Mapping human whole-brain structural networks with diffusion MRI

Abstract

Understanding the large-scale structural network formed by neurons is a major challenge in system neuroscience. A detailed connectivity map covering the entire brain would therefore be of great value. Based on diffusion MRI, we propose an efficient methodology to generate large, comprehensive and individual white matter connectional datasets of the living or dead, human or animal brain. This non-invasive tool enables us to study the basic and potentially complex network properties of the entire brain. For two human subjects we find that their individual brain networks have an exponential node degree distribution and that their global organization is in the form of a small world.

Figure 1. Mapping the network of brain structural connectivity with diffusion MRI is a process made of four steps.

First, Diffusion Spectrum MRI (DSI) is performed on a subject or sample. This acquisition provides a 3D diffusion function at every location in the brain. This data set is called a diffusion map. It is shaped by the local tissue characteristics, in particular by the orientation of axonal bundles existing in the brain. Second, based on this map we generate a number of 3D curves (called fibers) that follow the path laid by the white matter axonal bundles. Third, independently from the previous step, we use a heuristic that partitions the brain white matter-gray matter interface into small areas of equal surface (called Regions Of Interest-ROIs) covering the whole cortex and deep cerebral nuclei boundaries. Finally, in the fourth step, we combine the output of steps two and three: the ROIs become nodes and the fibers are transformed into edges in the resulting graph. This graph estimates the density of white matter connections between any two regions of gray matter.

Figure 2. Tractography.

A) The result of the “diffusion MRI acquisition” step. In every voxel of a coronal slide the Orientation Density Function (ODF) captures locally for every direction the diffusion “intensity”. B) Zoom in the centrum semi-ovale C) Each ODF is replaced by a set of vectors defining its local maxima. D) Fibers are computed following the local diffusion maxima; they are uniformly initiated over the whole brain white matter. See also Video S1 in Supporting Information.

Figure 3. Basic characteristics of nodes in the graph of brain connectivity.

P(d) [P(s)] is the probability that a randomly chosen node has the degree [strength] equal to d [s]. The node degree distribution (a) and node strength distribution (b) are lin-binned and plotted in log-lin scale. Color code: subject 1 (blue circles), subject 2 (green diamonds)

Figure 4. Basic characteristics of edges in the graph of brain connectivity.

(a) The distribution of edge lengths l in log-lin scale, lin-binned. (b) The distribution of edge weights w in log-log scale, log-binned. (c) Scatter plot of w vs l. The symbols are lin-binned average values for subject 1 (blue circles) and subject 2 (green diamonds).

Figure 5. Average shortest path <sp> and clustering coefficient c as a function of the number of edges in the brain graph |E'|.

The edges are chosen from the set of all edges E either giving the priority to the edges with high weights (“Top-weight edges”, left column), or based on a random subset of fibers (“Random fibers”, right column). As a reference we take a random graph with the same number of nodes and edges, and the same degree distribution. Color code: subject 1 (blue circles), subject 2 (green diamonds), random graph reference (black filled circles). The results are averaged over 10 realizations of the “random fibers” filtering and random graphs; the confidence intervals (not shown) are comparable with the symbol size.

Visual system white matter connectivity derived from tractography: Views from the left (a), from the top (b), zoomed anterior (c) and posterior (d).

White matter–gray matter interfaces: Magenta = posterior part of the thalamus, blue and gray = right and left V1, orange = V2, cyan = V3, red = V5. Fibers: yellow = homotopic V1, red = V1–V2, white = V2–V3, green = V2–V5, blue = lateral geniculate body–V1. See also Video S3 in Supporting Information.