Lagged and instantaneous dynamical influences related to brain structural connectivity

Abstract

Contemporary neuroimaging methods can shed light on the basis of human neural and cognitive specializations, with important implications for neuroscience and medicine. Indeed, different MRI acquisitions provide different brain networks at the macroscale; whilst diffusion-weighted MRI (dMRI) provides a structural connectivity (SC) coincident with the bundles of parallel fibers between brain areas, functional MRI (fMRI) accounts for the variations in the blood-oxygenation-level-dependent T2(*) signal, providing functional connectivity (FC). Understanding the precise relation between FC and SC, that is, between brain dynamics and structure, is still a challenge for neuroscience. To investigate this problem, we acquired data at rest and built the corresponding SC (with matrix elements corresponding to the fiber number between brain areas) to be compared with FC connectivity matrices obtained by three different methods: directed dependencies by an exploratory version of structural equation modeling (eSEM), linear correlations (C) and partial correlations (PC). We also considered the possibility of using lagged correlations in time series; in particular, we compared a lagged version of eSEM and Granger causality (GC). Our results were two-fold: firstly, eSEM performance in correlating with SC was comparable to those obtained from C and PC, but eSEM (not C, nor PC) provides information about directionality of the functional interactions. Second, interactions on a time scale much smaller than the sampling time, captured by instantaneous connectivity methods, are much more related to SC than slow directed influences captured by the lagged analysis. Indeed the performance in correlating with SC was much worse for GC and for the lagged version of eSEM. We expect these results to supply further insights to the interplay between SC and functional patterns, an important issue in the study of brain physiology and function.

Keywords: functional connectivity; functional magnetic resonance imaging; resting state; structural connectivity; structural equation modeling; tensor diffusion imaging.

Figure 1

Sketch for regions of interest (ROIs). Fifteen different ROIs were extracted from three different resting state networks: 1 ROI in the sensory motor (SM), 6 ROIs in the default mode network (DMN), and 8 ROIs in the executive control (ExC).

Figure 2

Structural, effective and functional connectivity matrices (SC, EC and FC, respectively). (A1) SC matrix calculated by the fiber number. Because many of the values in this matrix are very small, we plotted it in logarithmic scale only to enhance visibility. (A2–A4) EC (eSEM) and FC matrices (C and PC), all of them normalized in the [0, 1] range for comparison purposes. (B) Correlation-based similarity between SC and eSEM, C and PC, calculated either over all pairs or only on connected pairs. (C) Mean values of connectivity matrices separated in two groups: pairs such that they have non-zero fibers between them (structurally connected pairs, CP) and non-connected pairs (NCP). ^*p<0.01, otherwise means no statistical significance.

Figure 3

Connectivity values on specific links. All matrices eSEM, C, PC, and SC were normalized in the range [0, 1] for visualization purposes. The maximum values used for normalization in each case are shown, as well as the mean (μ) and the standard deviation (σ) values for all matrices.

Figure 4

Scatter plots between different connectivity matrices and separating in two groups: structurally connected pairs (CP) and non-connected pairs (NCP). Different panels are showing scatter plots of (A) (green rectangles) SC with eSEM, C and PC, (B) (red rectangles) eSEM with C and PC, (C) (blue rectangles) C with PC.

Figure 5

Mean values of structurally connected pairs (CP) and not connected pairs (NCP) across several lags in (A) Granger Causality and (B) eSEM. eSEM1, eSEM2, and eSEM3 (the same as GC1, GC2, and GC3) refers to lag = {1,2,3} for both eSEM and GC. Notice that, in all the cases, the differences found between the two groups were not significant according to the p-value. So, neither eSEM nor GC distinguished between CP and NCP.