Functional adaptation of bone mechanical properties using a diffusive stimulus originated by dynamic loads in bone remodelling

Functional adaptation of bone mechanical properties using a diffusive stimulus originated by dynamic loads in bone remodelling | 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 Functional adaptation of bone mechanical properties using a diffusive stimulus originated by dynamic loads in bone remodelling Rachele Allena, Daria Scerrato, Alberto Bersani, Ivan Giorgio This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3845178/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Apr, 2024 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted 7 You are reading this latest preprint version Abstract The present study proposes a mathematical model elucidating some aspects of the biomechanical stimulus involved in bone remodelling, which, in our assumptions, acts as a diffusive signalling agent for bones. The proposed mathematical model aims to scrutinize the behaviour of bone tissues and their evolution over time by better understanding the mechanisms of bone remodelling and offering new theoretical tools for developing more effective and efficient treatment strategies for bone defects, trauma, or diseases. The bone remodelling process involves adapting bone mechanical properties in response to dynamic loads. This adaptation is achieved through the diffusive stimulus created by these loads. The result is a functional adaptation of the bone, wherein it acquires the mechanical properties required to withstand the loads to which it is subjected. This phenomenon has significant implications for the study of bone physiology and biomechanics. As such, it is a topic of great interest to researchers and practitioners in the fields of orthopaedics, sports medicine, and related disciplines. In this contribution, the mechanical behaviour is modelled through a generalized three-dimensional deformable continuum that also takes into account the porous nature of the bone tissue with a nonlinear constitutive law. Since we have focused the study on the model of the stimulus and its interplay with the evolution of the tissue, an isotropic material symmetry is adopted to simplify the problem. This formulation is promising because it permits the bone tissue to evolve depending on the time-variability of the external mechanical loads, even if the source of the stimulus is assumed to be the strain energy density. Mathematics Subject Classification (2010). 74L15 Biomechanical solid mechanics. Bone remodelling Fick’s laws of diffusion Fourier’s laws of diffusion bio-mechanical stimulus Growth Mechanics. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Apr, 2024 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted Editorial decision: Revision requested 26 Feb, 2024 Reviews received at journal 26 Feb, 2024 Reviewers agreed at journal 13 Jan, 2024 Reviewers invited by journal 13 Jan, 2024 Editor assigned by journal 13 Jan, 2024 Submission checks completed at journal 10 Jan, 2024 First submitted to journal 08 Jan, 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. We do this by developing innovative software and high quality services for the global research community. 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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-3845178","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":266210530,"identity":"41ad805f-4630-4aa9-883e-02a53d8d8c51","order_by":0,"name":"Rachele Allena","email":"data:image/png;base64,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","orcid":"","institution":"Université Côte d'Azur","correspondingAuthor":true,"prefix":"","firstName":"Rachele","middleName":"","lastName":"Allena","suffix":""},{"id":266210531,"identity":"dd124b86-9094-4658-b17e-b22470d8ddb5","order_by":1,"name":"Daria Scerrato","email":"","orcid":"","institution":"Sapienza University of Rome","correspondingAuthor":false,"prefix":"","firstName":"Daria","middleName":"","lastName":"Scerrato","suffix":""},{"id":266210532,"identity":"60c96404-e969-47c8-85d1-d0b336034e50","order_by":2,"name":"Alberto Bersani","email":"","orcid":"","institution":"Sapienza University of Rome","correspondingAuthor":false,"prefix":"","firstName":"Alberto","middleName":"","lastName":"Bersani","suffix":""},{"id":266210533,"identity":"61f3b524-83b4-4ebf-9ad4-205fdab2d086","order_by":3,"name":"Ivan Giorgio","email":"","orcid":"","institution":"University of L'Aquila","correspondingAuthor":false,"prefix":"","firstName":"Ivan","middleName":"","lastName":"Giorgio","suffix":""}],"badges":[],"createdAt":"2024-01-08 10:44:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3845178/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3845178/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00033-024-02230-x","type":"published","date":"2024-04-21T08:47:09+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":55042234,"identity":"8a168361-33cc-4939-88e6-978fa3292545","added_by":"auto","created_at":"2024-04-21 08:47:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1567764,"visible":true,"origin":"","legend":"","description":"","filename":"Articolobone3D.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3845178/v1_covered_2ff08a21-bbdb-4e15-9002-4e82e55c96f4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Functional adaptation of bone mechanical properties using a diffusive stimulus originated by dynamic loads in bone remodelling","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":"Bone remodelling, Fick’s laws of diffusion, Fourier’s laws of diffusion, bio-mechanical stimulus, Growth Mechanics.","lastPublishedDoi":"10.21203/rs.3.rs-3845178/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3845178/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe present study proposes a mathematical model elucidating some aspects of the biomechanical stimulus involved in bone remodelling, which, in our assumptions, acts as a diffusive signalling agent for bones. 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