Sensitivity of structural and functional gradients to phenotypes and time.

a. Using the Schaefer 200-node 7-network parcellation (Schaefer et al., 2018), for each participant, we reconstructed structural connectomes from SIFT2-weighted FBC from probabilistic tractography and transformed them into fully-connected communicability matrices. Functional connectomes were blood-oxygenation-level-dependent responses averaged across the time-series. Structural and functional affinity matrices were created by calculating the normalised angle of each connectome. b. Diffusion-map embedding was applied to each affinity matrix. This is normalised by the anisotropic diffusion parameter α and subjected to eigen-decomposition. The eigenvectors are sorted by decreasing amount of variance explained. When the diffusion time t is 0, the eigenvalues are divided by 1 minus the eigenvalues. Else, they are raised to the power of t. As in prior work, diffusion-map embedding was applied to each hemisphere separately, to avoid detecting a lateralised component as the principal gradient. The left hemisphere was then rotated to the right using a Procrustes rotation. c. The first three structural (G1SC – G3SC) and functional (G1FC – G3FC) connectivity gradients for the neurotypical (NKI) and neurodivergent (CALM) data sets. d. Effects of neurotypicality on nodal communicability gradient values in the baseline session of CALM, where t-statistics were derived from a generalised linear model contrasting referred and control portions of CALM. e. The proportion of variance explained by the first 3 components for individual-level structural connectivity (left) and functional connectivity (right) gradients, respectively, as a function of data set. The middle line in the box plots represents median, flanked by the lower and upper quartiles represented by whiskers, respectively. Dots represent outliers. f. The proportion of variance accounted for by the first structural (left) and functional (right) gradients as a function of age. Individual points represent participants. * indicates a significant effect of dataset (p < 0.05) on variance explained within a linear mixed effects model controlling for head motion, sex, and age at scan. f. Group-level gradients derived from children and adolescents are highly similar across datasets and modalities, as shown by Spearman correlation coefficients. The lighter shades reflect functional connectivity, whilst the darker shades reflect communicability gradients. g. Within NKI, the proportion of variance in individual-level functional connectomes explained by the group-level functional connectome increases across development. h. Across development, within baseline referred CALM individuals, the variability (standard deviation) of communicability gradients decreases, whilst variability of functional gradients increases. i. Within the referred baseline portion of CALM, head motion is negatively related to pre-Procrustes alignment of individual-level structural and functional connectomes to the corresponding group gradients, with age and sex as non-significant predictors. Within all linear models, head motion and sex are controlled. j. Through a mediation model, within baseline NKI, the (direct) relationship between age and pre-Procrustes alignment of functional connectomes becomes non-significant after controlling for motion, where increased motion is linked to younger age and weaker alignment.

Validating manifold eccentricity as a measure of variability in structural and functional axis organisation.

a. Following prior work (Park et al., 2021), we defined manifold eccentricity as the Euclidean distance between each node’s 3-dimensional embedding in manifold space and the group manifold origin, for a given participant and modality. The structural embedding, across the first three structural gradients (G1 – G3) for a representative NKI participant is shown. b. Across datasets and modalities, increased manifold eccentricity is associated with increased network segregation. Each point represents a node, with CALM visualised in purple and NKI in green. c. A dominance analysis for the group-level structural and functional connectomes in CALM reveal distinct and modality-dependent contributions of measures of integration to manifold eccentricity.

Sensitivity of structural and functional manifold organisation to time and phenotype.

Normalised factor-smooth interaction between dataset (CALM in purple, NKI in green) and age when predicting a. structural or b. functional manifold eccentricity, at global and 7 intrinsic connectivity network levels (Yeo et al., 2011), respectively, within generalised additive mixed models (GAMM). Within each GAMM, age was a smooth covariate, whilst mean framewise displacement, sex, and data set were parametric covariates. Age-dataset interactions are plotted to control for the main effect of cohort. The statistical significance of the interaction between age and data set was determined by a parametric bootstrapped likelihood ratio test of the full model against a model with main effects only, simulated 10,000 times. 95% credible intervals were extracted by sampling the posterior distribution of the age-dataset interaction 10,000 times. Horizontal bars within each sub-plot represent developmental periods in which the first derivative of the age-dataset interaction was statistically significant, that is, when the associated simultaneous confidence intervals did not include zero (p < .05, two-tailed). The direction and colour of the arrow for structural global manifold eccentricity indicates a significant main effect of neurodiversity, such that structural global manifold eccentricity was significantly higher within the referred portion of CALM at baseline (N = 313) than within the control portion (N = 311). First derivatives for the smooth age term were plotted for GAMMs with a significant age-dataset interaction or age effect. The y-axis scale for the visual manifold eccentricity GAMM applies to all other intrinsic connectivity network plots. All p-values were corrected for multiple comparisons, within modalities, by controlling false discovery rates. Grey indicates effects not statistically significant at p ≤ .05. Vis, visual; SM, somato-motor; SA, salient/ventral attention; FP, fronto-parietal; DA, dorsal attention; DMN, default-mode network; Lim, Limbic.

Magnitude and variability of structure-function coupling are spatially patterned along a unimodal-transmodal axis, are sensitive to both development and dataset, and have statistically significant developmental trajectories centred within higher-order association networks.

a. To derive a nodal measure of structure-function coupling, for each region (green) we calculated the Euclidean distance with all other regions, within structural and functional manifolds separately, producing two 1 x 200 vectors, using the Schaefer 200-node 7-network parcellation (Schaefer et al., 2018). The Spearman rank correlation coefficient (rs) between these two vectors was the structure-function coupling measure. The larger the coupling coefficient, the more similar the embedding of each node in structural and functional manifold space, relative to all other networks. Note that a negative coupling value indicates anticorrelation. Structural and functional embeddings for a representative NKI participant are shown. Coupling was calculated at 8 levels of analysis: globally, and for 7 intrinsic connectivity networks (Yeo et al., 2011). b. Both structure-function coupling magnitude (top) and inter-individual variability (bottom) are patterned along a unimodal-transmodal axis, where the largest and least variable coupling is at the unimodal anchor, whilst the smallest and most variable coupling is at the transmodal anchor. Note that regions were ranked according to absolute coefficient of variation. c. Globally and within networks, structure-function coupling is consistent across datasets. Within each box plot, the box represents the lower quartile, median, and upper quartile, respectively. Circular points represent outliers. d. Alignment of novel and established absolute structure-function coupling metrics with the sensorimotor-association (SA) axis are visualised. The inset Spearman correlation plot of the 4 coupling measures shows moderate-to-strong correlations (pspin < 0.005 for all spatial correlations). The accompanying lollypop plot shows the alignment between the sensorimotor-to-association axis and each of the 4 coupling measures, with the novel measure coloured in light purple (pspin < 0.007 for all spatial correlations). e. Within a GAMM of global or network-level structure-function coupling as the outcome and using age and an age-dataset interaction as smooth covariates, alongside framewise displacement (averaged across modalities), sex, and dataset as parametric covariates, the age-dataset interaction was significantly linked to coupling in dorsal attention (pFDR = .008) and default-mode (pFDR = .007) networks. Age-dataset interactions are plotted to control for the main effect of cohort. Horizontal bars represent sensitive periods of development of structure-function coupling, calculated as statistically significant (non-zero confidence intervals) simultaneous first derivatives of age effects within GAMMs conducted separately for each dataset. Within both network partitions, age effects were stronger in NKI than CALM. Across all sub-plots, CALM is visualised in purple, and NKI in green. p-values were corrected for multiple comparisons by controlling false discovery rates, except for the main effects of age within separate dataset-specific GAMMs. Vis, visual; SM, somato-motor; SA, salient/ventral attention; FP, fronto-parietal; DA, dorsal attention; DMN, default-mode network; Lim, Limbic.

Dimensions of cognition, rather than psychopathology, are developmentally-sensitive predictors of structure-function coupling.

We applied principal component analysis with varimax rotation to obtain orthogonal dimensions of psychopathology and cognition, across all which CALM loaded more strongly onto than NKI. Within each box plot, the box represents the lower quartile, median, and upper quartile, respectively. Circular points represent outliers. a. The first dimension of psychopathology captures learning problems (‘LRN’), inattention (‘ATN’) and executive functioning (‘EF’). The second dimension captures aggression (‘AGG’) and hyperactivity/inattention (‘H/I’), whilst the third dimension captures peer relation difficulties (‘PR’). b. Visual search (‘VS’), number-letter switching (‘NLS’), motor speed (‘MTR’), and the Tower (‘TOW’) task loaded strongly onto the first cognitive dimension, reflecting executive functioning. Forward- and backward-digit spans (‘FDR’ and ‘BDR’) loaded strongly onto the second cognitive dimension, reflecting working memory. c. Cross-validated predictive accuracy of working memory for structure-function coupling of 5 networks within which we observed a significant interaction between age and working memory, namely somato-motor (‘SomMot’), dorsal attention (‘DorsAttn’), visual (‘Vis’), default-mode (‘Default’) and globally. The default-mode network is highlighted as having the strongest developmentally-sensitive relationship with working memory. Pairwise comparisons were made between consecutively-ordered networks, to reduce multiple comparisons. Predictive accuracy across all visualised networks was significantly greater than 0, as determined through a one-tailed t-test (all p < 0.001). d. Main effects of age are visualised within participants with low (n = 314, visualised in green) or high (n = 315, visualised in blue) scores on the second cognitive dimension, as determined by a median split, for structure-function coupling in the default-mode network. Parametric main effects of mean framewise displacement, sex, principal component 1 scores, and an interaction between age and factor 1 scores were included as covariates. 95% simultaneous confidence intervals derived from using the group-specific (high or low scores) generalised additive mixed model to predict structure-function coupling at equal intervals across the entire developmental range examined (6.17 – 19.17 years old).