Stimulation Artifact Source Separation (SASS) for assessing electric brain oscillations during transcranial alternating current stimulation (tACS)

Brain oscillations, e.g. measured by electro- or magnetoencephalography (EEG/MEG), are causally linked to brain functions that are fundamental for perception, cognition and learning. Recent advances in neurotechnology provide means to non-invasively target these oscillations using frequency-tuned amplitude-modulated transcranial alternating current stimulation (AM-tACS). However, online adaptation of stimulation parameters to ongoing brain oscillations remains an unsolved problem due to stimulation artifacts that impede such adaptation, particularly at the target frequency. Here, we introduce a real-time compatible artifact rejection algorithm (Stimulation Artifact Source Separation, SASS) that overcomes this limitation. SASS is a spatial filter (linear projection) removing EEG signal components that are maximally different in the presence versus absence of stimulation. This enables the reliable removal of stimulation-specific signal components, while leaving physiological signal components unaffected. For validation of SASS, we evoked brain activity with known phase and amplitude using 10 Hz visual flickers across 7 healthy human volunteers. 64-channel EEG was recorded during and in absence of 10 Hz AM-tACS targeting the visual cortex. Phase differences between AM-tACS and the visual stimuli were randomized, so that steady-state visually evoked potentials (SSVEPs) were phase-locked to the visual stimuli but not to the AM-tACS signal. For validation, distributions of single-trial amplitude and phase of EEG signals recorded during and in absence of AM-tACS were compared for each participant. When no artifact rejection method was applied, AM-tACS stimulation artifacts impeded assessment of single-trial SSVEP amplitude and phase. Using SASS, amplitude and phase of single trials recorded during and in absence of AM-tACS were comparable. These results indicate that SASS can be used to establish adaptive (closed-loop) AM-tACS, a potentially powerful tool to target various brain functions, and to investigate how AM-tACS interacts with electric brain oscillations. Highlights - Stimulation Artifact Source Separation (SASS), a real-time compatible signal decomposition algorithm for separating electric brain activity and stimulation signal artifacts related to amplitude-modulated transcranial alternating current stimulation (AM-tACS), is introduced - Employing SASS, phase and amplitude of single-trial steady state visual evoked potentials (SSVEPs) were reliably recovered from electroencephalography (EEG) recordings at the frequency targeted with AM-tACS - SASS enables assessment of single-trial oscillatory brain activity at the target frequency during stimulation and paves the way for online adaptation of stimulation parameters to ongoing brain oscillations


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Brain oscillations reflect neuronal cell-assembly formation causally linked to various brain functions, 57 such as perception (Fries, Schroder SASS identifies hidden and linearly separable data components that are maximally attributable to 137 transcranial electric stimulation and least attributable to brain activity. These components are then 138 rejected to achieve stimulation artifact suppression. SASS is based on a generalized eigenvalue 139 decomposition (joint diagonalization) of encephalographic covariance matrices during and in absence of 140 stimulation. It was shown that using an eigenvalue decomposition of the covariance matrix for Signal-141 Space Projection (SSP) (Uusitalo & Ilmoniemi, 1997) can be used to suppress tACS artifacts (Vosskuhl 142 et al., 2019), but this approach is agnostic to the spatial distribution of physiological brain activity 143 possibly limiting performance of artifact removal. In SSP, the data matrix becomes linearly separated 144 into orthogonal signal and noise subspaces. This is equivalent to an eigenvalue decomposition of the covariance matrix A, where the resulting components (which are orthogonal) can be ordered by the 146 amount of variance they explain: 147 The matrix P can then be constructed, which projects the data onto the vector subspace ("signal space") 148 orthogonal to the top few components explaining the most variance ("noise space"). This can be written 149 as a separation of the data into latent components, followed by a zeroing out of undesired components 150 and a projection back into the original sensor space: 151 To account for the spatial distribution of physiological brain activity, SASS was designed to identify 155 components that jointly maximize the variance attributable to stimulation artifacts and minimize the 156 variance attributable to brain activity. In SASS, a source separation matrix is computed from the joint 157 diagonalization of EEG sensor covariance matrices during (A) and in absence of stimulation (B), 158 respectively: 159 The ratio represents the ratio of signal power of component i during tACS relative to in absence of 162 tACS. Like SSP, SASS can be summarized in a single linear projection: 163 � and + denotes the pseudoinverse of (4) 165

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This approach is related to spatio-spectral decomposition (Nikulin, Nolte, & Curio, 2011), which also 167 involves a joint diagonalization of covariance matrices. Like SASS, SSD computes a spatial filter which 168 aims to increase the signal-to-noise ratio of narrowband EEG activity. Different to SASS, SSD contrasts 169 the covariance in the target frequency band against the covariance in neighboring frequency bands. This 170 distinguishes it from SASS, where covariances computed within the same frequency band during and in 171 absence of AM-tACS are contrasted. Importantly, in SASS a certain number of components must be 172 chosen for stimulation artifact rejection. We minimize residual artifacts by selecting the number of 173 components that minimizes the difference in signal power at the target frequency (as measured by mean 174 squared error across all channels  between cleaned data recorded during AM-tACS 175 and data recorded in absence of AM-tACS). 176 177

Electroencephalography (EEG) 178
A 64-channel EEG system (Bittium Corp., Oulu, Finland) with passive Ag/AgCl electrodes (Brain 179 Products GmbH, Gilching, Germany) was used to record electrical activity on the scalp. The amplifier 180 was set to DC-mode with a dynamic range of +/-430 V, a resolution of 51 nV/bit, and a range of 24 bit. 181 Electrode impedances were kept below 10 kOhm. Signals were sampled at 500 Hz with an anti-aliasing 182 filter applied at 125 Hz. Saturated electrodes were excluded from the analysis. Electrodes exhibiting 183 broadband power more than two orders of magnitude higher than the median in the condition without 184 AM-tACS were excluded from the analysis. time domain. We FIR filtered the data from 5 -15 Hz and applied the Hilbert transform to obtain the 232 signal envelope. Then, we windowed the data into 4 second segments centered on electrocardiogram 233 (ECG) R-peaks. We subtracted the temporal mean from each segment and tested for a significant 234 modulation at each timepoint using a permutation test. We compared the average envelope around an R-235 peak to the average envelopes computed using 1000 random placements of the segments. The resulting 236 p-values were Bonferroni-corrected for multiple comparisons. The permutation test was computed for 237 every channel. 238 239

Single-trial amplitude and phase 240
To compute single-trial amplitude and phase, the unsegmented bandpass filtered EEG data was Hilbert 241 transformed. Then, the data was segmented into 2 second trials corresponding to the presentation of each 242 visual flicker. Finally, instantaneous amplitude and phase difference between EEG and flicker was 243 computed for each timepoint and averaged within each trial to obtain a single data point per trial. For 244 visualization, the mean phase angle across trials was subtracted. 245 246

Statistical procedures 247
To test whether single-trial amplitudes during AM-tACS without SASS were larger than in absence of 248 AM-tACS, we employed a one-sided t-test for independent samples. To test whether single-trial 249 amplitudes during AM-tACS with SASS were smaller than during AM-tACS without SASS, we 250 employed a one-sided t-test for dependent samples. To test whether single-trial amplitudes during AM-251 tACS with SASS were different from single-trial amplitudes in absence of AM-tACS (i.e. whether any 252 residual artifacts remained after SASS), we employed a two-sided t-test for independent samples. Analogously to the case of single-trial amplitudes, we employed Wallraff tests (Zar, 1999) for dependent 259 or independent samples to test for differences in single-trial phases (relative to the visual flicker) within 260 each subject. In the dependent samples case, angular distances were compared using a Wilcoxon rank-261 sum test. In the independent samples case, angular distances were compared using a Mann-Whitney U 262 test. Phase locking values and mean single-trial amplitudes at the group level were statistically compared 263 using one-or two-sided Wilcoxon rank-sum tests. 264 To test for differences in single-trial amplitude between conditions across the entire sensor space, spatial 265 cluster-based permutation tests with threshold-free cluster enhancement (Smith & Nichols, 2009) Table 1). A power analysis revealed that, using SASS, a difference in means (residual artifact) 294 of above 0.174 and 0.972 µV, respectively (depending on the variances of single-trial amplitudes within 295 a subject), could have been detected (see Section 2.7). Single-trial SSVEP phase (relative to the visual 296 flicker) was significantly distorted during AM-tACS compared to data recorded in absence of AM-tACS. 297 Using SASS, single-trial SSVEP phase during AM-tACS was not different from single-trial SSVEP 298 phase recorded in absence of AM-tACS (Fig. 4B, Table 2). Figs. S3 and S4 depict the results seen in Fig.  299 4 for all study participants. 300

Properties of Stimulation Artifact Source Separation (SASS) 357
Depending on the experimental design and purpose of study, there are a number of properties of SASS 358 that users should consider. First, presumably due to spatially varying capacitive effects (Noury & Siegel,359 2017a), the topography of the AM-tACS artifact is frequency-dependent. Therefore, SASS must be 360 computed separately for each frequency band of interest (Fig. S7). Second, the optimal number of 361 components to reject (Section 2.1.2) may vary across participants. The eigenvalue spectrum and spatial 362 patterns of rejected components across all subjects are visualized in Fig. S6. Third, applying a time-and 363 frequency-domain analysis for a selected occipital channel across all study participants according to 364 (Noury et al., 2016) did not evidence any demodulations including intermodulation distortions at the 365 AM-tACS target frequency (Fig. S5). Fourth, due to time-varying covariances, SASS computed for one 366 dataset should not be applied to another dataset. This may lead to sub-optimal performance (Fig. S8). 367 Therefore, we advise to recompute SASS according to the covariance of the dataset it is applied to. This

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Up to now, there was no real-time compatible signal processing tool available for AM-tACS artifact 377 suppression that allows for recovering phase and amplitude of evoked brain responses at a single-trial 378 level. Here, we introduced SASS, a spatial filter based on a source separation matrix computed from joint 379 diagonalization of EEG sensor covariance matrixes at the target frequency recorded in absence and 380 during AM-tACS. To evaluate the effectiveness of SASS, we used a 10-Hz-SSVEP paradigm resulting 381 in evoked oscillatory brain responses with known frequency, amplitude and phase. Electric brain activity 382 was assessed using EEG across six healthy volunteers in absence and during AM-tACS targeting the 383 SSVEP frequency. Using SASS, single-trial SSVEP amplitude and phase information was restored to the level recorded in absence of stimulation (Fig. 4) across all study participants. Likewise, the SSVEP 385 topography was successfully recovered (Fig. 3) across all study participants. 386 Besides showing that SASS is an effective tool for separating electric brain activity and stimulation 387 artifacts at the frequency targeted by AM-tACS, our results pave the way for implementation of adaptive 388 stimulation paradigms in which the phase, amplitude and spatial distribution of the applied electric field 389 is adapted to ongoing brain oscillations. This may contribute to the development of more effective 390 stimulation approaches to target various brain functions and further elucidate the underlying mechanisms 391 of AM-tACS. 392 393 While 200 trials employed in the current study provide sufficient statistical power to detect residual 394 artifacts of above 0.174 and 0.972 µV, respectively, (Section 2.7) averaging of instantaneous phase 395 differences and amplitudes within each single trial may have masked residual artifacts. Furthermore, in 396 SASS, the sensor covariance matrix of physiological signals of interest is estimated from EEG data 397 recorded in absence of stimulation. However, this covariance may be affected by AM-tACS via 398 modulations of brain activity. Therefore, it cannot be ruled out that signal of interests are also attenuated 399 when applying SASS during AM-tACS (e.g., entrained endogenous brain oscillations). Further studies 400 are required to systematically assess this possibility. A similar issue may occur when SASS is 401 precomputed and applied to novel data (Fig. S8). Due to time-varying covariances, robust online 402 application of SASS will require methods for dynamically solving the eigenvalue problem and updating 403 the spatial filter. This can be achieved by a recursive solution to the underlying eigenvalue problem, 404 commonly used in real-time systems in other fields (Li et al., 2000). Future work will also need to include 405 a comprehensive validation for other electrode montages, exploring how the spatial relationship of 406 cortical sources and stimulation electrodes affects the performance of SASS. Finally, while in this work 407 we strived to validate SASS for AM-tACS, application of SASS in combination with other stimulation 408 protocols, e.g. conventional tACS, is also possible. However, depending on the magnitude of artifacts at 409 the frequencies of interest, more signal components may have to be rejected reducing the dimensionality 410 of data.