Influence of Cell Size and Porosity on Permeability in Bone Scaffold TPMS Structures

Influence of Cell Size and Porosity on Permeability in Bone Scaffold TPMS Structures | 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 Influence of Cell Size and Porosity on Permeability in Bone Scaffold TPMS Structures Hangming Shen, Chaojie Song, Lihong Yang, Yi Gan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5174277/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In bone tissue engineering, bone scaffold structures based on triply periodic minimal surfaces (TPMS) are of significant interest, with permeability being a key indicator of scaffold performance. This paper constructs three types of bone scaffold TPMS structures—Diamond (D), Gyroid (G), and IWP—in both sheet (S) and network (N) forms, and it specifically investigates the impact of two structural parameters—cell size and porosity—on the permeability of these porous structures through numerical simulation. The results demonstrate that permeability increases with both cell size and porosity. Among the structures, the IWP type exhibits significantly higher permeability compared to the other two types. Under identical conditions, N-form structures show superior permeability over S-form structures within the same type. Additionally, empirical formulae for calculating the permeability of the three N-form structures, based on the two parameters of cell size and porosity, are derived. These formulae have been experimentally validated, demonstrating that the errors within a reasonable and acceptable range. These findings provide theoretical guidance for the optimized design and practical application of bone scaffold TPMS structures. TPMS Permeability Empirical formula Porosity Bone Scaffold Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-5174277","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":366313670,"identity":"4c31d41b-fe95-4009-9d12-38873de3494b","order_by":0,"name":"Hangming Shen","email":"","orcid":"","institution":"University of Shanghai for Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Hangming","middleName":"","lastName":"Shen","suffix":""},{"id":366313671,"identity":"242262b3-4807-4010-a9a7-a539e85beba6","order_by":1,"name":"Chaojie Song","email":"","orcid":"","institution":"University of Shanghai for Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Chaojie","middleName":"","lastName":"Song","suffix":""},{"id":366313672,"identity":"60002fcf-cbb2-491f-a670-4a8c854228b9","order_by":2,"name":"Lihong Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYBACPgkIncDPzHz4AVFa2GBaJNvZ0gxI02JwnkdBgjgt0j2Gnwt+1eUZH+ZhMGCosYkmrEXmjLH0zL7DxWaHeQ88YDiWlttA2GE5BtK8PQcStx3mSzBgbDhMlBbj37w9dYmbm3kMJIjVYibN84M5cQMz8VrSyqx5Gw4nzjgMDOQEYvzCL5G8+TbPn7rE/v7Dhx98qLEhrIWBgcOAgbENyk4grBwE2B8wMPwhTukoGAWjYBSMUAAAdt08KwsdMcAAAAAASUVORK5CYII=","orcid":"","institution":"University of Shanghai for Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Lihong","middleName":"","lastName":"Yang","suffix":""},{"id":366313673,"identity":"7836fd2d-b9b7-4948-b962-d0c8348ef9b6","order_by":3,"name":"Yi Gan","email":"","orcid":"","institution":"University of Shanghai for Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Gan","suffix":""}],"badges":[],"createdAt":"2024-09-29 09:53:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5174277/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5174277/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":69489797,"identity":"84afe305-4795-441e-bd42-4927f7f041fc","added_by":"auto","created_at":"2024-11-21 02:31:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":976653,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5174277/v1_covered_1252a06e-6894-4857-8cc7-a72f7c1c7613.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Influence of Cell Size and Porosity on Permeability in Bone Scaffold TPMS Structures","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"TPMS, Permeability, Empirical formula, Porosity, Bone Scaffold","lastPublishedDoi":"10.21203/rs.3.rs-5174277/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5174277/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn bone tissue engineering, bone scaffold structures based on triply periodic minimal surfaces (TPMS) are of significant interest, with permeability being a key indicator of scaffold performance. This paper constructs three types of bone scaffold TPMS structures\u0026mdash;Diamond (D), Gyroid (G), and IWP\u0026mdash;in both sheet (S) and network (N) forms, and it specifically investigates the impact of two structural parameters\u0026mdash;cell size and porosity\u0026mdash;on the permeability of these porous structures through numerical simulation. The results demonstrate that permeability increases with both cell size and porosity. Among the structures, the IWP type exhibits significantly higher permeability compared to the other two types. Under identical conditions, N-form structures show superior permeability over S-form structures within the same type. Additionally, empirical formulae for calculating the permeability of the three N-form structures, based on the two parameters of cell size and porosity, are derived. These formulae have been experimentally validated, demonstrating that the errors within a reasonable and acceptable range. 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