PSIs of EEG With Refined Frequency Decomposition Could Prognose Motor Recovery Before Rehabilitation Intervention

Stroke often leads to permanent impairment in motor function. Accurate and quantitative prognosis of potential motor recovery before rehabilitation intervention can help healthcare centers improve resources organization and enable individualized intervention. The context of this paper investigated the potential of using electroencephalography (EEG) functional connectivity (FC) measures as biomarkers for assessing and prognosing improvement of Fugl-Meyer Assessment in upper extremity motor function (<inline-formula> <tex-math notation="LaTeX">${\Delta \textit {FMU}}{)}$ </tex-math></inline-formula> among participants with chronic stroke. EEG data from resting and motor imagery task were recorded from 13 participants with chronic stroke. Three functional connectivity methods, which were Pearson correlation measure (PCM), weighted Phase Lag Index (wPLI) and phase synchronization index (PSI), were investigated, under three regions of interest (inter-hemispheric, intra-hemispheric, and whole-brain), in two statues (resting and motor imagery), with 15 refined center frequencies. We applied correlation analysis to identify the optimal center frequencies and pairs of synchronized channels that were consistently associated with <inline-formula> <tex-math notation="LaTeX">${\Delta \textit {FMU}}$ </tex-math></inline-formula>. Predictive models were generated using regression analysis algorithms based on optimized center frequencies and channel pairs identified from the proposed analysis method, with leave-one-out cross-validation. We found that PSI in the Alpha band (with center frequency of 9Hz) was the most sensitive FC measures for prognosing motor recovery. Strong and significant correlations were identified between the predictions and actual <inline-formula> <tex-math notation="LaTeX">${\Delta \textit {FMU}}$ </tex-math></inline-formula> scores both in the resting state (<inline-formula> <tex-math notation="LaTeX">$\text{R}^{{2}}=0.79$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\text{P}< 0.001$ </tex-math></inline-formula>, N=13) and motor imagery (<inline-formula> <tex-math notation="LaTeX">$\text{R}^{{2}}=0.65$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\text{P}< 0.001$ </tex-math></inline-formula>, N=13). Our results suggested that EEG connectivity measured with PSI in resting state could be a promising biomarker for quantifying motor recovery before motor rehabilitation intervention.


PSIs of EEG With Refined Frequency Decomposition Could Prognose Motor Recovery
Before Rehabilitation Intervention

I. INTRODUCTION
S TROKE is the most common cause for motor impair- ment among adults [1], [2], [3].Currently, analysis of motor impairment and assessment of motor function status after stroke in clinical practice is primarily based on questionnaire-based assessments conducted by healthcare professionals, which is labor-intensive and partially subjective.Existing studies have shown that biomarkers from functional magnetic resonance imaging (fMRI) and electroencephalographic (EEG) can reflect functional performance of human brain [4], [5].For example, resting-state fMRI studies have shown that functional connectivity (FC) between the M1 of the primary motor cortex and supplementary motor area shows a positive correlation with the motor recovery in patients with chronic stroke, providing a promising method to prognose motor recovery of upper limb after rehabilitation [6], [7], [8], [9].Compared with fMRI, EEG is more economic, convenient and direct, as it records the electrical neural activities of the brain [10], [11].Recent studies have shown that the FC measures based on EEG signals can be an important parameter for analyzing brain functional status [12], [13], [14].For example, Wu et al. found that the inter-hemispheric EEG phase synchronization correlated with National Institutes of Health Stroke Scale (NIHSS) score [2].Riahi et al. explored the relationship between resting state EEG functional connectivity and FMA upper limb scores [15].Kawano et al. explored the relationship between inter-hemispheric EEG-based PSI from Alpha and Beta bands and several motor function performance measures (i.e., functional independent measure, NIHSS and FMA scores) [16].Existing papers were mainly focused on motor function assessment applications, which only investigated the correlations between bio-markers and patients' motor function state.However, biomarkers associated with predicting motor recovery after rehabilitation might be of more value for rehabilitation purposes with broader clinical applications.Accurate and objective evaluation of potential motor function recovery could aid healthcare professionals with patient stratification, which would further facilitate individualized medical intervention and improve healthcare resource organization efficiency.Methods associated with prognosis of motor recovery could also help us better understand the process of motor rehabilitation and provide more insights into the neuroscientific mechanism of human brain.
In the past decades, efforts have been made to identify biomarkers to assess and prognose motor recovery in patients with stroke as a way to improve the efficiency of rehabilitation and partially reduce the burden on healthcare institutions [17], [18].Several existing studies have demonstrated the importance of MRI-based metrics such as functional connectivity and lesion size to predict recovery.Tozlu et al. investigated differences in inter-hemispheric functional connectivity based on MRI before intervention can predict post-intervention motor rehabilitation in patients with stroke, which could potentially assist in developing personalized treatment strategies [19].Kelly et al. reported network connections in motor-related areas could provide a predictive framework for neuroplasticity in the brain, which could potentially better predict clinical recovery after stroke [20].Most existing motor recovery sensitive biomarkers were derived using data from clinical equipment like MRIs, which were financially inefficient and heavily occupied in clinical practice.Biomarkers based on simple and functional signal acquisition methods, such as EEG, would greatly contribute to the integration of biomarkers into clinical workflow.
Several research papers have also reported a correlation between several EEG biomarkers and potential motor function recovery.Functional connectivity of Alpha and Beta bands in motor-related regions was found to be correlated with motor recovery.For example, Li et al. reported that pre-intervention weighted phase lag indices of the ipsilateral premotor cortex in task EEG showed a strong significant correlation with motor improvement in patients with stroke [21].Vatinno et al. reported that pre-intervention ipsilateral sensorimotor connectivity based on coherence in task EEG was able to predict improvements in upper limb motor function in chronic stroke patients after vibratory stimulation treatment, suggesting initial motor connectivity was significantly associated with motor scores at two weeks [22].Saes et al. showed brain symmetry index (BSI) in Theta band was one of the best predictors of FMU at 26 weeks after stroke.Higher BSI at baseline implied more motor impairment [23], [24].Hoshino et al. found the amplitude envelope correlation (AEC) of the Alpha and Beta bands in M1-PMC at week 4 was found to be able to predict the FMA score at week 8 after stroke, and the feasibility of pre-intervention functional connectivity to forecast neurological recovery was demonstrated in both resting and task EEG [25].In addition, improvements of motor performance showed a positive correlation with the network index degree in Beta band and pre-intervention network interactions in the ipsilesional M1 before rehabilitation contribute to the recovery of neurological impairment [26].Prediction of post-rehabilitation FMUs has been researched mainly based on motor related regions as seed points, and evaluated network connectivity measures between different seed points to generate motor-related regional interaction networks.This method has been gradually accepted in related research fields to reflect the level of synchronization in different regions of the brain [15].Kawano et al. reported a correlation between the improvement in motor function and the average PSI of intra-hemispheric channel pairs can be used as an indicator for motor recovery [27].However, existing predictive biomarkers are mainly based on the functional connectivity averaged in motor related regions and using regional connectivity measures might overlook the effect of synchronization between individual channels.Despite the correlation analysis results were inspiring, the accuracy of existing motor recovery biomarkers was generally low and far from satisfaction for practical applications.Refined frequency components and channel-wise distribution [15], [28] of the FCs should be investigated to optimize the prognosis accuracy and elucidate possible electrophysiological representations of potential motor recovery.
In this paper, we propose a new approach that explores the effect of three functional connectivity measurements, Pearson correlation measure (PCM), wPLI and PSI, in evaluating the potential motor recovery before rehabilitation intervention under different spatial regions of interest, with refined center frequency bands.FMU scores were collected before the intervention (T0) and after three weeks of rehabilitation (T1).∆F MU was calculated as the difference between FMU scores at T0 and T1 to quantify motor recovery.EEG data were only recorded at T0. Three functional connectivity measures were extracted using PCM, wPLI and PSI.A modified version of calculating PSI is proposed and validated in this paper, which further divided the original five EEG frequency bands (Delta, Theta, Alpha, Beta, Gamma) into 15 sub-bands, to calculate the brain synchronization activities in EEG data.A two-step correlation analysis (with p<0.05 and p<0.01) was performed and validated to screen the optimal center frequencies which were highly associated with potential motor recovery (∆F MU ).The channel pairs with top contributions were identified using partial least squares correlation (PLSC) analysis.The selected connectivity measures from designated center frequency and channel pairs were used as independent variables to build a predictive model for predicting ∆F MU .The resulted model was able to evaluate potential motor recovery before the intervention treatment based on the EEG characteristics with good accuracy.The results in this paper demonstrated the preliminary feasibility of the proposed method in predicting motor rehabilitation after three weeks' intervention, by only using baseline EEG connectivity features before intervention.

II. METHODS AND MATERIALS A. Participants
Thirteen participants with chronic stroke were recruited in this paper (12 male, one female with average age 55. 23,  [29]).All participants were informed of the complete experimental procedures.Written informed consent was obtained from all the participants at enrollment.Table I summarized all the participants' demographic information including age, gender, side of the lesion, FMU and ∆F MU .

B. Study Protocol
All recruited participants received a three-week (with a total of 11 sessions) brain-computer interface driven functional electrical stimulation (BCI-FES) rehabilitation.FMU scores were collected before the intervention (T0) and after three weeks of rehabilitation (T1) by a professional physical therapist with more than six years' experience of clinical practice.Resting and motor imagery EEG data were acquired at T0 session.During the intervention sessions, the current intensity of the FES device was tuned individually for each participant to reach full wrist joint extension according to each participant's wrist range of motion.The frequency of FES stimulation was set to 25 Hz.
Thirteen volunteers managed to return for FMU assessment after three weeks of rehabilitation and paired t-tests showed that participants' motor function improved significantly (p<0.001) after rehabilitation.Clinical improvement of patients was calculated by subtracting their corresponding scores at T0 from T1.According to Table I, one participant demonstrated no change in FMU score, and three more participants had minimal improvement of one point before and after the training.Four participants demonstrated minor improvements of 4-9 points and five participants demonstrated solid and major improvements of 10-13 points.

C. EEG Data Acquisition
During the EEG data acquisition, participants were instructed to perform resting and motor imagery (MI) according to the instructions on the monitor.The experimental process consisted of three parts: preparation phase, resting tasks, and MI tasks.In the preparation phase, the participants were requested to remain stationary, minimize physical activities, and prepare to start the experiment.When the resting cue was shown on the screen, the participant was required to remain rest for six seconds.When the MI cue appeared on the screen, the participants were required to perform MI for six seconds.Each session consisted of ten trials, and the participants were required to keep stationary throughout the session to avoid artifacts.A 32-channel EEG acquisition device was used to acquire the EEG data at a sampling rate of 250 Hz, with a 10-20 system configuration and M1 and M2 as the reference.Data acquired from M1, M2 channels were not involved in the study.EEG data from the rest 30 electrodes were selected for the study, as shown in Fig. 1.

D. EEG Data Processing
Considering only a limited number of participants were recruited in this study, and the side of the stroke lesion would affect the results in the connectivity analysis, EEG data from participants with right hemisphere impairments were swapped between the corresponding left and right hemispheric channels before any data analysis was conducted [3], [30].During preprocessing, a finite band-pass filter (1-45Hz) was applied to the EEG data, followed by a down sampling of the raw data to 200 Hz.Then, the common average reference (CAR) was applied to the EEG data.Considering the influence of artifacts such as eye movements and EMG on data analysis, independent component analysis (ICA) was performed to further mitigate the effect of artifacts.EEG epochs were created according to the task cue, with six seconds of EEG data segmented for each epoch, which contained 1200 temporal sample points.The segmented EEG data were visually inspected to ensure the data quality.We used the complex Morlet wavelet transformation to extract the band power and phase information of the EEG [27], [31].The phase information obtained from EEG data can be used to calculate the instantaneous functional connectivity between channel pairs.For the wavelet filters, different center frequencies and wavelet cycle counts n co determined the component characteristics [32].According to the classical five frequency bands decomposition of EEG analysis, which were Delta band (1-4 Hz), Theta band (4-8 Hz), Alpha band (8-15 Hz), Beta band (15-30 Hz), and Gamma band (30-45 Hz), each standard frequency band was further divided into three sub-bands with refined center frequencies, which were Delta (2, 3, 4 Hz), Theta (5, 6, 7 Hz), Alpha (9,11,13 Hz), Beta (16,21,27 Hz) and Gamma (34,39,45 Hz), to construct wavelet filters with 15 center frequencies.Wavelet filters were used to extract the EEG phase information of each refined sub-frequency bands.The wavelet cycle counts n co of Delta band was set to 4, and was increased with a step size of 1, for Theta band, Alpha band, Beta band and Gamma band respectively.

E. Functional Connectivity Measure
We used three different functional connectivity algorithms to calculate undirected functional connectivity at all frequencies.Both linear and nonlinear measures were applied to measure the level of synchronization between different brain regions.All algorithms were implemented based on Python, and the processing algorithms were listed below: (1) PCM was used to analyze the linear interaction between any two electrodes, reflecting the neural correlation of different regions [33].
(2) wPLI was included to evaluate the synchronization between electrodes by calculating the weighting of phase differences and the instantaneous amplitude [34].
(3) PSI was included to represent the degree of synchronization between brain regions, and it is quantified by measuring the phase difference in the complex domain [16], [27], [35].
For 15 sub-bands and two states of EEG, connectivity information was calculated by enumerating all pairs of channels of each frequency band.A mean value was returned for all epochs from each participant.Among 13 participants, three FC measures with three ROIs were used to calculate the regional FCs to investigate the correlation in prognosing motor recovery.
2) Intra-hemispheric FCs: We took the left hemisphere as the primary ROI in this paper, and the number of electrodes in the left hemisphere was 12.For the intra-hemispheric FCs, 66 (i.e., C 2 12 = 12 × 11 ÷ 2) FC values were calculated for each epoch among the channels located on the left hemisphere, based on the EEG data from resting and MI tasks, respectively.3) Inter-hemispheric FCs: According to the EEG acquisition montage (Fig. 1.),The left and right hemisphere had 12 channels, respectively.And thus, 144 (i.e., A 12 12 = 12 × 12) FC values were calculated for the EEG data.

F. Statistical Analysis
In this paper, all the statistical analysis was done on Python using SciPy.Due to the discrete nature of the FMU scores, we used the Spearman's correlation analysis [28], [36], [37] to evaluate the predictive performance among the FCs from three ROIs conditions (intra-hemispheric FC, interhemispheric FC, whole-brain FC).In addition, to quantify the potential improvement of the patients' FMU scores before rehabilitation, we included several regressive models with a leave-one-out paradigm, where FCs were used as the independent variables, and ∆FMUs (improvement between pre and post intervention) were set as the dependent variable.By comparing the resulted correlation coefficient between different FCs and ∆FMUs, a biomarker model based on EEG FCs was optimized to evaluate potential motor function recovery before stroke rehabilitation.All statistical analysis was performed at the significant level P<0.05.

A. Frequency Analysis Results
In order to investigate the effect of center frequency on the correlation between FCs and ∆FMU [21], we analyzed three functional connectivity measures (PCM, wPLI and PSI), with three ROIs (inter-hemispheric FC, intra-hemispheric FC, and whole brain FC) under two EEG tasks.As shown in Fig. 2, we first calculated the FC matrices for the two EEG tasks.The FC matrix size in the intra-hemispheric FC method was 12 × 12, which contained 66 valid repetition-free FC values for each participant.The inter-hemispheric FC matrix size was 12 × 12, which contained 144 valid repetition-free FC values for each participant, and the whole-brain FC matrix size was 30 × 30 which contained 435 valid repetition-free FC values for each participant.
For intra-hemispheric FC, the FC indices at the same position of each participant's FC matrix were selected for each frequency, and a 13 × 1 FC vector could be created, 66 correlation coefficients were calculated between each vector and ∆FMU, at 15 center frequencies.For inter-hemispheric FC, 144 correlation coefficients were calculated between each vector and ∆FMU, at 15 center frequencies.For wholebrain FC, 435 correlation coefficients were calculated with decomposed 15 center frequencies.According to the above analysis methods, the differences in the effects of different frequencies on the correlation between functional connectivity index and ∆FMU were compared at the significance level of both p<0.05 and p<0.01, and the dominant center frequencies with the highest number of significant correlations were identified in both EEG tasks.
Fig. 3 summarized the number of positively correlated channels between FCs at T0 and ∆FMU, using resting state EEG.The number of negatively correlated channels were generally low and aggregated at high center frequencies, which were not consistent under different analysis conditions.In addition, most existing literatures suggested motor function related FCs primarily focused on Alpha band and our results on negative correlations were consistent with results reported in the literature [2], [15], [16].For the sake of clarity and conciseness, FCs with negative correlations with ∆FMU were not included in the following analysis, which was the same as methods in [15].
1) Resting State: For PCM, the highest number of significant positive correlations located at 9 Hz center frequency for all three spatial connections, when screening with a significance level of P<0.05.125, 39, and 34 channel pairs showed significant correlations, under three ROI configurations respectively (Fig. 3(a)).However, at the significance level of P<0.01, 11 Hz showed the highest number of significant correlations, while the center frequency band of 9 Hz ranked at the second place.
For wPLI, the highest number of significant correlations located at 11 Hz for all three spatial connections, when screening with a significance level of P<0.05.150, 42, and 44 channel pairs showed significant correlations, under three ROI configurations respectively (Fig. 3(b)).Additionally, with a significance level of P<0.01, wPLI also showed the highest number of correlations with ∆FMU at 11Hz.These findings highlighted the significance of wPLI in correlation to ∆FMU at 11 Hz.
For PSI, the highest number of significant correlations located at 9 Hz for all three spatial connections, when screening with a significance level of P<0.05.Three ROIs showed significantly positive correlations of 121, 36, and 38 channel pairs, respectively (Fig. 3(c)).Additionally, with a significance level of P<0.01, PSI also showed the highest number of correlations with ∆FMU at 9Hz.There were 57, 17, and 15 channel pairs that showed significant positive correlations, respectively.
These results suggested that the low Alpha band plays an important role in the correlation analysis between the FCs and ∆FMU in resting state EEG.
2) Motor Imagery Task: For PCM, the highest number of significant positive correlations was at 9 Hz for all three ROIs, when screening with a significance level of P<0.05.113, 37, and 28 channel pairs showed significant positive correlations, under three ROI configurations respectively (Fig. 3(d)).
In addition, at the significance level of P<0.01, 9 Hz showed the highest number of significant correlations.
For wPLI, the highest number of significant positive correlations was still at 11 Hz for all three spatial connections, when screening with a significance level of P<0.05.149, 42, and 41 channel pairs showed significant positive correlations, under three ROI configurations respectively (Fig. 3(e)).Additionally, with a significance level of P<0.01, wPLI also showed the highest number of correlations with ∆FMU at 11Hz.These findings highlight the significance of wPLI in correlation to ∆FMU at 11 Hz.
For PSI, the number of significant positive correlations was the highest at 9 Hz for all three spatial connections, when screening with a significance level of P<0.05.133, 39, and 38 channel pairs showed significant positive correlations, under three ROI configurations respectively (Fig. 3(f)).Additionally, with a significance level of P<0.01, PSI also showed the highest number of correlations with ∆FMU at 9Hz.There were 56, 19, and 14 channel pairs that showed significant positive correlations, respectively.
These results also supported that the low Alpha band plays an important role in the correlation analysis between the FCs and ∆FMU in MI EEG.The wPLI at center frequency of 11 Hz and PSI at center frequency of 9 Hz were found to be the most significant in indicating potential motor recovery in both resting and task EEG.The most significant center frequency for PCM was also located at center frequency of 9Hz.

B. Spatial Distribution Analysis Results of the Common Channel Pairs
In this section, correlation analysis and Partial Least Squares Covariance (PLSC) methods were applied to identify the most consistent contributing channel at each frequency.Firstly, the Spearman's correlation analysis method was applied to identify the common channel pairs with significant correlation across different frequencies.Secondly, PLSC was applied to analyze the contribution of FCs to ∆FMU under all selected channel pairs, returning with the most consistent within top five contributing channels across all frequencies.Fig. 4 summarized the Spearman's correlation analysis results of the identified channel pairs in combination with the optimized frequency in the previous section.Resting EEG results indicated a significant correlation between PCM at 9 Hz and ∆FMU with common top contributing channels as C3-P3 (r=0.827,p<0.001),TP7-P3 (r=0.678,p=0.011) and TP7-CPz (r=0.678,p=0.011).Between wPLI at 11 Hz and ∆FMU, the common top contributing channels were C3-P3 (r=0.739,p=0.004),TP7-P3 (r=0.678,p=0.011), and Fz-P4 (r=0.791,p=0.001).For PSI with center frequency of 9 Hz, the common top contributing channels were C3-P3 (r=0.816,p<0.001),P7-P3 (r=0.777,p=0.002), and Cz-F8 (r=0.772,p=0.002).
We also validated the correlation between the FCs of the common top contributing channel pairs in MI EEG at the optimized center frequency respectively.The common top three contributing channel pairs based on PCM, wPLI and PSI were selected via PLSC.The Spearman's correlation analysis results of FC values from the identified channel pairs were also shown in Fig. 4, in combination with the optimized frequency in the previous section.Similar results were found between resting and motor imagery EEG.For PCM, at center frequency of 9Hz, C3-P3 (r=0.811,p=0.001),TP7-P3 (r=0.678,p=0.011),TP7-CPz (r=0.656,p=0.015) were identified as shared contributing channels.For wPLI, we found that C3-P3 (r =0.722, p =0.001), Fz-P4 (r =0.775, p =0.002) and Cz-F8 (r =0.783, p =0.002) at 11 Hz were the common top contributing channel pairs.For PSI, C3-P3 (r=0.772,p=0.002),P7-P3 (r=0.772,p=0.002) and FZ-P4(r=0.777,p=0.002) at 9 Hz were found to be the common top contributing channel pairs correlated with ∆F MU .

C. Regression Analysis Results
To evaluate the feasibility of using FC as a biomarker for quantifying potential ∆FMU before rehabilitation intervention, we included several regression analysis methods to the FCs features from the identified channel pairs and optimal center frequencies.The FCs of the three channel pairs at the selected center frequencies were used as the feature inputs to evaluate the ∆FMU for each stroke participant, before rehabilitation intervention, using the leave-one-out cross validation, based on EEG data acquired from the two tasks.We compared final models' performance based on (1) PCM at 9Hz, (2) wPLI at 11Hz, (3) PSI at 9Hz, using Partial Least Squares Regression (PLSR), Multiple Linear regression (ML), Random Forest (RF) and Ridge Regression (Ridge) as regressors.
Fig. 5 presented the R 2 values of the three FC measures of two states.The model based on PSIs demonstrated the highest predictive performance in the two EEG tasks, as shown in Table II and Table III.The RMSEs were calculated between the predicted ∆FMU and actual ∆FMU for each participant based on leave-one-out method.Predictive models demonstrated strong statistical significance (p<0.001) with R 2 of 0.79 in resting EEG and 0.65 in task EEG.
Fig. 6 showed the fitted linear model of predicted and actual ∆FMU.The scatter dots distributed closely in alignment with the fitted straight line, suggesting that the actual ∆F MU of the participants were generally in agreement with the predicted results of the proposed PSI-based model.Compared to MI EEG, the PSI based on resting state EEG at Alpha band (9Hz) showed the best performance with channel pairs of C3-P3, P7-P3, and Cz-F8.

IV. DISCUSSION
This study investigated the preliminary feasibility of different functional connectivity measures and frequency bands using resting and task EEG in quantifying potential motor recovery among participants with chronic stroke.A two-step approach was used in this paper, which contained frequency analysis and spatial FC analysis.In the frequency band analysis, for PCM and PSI, Alpha (9Hz) was the most significant center frequency correlated with motor recovery, while wPLI at 11 Hz was the most significant center frequency.Alpha (9Hz) PSI was identified as the most promising biomarker for potential motor recovery.We further selected channel pairs with top contributions in assessing motor recovery before intervention, which suggested C3-P3, P7-P3 and Cz-F8 based on PSI as the best channel pairs for motor recovery.The final model was able to predict motor recovery in participants with chronic stroke before three weeks' rehabilitation with good accuracy, using FC measures of EEG before the rehabilitation intervention.
In the field of motor rehabilitation, previous studies have demonstrated that EEG-based FCs have the potential to correlate with motor improvements in participants with chronic stroke.Takashi et al. reported that FCs between ipsilateral hemispheric electrodes at 4 weeks post-stroke was found to be a significant predictor of motor function at 8 weeks poststroke [25].Rihui et al. reported the FC in the ipsilateral hemispheric premotor cortex was positively correlated with

TABLE II PREDICTION OF ∆FMU THROUGH FOUR REGRESSTION METHODS USING LEAVE-ONE-OUT CROSS-VALIDATION IN THE RESTING EEG
the motor recovery after a 4-week intervention [21].Using coherence measures, Ruben et al. reported that FCs in the somatosensory cortex of the unaffected hemisphere associated with clinical recovery of stroke patients at 2 months, which reflected the importance of contralateral hemispheric FC integrity in prognosing rehabilitation of upper limb [38].Although the literature showed that using FCs from specific ROIs could indicate motor recovery.The accuracy of the existing methods was generally low.
In our study, the effect of single-channel FCs with refined center frequencies was investigated in quantifying motor recovery before rehabilitation intervention.Three functional connectivity measures (i.e., PCM, wPLI and PSI) were investigated separately using EEG data collected from participants with chronic stroke before rehabilitation, to analyze and compare the resulted model performance.Our findings suggested that low Alpha band, especially 9 Hz PSI from resting state EEG can be an objective prognostic biomarker for motor recovery, with high accuracy.

A. Effect of Center Frequency in Quantitively Evaluating Potential Motor Recovery
We optimized the center frequency bands by refining the classical Delta, Theta, Alpha, Beta, and Gamma bands into 15 sub-bands to analyze the correlation between different center frequency bands and motor recovery.The wPLI of Alpha band with the center frequency of 11 Hz has been identified as the most relevant frequency band to potential motor recovery.However, the results for the PCM and PSI were with low Alpha band with the center frequency of 9 Hz.The frequency analysis results of wPLI were consistent with the results from previous studies.For example, during the analysis of changes in cortical excitability in stroke patients before and after transcranial direct current stimulation (tDCS), it was reported  that a stronger debiased wPLI in the Alpha band was associated with increased corticospinal excitability, and subsequently patients with stroke had more clinical improvements after the intervention [39].PLI from Alpha band (center frequency of 11Hz) was also the frequency band prominently correlated with motor function in previous study [15].Li et al. reported that higher baseline intensity of wPLI in the Alpha band within the ipsilateral lesion hemisphere was able to predict motor improvement [21].These results suggested that wPLI in Alpha (especially with center frequency of 11 Hz) band correlated with the potential of motor improvements in patients with chronic stroke.In addition, our results also suggested that PCM and PSI in Alpha band (especially with center frequency of 9 Hz) demonstrated the most significant correlations with ∆F MU .These results were different from the results in the literature, where Beta band was the most prominent frequency for PCM [40] and Theta band for PSI [27].Those discrepancies in the results can be explained by alternations in brain associated with stroke recovery over time.Most previous studies on PCM and PSI were focused on the subacute phase of stroke (3 weeks to 6 months post-stroke).Early post-stroke Beta and Theta rhythms played an important role in motor recovery [26].However, the present study was performed on participants with chronic stroke, where Alpha rhythms were reported as the dominant EEG frequency in the chronic phase of stroke [41].

B. Effect of Channel Pairs in Quantitively Evaluating Potential Motor Recovery
Correlation analysis was conducted to extract consistent top contributing channels at different center frequencies with three investigated FC measures.We used the PLSC to rank the contribution of the FC measures to identify the common top contributing channels across frequencies.We repeated this analysis method in both resting and MI task in the three FC measurements, respectively.We did not use PLSC contribution scores directly as the criteria in our study because the contribution scores varied greatly across participants and trials.
According to the results presented in this paper, we found that PSIs from C3-P3 and P7-P3 were the most consistent channel pairs associated with ∆FMU in both resting and MI EEG.The difference between the channel pairs in resting and MI state EEG were Cz-F8 and Fz-P4 channel pairs.For all three FC measures, contribution scores from C3-P3 were always identified as the common top contributing channels.It was clear that C3-P3 synchronization was the major functional connection for characterizing activities from primary motor cortex [42].This functional connection was the key in motor control and somatosensory feedbacks.C3-P3 FCs were also one of the common top contributing channel pairs in both resting and motor imagery EEGs, which demonstrated fundamental brain function of motor function.These results partially demonstrated the validity of our results.On the other hand, enhanced synchronization within motor-related regions of the ipsilateral hemisphere correlated with higher potential of motor recovery, which was also consistent with results in the literature [25].Taking results of PSI as an example, the correlation between P3-P7 PSI and motor recovery was intriguing.Considering both of these two channels located on the somatosensory cortex of less impaired side from stroke, it was possible that the processing of spatial somatosensory information inputs contributed to the formation of motor awareness in participants with chronic stroke, which led to higher motor function improvement from the rehabilitation intervention [34].Cz-F8 PSI was a functional connectivity measure with an inter-hemispheric connection.According to the literature, higher levels of synchronization in central and prefrontal regions also facilitated motor recovery.These results were consistent with the results published in [16].According to the analysis of PSIs of the MI task, the activities from P4, P3, C3, and C4 channels were closely related to potential of motor recovery.
In addition, PSIs from Fz-P4 were also found positively associated with motor recovery and were a major contributing feature for quantitively evaluating the potential of motor recovery before intervention.Previous studies showed that in motor imagery tasks, the functional connectivity of coherence-based F-P channels correlated to the potential motor rehabilitation [38].Synchronized activities between contralateral hemisphere via corpus callosum assisted the rehabilitation of the affected hemisphere and thus enhanced motor recovery through increased neuroplasticity.Another study reported that activities from contralateral hemispheric motor-related regions were also significantly correlated with motor recovery in FMU, which also confirmed our results in this paper [27].Furthermore, in a longitudinal FMRI study, upregulation of contralateral hemispheric activity was positively associated with recovery in patients with aphasia after stroke [43].
Our findings of this paper are in agreement with the results published in the literature, which demonstrate a strong and significant correlation between designated functional connectivity measures of the contralateral/ipsilateral hemisphere and potential motor recovery.

C. Evaluation of Regression Model Using PSI
Finally, functional connectivity indices from the channel pairs analysis were used as features to generate a model with higher performance in quantifying potential motor recovery.Four regressive methods were included in the analysis.Crossvalidation results demonstrated that the selected PSIs of 9 HZ center frequency showed the best performance for both resting and task EEG.The final regressive models were generated based on PSIs from three covariate variables, and the power analysis [44], [45] result suggested 11 participants (n1 = 10.462) were needed to demonstrate statistical significance for rest state model and 13 participants (n2 = 12.669) were needed to demonstrate statistical significance for the motor imagery state model, which were in alignment with the number of participants recruited in this study.The R 2 values of the optimized regressive models reached 0.79 in the resting state and 0.65 in the MI task.Multiple linear regression for resting EEG and Random Forest for MI EEG outperformed the performance of existing models using different regression methods and motor recovery sensitive feature inputs.For example, Majeed et al. reported that the prediction of FMU improvement was challenging and only achieved an average performance of 65.3±15.3%[46].Although PCM and wPLI showed promising performance in prognosis of motor recovery, PSI-based models achieved higher accuracy with lower errors.Compared to PSI, wPLI might be overly conservative in assessing functional connectivity, and thus underestimated the level of synchronization [47].Furthermore, the sign function of the wPLI could be considered as a thresholding/screening mechanism, and when the phase was processed through such method, it might have resulted in the loss of information.Therefore, the PSI measures contained more information in quantifying FCs.Compared with PCM, PSI-selected channels pairs primarily located in the ipsilateral hemisphere near the motor cortex area and in the contralateral hemisphere.Those features were more effective as independent variables than PCM-selected channel pairs, which primarily aggregated in the ipsilateral hemisphere.Westlake et al. reported that preserved effective connectivity in the motor cortex of the more impaired hemisphere and functional connectivity in the contralateral hemisphere were essential for prognosis of recovery [48].Another study also found that pre-intervention differed in motor thresholds between the affected and unaffected hemispheres, which could be another potential predictor of FMU after intervention treatment [19].Results from these studies confirmed our results in this study, which suggested that PSI of 9 Hz center frequency EEG could accurately predict motor improvement before intervention in stroke patients.Such technology could assist healthcare professionals in developing individualized treatment strategies and provide fundamental support for clinical stratification.

V. LIMITATIONS
In this paper, we designed and investigated a method to evaluate potential motor recovery using FC measures with refined frequency bands, in participants with chronic stroke before rehabilitation intervention.The optimized model was built based on PSI features selected via a two-step analysis.Theoretically, it was possible that linear correlation coefficient might not be the best feature selection criteria for building predictive models for motor recovery.However, due to the focus of this paper was on the preliminary feasibility of quantitatively evaluate potential motor recovery using PSIs before rehabilitation intervention, future studies using other feature extraction and selection algorithms should be conducted to further optimize the model performance.Secondly, the models in this manuscript were generated based on EEG data collected before rehabilitation, due to issues related to study design and data availability.Longitudinal studies could be conducted to further validate the long-term effects of the proposed method.In addition, the sample size of this study was intrinsically small, the conclusions from this paper might be affected by the specific EEG data distribution of the participants involved in this study.Future studies should be conducted with a larger population to further validate the findings in this paper.

VI. CONCLUSION
In this study, we investigated the preliminary feasibility of using functional connectivity measures as biomarkers for evaluating potential motor recovery before rehabilitation intervention, in participants with chronic stroke.We integrated correlation analysis with regression analysis to identify the prominent contributing frequencies and channel pairs.Three functional connectivity measures (PCM, wPLI and PSI) were investigated and four regressive algorithms (Partial Least Squares Regression, Multiple Linear regression, Random Forest and Ridge Regression) were used to generate the predictive models.We found that the resting state PSIs at 9Hz were the most sensitive FC measures of potential motor recovery before the rehabilitation intervention.The optimized model achieved R 2 of 0.79 in the resting state and 0.65 in the MI task.Our results suggested that optimized models based on PSIs were able to quantitatively evaluate motor recovery with decent accuracy before rehabilitation intervention, which might have great potentials in healthcare center resource organization, clinical stratification and individualized intervention for patients with stroke.

Fig. 2 .
Fig. 2. The flow chart of the functional connectivity analysis process investigated in this paper.

Fig. 3 .
Fig. 3.The number of channel pairs with significant positive correlations between three functional connectivity measures and ∆FMUs in both resting state and MI task.Y-axis indicates the number of channel pairs with significant correlations for each center frequency (x-axis).(a) Number of correlated channels at p<0.05 and p<0.01 in the three ROIs at resting state for PCM.(b) Number of correlated channels at p<0.05 and p<0.01 in the three regions of interest at resting state for wPLI.(c) Number of correlated channels at p<0.05 and p<0.01 in the three ROIs at resting state for PSI.(d) Number of correlated channels at p<0.05 and p<0.01 in the three ROIs at MI task state for PCM.(e) Number of correlated channels at p<0.05 and p<0.01 in the three ROIs at the MI task state for wPLI.(f) Number of correlated channels at p<0.05 and p<0.01 in the ROIs at the MI task state for PSI.Solid line represents p<0.05, dashed line represents p<0.01.

Fig. 4 .
Fig. 4. Top three contribution channel pairs for different functional connectivity measurements.The color bar represents the level of the correlation between the identified channel connectivity measurements and ∆FMU.Level of significance: * represents p<0.05, * * represents p<0.01, * * * represents p<0.001.

Fig. 6 .
Fig. 6.The actual ∆FMU and prediction of the optimized models in resting and MI tasks using the leave-one-out cross validation: (a) Model performance of PSIs from C3-P3, P7-P3, Cz-F8 at Alpha band (9 Hz) for the resting task.(b) Model performance of PSIs from C3-P3, P7-P3, Fz-P4 at Alpha (9 Hz) for the MI task.

TABLE III PREDICTION
OF ∆FMU THROUGH FOUR REGRESSTION METHODS USING LEAVE-ONE-OUT CROSS-VALIDATION IN TASK EEG