Predicting human resting-state functional connectivity from structural connectivity

Abstract

In the cerebral cortex, the activity levels of neuronal populations are continuously fluctuating. When neuronal activity, as measured using functional MRI (fMRI), is temporally coherent across 2 populations, those populations are said to be functionally connected. Functional connectivity has previously been shown to correlate with structural (anatomical) connectivity patterns at an aggregate level. In the present study we investigate, with the aid of computational modeling, whether systems-level properties of functional networks--including their spatial statistics and their persistence across time--can be accounted for by properties of the underlying anatomical network. We measured resting state functional connectivity (using fMRI) and structural connectivity (using diffusion spectrum imaging tractography) in the same individuals at high resolution. Structural connectivity then provided the couplings for a model of macroscopic cortical dynamics. In both model and data, we observed (i) that strong functional connections commonly exist between regions with no direct structural connection, rendering the inference of structural connectivity from functional connectivity impractical; (ii) that indirect connections and interregional distance accounted for some of the variance in functional connectivity that was unexplained by direct structural connectivity; and (iii) that resting-state functional connectivity exhibits variability within and across both scanning sessions and model runs. These empirical and modeling results demonstrate that although resting state functional connectivity is variable and is frequently present between regions without direct structural linkage, its strength, persistence, and spatial statistics are nevertheless constrained by the large-scale anatomical structure of the human cerebral cortex.

Fig. 1.

Overall SC-rsFC relationships. (A) Scatter plot (single acquisition, 20 min) of rsFC against SC at high resolution for participant B, showing edges with nonzero SC. (B) Scatter plot (single run, 16 min) of simulated rsFC against SC (from participant B) at high resolution, showing edges with nonzero SC. (C) The probability densities of rsFC values between structurally connected and unconnected region pairs, data for participant B at the high resolution. (D) Same as (C), but for simulated rsFC. (E) ROC curves, indicating the signal detection performance when inferring SC by thresholding empiricial (green) and simulated (dark blue) rsFC maps at the high resolution.

Fig. 2.

Role of distance. (A) Scatter plot of interregional rsFC against the inverse of the inter-regional fiber distance. (B) Scatter plot of residuals from (A) plotted against SC, at the low resolution. (C) Three-dimensional scatter plot, showing the relationship between SC, rsFC, and inverse fiber distance. The superimposed plane shows the fit of the bivariate linear model. Points above the plane of best-fit are light blue, points below are dark blue.

Fig. 3.

Computational model of functional connectivity. (A) Scatter plot of empirical rsFC versus simulated rsFC obtained from the nonlinear model, down-sampled to the low resolution. (B) Comparison of SC, rsFC (empirical), and rsFC (nonlinear model) for 2 single-seed regions, the posterior cingulate in the right hemisphere (rPC) and the precuneus in the left hemisphere (lPCUN). The plot displays SC and rsFC values for the seed regions in relation to all 66 regions within the corresponding low-resolution matrices. (C) Mapping of SC, rsFC (empirical), and rsFC (modeled) within the DMN. Warmer colors indicate stronger SC and rsFC. Within the posterior cingulated/precuneus, medial orbitofrontal cortex and lateral parietal cortex in both hemispheres we selected a cluster of 5 ROIs at positions that most closely matched the coordinates of peak foci of the DMN (31). These 30 ROIs served as the seeds from which SC and rsFC were determined. (D) Structural connectivity within the DMN. We selected the top 200 most correlated ROIs within the DMN (see Fig. S5D) and plotted all structural connections among them.