A need for time-varying models to suppress artefacts of tACS in the M/EEG

Rhythmic modulation of brain activity by transcranial alternating current stimulation (tACS) can entrain neural oscillations in a frequency- and phase-specific manner. However, large stimulation artefacts contaminate concurrent 'online' neuroimaging measures, including magneto- and electro-encephalography (M/EEG) -- restricting most analyses to periods free from stimulation ('offline' aftereffects). While many published methods exist for removing artefacts of tACS from M/EEG recordings, they universally assume linear artefacts: either time-invariance (i.e., an artefact is a scaled version of itself from cycle to cycle) or sensor-invariance (i.e., artefacts are scaled versions of one another from sensor to sensor). However, heartbeat and respiration both nonlinearly modulate the amplitude and phase of these artefacts, predominantly via changes in scalp impedance. The spectral symmetry this introduces to the M/EEG spectra may lead to false-positive evidence for entrainment around the frequency of tACS, if not adequately suppressed. Good electrophysiological evidence for entrainment therefore requires that tACS artefacts are fully accounted for before comparing online spectra to a control (e.g., as might be observed during sham stimulation). Here I outline an approach to linearly solve templates for tACS artefacts, and demonstrate how event-locked perturbations to amplitude and phase can be introduced from simultaneous recordings of heartbeat and respiration -- effectively forming time-varying models of tACS artefacts. These models are constructed for individual sensors, and can therefore be used in contexts with few EEG sensors and with no assumption of artefact collinearity. I also discuss the feasibility of this approach in the absence of simultaneous recordings of heartbeat and respiration traces.