We divided a fully preprocessed and quality controlled subsample of the ABCD dataset that had structural and resting-state functional MRI (fMRI) data available into Discovery (N = 3504, i.e., 2/3 of the dataset) and Replication (N = 1747, i.e., 1/3 of the dataset) subsamples, using randomized data partitioning with both subsamples being matched on age, sex, ethnicity, acquisition site, and overall psychopathology (i.e., scores of the first principal component derived from the 118 items of the CBCL). After applying dimensionality reduction to imaging features, we ran a PLS analysis in the Discovery subsample to associate imaging phenotypes and CBCL items (Figure 1a–c). Significant components, identified using permutation testing, were comprehensively described, and we assessed associations to sensory-to-transmodal functional gradient organization for macroscale contextualization. We furthermore related findings to initially held out measures of white matter architecture and task-based fMRI patterns that were available in subsets of participants. Finally, we repeated our analyses in the Replication subsample and assessed generalizability when using Discovery-derived loadings in the Replication subsample. Measures of brain structure and resting-state fMRI were chosen for the main analyses as they (1) have been acquired in the majority of ABCD subjects, (2) represent some of the most frequently acquired, and widely studied imaging phenotypes, and (3) profile intrinsic gray matter network organization. Nevertheless, we also conducted post hoc analyses in smaller subsamples based on diffusion-based measures of fiber architecture (i.e., FA and MD) and functional connectivity during tasks tapping into executive and reward processes. Of note, the findings presented in this paper focus on within-sample statistics, although out-of-sample statistics are reported for LC1–3 in their respective subsections. We found low generalizability of model statistics to unseen data, which was likely due to sample-specific variations in structural and functional imaging features, indicating a small amount of explained variance in brain–behavior relationships.

PLS analysis revealed five significant LCs (all p = 0.001 after permuting the first five LCs 10,000 times, accounting for site and false discovery rate [FDR]) in the discovery sample. They explained 21%, 4%, 3%, 3%, and 2% of covariance between the imaging and behavioral data, respectively (Figure 1—figure supplement 1). LC1, LC2, LC3, and LC5 recapitulated the dimensions previously reported (Michelini et al., 2019), that is, general psychopathology (LC1), internalizing vs. externalizing (LC2), neurodevelopmental (LC3), and detachment (LC5) (Supplementary file 1a). For the remainder of this article, we focus on LC1–LC3, as they were strongly correlated to previously identified factors (see Supplementary file 1a for details), and have been more thoroughly documented previously (Holmes et al., 2021; Michelini et al., 2019; Modabbernia et al., 2022). LC1–LC3 remained statistically significant when using within- and out-of-sample statistics, although out-of-sample generalizability of was low overall (range of r = 0.03–0.07 for the first three latent components).

LC1 (r = 0.36, permuted p < 0.001; out-of-sample generalizability of model statistics: r = 0.03, permuted p < 0.001; Figure 2a) recapitulated a previously described p factor (Alnæs et al., 2018; Caspi et al., 2014; Elliott et al., 2018; Kaczkurkin et al., 2018; Kebets et al., 2019; Lahey et al., 2011; Romer et al., 2018; Shanmugan et al., 2016; Van Dam et al., 2017), and strongly correlated (r = 0.64, p < 0.001; Supplementary file 1a) with the p factor derived from CBCL items by Michelini et al., 2019. All symptom items loaded positively on LC1 – which is expected given prior data showing that every prevalent mental disorder loads positively on the p factor (Lahey et al., 2012). The top behavioral loadings included being inattentive/distracted, impulsive behavior, mood changes, rule breaking, and arguing (Figure 2b, see Supplementary file 1b for all behavior loadings). Greater (i.e., worse) psychopathology was, overall, mainly associated with volume and thickness reductions, while the pattern of surface area associations was more mixed encompassing increases as well as decreases (Figure 2c, see Figure 2—figure supplement 1 for uncorrected structural imaging loadings, and Figure 2—figure supplement 2 for subcortical volume loadings). Greater psychopathology was also associated with patterns of large-scale network organization (Schaefer et al., 2018; Yeo et al., 2011), namely increased RSFC between the default and executive control, default, dorsal and ventral attention networks, and decreased RSFC between the two attention networks, between visual and default networks, and between control and attention networks (Figure 2d, see also Figure 2—figure supplement 2 for a zoom on subcortical–cortical loadings, and Figure 2—figure supplement 3 for uncorrected RSFC loadings). Spatial correlations between modality-specific loadings are reported in Supplementary file 1c.

LC2 (r = 0.34, permuted p < 0.001; out-of-sample generalizability of model statistics: r = 0.05, permuted p < 0.001; Figure 3a) contrasted internalizing vs. externalizing symptoms – two broad dimensions that are driven by covariation of symptoms among internalizing and externalizing disorders (Lahey et al., 2012; Lahey et al., 2011). Here, higher (i.e., positive) behavior loadings indicated increased internalizing symptoms, such as fear or anxiety, worrying, and feeling self-conscious, while lower (i.e., negative) behavior loadings expressed increased externalizing symptoms, such as aggressivity and rule-breaking behaviors (Figure 3b, Supplementary file 1b). At the brain level, greater internalizing symptoms were associated with widespread decreases in cortical thickness, and mixed patterns of increases and decreases in surface area and volume (Figure 3c). In terms of brain organization, worse internalizing symptoms reflected lower RSFC within the somatomotor network and between the somatomotor and attention networks, and higher RSFC between the somatomotor network and the default and control networks (Figure 3d). Spatial correlations between modality-specific loadings are reported in Supplementary file 1c. Note that these brain patterns were inversely related to greater/worse externalizing symptoms, for example, increased thickness, higher RSFC within the somatomotor network.

LC3 (r = 0.35, permuted p < 0.001; out-of-sample generalizability of model statistics: r = 0.07, permuted p < 0.001; Figure 4a) was driven by neurodevelopmental symptoms, such as concentration difficulties and inattention, daydreaming, and restlessness (Figure 4b, Supplementary file 1b), which were contrasted to a mix of symptoms characterized by emotion dysregulation. Greater neurodevelopmental symptoms were associated with increased surface area and volume in temporoparietal regions and decreased surface area and volume in prefrontal as well as in occipital regions, but also with increased thickness in temporo-occipital areas and decreased thickness in prefrontal regions (Figure 4c). Worse neurodevelopmental symptomatology was also related to decreased RSFC within most cortical networks such as the default, control, dorsal, and ventral attention, and somatomotor networks, and increased RSFC between control, default, and limbic networks on the one side, and attention and somatomotor networks on the other side (Figure 4d). Spatial correlations between modality-specific loadings are reported in Supplementary file 1c.

The primary functional gradient explained 28% of the RSFC variance, and differentiated primary somatosensory/motor and visual areas from transmodal association cortices (Figure 5b). These results replicated previous findings obtained with RSFC in a healthy adult cohort (Margulies et al., 2016). Since previous research had found that the sensory-to-transmodal gradient only becomes the ‘principal’ gradient around 12–13 years old (Dong et al., 2021), we also computed gradients without aligning it to the Human Connectome Project (HCP) gradient to verify whether the gradient order would change, but found the principal gradient to be virtually identical to its aligned counterpart (Figure 5—figure supplement 1). We note that the second gradient (contrasting somatosensory/motor and visual areas) explained almost the same amount of variance as the first gradient (i.e., 26%, see Figure 5a), which may suggest that participants in our sample have only recently transitioned toward a more mature functional organization, that is, more spatially distributed (Dong et al., 2021). Next, we tested whether imaging loadings associated to the LCs would follow this sensory-to-transmodal axis (Sydnor et al., 2021) by assessing spatial correspondence while adjusting for spatial autocorrelations via spin permutation tests (Alexander-Bloch et al., 2018) (see Supplementary file 1d). Between-network RSFC loadings for LC1 and LC3 showed a strong positive correlation to the principal gradient (LC1: r = 0.43, p_spin < 0.001; LC3: r = 0.33, p_spin < 0.001; Figure 5d), that is, between-network connectivity was higher in transmodal regions and lower in sensory areas. Within-network RSFC loadings for LC1, LC2, and LC3 also showed a significant albeit weak correlation with the sensory-to-transmodal gradient LC1: r = −0.14, p_spin = 0.010; LC2: r = 0.13, p_spin = 0.032; LC3: r = 0.17, p_spin = 0.017 (Figure 5d), that is, within-network FC was higher in sensory regions in LC1, and in higher-order regions in LCs 2–3. A similar pattern of findings was observed when cross-validating between- and within-network RSFC loadings to an RSFC gradient derived from an independent dataset (HCP), with strongest correlations seen for between-network RSFC loadings for LC1 and LC3 (LC1: r=0.50, p_spin < 0.001; LC3: r = 0.37, p_spin < 0.001). Of note, we obtained similar correlations when using T1w/T2w ratio in the same participants, a proxy of intracortical microstructure and hierarchy (Glasser and Van Essen, 2011). Specifically, we observed the strongest association between this microstructural marker of the cortical hierarchy and between-network RSFC loadings related to LC1 (r = −0.43, p_spin < 0.001). None of the structural loadings were associated with principal gradient scores.

Our final analysis related out findings to white matter architecture and assessed the stability of functional organization across three cognitive states including reward, (emotional) working memory, and impulsivity (Figure 6, also see Figure 2—figure supplement 3 for uncorrected task FC patterns). Greater psychopathology (LC1) was related to widespread decrease in FA and MD in all white matter tracts (see Supplementary file 1e for diffusion-based loadings and Z-scores for all white matter tracts). Higher internalizing and lower externalizing symptoms (LC2) were associated to higher FA within the left superior corticostriate-frontal and corticostriate tracts, and higher MD within the foreceps major and parahippocampal cingulum. Finally, greater neurodevelopmental symptoms (LC3) were related to decreased FA within the right cingulate cingulum, and within the left superior, temporal, and parietal longitudinal fasciculus.

Regarding task FC organization, many patterns appeared to mirror those seen during rest. Greater psychopathology was associated with higher FC between control and default network across all states, including rest (Figure 6c). LC1 was also related to higher FC between sensory and attention networks during the Emotional N-back (EN-back task), and decreased FC between control and attention networks during Monetary Incentive Delay (MID) and Stop Signal Task (SST) tasks. LC2 was related to decreased FC within the default network and between the default and control networks across all states, increased FC between somatomotor and control networks during MID and EN-back tasks, and between somatomotor and default network during EN-back and SST tasks. Finally, task FC patterns related to LC3 were similar to those observed during rest, for example, decreased within-network FC and higher FC between default and attention networks.

We implemented different approaches to evaluate the robustness and potential generalizability of our findings. First, we performed a completely independent replication of the analysis pipeline in an unseen sample of participants (see Figure 7). We observed significant correlations between behavioral loadings of LCs 1–3 across discovery and replication samples (r = 0.63–0.97). In terms of imaging loadings, RSFC loadings were replicated in LCs 1–3 (r = 0.11–0.29, p_spin < 0.05); thickness loadings were replicated in LCs 1–3 (r = 0.15–0.55, p_spin < 0.05); volume loadings were replicated in LCs 1–2 (r = 0.18–0.19, p_spin < 0.05) but not LC3 (r = 0.02, p = 0.467); finally, surface area loadings were only replicated in LC2 (r = 0.15, p_spin = 0.040). However, independently re-calculating model statistics in the replication sample may yield inflated effect sizes in estimating out-of-sample prediction. We addressed this limitation by applying all model weights computed in the discovery sample to the replication sample data. We first applied the imaging principal components analysis (PCA) coefficients computed in the discovery cohort to the raw replication cohort data. Resulting PCA scores and behavioral data were then normalized using the mean and standard deviation of corresponding data in the discovery cohort. Cross-validated composite scores were generated by multiplying singular value decompositions of the discovery cohort data with the normalized imaging PCA and behavioral data from the replication sample. Modality-specific and behavioral loadings were recovered by correlating cross-validated composite scores with normalized replication sample data. With this approach, we found that out-of-sample prediction was overall high across LCs 1–3 for behavioral loading (r = 0.94–0.97), and lower for imaging loadings (r = 0.16–0.29). These analyses suggest that questionnaire item loadings were highly replicable across discovery and replication cohorts but indicate lower generalizability of structural and functional network loadings. This lower replicability of brain features also affected out-of-sample prediction statistics linking imaging features and behavior (cross-validated composite scores), which were generally low across LCs but remained statistically significant (LC1 r = 0.03; LC2 r = 0.05; LC3 r = 0.07; all permuted p < 0.001 after permuting the first five LCs 10,000 times, accounting for site and FDR).

To make sure that our findings were robust to different PCA thresholds, we repeated our analyses while keeping principal components that explained 10%, 30%, 70%, and 90% of variance in each imaging modality (instead of 50% as for the main analysis). Both behavior and imaging loadings were highly similar to those in our main analysis, though we note that similarity was lower in the control analysis that kept principal components explaining 10% of the data, which is likely due to the very low dimensionality of the data (i.e., 14 principal components) (Supplementary file 1f). Third, to account for redundancy within structural imaging metrics included in our main PLS model (i.e., cortical volume is a result of both thickness and surface area), we also repeated our main analysis while excluding cortical volume from our imaging metrics. Findings were very similar to those in our main analysis, with an average absolute correlation of 0.898 ± 0.114 across imaging composite scores of LCs 1–5. Considering scan quality in T1w-derived metrics (from manual quality control ratings) yielded similar results to our main analysis, with an average correlation of 0.986 ± 0.014 across imaging composite scores. Additionally considering head motion parameters from diffusion imaging metrics in our model yielded consistent results to those in our main (mean r = 0.891, SD = 0.103; r = 0.733–0.998). Moreover, repeating the PLS analysis while excluding ethnicity as a model covariate yielded overall similar imaging and behavioral composites scores across LCs to our original analysis. Across LCs 1–5, the average absolute correlations reached r = 0.636 ± 0.248 for imaging composite scores, and r = 0.715 ± 0.269 for behavioral composite scores. Removing these covariates seemed to exert stronger effects on LC3 and LC4 for both imaging and behavior, as lower correlations across models were specifically observed for these components.

We also explored associations between age/sex and psychopathology dimensions. Notably, we found that male participants had higher composite scores on LC1 (p factor) and LC3 (neurodevelopmental symptoms), while female participants had higher composite scores on LC2 (internalizing symptoms) (Figure 1—figure supplement 2). Furthermore, both imaging and behavior scores for LC2 (internalizing/externalizing symptoms) were significantly albeit weakly correlated with age and age² (r = 0.04–0.05, ps < 0.028; Supplementary file 1g).

Lastly, although the current work aimed to reduce intrinsic correlations between variables within a given modality through running a PCA before the PLS approach, intrinsic correlations between measures and modalities may potentially be a remaining factor influencing the PLS solution. We thus provided an additional overview of the intrinsic correlations between the different neuroimaging data modalities in the supporting results (Supplementary file 1c). We found that volume loadings were correlated with thickness and surface area loadings across all LCs, in line with the expected redundancy of these structural modalities. While between- and within-network RSFC loadings were also significantly correlated across LCs, their associations to structural metrics were more variable.

We considered data from 11,875 children from the ABCD 2.0.1 release. The data were collected on 21 sites across the United States (https://abcdstudy.org/contact/), and aimed to be representative of the socio-demographic diversity of the US population of 9–10 year old children (Garavan et al., 2018). To ensure that the study had enough statistical power to characterize a large variety of developmental trajectories, the ABCD study aimed for 50% of their sample to exhibit early signs of internalizing/externalizing symptoms (Garavan et al., 2018). Ethical review and approval of the protocol was obtained from the Institutional Review Board (IRB) at the University of California, San Diego, as well as from local IRB (Auchter et al., 2018). Parents/guardians and children provided written assent (Clark et al., 2018). After excluding participants with incomplete structural MRI, resting-state functional MRI (rs-fMRI), or behavioral data, MRI preprocessing, and quality control, and after excluding sites with less than 20 participants, our main analyses included 5251 unrelated children (2577 female [49%], 9.94 ± 0.62 years old, 19 sites). We divided this sample into Discovery (N = 3504, i.e., 2/3 of the dataset) and Replication (N = 1747, i.e., 1/3 of the dataset) subsamples, using randomized data partitioning with both subsamples being matched on age, sex, ethnicity, acquisition site, and overall psychopathology (i.e., scores of the first principal component derived from the 118 items of the Achenbach CBCL Achenbach and Rescorla, 2013). Figure 1d shows the distribution of these measures in the two samples.

The parent-reported CBCL (Achenbach and Rescorla, 2013) is comprised of 119 items that measure various symptoms in the child’s behavior in the past 6 months. Symptoms are rated on a three-point scale from (0 = not true, 1 = somewhat or sometimes true, 2 = very true or always true). We used 118/119 items (see Supplementary file 1h for a complete list of items); one item was removed (‘Smokes, chews, or sniffs tobacco’) as all participants from the discovery sample scored ‘0’ for this question. In the replication sample, another item (‘Uses drugs for nonmedical purposes – don’t include alcohol or tobacco’) was removed for the same reason. Prior to the PLS analysis, effects of age, age², sex, site, and ethnicity were regressed out from the behavioral and imaging data using a multiple linear regression to ensure that the LCs would not be driven by possible socio-demographic confounders (Kebets et al., 2021; Kebets et al., 2019; Xia et al., 2018). The imaging and behavioral residuals of this procedure were input to the PLS analysis. Of note, the inclusion of ethnicity as a covariate in imaging studies has been recently called into question (Saragosa-Harris et al., 2022). In the present study, we included this variable in our main model as a proxy for social inequalities relating to race and ethnicity alongside biological factors (age and sex) with documented effects on brain organization and neurodevelopmental symptomatology queried in the CBCL. We nonetheless quantified the potential effect of this covariate in our main analyses by assessing the consistency of composite scores in a model excluding race and ethnicity covariates (see Generalizability and control analyses).

MR images were acquired across 21 sites in the United States with harmonized imaging protocols for GE, Philips, and Siemens scanners (Casey et al., 2018). The imaging acquisition protocol consisted of a localizer, T1-weighted images, two runs of rs-fMRI, diffusion-weighted images, T2-weighted images, one to two more runs of rs-fMRI, and the three task-fMRI acquisitions. Full details about the imaging acquisition protocol can be found elsewhere (Casey et al., 2018). Scans acquired on the Philips scanner were excluded due to incorrect processing, as recommended by the ABCD consortium.

T1-weighted (T1w) images were acquired using a 3D sequence (1 mm isotropic, Repetition time [TR] = 2500 ms, Echo time [TE] = 2.88 ms, Inversion time [TI] = 1060 ms, flip angle = 8°, matrix = 256 × 256, Field of view [FOV] = 256 × 256 mm², 176 axial slices) on the Siemens Prisma scanner. Almost identical parameters were used on the GE 750 scanner (except for TE = 2 ms, 208 axial slices). As head motion is an important concern for (pediatric) imaging, real-time motion detection and correction were implemented for the structural scans and for rs-fMRI at the Siemens sites.

The rs- and task-fMRI data were acquired using a multiband echo planar imaging (EPI) sequence (2.4 mm isotropic voxels, TR = 800 ms, TE = 30 ms, flip angle = 52°, slice acceleration factor 6, matrix = 90 × 90, FOV = 216 × 216 mm², 60 axial slices) with fast integrated distortion correction. Twenty minutes of rs-fMRI data were acquired in four runs, and participants were instructed to keep their eyes open while passively watching a cross hair on the screen. The three fMRI tasks included an MID task, which measures domains of reward processing, an EN-back task which engages memory and emotion processing, and an SST that engages impulsivity and impulse control. Details about the tasks paradigms and conditions can be found elsewhere (Casey et al., 2018). For each participant, there were two runs for each fMRI task.

Diffusion MR images were acquired using a multiband EPI sequence (slice acceleration factor 3) and included 96 diffusion directions, seven b = 0 frames, and four b-values (6 directions with b = 500 s/mm², 15 directions with b = 1000 s/mm², 15 directions with b = 2000 s/mm², and 60 directions with b = 3000 s/mm²). Acquisition parameters were almost identical between Siemens (TR = 4100 ms, TE = 88 ms, flip angle = 90°̊, matrix = 140 × 140, FOV = 240 × 240 mm², 81 axial slices) and GE 750 scanners (TR = 4100 ms, TE = 81.9 ms, flip angle = 77°, matrix = 140 × 140, FOV = 240 × 240 mm², 81 axial slices).

We used minimally preprocessed T1w, fMRI, and diffusion MRI data (Hagler et al., 2019). The processing steps for each imaging modality are detailed below: (a) Structural MRI processing. T1w images underwent gradient warp correction, bias field correction, and were resampled to a reference brain in standard space with isotropic voxels (Hagler et al., 2019). They were further processed using FreeSurfer 5.3.0 (Dale et al., 1999; Fischl et al., 1999a; Fischl et al., 1999b; Ségonne et al., 2004; Ségonne et al., 2007). Cortical surface meshes were generated for each participant, and registered to a common spherical coordinate system (Fischl et al., 1999a, Fischl et al., 1999b). Participants that did not pass recon-all quality control were excluded. (b) fMRI processing. The same processing was applied to both rs- and task-fMRI data. ABCD initial processing included motion correction, B0 distortion correction, grad warp correction for distortions due to gradient nonlinearities, and resampling to an isotropic resolution. fMRI data further underwent: (1) removal of initial frames Hagler et al., 2019; (2) alignment of structural and functional images using boundary-based registration (Greve and Fischl, 2009). Runs with boundary-based registration cost >0.6 were excluded. Framewise displacement (FD) (Jenkinson et al., 2002) and voxel-wise differentiated signal variance (DVARS) (Power et al., 2012) were computed using fsl_motion_outliers. Frames with FD >0.3 mm or DVARS >50, along with one frame before and two frames after, were considered as outliers and subsequently censored. Uncensored segments of data fewer than five contiguous frames were also censored (Gordon et al., 2016; Kong et al., 2019). Runs with >50% frames censored and/or max FD >5 mm were excluded. Participants with less than 4 min of data were also removed. Nuisance covariates including global signal, six motion parameters, averaged ventricular and white matter signal, along with their temporal derivates, were regressed out of the fMRI time series. Censored frames were not considered in the regression. Data were interpolated across censored frames using least squares spectral estimation (Power et al., 2014). A bandpass filter (0.009–0.08 Hz) was applied. Finally, preprocessed time series were projected onto FreeSurfer fsaverage6 surface space and smoothed using a 6-mm full-width half maximum kernel. (c) Diffusion MRI processing. Initial processing included eddy current distortion, motion correction, B0 distortion correction, grad warp correction, and resampling to an isotropic resolution. Major white matter tracts were labeled using AtlasTrack, a probabilistic atlas-based method for automated segmentation (Hagler et al., 2009). Structural MRI images were nonlinearly registered to the atlas and diffusion MRI-derived diffusion orientation for each participant were compared to the atlas fiber orientations, refining a priori tract location probabilities, individualizing the fiber tract ROIs, and minimizing the contribution from regions inconsistent with the atlas (Hagler et al., 2019). Processed diffusion MRI data were available in 10,186 participants, among which 3275 overlapped with the Discovery sample (93%).

RSFC was computed as the Pearson’s correlation between the average timeseries among 400 cortical (Schaefer et al., 2018) and 19 subcortical (Fischl et al., 2002) regions (Figure 1a), yielding 87,571 connections for each participant. Censored frames were not considered when computing FC. Age, age², sex, site, ethnicity, head motion (mean FD), and image intensity (mean DVARS) were further regressed out from the RSFC data.

Surface area, thickness, and volume were extracted from the same 400 cortical regions (Schaefer et al., 2018). Age, age², sex, site, and ethnicity were also regressed out from each parcel-wise structural measure; cortical thickness and volume measures were additionally adjusted for total intracranial volume, and surface area additionally for total surface area.

To reduce data dimensionality before combining the different imaging modalities, we applied PCA over each feature (i.e., surface area, cortical thickness, cortical volume, and RSFC), and selected PCA scores of the number of components explaining 50% of the variance within each data modality, before concatenating them (see Figure 1b). The chosen 50% threshold sought to balance the relative contribution of modalities – to prevent the relatively larger number of RSFC features (compared to structural features) from overpowering the analyses; however, we also report results for different thresholds (see Generalizability and control analyses). We obtained 50, 58, 57, and 256 principal components for surface area, thickness, volume, and RSFC, respectively, resulting in 421 components in total.

The relative importance of each imaging modality for LCs 1–5 is shown in Figure 1—figure supplement 3. To determine the relative contribution of each imaging data modality to the imaging loadings associated with each LC, we computed Pearson’s correlations between the ‘full’ imaging composite scores (Xpca×V) and the modality-specific imaging composites scores (Xpca×Vmodality). Modality-specific imaging composite scores were computed by multiplying the imaging data (Xpca) by the imaging saliences (V) after turning into zero all the values of the other modalities and keeping only the saliences of that specific modality. For example, when computing the relative importance of surface area loadings, only the first 50 rows of V are kept (i.e., the number of surface area features kept after PCA), while the rest of the rows are replaced by zeros.

PLS correlation analysis (McIntosh and Lobaugh, 2004; McIntosh and Mišić, 2013) was used to identify latent components (LCs) that optimally related children’s symptoms (indexed by the CBCL) to structural and functional imaging features (Figure 1c). PLS is a multivariate data-driven statistical technique that aims to maximize the covariance between two data matrices by linearly projecting the behavioral and imaging data into a low-dimensional space.

The PLS analysis was computed as follows. The imaging and behavior data are stored in matrices Xpca (participants × principal component scores from multimodal imaging data) and Y (participants × CBCL items), respectively. After Z-scoring Xpca and Y (across all participants), we computed the covariance matrix R:R=YT×Xpca

followed by singular value decomposition of R:R=U×S×VT

which resulted in three low-dimensional matrices: U and V are the singular vectors comprised of behavioral and imaging weights (akin to coefficients in PCA), while S is a diagonal matrix comprised of the singular values. Next, we computed LX and LY by projecting X and Y onto their respective weights V and U:LX=Xpca×VLY=Y×U

The matrices obtained are the imaging and behavioral composite scores, and reflect the participants’ individual imaging and behavioral contribution to each LC (akin to factor scores in PCA). The contribution of each variable to the LCs was determined by computing Pearson’s correlations between participants’ composite scores and their original data, which we refer to as loadings. The covariance explained by each LC was computed as the squared singular value divided by the squared sum of all singular values. Statistical significance of the LCs was assessed using permutation testing (10,000 permutations accounting for site) over the singular values of the first five LCs, while accounting for acquisition site (i.e., data were permuted between participants from the same site). Loading stability was determined using bootstraps, whereby data were sampled 1000 times with replacement among participants from the same site. Bootstrapped Z-scores were computed by dividing each loading by its bootstrapped standard deviation. To limit the number of multiple comparisons, the bootstrapped rs- and task FC loadings were averaged across edge pairs within and between 18 networks, before computing Z-scores. The bootstrapped Z-scores were converted to p-values and FDR-corrected (q < 0.05) along with other posthoc tests. The procedure was performed in both the discovery and replication samples.

To map psychopathology-related structural and functional abnormalities along the sensory-to-transmodal gradient of brain organization, we applied diffusion map embedding (Coifman et al., 2005), a nonlinear dimensionality reduction technique to the RSFC data. Essentially, strongly interconnected parcels will be closer together in this low-dimensional embedding space (i.e., have more similar scores), while parcels with little or no inter-covariance will be further apart (and have more dissimilar scores). Previous work has shown that spatial gradients of RSFC variations derived from nonlinear dimensionality reduction recapitulate the putative cortical hierarchy (Bernhardt et al., 2022; Margulies et al., 2016; Mesulam, 1998), suggesting that functional gradients might approximate an inherent coordinate system of the human cortex. To derive the functional gradient, we first calculated a cosine similarity matrix from the average RSFC matrix of our full sample (i.e., discovery and replication samples together, N = 5,251). This matrix, thus, captures similarity in connectivity patterns for each pair of regions. Following prior studies (Margulies et al., 2016), the RSFC was initially thresholded to only contain the top 10% entries for each row, that is, the 10% strongest connections of each region. The α parameter (set at α = 0.5) controls the influence of the density of sampling points on the manifold (α = 0, maximal influence; α = 1, no influence), while the t parameter (set at t = 0) scales eigenvalues of the diffusion operator. These parameters were set to retain the global relations between data points in the embedded space, following prior applications (Hong et al., 2019; Margulies et al., 2016; Paquola et al., 2019). To facilitate comparison with previous work (Margulies et al., 2016), the connectivity gradient we derived from our ABCD sample was aligned to gradients derived from the HCP healthy young adult dataset, available in the BrainSpace toolbox (de Wael et al., 2020), using Procrustes alignment. In a control analysis, we also computed connectivity gradients without aligning them to the HCP dataset to verify whether the gradients’ order would change, as a recent study has shown that the principal gradient transitioned from the somatosensory/motor-to-visual to the sensory-to-transmodal gradient between childhood and adolescence (Dong et al., 2021). Finally, for gradient-based contextualization of our findings, we computed Pearson’s correlations between cortical PLS loadings (within each imaging modality) and scores from the first gradient (i.e., recapitulating the sensory-to-transmodal axis of cortical organization). Statistical significance of spatial associations was assessed using 1000 spin tests that control for spatial autocorrelations (Alexander-Bloch et al., 2018), followed by FDR correction for multiple comparisons (q < 0.05).

Task FC and diffusion tensor metrics were also explored in a post hoc association analyses in smaller subsamples. Following the same pipeline as for the rs-fMRI data, FC was computed across the entire timecourse of each fMRI task (thereby capturing both the active task and rest conditions), that is, the MID task, which measures domains of reward processing, the EN-back task, which evaluates memory and emotion processing, and the SST, which engages impulsivity and impulse control. Details about task paradigms and conditions can be found elsewhere (Casey et al., 2018). After excluding subjects that did not pass both rs- and task-fMRI quality control, MID and SST data were available in 2039 participants, while EN-back data were available in 3435 participants. A total of 1195 of participants overlapped across the three tasks and the discovery sample (39%). Task FC data were corrected for the same confounds as RSFC (i.e., age, age², sex, site, ethnicity, mean FD, and mean DVARS). Diffusion tensor metrics included FA and MD in 35 white matter tracts (Hagler et al., 2009). FA measures directionally constrained diffusion of water molecules within the white matter and MD the overall diffusivity, and both metrics have been suggested to index fiber architecture and microstructure. Effects of age, age², sex, site, and ethnicity were regressed out from the FA and MD measures. We tested another model which additionally included head motion parameters as regressors in our analyses of FA and MD measures and assessed the consistency of findings from both models.

The contribution of task FC and diffusion MRI features was computed by correlating participants’ task FC and diffusion MRI data with their imaging and behavior composite scores (from the main PLS analysis using structural and RSFC features). As for other modalities, the loadings’ stability was determined via bootstraps (i.e., 1000 samples with replacement accounting for site).

Several analyses assessed reliability. First, we repeated the PLS analysis in the replication sample (N = 1,747, i.e., 1/3 of our sample), and tested the reliability of our findings by computing Pearson’s correlations between the obtained behavior/imaging loadings with the original loadings. We also assessed the generalizability of our findings by applying model weights computed in the discovery sample to the replication sample data. Second, we repeated the PLS analyses while keeping principal components explaining 10–90% of the variance within each imaging modality, and compared resulting loadings to those of our original model (which kept principal components explaining 50% of the variance) via Pearson’s correlation between loadings. For imaging loadings, we computed correlations for each imaging modality, then averaged correlations across all imaging modalities. As cortical volume is a result of both thickness and surface area, we repeated our main PLS analysis while excluding cortical volume from our imaging metrics and report the consistency of these findings with our main model. We also considered manual quality control ratings as a measure of T1w scan quality. This metric was included as a covariate in a multiple linear regression model accounting for potential confounds in the structural imaging data, in addition to age, age², sex, site, ethnicity, intracranial volume (ICV), and total surface area. Downstream PLS results were then benchmarked against those obtained from our main model.

We also further assessed the effects of socio-demographic profiles of our participant sample. Effects of age and sex differences on the LCs were assessed by computing associations between participants’ imaging/behavior composite scores and their age and sex, using either t-tests (for associations with sex) or Pearson’s correlations (for associations with age). Post hoc tests were corrected for multiple comparisons using FDR correction (q < 0.05). We also assessed the replicability of our findings when removing race and ethnicity covariates prior to computing the PLS analysis and correlating imaging and behavioral composite scores across both models.