Normalized Isometry Index as a bounded force-velocity metric for assessing mechanical stimulus in isometric and low-velocity muscle contractions

Normalized Isometry Index as a bounded force-velocity metric for assessing mechanical stimulus in isometric and low-velocity muscle contractions | 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 Method Article Normalized Isometry Index as a bounded force-velocity metric for assessing mechanical stimulus in isometric and low-velocity muscle contractions Dobrochna Fryc This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9431504/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 Quasi-isometric high intensity training was proven to induce hypertrophy and type II to type I muscle fiber shift. While advances in musculoskeletal modeling enable detailed muscle force estimation, a stable metric for quantifying mechanical stimulus under isometric and low-velocity conditions remains lacking. The question arises weather a stable, bounded force-velocity metric can be formulated to accurately quantify mechanical stimulus under isometric and low-velocity conditions in musculoskeletal modeling. The proposed index was mathematically and empirically evaluated to determine its structural validity and physiological relevance. Optimization of the velocity attenuation coefficient was grounded in literature describing contraction-velocity-dependent muscle fiber adaptations, ensuring physiological plausibility. Redundancy was tested with the use of exemplary experimental data derived from musculoskeletal modeling. Analytical assessment confirmed monotonicity with respect to force, boundedness across the velocity domain, numerical stability, and a coherent force-velocity interaction structure. Correlation analyses demonstrated significant yet non-redundant associations with the component variables, supporting construct validity. Isometry Index avoided singularities at low velocities and provided a stable, interpretable representation of force-velocity behavior under both isometric and quasi-isometric conditions. The index was verified to provide a stable, interpretable, and physiologically grounded unitless scalar measure of force-velocity interactions in near-isometric conditions. Biomedical Engineering hypertrophy power adaptation fiber training Full Text Additional Declarations The authors declare no competing interests. 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-9431504","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":623919285,"identity":"a605d726-ffe6-45ab-ba61-78d50cdf49a2","order_by":0,"name":"Dobrochna Fryc","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIiWNgGAWjYDCCAzxgEogZHwAJGwYGdgZGINeCGC3MBkAiDUiDuRJEazlMWAvf8d5jHz7U3Mnjb2Bm+8xTcz6Pn5n9wQHGHbi1SJ45lzxzxrFnxRIHmJln8xy7XSzZzGNwgPEMbi0GN3KMmXkbDic2HOA/DGTcTtxwmIfhAGMbEVrmA20BMs4BtYAcRoyWDRAtB4BaGAzwagH5hXHGscOJGw8zMzPOOZYM8UsiHr8AQ+www4eaw4nzjjczM7ypscvjZ29/+ODjDhucWhAAGB1MwDhKAHMSG4jQAQKMP2BaGInVMgpGwSgYBSMBAABZulpKaMkbJAAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-4498-7041","institution":"Silesian University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Dobrochna","middleName":"","lastName":"Fryc","suffix":""}],"badges":[],"createdAt":"2026-04-15 23:56:31","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9431504/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9431504/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107126429,"identity":"ad1482d1-036f-4c42-963d-78705b53d171","added_by":"auto","created_at":"2026-04-17 05:57:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":418672,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscriptpreprint.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9431504/v1_covered_2e63acab-ae2f-4b8d-8706-81be0eb77cb4.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eNormalized Isometry Index as a bounded force-velocity metric for assessing mechanical stimulus in isometric and low-velocity muscle contractions\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Silesian University of Technology","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":"hypertrophy, power, adaptation, fiber, training","lastPublishedDoi":"10.21203/rs.3.rs-9431504/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9431504/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eQuasi-isometric high intensity training was proven to induce hypertrophy and type II to type I muscle fiber shift. 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