Ephaptic coupling is the phenomenon where the various axons in an axon tract contribute to the evolution of the voltage variable on each axon. In this paper, we relax the central assumption of electroneutrality used by Reutskiy et al. That assumption is based on charge conservation laws. However, we present data from the literature in support of this relaxation. Thus we are able to justify the presence of negative entries in the geometric W matrix. These negative entries then impact the action potential conduction profiles of the axons in the tract. These “signed” and coupled tracts can be envisioned as bearers of neural information which is akin to that borne by a synapse.
References
[1]
Gershenfeld, N.A. (1999) The Nature of Mathematical Modeling. Cambridge University Press, Cambridge.
[2]
Reutskiy, S., Rossoni, E. and Tirozzi, B. (2003) Conduction in Bundles of Demyelinated Nerve Fibers: Computer Simulation. Biological Cybernetics, 89, 439-448. https://doi.org/10.1007/s00422-003-0430-x
[3]
Ruffini, G., Salvador, R., Tadayon, E., Sanchez-Todo, R., Pascual-Leone, A. and Santarnecchi, E. (2020) Realistic Modeling of Mesoscopic Ephaptic Coupling in the Human Brain. PLOS Computational Biology, 16, e1007923. https://doi.org/10.1371/journal.pcbi.1007923
[4]
Chawla, A., Morgera, S. and Snider, A. (2019) On Axon Interaction and Its Role in Neurological Networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 18, 790-796. https://doi.org/10.1109/TCBB.2019.2941689
[5]
Pikovsky, A., Rosenblum, M. and Kurths, J. (2003) Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge.
[6]
Johnson, M.D., Dweiri, Y.M., Cornelius, J., Strohl, K.P., Steffen, A., Suurna, M., Soose, R.J., Coleman, M., Rondoni, J., Durand, D.M. and Ni, Q. (2021) Model-Based Analysis of Implanted Hypoglossal Nerve Stimulation for the Treatment of Obstructive Sleep Apnea. Sleep, 44, S11-S19. https://doi.org/10.1093/sleep/zsaa269
[7]
Yoo, P.B., Lubock, N.B., Hincapie, J.G., Ruble, S.B., Hamann, J.J. and Grill, W.M. (2013) High-Resolution Measurement of Electrically-Evoked Vagus Nerve Activity in the Anesthetized Dog. Journal of Neural Engineering, 10, Article ID: 026003. https://doi.org/10.1088/1741-2560/10/2/026003
[8]
Bucksot, J.E., Wells, A.J., Rahebi, K.C., Sivaji, V., Romero-Ortega, M., Kilgard, M.P., Rennaker, R.L. and Hays, S.A. (2019) Flat Electrode Contacts for Vagus Nerve Stimulation. PLOS ONE, 14, e0215191. https://doi.org/10.1371/journal.pone.0215191
[9]
Peters, M.J., Stinstra, G. and Hendriks, M. (2001) Estimation of the Electrical Conductivity of Human Tissue. Electromagnetics, 21, 545-557. https://doi.org/10.1080/027263401752246199
[10]
Kramer, G. (2003) Capacity Results for the Discrete Memoryless Network. IEEE Transactions on Information Theory, 49, 4-21. https://doi.org/10.1109/TIT.2002.806135
