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

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

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