The modelling of the action potentials in myelinated nerve fibres (2406.18590v3)

Abstract: The initial version of the planned paper has gone through a major revision in 2025. First, the paper ended up growing a bit too long, and as a result of that, we decided to split it into two parts. The first part focuses on the model for the unmyelinated case and its behaviour, and the second part focuses on including the influence of myelination into the model. Second, when the initial version of the manuscript was going through the review process, it became evident that the way the content was presented was somewhat confusing for readers with a background in the experimental side of research into nerve processes. As a result, we went through a major revision, redoing all the numerical simulations with parameters that are closer to what Hodgkin and Huxley used in their classical paper from 1952, where the Hodgkin-Huxley model was initially introduced. The second major change was to change the logic how the specific inductance value is chosen for the numerical example - in the previous version it was chosen by aiming for a specific propagation velocity when the axon radius was chosen as 1 micrometre, in the updated version the value is chosen to get the AP propagation velocity which was experimentally observed in the HH 1952 paper at the same parameters as were used in that paper. Part 1 - On hyperbolicity for nerve pulse propagation in axons. Part 2 - The modelling of the action potentials in myelinated nerve fibres.