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

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_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_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_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.