Concurrent EEG with Frequency-Shift-Keyed (FSK) Temporal Interference (TI)
DOI: Pending DOI
Synopsis
An oscillation that undergoes an instantaneous change in frequency from f1 to f2 will cause a ripple artefact in any filters which have f1 and f2 in their stopband. Filters are typically deployed at the front-end of EEG instrumentation, either in hardware or software. Temporal Interference (TI) traditionally uses two alternating currents, each of which have constant frequencies for the duration of a therapy session. Novel iterations of TI deployments have been demonstrated that intermittently introduce the difference in frequency for short bursts or pulses. This is achieved by changing the frequency on one of the currents, instantaneously, from f1 to f2 (and back to f1 after a defined duration). This switch will cause an artefact in concurrently recorded EEG. This work presents a strategy to mitigate the resulting artefact’s effect on EEG analysis.
Background
Neurodegenerative and neuropsychiatric disorders, including Alzheimer's disease (AD), Parkinson's disease (PD), and major depressive disorder (MDD), affect hundreds of millions globally and represent a growing burden as populations age1. Pharmacological interventions are often limited by side effects, variable efficacy, and an inability to target specific neural circuits. Non-invasive neuromodulation has therefore emerged as a promising therapeutic avenue, with techniques such as transcranial electrical stimulation (tES) and, more recently, temporal interference (TI) stimulation2 offering the potential to modulate deep brain structures non-invasively3.
Electroencephalography (EEG) is a uniquely valuable tool for evaluating these interventions, providing high temporal resolution insight into the neural dynamics underlying stimulation effects. Concurrent EEG–stimulation recordings can illuminate mechanisms of action, identify biomarkers of response, and ultimately inform clinical efficacy. However, recording EEG during tES is technically challenging: stimulation introduces large artefacts that obscure the underlying neural signal, and robust artefact removal remains an open problem4.
As neuromodulation paradigms evolve, established artefact removal methods often fail to generalise to newer waveforms. Frequency-shift-keyed (FSK) TI, also known as theta-burst TI5, presents a particularly novel artefact profile that existing pipelines cannot adequately address.
This work tackles this problem by introducing a strategy to control the artefact’s profile (magnitude, polarity) without effecting the TI envelope. Further demonstrated is a method to validate the amelioration of the artefact’s influence on EEG analysis from a bench-top platform, enabling reliable analysis of neural responses to FSK-TI.
Methods
A resistive H-bridge load was used as a stimulation load. The load sets the operating point of the stimulator to a state typical of human experiments (~2.4 kΩ per stimulation channel). The load scales the voltage of the LPF/EEG input to an appropriate range using resistive division (0.224 V). Stimulation currents (I1 and I2) were set to 2mA each.
The TI waveforms are generated using Direct Digital Synthesisers (DDS). The DDS can dynamically toggle between the two frequencies in real-time. The DDS outputs a digital signal which, when switching from high to low, is used to flag the current phase angle of the waveform (zero-crossing negative to positive) - therefore triggering an interrupt service routine (ISR) on a microcontroller. The ISR uses a time delay before commanding the DDS to change frequency – to target exact phase angle for a frequency switch.
The load was stimulated with I1 at 2000Hz and I2 switching from 2000Hz to 2100Hz; 100ms and 10ms inter-pulse interval (IPI) and pulse-width (PW) respectively, and 90/270° switching angles. A 7th order Butterworth lowpass with a 90Hz cutoff frequency was used for EEG recording. Two repetitions of four conditions were recorded; condition A switched frequency at 90° fixed, B at 90° vs 270° interleaved, C at 90° or 270° randomly, and D did not switch frequency at all.
Each recording was 240s, with the first and last 60s discarded (to remove transients from start-up and shutdown). The remaining 120s was segmented into 1s epochs from which canonical band power metrics were extracted, from 3 to 43Hz. 23 to 33Hz was omitted due to an unrelated environmental artefact. A linear model in R was constructed with epoch number and condition as predictors. Estimated marginal means were computed for each condition and contrasted against the no-switching control condition using Dunnett's correction for multiple comparisons.
Results
A high frequency waveform with an instantaneous change in frequency causes an artefact closely resembling that of an impulse response (Figure, B.ii). Not controlling this artefact leads to artefactual contamination of both time-domain and frequency-domain analysis of concurrently recorded EEG (Figure, D.ii, D.iii).
Switching from f1 to f2 will elicit a response which is equal in magnitude but opposite in polarity to switching from f2 back to f1 (Figure, B.ii). The response magnitude scales with the distance in Hz between f2 and f1 - though it is a non-linear relationship, being relative to the frequency response of the filter.
The TI envelope waveform is dependent on the difference in frequency (Δf) - or relative phase difference - between f2 and f1. In FSK-TI, the envelope will oscillate according to Δf when I2 is oscillating at f2, and it will remain fixed as a function of the phase difference between I2 and I1 (when I2 are both oscillating at f1). The envelope is not affected by the absolute phase angle of I2 at the instant it changes frequency. The absolute phase angle of I2 when it switches frequency controls both the polarity and magnitude of the LPF’s response. Switching at the ‘optimal’ phase angle (θoptimal) can almost fully remove the response (Figure, C). Finally, switching at θoptimal vs θoptimal +180° will always result in the same magnitude of response, but opposite polarity.
Interleaving each successive frequency switch to begin at θoptimal or θoptimal + 180° will result in suppression of time-domain epoch analysis (Figure, D.ii, green) but leave contamination in frequency domain for long recordings (Figure, D.iii, green). Randomly toggling between a switch at θoptimal or θoptimal + 180° on a per-pulse basis results in suppression of the artefact in both time and frequency domains (Figure, D.ii, red, D.iii, red).
Theta magnitude (between 3 to 8Hz) with no pulses had a mean of 3.754μV. Differences in theta magnitude relative to no-pulse control were small and non-significant for all conditions (fixed: Δ=-0.0342μV, t(955)=-0.468, p=0.9085; interleaved: Δ=-0.098μV, t(955)=-1.344, p=0.3967; randomised: Δ=-0.0768μV, t(955)=-1.05, p=0.5776).
Alpha magnitude (between 8 and 13Hz) with no pulses had a mean of 3.629μV. Differences in the alpha magnitude relative to no-pulse control were small and non-significant for all conditions (fixed: Δ=0.0793μV, t(955)=1.1, p=0.5491; interleaved: Δ=-0.084μV, t(955)=-1.16, p=0.5077; randomised: Δ=-0.056μV, t(955)=-0.774, p=0.7538).
Beta was divided into four ranges to match bandwidth of theta and alpha per division. Beta1 magnitude (13 to 18Hz) with no pulses had a mean of 3.673μV. Differences in beta1 magnitude were small and non-significant for all conditions (fixed: Δ=0.0375μV, t(955)=0.512, p=0.8904; interleaved: Δ=-0.0577μV, t(955)=-0.788, p=0.7453; randomised: Δ=-0.032μV, t(955)=-0.441, p=0.9189).
Beta2 magnitude (between 18 and 23Hz) with no pulses had a mean of 3.524μV. Differences in beta2 magnitude were significant for only fixed switching angle condition (fixed: Δ=0.197μV, t(955)=2.878, p=0.0117; interleaved: Δ=0.025μV, t(955)=0.366, p=0.9447; randomised: Δ=0.115μV, t(955)=1.680, p=0.2271).
Beta3 magnitude (between 33 and 38Hz) with no pulses had a mean of 3.627μV. Differences in beta3 magnitude were insignificant for all conditions, though close to significance for interleaved (fixed: Δ=-0.11μV, t(955)=-1.473, p=0.3252; interleaved: Δ=0.173μV, t(955)=2.323, p=0.0554; randomised: Δ=0.06μV, t(955)=0.816, p=0.7287).
Beta4 magnitude (between 38 and 43Hz) with no pulses had a mean of 3.442μV. Differences in beta2 magnitude were significant for both fixed switching angle and randomised switching angle (fixed: Δ=0.489μV, t(955)=7.209, p<0.0001; interleaved: Δ=0.0387μV, t(955)=0.571, p=0.8634; randomised: Δ=0.308μV, t(955)=4.542, p<0.0001).
Discussion
Effectiveness of mitigation can be expected to deteriorate as recorded frequencies approach (2n-1)/(2*PW), where n is any integer. Inversely, effectiveness improves as recorded frequencies approach n/PW (artefact profile follows a comb filter). Results show that differences between conditions with control only begin to emerge as the frequency approaches 50Hz (agreeing with theoretical expectation for PW of 10ms), where significant differences emerge earliest when using a fixed switching angle. For these exact switching parameters, EEG analysis can be performed on the theta and alpha ranges, and low beta if randomising or interleaving switching angle.
The instantaneous change in frequency demonstrates a perturbative nature identical to that of a unit impulse – and therefore it’s shape for a given parameter combination can be well predicted by an experimenter. The exact filter-response waveform can vary between that identical to an impulse-response, to the time-derivative of its impulse response, approaching the latter as the overall magnitude gets smaller. This transitional nature depends on the filter type and the order. The derivative of an impulse response scales it’s frequency spectrum linearly with frequency.
The effect of phase angle on frequency-switch artefact can be synthetically investigated with signal processing software to get an approximation of theoretical best phase angle for an experiment’s parameters. The spectral footprint of the artefact is determined as a function of the current/voltage amplitudes, IPI, PW, phase-angle of switching and filter frequency response – highlighting the need for experimenters to consider their parameters’ effects on the EEG canonical bands. Further – the importance of a control strategy (e.g. randomly toggling the switching angle) is demonstrated for time and frequency domain analysis.
Disclosures
Nothing to disclose by any author(s).
References
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