Gradients of structure-function tethering across neocortex

Abstract

The white matter architecture of the brain imparts a distinct signature on neuronal coactivation patterns. Interregional projections promote synchrony among distant neuronal populations, giving rise to richly patterned functional networks. A variety of statistical, communication, and biophysical models have been proposed to study the relationship between brain structure and function, but the link is not yet known. In the present report we seek to relate the structural and functional connection profiles of individual brain areas. We apply a simple multilinear model that incorporates information about spatial proximity, routing, and diffusion between brain regions to predict their functional connectivity. We find that structure-function relationships vary markedly across the neocortex. Structure and function correspond closely in unimodal, primary sensory, and motor regions, but diverge in transmodal cortex, particularly the default mode and salience networks. The divergence between structure and function systematically follows functional and cytoarchitectonic hierarchies. Altogether, the present results demonstrate that structural and functional networks do not align uniformly across the brain, but gradually uncouple in higher-order polysensory areas.

Keywords: connectome; cortical gradient; structure–function.

Fig. 1.

Node-wise structure–function relationships. Local, node-wise structure–function relationships are estimated by fitting a multilinear regression model for each node separately. For a given node $i$, the response or dependent variable is the functional connectivity between node $i$ and node $j\hspace{0.17em}\ne \hspace{0.17em}i$. The predictor or independent variables are the geometric and structural relationships between $i$ and $j$, including the Euclidean distance, path length, and communicability. The “observations” are individual $i,j$ relationships. Model parameters (intercept $b_0$ and regression coefficients $b_1$, $b_2$, and $b_3$) are then estimated by ordinary least squares. Goodness of fit for each node $i$ is quantified by $R_i^2$ between observed and predicted functional connectivity.

Fig. 2.

Convergent and divergent structure–function relationships across neocortex. (A) Local structure–function correspondence, estimated by node-wise $R^2$ from the multilinear model. The histogram shows a wide distribution of $R^2$ values across 1,000 nodes at the highest resolution. (B) The spatial distribution of structure–function correspondence. Nodes are colored and sized in inverse proportion to $R^2$; nodes with weaker structure–function correspondence are larger. High correspondence is observed in primary sensory and motor cortices, while lower correspondence is observed in transmodal cortex. (C) Correlation between structural and functional centrality and structure–function correspondence. Shown are scatter plots between node-wise $R^2$ and structural and functional centrality, estimated by binary degree and weighted strength, respectively. The low correlations suggest that the correspondence between structure and function does not trivially depend on the structural or functional connectedness of a node. For the same results at other parcellation resolutions, see SI Appendix, Fig. S1.

Fig. 3.

Structure–function tethering across cognitive systems and cytoarchitectonic classes. Node-wise $R^2$ values are averaged according to their membership in resting-state networks or cytoarchitectonic classes. To determine whether the mean value for each network or class is statistically significant, a null distribution is constructed by spherical projection and rotation (10,000 repetitions). The network- or class-specific mean $R^2$ is then expressed as a z score relative to this null distribution. Statistically significant networks/classes are shown in color; nonsignificant networks/classes are shown in gray. Yeo networks: da, dorsal attention; dm, default mode; fp, frontoparietal; lim, limbic; sm, somatomotor; va, ventral attention; vis, visual. von Economo classes: ac1, association cortex; ac2, association cortex; ic, insular cortex; lb, limbic regions; pm, primary motor cortex; ps, primary sensory cortex; pss, primary/secondary sensory.

Fig. 4.

Structure–function divergence across large-scale functional network gradients. Large-scale functional network gradients were identified by applying diffusion map embedding to the normalized graph Laplacian of the correlation matrix. (A) The first gradient runs from primary, unimodal cortex to transmodal cortex and resembles the vertex-wise map originally reported by Margulies et al. (18). (B) Node-wise structure–function $R^2$ values are anticorrelated with positions along this gradient, suggesting that structure and function closely correspond in unimodal cortex but diverge in transmodal cortex. (C) Red: empirical Spearman correlation between the first gradient and structure–function $R^2$ values. Blue: null distribution of Spearman correlation coefficients derived using spherical projections.