This paper derives rigorous statements concerning the propagation velocity of action potentials in axons. The authors use the Green’s function approach to approximate the action potential and find a relation between conduction velocity and the impulse profile. Computer simulations are used to bolster the analysis.
References
[1]
Chawla, A. and Morgera, S.D. (2014) Ephaptic Synchronization as a Mechanism for Selective Amplification of Stimuli. BMC Neuroscience, 15, Article No. P87. https://doi.org/10.1186/1471-2202-15-S1-P87
[2]
Scott, A.C. (2002) Neuroscience: A Mathematical Primer. Springer-Verlag, New York.
[3]
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.
[4]
Chawla, A., Morgera, S.D. and Snider, A.D. (2021) Fields, Geometry, and Their Impact on Axon Interaction. Journal of Applied Mathematics and Physics, 9, 751-778. https://doi.org/10.4236/jamp.2021.94053
[5]
Chawla, A. and Morgera, S.D. (2022) On the Geometry of Interacting Axon Tracts in Relation to Their Functional Properties. https://doi.org/10.1101/2022.03.29.486317
[6]
FitzHugh, R. (1955) Mathematical Models of Threshold Phenomena in the Nerve Membrane. The Bulletin of Mathematical Biophysics, 17, 257-278. https://doi.org/10.1007/BF02477753
[7]
Markin, V.S. (1970) Electric Interaction of Parallel Nonmyelinized Nerve Fibers. I. Change in the Excitability of an Adjacent Fiber. Biofizika, 15, 120-129.
[8]
Debanne, D., Campanac, E., Bialowas, A., Carlier, E. and Alcaraz, G. (2011) Axon Physiology. Physiological Reviews, 91, 555-602. https://doi.org/10.1152/physrev.00048.2009
[9]
Frankenhaeuser, B. and Huxley, A.F. (1964) The Action Potential in the Myelinated Nerve Fibre of Xenopus laevis as Computed on the Basis of Voltage Clamp Data. The Journal of Physiology, 171, 302-315. https://doi.org/10.1113/jphysiol.1964.sp007378
[10]
Halter, A. (1989) A Distributed-Parameter Model for Myelinated Nerve Fibre. Ph.D. Thesis, Rice University, Texas, AAT9136095.
[11]
Goldman, L. and Albus, J.S. (1968) Computation of Impulse Conduction in Myelinated Fibers; Theoretical Basis of the Velocity-Diameter Relation. Biophysical Journal, 8, 596-607. https://doi.org/10.1016/S0006-3495(68)86510-5
[12]
Hodgkin, A.L. and Huxley, A.F. (1952) A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve. The Journal of Physiology, 117, 500-544. https://doi.org/10.1113/jphysiol.1952.sp004764
[13]
Landahl, H.D. and Podolsky, R.J. (1949) On the Velocity of Conduction in Nerve Fibre with Saltatory Transmission. The Bulletin of Mathematical Biophysics, 11, 19-27. https://doi.org/10.1007/BF02477911
[14]
Malmivuo, J. and Plonsey, R. (1995) Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields. Oxford University Press, Oxford. https://doi.org/10.1093/acprof:oso/9780195058239.001.0001
[15]
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
[16]
Rushton, W.A.H. (1951) A Theory of the Effects of Fibre Size in Medullated Nerve. The Journal of Physiology, 115, 101-122. https://doi.org/10.1113/jphysiol.1951.sp004655
[17]
Snider, A.D. (2006) Partial Differential Equations: Sources and Solutions. Dover Publications, Mineola.
[18]
Waxman, S.G. and Wood, S.L. (1984) Impulse Conduction in Inhomogeneous Axons: Effects of Variation in Voltage-Sensitive Ionic Conductances on Invasion of Demyelinated Axon Segments and Preterminal Fibers. Brain Research, 294, 111-122. https://doi.org/10.1016/0006-8993(84)91314-3
[19]
Waxman, S.G. (1988) Biophysical Mechanisms of Impulse Conduction in Demyelinated Axons. Advances in Neurology, 47, 185-213.
[20]
Matsumoto, G. and Tasaki, I. (1977) A Study of Conduction Velocity in Nonmyelinated Nerve Fibers. Biophysical Journal, 20, 1-13. https://doi.org/10.1016/S0006-3495(77)85532-X
