{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:22:31Z","timestamp":1772252551660,"version":"3.50.1"},"reference-count":76,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2016,10,27]],"date-time":"2016-10-27T00:00:00Z","timestamp":1477526400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["14-35-00005"],"award-info":[{"award-number":["14-35-00005"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibers. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualization, such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously-made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilize finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.<\/jats:p>","DOI":"10.3390\/computation4040042","type":"journal-article","created":{"date-parts":[[2016,10,27]],"date-time":"2016-10-27T10:17:52Z","timestamp":1477563472000},"page":"42","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Mathematical Spline-Based Model of Cardiac Left Ventricle Anatomy and Morphology"],"prefix":"10.3390","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4053-8895","authenticated-orcid":false,"given":"Sergei","family":"Pravdin","sequence":"first","affiliation":[{"name":"Department of Mathematical Modeling in Cardiology, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences (IMM UB RAS), 16 S. Kovalevskoy Street, 620990 Ekaterinburg, Russia"},{"name":"Mathematical Modeling in Physiology and Medicine with Use of Supercomputer Technologies, Ural Federal University, 19 Mira Street, 620002 Ekaterinburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"H279","DOI":"10.1152\/ajpheart.00324.2011","article-title":"Electromechanical models of the ventricles","volume":"301","author":"Trayanova","year":"2011","journal-title":"Am. J. Physiol. Heart Circ. Physiol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1161\/01.RES.55.3.358","article-title":"A computer study of the left ventricular performance based on fiber structure, sarcomere dynamics, and transmural electrical propagation velocity","volume":"55","author":"Beyar","year":"1984","journal-title":"Circ. 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