Nonlinearities and timescales in neural models of temporal interference stimulation

In temporal interference (TI) stimulation, neuronal cells react to two interfering sinusoidal electric fields with a slightly different frequency ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:mrow><mml:msub><mml:mi>f</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> </mml:mrow> <mml:annotation>${f}_{1}$</mml:annotation></mml:semantics> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:mrow><mml:msub><mml:mi>f</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:mrow> <mml:annotation>${f}_{2}$</mml:annotation></mml:semantics> </mml:math> in the range of about 1-4 kHz, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:mrow><mml:mo>∣</mml:mo> <mml:msub><mml:mi>f</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>-</mml:mo> <mml:msub><mml:mi>f</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:mo>∣</mml:mo></mml:mrow> </mml:mrow> <mml:annotation>$| {f}_{1}-{f}_{2}| $</mml:annotation></mml:semantics> </mml:math> in the range of about 1-100 Hz). It has been previously observed that for the same input intensity, the neurons do not react to a purely sinusoidal signal at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:mrow><mml:msub><mml:mi>f</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> </mml:mrow> <mml:annotation>${f}_{1}$</mml:annotation></mml:semantics> </mml:math> or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:mrow><mml:msub><mml:mi>f</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:mrow> <mml:annotation>${f}_{2}$</mml:annotation></mml:semantics> </mml:math> . This study seeks a better understanding of the largely unknown mechanisms underlying TI neuromodulation. To this end, single-compartment models are used to simulate computationally the response of neurons to the sinusoidal and TI waveform. This study compares five different neuron models: Hodgkin-Huxley (HH), Frankenhaeuser-Huxley (FH), along with leaky, exponential, and adaptive-exponential integrate-and-fire (IF). It was found that IF models do not entirely reflect the experimental behavior while the HH and FH model did qualitatively replicate the observed neural responses. Changing the time constants and steady state values of the ion gates in the FH model alters the response to both the sinusoidal and TI signal, possibly reducing the firing threshold of the sinusoidal input below that of the TI input. The results show that in the modified (simplified) model, TI stimulation is not qualitatively impacted by nonlinearities in the current-voltage relation. In contrast, ion channels have a significant impact on the neuronal response. This paper offers insights into neuronal biophysics and computational models of TI stimulation.