We present a new method for removing artifacts in electroencephalography (EEG) records during Galvanic Vestibular Stimulation (GVS). The main challenge in exploiting GVS is to understand how the stimulus acts as an input to brain. We used EEG to monitor the brain and elicit the GVS reflexes. However, GVS current distribution throughout the scalp generates an artifact on EEG signals. We need to eliminate this artifact to be able to analyze the EEG signals during GVS. We propose a novel method to estimate the contribution of the GVS current in the EEG signals at each electrode by combining time-series regression methods with wavelet decomposition methods. We use wavelet transform to project the recorded EEG signal into various frequency bands and then estimate the GVS current distribution in each frequency band. The proposed method was optimized using simulated signals, and its performance was compared to well-accepted artifact removal methods such as ICA-based methods and adaptive filters. The results show that the proposed method has better performance in removing GVS artifacts, compared to the others. Using the proposed method, a higher signal to artifact ratio of −1.625 dB was achieved, which outperformed other methods such as ICA-based methods, regression methods, and adaptive filters.
Brain stimulation by means of electrical currents has been employed in neurological studies for therapy purposes for many years [
Measured EEG data during 72 seconds of GVS stimulation and 60 seconds before and after applying the GVS.
Considering that the frequency spectra of the neural signals and GVS artifacts overlap, filtering the frequency components of GVS artifacts results in the loss of the original neural signals. The four major EEG frequency bands are Delta (the lowest frequency band up to 4 Hz), Theta (4 Hz to 8 Hz), Alpha (8 Hz to 12 Hz), and Beta (12 Hz to 30 Hz). In order to analyze and understand the effect of GVS on EEG patterns, it is essential to be able to remove the artifact signals from the frequency band of interest, before establishing any GVS-EEG interaction models.
There are various methods to remove different types of artifacts, such as myogenic artifacts [
We propose a novel method for GVS artifacts removal by combining time-series regression methods and wavelet decomposition methods. To enhance the precision of the artifact estimation using regression models, the models should account for the complex behavior of the GVS interactions in the frequency domain. So we decomposed the recorded EEG and GVS signals into different frequency bands and then used regression models to estimate the GVS artifacts in each frequency band. We used multiresolution wavelet analysis to decompose nonstationary EEG signals in the time-frequency plane. Both the discrete wavelet transform (DWT) and the stationary wavelet transform (SWT) algorithms were employed, and the results were compared. To estimate the GVS current distribution through the scalp using time-series regression methods based on biophysical models, we used and compared the performance of different parametric regression models, such as discrete-time polynomials, nonlinear Hammerstein-Wiener, and state-space models.
In this study, we firstly used simulated data to assess and optimize the performance of the proposed method using various regression models and different wavelet algorithms. The resulting optimized method was then applied to real data. We compared the results of the proposed method and other methods, such as ICA, using both simulated and real data. This paper is organized as follows: Section
The EEG recording was carried out with a NeuroScan SynAmps2 system, with 20 electrodes located according to the international 10–20 EEG system (Table
EEG channels.
ch1 | ch2 | ch3 | ch4 | ch5 | ch6 | ch7 | ch8 | ch9 | ch10 |
FP1 | FP2 | F7 | F3 | Fz | F4 | F8 | T7 | C3 | Cz |
| |||||||||
ch11 | ch12 | ch13 | ch14 | ch15 | ch16 | ch17 | ch18 | ch19 | ch20 |
C4 | T8 | P7 | P3 | Pz | P4 | P8 | O1 | O2 | Ref |
The GVS signal was applied using a Digitimer DS5 isolated bipolar current stimulator. This stimulator can generate a stimulation current with a waveform proportional to the controlling voltage applied to its input. The waveform was generated using LabVIEW and sent to the stimulator through a National Instrument (NI) Data Acquisition (DAQ) board. In this study, we applied a zero-mean pink noise current, with a 1/
To quantitatively assess and optimize the performance of the proposed method and compare the accuracy of different methods in removing the GVS artifacts from the EEG recordings, we used simulated data. The simulation study was carried out by combining the clean (artifact free) EEG recordings with the simulated GVS contamination. To simulate the actual process of the GVS contamination, we paid attention to the physical structure of the electrode-skin interface and the electrical impedance of the head between the points that the EEG and the GVS electrodes are placed. As the skull impedance is much higher than scalp impedance [
Electrical equivalent circuit for the electrode-skin interface and the underlying skin [
In this electrical equivalent circuit,
Fit percentage between the simulation output and the measured EEG at each channel.
The fit percentage is a measure of the relative energy fraction in the simulated GVS artifact calculated as given by:
The results show that the fitness of simulated GVS artifact is higher at the EEG electrodes which are closer to the GVS electrodes and it is lower at further channels like channel 15 (Pz), channel 10 (Cz), channel 5 (Fz), channel 1 (FP1), and channel 2 (FP2). According to (
We calculated the impedance models using the entire EEG data collected in each trial (70 seconds). To address the concern about the time-variant properties of the scalp impedance, we computed the impedance models for shorter time intervals (e.g., 1s, 2s, 5s, 7s, 10s, and 14s) and analyzed the fitness of the simulated GVS artifact with the measured EEG data (Figure
The fit percentage for the simulated GVS artifact at channel 18 for time intervals (a) 1 sec, (b) 2 sec, (c) 5 sec, (d) 7 sec, (e) 10 sec, and (f) 14 sec.
The results show that the fitness of the models does not vary for different lengths of time intervals, and for different time intervals it is very close to the fitness of the output model using the entire 70 seconds EEG data, which is around 87%. The above results indicate that the impedance of the scalp can be represented by one transfer function for the entire trial. To simulate the measured EEG data during the GVS, we combined the simulated GVS artifacts with the clean EEG data collected right before the GVS is applied, in order to get a global data set with known EEG and GVS artifact components. This facilitates a quantitative comparison of the effectiveness of the method in removing the undesirable artifact signals.
The injected GVS current and the EEG signals are recorded concurrently by the measurement system, while the GVS current distribution through the scalp contaminates the recorded EEG signals. We can use the recorded GVS current as a reference to identify the GVS artifacts in the measured EEG signals. To identify the GVS artifacts in the contaminated EEG signals, we applied time-series regression methods using different model structures. One class of model structures is the
Here
Another class of model structures is Hammerstein-Wiener model, which uses one or two static nonlinear blocks in series with a linear block. This model structure can be employed to capture some of the nonlinear behavior of the system. The linear block is a discrete transfer function, represents the dynamic component of the model, and will be parameterized using an Output-Error model similar to the previous model. The nonlinear block can be a nonlinear function such as dead-zone, saturation, or piecewise-linear functions. As we have not observed any dead-zone or saturation type of nonlinearity in our data, we chose the piecewise-linear function by which we can break down a nonlinear system into a number of linear systems between the breakpoints.
We also used
Adaptive filtering is another approach to remove artifacts. This method is specifically suitable for real time applications. The adaptive filter uses the received input data point to refine its properties (e.g., transfer function or filter coefficients) and match the changing parameters at every time instant. These filters have been employed to remove different EEG artifacts [
In our application, the primary input to the adaptive filter system is the measured contaminated EEG signal
or
Among the various optimization techniques, we chose the Recursive Least-Squares (RLS) and the Least Mean Squares (LMS) for our application. In the section “Comparison of the performance of different artifact removal methods”, we compared the results of adaptive filters with those of the other methods.
In this section, we explain how we employ the wavelet methods to enhance the performance of our artifact removal method. The applied GVS current in this study is a pink noise with frequency band of 0.1–10 Hz. Both the GVS current and the EEG data are acquired at the sampling rate of 1000 Hz. After antialiasing filtering, the signals are in a frequency range of 0–500 Hz. The following is the power spectrum of the GVS current using
The GVS current power spectrum.
As shown above, the main GVS frequency components are in the range of 0.1 to 10 Hz. To achieve the best fit between the estimated GVS contribution and the measured EEG at each EEG channel, we broke down the recorded GVS current and the contaminated EEG data into various frequency bands by means of wavelet analysis and estimated the GVS artifacts in each frequency band. Wavelet transform is able to construct a high resolution time-frequency representation of nonstationary signals like EEG signals. In wavelet transform, the signal is decomposed into a set of basis functions, obtained by dilations and shifts of a unique function
Frequency bands for approximation and details components.
L1 | L2 | L3 | L4 | L5 | L6 | |
---|---|---|---|---|---|---|
Approximation | 0–250 | 0–125 | 0–62.5 | 0–31.25 | 0–15.75 | 0–7.87 |
Details | 250–500 | 125–250 | 62.5–125 | 31.25–62.5 | 15.75–31.25 | 7.87–15.75 |
| ||||||
L7 | L8 | L9 | L10 | L11 | L12 | |
| ||||||
Approximation | 0–3.93 | 0–1.96 | 0–0.98 | 0–0.49 | 0–0.24 | 0–0.12 |
Details | 3.93–7.87 | 1.96–3.93 | 0.98–1.96 | 0.49–0.98 | 0.24–0.49 | 0.12–0.24 |
The ICA component attributed to the stimulus artifact, 72 seconds in the middle.
We tried two approaches to remove the artifact. The first approach is to zero out the artifact signals from the components that account for the GVS parasitic influence and obtain a new cleaned-up source matrix
The ICA component attributed to the stimulus artifact after applying the threshold.
Eventually, we reconstruct ICA-corrected EEG signals as:
In the proposed method, we decomposed the EEG and GVS current signals in 12 frequency bands (Table
Flowchart of the process for detecting GVS artifacts in the proposed method.
The estimated GVS artifact frequency components are subtracted from the contaminated EEG frequency components. The wavelet decomposition enables us to focus on the frequency bands of interest and calculate the estimated GVS artifacts in each frequency band independently; thus the regression method can deal better with some nonlinear behaviors of the skin in the frequency domain. This wavelet-based time-frequency analysis approach enhances the performance of the artifact removal method. The cleaned-up signal is reconstructed from the proper frequency components of the estimated GVS signal components in the frequency range of interest (e.g., 1 Hz to 32 Hz). We calculated the correlation coefficients between the GVS signals and the estimated GVS artifacts reconstructed from different frequency bands, and we observed that the regression results improve when we reconstruct the estimated GVS artifact components from corresponding frequency bands separately.
The result of the correlation analysis is tabulated in Table
Correlation between the GVS signal and the estimated GVS artifact reconstructed from different frequency components.
Estimated GVS artifact without wavelet decomposition | Estimated GVS artifact from 0.12 Hz to 250 Hz | Estimated GVS artifact from 0.24 Hz to 125 Hz | Estimated GVS artifact from 0.49 Hz to 62.5 Hz | |
| ||||
Correlation | 0.6960 | 0.8463 | 0.9168 | 0.9725 |
| ||||
Estimated GVS artifact from 0.49 Hz to 31.25 Hz | Estimated GVS artifact from 0.49 Hz to 15.75 Hz | Estimated GVS artifact from 0.98 Hz to 31.25 Hz | Estimated GVS artifact from 0.98 Hz to 15.75 Hz | |
| ||||
Correlation | 0.9776 | 0.9769 | 0.9899 | 0.9899 |
The result shows that the correlation between the GVS signal and the estimated GVS artifact significantly increases by using wavelet decomposition method. We applied the wavelet transform to remove frequency components lower than 0.98 Hz and higher than 31.25 Hz, which are not of the main interest, and the correlation between the GVS signal and estimated GVS artifact was increased up to 0.9899.
We employed both SWT and DWT algorithms in the proposed artifact removal method. The difference between SWT and DWT algorithms was briefly explained in the wavelet analysis section. We also used various regression models to estimate the GVS artifact. To assess the performance of the proposed method using different algorithms and models, we applied our method to the simulated data and examined the cleaned-up EEG signals in comparison with the original artifact-free EEG signals. For this assessment, not only did we calculate the correlation between the artifact-removed EEG signals and the original artifact-free EEG signals, but also we measured the fitness of the artifact-removed signals based on the
We measured the performance of the proposed method based on the correlation (
Correlation and normalized residual sum of squares between the artifact-removed signals and the original artifact-free EEG signals for simulated data using different wavelet decomposition algorithms.
DWT db3 | DWT db4 | DWT db5 | DWT db6 | DWT sym3 | DWT sym4 | DWT sym5 | DWT sym6 | |
---|---|---|---|---|---|---|---|---|
Corr. | 0.8781 | 0.9023 | 0.9155 | 0.9242 | 0.8781 | 0.9023 | 0.9156 | 0.9242 |
|
0.5517 | 0.4870 | 0.4503 | 0.4255 | 0.5517 | 0.4870 | 0.4503 | 0.4255 |
| ||||||||
SWT db3 | SWT db4 | SWT db5 | SWT db6 | SWT sym3 | SWT sym4 | SWT sym5 | SWT sym6 | |
| ||||||||
Corr. | 0.9932 | 0.9933 | 0.9933 | 0.9932 | 0.9932 | 0.9933 | 0.9933 | 0.9932 |
|
0.1710 | 0.1700 | 0.1705 | 0.1714 | 0.1710 | 0.1700 | 0.1705 | 0.1714 |
The results show that SWT algorithm has a superior performance compared to DWT algorithm, and between different mother wavelets both Daubechies and Symlet wavelets with order of 4 performed better than the others.
Another step to improve the performance of the method, is finding an optimum regression method to calculate the estimated GVS artifacts as accurate as possible. We used three different classes of model structure, Output-Error (OE) as a simple special case of the general polynomial model, Hammerstein-Wiener with the piecewise-linear function, and Space-State models, which were all introduced in the “Regression-based approach” section. We employed these models with different orders in the proposed artifact removal method and applied the proposed method using each of these models to the simulated data. In order to compare the performance, we used SWT with Daubechies 4 to decompose the contaminated signals, estimated the GVS artifact using different models, and then assessed the performance in terms of the correlation and the normalized residual sum of squares between the original artifact-free signal and the artifact-removed signal reconstructed in the frequency range lower than 31.25 Hz. The results are tabulated in Table
Correlation and normalized residual sum of squares between the artifact-removed signals and the original artifact-free EEG signals for simulated data using different models for estimating the GVS artifacts.
OE2 | OE3 | OE4 | OE5 | NLHW2 | |
---|---|---|---|---|---|
Corr. | 0.9933 | 0.9933 | 0.9933 | 0.9822 | 0.9934 |
|
0.1700 | 0.1701 | 0.1704 | 0.2267 | 0.1711 |
| |||||
SS2 | SS3 | SS4 | NLHW3 | NLHW4 | |
| |||||
Corr. | 0.9933 | 0.8105 | 0.7466 | 0.9926 | 0.9851 |
|
0.1704 | 0.7628 | 0.9174 | 0.1230 | 0.1725 |
For nonlinear Hammerstein-Wiener models we used the piecewise-linear function and broke down the EEG signal into a number of intervals. We tried a various number of intervals and observed that, with 4 intervals (or less), we could get the highest correlation and the least residual.
The results show that, between all those models, both Output-Error and nonlinear Hammerstein-Wiener have better performance. We employed these regression models to maximize the performance of the proposed method, then we applied the proposed method to the real data.
We also used two ICA-based methods for removing the artifact: filtering out the artifact components and applying a threshold on the artifact components amplitude to remove the artifact spikes beyond the threshold.
To assess the performances of the ICA methods on the simulated data, we calculated both the correlation and the normalized residual sum of squares between the artifact-removed EEG signals and the original artifact-free EEG signals.
We compared the ICA-based methods with the proposed methods using the Output-Error and nonlinear Hammerstein-Wiener models order 2, along with 12-level STW decomposition with DB4 mother wavelet (Tables
Correlation and normalized residual sum of squares between the artifact-removed signals and the original artifact-free EEG signals for simulated data using the proposed method and ICA-based methods.
Removing the ICA artifact component | Applying threshold to the ICA artifact component | SWT decomposition with DB4 modeled with OE2 | SWT decomposition with DB4 modeled with NLHW2 | |
---|---|---|---|---|
Corr. | 0.6445 | 0.6171 | 0.9933 | 0.9934 |
|
0.9567 | 1.0241 | 0.1700 | 0.1711 |
Correlation between the GVS signals and the estimated GVS artifact extracted from EEG signals for real data using the proposed method and ICA-based methods.
Removing the ICA artifact component | Applying threshold to the ICA artifact component | SWT decomposition with DB4 modeled with OE2 | SWT decomposition with DB4 modeled with NLHW2 | |
---|---|---|---|---|
Corr. | 0.6859 | 0.6858 | 0.8743 | 0.8743 |
We applied different artifact removal methods on real EEG data acquired during application of GVS. We used the data from channel O1 (occipital EEG) of different subjects in EEG/GVS studies. We applied stimulation signals of different amplitudes in our experiments and observed consistent results from these experiments. By calculating the correlation coefficients between the GVS signals and the estimated GVS artifacts, we compared the performance of these methods. First we compare ICA-based, regression-based, and adaptive filters without using the wavelet analysis. Then we use the proposed method where the wavelet analysis was employed to improve the performance of our artifact removal method.
The best algorithms for ICA-based methods, best models for regression-based methods and best filters for adaptive filtering methods were selected. Between different ICA algorithms (as mentioned in the section “ICA-based artifact removal methods”), the extended Infomax showed better results. Between regression-based methods (as previously introduced in the section “Regression-based artifact removal methods”), OE order 2 showed better performance, and between adaptive filters (as previously introduced in the section “Adaptive filtering methods for artifact removal”), RLS filter with the forgetting factor of 0.99997, the filter length of 2, LMS filter with the adaptation gain of 0.5, and the filter length of 3 had better performance. We tabulated (Table
Correlation between the GVS signals and the estimated GVS artifact extracted from EEG signals for real data using different methods.
Method | Correlation |
---|---|
ICA-Infomax method (remove the artifact component) | 0.6859 |
ICA-Infomax method (threshold the artifact component) | 0.6858 |
Regression method with OE2 | 0.7673 |
RLS Adaptive filter (forgetting factor: 0.99997, length: 2) | 0.7615 |
LMS Adaptive filter (adaptation gain: 0.5, length: 3) | 0.7010 |
The results show that, between all the above methods, the regression-based methods are able to estimate the GVS artifacts with higher correlation with the original GVS signals. Thus, we employed the regression-based method along with the wavelet analysis in our proposed method to achieve the best performance in removing GVS artifact. The wavelet decomposition method improves the estimation of the GVS artifacts in both correlation performance and robustness. This is due to the separate transfer function estimations for each frequency band, aspect that makes it less prone to nonlinear skin behavior or to other noise sources. Furthermore, with wavelet decomposition, we can filter out the frequency components that are not of interest. Removing those frequency components can improve the results of the regression analysis as well. The cleaned EEG data is reconstructed from the frequency range of interest (e.g., 1 Hz to 32 Hz).
Using a correlation analysis, we show how the wavelet-based time-frequency analysis approach enhances the performance of the artifact removal method. We calculated the correlation coefficients between the GVS signals and the estimated GVS artifacts reconstructed from different frequency bands (tabulated in Table
Correlation between the GVS signal and the estimated GVS artifact reconstructed from different frequency components for real data.
Frequency band | Correlation |
---|---|
Estimated GVS artifact without wavelet decomposition | 0.7673 |
Estimated GVS artifact from 0.12 Hz to 250 Hz | 0.8463 |
Estimated GVS artifact from 0.24 Hz to 125 Hz | 0.9168 |
Estimated GVS artifact from 0.49 Hz to 62.5 Hz | 0.9725 |
Estimated GVS artifact from 0.49 Hz to 31.25 Hz | 0.9776 |
Estimated GVS artifact from 0.49 Hz to 15.75 Hz | 0.9769 |
Estimated GVS artifact from 0.98 Hz to 31.25 Hz | 0.9899 |
Estimated GVS artifact from 0.98 Hz to 15.75 Hz | 0.9899 |
As shown in Table
So far, we showed the proposed method has superior performance than the other methods when it is applied to low-amplitude stochastic GVS signals up to 1 mA. We also applied our artifact removal method to EEG/GVS data sets collected by our other collaborator in the Sensorimotor Physiology Laboratory, where higher amplitude pink noise GVS up to 3100
Correlation between the GVS signal and the estimated GVS artifact using the proposed method (red) and the ICA method (blue) for different GVS amplitudes.
In the section “The proposed artifact removal method”, we optimized the proposed method using the simulated data. To find the optimum algorithms for signal decomposition, we compared the SWT and DWT decomposition algorithms using different mother wavelets (the results shown in Table
In the optimized algorithm, we employed the SWT decomposition algorithm using DB4 mother wavelet and decomposed the signals into 12 frequency bands. This enabled us to separate the GVS artifact into different frequency bands and estimate the artifact using a time-domain regression model. The comparison of the different model structures shows that the Output-Error (OE) and the nonlinear Hammerstein-Wiener order 2 have similar performances, better than the other models.
In the previous section, we compared the performance of different methods and observed that how the combining of wavelet decomposition and regression analysis (Table
Using the proposed method, we can focus on specific frequency bands and remove the GVS artifact with better performance in each frequency band, separately. Figures
The fit percentage of the detail components of the estimated GVS artifacts using the OE model order 2 in each frequency band.
The correlation between the detail components of the estimated GVS signals and the GVS signals for the simulated data using the OE model order 2 in each frequency bands.
The results show that for frequency components L6 to L10, which correspond approximately to 8–16 Hz, 4–8 Hz, 2–4 Hz, 1-2 Hz, and 0.5–1 Hz bands, we can achieve higher performance in rejecting the GVS artifacts separately. One of the reasons of the robustness of the method is building separate equivalent transfer functions for the GVS signals for each frequency band which helps in maintaining the performance of the algorithms for a large range of GVS intensity levels and frequency ranges. To illustrate the importance of the wavelet analysis, we depicted the artifact-removed signals using different frequency components (Figures
The occipital EEG channel data after applying the proposed artifact removal method using the frequency components lower than 64 Hz.
The occipital EEG channel data after applying the proposed artifact removal method using the frequency components between 1 Hz to 32 Hz.
The occipital EEG channel data after applying the proposed artifact removal method using the frequency components between 1 Hz to 16 Hz.
Figure
In the section “Simulated data”, we showed that by simulating the skin impedance and estimating the transfer function of the skin (one function for the whole frequency range), we could reconstruct a major portion of the GVS artifact. As an example, for channel 18, around 87% of the GVS artifact was reconstructed (Figure
Using the wavelet decomposition, we were able to reconstruct up to 96% of the GVS artifact components in some frequency bands, especially in the frequency range of the GVS signals (Figure
We showed that the use of the wavelet decomposition can improve the time domain regression approach to estimate the GVS artifacts. By means of the combination of the regression and wavelet analysis in the proposed artifact removal method, we were able to focus on different frequency bands and significantly improve the SAR of the contaminated EEG data in specific frequency bands.
The proposed method and the ICA-based methods behave differently in rejecting the GVS artifact. We observed a high correlation between the estimated GVS artifacts and the original GVS signals using the proposed method, but we could not obtain a good correlation using the ICA-based methods.
As illustrated earlier, we cannot completely remove the GVS contamination in all frequency ranges (e.g., over 16 Hz). Removing the whole GVS artifacts remains a problem for the future approaches.
In this study we also observed that nonlinear Hammerstein-Wiener model of the second order, using piecewise-linear blocks with 4 breakpoints (or less), provided the same performance as the Output-Error model of the second order. This implies that the relationships between the GVS artifacts at the EEG electrodes and the injected GVS current are linear and remain constant over the entire epoch. Our simulation study results also showed that the impedance models between the EEG electrodes and the GVS electrodes remain constant over the entire epoch (Figure
We also showed that, when we apply the proposed method to remove the GVS artifacts, less distortion is introduced in the cleaned EEG signals, compared to the distortion that the other methods (e.g., ICA-based methods) introduce. Furthermore, using the proposed method, we do not need to collect and process all EEG channels as in the ICA-based analysis; therefore it is much faster than the ICA-based methods. This allows us to have a simple experimental setup for collecting EEG signals with less EEG channels for the GVS studies which makes the preparation for the data acquisition session take less time before the subject gets tired, and more myogenic and ocular artifacts are introduced. Compared to the ICA methods, the proposed method is easier to be implemented in a real time system for future applications.
The authors would like to thank the research team of Professor Martin J. McKeown, from Pacific Parkinson’s Research Centre, and also the research team of Professor Jean-Sébastien Blouin, from the Sensorimotor Physiology Laboratory, University of British Columbia, for the collection of the experimental data and for the useful dialogs during our work.