Simple 2D Analytical Model"],"prefix":"10.3390","volume":"12","author":[{"given":"Francesco","family":"Nappi","sequence":"first","affiliation":[{"name":"Centre Cardiologique du Nord de Saint-Denis, Paris 36 Rue des Moulins Gmeaux, 93200 Saint-Denis, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Angelo Rosario","family":"Carotenuto","sequence":"additional","affiliation":[{"name":"Department of Structures for Engineering and Architecture, University of Napoli Federico II, 80125 Naples, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sanjeet Singh","family":"Avtaar Singh","sequence":"additional","affiliation":[{"name":"Department of Cardiac Surgery, Golden Jubilee National Hospital, Clydebank G81 4DY, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christos","family":"Mihos","sequence":"additional","affiliation":[{"name":"Columbia University Division of Cardiology at the Mount Sinai Heart Institute, Miami Beach, FL 33140, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Massimiliano","family":"Fraldi","sequence":"additional","affiliation":[{"name":"Department of Structures for Engineering and Architecture, University of Napoli Federico II, 80125 Naples, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e57","DOI":"10.1016\/j.jacc.2014.02.536","article-title":"2014 AHA\/ACC guideline for the management of patients with valvular heart disease: A report of the American college of cardiology\/American heart association task force on practice guidelines","volume":"63","author":"Nishimura","year":"2014","journal-title":"J. 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