关键词: Hodgkin–Huxley model, hyperpolarization-activated cation current, conduction failure, conduction velocity

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.

Key words: Hodgkin–Huxley model, hyperpolarization-activated cation current, conduction failure, conduction velocity