Designing energy-conserving surrogate models for the coupled,non-linear responses of intervertebral discs

Designing energy-conserving surrogate models for the coupled,non-linear responses of intervertebral discs | 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 Designing energy-conserving surrogate models for the coupled,non-linear responses of intervertebral discs Maria Hammer, Tizian Wenzel, Gabriele Santin, Laura Meszaros-Beller, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3073632/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Jan, 2024 Read the published version in Biomechanics and Modeling in Mechanobiology → Version 1 posted 9 You are reading this latest preprint version Abstract The aim of this study was to design physics-preserving and precise surrogate models of the non-linear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) disc models, weused greedy kernel and polynomial approximations of second, third and fourth order to train surrogate models for the scalar force-torque-potential. Doing so, the resulting models of the elastic IVD responses ensured the conservation of mechanical energy through their structure. At the sametime, they were capable of predicting disc forces for the full physiological range of motion andfor the coupling of all six degrees of freedom of an intervertebral joint. The performance of allsurrogate models for a subject-specific L4|5 disc geometry was evaluated both on training and test data obtained from uncoupled (one-dimensional), weakly coupled (two-dimensional),and random movement trajectories in the entire six-dimensional (6d) physiological displacement range, as well as on synthetic kinematic data. We observed highest precisions for the kernel surrogate followed by the fourth order polynomial model. Both clearly outperformed the second order polynomial model which is equivalent to the commonly used stiffness matrix in neuro-musculoskeletal simulations.Hence, the proposed model architectures have the potential to improve the accuracy, and, therewith, validity of load predictions in neuro-musculoskeletal spine models. Biomechanics intervertebral disc kernel approximation spine modeling elastic surrogates Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Jan, 2024 Read the published version in Biomechanics and Modeling in Mechanobiology → Version 1 posted Editorial decision: Major revision 20 Sep, 2023 Reviews received at journal 16 Sep, 2023 Reviews received at journal 13 Aug, 2023 Reviewers agreed at journal 28 Jul, 2023 Reviewers agreed at journal 27 Jul, 2023 Reviewers invited by journal 04 Jul, 2023 Editor assigned by journal 19 Jun, 2023 Submission checks completed at journal 16 Jun, 2023 First submitted to journal 16 Jun, 2023 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-3073632","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":210659749,"identity":"641d93eb-d0a5-4d8d-ad28-3f5c14517aa7","order_by":0,"name":"Maria 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