Advancing Sensitivity Analysis of an Intervertebral Disc Finite Element Model: A Comparative Approach Using Neural Networks

Advancing Sensitivity Analysis of an Intervertebral Disc Finite Element Model: A Comparative Approach Using Neural Networks | 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 Advancing Sensitivity Analysis of an Intervertebral Disc Finite Element Model: A Comparative Approach Using Neural Networks Gabriel Gruber, Matan Atad, Marx Ribeiro, Luis Fernando Nicolini, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5440602/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 3 You are reading this latest preprint version Abstract Introduction: Sensitivity analysis (SA) is essential for identifying influential input parameters in finite element (FE) models, such as those of the intervertebral disc (IVD). However, in complex IVD models, efficient methods often lack accuracy, while precise methods are computationally prohibitive. Surrogate models, like neural networks (NNs), provide a solution by enabling both efficient and accurate SA of such models. Methods: This study leveraged an NN surrogate trained on an L4L5 IVD FE model to compare variance-based methods (Sobol analysis and Fourier Amplitude Sensitivity Test), the gradient-based Integrated Gradients (IG) approach, and linear model-based SA methods (CoD-ratio, CAR²-ratio, and Pearson’s correlation coefficients) for their applicability. Performance evaluation of each method involved mean absolute deviation and Normalized Discounted Cumulative Gain (NDCG) scores, with Sobol analysis results as the reference. A detailed SA of the model was conducted using Sobol analysis results to examine total-order and interaction effects of the model parameters. Results: All methods effectively identified influential parameters, as indicated by high NDCG scores. Only variance-based methods, though, consistently quantified parameter influence and captured interactions. Neglecting interaction effects resulted in unexplained variances up to 25%, highlighting the need to consider total-order effects. Key model parameters were those related to fiber orientation and annulus fibrosus stiffness. Conclusion: Variance-based global SA methods, enabled by the NN surrogate, were essential for fully understanding the FE model sensitivity, capturing total-order effects and parameter interactions. The IG method effectively identified key parameters, while the novel application of the NDCG scores demonstrated the strength of surrogate-assisted methods in assessing parameter influence. FEM IVD sensitivity analysis Sobol analysis surrogate model Integrated Gradients Full Text Additional Declarations Competing interest reported. JSK is Co-Founder of Bonescreen GmbH. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Cite Share Download PDF Status: Under Revision Version 1 posted Editor assigned by journal 16 Nov, 2024 Submission checks completed at journal 14 Nov, 2024 First submitted to journal 12 Nov, 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-5440602","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":378856752,"identity":"029ef693-2790-4f6f-bc08-77bac4685c5f","order_by":0,"name":"Gabriel Gruber","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAs0lEQVRIiWNgGAWjYLACxgYGBn4wi40ULZJtJGsxOEasFnkH9mufeXfY5Bvf7zHdwFBmQ1iL4QGe4tm8Z9Istx3jMbvBcC6NCC0NPMnMvG2HDcxAWhjbDhOt5b+BcRtYy38i/MLAfhio5YCBARtYywHCWgyYeZgZ555JNpA4llZ2I+FcMhG2tLc/Zni7w86Av/nwthsfyuyIsOUwjwGCl0BYA9CWBvYHxKgbBaNgFIyCkQwAorg0yR1z9mAAAAAASUVORK5CYII=","orcid":"","institution":"Institute for Neuroradiology, TUM University Hospital, School of Medicine and Health, Technical University of Munich","correspondingAuthor":true,"prefix":"","firstName":"Gabriel","middleName":"","lastName":"Gruber","suffix":""},{"id":378856753,"identity":"0e119db9-5a3b-4e38-a064-acd52b7c9e2e","order_by":1,"name":"Matan Atad","email":"","orcid":"","institution":"Institute for Neuroradiology, TUM University Hospital, School of Medicine and Health, Technical University of Munich","correspondingAuthor":false,"prefix":"","firstName":"Matan","middleName":"","lastName":"Atad","suffix":""},{"id":378856754,"identity":"6dd2501b-a48d-41ea-b4ef-d6fd71099959","order_by":2,"name":"Marx Ribeiro","email":"","orcid":"","institution":"University Hospital Halle, Martin-Luther-University Halle-Wittenberg","correspondingAuthor":false,"prefix":"","firstName":"Marx","middleName":"","lastName":"Ribeiro","suffix":""},{"id":378856755,"identity":"26fc8b4a-d42a-45cc-bd58-0d951bf63985","order_by":3,"name":"Luis Fernando Nicolini","email":"","orcid":"","institution":"Federal University of Santa Maria","correspondingAuthor":false,"prefix":"","firstName":"Luis","middleName":"Fernando","lastName":"Nicolini","suffix":""},{"id":378856756,"identity":"46f21a08-0e8c-4407-8146-c447958e7b28","order_by":4,"name":"Tanja Lerchl","email":"","orcid":"","institution":"Institute for Neuroradiology, TUM University Hospital, School of Medicine and Health, Technical University of Munich","correspondingAuthor":false,"prefix":"","firstName":"Tanja","middleName":"","lastName":"Lerchl","suffix":""},{"id":378856757,"identity":"81570d61-24f5-4a0a-aca7-ab68f09059cb","order_by":5,"name":"Jan S. 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However, in complex IVD models, efficient methods often lack accuracy, while precise methods are computationally prohibitive. Surrogate models, like neural networks (NNs), provide a solution by enabling both efficient and accurate SA of such models.\u003c/p\u003e\u003ch2\u003eMethods:\u003c/h2\u003e\u003cp\u003eThis study leveraged an NN surrogate trained on an L4L5 IVD FE model to compare variance-based methods (Sobol analysis and Fourier Amplitude Sensitivity Test), the gradient-based Integrated Gradients (IG) approach, and linear model-based SA methods (CoD-ratio, CAR\u0026sup2;-ratio, and Pearson\u0026rsquo;s correlation coefficients) for their applicability. Performance evaluation of each method involved mean absolute deviation and Normalized Discounted Cumulative Gain (NDCG) scores, with Sobol analysis results as the reference. A detailed SA of the model was conducted using Sobol analysis results to examine total-order and interaction effects of the model parameters.\u003c/p\u003e\u003ch2\u003eResults:\u003c/h2\u003e\u003cp\u003eAll methods effectively identified influential parameters, as indicated by high NDCG scores. Only variance-based methods, though, consistently quantified parameter influence and captured interactions. Neglecting interaction effects resulted in unexplained variances up to 25%, highlighting the need to consider total-order effects. Key model parameters were those related to fiber orientation and annulus fibrosus stiffness.\u003c/p\u003e\u003ch2\u003eConclusion:\u003c/h2\u003e\u003cp\u003eVariance-based global SA methods, enabled by the NN surrogate, were essential for fully understanding the FE model sensitivity, capturing total-order effects and parameter interactions. The IG method effectively identified key parameters, while the novel application of the NDCG scores demonstrated the strength of surrogate-assisted methods in assessing parameter influence.\u003c/p\u003e","manuscriptTitle":"Advancing Sensitivity Analysis of an Intervertebral Disc Finite Element Model: A Comparative Approach Using Neural Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-05 17:38:15","doi":"10.21203/rs.3.rs-5440602/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorAssigned","content":"","date":"2024-11-16T10:32:05+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-11-14T06:21:00+00:00","index":"","fulltext":""},{"type":"submitted","content":"Biomechanics and Modeling in Mechanobiology","date":"2024-11-12T14:58:19+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":"96e27ce0-bf22-4052-b684-e801e2d2a731","owner":[],"postedDate":"December 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2025-01-09T23:08:13+00:00","versionOfRecord":[],"versionCreatedAt":"2024-12-05 17:38:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5440602","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5440602","identity":"rs-5440602","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}