framework: Unveiling the brain asymmetry alterations and longitudinal changes after stroke using resting-state EEG

Hemispheric asymmetry or lateralization is a fundamental principle of brain organization. However, it is poorly understood to what extent the brain asymmetries across different levels of functional organizations are evident in health or altered in brain diseases. Here, we propose a framework that integrates three degrees of brain interactions (isolated nodes, node–node, and edge–edge) into a unified analysis pipeline to capture the sliding window-based asymmetry dynamics at both the node and hemisphere levels. We apply this framework to resting-state EEG in healthy and stroke populations and investigate the stroke-induced abnormal alterations in brain asymmetries and longitudinal asymmetry changes during poststroke rehabilitation. We observe that the mean asymmetry in patients was abnormally enhanced across different frequency bands and levels of brain interactions, with these abnormal patterns strongly associated with the side of the stroke lesion. Compared to healthy controls, patients displayed significant alterations in asymmetry fluctuations, disrupting and reconfiguring the balance of inter-hemispheric integration and segregation. Additionally, analyses reveal that specific abnormal asymmetry metrics in patients tend to move towards those observed in healthy controls after short-term brain-computer interface rehabilitation. Furthermore, preliminary evidence suggests that baseline clinical and asymmetry features can predict poststroke improvements in the Fugl-Meyer assessment of the lower extremity (mean absolute error of about 2). Overall, these findings advance our understanding of hemispheric asymmetry. Our framework offers new insights into the mechanisms underlying brain alterations and recovery after a brain lesion, may help identify prognostic biomarkers, and can be easily extended to different functional modalities.

Brain function and dynamics emerge from the underlying structural substrate and multi-level interactions between brain areas (Faskowitz et al., 2020;Axer and Amunts, 2022;Thiebaut de Schotten and Forkel, 2022).Complex behavior and brain function involve the participation of local and distributed brain regions (Thiebaut de Schotten and Forkel, 2022;Labache et al., 2023).Spontaneous or resting-state neural activity represents a certain type of baseline for the brain and is associated with behavior (Gotts et al., 2013;Ramot and Martin, 2022).As resting-state neuroimaging data are irrelevant to task competence and easy to acquire, they are widely used in almost all research or clinical settings.The present study focused on brain asymmetry in spontaneous neural activity.
However, the current field of brain asymmetry lacks a systematic research framework and the quantitative assessment of brain asymmetry is substantially heterogeneous across studies, which has hampered our understanding of brain asymmetry, exploration of neural biomarkers, and clinical application of asymmetries.Specifically, brain asymmetry measures derived from EEG are mainly based on the inter-hemispheric difference in power spectral density (PSD) and generally reflect hemisphere-level non-directional asymmetries (Mane et al., 2019;Hao et al., 2022a;Corsi et al., 2023); for fMRI, brain asymmetry is mostly investigated at the voxel or region level based on the difference of functional connectivity (FC) between the homologous connection pairs or the difference of graphtheoretic properties derived from FC between homotopic brain regions (Gotts et al., 2013;Gracia-Tabuenca et al., 2018;Wu et al., 2022;Labache et al., 2023).However, in neuroscience, it is difficult to know the extent and location of the distribution of the true effect in advance, and it is more appropriate to characterize the asymmetry both local and global.In addition, from investigating isolated nodes (e.g., channels or brain regions) to node-node FC, there is increasing interest in more fine-grained brain interactions to uncover more promising features (Helwegen et al., 2023).Isolated nodes can be regarded as brain networks without edges, and the attributes of isolated nodes (e.g., nodal PSD) can be investigated.The node-centric brain network/FC captures pairwise interactions between nodes.Edge-centric FC, which reflects the interactions between edges (i.e., node-node connections), offers a new perspective on our understanding of more complex brain interactions than traditional node-centric FC (Faskowitz et al., 2020;Idesis et al., 2022).It remains unknown whether brain asymmetries are encoded in the edge-centric FC of both normal and abnormal brain circuits.Moreover, the brain, as a dynamic distributed system, has been supported by evidence from neuroimaging studies (Allen et al., 2014;Favaretto et al., 2022;Hao et al., 2022b;Peng et al., 2023).Despite progress in brain asymmetry using static PSD or FC measures, little is known about asymmetry dynamics in health and brain diseases (Wu et al., 2022).Furthermore, considerable work has been conducted on asymmetries derived from intra-hemispheric connectivity (Gracia-Tabuenca et al., 2018;Sha et al., 2022;Craig et al., 2023;Vecchio et al., 2023).The asymmetries of interhemispheric connectivity remain unclear, albeit studies have shown the important role of inter-hemispheric connectivity in sustaining asymmetry and brain function (Siegel et al., 2016;Karolis et al., 2019;Thiebaut de Schotten and Forkel, 2022).
Here, we propose a "Comprehensive Analysis for Multi-level Brain Asymmetry" (CAMBA) framework to take a step forward in addressing these gaps.The CAMBA framework contributes to three aspects.First, we integrate multi-level brain interactions (i.e., isolated nodes, node-node, and edge-edge) into this framework to characterize brain asymmetry more systematically.Second, we map these coarse-to-fine interactions into measures at the unified node level to decrease the potential power loss and then depict the asymmetry dynamics at both the node and hemisphere levels.Third, we considered hemispheric asymmetries of both intra-and inter-hemispheric interactions to aggregate the sources of the maintained brain asymmetry.As a test, we applied our CAMBA framework to resting-state EEG data from healthy individuals and stroke patients.We first explored asymmetry patterns in healthy and stroke populations and local and global asymmetry alterations after stroke.Given that neuroplasticity (Pichiorri et al., 2015;Pirovano et al., 2022;Sanders et al., 2022) and brain asymmetry (Ang et al., 2015;Mane et al., 2019) are associated with the intervention, we next examined the extent to which brain asymmetry would be altered by lower-extremity brain-computer interface (BCI) rehabilitation training and tested the relationship between longitudinal changes in asymmetry and improvement of lower-extremity motor function.BCI-based stroke rehabilitation is relatively recent, and studies in this field have mostly focused on the upper extremities (Ang and Guan, 2015;Coscia et al., 2019;Romero-Laiseca et al., 2020;Xu et al., 2023).Further evidence is required to elucidate the effectiveness and mechanisms of this new rehabilitative strategy.
Finally, to demonstrate the potential clinical value of this framework, we constructed multiple machine-learning models based on baseline clinical and neural features to predict improvements in lower-extremity function after BCI training.
Notably, our CAMBA framework can easily be extended to other functional modalities (e.g., resting-state fMRI) and signal spaces (e.g., source reconstruction of scalp EEG).Since statistical inference at coarser brain scales may be more powerful (Helwegen et al., 2023), homotopic areal-level parcellations (Yan et al., 2023) can be a useful dimensionality reduction tool for studying brain asymmetry in resting-state fMRI and source-space EEG.Overall, this framework may be particularly powerful for studying intrinsic brain asymmetry, identifying biomarkers for various brain disorders, tracking changes in the recovery process, and guiding individual treatment.

Materials and Methods
Fig. 1 illustrates the main modules and key concepts of the CAMBA framework applied to resting-state EEG datasets.The details of each part of Fig. 1 are presented throughout Sections 2.2-2.7.

Datasets
Three resting-state EEG datasets from more than 100 subjects were included in the present study.Details of the datasets are presented below.The EEG datasets were based on usable data acquired from healthy participants (n = 20) and non-acute stroke patients (n = 121) between March 2019 and July 2022 from the Beijing Tsinghua Changgung Hospital.
Part of the datasets were used in other studies published by our group (Hao et al., 2022b;Lin et al., 2022).We excluded participants with poor EEG data quality, bilateral stroke lesions, or previous neurological or psychiatric diseases.
In the end, the first dataset (Dataset I) consisted of EEG data from 18 healthy participants ( 14 In brief, the BCI active rehabilitation system in the present study is a closed-loop neuromodulation system that detects motor imagery of ankle dorsiflexion to trigger multi-sensory feedback for neurorehabilitation.See Supplementary Methods for details on the BCI rehabilitation training protocol.For the control group (CTL), robotic-based rehabilitation is passive and the ankle robot is driven by a servo motor controlled by a digital signal processor; as described in a previous study (Zhai et al., 2021).The first 18 subjects of BCI groups were selected according to the time of EEG acquisition for testing the differences between BCI (n = 18; 16 males; age range, 37.4-80.1 years; 8 with left-sided stroke; 17 subacute patients; days post-stroke median, 52.2 days) and CTL (n = 18; 15 males; age range, 31.7-76.8years; 8 with left-sided stroke; 18 subacute patients; days post-stroke median, 45.5 days) groups and longitudinal changes within each group, and the remaining five were as a predefined independent test dataset (3 males; age range, 35.1-69.2years; 4 with leftsided stroke; 4 subacute patients; days post-stroke median, 54 days) for the outcome prediction task (see Section 2.7.2).The duration of both the BCI and CTL rehabilitation protocols was two weeks.EEG and clinical data in Dataset III were collected at baseline (T0) and after 10 sessions (five times a week over two weeks) of lower-limb rehabilitation training (T1).The Fugl-Meyer Assessment for the Lower Extremity (FMA-LE) was used to evaluate the motor function of the lower limb at both T0 and T1 (Gladstone et al., 2002).
The FMA-LE ranges from 0 to 34, with a higher score indicating better function.Please see Table S1 for descriptive statistics of clinical characteristics in the datasets, and the demographic details of each subject are available online (see Data and Code Availability Statement).

EEG acquisition and preprocessing
All resting-state EEG data were recorded using a 64-channel 24-bit resolution EEG system (Neusen W64, Neuracle Inc.) at a sampling rate of 1000 Hz for approximately five minutes.The EEG data were referenced to CPz and grounded to AFz.The channel locations are shown in Fig. S1.During the resting-state recording, the participants were asked to sit still and remain awake with their eyes closed, and the impedance of each electrode was kept below 20 kΩ.
The EEG data were preprocessed offline using a previously described analysis pipeline based on the EEGLAB toolbox (version 2019.0) and in-house MATLAB (R2022b) functions (Hao et al., 2022b).Here, we provide a brief outline of the processing steps.(1) EEG recordings were bandpass filtered (1-45 Hz) using lowpass and high pass finite impulse response filters with a zero-phase shift.(2) EEG data were downsampled to 250 Hz. (3) Bad channels were discarded semi-automatically and their signals were interpolated through spherical interpolation.(4) EEG data were re-referenced to the average across all channels and the values of the original reference channel (i.e., CPz) were restored.( 5) Artifacts (e.g., eye movements and muscle activity) were removed after independent component analysis and visual inspection.Statistical information on the percentage of good channels and bad independent components is presented in Table S1.interactions (i.e., isolated node, node-node, and edge-edge interactions) were constructed using denoised data.The dynamic power spectral density (PSD) was calculated for each isolated node using a sliding timewindow approach.For each time window, functional connectivity (FC) was used to estimate node-node interaction.The edge-edge interaction was computed as the correlation coefficient between the connection strength series of the two corresponding node pairs.(C) The complex network analysis approach was performed to extract graph-theoretic properties from dynamic FC and edge-centric FC, unifying multi-level brain interactions to node-level measures.(D) The brain asymmetry index was calculated at both node and hemisphere levels.Three metrics (mean asymmetry index, MAI; asymmetry fluctuation, AF; asymmetry correlation, AC) were extracted to characterize brain asymmetry.(E) Cluster-based statistics (CBS) and Bonferroni-Holm (BH) methods were used to correct multiple comparisons.Classification and regression models were developed using measures of brain asymmetry.SVM, support vector machine; SVR, support vector regression; RF, random forest; ANN, artificial neural network.

Multi-level interaction construction
As shown in Fig. 1B, the CAMBA framework considers brain interactions at three levels from simple to complex: isolated node, node-node interactions, and edge-edge interactions.Time-varying interactions among regions manifest as brain dynamics and local and distributed system participation.In this study, we adopted a sliding-window approach to capture brain dynamics.

Isolated node
To obtain the parameter of the isolated node signal itself, we calculated the PSD for each channel.The nodal PSD shows the distribution of the signal power of a node.Four frequency bands were defined and used in the following analyses: delta (1-4 Hz), theta (4-8 Hz), alpha (8-13 Hz), and beta (13-30 Hz).Given that the signal-to-noise ratio decreased at higher frequencies, we did not consider brain activities above 30 Hz in the current study.
Dynamic PSD (i.e., without average across windows) was computed for each recording and each channel (Welch's method, Hamming window, 2 s window, 50% overlap).

Node-node interaction
Dynamic FC was used to model the interactions between nodal neural signals.To eliminate or substantially reduce the negative effects of volume conduction of scalp EEG (Nunez and Srinivasan, 2006;Smith et al., 2022), the reference-independent scalp Laplace spatial filter (Kayser and Tenke, 2006) was applied to the preprocessed data, and then a volume conduction-insensitive method, weighted phase-lag index (wPLI) (Vinck et al., 2011), was used to construct FC.The complex Morlet wavelet method was used to extract instantaneous amplitudes and phases.The central frequencies were logarithmically spaced between 2 Hz and 30 Hz in 20 steps.Correspondingly, the number of cycles increased from 4 to 8 in logarithmic steps.The full width at half maximum (FWHM) ranged from about 750 to 100 ms, decreasing with increasing wavelet central frequency (Cohen, 2019).
Correspondingly, the spectral FWHM ranged from 1.2 to 8.8 Hz.The FC strength between the analytic signals of channels x and y for each time window was computed over time using the following equation: where ℑ(  ) indicates the imaginary part of the cross-spectral density of channels x and y at time point t, the sgn function returns the sign of the value, and N is the number of time points.
Dynamic FC was calculated using the sliding-window approach (window length of 2 s and 50% overlap).The size of the dynamic FC is  ×  ×  ×  for each recording.F, N, and T are the numbers of frequency points, channels, and time windows, respectively.
Dynamic FC was then averaged across frequency points within each canonical frequency band (i.e., delta, theta, alpha, and beta).

Edge-edge interaction
We proposed a method of constructing edge-centric FC based on the dynamic FC to evaluate the interaction between the edges.It is also inspired by edge-centric analysis in fMRI, which focuses on moment-by-moment co-fluctuations between nodes and calculates the mean of the element-wise product of two z-scored nodal time series (Faskowitz et al., 2020;Idesis et al., 2022).In this study, we estimated edge-edge interactions based on dynamic FC, considering the balance between time and space complexity and the coherency of the analysis.For each frequency band, the dimensions of the dynamic FC are

Intra-and inter-hemispheric connectivity
For node-and edge-centric FC, whole-brain connectivity encompasses both intra-and inter-hemispheric connections.Although the homotopic connections themselves do not contribute to the asymmetry, they represent only a small fraction of the inter-hemispheric connections, and asymmetries may also emerge from inter-hemispheric connectivity involving homotopic connections.To better understand brain asymmetry, we considered both intra-and inter-hemispheric connectivity.Two points need to be clarified.(1) To make adequate use of the data, eight channels in the midline (Fig. S1) were assigned to both hemispheres, as they participated in the brain networks of both hemispheres.It is equivalent to 34 nodes in each hemisphere for intra-and inter-hemispheric connectivity.(2) Only the "nodes" (i.e., edges in FC) within the left or right hemisphere of the edge-centric FC were considered.There were 561 (34 × 33/2) "nodes" in each hemisphere of intra-and interhemispheric connectivity in edge-centric FC.

Node-level measures extraction
In the current study, the graph theoretical analysis (Rubinov and Sporns, 2010) was performed to derive node-level measures from dynamic FC and edge-centric FC.There are three main reasons for this mapping from higher to lower dimensions.(1) It can reduce the number of statistical tests and false positives.
(2) Graph theoretical analysis is a powerful tool to characterize complex networks from which biologically meaningful measures can be extracted (Sha et al., 2022;Wu et al., 2022;Craig et al., 2023).
(3) The brain interactions at the three levels can be studied at the unified node level.

Node-centric FC
To extract the node-level measures, the dynamic node-centric FC was first thresholded to a weighted undirected network.As previous findings have cautioned against using proportional thresholding in case-control studies (Cohen, 2014;Hallquist and Hillary, 2019), we applied an absolute threshold to the dynamic FC.For each frequency band, the threshold is determined in two steps.First, the average FC of healthy individuals and stroke patients was pooled.Second, the threshold was empirically set to one standard deviation above the median FC value (Cohen, 2014).
Four node-level graph-theoretic properties were extracted from the FC of each time window and frequency band of each recording using the Brain Connectivity Toolbox (Rubinov and Sporns, 2010) and in-house code, that is, the node strength (NS), betweenness centrality (BC), local efficiency (LE), and clustering coefficient (CC).
Among them, NS and BC portray the hub or centrality properties of the nodes in the network, and CC and LE represent segregation properties that reflect the local information transfer capability of the network.Normalized NS and BC were used to exclude the influence of the number of nodes.Note that nodal LE and CC are not available for interhemispheric connectivity, as they are all zero.The calculation formula for each measure and additional explanation are available elsewhere (Rubinov and Sporns, 2010;Cohen, 2014;Sha et al., 2022).For each frequency band, the dimension of each node-level measure of intra-and inter-hemispheric connectivity is 34 × , where T indicates the number of time windows.

Edge-centric FC
As an exploratory and preliminary analysis, considering the computational cost corresponding to the high dimensionality of edge-centric FC, only one network measure, i.e., normalized NS, was computed for each "node" in edge-centric FC and was denoted as eNS.Thresholding is not necessary for computing eNS and was not performed here.For example, the normalized NS of an edge {, } is   , and   is allocated to both nodes i and j.To obtain the node-level eNS, all values assigned to one node were averaged to a single value.For each frequency band, the dimension of each node-level measure of intra-and inter-hemispheric connectivity is 34 × 1.

Brain asymmetry measures calculation
To quantify the brain asymmetry index (BAI) for each node-level measure, we characterized hemispheric asymmetry at two levels: node and hemisphere levels.

Node-level asymmetries
The node-level BAI of each frequency band in the PSD was calculated using the following formula: where F is the number of frequency points in this band and (, , )and (, , ) represent the PSD at frequency f in the time window t from node i in the left hemisphere and homologous node in the right hemisphere, respectively.This definition is similar to the previous brain symmetry index (van Putten, 2007;Sheorajpanday et al., 2009) but retains the direction of asymmetry at the node level.For each band, the dimension of BAI is 26 ×  (no eight midline channels; see Fig. S1) and T indicates the number of time windows.
For node-level network measures (i.e., NS, BC, LE, CC, and eNS) in each frequency band, BAI was calculated as the difference between the values of the left and right hemispheres: which the sizes of BAI, L, and R are 34 ×  in NS, BC, LE, and CC, and are 34 × 1 in eNS.
Note that a commonly used index similar to that in PSD, i.e., ( − )/( + ), was not used in the current study, as the denominator could sometimes be zero in certain network measures.

Hemisphere-level asymmetries
The hemisphere-level BAI for each frequency band was computed as the dissimilarity between the left and right hemispheres as follows: where () and () represent the node-level measures in the time window  = 1,2, … , , and ((), ()) indicates the Spearman correlation coefficient between () and ().Hemisphere-level BAI in the PSD can be calculated as the average across the dissimilarities of the frequency points in each frequency band.But for simplicity, the hemisphere-level BAI was calculated only for the network measures in the current study.
Note the size of the BAI is 1 ×  in NS, BC, LE, and CC, and a real value in eNS.

Asymmetry metrics derived from the BAI
To characterize the asymmetry dynamics, three metrics were utilized in this study: mean asymmetry index (MAI), asymmetry fluctuation (AF), and asymmetry correlation (AC).The MAI is defined as the average BAI across all the time windows.The LF is defined as the standard deviation of the BAI across all time windows, which reflects the variability of the asymmetry dynamics.Inspired by previous research (Rosch et al., 2018), the Spearman correlation between adjacent asymmetry vectors in the node-level BAI was calculated to explore the temporal variability of brain asymmetry.The correlation dynamic sequence consisted of these temporally ordered Spearman correlation coefficients.If the BAI in each frequency band of a recording consists of T time windows, then the correlation dynamic sequence is a vector containing  − 1 elements.The AC is defined as the mean of the correlation dynamic sequence.The asymmetry metrics used in this study are summarized in Table S2.

Statistical inference
All statistical tests were performed using custom MATLAB codes.In this study, a substantial number of statistical tests were performed across different nodes and frequency bands.However, asymmetry metrics are not independent across different nodes, frequency bands, and network measures.To maintain the balance between statistical power and false positives, the cluster-based statistics (CBS) method (Maris and Oostenveld, 2007) was employed to correct for multiple testing of nodal measures.The CBS methods account for the spatial dependence of the data, which may drastically increase the statistical power with weak control of familywise error (Maris and Oostenveld, 2007;Nichols and Hayasaka, 2016).Then, the Bonferroni-Holm (BH) method (Holm, 1979) was utilized to correct multiple comparisons of frequency bands.All tests were two-tailed with a significance level of 0.05.
The CBS and network-based statistics (NBS) (Zalesky et al., 2010) methods share the same fundamental principle, with NBS serving as an extension of CBS specifically for functional connectivity.Following the channel-by-channel univariate statistical tests, the p-values of all channels were binarized using a cluster-forming threshold (i.e., p = 0.05).
Channels with p-values below this threshold were used to identify the clusters.The neighboring channels of a given channel were set manually, as depicted in Fig. S1.In summary, the CBS method involves four steps: (1) Perform channel-by-channel statistical tests to obtain p-values and statistics (e.g., t-value).
(2) Apply the cluster threshold to the p-values to identify clusters and quantify the size of each cluster (positive or negative effect), such as the number of nodes or the sum of the statistics within the cluster.(3) Randomly shuffle the signs (for one-sample or within-subjects design), labels (for between-subjects design), or orders (for correlation analysis) of the subjects, and repeat steps ( 1) and ( 2) to record the maximum absolute size of the positive and negative clusters.
(4) Repeat step (3) D times (e.g., 5000 in this study) to construct null distributions for the largest positive cluster (  ) and the largest negative cluster (  ).For instance, the p-value of a specific observed positive cluster i is determined using the following equation: where B represents the number of times out of D that the values in   are larger than the size of the observed cluster i.To prevent permutation p-values from reaching zero, one is added to both the numerator and the denominator.The determination of p-values for observed negative clusters is similar.As there is no a priori hypothesis on the effect direction, the p-values were corrected by multiplying them by two (equivalent to Bonferroni correction) (Meyer et al., 2021).
To evaluate the extent to which the node-level MAI metrics of healthy controls (HC), patients with left-sided stroke (Stroke L), and patients with right-sided stroke (Stroke R) may be evident, the CBS method was employed using the Wilcoxon signed-rank test as the univariate test.The cluster size (cs) was defined as the number of nodes within a cluster.
To compare Stroke L vs. HC and Stroke R vs. HC, the CBS method with the Wilcoxon rank-sum test was used for the node-level MAI and AF metrics.In this case, the cs is defined as the number of nodes in a cluster.The Wilcoxon rank-sum test was used for hemisphere-level MAI, AF, and AC metrics.If the p-value was calculated using a normal approximation method for the aforementioned non-parametric tests, the corresponding zstatistic was provided.
To investigate the impact of different rehabilitation training strategies on brain asymmetry, the paired t-test was conducted as the univariate test for CBS or hemispherelevel tests on asymmetry metrics that exhibited significant differences between stroke patients and HC.This was mainly to reduce the number of comparisons.Additionally, as most of the changes (T1 vs. T0) in asymmetry metrics satisfied a normal distribution (Shapiro-Wilk test), using parametric tests may increase statistical power.The cs was defined as the absolute sum of the t-values within the cluster.
Finally, to explore the relationship between changes in brain asymmetry metrics and changes in FMA-LE for the BCI and CTL groups, Pearson correlation was utilized as the univariate test for CBS or hemisphere-level tests.The cs is defined as the absolute sum of correlation coefficients within a cluster.Note that only the asymmetry metrics in the alpha and beta frequency bands, which have been demonstrated to be associated with motor function (Wu et al., 2015;Riahi et al., 2020), were examined to reduce the number of tests.

Classification
To further investigate the contributions of the stroke lesion side to brain asymmetry patterns, we used three classification algorithms: linear kernel support vector machine (SVM), random forest (RF), and artificial neural network (ANN; specifically, multilayer perceptron).The goal was to distinguish between Stroke L (n = 45) and Stroke R (n = 38) cases.The classifiers were implemented using the Python scikit-learn package (version 0.24.2).As the MAI metrics (n = 36) preserve directional information, we used the average across all nodes of each MAI metric as the input features.No additional feature screenings were performed.To estimate the performance of each machine-learning model with low bias, given the relatively small dataset, we adopted a nested leave-one-out cross-validation (LOOCV) procedure.For a detailed depiction of the nested LOOCV procedure, please refer to Fig. S2.The features were performed min-max normalization.The optimal hyperparameters were tuned within the inner LOOCV loop and the final model was refitted with the entire training set using the best parameters and tested on the corresponding outer test set.Note that the make_pipeline function was used to prevent potential leakage.The receiver operating characteristic (ROC) curve was generated, and the area under the ROC curve (AUC) was computed as a performance metric for classification.

Regression
To explore the potential of asymmetry and clinical features in predicting the prognosis of lower-extremity BCI rehabilitation training, we developed three types of regression models: support vector regression (SVR) with a radial basis function kernel, RF regression, and ANN regression.The main idea was to use baseline features to predict FMA-LE changes after the intervention.The clinical features included age, poststroke time, and baseline FMA-LE.Similar to the classification task, a nested LOOCV approach was implemented to assess the performance of regression models.In this study, a correlationbased feature selection method was used to determine the consensus features across all the LOOCV outer loops (Parvandeh et al., 2020) to reduce the dimensionality of the feature space (see Fig. S2 for detailed procedures).Briefly, for each outer loop, the Spearman correlation between each feature at T0 and FMA-LE change was assessed in the training set (i.e., the data entering the inner loop), considering a feature as a candidate if the correlation was statistically significant (without correction for multiple comparisons across different frequency bands).The final features for each regression model consisted of consensus features identified across all iterations (n = 18).For the selected node-level features, the values within the significant cluster were averaged to reduce dimensionality.
The mean absolute error (MAE) and root mean squared error (RMSE) were used as evaluation metrics for the regression models.To evaluate the generalizability of the regression models, we used consensus features and adopted the LOOCV approach based on the entire dataset (n = 18) to construct the final model.We then evaluated the performance using an independent dataset (n = 5, Section 2.1).
To investigate the importance and contribution of each feature to the prediction of the corresponding training set) should be equal to the predicted value for this sample.We evaluated the importance of each feature for each regression model using the mean of the absolute SHAP values across all samples for each feature (global explanation) and the contribution of each feature to the predicted value of a subject by using the SHAP values of features for this subject (local explanation).

Different asymmetry patterns in health and stroke populations
We first examined the extent to which and how functional asymmetries in multi-level brain interactions were reflected in healthy individuals and patients with one unilateral stroke lesion.To do so, we applied the CAMBA framework to the resting-state EEG Dataset I (HC, n = 18) and Dataset II (Stroke L, n = 45; Stroke R, n = 38).There were no significant differences between HC and stroke patients or between Stroke L and Stroke R in terms of demographic and clinical characteristics (see Table S1).We examined the mean asymmetry patterns using the MAI of the nine node-level measures (Table S2) in four frequency bands for each group (Section 2.6).Here, the MAI of each measure refers to the average of the node-level differences between left and right hemispheres across all time windows (Section 2.5.3).
Fig. 2A shows, in summary, the mean asymmetry pattern and size of the clusters, where the effect was most pronounced for the nine node-level measures in different groups (HC, Stroke L, and Stroke R) and different frequency bands (beta, alpha, theta, and delta).
The topographic distribution of each node-level measure in the HC, Stroke L, and Stroke R are shown in Fig. S3, and clusters with pronounced asymmetry effects are marked in the topographic maps.Detailed statistical results are listed in Table S3.Broadly, no measures of HC exhibited significant leftward or rightward asymmetry after the CBS and BH corrections for multiple comparisons.However, significant asymmetries were observed in stroke patients, involving measures across all four frequency bands and three levels of brain interactions (Figs.2A and S3, and Table S3).Specifically, for healthy individuals, PSD in the alpha band and NS of inter-hemispheric connectivity in the delta band showed a marginally significant rightward (p = 0.064, cs = 4 nodes) and leftward (p = 0.064, cs = 2 nodes) asymmetry, respectively.For Stroke L, we found significant rightward asymmetries  S3).Compared with healthy individuals, stroke patients showed stronger mean asymmetry patterns, and they had a considerable association with the lesion side.However, the significant mean asymmetry patterns across measures and frequency bands after stroke were driven by clusters of different sizes or locations (Fig. S3).
Furthermore, Fig. S3 reveals that stroke-induced functional damage spreads to both hemispheres and is not restricted to the ipsilesional hemisphere.Significant alterations in the mean asymmetries after stroke were sculpted by the mixed effect of changes in the left and right hemispheres.The node-level NS of beta intra-hemispheric connectivity was used as an example to illustrate this in detail (Fig. 2B).It was nearly symmetrical in the HC group and was characterized by strength dominance in the central and posterior regions.
Notably, an overall decrease in strength was observed in stroke patients in both hemispheres.Nevertheless, significant rightward and leftward asymmetries were observed in Stroke L and Stroke R, respectively.For more refined insight, we calculated the mean intra-hemispheric connectivity in the beta band for each group (Fig. 2B).Nearly completely symmetric connectivity and NS patterns were shown in HC, whereas substantial connectivity disruption and NS reduction in the affected hemisphere were observed in both Stroke L and Stroke R. in the first column use a color bar with a range from the minimum to maximum value of each map's own, whereas maps in the second column use a consistent range of the color scale from the minimum to maximum value across all three plots.The significant leftward and rightward asymmetries are marked with red dots at the channel locations in the corresponding cluster in the left and right hemispheres, respectively.We also show the mean intra-hemispheric functional connectivity and NS for HC (third column), Stroke L (fourth column), and Stroke R (fifth column).For better visualization, only connections greater than one standard deviation above the mean connectivity values were displayed.The size of each bubble corresponds to the of the corresponding node.See also Fig. S3 for more results.

Abnormal alterations in node-and hemisphere-level asymmetries after
Next, we investigated how the asymmetry patterns were altered in stroke patients compared with healthy individuals.To do so, we compared the node-and hemisphere-level asymmetry metrics of the brain asymmetry dynamics between stroke patients and HC.The statistical results of the node-level metrics were corrected by CBS first for nodes and then BH for frequency bands, and those of the hemisphere-level metrics were corrected by BH for frequency bands.See Tables S4 and S5 for complete results.

Node-level alterations
After stroke, specific MAI measures exhibited significant local or distributed alterations compared to HC, and the preference for alterations appeared to be different in For node-level AF metrics, all significant findings revealed that the temporal variability of the asymmetry index was significantly increased after stroke compared with HC (Figs. 3A and S6, and Table S4).For a certain measure, Stroke L and Stroke R generally showed similar alteration patterns.However, the effect distributions of differences between stroke patients and HC vary according to different measures.For example, as shown in Fig. 3B, a significantly larger AF of PSD was observed for Stroke L vs. HC (beta, p = 0.012, cs = 7 nodes; delta, p = 0.034, cs = 5 nodes) and Stroke R vs. HC (beta, p = 0.014, cs = 7 nodes; delta, p = 0.027, cs = 4 nodes) in the region adjacent to the midline (i.e., fronto-occipital axis).Significantly increased AF of LE from intrahemispheric connectivity was found in Stroke L vs. HC (beta, p = 0.011, cs = 27 nodes; delta, p = 0.002, cs = 30 nodes) and Stroke R vs. HC (beta, p = 0.002, cs = 26 nodes; delta, p = 0.002, cs = 28 nodes), and the differences were driven by most of the nodes.
Furthermore, the AF anomaly increase could be found in all four frequency bands and both intra-and inter-hemispheric connectivity.

Hemisphere-level alterations
Given that hemisphere-level asymmetries did not indicate the direction of asymmetry, Stroke L and Stroke R were merged into a stroke patient group (n = 83) to increase statistical power.All the results (also including those of Stroke L/Stroke R vs. HC) are summarized in Table S5.
The hemisphere-level MAI metrics showed the most prominent differences (i.e., = 4.743) and BC (p = 0.017, z = 2.853) of inter-hemispheric connectivity (Fig. 3C).In the low-frequency bands, only the eNS of delta inter-hemispheric connectivity showed a significant difference between stroke patients and HC (p = 0.006, z = 3.186).
Next, we compared hemisphere-level AF metrics between stroke patients and HC.
The most significant differences were observed in the beta and delta bands.As seen in Fig. 3C, an opposite alteration pattern was found for stroke patients vs. HC in the beta and delta Finally, we investigated the extent of hemisphere-level dynamic correlation patterns of brain asymmetries (i.e., AC metrics) deficits in stroke patients.The hemisphere-level AC metrics showed alteration patterns similar to those of AF metrics.For stroke patients vs. HC, a significant decrease was observed in all AC metrics in the beta band, except for the PSD (Fig. 3C).In contrast, delta LE (p = 0.005, z = 3.208) and delta CC (p = 0.004, z = 3.270) of intra-hemispheric connectivity showed a significant increase in stroke patients compared with HC.
In summary, multiple lines and levels of evidence suggest that the disruption of brain function in stroke is multi-domain (i.e., time, frequency, and space), with a dynamic balance of segregation and integration between the left and right hemispheres broken, and abnormal patterns spanned all levels of brain interactions and reflected in both intra-and intra-hemispheric connectivity.

Prediction of stroke lesion side based on node-level MAI metrics
The findings suggest that asymmetry patterns in node-level MAI metrics are associated with the lesion side of the stroke (see Section 3.1).Beyond this explanatory description, we constructed three machine-learning prediction models (i.e., SVM, RF, and ANN) based on node-level MAI metrics to classify left-sided stroke (n = 45) or right-sided stroke (n = 38).To reduce the dimensionality of the features, we averaged each node-level MAI metric across all nodes, resulting in 36 features (Table S3) for each subject.Notably, feature selection was not performed.To avoid data leakage, we used the nested LOOCV procedure, which performs data normalization and hyperparameter selection in the inner LOOCV loop and returns the best model for the outer LOOCV loop to evaluate performance in the test set (Fig. S2).We used the AUC to evaluate the performance of each model in distinguishing between the left-and right-sided strokes.As shown in Fig. S7, all three AUCs were greater than 0.85 (0.853 for SVM, 0.888 for RF, and 0.861 for ANN).As an AUC of 0.8 to 0.9 is considered excellent discrimination (Hosmer Jr et al., 2013), We further demonstrated the underlying link between lesion location and mean asymmetry patterns in stroke patients.

Longitudinal changes in brain asymmetry under different stroke rehabilitation strategies
A critical unanswered question is how rehabilitation strategies underpin functional recovery.Here, we utilized data from two rehabilitation treatments: BCI active rehabilitation (n = 18) and robotic-based passive rehabilitation (n = 18) to investigate how they induce changes in asymmetry metrics (i.e., MAI, AF, AC; see Section 2.5.3).
Considering the small sample size and strong link between node-level MAI metrics and the lesion sides, we flipped the MAI metrics (i.e., multiplied by −1) in patients with rightsided stroke in both groups.To reduce the number of comparisons, the focused on asymmetry metrics with significant differences between stroke patients and HC (see Section 3.2) and investigated their longitudinal changes in BCI and CTL groups.All statistical results are listed in Tables S6 and S7.
No significant differences were found between the BCI and CTL groups in terms of clinical characteristics (Table S1).There was also no significant difference (p = 0.In addition, for hemisphere-level metrics, the findings revealed that the BCI group showed a significant increase in the AF of NS of inter-hemispheric connectivity in the beta band (p = 0.012, t = 2.809), and a significant decrease in the three metrics of intra-   S7.

Longitudinal changes in brain asymmetry were correlated with changes in lower extremity function
Neuroplasticity is thought to underlie functions that can be improved after stroke impairment.If there are significant improvements in motor function after rehabilitation training, some changes in the brain structure and function must underpin the functional improvements, even if only small changes are involved.Therefore, we examined the relationship between changes in brain asymmetry metrics and changes in lower-limb motor function scores (i.e., FMA-LE).Here, only the metrics in the alpha and beta bands associated with motor function were examined to reduce the number of comparisons.In the BCI group, we found significant correlations between changes in asymmetry and FMA-LE in four node-level MAI metrics of intra-hemispheric connectivity: NS (alpha, p = 0.022, = 4.946), BC (beta, p = 0.019, cs = −2.419),LE (alpha, p = 0.020, cs = 8.941), and CC (alpha, p = 0.021, cs = 9.662), and in the node-level AF of BC (beta, p = 0.008, cs = 2.472) for inter-hemispheric connectivity (Fig. 5 and Tables S8 and S9).The sign of cs indicates a positive or negative correlation.Meanwhile, the changes in hemisphere-level AF of NS (alpha, p = 0.049, r = −0.528)and BC (beta, p = 0.046, r = −0.532) of inter-hemispheric connectivity were also significantly correlated with the changes in FMA-LE.However, none of the changes in asymmetry metrics in the CTL group were significantly associated with changes in FMA-LE.
Fig. 5A shows the correlations between pairwise combinations of changes in features (i.e., seven asymmetry metrics and FMA-LE).Note that the average across the nodes within the cluster is used for the node-level asymmetry metrics.It can be found that the correlations between node-level asymmetry metrics were broadly stronger than those between node-level measures and hemisphere-level measures.Fig. 5B illustrates three of the seven asymmetry metrics whose changes were significantly correlated with the changes in FMA-LE and the corresponding cluster that drives the correlation.Additionally, significant correlations were observed among the three asymmetry metrics, although the brain regions involved were different (Fig. 5 and Table S10).Together, these findings suggest that neural effort during active BCI rehabilitation across patients on the same task may give rise to more similar patterns of functional plasticity compared with the CTL group, which in turn is associated with improvements in lower limb function.See Tables S8-10 for more details.S10.
(B) Three node-level asymmetry metrics in Fig. 5A are shown with scatterplots, regression lines, and topographic maps.Clusters with p-values smaller than 0.05 were outlined in the topographic maps.

Prediction of the change of FMA-LE using baseline features
Despite the important findings in Section 3.5 in the BCI group, we further constructed a prognostic prediction model based on baseline features to predict FMA-LE improvements after rehabilitation training to reveal the potential clinical values of asymmetry metrics.
The optional features include three clinical features (age, time poststroke, and baseline FMA-LE), 64 node-level asymmetry metrics (nine MAI and seven AF metrics; four bands), and 84 hemisphere-level asymmetry metrics (eight MAI, six AF, and seven AC metrics; four bands).We also used the nested LOOCV approach and adopted the idea of consensus features based on nested cross-validation for feature selection (see Section 2.7.2, and Fig. S2).Fig. 6A shows the categorization of the final 16 selected features, where the nodelevel features were mainly derived from the parieto-occipital and prefrontal regions.
Similar to the classification task, the results of three models (i.e., SVR, RF, ANN) were shown, and MAE and RMSE were used to assess the predictive performance of the models.
As shown in Fig. 6B, the best performance was obtained from the SVR model (MAE = 1.488,RMSE = 2.072) compared with the RF (MAE = 2.085, RMSE = 2.624) and ANN (MAE = 1.822,RMSE = 2.329) regression models.Considering the potential data leakage in the feature selection procedure, we used another independent dataset (n = 5) and obtained similar results, especially for the SVR model (Fig. 6B and Table S11).The results demonstrate the predictive value of the selected features.The model parameters and the actual and predicted values for each patient are listed in Table S11.
To assess the importance/contribution of features to the model prediction, we used SHAP values to achieve global and local explanations of features for each regression model (Section 2.7.2). Fig. 6C shows the feature importance/contribution in each model, i.e., the average of the absolute SHAP values of each feature across all subjects.The feature importance was different across models, but the baseline FMA-LE, hemisphere-level AF of BC of beta inter-hemispheric connectivity, node-level MAI of BC and LE of beta intrahemispheric connectivity, and AC of CC of theta intra-hemispheric connectivity were all in the top half of the feature importance in all three models.Fig. 6D shows the contribution of each feature to the final predicted outcome in the SVR model for one subject with an actual FMA-LE improvement of 6 points.The final predicted value of 5.762 was the sum of the base value (i.e., the average of the predicted values across all training samples: 5.204) and the SHAP value of each feature.These analyses demonstrate the potential of specific clinical and asymmetry metrics as prognostic biomarkers and allow their explanation at both global and local levels.S11.(C) The importance/contribution of each consensus feature to each of the three models was assessed based on the global explanation of the SHAP values.The features were ranked according to their mean importance across the three models (scatters).In feature naming connected by underscores, "Inter" = inter-hemispheric connectivity, "Intra" = intra-hemispheric connectivity, "node" = node level, and "hemi" = hemisphere level.For example, "Inter_hemi_AF_BC_beta" indicates the hemisphere-level AF of BC of inter-hemispheric connectivity in the beta band.If two clusters are selected from one node-level metric, the "1" and "2" suffix is added to the end of the name for differentiation.

Discussion
In this study, we applied our proposed CAMBA framework to different populations to investigate the brain asymmetry of multi-level brain interactions.The present results provide evidence from different perspectives that stroke leads to significant alterations in brain asymmetry across coarse-to-fine brain interactions and different frequency bands.
Stroke-induced alterations are evident in the asymmetry metrics derived from both intraand inter-hemispheric connectivity.Additionally, we demonstrated that poststroke functional recovery was accompanied by longitudinal changes in hemispheric asymmetry.
Our preliminary findings show that specific baseline features are potential biomarkers for individual-level prognostic prediction.Collectively, the present study advances our understanding of the brain asymmetry patterns in poststroke brain asymmetry alterations.
The proposed framework has the potential to track longitudinal changes and identify biomarkers with prognostic value for various neurological and psychiatric brain disorders.

Strengths of the CAMBA framework
Although progress has been made in understanding brain asymmetries and their abnormal alterations using PSD or node-centric FC, the brain asymmetry of asymmetry dynamics and multi-level brain interactions has rarely been studied, especially for EEG.
Specifically, PSD-based brain asymmetry metrics, such as the pairwise-derived brain symmetry index (Sheorajpanday et al., 2009), are often used as candidate EEG biomarkers for the monitoring or prognosis of neurological disorders (van Putten, 2007;Mane et al., 2019;Duan et al., 2021).However, they are generally used as measures of absolute hemisphere-level mean asymmetry and can neither reflect the asymmetry changes over time nor allow for exploration of the clustered or focal asymmetry effects.Moreover, previous studies have demonstrated the reliability and potential of graph-theoretic properties for detecting brain asymmetry in structural and functional connectivity (Gotts et al., 2013;Gracia-Tabuenca et al., 2018;Sha et al., 2022;Wu et al., 2022;Craig et al., 2023).
Graph-theoretic properties reflect network topology and organization and are important for studying and understanding brain networks (Rubinov and Sporns, 2010).Inter-hemispheric connectivity is related to asymmetry in intra-hemispheric connectivity and plays an important role in maintaining brain asymmetry (Gracia-Tabuenca et al., 2018;Karolis et al., 2019).However, to what extent and at what locations inter-hemispheric connectivity exhibits brain asymmetry is not yet known.Furthermore, brain asymmetry in edge-centric FC is a new topic to be investigated (Faskowitz et al., 2020).
Our CAMBA framework provides solutions to address these gaps and comprehensively analyze brain asymmetry from multiple perspectives.The three levels of brain interactions (i.e., isolated node, node-node, and edge-edge) were transformed into measures at the unified node level.This makes our analysis more homogeneous and significantly reduces the number of tests and potential loss of power (Helwegen et al., 2023).It is worth noting that this study only provides application examples of the CAMBA framework to resting-state EEG and does not limit the definitions of the properties of isolated nodes and of the interactions between nodes or edges.For example, in addition to undirected brain networks/FC, directed brain networks/effective connectivity (EC) is another methodology for studying interactions between brain signals, with the expectation of being able to measure causal effects, such as Granger causality (Granger, 1969), convergent cross mapping (Sugihara et al., 2012), and generalized partial directed coherence (Baccala et al., 2007).Graph-theoretic properties can also be derived from the EC (Rubinov and Sporns, 2010).Our framework supports multi-level and multiperspective brain asymmetry measures and is a powerful tool to study abnormal asymmetry patterns induced by brain diseases and to discover meaningful biomarkers.

Stroke-induced alterations in multi-level brain asymmetry dynamics
Hemispheric specialization is a fundamental feature of brain function organization (Karolis et al., 2019;Labache et al., 2023), and there is a dynamic balance of the integration and separation between two hemispheres (Favaretto et al., 2022;Wu et al., 2022).In healthy individuals, we observed a tendency towards rightward node-level MAI of alpha PSD and leftward node-level MAI of delta NS derived from inter-hemispheric connectivity (Fig. S3) but did not survive after rigorous multiple-comparison correction.Our interpretation of this is that, for resting-state data in healthy individuals, the distribution of the effect of brain asymmetry may be at a lower level in most regions of the brain (Gracia-Tabuenca et al., 2018).In this study, healthy individuals served primarily as controls for stroke patients, and the findings suggest that brain asymmetry after stroke is primarily determined by brain damage rather than by intrinsic brain asymmetry.However, our framework is also applicable to investigate brain asymmetry in healthy populations, but it is recommended to use larger sample sizes to enhance statistical power.Many large functional imaging datasets for healthy individuals are available that provide the conditions for conducting these studies; for example, there are "LEMON" (Babayan et al., 2019) and "CHBP" (Valdes-Sosa et al., 2021) datasets for both resting-state EEG and fMRI.
Here, for the first time, alterations in brain asymmetry dynamics after stroke in multilevel interactions were explored.Our results showed that the mean asymmetry patterns were significantly altered after the stroke, which is consistent with previous findings (Siegel et al., 2016;Saes et al., 2019;Vecchio et al., 2023).There are strong associations between node-level mean asymmetry patterns and the lesion side.Notably, the stroke lesion is the cause of the altered mean asymmetry patterns, but the location and extent to which the mean asymmetry of the different levels of interactions and the different frequency bands are significantly altered are to be addressed using our framework.Stroke lesions elicit widespread functional anomalies (Siegel et al., 2016) that extend beyond perilesion regions (Fig. S3), and the normal balance of integration and separation between the two hemispheres was disrupted (Favaretto et al., 2022).However, the significant alterations in node-level mean asymmetry were not driven by all the nodes, but instead by the cluster effects (size and location vary with measures).Using the LE of inter-hemispheric connectivity as an example, significant alterations in the node-level mean asymmetry in stroke patients compared to healthy individuals were more pronounced in the frontalcentral region (Fig. S4), which may guide the selection of regions of interest for future studies.Moreover, our analysis highlights that asymmetry dynamics exhibit significantly increased node-level fluctuation/variability (i.e., node-level AF) across all frequency bands.
This indicates that stroke altered the dynamic balance between integration and segregation and made it more unstable (Favaretto et al., 2022).Furthermore, hemisphere-level AF and AC metrics demonstrated distinct patterns of alterations in the high-and low-frequency bands in stroke patients relative to healthy individuals, exhibiting decreased values in the high-frequency bands and increased values in the low-frequency bands.This may be explained by a combination of two factors: the functional anomalies caused by stroke, and the reconfiguration of brain function between frequency bands to achieve rebalancing after stroke.Overall, our findings make clear that stroke-induced alterations in brain dynamics are evident at both node and hemisphere levels across multi-level interactions and frequency bands and improve our understanding of brain asymmetry after stroke.

BCI stimulates brain neuroplastic changes underlying the poststroke motor recovery
Stroke often leads to severe impairment of the upper and lower extremity motor function, significantly affecting patients' daily lives.Neuroplastic changes in the brain during the rehabilitation process are the basis for the recovery of motor function.In contrast to passive robot-assisted motor rehabilitation, BCI-based post-stroke motor rehabilitation utilizes active neural effort to trigger real-time (multi-sensory) feedback from external (Coscia et al., 2019;Romero-Laiseca et al., 2020;Yuan et al., 2021;Mane et al., 2022).Through contingent activation of motor cortex outputs and inputs, BCI can induce Hebbian plasticity, leading to improvements in motor function (Chaudhary et al., 2016;Bundy et al., 2017;Mane et al., 2022).Current evidence supports the notion that shortterm neurofeedback training of the upper extremity can induce plastic changes in brain structure and function, and improve upper extremity motor function (Ang and Guan, 2015;Pichiorri et al., 2015;Mane et al., 2019;Sanders et al., 2022).However, the efficacy and mechanism of BCI training for the lower extremities remain uncertain and lack sufficient evidence.
Neuroplasticity can reshape the brain by modifying existing circuits and creating new ones.Different rehabilitation treatments can induce distinct neuroplasticity and functional reorganization (Chaudhary et al., 2016;Biasiucci et al., 2018;Mane et al., 2019;Sanders et al., 2022).Additionally, individual patients may exhibit considerable variation in neurorehabilitation pathways, depending on the extent and location of the injury.Our findings showed that specific the hemisphere-level metrics of brain asymmetry in the BCI group shifted from an abnormal pattern to that observed in the healthy population (Fig. 4).
Furthermore, longitudinal changes in specific brain asymmetry metrics before and after treatment were strongly correlated with changes in lower-limb motor function scores (Fig. 5).However, the CTL group did not exhibit such patterns.Our findings suggest that brain neuroplasticity induced by active neural involvement is more consistent among individuals in the BCI group, whereas it is more randomized and individualized in the CTL group.The presence of abnormal brain asymmetry patterns after stroke may reflect functional compensation, which diminishes in the BCI group as the motor function improves.This recovery trend of brain asymmetry in the BCI group may be associated with the BCI closed-loop neurofeedback in promoting greater "physiological" recruitment of the affected hemisphere (Pichiorri et al., 2015).However, whether the poststroke rehabilitation pathway tends to align with the pattern observed in healthy individuals or diverges further may be related to the rehabilitation treatment approach and individual status.Further evidence is needed to investigate this issue.

Implications in the clinical brain disorder field
In clinical settings, the prognostic outcome of patients is a key concern.A large body of neuroimaging studies have been devoted to extracting features with predictive value or discovering meaningful biomarkers (Burke et al., 2014;Nicolo et al., 2015;Trujillo et al., 2017;Mane et al., 2019).However, a significant correlation between baseline features with post-treatment outcomes or treatment gains is not sufficient to establish a claim of prediction (Poldrack et al., 2020).Building predictive models with generalizability and utility based on baseline features is a critical, but challenging, clinical topic.
In the present study, we extended brain asymmetry analysis to multi-level brain interaction and brain dynamics, providing more opportunities for the discovery of meaningful biomarkers to track changes in brain function over time and make prognosis predictions.Our results showed that all three prediction models constructed using baseline features to predict gains in lower-limb motor function achieved an MAE of approximately two points and demonstrated favorable generalizability to new data (Fig. 6B).Moreover, we elucidated the feature contribution at the global and local levels (Figs.6C and D), although we could not establish a causal relationship between the baseline features and changes in lower limb function.The top five features according to the average feature importance across the three models were baseline FMA-LE, hemisphere-level AF of BC of beta inter-hemispheric connectivity, node-level MAI of BC and LE of beta intrahemispheric connectivity, and node-level MAI of delta PSD.Baseline FMA-LE was negatively correlated with the longitudinal change in FMA-LE; the remaining four asymmetry metrics (absolute values) were negatively correlated with baseline FMA-LE but positively correlated with the change in FMA-LE.This suggests that the better the lower extremity function at baseline, the smaller the brain asymmetry metrics (absolute values).Together, these five most important features suggested that greater functional improvement after BCI rehabilitation was associated with poorer baseline status (within a certain range).Our results indicated that the beta band has a strong relationship with sensorimotor function (Wu et al., 2015;Zich et al., 2023) and a larger feature space will have a better chance of capturing features related to the outcome.To the best of our knowledge, our study is the first to demonstrate the reliable prediction of gains in poststroke lower extremity motor function using baseline lower extremity motor function scores and brain asymmetry features.
Of note, previous studies have shown significant changes in the inter-hemisphere and ipsilesional EC in the alpha and beta bands in stroke patients undergoing rehabilitation treatment (Pirovano et al., 2022), a significant correlation between increased ipsilesional connectivity in the beta band and functional improvement (Pichiorri et al., 2015), and information flow plays a relevant role in the reorganization of the motor network after rehabilitation (Pirovano et al., 2022;Bistriceanu et al., 2023).Therefore, combining the CAMBA framework with EC will expand our understanding of brain asymmetry after stroke (e.g., connectivity between homotopic regions may also contribute to brain asymmetry), and may also provide more potentially effective features for stroke prognosis prediction.From an application perspective, the proposed framework may be attributed to  (Hayashi et al., 2022).This provides an opportunity to develop new treatments to modulate specific brain asymmetry metrics to bring them closer to the levels of the healthy population, with the expectation of achieving functional improvements.

Limitations and future directions
Some considerations/limitations regarding the quantification of brain asymmetry should be mentioned.First, this study utilized the wPLI approach to construct FC, and the results under other FC and effective connectivity construction methods were not explored.
Second, the window length was chosen based on the stationarity of the data within the window, the lengths of the wavelets, and previous studies (Trujillo et al., 2017;Qiu et al., 2020;Padfield et al., 2021).Future investigations will need to consider their own experimental paradigm and frequency range of interest.Third, considering the consistency across analyses and computational cost, we did not consider global-level graph-theoretic properties (e.g., small-world properties) and many other graph-theoretic properties of edgecentric FC.However, other graph-theoretic properties, where applicable, can be calculated and analyzed under our framework by referring to the examples in this study.Fourth, we applied CAMBA only to resting-state EEG data and analyzed them in the sensor space considering the effect of stroke lesions on the accuracy of head models, but the framework can be easily extended to other functional modalities and signal spaces.Finally, given the considerable heterogeneity among stroke patients, more samples are needed to construct prognostic prediction models for clinical applications.
The findings of our work establish a general framework that maps multi-level brain interactions onto a unified brain asymmetry analysis pipeline, with some key future questions readily following.First, how do brain asymmetry trajectories change with age over a broader age span (e.g., from infancy to adolescence to adulthood to older age)?
Developing a normative model of brain asymmetry would offer insight into the functional alterations associated with various neurological and psychiatric disorders.Moreover, this focused on resting-state scalp EEG, and further studies are needed to investigate brain symmetry patterns in EEG source space and explore the correlations between brain asymmetry in different modalities.The most recent homotopic-areal-level parcellations of the brain provide powerful tools for investigating brain asymmetries in different functional modalities in the same space (Yan et al., 2023).Such investigations will lay the foundation for a deeper understanding and interpretation of brain asymmetry.

Conclusion
This paper presents a comprehensive framework for the analysis of brain asymmetry, integrating multi-level brain interactions and application to resting-state EEG in healthy and stroke populations.Overall, the proposed framework can be used to detect inherent brain asymmetries as well as local and global asymmetry alterations after brain disease.
Moreover, our findings highlight the role of asymmetry dynamics and the collective role of intra-and inter-hemispheric connectivity in sustaining brain asymmetry.Importantly, brain asymmetry metrics hold the potential for examining brain-behavior associations in various neurological and psychiatric brain disorders and can even be utilized for constructing prognostic prediction models.Furthermore, our framework can easily be extended to other functional modalities, signal spaces, and clinical application settings.

Fig. 2 .
Fig. 2. Healthy individuals and stroke patients show distinct asymmetry patterns in the mean asymmetry index of various node-level measures.(A) Bubble charts represent the asymmetry patterns of healthy controls (HC), patients with left-sided stroke (Stroke L), and patients with right-sided stroke (Stroke R) in four frequency bands (i.e., beta, alpha, theta, and delta).The x-axis shows the acronyms for the node-level measures (e.g., PSD = power spectral density), and see Section 2.4 for definitions of the other acronyms.Only the clusters with the smallest p-value are shown, and the size of the bubble corresponds to the number of nodes within the cluster.Note that if the p-values all nodes are not lower than the pre-cluster threshold, no cluster is available to show.Warm colors represent leftward asymmetry and cool colors represent rightward asymmetry.The gradient color represents −log10(p).The bar plots indicate the total number of measures with significant leftward (orange) or rightward (blue) asymmetry that survived after multiple comparison corrections using CBS and BH methods.(B) Topographic maps showing the group median distribution of mean NS across time windows of beta intra-hemispheric connectivity for each group.Maps Stroke L and Stroke R. As shown in Figs.3A and S4, for Stroke L vs. HC, significant increase in asymmetries were found in PSD (delta, p = 0.013, cs = 8 nodes; theta, p = 0.002, cs = 11 nodes), five MAI metrics (all in low-frequency bands) derived from intrahemispheric connectivity: NS (delta, p = 0.005, cs = 12 nodes), LE (delta, p = 0.002, cs = 19 nodes), CC (delta, p = 0.002, cs = 27 nodes; theta, p = 0.029, cs = 14 nodes), and eNS (theta, p = 0.006, cs = 8 nodes), and eNS (theta, p = 0.012, cs = 4 nodes; alpha, p = 0.031, cs = 3 nodes) of inter-hemispheric connectivity.On the other hand, significantly decreased asymmetries were observed in the LE (beta, p = 0.046, cs = 11 nodes) of intra-hemispheric connectivity and NS (delta, p = 0.032, cs = 3 nodes; theta, p = 0.011, cs = 4 nodes) of interhemispheric connectivity.Conversely, for Stroke R vs. HC, only significantly increased asymmetries were shown in six MAI metrics (five of six in the high-frequency bands) derived from intra-hemispheric connectivity: NS (beta, p = 0.003, cs = 12 nodes), BC (theta, p = 0.011, cs = 3 nodes), LE (alpha, p = 0.012, cs = 16 nodes; beta, p = 0.005, cs = 18 nodes), and CC (alpha, p = 0.024, cs = 18 nodes; beta, p = 0.013, cs = 18 nodes).Notably, the node-level MAI metrics produced highly similar results after adjusting for the bilateral sum (i.e., the mean of the sums across time windows) (Figs.S5).
greater left-right hemispheric dissimilarity) in the beta band between stroke patients and HC: NS (p = , z = 4.157), LE (p = , z = 5.089), and CC (p = , z = 4.246) of intra-hemispheric connectivity, and NS (p = , z bands.More specifically, in the beta band, the hemisphere-level AF metric in stroke patients was significantly lower in the NS (p = 0.032, z = −2.551)and LE (p = 0.006, z = −3.164) of intra-hemispheric connectivity, and NS (p = 0.041, z = −2.569) of interhemispheric connectivity, whereas in the delta band, it was significantly greater in the NS (p = 0.011, z = 2.986) and CC (p = 0.050, z = 2.498) of intra-hemispheric connectivity.Of note, these results appear to indicate opposite patterns of modulation in the frequency domain by stroke to MAI and AF metrics at the node and hemisphere levels.

Fig. 3 .
Fig. 3. Altered asymmetries at the node and hemisphere levels in stroke patients compared with healthy controls.(A) Bubble charts represent the asymmetry alterations in Stroke L and Stroke R compared to HC in the node-level mean asymmetry index (MAI) and asymmetry fluctuation (AF) in four frequency bands (beta, alpha, theta, and delta).Similar to Fig. 2, the x-axis shows the acronyms used for node-level metrics.Only the clusters with the smallest p-value are shown, and the size of the bubble corresponds to the number of nodes within the cluster.Note that if the p-values of all nodes are not lower than the pre-cluster threshold, no cluster is available to show.Warm colors represent Stroke L or Stroke R greater than HC, and cool colors represent Stroke L or Stroke R smaller than HC.The gradient color represents −log10(p).(B) Stroke L andStroke R have similar patterns of alterations in node-level AF metrics compared with HC.We used the nodelevel AF metrics of HC and stroke patients on PSD (beta and delta) and LE of intra-hemispheric connectivity 589, z = −0.540) in baseline FMA-LE between the BCI (median, 19; range, 6-26) and CTL (median, 20; range, 4-27) groups.FMA-LE showed a significant increase in both BCI (p = , z = 3.731) and CTL (p = , z = 3.641) groups at T1 compared with T0.However, the BCI group exhibited greater FMA-LE changes (p = 0.038, z = 2.123) relative to the CTL group.No node-level asymmetry metrics showed significant changes in either group after CBS correction (cs computed as the sum of the t values within the cluster).However, the BCI group showed a trend of reduction in the AF of BC (p = 0.072, cs = −4.910)and LE (p = 0.076, cs = −5.108) of delta intra-hemispheric connectivity.The sign of cs indicates the direction of the change.
hemispheric connectivity in the delta band: AF of NS (p = 0.016, t = −2.667),AC of LE (p = 0.006, t = −3.151),and AC of CC (p = 0.010, t = −2.915).For the CTL group, only the MAI of NS of intra-hemispheric connectivity in the beta band (p = 0.026, t = −2.446)showed a significant change after treatment.Furthermore, an analysis of covariance on each above-significant metric, with baseline measures as covariates, was performed.As shown in Fig.4, three of the five metrics exhibited a significant main effect of group (BCI vs. CTL): AF of NS of inter-hemispheric connectivity in the beta band (p = 0.033, t = 2.224), and AC of LE (p = 0.046, t = −2.073)and CC (p = 0.022, t = −2.405) of intrahemispheric connectivity in the delta band.Overall, the results of the clinical and neural features revealed that BCI rehabilitation training was more effective in functional improvement and converging the abnormal brain asymmetries toward the pattern of HC compared to the CTL group (Fig.4).

Fig. 4 .
Fig. 4. Longitudinal changes in brain asymmetries in stroke patients using different rehabilitation training strategies.(A) Hemisphere-level AF of NS of inter-hemispheric connectivity in the beta band.(B) Hemisphere-level AC of LE of intra-hemispheric connectivity in the delta band.(C) Hemisphere-level AC of CC of intra-hemispheric connectivity in the delta band.Paired t-tests were used to test the changes between baseline (T0) and after treatment (T1) for each group.The lines between each node pair depict the changes for each individual.Between-group comparisons at T1 were performed by analysis of covariance (ANCOVA), controlling for baseline values.The median line of each metric in the HC group is also provided.The box bounds indicate the 25th and 75th percentiles and the center line indicates the median, whiskers correspond to the minimum and maximum data values, and outliers are displayed as dots.The detailed results are listed in TableS7.

Fig. 5 .
Fig. 5. Correlations between longitudinal changes in brain asymmetry metrics and FMA-LE in the BCI group.(A) Correlation across subjects between changes in FMA-LE and asymmetries, and correlations among changes in asymmetries (Pearson correlation).Metrics in black font indicate asymmetry measures at the node level, whereas those in gray font indicate asymmetry measures at the hemisphere level.For visualization, we averaged the values of the nodes within the cluster for the node-level asymmetry metric.r indicates the correlation coefficient.*p < 0.05, **p < 0.01, ***p < 0.001.The data for Fig. 5A can be found in TableS10.

Fig. 6 .
Fig. 6.Prediction of improvement in lower limb motor function using baseline clinical and asymmetry features in the BCI group.(A) The 16 selected consensus features are grouped in different manners.The topographic map depicts the number of times each node was selected for node-level asymmetry features.(B) The performance of each of the three machine learning models is demonstrated with a scatterplot with MAE and RMSE.The green border and font correspond to the extra new samples.The data of Fig. 6B are listed in TableS11.(C) The importance/contribution of each consensus feature to each of the three models was (D) Contribution of each feature to the individual prediction (local explanation).A stroke patient with BCI rehabilitation training improved the FMA-LE by 6 points.The base value (5.204 points) shows the average predictive value in the training set (SVR, outer loop of the nested LOOCV).Features with positive SHAP values (red) contribute to the increase in estimation over the base value, while features with negative SHAP values (blue) contribute to the decrease.The length of the arrow indicates the absolute SHAP value and the corresponding input feature value is annotated below the arrow.The sum of the base value and the SHAP values of all features is equal to the predicted value for this subject (5.762 points).
three aspects of clinical settings.(1) It can be used to detect alterations in brain asymmetry, identify biomarkers to track changes in the recovery process, and provide prognosis prediction of a specific rehabilitation strategy (Sections 4.2-4.4).(2) It can also be used to guide the clinically individual treatment options.For example, first, build predictive models for different interventions using baseline clinical features and brain asymmetry metrics extracted from the framework.Then, the outcome predictions of a new patient can be obtained using the models for different treatment strategies, and finally, complementary support for the selection of the individualized treatment strategy (e.g., the option with the highest predicted score).(3) It may assist in the development of new treatments.For example, in this study, we revealed that specific asymmetry metrics tended to reach the level of healthy individuals during rehabilitation training.Studies have shown that through a specific BCI system, subjects can regulate inter-hemispheric inhibition by modulating one side's excitability and maintaining constant contralateral excitability