Exploring the association between EEG microstates during resting-state and error-related activity in young children

The error-related negativity (ERN) is a negative deflection in the electroencephalography (EEG) waveform at frontal-central scalp sites that occurs after error commission. The relationship between the ERN and broader patterns of brain activity measured across the entire scalp that support error processing during early childhood is unclear. We examined the relationship between the ERN and EEG microstates – whole-brain patterns of dynamically evolving scalp potential topographies that reflect periods of synchronized neural activity – during both a go/no-go task and resting-state in 90, 4–8-year-old children. The mean amplitude of the ERN was quantified during the − 64 to 108 millisecond (ms) period of time relative to error commission, which was determined by data-driven microstate segmentation of error-related activity. We found that greater magnitude of the ERN associated with greater global explained variance (GEV; i.e., the percentage of total variance in the data explained by a given microstate) of an error-related microstate observed during the same − 64 to 108 ms period (i.e., error-related microstate 3), and to greater parent-report-measured anxiety risk. During resting-state, six data-driven microstates were identified. Both greater magnitude of the ERN and greater GEV values of error-related microstate 3 associated with greater GEV values of resting-state microstate 4, which showed a frontal-central scalp topography. Source localization results revealed overlap between the underlying neural generators of error-related microstate 3 and resting-state microstate 4 and canonical brain networks (e.g., ventral attention) known to support the higher-order cognitive processes involved in error processing. Taken together, our results clarify how individual differences in error-related and intrinsic brain activity are related and enhance our understanding of developing brain network function and organization supporting error processing during early childhood.


Introduction
The error-related negativity (ERN), a negative-going event-related potential (ERP) that peaks within 100 milliseconds (ms) of error commission at fronto-central scalp locations, is a psychophysiological marker of early performance monitoring associated with recognition and subsequent response to error (Gehring et al., 2012). In line with prior studies reporting marked changes in goal-directed behavior over the course of development, ERP research has similarly suggested that the ERN increases in strength from early childhood to adolescence and young adulthood (Boen et al., 2022;Tamnes et al., 2013). More speci cally, a meta-analysis by Boen et al. (2022) recently reported a more negative ERN with increasing age in 3-28year-olds with a small-to-medium effect size. As a result, maturational changes in the ERN have been suggested to potentially re ect the ongoing development of brain function and organization supporting error identi cation, processing, and subsequent goal-directed behavior (Boen et al., 2022;Tamnes et al., 2013). However, as observed in prior functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) studies, error commission recruits a temporally evolving network of distributed and coordinated brain regions (Menon et al., 2001;Stevens et al., 2007;Völker et al., 2018) that may differ across development and are unlikely to be accurately captured by conventional ERP waveform analysis. That is, while the temporal (i.e., time window of interest) and spatial (i.e., electrodes of interest) assumptions generally used to inform a priori hypotheses concerning the ERN are likely to accurately capture local neural dynamics of error-related activity, they leave more global patterns potentially re ective of important developmental and/or individual-level differences largely underrepresented. As a result, how the ERN is associated with broader patterns of whole-brain activity supporting error processing remains unclear and needs further investigation using data-driven approaches that capitalize on the full temporal-spatial information available from EEG. Findings generated from these types of analyses are likely to be highly informative for understanding individuallevel neurobiological differences in error processing and their association with developmental changes in behavior and cognition.
One multivariate, data-driven approach for characterizing the spatiotemporal dynamics of large-scale neural networks using EEG is microstate analysis (see Michel & Koenig, 2018 for a review). Microstates are patterns of scalp potential topographies, identi ed with clustering algorithms (e.g., k-means), that are stable in spatial location for very short periods of time (typically less than ~ 150 ms) and re ect rapidly evolving states of synchronized activity in the brain (Michel & Koenig, 2018). Microstate analysis can be performed on both task-evoked and resting-state data. As a result, the direct comparison of task-evoked and resting-state microstates using similarly de ned units of measurement that characterize the temporal and spatial information of whole-brain activity is possible. Available temporal measures include global explained variance (GEV; percentage of total variance in the data explained by a given microstate), average duration in ms, coverage (i.e., percentage of recording time for which a given microstate is present), and occurrence (i.e., frequency per second; Michel & Koenig, 2018). While the nature of data collection is likely to shape the temporal properties of microstates identi ed during error processing or resting-state, as suggested by prior fMRI research demonstrating similar functional brain network structure and organization during task and rest (Cole et al., 2014; M. D. Fox & Raichle, 2007), a high degree of spatial overlap between individual microstates is expected given the signi cant likelihood of overlapping neural sources. Critically, if error-evoked activity and features of microstates identi ed at rest are associated as well, it may also be possible to predict the development of error processing and associated behavior and cognition from a much younger age when ERN data collection is not feasible (e.g., infants who are unable to perform tasks that elicit the ERN). As a result, understanding the associations between microstates generated using task versus resting-state data from the same individual children is highly likely to enhance our understanding of developing brain network function and organization supporting error processing.
Prior work in adults indicates that the time before and after error commission, time-locked to the behavioral response (e.g., button press), can be viewed as a sequence of a limited number of microstates with stable topographies that increase and decrease in strength or global eld power (GFP; Pourtois, 2011;Vocat et al., 2008). Each microstate within the sequence re ects the activity of a different con guration of active populations of neurons whose electrical potentials propagate to the scalp through volume conduction (Michel & Koenig, 2018). As a result, the period of time immediately surrounding the peaks of conventional ERP components are almost always contained within a window of time represented by one of the identi ed microstates. When the group-level microstates from the grand-averaged, error-evoked data are t back to the data of individual participants via spatial correlation (i.e., back tting), individual differences in the temporal properties of each microstate become apparent across participants. As a result, a data-driven window of time for quantifying the given properties of an ERP of interest can be delineated, obviating the need to subjectively choose (either a priori or from grandaveraged waveforms) a window of time to investigate (e.g., measuring the ERN during the 0-100 ms period relative to error commission). Microstate analyses using resting-state EEG data have typically revealed 4-7 data-driven microstates that are remarkably highly spatially similar across participants and studies (Michel & Koenig, 2018). Importantly, simultaneous EEG-fMRI and EEG source imaging studies have demonstrated that the spatial patterns of EEG resting-state microstates resemble well-known fMRI resting-state networks (Bréchet et al., 2019;Custo et al., 2017). At the individual-level, prior work has also suggested that the temporal properties of each microstate (i.e., GEV, duration, coverage, and occurrence) show good internal consistency and test-retest reliability when as little as two minutes of resting-state data are used (Liu et al., 2020). Notably, the results of microstate analysis have also been shown to be unaffected by choice of the EEG reference (e.g., average or mastoids) (Michel & Koenig, 2018). This is particularly advantageous because previous research has shown differences in the ERN's amplitude and quality depending on the reference used (Clayson et al., 2021). As a result, prior research suggests that systematically examining the associations between EEG microstates identi ed during task or at rest can be undertaken in a systematic and rigorous fashion at any age when this type of data can be collected.
In adults, data investigating how EEG microstates identi ed during rest are associated with those identi ed during error processing and to behavior are only beginning to emerge. More speci cally, Kleinert et al. (2022) recently reported that fewer, but longer lasting microstates during rest (which according to the authors indicated more stable mental processing), regardless of microstate class, were associated with increased neural activity in the left insula and inferior frontal gyrus during a go/no-go task and with greater self-reported self-control. While to our knowledge no study has investigated microstates during error processing in young children, one recent study did assess awake resting-state EEG microstates exclusively during early childhood (Bagdasarov et al., 2022). More speci cally, in a cross-sectional sample of 4-8-year-olds, we found sex-effects in the duration (i.e., males > females) of a microstate with an anterior-posterior orientation (i.e., microstate 3), and age by sex interaction effects for all of the temporal properties (i.e., generally, they decreased with increasing age for males but were constant for females) of a microstate with a centrally posterior orientation (i.e., microstate 4; Bagdasarov et al., 2022).
Further, using source localization techniques, we found that microstates 3 and 4 were associated with brain networks previously identi ed in prior fMRI research to support higher-order cognitive functions (Bagdasarov et al., 2022). While these results suggest that similar microstates may be identi ed during error processing, and meaningfully related to neural markers of error-related activity, this has not been directly investigated in children. Therefore, given our recent resting-state EEG microstate ndings and well documented changes in self-regulation during early childhood, an important next step is to directly investigate whether microstates identi ed during error processing and during rest are associated with each other and related to behavior in young children.
The current study aimed to investigate whether microstates during eyes-closed resting-state would associate with error-related neural activity (assessed using both microstate and ERP waveform analyses) during a go/no-go task in 90, 4-8-year-old children using high-density EEG. At the group-level, based on our prior work and that of others using a data-driven approach for microstate identi cation (Bagdasarov et al., 2022;Tomescu et al., 2018), we hypothesized that microstate analysis of resting-state EEG would produce 4-7 resting-state microstates. We also hypothesized, based on previous work on the ERN (Boen et al., 2022;Tamnes et al., 2013), that a microstate -which we will refer to as the error-related microstate hereafter -whose maximal activity would be at a fronto-central or central scalp location would de ne the peak of the ERN waveform surrounding error commission; thus, also de ning the electrodes for which the ERN would be maximally negative. Further, we hypothesized that this microstate would have the highest spatial correlations with resting-state microstates that 1) have been suggested in previous work to represent brain networks involved in higher-order cognitive functions (Bagdasarov et al., 2022;Custo et al., 2017), and 2) have a central maximum along the longitudinal axis of the brain. At the individual-level, we hypothesized that an enhanced ERN during the period of time represented by the errorrelated microstate would be correlated with greater GEV values of the error-related microstate. We also hypothesized that both an enhanced ERN and greater GEV values of the error-related microstate would be correlated with greater GEV values of resting-state microstates that were highly spatially correlated with the error-related microstate. We chose GEV as our temporal parameter of interest because it represents the degree to which a particular microstate describes the dataset or time window of interest (i.e., it is easily interpretable), and can be compared between resting-state and task-evoked data (i.e., it measures the same property of neural activity in both types of data; i.e., goodness-of-t or the sum of variances of the EEG data explained by a given microstate, normalized by GFP). Source localization of the error-related and resting-state microstates of interest was also carried out to identify overlapping patterns of brain activity. Given prior work reporting negative associations between ERN amplitude and measures of anxiety and anxiety risk in young children (Meyer, 2017), we hypothesized that an enhanced ERN would be correlated with greater parent-reported anxiety and behavioral inhibition. Lastly, following research suggesting that resting-state microstates de ned by spatial topographies with central maxima along the longitudinal axis of the brain are associated with higher-order cognitive functions (Bagdasarov et al., 2022;Custo et al., 2017), we hypothesized that the GEV of these topographies would be correlated with greater parent-reported effortful control.

Methods
Participants were 90, 4-8-year-old children recruited from a database maintained by the Department of Psychology and Neuroscience at Duke University and community events. Recruitment details including inclusion and exclusion criteria are provided in the supplementary materials. All research was approved by Duke University's Institutional Review Board and carried out in accordance with the Declaration of Helsinki. Caregivers provided informed consent and children provided verbal assent. Compensation was provided for study participation. Participant demographics are described in Table 1. . Children viewed images of aliens and astronauts as they appeared on a screen for 500 ms, followed by an intertrial interval, which was either 1000, 1500, or 2000 ms. They were instructed to "shoot" the aliens by pressing a button ("go" trials) and "save" the astronauts by withholding button-press ("no-go" trials). Pressing the button when an alien appeared was considered a correct "go" response while pressing the button when an astronaut appeared was considered an erroneous "no-go" response. After learning how to play the game during a practice round, children completed 120 "go" and 80 "no-go" trials. Both resting-state and go/no-go paradigms were presented with E-Prime software (Psychological Software Tools, Pittsburgh, PA).
O ine preprocessing was performed with EEGLAB (Delorme & Makeig, 2004) in MATLAB (MathWorks, Natick, MA). The preprocessing steps of continuous resting-state and task data overlapped but differed in some of their parameters. Details are provided in the supplementary materials and in custom scripts available on https://github.com/DEEDLabEEG. Brie y, 24 outer ring channels that often contain a large amount of artifact in developmental data were removed due to their location near the base of the skull or on the neck or face. Data were downsampled to 250 Hz, and bandpass ltered (1-40 Hz for resting; 0.1-40 Hz for task). After ltering, electrical line noise was still present in some participants' data and attenuated using CleanLine (T. Mullen, 2012). Bad channels were removed and interpolated using spherical splines if they were 1) at for more than 5 seconds, 2) contained more than 4 standard deviations of line noise relative to all other channels, or 3) correlated at less than .80 to surrounding channels. Following, data were re-referenced to the average. A copy of the original source data was created, cleaned using Artifact Subspace Reconstruction (ASR; T. R. Mullen et al., 2015; i.e., artifacted periods were removed using a burst criterion of 20 as recommended by Chang et al., 2020), and submitted to extended infomax independent component analysis (ICA; Lee et al., 1999) with principal component analysis (PCA) dimensionality reduction (i.e., 30 and 50 components, for resting and task data, respectively). The ICLabel plugin was used to ag components that had a probability of at least .70 of being related to eye or muscle artifacts (Pion-Tonachini et al., 2019). The resulting ICA elds and ags were subsequently copied over to the original source data and agged ICA components were removed.
Resting-state data was segmented into nonoverlapping one-second epochs. Epochs were removed using the TBT plugin (Ben-Shachar, 2018) if at least 10 channels contained 1) amplitudes > 100 or < -100 µV, or 2) joint probabilities (i.e., probabilities of plausible activity) above 3 standard deviations for local or global thresholds. Correct "go" trials and erroneous "no-go" trials were segmented − 500 to 800 ms relative to the button-press, and baseline corrected during the − 500 to -300 ms period. The same epoch rejection criteria were applied, except amplitude-based rejection values were relaxed to > 150 or < -150 µV, and one additional criteria was added: epochs with at least 10 channels containing peak-to-peak amplitudes exceeding 100 µV within 200 ms windows sliding by 20 ms were also removed. For both types of data, if less than 10 channels met rejection criteria, the epoch was not removed, but the channels were interpolated for that epoch only. For task data, correct "go" trials and erroneous "no-go" trials were separately averaged for each participant after removing trials where the button-press occurred less than 100 ms after the stimulus or more than 2000 ms after the stimulus. A summary of the behavioral data (reaction time and accuracy means) is provided in the supplementary materials.
Data quality was rigorously assessed. Participants who did not pass EEG data quality checks were excluded from further analyses (see supplementary materials). Following exclusion of participants, the minimum amount of resting-state data across participants was 157 seconds. To reduce potential effects of varying data lengths on analyses, participants' resting-state data were trimmed to their rst 157 seconds, exceeding the previously published two-minute mark for the reliability of resting-state microstate analysis (Liu et al., 2020). For event-related data, following exclusion of participants, the minimum number of correct "go" and erroneous "no-go" trials was 21 and 6, respectively. Previous work has shown that the ERN can be reliability quanti ed using a minimum of 6 trials for each condition (Olvet & Hajcak, 2009).

Microstate Analysis
Microstate analysis of resting-state data was performed in Cartool (Brunet et al., 2011). First, at the individual-level, a spatial lter was applied to each participant's data to remove topographic outliers and smooth topographies . Topographies at global eld power (GFP) peaks representing timepoints of the highest signal-to-noise ratio were extracted ( resulting in k optimal clusters for each of 50 epochs. Next, at the group-level, the 50 sets of k optimal clusters from each participant were combined resulting in 4,500 sets (90 participants x 50 sets). 100 epochs each composed of 1000 randomly sampled sets (covering 98.8% of the sets) were submitted to a polarity-invariant modi ed k-means cluster analysis, which was set to repeat 100 times and identify 1-15 clusters of topographies for each epoch. The meta-criterion determined the optimal number of clusters for each epoch, resulting in k optimal clusters for each of 100 epochs. Lastly, these 100 sets were combined and submitted to a nal polarity-invariant modi ed k-means cluster analysis, which was set to repeat 100 times and identify 1-15 clusters of topographies. The meta-criterion determined the optimal number of group-level resting-state microstates. The resampling approach is thought to improve the reliability of k-means clustering and has been used in recent work (Bagdasarov et al., 2022;Férat et al., 2022).
The group-level resting-state microstates were then back tted to each participant's original, spatially ltered data, including all data points (not just at GFP peaks). The data was normalized by the median of GFP to account for individual differences in scalp potential due to varying skull conductivity. Back tting involved calculating the spatial correlation between each microstate at the group-level and each individual data point for each participant, such that the microstate with the highest correlation was assigned to that data point. The polarity of maps was ignored when calculating the correlation and the minimum correlation for data points assigned to a microstate was 50%. After back tting, temporal smoothing (window half-size of 32 ms, Besag factor of 10; Pascual-Marqui et al., 1995) was applied, and improbably small segments were removed, such that segments smaller than 32 ms were divided in half with the rst half added to the preceding segment and the second half added to the proceeding segment. The back tting procedure produced values of each microstate's GEV for each participant.
Microstate analysis of the grand-averaged (i.e., averaged across participants), spatially ltered, errorrelated activity was performed in one stage in Cartool. Error-related activity was calculated by subtracting correct "go" activity from erroneous "no-go" activity. Topographies at each timepoint (not just at GFP peaks), except for timepoints during the baseline period, were extracted and submitted to a modi ed kmeans cluster analysis, which accounted for polarity, repeated 300 times, and identi ed 1-20 clusters of topographies. The meta-criterion determined the optimal number of clusters. Each timepoint of the grandaveraged data was then sequentially labeled with one of the topographies. The microstate surrounding the button-press -the error-related microstate -was identi ed by visual inspection of the segmented grand-averaged data. This microstate was back tted to each participant's original, spatially ltered, averaged, error-related activity using the same procedure as described for resting-state data; however, polarity was accounted for, the minimum spatial correlation was . 25

Source Localization of Microstates
Six thousand solution points were distributed equally in a grey matter-constrained head model of a child MRI brain volume template. The EEG net template was co-registered to the MRI head model.

Microstate-Guided ERN Waveform Analysis
The error-related microstate de ned the window of time coinciding with the ERN (i.e., immediately prior to and following the button press) and channels (i.e., a pool of channels that were maximally negative). For each participant, the mean activity during the microstate-identi ed window of time and across microstate-identi ed channels was calculated separately for correct "go" and erroneous "no-go" trials. Reliability via internal consistency values were calculated using the ERP Reliability Analysis toolbox (Clayson & Miller, 2017). Following previous research, unstandardized residual values from a regression model in which participants' correct "go" values were entered as the independent variable and erroneous "no-go" values were entered as the dependent variable were calculated (Meyer et al., 2017; see supplementary materials) and used in subsequent analyses. This procedure removed any variance in the erroneous "no-go" activity accounted for by correct "go" activity, which also tends to elicit a response similar to but smaller than the error-related response (Coles et al., 2001). We also calculated the ERN with other common scoring procedures and show high correlations between the values of all methods in the supplementary materials.

Parent-Report Questionnaires
Preschool Anxiety Scale (PAS) The PAS is a 28-item parent-report measure of child anxiety during the preschool years (Spence et al., 2001

Data-Driven Selection of Resting-State Microstates of Interest
It was hypothesized that the spatial and temporal properties of the error-related microstate of interest (i.e., the microstate coinciding with the ERN) would relate to resting-state microstates that were similar in their spatial topographies. As such, a polarity-invariant spatial correlation between the error-related microstate of interest and each of the resting-state microstates was calculated to determine the resting-state microstates of interest for subsequent statistical analyses.

Statistical Approach
Hierarchical regression and linear regression analyses were performed in R (R Core Team, 2022). First, for each of eight models, multivariate outliers were identi ed by the Minimum Covariance Determinant and removed (Rousseeuw & Driessen, 1999). For hierarchical regression analyses (models 1-6), age and sex were entered in the rst step. In the second step, the independent variable of interest was added (models

Results
The meta-criterion revealed six resting-state microstates (Fig. 1a) and 10 error-related microstates (Fig.   1b). The error-related microstate of interest was error-related microstate 3, which occurred from − 64 ms prior to and 108 ms following the button-press and coincided with the ERN. It was con rmed that the majority of participants had error-related microstate 3 during the − 64 to 108 ms period, and that errorrelated microstate 3 was present to a much smaller extent during other periods outside of this window (see supplementary materials). Visualization of the topography of error-related microstate 3 revealed maximally negative activity at central locations (i.e., Cz). As such, quanti cation of the ERN was performed for a pool of channels surrounding Cz (see supplementary materials for region-of-interest).
Further, visualization of the grand-averaged difference ERN waveform across participants con rmed that its most negative peak was contained within the − 64 to 108 ms period (Fig. 2). Reliability of all neural measures are provided in the supplementary materials. Spatial correlations revealed that resting-state microstates 4 and 6 had the highest topographic similarity with error-related microstate 3 (correlations of .80 and .51, respectively) while the other microstates were highly dissimilar (correlations below .20; see supplementary materials). Descriptive statistics of the temporal parameters of each microstate and questionnaire data are presented in the supplementary materials. Given ongoing debate about how to select the optimal number of resting-state microstates -whether selection should be based on previous research, objective data-driven methods, or some combination thereof -spatial correlations between the topographies of four-and six-state solutions and correlations between their temporal parameters are provided in the supplementary materials as well.

Regression Analyses
Results of regression analyses are summarized below. Additional details are provided in the supplementary materials, including results with outliers included in models (neither the signi cance of models nor direction of effects change with outliers included).

Sources
Source localization results are presented in Fig. 4. Overlap between identi ed sources for error-related microstate 3 and resting-state microstate 4 are presented in both Fig. 4 and Table 2. In addition to the sources listed in Table 2 from center of mass analyses, the following sources were also observed in both error-related microstate 3 and resting-state microstate 4: Left precentral gyrus, bilateral paracentral lobules, bilateral superior frontal gyri, bilateral cingulate gyri, bilateral precuneus, left fusiform gyrus, and right inferior temporal gyrus.  Note. Clusters organized from largest to smallest in volume. Clusterization performed in AFNI with the following parameters: Level 3 clustering method (i.e., faces or edges or corners) with minimum cluster size of 1 voxel. * Schaefer-Yeo AFNI 2021 parcellation (7 networks, 100-area). Note. Percentages represent the mathematical intersection of localized microstate sources and functional network sources from the Schaefer-Yeo AFNI 2021 parcellation (7 networks, 100-area). Percentages for each column do not add up to 100% because sources may be located outside of canonical networks.

Discussion
The current study investigated the association between EEG microstate spatial topographies and related properties during resting-state and error-related activity in a large sample of 4-8-year-old children. A priori de ned quantitative criteria indicated that a sequence of 10 unique microstates characterized EEG data collected during a go/no-go task and that six microstates were representative of the unique spatial topographies present in resting-state EEG data. Of the 10 error-related microstates identi ed, error-related microstate 3 captured the peak of the ERN waveform and was most topographically similar to restingstate microstates 4 and 6, being most similar to resting-state microstate 4. Using regression analyses, an enhanced ERN was found to be associated with greater GEV values of error-related microstate 3 and resting-state microstate 4. Further, greater GEV values of error-related microstate 3 were associated with greater GEV values of resting-state microstate 4. Conversely, neither ERN nor GEV values of error-related microstate 3 were associated with GEV values of resting-state microstate 6. Source localization of resting-state microstate 4 and error-related microstate 3 identi ed overlapping patterns of brain activity in canonical functional networks shown in prior fMRI research to support higher-order cognitive processes (e.g., ventral attention network). Further, an enhanced ERN was associated with greater parent-reported child behavioral inhibition but not anxiety symptoms. There was no association between GEV values of resting-state microstate 4 and effortful control as measured by parent-report. Overall, results show promise for understanding how individual differences in error-related and intrinsic brain activity during early childhood may be related to each other and to behavior and cognition. They also provide, for the rst time, information about the functional signi cance of resting-state microstates during early childhood.
Supporting error-related microstate 3 as a global measure of distributed and coordinated brain regions involved in error commission processes, we found that greater error-related microstate 3 GEV values were associated with an enhanced ERN (i.e., a stronger psychophysiological response to error commission). As in prior research, ERN amplitude in the current study measured neural activity localized to a central region of the scalp where error-related activity was maximal. While useful for understanding local neural dynamics, measuring error-related activity in this way is unlikely to fully capture the spatially and temporally evolving network of brain regions involved in error processing. As discussed previously, a microstate analytic approach overcomes this limitation and allows for the identi cation and measurement of unique spatiotemporal topographies that capture global neural dynamics across the entire scalp during error-related processing. Given that an association between data extracted from these two approaches would be anticipated (i.e., global encompasses local), it is not surprising that the current study found individual differences in the ERN to be associated with those of a speci c topographical representation of error-related activity across the entire scalp (i.e., error microstate 3). However, while expected, by directly demonstrating this association the current study supports the use of task-related microstates to further de ne the functional properties of those identi ed in the absence of an explicit task (e.g., resting-state). And, as a result, the current ndings are a critical step forward for informing future EEG microstate studies of error-related brain function and organization in developmental (e.g., infants) or psychiatric (e.g., autism spectrum disorder) groups unable to successfully perform and/or comply with explicit tasks.
Both an enhanced ERN and greater GEV values of error-related microstate 3 associated with greater GEV values of resting-state microstate 4 in our sample of young children. That is, individual differences in both the local and global neural dynamics of error processing were re ected in individual differences in resting-state data, and vice versa. In an overlapping, but not identical sample of participants, we previously found that a microstate with a central maximum along the longitudinal axis of the brain represented brain networks involved in higher-order cognitive functions (Bagdasarov et al., 2022 to measure developmental changes in neurobiological correlates of speci c higher-order psychological constructs (e.g., those indexing error processing or performance monitoring) as early as the preschool period. However, future research investigating the associations between EEG microstates identi ed during rest and systematic measurements of relevant behavior (e.g., orienting and/or sustaining attention) will be necessary to establish the potential functional speci city of any microstate more fully whether identi ed at rest or during task.
Source localization of resting-state microstate 4 and error-related microstate 3 revealed that overlap in neural generators was greatest for the canonical somatomotor network. The somatomotor network, which includes regions of the brain involved in sensory processing, motor planning, and motor execution, was most represented in the overlap of sources from resting-state and error-related data as shown in Tables 2 and 3. In line with this nding, previous work using fMRI in adults demonstrated that errorrelated activity elicited activation in a network of somatomotor areas (Hester et al., 2004), and that the amplitude of the ERN related to the strength of functional connectivity between the dorsal anterior cingulate cortex (dACC) and motor regions of the brain (Gilbertson et al., 2021). Interestingly, when examining the sources of error-related microstate 3 and resting-state microstate 4 individually, an area within the dACC was only present for error-related microstate 3. As a result, ndings from the current study suggest that somatomotor activity is involved in neural response to error in young children, potentially through connectivity with other task-induced patterns of neural activity (e.g., dACC).
Importantly, they also suggest that the overlapping somatomotor regions shared between error-related and resting-state microstates may act as part of a larger network of regions involved in cognitive control that can also be identi ed using resting-state data (Gordon et al., 2023). However, future research will be required to directly investigate the presence and potential role of somatomotor cortex across multiple tasks requiring coordinated network activity. The next largest percentage of overlap in sources for restingstate microstate 4 and error-related microstate 3 was found in the ventral attention network (Table 3). Given a large and growing body of work showing support for the relationship between ERN amplitude and measures of anxiety and anxiety risk in children, we conducted regression analyses to assess whether the ERN's amplitude related to parent-report measures of anxiety symptoms and behavioral inhibition. Our results revealed that the relationship between the ERN and individual differences in anxiety and anxiety risk is complex. While an enhanced ERN associated with greater levels of behavioral inhibition, a known risk factor for the future development of anxiety in children and adults (Rosenbaum et al., 1993;Sandstrom et al., 2020), the ERN showed no relationship with anxiety symptoms. This discrepant nding, which was contrary to our hypotheses, suggests that our measures of behavioral inhibition and anxiety likely quanti ed related but distinct psychological phenomena, and that the ERN in our sample may be a more speci c marker of behavioral inhibition than of anxiety. In fact, the BIS scale assessed children's sensitivity to negative outcomes and their tendency to inhibit their behavior in response to potential threat or punishment (Carver & White, 1994). On the other hand, the PAS measured the number and severity of children's anxiety symptoms (Spence et al., 2001). Therefore, the BIS scale measured a temperamental trait while the PAS measured a mental state that is likely in uenced by factors beyond temperament. In addition, the ERN during early childhood may re ect a neurobiological vulnerability to anxiety that is not yet expressed as speci c symptoms but is captured in measures of anxiety risk, such as the BIS scale. It may also be possible that sample characteristics -a normative, non-clinically anxious sample of participants -were responsible for null ndings between the ERN and speci c anxiety symptoms.
Previous work examining the relationship between the ERN and normative variations in anxiety found that the strength and direction of their association changed across childhood. For example, in nonclinically anxious younger children, the ERN was blunted, while in non-clinically anxious older children and adolescents the ERN was enhanced (Meyer, 2017). Given the relatively narrow range of participants' ages in the current study (i.e., 4-8 years), it was not possible to assess a similar moderating role of age, but it is likely an important factor to consider in future work.
Effortful control -the ability to inhibit a dominant response in order to perform a subdominant response, to detect errors, and to engage in planning -relies on attentional resources to move, focus, and sustain attention as needed (Rueda, 2012 In addition to characterizing global patterns of electrical activity, we used microstate analysis to provide an objective, data-driven window of time for which the mean amplitude of the ERN was measured. This is a unique advantage over other approaches that rely on previous research or subjective inspection of waveform peaks and scalp topographies to determine measurement windows. While beyond the scope of the currents study, it may be important for future work to examine the relationship between ERPs measured during traditional windows of time compared to those derived from the results of microstate segmentation. In fact, different measurement windows may quantify distinct neurobiological phenomena (e.g., wider windows may capture neural activity from greater regions of the brain representing the evolving networks of sources during error processing), and selection of one over the other may impact brain-behavior relationships.
Not unique to the current study, microstate analysis relies on the group-level back tting of microstates to participant-level data. While the derivation of group-level microstates considers the data of all participants, it may not be the best approach for assessing individual differences between the temporal parameters of microstates and individual differences in behavior. Future work should try to understand whether group-level segmentation and back tting impacts brain-behavior relationships. For example, our null ndings between the GEV values of resting-state microstate 4 and effortful control may have been the result of the loss of important microstate topographies during group-level microstate segmentation. If group-level segmentation and back tting impacts brain-behavior relationships, then new methods using the microstates approach should be developed to better assess individual differences in microstate topographies.
While cross-sectional, the results of the current study show promise for investigating potential longitudinal relationships between resting-state and error-related activity. From the current study, we know that both the amplitude of the ERN and GEV values of error-related microstate 3 relate to resting-state microstate 4. Therefore, a longitudinal relationship may exist between resting-state microstate 4 measured during infancy and error-related microstate 3 measured during the preschool and school-age years. If so, we may be able to predict the development of error processing from a much younger age when resting-state, but not error-related EEG data can be reliably collected. In addition, since behavioral inhibition shows relative continuity across the lifespan from infancy through adulthood (N. A. Fox et al., 2005), it may be possible to predict neurobiological risk for anxiety with resting-state data before measurement of the ERN is possible (e.g., infancy), and many years before symptoms of anxiety begin to emerge. As a result, early interventions can be more effectively implemented at younger ages to mitigate risk.

Conclusion
In a young sample of 90, 4-8-year-old children, we identi ed associations between the ERN and wholebrain patterns of error-related and resting-state brain activity using EEG microstate analyses. As a result, the current study provides novel insights into how error-related and resting-state EEG microstate are associated with each other and how this type of approach can be used to further clarify the functional signi cance of resting-state microstates. Future longitudinal research is now needed to build on these ndings and to enhance our neurodevelopmental understanding of error processing as early as infancy.

Declarations
CRediT -Authorship with Lucie Bréchet who is also a guest editor. The authors declare that they have no other known competing nancial interests or personal relationships that could have appeared to in uence the work reported in this paper.
Data statement -The data that support the ndings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.
Funding -This study was supported by the National Institute of Mental Health (R01MH110488 to MSG). Resting-state and error-related microstates.
Note.Resting-state microstates (a) were derived from a polarity-invariant clustering algorithm, while errorrelated microstates (b) were derived from a polarity-variant clustering algorithm. The dashed red line (b) represents the time of button-press. The highlighted shaded grey area (b) represents the time period of error related microstate 3. GEV = global explained variance. Note.Asterisk (*) indicates that the variable was square root transformed (see supplementary materials).
Note. Sagittal slices (x plane) are presented as left (positive coordinates) to right (negative coordinates) parts of the brain. Coronal slices (y plane) are presented as anterior (negative coordinates) to posterior (positive coordinates) parts of the brain. Axial slices (z plane) are presented as inferior to superior parts of the brain.

Supplementary Files
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