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 streamline counts 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. 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. e. The proportion of variance accounted for by the first structural (left) and functional (right) gradients as a function of age. Individual points represent participants. In d and e, NKI is visualised in green, and CALM in purple.

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. The distribution of the coefficient of variation of nodal manifold eccentricity, averaged across participants, as a function of data set and modality. Dotted lines represent means. Lighter tones represent structural manifolds, and darker represents functional. Vertical green arrows represent the significantly larger mean nodal manifold eccentricity coefficient of variation for NKI, across both modalities. c. Pearson correlation coefficients between group-level nodal manifold eccentricity and local graph theory metrics, in structural (top) and functional (bottom) manifolds, respectively. Across b and c, NKI is visualised in green, and CALM in purple. Across a and c, each point represents a node in the Schaefer 200-node 7-network parcellation (Schaefer et al., 2018). SC, structural connectivity; FC, functional connectivity.

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). 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 smallest and least variable coupling is at the unimodal anchor, whilst the largest 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. Within a GAMM predicting global or network-level structure-function coupling 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 a highly statistically significant predictor of 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. 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, in network divisions within which an interaction between age and the second cognitive dimension was a statistically significant (pFDR ≤ .05) predictor of global, somatomotor, dorsal attention, and default-mode (left to right) structure-function coupling. 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). Only developmental effects between coupling and cognitive dimensions are visualised, as structure-function coupling was not significantly statistically associated with dimensions of psychopathology. Across all plots, statistically significant effects are marked * for p ≤ .05, ** for p ≤ .01, and *** for p ≤ .001.