A 3D Convolutional Neural Network for Design Optimization of Minimal Surface Scaffolds in Bone Tissue Engineering

A 3D Convolutional Neural Network for Design Optimization of Minimal Surface Scaffolds in Bone Tissue Engineering | 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 3D Convolutional Neural Network for Design Optimization of Minimal Surface Scaffolds in Bone Tissue Engineering Innocent Bwengye, Emmanuel Ahishakiye, William Wasswa, Johnes Obungoloch This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8295059/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 Triply periodic minimal surfaces (TPMS) have emerged as promising scaffold architectures for bone tissue engineering due to their ability to balance mechanical stiffness with fluid transport. However, evaluating these trade-offs typically requires separate finite element (FEA) and computational fluid dynamics (CFD) analyses, which are computationally expensive and hinder large-scale design exploration. In this study, we propose a multitask 3D convolutional neural network (3D-CNN) surrogate that jointly predicts apparent elastic modulus ( \(\:{E}_{app}\) ), permeability ( \(\:k\) ), effective diffusivity ( \(\:{D}_{eff}\) ), and a wall shear stress (WSS)-exposure metric from voxelized TPMS geometries. The model was trained on 30 scaffold designs spanning Gyroid, Schwarz-P, and Diamond families, with iso-threshold and unit-cell variations covering porosities of 0.55–0.80. Results demonstrate high predictive performance ( \(\:{R}^{2}>0.90\) across targets), with up to 35% error reduction compared to analytical baselines such as Kozeny–Carman and Bruggeman formulations. Pareto analysis revealed distinct family-specific trade-offs, with Gyroid scaffolds achieving the most stable shear metrics, while Schwarz-P and Diamond offered higher transport efficiency at moderate stiffness levels. This model provides a reproducible, physics-aware surrogate for rapid scaffold evaluation and optimization, offering significant potential to accelerate scaffold design for bone tissue engineering. TPMS scaffolds multitask 3D-CNN permeability effective diffusivity bone tissue engineering 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-8295059","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":563753316,"identity":"ed98d787-756b-47c0-9e50-c801ccb7543a","order_by":0,"name":"Innocent 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Engineering","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 scaffolds, multitask 3D-CNN, permeability, effective diffusivity, bone tissue engineering","lastPublishedDoi":"10.21203/rs.3.rs-8295059/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8295059/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTriply periodic minimal surfaces (TPMS) have emerged as promising scaffold architectures for bone tissue engineering due to their ability to balance mechanical stiffness with fluid transport. However, evaluating these trade-offs typically requires separate finite element (FEA) and computational fluid dynamics (CFD) analyses, which are computationally expensive and hinder large-scale design exploration. In this study, we propose a multitask 3D convolutional neural network (3D-CNN) surrogate that jointly predicts apparent elastic modulus (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{app}\\)\u003c/span\u003e\u003c/span\u003e), permeability (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e), effective diffusivity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{eff}\\)\u003c/span\u003e\u003c/span\u003e), and a wall shear stress (WSS)-exposure metric from voxelized TPMS geometries. The model was trained on 30 scaffold designs spanning Gyroid, Schwarz-P, and Diamond families, with iso-threshold and unit-cell variations covering porosities of 0.55\u0026ndash;0.80. Results demonstrate high predictive performance (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{2}\u0026gt;0.90\\)\u003c/span\u003e\u003c/span\u003e across targets), with up to 35% error reduction compared to analytical baselines such as Kozeny\u0026ndash;Carman and Bruggeman formulations. Pareto analysis revealed distinct family-specific trade-offs, with Gyroid scaffolds achieving the most stable shear metrics, while Schwarz-P and Diamond offered higher transport efficiency at moderate stiffness levels. This model provides a reproducible, physics-aware surrogate for rapid scaffold evaluation and optimization, offering significant potential to accelerate scaffold design for bone tissue engineering.\u003c/p\u003e","manuscriptTitle":"A 3D Convolutional Neural Network for Design Optimization of Minimal Surface Scaffolds in Bone Tissue Engineering","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-22 03:29:12","doi":"10.21203/rs.3.rs-8295059/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"69781528-4f87-493a-8b6b-f019b2f3ef4b","owner":[],"postedDate":"December 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-01-19T08:44:35+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-22 03:29:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8295059","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8295059","identity":"rs-8295059","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}