Mathematical analysis of a 1D-3D coupled problem in cardiac electrophysiology

Mathematical analysis of a 1D-3D coupled problem in cardiac electrophysiology | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Mathematical analysis of a 1D-3D coupled problem in cardiac electrophysiology Khouloud Kordoghli, Saloua Mani Aouadi, Nejib Zemzemi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4151419/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Dec, 2024 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted 9 You are reading this latest preprint version Abstract The objective of this paper is to analyze a coupled problem that describes the propagation of the electric wave in the heart. The problem comprises coupled partial differential equations posed on a three-dimensional domain representing the heart and on a one-dimensional tree representing the Purkinje network. Each system of PDEs is itself coupled to ordinary differential equations that describe the electrical activity at the cellular level. We establish the existence of a unique solution, utilizing a fixed-point approach with a judicious and non-conventional choice of functional spaces and contraction. 2010 Mathematics Subject Classification. Primary 35Q92, Secondary: 35R30. Inverse problem optimal control bidomain model cardiac electrophysiology optimization method conductivity parameters. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 27 Dec, 2024 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted Editorial decision: Revision requested 22 Aug, 2024 Reviews received at journal 22 Aug, 2024 Reviews received at journal 19 Jul, 2024 Reviewers agreed at journal 20 Apr, 2024 Reviewers agreed at journal 05 Apr, 2024 Reviewers invited by journal 04 Apr, 2024 Editor assigned by journal 23 Mar, 2024 Submission checks completed at journal 23 Mar, 2024 First submitted to journal 22 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4151419","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":283806986,"identity":"cf49fef6-2422-4848-89f1-39403fb7aa52","order_by":0,"name":"Khouloud Kordoghli","email":"","orcid":"","institution":"Tunis El Manar University","correspondingAuthor":false,"prefix":"","firstName":"Khouloud","middleName":"","lastName":"Kordoghli","suffix":""},{"id":283806987,"identity":"68edfe06-bfe7-4846-ad4b-a6926e140df4","order_by":1,"name":"Saloua Mani Aouadi","email":"","orcid":"","institution":"Tunis El Manar University","correspondingAuthor":false,"prefix":"","firstName":"Saloua","middleName":"Mani","lastName":"Aouadi","suffix":""},{"id":283806988,"identity":"506f0a98-d8c1-4aaa-860a-f67637662da5","order_by":2,"name":"Nejib Zemzemi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7UlEQVRIie3OsYrCMBzH8b8E2iXg2kH0CYQcQtS3SRAcpXBLh6M66SK4dhCfQZdODpFgXQKucbIuzsLB4WgjoiAYb3TId/qR8CEBcLk+MyYfMwoAUDGi/xN1I+rNM+i+SsPbsJGmPzjIEOJqfSLX88Os1WuOUA6r5WvSHgsmE/AaVGRdzdPguyI9AuL4mhDNmMSAeboaU0N4goCgk7CQfW5I0E9l+U/zqSH+CYSNaDCEMJphT/OBIZjYiSo+lhD2lSqPapZdSSisZKM6v2EU1+hWHnfnn5gn5c0itxEAzAr4dGYFAP6be5fL5XJdABpJWCICOOe8AAAAAElFTkSuQmCC","orcid":"","institution":"Inria Bordeaux - Sud-Ouest Research Centre","correspondingAuthor":true,"prefix":"","firstName":"Nejib","middleName":"","lastName":"Zemzemi","suffix":""}],"badges":[],"createdAt":"2024-03-22 18:05:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4151419/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4151419/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00033-024-02371-z","type":"published","date":"2024-12-27T15:57:12+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":72640737,"identity":"3ab5a614-a6d0-4402-aa96-8f7772e895e7","added_by":"auto","created_at":"2024-12-30 16:09:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":299144,"visible":true,"origin":"","legend":"","description":"","filename":"PaperPbDirectKhouloudSalouaNejib.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4151419/v1_covered_e0a70034-e0b9-4a76-8c67-d6a595afa47c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mathematical analysis of a 1D-3D coupled problem in cardiac electrophysiology","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"zeitschrift-fur-angewandte-mathematik-und-physik","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"zamp","sideBox":"Learn more about [Zeitschrift für angewandte Mathematik und Physik](http://link.springer.com/journal/33)","snPcode":"33","submissionUrl":"https://submission.nature.com/new-submission/33/3","title":"Zeitschrift für angewandte Mathematik und Physik","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Inverse problem, optimal control, bidomain model, cardiac electrophysiology, optimization method, conductivity parameters.","lastPublishedDoi":"10.21203/rs.3.rs-4151419/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4151419/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe objective of this paper is to analyze a coupled problem that describes the propagation of the electric wave in the heart. 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