A Mathematical Characterization of Neural Activation Induced by Temporal Interference Stimulation

TL;DR

This paper develops a mathematical framework combining phase-plane analysis and singular perturbation methods to understand how temporal interference stimulation activates neurons, revealing the roles of amplitude and beat frequency.

Contribution

It introduces a novel mathematical analysis of TIS effects on neurons, integrating differential equations with simulations to clarify activation conditions.

Findings

Neuron activation depends on amplitude and beat frequency of TIS.

Mathematical conditions for quiescence, transient, and persistent firing are identified.

The framework predicts neuronal responses to different TIS parameters.

Abstract

Temporal Interference Stimulation (TIS) is a non-invasive neuromodulation technique in which two high-frequency sinusoidal currents with slightly different frequencies generate a low-frequency envelope that can activate deep neural structures. This study investigates the conditions under which TIS elicits action potentials in a single neuron modeled by the FitzHugh-Nagumo system. This research integrates phase-plane analysis and geometric singular perturbation to develop a mathematical framework for analyzing TIS. By combining a mathematical analysis of differential equations with computer simulations, the study elucidates how the amplitudes and beat frequency jointly determine whether the neuron remains quiescent, exhibits only transient responses, or undergoes persistent (tonic) firing.