A Multi-compartment Homogenized Perfusion Model for Deforming Hierarchical Vasculature

A Multi-compartment Homogenized Perfusion Model for Deforming Hierarchical Vasculature | 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 A Multi-compartment Homogenized Perfusion Model for Deforming Hierarchical Vasculature Jannes Hohl, Adnan Ebrahem, Etienne Jessen, Marco F.P. ten Eikelder, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6211022/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Dec, 2025 Read the published version in Biomechanics and Modeling in Mechanobiology → Version 1 posted 15 You are reading this latest preprint version Abstract The simulation of tissue perfusion based on highly detailed synthetic vasculature that often consists of multiple supplying and draining trees with millions of vascular segments is computationally expensive. Converting highly detailed synthetic vasculature into a homogenized continuum flow representation offers a computationally efficient alternative. In this paper, we investigate such a modeling approach that retains the essential features of potentially deforming hierarchical vascular networks. It is based on multi-compartment homogenization, where each compartment represents homogenized perfusion via a Darcy-type flow model associated with vascular segments at a specific spatial resolution in one individual tree of the network. The compartments are coupled through a pressure-dependent mass exchange, applied in a smeared manner everywhere within the perfusion domain. Key parameters, namely the permeability tensors of each compartment and the intercompartmental perfusion coefficients, are estimated directly from the vascular segments of the synthetic vasculature using averaging techniques. For scenarios involving deformation, such as in a pumping heart or a regenerating liver, we introduce a computationally efficient parameter update based on geometric mapping. We demonstrate the effectiveness and accuracy of the approach for several benchmark examples, including full-scale liver perfusion. Tissue perfusion hierarchical vasculature synthetic tree generation multi-compartment homogenization Darcy-type flow liver perfusion Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 24 Dec, 2025 Read the published version in Biomechanics and Modeling in Mechanobiology → Version 1 posted Editorial decision: Revision requested 02 May, 2025 Reviews received at journal 01 May, 2025 Reviews received at journal 29 Apr, 2025 Reviews received at journal 23 Apr, 2025 Reviews received at journal 23 Apr, 2025 Reviews received at journal 17 Apr, 2025 Reviewers agreed at journal 24 Mar, 2025 Reviewers agreed at journal 24 Mar, 2025 Reviewers agreed at journal 24 Mar, 2025 Reviewers agreed at journal 23 Mar, 2025 Reviewers agreed at journal 22 Mar, 2025 Reviewers invited by journal 22 Mar, 2025 Editor assigned by journal 15 Mar, 2025 Submission checks completed at journal 13 Mar, 2025 First submitted to journal 12 Mar, 2025 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6211022","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":435083897,"identity":"32383731-ccef-4794-a0be-e813f7c8bfc1","order_by":0,"name":"Jannes Hohl","email":"data:image/png;base64,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","orcid":"","institution":"TU Darmstadt","correspondingAuthor":true,"prefix":"","firstName":"Jannes","middleName":"","lastName":"Hohl","suffix":""},{"id":435083898,"identity":"d6134b4f-6c25-4dd5-abd7-6a84fdccfb75","order_by":1,"name":"Adnan Ebrahem","email":"","orcid":"","institution":"TU Darmstadt","correspondingAuthor":false,"prefix":"","firstName":"Adnan","middleName":"","lastName":"Ebrahem","suffix":""},{"id":435083900,"identity":"3d9db002-8dc5-4d3f-8d59-c4c17542fe8e","order_by":2,"name":"Etienne Jessen","email":"","orcid":"","institution":"TU Darmstadt","correspondingAuthor":false,"prefix":"","firstName":"Etienne","middleName":"","lastName":"Jessen","suffix":""},{"id":435083901,"identity":"d6287f7c-39b5-470a-a639-5622938bdfd3","order_by":3,"name":"Marco F.P. ten Eikelder","email":"","orcid":"","institution":"TU Darmstadt","correspondingAuthor":false,"prefix":"","firstName":"Marco","middleName":"F.P. ten","lastName":"Eikelder","suffix":""},{"id":435083903,"identity":"537644ff-63bb-4256-a59c-6668b252c390","order_by":4,"name":"Dominik Schillinger","email":"","orcid":"","institution":"TU Darmstadt","correspondingAuthor":false,"prefix":"","firstName":"Dominik","middleName":"","lastName":"Schillinger","suffix":""}],"badges":[],"createdAt":"2025-03-12 10:08:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6211022/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6211022/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10237-025-02026-6","type":"published","date":"2025-12-24T15:58:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":99172889,"identity":"3d8c4ab4-ae35-442b-ab1e-f2cf850bec76","added_by":"auto","created_at":"2025-12-29 16:11:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":17416743,"visible":true,"origin":"","legend":"","description":"","filename":"AMulticompartmentHomogenizedPerfusionModelforDeformingHierarchicalVasculature.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6211022/v1_covered_ea15bbf6-c8db-41e7-ab22-243697f48b03.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Multi-compartment Homogenized Perfusion Model for Deforming Hierarchical Vasculature","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":"biomechanics-and-modeling-in-mechanobiology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmmb","sideBox":"Learn more about [Biomechanics and Modeling in Mechanobiology](http://link.springer.com/journal/10237)","snPcode":"10237","submissionUrl":"https://submission.nature.com/new-submission/10237/3","title":"Biomechanics and Modeling in Mechanobiology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Tissue perfusion, hierarchical vasculature, synthetic tree generation, multi-compartment homogenization, Darcy-type flow, liver perfusion","lastPublishedDoi":"10.21203/rs.3.rs-6211022/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6211022/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The simulation of tissue perfusion based on highly detailed synthetic vasculature that often consists of multiple supplying and draining trees with millions of vascular segments is computationally expensive. Converting highly detailed synthetic vasculature into a homogenized continuum flow representation offers a computationally efficient alternative. In this paper, we investigate such a modeling approach that retains the essential features of potentially deforming hierarchical vascular networks. It is based on multi-compartment homogenization, where each compartment represents homogenized perfusion via a Darcy-type flow model associated with vascular segments at a specific spatial resolution in one individual tree of the network. The compartments are coupled through a pressure-dependent mass exchange, applied in a smeared manner everywhere within the perfusion domain. Key parameters, namely the permeability tensors of each compartment and the intercompartmental perfusion coefficients, are estimated directly from the vascular segments of the synthetic vasculature using averaging techniques. For scenarios involving deformation, such as in a pumping heart or a regenerating liver, we introduce a computationally efficient parameter update based on geometric mapping. We demonstrate the effectiveness and accuracy of the approach for several benchmark examples, including full-scale liver perfusion.","manuscriptTitle":"A Multi-compartment Homogenized Perfusion Model for Deforming Hierarchical Vasculature","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-01 05:34:56","doi":"10.21203/rs.3.rs-6211022/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-05-02T10:54:29+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-01T21:49:13+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-29T17:18:57+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-23T18:27:14+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-23T18:04:00+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-17T07:29:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"323672912001432451378077957892179828977","date":"2025-03-24T22:23:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"339830030009924946184262756569689062080","date":"2025-03-24T19:28:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"10363835890267276263247707822832843058","date":"2025-03-24T17:21:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"201251430228974873294402380896772206663","date":"2025-03-23T09:04:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"52360818668124695284692152086376162920","date":"2025-03-22T22:56:09+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-22T22:08:38+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-15T15:22:56+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-03-13T14:18:09+00:00","index":"","fulltext":""},{"type":"submitted","content":"Biomechanics and Modeling in Mechanobiology","date":"2025-03-12T10:02:09+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"biomechanics-and-modeling-in-mechanobiology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmmb","sideBox":"Learn more about [Biomechanics and Modeling in Mechanobiology](http://link.springer.com/journal/10237)","snPcode":"10237","submissionUrl":"https://submission.nature.com/new-submission/10237/3","title":"Biomechanics and Modeling in Mechanobiology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"e20b8ee2-4236-4319-95b5-5f48c0c52bc4","owner":[],"postedDate":"April 1st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-12-29T16:08:33+00:00","versionOfRecord":{"articleIdentity":"rs-6211022","link":"https://doi.org/10.1007/s10237-025-02026-6","journal":{"identity":"biomechanics-and-modeling-in-mechanobiology","isVorOnly":false,"title":"Biomechanics and Modeling in Mechanobiology"},"publishedOn":"2025-12-24 15:58:05","publishedOnDateReadable":"December 24th, 2025"},"versionCreatedAt":"2025-04-01 05:34:56","video":"","vorDoi":"10.1007/s10237-025-02026-6","vorDoiUrl":"https://doi.org/10.1007/s10237-025-02026-6","workflowStages":[]},"version":"v1","identity":"rs-6211022","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6211022","identity":"rs-6211022","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}