Publication:
Propagation Failure Along Myelinated Nerves

Thumbnail Image
Files
01.pdf (1.08 MB)
Official URL
http://www.springerlink.com/content/r54558750281n137/fulltext.pdf
Full text at PDC
Publication Date
2011
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Citations
Google Scholar
Exportar
DC QDC MarcXML RDF MODS METS ORE-ATOM
Research Projects
Organizational Units
Journal Issue
Abstract
Propagation of traveling pulses in the myelinated Hodgkin-Huxley model is studied. The nerve impulse is a traveling wave with two components. At the Ranvier nodes, it behaves as a discrete traveling pulse. Wave motion through the internodal regions is then driven by this traveling pulse. We give analytical characterizations of the parameter ranges for which nerve impulses fail to propagate by exploiting time scale separation and the active node approximation, which reduces the dynamics of infinite fibers to the evolution of a few nodes. Simple recipes to predict the speed of the impulses and the widths of their peaks are also given. Predictions are in good agreement with the information provided by numerical simulations.
Description
UCM subjects
Biomatemáticas , Ecuaciones diferenciales
Unesco subjects
2404 Biomatemáticas , 1202.07 Ecuaciones en Diferencias
Keywords
Citation
Anderson, A.R.A., Sleeman, B.D.: Wave front propagation and its failure in coupled systems of discrete bistable cells modelled by FitzHugh-Nagumo dynamics. Int. J. Bifurc. Chaos 5, 63–74 (1995) Beeler, G.W., Reuter, H.: Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. 268, 177–210 (1977) Bell, J., Costner, C.: Threshold behavior and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons. Q. Appl. Math. 42, 1–13 (1984) Binczak, S., Eilbeck, J.C., Scott, A.C.: Ephaptic coupling of myelinated nerve fibers. Physica D 148, 159– 174 (2001) Carpio, A.: Asymptotic construction of pulses in the Hodgkin–Huxley model for myelinated nerves. Phys. Rev. E 72, 011905 (2005a) Carpio, A.: Wave trains, self-oscillations and synchronization in discrete media. Physica D 207, 117–136 (2005b) Carpio, A., Bonilla, L.L.: Wave front depinning transition in discrete one dimensional reaction-diffusion systems. Phys. Rev. Lett. 86, 6034–6037 (2001) Carpio, A., Bonilla, L.L.: Depinning transitions in discrete reaction-diffusion equations. SIAM J. Appl. Math. 63, 1056–1082 (2003a)
URI
https://hdl.handle.net/20.500.14352/42107
Collections
Artículos