Conduction failure in axonal signal propagation: Effects of Ih in a Hodgkin-Huxley cable model

doi:10.1088/1674-1056/ae5c7a

Abstract Axonal conduction failure, characterized by spike loss during propagation, represents a fundamental nonlinear phenomenon underlying unreliable signal conduction in excitable media, but its dynamical origins remain unclear. Here, we develop a Hodgkin-Huxley cable model to investigate conduction failure during axonal propagation, incorporating the hyperpolarization-activated cyclic nucleotide-gated ($I_{h}$) current. By varying the $I_{h}$ conductance $g_{h}$, diffusion coefficient $D$, stimulation period $T_{\rm s}$, and temperature $T$, we quantify conduction reliability using conduction rate and conduction velocity. Increasing $g_{h}$ elevates the resting potential and expands the parameter region supporting faithful conduction. Conduction rate maps in the ($T_{\rm s}$, $D$) plane reveal that reliable conduction requires sufficient axial diffusion and appropriate input timing. Conduction velocity increases monotonically with $D$ but shows nontrivial dependence on $T_{\rm s}$ and $g_{h}$. Temperature reshapes axonal conduction dynamics by suppressing spike initiation at low $T$ and inducing spike multiplication at high $T$. Bifurcation analysis links these effects to $T$- and $g_{h}$-dependent shifts of saddle-node and Hopf bifurcation boundaries.

Keywords: Hodgkin-Huxley model hyperpolarization-activated cation current conduction failure conduction velocity

Received: 06 March 2026
Revised: 04 April 2026
Accepted manuscript online: 08 April 2026

PACS:	87.19.lq	(Neuronal wave propagation)
	02.30.Oz	(Bifurcation theory)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12172269).

Corresponding Authors: Yong Xie
E-mail: yxie@mail.xjtu.edu.cn

Cite this article:

Rong Hu(胡榕) and Yong Xie(谢勇) Conduction failure in axonal signal propagation: Effects of I_h in a Hodgkin-Huxley cable model 2026 Chin. Phys. B 35 068706

[1] Weidner C, Schmelz M, Schmidt R, Hammarberg B, Østavik K, Hilliges M, Torebjörk H E and Handwerker H O 2002 J. Neurosci. 22 6704
[2] Debanne D 2004 Nat. Rev. Neurosci. 5 304
[3] Debanne D and Boudkkazi S 2010 New Aspects of Axonal Structure and Function (Boston : Springer US) pp. 55
[4] Swadlow H A, Kocsis J D and Waxman S G 1980 Annu. Rev. Biophys. 9 143
[5] Swadlow H A and Waxman S G 1976 Exp. Neurol. 53 128
[6] Bullock T H 1951 J. Physiol. 114 89
[7] Hodgkin A L and Huxley A F 1952 J. Physiol. 117 500
[8] Bielefeldt K and Jackson M B 1993 J. Neurophysiol. 70 284
[9] Soleng A F, Chiu K and Raastad M 2003 J. Physiol. 552 459
[10] Bean B P 2007 Nat. Rev. Neurosci. 8 451
[11] Ratté S, Hong S, De Schutter E and Prescott S A 2013 Neuron 78 758
[12] Tigerholm J, PeterssonME, Obreja O, Eberhardt E, Namer B,Weidner C, Lampert A, Carr R W, Schmelz M and Fransén E 2015 Biophys. J. 108 1057
[13] Rama S, Zbili M and Debanne D 2018 Curr. Opin. Neurobiol. 51 37
[14] Yan H, Yan J, Yu L and Shao Y F 2024 Chin. Phys. B 33 058801
[15] Sun J, Li X, Sun Y, Xiong Z and He J 2026 Chin. Phys. B 35 010501
[16] Pape H C and McCormick D A 1989 Nature 340 715
[17] Tang Z Q and Trussell L O 2015 J. Neurosci. 35 4540
[18] Biel M, Wahl-Schott C, Michalakis S and Zong X 2009 Physiol. Rev. 89 847
[19] Khurana S, Remme M W H, Rinzel J and Golding N L 2011 J. Neurosci. 31 8936
[20] Orio P, Parra A, Madrid R, González O, Belmonte C and Viana F 2012 J. Neurophysiol. 108 3009
[21] Byczkowicz N, Eshra A, Montanaro J, Trevisiol A, Hirrlinger J, Kole M H, Shigemoto R and Hallermann S 2019 eLife 8 e42766
[22] Lu M, Gu H and Zhang X 2024 Cogn. Neurodyn. 18 2433
[23] Tigerholm J, Petersson M E, Obreja O, Lampert A, Carr R, Schmelz M and Fransén E 2014 J. Neurophysiol. 111 1721
[24] Hodgkin A L 1954 J. Physiol. 125 221
[25] Ermentrout B 2002 Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students (Philadelphia: SIAM)
[26] Wu Y,Wang Q, Granger J, Reyes Gaido O, Lopez-Cecetaite G, Aguilar E N, Ludwig A, Moroni A, BianchetMA and AndersonME 2025 Nat. Commun. 16 2102

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Conduction failure in axonal signal propagation: Effects of I_h in a Hodgkin-Huxley cable model

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