Transforming of scalp EEGs with different channel locations by REST for comparative study

Objective: The diversity of electrode placement systems brought the problem of channel location harmonization in large-scale electroencephalography (EEG) applications to the forefront. Therefore, our goal was to resolve this problem by introducing and assessing the reference electrode standardization technique (REST) to transform EEGs into a common electrode distribution with computational zero reference at infinity offline. Methods: Simulation and eye-closed resting-state EEG datasets were used to investigate the performance of REST for EEG signals and power configurations. Results: REST produced small errors (the root mean square error (RMSE): 0.2936 – 0.4583; absolute errors: 0.2343 – 0.3657) and high correlations ( > 0.9) between the estimated signals and true ones. The comparison of configuration similarities in power among various electrode distributions revealed that REST induced infinity reference could maintain a perfect performance similar ( > 0.9) to that of true one. Conclusion: These results demonstrated that REST transformation could be adopted to resolve the channel location harmonization problem in large-scale EEG applications.


Introduction
Compared with other neuroimaging techniques, scalp electroencephalography (EEG) is noninvasive, affordable, portable and excellent compatibility with environments and systems.Thus, there is an increasing amount of interest in EEG due to its irreplaceable value in brain science.And, it has been applied in a wide of fields and plays important roles in brain disease studies (Babiloni et al., 2016;Wutzl et al., 2021), multimodal fusion (Chang and Chen, 2021;Dong et al., 2014), brain-computer interfaces (Gonzalez-Astudillo et al., 2021) and cognitive neuroscience studies (Cohen, 2017;Si et al., 2019).Meanwhile, the recommendations for open science (Koch and Jones, 2016) and the rise of cloud neuroscience (Neuro Cloud Consortium et al., 2016) have further led to more efforts with large-scale EEG applications in the EEG community.So that, there is being accumulation of a number of public large EEG datasets such as the TUH-EEG Corpus dataset with more than 30,000 clinical EEGs (https://isip.piconepress.com/projects/tuh_eeg/) (Obeid and Picone, 2016) and the OpenNeuro platform including 146 EEG datasets with ~6267 individuals from different sites (https://openneuro.org/)(Markiewicz et al., 2021), as well as EEG cohort studies such as the YOUth cohort (https://www.uu.nl/en/rese arch/youth-cohort-study/youth) (Onland-Moret et al., 2020), the Healthy Brain and Child Development Study (HBCD) (https://heal.nih.gov/research/infants-and-children/healthy-brain) and the Healthy Brain Network (HBN) project (https://healthybrainnetwork.org/)(O'Connor et al., 2017).
Currently, there are a number of electrode distribution systems including international 10-20 (Jasper, 1958;Klem et al., 1999), international 10-10 ( Chatrian et al., 1985), Geodesic Sensor Net (GSN) (Tucker, 1993) and 10-5 percent (Oostenveld and Praamstra, 2001) systems etc.And the extended 10-20 system has been accepted and endorsed as the standard of the EEG community including the American Electroencephalographic Society (Klem et al., 1999) and the International Federation of Societies for Electroencephalography and Clinical Neurophysiology (Nuwer et al., 1998).In general, EEG equipment manufacturers are using different hardware systems with different electrode placement systems.For example, the EEG data recorded by the Brain Product EEG system is configured with 10-20 system, while the data recorded by the Electrical Geodesics Incorporated (EGI) EEG system is configured with GSN system.So that, different EEG systems with different electrode placements are used in different institutes in real EEG practices, especially in large-scale multi-center open EEG datasets (Markiewicz et al., 2021).Noting that, even the claimed 10-20 system is used in the EEG recording system, there may be nonnegligible difference of channel locations between two EEG equipment manufacturers such as Brain Products and NeuroScan companies.Therefore, the diversity of electrode placement systems brought the problem of channel location harmonization in large-scale EEG applications to the forefront.And, it further leads to an even greater need for offline channel location harmonization or transformation in processing these multi-center or open EEG data sets, especially in multi-center EEG plans (O'Connor et al., 2017;Onland-Moret et al., 2020) or multinational EEG norm studies (Li et al., 2022).However, to our knowledge, there are few works to solve the problem of channel location harmonization in large-scale EEG applications.
This work attempted to solve channel location harmonization problem by introducing the reference electrode standardization technique (REST) (Dong et al., 2017); D. (Yao, 2001) for transforming different channel locations to a standard electrode coordinate system offline, and investigated the performance of REST on transformation.REST is a novel method that approximately converts an average or unipolar reference into a zero reference (Dong et al., 2017); D. (Yao, 2001), which has been increasingly used by EEG groups worldwide (D.Z. (Yao et al., 2019).By using REST for transformation of channel locations and standardization of reference, it could be essential to further release these multi-center or open EEG data sets from limited offline explorations.Noting that, the REST induced IR reference could provide many consistent and reliable results in EEG offline analyses, such as EEG spectra (Federico (Chella et al., 2017); D. (Yao et al., 2005), ERP topographies (Dong et al., 2019;Qin et al., 2017); D. (Yao et al., 2007) and EEG networks (F.(Chella et al., 2016); (Qin et al., 2010).However, the performance of REST on montage harmonization has not yet been reported.This study is the first to transfer EEGs with different montages to a standard electrode distribution system using REST and detect the feasibility with practical EEG data, as is expected to facilitate explorations of EEG datasets.
In our work, the performance of REST was first quantified using a simulation dataset generated from a real resting-state eye-closed EEG dataset.Indices including the root mean square error (RMSE), absolute error and Pearson's correlation between the signal transformed by REST and the true one were calculated.Next, the power spectrum analysis was conducted on the EEGs from two datasets (a lab collected and an open datasets) to investigate performances of REST.

Data collection
Dataset 1 of simulated EEGs with the reference at infinity was generated from a three-concentric sphere head model according to previous papers (Dong et al., 2017); D. (Yao, 2001); D. (Yao et al., 2005) (Fig. 1).The radii were normalized by the radius of the head, and consisted of the three concentric spheres were 0.87 (radius of the brain), 0.92 (radius of the skull), and 1.0 (radius of the scalp).The relative conductivities were 1.0 (brain), 0.0125 (skull) and 1.0 (scalp).Then, a geometrically triangular grid based on the standard brain (normalized by the radius of the scalp) were implemented in the equivalent source model (a total of 6144 sources).Lead field matrices of different channel locations (details of channel locations can be seen in Table 1) were calculated first.Next, a source signal with Gaussian noise (signal-to-noise ratio was set at 10) was assumed on a random cortical surface of a brain region.And then, simulated scalp EEGs with different channel locations were calculated based on the those lead field matrices.The whole simulation process was repeated 200 times, and the sampling rate was set at 500 Hz.
Dataset 2 of resting-state (eye closed) scalp EEGs were obtained from 41 right-handed healthy adults (9 women/32 men, mean age 23.9 ± 1.6 years old) using a 62-channel EEG system (Brain Products GmbH, Gilching, Germany) with a FCz recording reference.The channel locations of 61 channels are showed in Fig. 1B (extended 10-20 system, BP-61).The sampling rate was 500 Hz and the EEG data were online bandpass filtered (0.01-100 Hz).The impedance was kept below 5 kΩ during recording.The experiment was approved by the local Ethics Committee of the University of Electronic Science and Technology of China, and written informed consents were obtained from all subjects before experiment.
Dataset 3 of resting-state (eye closed) scalp EEGs were obtained from an open dataset (Alexander et al., 2017).A total of 26 EEGs of right-handed healthy adults (16 women/10 men, mean age 19.7 ± 1.2 years old) were used.High-density EEG data were recorded using a 128-channel EEG geodesic hydrocel system (GSN-HydroCel-128) by Electrical Geodesics Inc. (EGI) in a sound-shielded room.The sampling rate was 500 Hz, and the EEG data were online bandpass filtered (0.1-100 Hz).The original recording reference is at Cz (vertex of the head), and the impedance was kept below 40 kΩ.
For two real datasets, a quality assessment (QA) tool from the WeBrain platform (https://webrain.uestc.edu.cn/)(Dong et al., 2021) was first used to detect and reject bad blocks with artifacts including constant or NaN/Inf signals, unusually high or low amplitudes, high or power frequency noises, and low correlation signals.The main QA processing contained: 1) EEG signals were high-pass filtered (>1 Hz); 2) continuous EEG data were segmented as a mass of 1 second windows; 3) different artifacts in small windows of each channel were detected; and 4) data quality masks were calculated to obtain continuous good data blocks.Next, continuous EEG raw data were offline filtered with a bandpass of 1-40 Hz, and further analyses were conducted on those uncontaminated epochs (length is 5 s) of clean EEG data.

Implementation of REST
The reference electrode standardization technique (REST) was based on a distributed source model (Dong et al., 2017); D. (Yao, 2001); D. (Yao et al., 2005).The potential P (N channels × T time points) on a scalp with an electrode distribution can be generated from the function of a lead-field matrix L (N channels × K sources) with an active source S (K sources × T time points).Here, the matrix L represents the forward model theoretically calculated with the infinity reference.
where p j i , 1≤j≤N, 1≤i≤T is a potential sample at the jth channel and ith time point.For a scalp point referenced recordings (P e ) or average referenced recordings (P avg ), the scalp recording models of an electrode distribution can be expressed as: (2) where w is a column vector (N×1) with each of its elements being unity, i.e.
; p e is a row vector (1×T) in P corresponding to a scalp point reference; l e is the row vector (1×K) in L corresponding to the reference electrode; L e is a lead-field matrix (N ×K) with a scalp point reference; p avg is a row vector (1×T) in P corresponding to the average reference; L avg is a lead-field matrix (N ×K) with the average reference; N is the number of EEG channels; K is the number of active sources.Considering a scalp recording with a target electrode distribution (M channels), the scalp potentials for the reference at infinity, PM×T , can be modeled as: where pj i , 1≤j≤M, 1≤i≤T is a potential sample of the target electrode distribution at the jth channel and ith time point; S is the neural source potentials with size K×T; and L is a lead-field matrix (size is M×K) with the reference at infinity.Based on the equivalent source technique (D. (Yao, 2000), the neural source potentials S in the brain are the same, and the use of the reference does not influence the source localization (Geselowitz, 1998).Then, combing with Eqs. ( 1)-( 3), S can be estimated by the scalp EEG potentials: where L + , L + e and L + avg (with size K×N) are the Moore-Penrose generalized inverses of matrices L, L e and L avg , respectively; and Ŝ is the estimation of the reconstructed equivalent sources using the scalp potentials.Then, combining Eq. ( 4), the estimated source potentials can be forwarded to the scalp channels of target electrode distribution to reconstruct all potentials with the infinity reference: e P e = LL + avg P avg (6) where P represents the potentials of the target scalp electrodes with reference at infinity; Ŝ is the estimation of reconstructed equivalent sources; L is a lead-field matrix (size is M×K) of the target scalp channels with the reference at infinity; L + , L + e and L + avg (with size K×N) are the Moore-Penrose generalized inverses of matrices L, L e and L avg , respectively.More details of the REST algorithm can be seen in Yao et al. (Dong et al., 2017); D. (Yao, 2001); D. (Yao et al., 2005) and the tool (EEGLABPluginVersion-REST_v1.2_20200818) can be downloaded from http://www.neuro.uestc.edu.cn/name/shopwap/do/index/content/96 for free.

Method assessment
To assess the performance of REST method in EEG analysis, simulations were assumed using dataset 1.First, the true scalp EEG data of the target electrode distribution  with the reference at infinity were generated.Next, the REST method can convert the EEG signals of original electrode distributions with the reference at infinity into target electrode distributions with the reference at infinity (Dong et al., 2017); D. (Yao, 2001); D. Z. (Yao et al., 2019).Performances of the REST were quantified using the root mean square error (RMSE), absolute error and Pearson's correlation between the signal transformed by REST and the true one (Dong et al., 2023;Dong et al., 2021).Meanwhile, because spherical spline interpolation (SSI) (Freeden, 1984;Perrin et al., 1989) is the most common bad channel interpolation method used in the EEG field.SSI was used to reconstruct all potentials of the target electrode distribution, and performances of REST and SSI were compared.
Furthermore, as a most conventional cut-in point for EEG studies, the power spectrum analysis was conducted on the EEGs of datasets 2 and 3 (with the reference at infinity) to investigate performances of REST.Using the EEG tool WB_EEG_CalcPower (v1.0) on the WeBrain platform (https://webrain.uestc.edu.cn/)(Dong et al., 2021), the relative power (power of specific band/total power across full band 1-40 Hz) of each channel was calculated by time-frequency analysis with fast-Fourier transform (FFT) in the typical EEG frequency bands (delta: 1-4 Hz, theta: 4-8 Hz, alpha: 8-12.5 Hz, beta: 12.5-30 Hz, gamma: 30-40 Hz).Next, kernel smoothing probability densities for power indices with electrode distributions were estimated; and then, correlations (R) of probability densities for power indices were calculated.

Discussion
This work focused on whether the REST could transform EEGs with different electrode distributions into a common electrode distribution and to solve channel location harmonization problem in large-scale EEG applications.The comparison of configuration similarities in signals among various electrode distributions revealed that REST induced IR could maintain a perfect performance similar to that of true one.The power result of two real data sets further indicated that REST could orient toward a satisfied channel location harmonization.

Validation of REST transformation
Currently, a number of electrode distribution systems including international 10-20 (Jasper, 1958;Klem et al., 1999), international 10-10 ( Chatrian et al., 1985), Geodesic Sensor Net (GSN) (Tucker, 1993) and 10-5 percent (Oostenveld and Praamstra, 2001) systems etc. had been proposed in EEG fields.And, different electrode placement systems were configurated in different hardware systems of EEG manufacturers.Due to the fact that scalp EEG equipment is affordable, several EEG systems with different electrode placements are used in institutes in real EEG practices, especially in large-scale multi-center open EEG datasets (Markiewicz et al., 2021).However, because there are few solutions for the problem of channel location harmonization, EEGs generated from recorder systems with different electrode distributions are hard to be used together, which may limit large-scale EEG applications and plans.To solve this problem, the reference electrode standardization technique  (REST) (Dong et al., 2017); D. (Yao, 2001); D. (Yao et al., 2005) was introduced to transform such EEGs with different electrode distributions and derive a computational zero reference at infinity (IR).The performances of the REST method were investigated by calculating the root mean square error (RMSE), absolute error and Pearson's correlation between the signal transformed by REST and the true one.As shown in Figs.2-3, REST produced small errors and high correlations between the estimated signals of different channel placements and true ones.According to Eqs. 5 and 6, REST is based on the equivalent sources model (Geselowitz, 1998;Pascualmarqui and Lehmann, 1993), electrode montage and head model, and the transform matrix LL + avg that describes the relationship from an electrode montage to another montage is physically based and reasonable (Dong et al., 2017;Hu et al., 2019); D. (Yao, 2001); D. Z. (Yao et al., 2019).That is, REST has the ability to approximately convert an EEG with an electrode distribution into a new EEG with target electrode distribution and computational ideal zero reference, and has physical meaning.In addition, considering that the method spherical spline interpolation (SSI) (Freeden, 1984;Perrin et al., 1989) is the most common bad channel interpolation method used in the EEG field, it can be also used to reconstruct all potentials of the target electrode distribution while imposing channels of target electrode placement are "bad channels" and channels of original electrode placement are "good channels".Here, performances of REST and SSI were further compared.Results (Figs. 4-5, S1-S5) showed that REST  produced smaller errors and higher correlations than SSI (except GSN-HydroCel-33).It is consistent with a previous study that REST has better interpolation performance than SSI (Dong et al., 2021).Meanwhile, previous studies (Dong et al., 2023;Hu et al., 2018); D. Z. (Yao et al., 2019) have shown that the number of channels and channel placement might affect the performance of REST in transformation of scalp EEG signals, it perhaps is the reason of a little higher errors of REST than SSI for situation of GSN-HydroCel-33.Overall, REST performed well in transformation, and it implied that REST is a satisfied bridge linking EEGs of different electrode distributions to a common electrode distribution with computational ideal zero reference.

Feasibility of REST transformation in real EEGs
Next, using two real EEG datasets, the power indices of the original (BP61 or GSN-HydroCel-128) and target  electrode distributions were calculated to investigate performances of REST.For both datasets, the spectral analyses revealed dominant activations in frontal regions in delta band, frontoparietal regions in theta band, occipital regions in alpha band and temporal regions in beta and gamma bands.Consistent with these current studies (Chen et al., 2008;Dong et al., 2023); D. (Yao et al., 2005), the configurations of power implicated that the IR reference by REST could reveal the most recognizable characteristics of healthy adults during eye-closed resting-state.Further, results also showed that REST in resulted power indices highly similar to the ones of original electrode distributions.Therefore, the diversity of electrode placement systems may be relaxed using REST offline transformation.And, it further satisfy the needs of offline channel location transformation in processing those multi-center or open EEG data sets, especially in multi-center EEG plans (O'Connor et al., 2017;Onland-Moret et al., 2020) or multinational EEG norm studies (Li et al., 2022).In addition, it has also been confirmed in some simulations and real experiments that REST could significantly reduce the distortion of power patterns compared to AR, Cz and LM references (Federico (Chella et al., 2017); D. (Yao et al., 2005).It is thus suggested that REST could be applied in standardization of EEGs with different electrode placement systems for offline analyses.

Limitations
There are some of limitations in current studies.First, the current work focuses on the offline REST transformation.During EEG recording, there may be potential influences of artifacts on the REST display online, and the online transforming version of REST perhaps is need to be further studied to facilitate online explorations of EEG recordings.Second, as a novel offline re-referencing method, REST has been integrated into the EEG preprocessing pipeline on the WeBrain cloud platform (htt ps://webrain.uestc.edu.cn/)(Dong et al., 2021), as well as other MAT-LAB tool versions (https://www.neuro.uestc.edu.cn/name/shopwap/do/index/content/96) (Dong et al., 2017;Dong et al., 2018).The current variation of REST will be integrated in these tools as soon.At last, because REST and SSI can be seen as kinds of interpolation methods, large errors may be caused by transforming EEGs from less channels to more channels.And, it needs to be investigated in the future.

Conclusion
This study focused on whether the REST transformation could be adopted to resolve the offline channel location harmonization problem in large-scale EEG applications.Results of 3 datasets demonstrated that REST might be an effective and robust solution for transforming EEGs with different electrode distributions into a common electrode distribution, and could therefore harmonize these data for further analysis by deriving a favorable offline reference IR.

Declaration of Competing Interest
None

Fig. 1 .
Fig. 1.Simulation setup and channel locations.A) a three-concentric sphere head model was used to generate simulated EEG data.B) 15 channel locations are showed.

Table 1
Instructions of channel locations.