Multi-Tongue Frequency Fractal Dynamics in Hodgkin-Huxley Neurons Induced by Temporal Interference Stimulation

TL;DR

This study reveals that temporal interference stimulation induces complex, self-similar fractal frequency responses in Hodgkin-Huxley neurons, expanding understanding of neuronal excitability under multi-frequency stimulation.

Contribution

It uncovers the fractal, hierarchical frequency response patterns in Hodgkin-Huxley neurons under temporal interference stimulation, a novel insight into neuronal dynamics.

Findings

Fractal, multi-tongue frequency responses emerge under TI stimulation.

Response structures grow with observation time, showing self-similarity.

Fractal count depends on ion channel conductances.

Abstract

We investigate neuronal excitability in the Hodgkin-Huxley model under temporal interference (TI) stimulation in a previously unexplored sub-Hz resonant regime and uncover a striking nonlinear response that we term 'multi-tongue frequency fractals'. Unlike single-frequency driving, which yields a smooth resonant valley, dual-frequency excitation fragments this response into a hierarchy of sharply modulated tongues whose number and structure grow with observation time, revealing clear self-similar architecture. These features emerge from transitions between non-cascaded and cascaded high-harmonic and sub-harmonic generation as detuning varies, and are maximized near the intrinsic ionic timescale at omega ~ 0.2 rad/s. Parameter sweeps show that the fractal count is higher for higher potassium conductances, lower sodium conductances and lower leak conductances. These results demonstrate that TI stimulation can elicit rich, hierarchically organized frequency responses even in classical excitable membranes, revealing fractal organization in Hodgkin-Huxley dynamics.