Adaptive strategy for the statistical analysis of connectomes

Abstract

We study an adaptive statistical approach to analyze brain networks represented by brain connection matrices of interregional connectivity (connectomes). Our approach is at a middle level between a global analysis and single connections analysis by considering subnetworks of the global brain network. These subnetworks represent either the inter-connectivity between two brain anatomical regions or by the intra-connectivity within the same brain anatomical region. An appropriate summary statistic, that characterizes a meaningful feature of the subnetwork, is evaluated. Based on this summary statistic, a statistical test is performed to derive the corresponding p-value. The reformulation of the problem in this way reduces the number of statistical tests in an orderly fashion based on our understanding of the problem. Considering the global testing problem, the p-values are corrected to control the rate of false discoveries. Finally, the procedure is followed by a local investigation within the significant subnetworks. We contrast this strategy with the one based on the individual measures in terms of power. We show that this strategy has a great potential, in particular in cases where the subnetworks are well defined and the summary statistics are properly chosen. As an application example, we compare structural brain connection matrices of two groups of subjects with a 22q11.2 deletion syndrome, distinguished by their IQ scores.

Figure 1. Power of detecting affected atoms and partially affected subsets depending on the proportion .

For the multiplicity correction, the Bonferroni procedure is used. Three different values of the subsets' size (4, 8 or 16) and two different values of the raw effect Δ (1 or 2). The other parameters are: .

Figure 2. Power of detecting affected atoms and partially affected subsets depending on the proportion .

For the multiplicity correction, the BH95 procedure is used. Three different values of the subsets' size (4, 8 or 16) and two different values of the raw effect Δ (1 or 2) are used. The other parameters are: .

Figure 3. Illustration of the different types of subnetworks within a brain network.

In the right side, a connection matrix is presented. In the left side, the connectivity between two groups of node is presented which defines three subnetworks of two types. The first type represents the intra-connection within the same subset of nodes (the red and the green subnetworks) and whose corresponding blocks are localized on the diagonal of the global connection matrix (the red and the green blocks). The second type represents the interconnections between the two subsets of nodes (the yellow subset). Its corresponding block is localized out of the diagonal in the global connection matrix (the yellow block).

Figure 4. Extraction of a Whole Brain Structural Connection Matrix.

A–B. MRI Acquisition: (A) high-resolution T1-weighted image and (B) diffusion images. The T1 is registered on the diffusion images. In every imaged voxel the Orientation Density Function (ODF) is extracted from the diffusion images. C. Whole brain tractography provides an estimate of axonal trajectories across the WM. D. Cortex partitioning into 83 gyral-based parcels using the Freesurfer software (http://surfer.nmr.mgh.harvard.edu). E. Creation of the low-resolution structural connection matrix, representing the fiber density between every pair of the 83 parcels (upper left and lower right blocks: connections in the right, respectively left hemisphere; off-diagonal blocks: inter-hemispheric connections).