{"paper_id":"1fe2ee08-1403-4fed-8f3c-067b10fd6b78","body_text":"The modelling of the action potentials in myelinated nerve fibres | 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 The modelling of the action potentials in myelinated nerve fibres Kert Tamm, Tanel Peets, Jüri Engelbrecht This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7507124/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Jan, 2026 Read the published version in Biomechanics and Modeling in Mechanobiology → Version 1 posted 9 You are reading this latest preprint version Abstract The classical Hodgkin-Huxley model describes the propagation of an axon potential (AP) in unmyelinated axons. In many cases, the axons have a myelin sheath, and the experimental studies have then revealed significant changes in the velocity of APs. In this paper, a theoretical model is proposed describing the AP propagation in myelinated axons. As far as the velocity of an AP is affected, the basis of the model is taken after Lieberstein, who included the possible effect of inductance that might influence velocity, into the governing equation. The proposed model includes the structural properties of the myelin sheath: the μ-ratio (the ratio of the length of the myelin sheath and the node of Ranvier) and g-ratio (the ratio of the inner-to-outer diameter of a myelinated axon) through parameter γ. The Lieberstein model can describe all the essential effects characteristic to the formation and propagation of an AP in an unmyelinated axon. Then, a phenomenological model (a wave-type equation) for a myelinated axon is described, including the influence of the structural properties of the myelin sheath and the radius of an axon. The numerical simulation using the physical variables demonstrates the changes in the velocity of an AP. These results match well the known effects from experimental studies. action potential nerve fibre myelinated axon velocity mathematical modelling Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 08 Jan, 2026 Read the published version in Biomechanics and Modeling in Mechanobiology → Version 1 posted Editorial decision: Revision requested 05 Oct, 2025 Reviews received at journal 28 Sep, 2025 Reviews received at journal 26 Sep, 2025 Reviewers agreed at journal 11 Sep, 2025 Reviewers agreed at journal 03 Sep, 2025 Reviewers invited by journal 03 Sep, 2025 Editor assigned by journal 03 Sep, 2025 Submission checks completed at journal 02 Sep, 2025 First submitted to journal 01 Sep, 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-7507124\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":509824156,\"identity\":\"1da539f4-a0fd-4679-9b64-d936ebf0570b\",\"order_by\":0,\"name\":\"Kert Tamm\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIiWNgGAWjYBACCTiLvYGB4QGQNiBCC2MDQwKQxXOYgSEhgSQtEslEapFs733+gPGHXbTuzPcHPyT+sJE3Z2A++ACfFmme44ZAW5Jzt91OZpZISEgz3NnAlozXJjmJNJDDmEFaGIBaDicYHOAxk8CrRf4ZSEt97rabh5l/JCT8B2rh//4Dr8Mk2EBaDuduu8HMBrTlAMgWNnw6GCR70hhnJKQdz912JtnMIiEt2XDDYTZjvA6TOH6M4cMHm+rcbccPPr7xwcZO3uB488MPeK0BgQQUHjNB9aNgFIyCUTAKCAEAKstKgU4FRD0AAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Tallinn University of Technology\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Kert\",\"middleName\":\"\",\"lastName\":\"Tamm\",\"suffix\":\"\"},{\"id\":509824157,\"identity\":\"bb1f88e9-3b58-4108-832c-84a308208cf1\",\"order_by\":1,\"name\":\"Tanel Peets\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Tallinn University of Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Tanel\",\"middleName\":\"\",\"lastName\":\"Peets\",\"suffix\":\"\"},{\"id\":509824158,\"identity\":\"ea9ad65a-558b-4768-b1e1-de83d60d0c05\",\"order_by\":2,\"name\":\"Jüri Engelbrecht\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Tallinn University of Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Jüri\",\"middleName\":\"\",\"lastName\":\"Engelbrecht\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2025-09-01 10:08:32\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-7507124/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-7507124/v1\",\"draftVersion\":[],\"editorialEvents\":[{\"content\":\"https://doi.org/10.1007/s10237-025-02030-w\",\"type\":\"published\",\"date\":\"2026-01-08T15:59:30+00:00\"}],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":100070105,\"identity\":\"696d59d8-1239-4822-8127-a72b78f67edc\",\"added_by\":\"auto\",\"created_at\":\"2026-01-12 16:16:25\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":3371365,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"MyelinatedAParticleBMMBseconditerationfinal.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7507124/v1_covered_d8baecb6-275d-4cd5-a409-52a9fc3be08f.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"The modelling of the action potentials in myelinated nerve fibres\",\"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\":\"info@researchsquare.com\",\"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\":\"action potential, nerve fibre, myelinated axon, velocity, mathematical modelling\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-7507124/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-7507124/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThe classical Hodgkin-Huxley model describes the propagation of an axon potential (AP) in unmyelinated axons. 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