5-A. Average artifact subtraction
[25]For each EEG channels, the data was first up-sample to 20 KHz and separated into segments by onsets of scans. The term “scan segments” refers to those segments of EEG.
The first channel was used to align the scan segments. The average waveform of scan segments was taken as a reference. Waveform of each segment was then shifted to maximize the correlation with the reference. The same shifting amount was then applied to every channels.
Each of the scan segments was a 1 × 𝑞𝑞 (q = interpolated time points spanning each scan, 40,000 in this case) vector. The GA template for each scan segments 𝒀𝒀𝑗𝑗ℎ was then estimated as:
𝐀𝐀𝑗𝑗 =𝐾𝐾1∑𝑙𝑙∈I(𝑗𝑗)𝒀𝒀𝑙𝑙ℎ Eq.3
Where l = 1, 2… N as the segments number, 𝑨𝑨𝑗𝑗 is a 1 × q vector of the GA template for segment j, and l was an index of the different scan segments, 𝒀𝒀𝑙𝑙ℎ, to be averaged. I(j) was an index function determines which segments were included in the average, which was ranged in [j-7, …, j-1, j+1, …, j +7] in this work, so the amount of included segment K was 15. The GA template, 𝑨𝑨𝑗𝑗, was then scaled by a constant 𝛼𝛼𝑗𝑗 to
5-B. Heart beat detection
As a prerequisite to removing PAs, QRS complexes was detected from EKG channel. The EKG channel was first band-pass filtered from 7 to 40 Hz, than a moving average filter of samples in 28 ms intervals was applied to suppress electromyogram noise[36, 83], denoted as 𝒙𝒙𝑓𝑓. The detection of QRS complexes was based on the positive value of k-Teager energy[84, 85], 𝒆𝒆𝑡𝑡, of filtered EKG signal 𝒙𝒙𝑓𝑓:
𝒆𝒆𝑡𝑡 = 𝑚𝑚𝑚𝑚𝑥𝑥 ([𝒙𝒙𝑓𝑓(𝑛𝑛)]2− 𝒙𝒙𝑓𝑓(𝑛𝑛 − 𝑘𝑘)𝒙𝒙𝑓𝑓(𝑛𝑛 + 𝑘𝑘), 0) Eq.5 The main period k in samples was tuned to sensitize pulse related frequency band:
𝑘𝑘 =4𝑓𝑓𝑓𝑓𝑠𝑠
𝑑𝑑 Eq.6
Where 𝑓𝑓𝑠𝑠 was the sampling rate (down-sampled to 500 Hz) and 𝑓𝑓𝑑𝑑 was the 10th harmonic frequency of expected heart rate (enough for describing QRS complexes [36]), which was set as 10Hz in this work.
An adaptive threshold was applied to 𝒆𝒆𝑡𝑡 for detecting every ‘r’ peaks of the QRS complexes [83]. The MFR threshold is calculated as the sum of three thresholds: 1) M- the steep-slope threshold, 2) F- the integrated threshold and 3 R- the beat expectation threshold. The ‘r’ peak is detected in certain time points that its k-Teager energy surpass the summation of the three thresholds. The M threshold decreased in an interval 200 to 1200 ms after last ‘r’ detection to 60% of the M threshold at the last ‘r’ time point, which prevented overestimation of ‘r’ peaks. A queue with the 5 last maximum 𝒆𝒆𝑡𝑡
in an interval 2
3𝑅𝑅𝑚𝑚 to 𝑅𝑅𝑚𝑚 after that. A queue with the 5 last ‘r-r’ intervals was updated at any new ‘r’ peak detection. 𝑅𝑅𝑚𝑚 was the mean value of the queue.
5-C. Optimal basis set (OBS) subtraction for pulse artifact
[36]The PA in each EEG channel was assumed to have few typical shapes, referred as basis, in an interval of time near each ‘r’ peaks, which can be determined by temporal PCA[36] . Each EEG channel was separated into sections centered at each ‘r’ peaks shifted forward in time by 210 ms and with range as 1.5 times median ‘r-r’ interval (mRR), referred as a pulse section 𝒀𝒀𝑟𝑟𝑃𝑃 (with size 1 × m𝑅𝑅𝑅𝑅), where r was the number of that section, 𝑟𝑟 ∈ [1, 𝑅𝑅], R was the total number of ‘r’ peaks detected. PA in each pulse section was modeled by PCA among all the pulse sections 𝒀𝒀𝑃𝑃 after removal the 1st order trend of each sections. Few top PCs were enough for modeling of PA in each pulse section, and top 4 PCs 𝑩𝑩𝑃𝑃 (with size = 4 × m𝑅𝑅𝑅𝑅) were selected as the bases of PAs in this work. Then
cannot be expected. We calculated the portion of average PA waveform that still reside in power after using different PCs in PA subtraction at Oz channel in EEG-only case. To exclude the stimulus responses, the pulse sections within the range of 1s before and 1s after the onset of stimuli were excluded in the calculation. The result showed that the portion of average PA waveform and its variation can be reduced more after using more PCs in PA subtraction, and using 4 PCs reduced the power to less than 1% (Figure 6-A).
There were less than 0.1% power reduction using additional PC. Averaging among all channels, 86% of average PA waveforms were subtracted using 4 PCs in PA subtraction.
This significant result was accordance with previous work [36].
Figure 9 Portion of average power resided after PA removal. (A) PA residue in portion
of power of average waveform of pulse sections in Oz channel. (B) Power of average PA waveform (orange bars) and power of average PA residue waveform (blue bars) in
each channels. The pulse sections was averaged in sections before and after PA subtraction to form average waveform of PA and PA residue. The power of waveforms
was calculated as mean square of waveforms in time.
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