Data-informed reconstruction of a bipennate muscle’s aponeurosis and its fibre distribution for performing continuum-mechanical simulations

Data-informed reconstruction of a bipennate muscle’s aponeurosis and its fibre distribution for performing continuum-mechanical simulations | 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 Data-informed reconstruction of a bipennate muscle’s aponeurosis and its fibre distribution for performing continuum-mechanical simulations Animesh Ranjan, Okan Avci, Oliver Röhrle This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6313013/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Jul, 2025 Read the published version in Biomechanics and Modeling in Mechanobiology → Version 1 posted 9 You are reading this latest preprint version Abstract Alternatives to Diffusion-Tensor Imaging tractography methods for determining fibre orientation fields in skeletal muscle include Laplacian flow simulations. Such methods require flux boundary conditions (BCs) at the tendons and/or along the inner aponeuroses, which can significantly influence the gradients of the resulting Laplacian flow. Herein, we propose a novel method based on solving the 3D steady-state thermal heat equations to determine the fibre architecture in a bi-pennate muscle, specifically the rectus femoris. Additionally, we propose a semi-automated algorithm that provides the geometrical representation of the anterior aponeurosis, which, along with the thermal-based fibre field, is particularly well-suited for Finite Element (FE) simulations. The semi-automated reconstruction of the aponeurosis shows a good correlation with manual segmentation, yielding a dice coefficient (DSC) of 0.83. The metamodel-based approach resulted in fluxes with a mean angular deviation of 14.25° ± 10.36° and a fibre inclination from the muscle's longitudinal axis of 0.44° ± 4.48°. Comparing the mechanical output of the same rectus femoris muscle geometry informed by the two respective fibre architectures showed that the most significant contributing factor was the relative fibre inclination. Compared to the standard deviation in the undeformed configuration (0.44° ± 4.48°), the standard deviation of relative fibre inclination during passive stretching at low applied loads, for instance, at 30% of the maximum applied load, showed a significant decrease (0.49° ± 2.24°). Similarly, at maximum isometric contraction, the relative fibre inclinations at 10% initial fibre pre-stretch are 0.19° ± 1.23°, indicating a drop in standard deviation from the undeformed configuration (0.44° ± 4.48°). The current study demonstrates that despite the initial deviations in fibre orientations and relative fibre inclinations, thermal flux-based fibre orientations not only exhibit comparable results to DTI-based fibre tractography for the macroscopic analysis of the rectus femoris but also result in homogeneous stretch fields and improved numerical convergence. The proposed methods may be applied to determine inner aponeuroses of other bi- or multi-pennate muscles, enabling efficient in-silico computations of the musculoskeletal system. Rectus Femoris aponeurosis Diffusion Tensor Imaging Finite Element Method in-silico analysis fibre tractography Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 22 Jul, 2025 Read the published version in Biomechanics and Modeling in Mechanobiology → Version 1 posted Editorial decision: Revision requested 27 May, 2025 Reviews received at journal 26 May, 2025 Reviews received at journal 16 May, 2025 Reviewers agreed at journal 24 Apr, 2025 Reviewers agreed at journal 23 Apr, 2025 Reviewers invited by journal 01 Apr, 2025 Editor assigned by journal 30 Mar, 2025 Submission checks completed at journal 27 Mar, 2025 First submitted to journal 26 Mar, 2025 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. 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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-6313013","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":441723051,"identity":"ef4f9cc6-47f4-4b21-be44-df73ad4ef2b5","order_by":0,"name":"Animesh Ranjan","email":"data:image/png;base64,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","orcid":"","institution":"Fraunhofer Institute for Manufacturing Engineering and Automation","correspondingAuthor":true,"prefix":"","firstName":"Animesh","middleName":"","lastName":"Ranjan","suffix":""},{"id":441723058,"identity":"3d1041ff-e3e5-4603-be63-750db809ab2d","order_by":1,"name":"Okan Avci","email":"","orcid":"","institution":"Fraunhofer Institute for Manufacturing Engineering and Automation","correspondingAuthor":false,"prefix":"","firstName":"Okan","middleName":"","lastName":"Avci","suffix":""},{"id":441723060,"identity":"f759c6e2-0d2f-459f-8b23-e9607eb3d4df","order_by":2,"name":"Oliver Röhrle","email":"","orcid":"","institution":"University of Stuttgart","correspondingAuthor":false,"prefix":"","firstName":"Oliver","middleName":"","lastName":"Röhrle","suffix":""}],"badges":[],"createdAt":"2025-03-26 13:53:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6313013/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6313013/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10237-025-01989-w","type":"published","date":"2025-07-22T15:57:37+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":87756698,"identity":"7a0ae5f3-c35b-495f-a527-f5f135324a57","added_by":"auto","created_at":"2025-07-28 16:07:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2643926,"visible":true,"origin":"","legend":"","description":"","filename":"SubmittedVersion.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6313013/v1_covered_e10b52c6-7a60-426a-b167-fa5e9d9a8f98.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Data-informed reconstruction of a bipennate muscle’s aponeurosis and its fibre distribution for performing continuum-mechanical simulations","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":"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},"keywords":"Rectus Femoris, aponeurosis, Diffusion Tensor Imaging, Finite Element Method, in-silico analysis, fibre tractography","lastPublishedDoi":"10.21203/rs.3.rs-6313013/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6313013/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Alternatives to Diffusion-Tensor Imaging tractography methods for determining fibre orientation fields in skeletal muscle include Laplacian flow simulations. Such methods require flux boundary conditions (BCs) at the tendons and/or along the inner aponeuroses, which can significantly influence the gradients of the resulting Laplacian flow. Herein, we propose a novel method based on solving the 3D steady-state thermal heat equations to determine the fibre architecture in a bi-pennate muscle, specifically the rectus femoris. Additionally, we propose a semi-automated algorithm that provides the geometrical representation of the anterior aponeurosis, which, along with the thermal-based fibre field, is particularly well-suited for Finite Element (FE) simulations. The semi-automated reconstruction of the aponeurosis shows a good correlation with manual segmentation, yielding a dice coefficient (DSC) of 0.83. The metamodel-based approach resulted in fluxes with a mean angular deviation of 14.25° ± 10.36° and a fibre inclination from the muscle's longitudinal axis of 0.44° ± 4.48°. Comparing the mechanical output of the same rectus femoris muscle geometry informed by the two respective fibre architectures showed that the most significant contributing factor was the relative fibre inclination. Compared to the standard deviation in the undeformed configuration (0.44° ± 4.48°), the standard deviation of relative fibre inclination during passive stretching at low applied loads, for instance, at 30% of the maximum applied load, showed a significant decrease (0.49° ± 2.24°). Similarly, at maximum isometric contraction, the relative fibre inclinations at 10% initial fibre pre-stretch are 0.19° ± 1.23°, indicating a drop in standard deviation from the undeformed configuration (0.44° ± 4.48°). The current study demonstrates that despite the initial deviations in fibre orientations and relative fibre inclinations, thermal flux-based fibre orientations not only exhibit comparable results to DTI-based fibre tractography for the macroscopic analysis of the rectus femoris but also result in homogeneous stretch fields and improved numerical convergence. 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