How to Direct the Edges of the Connectomes: Dynamics of the Consensus Connectomes and the Development of the Connections in the Human Brain

Abstract

The human braingraph or the connectome is the object of an intensive research today. The advantage of the graph-approach to brain science is that the rich structures, algorithms and definitions of graph theory can be applied to the anatomical networks of the connections of the human brain. In these graphs, the vertices correspond to the small (1–1.5 cm2) areas of the gray matter, and two vertices are connected by an edge, if a diffusion-MRI based workflow finds fibers of axons, running between those small gray matter areas in the white matter of the brain. One main question of the field today is discovering the directions of the connections between the small gray matter areas. In a previous work we have reported the construction of the Budapest Reference Connectome Server http://connectome.pitgroup.org from the data recorded in the Human Connectome Project of the NIH. The server generates the consensus braingraph of 96 subjects in Version 2, and of 418 subjects in Version 3, according to selectable parameters. After the Budapest Reference Connectome Server had been published, we recognized a surprising and unforeseen property of the server. The server can generate the braingraph of connections that are present in at least k graphs out of the 418, for any value of k = 1, 2, …, 418. When the value of k is changed from k = 418 through 1 by moving a slider at the webserver from right to left, certainly more and more edges appear in the consensus graph. The astonishing observation is that the appearance of the new edges is not random: it is similar to a growing shrub. We refer to this phenomenon as the Consensus Connectome Dynamics. We hypothesize that this movement of the slider in the webserver may copy the development of the connections in the human brain in the following sense: the connections that are present in all subjects are the oldest ones, and those that are present only in a decreasing fraction of the subjects are gradually the newer connections in the individual brain development. An animation on the phenomenon is available at https://youtu.be/yxlyudPaVUE. Based on this observation and the related hypothesis, we can assign directions to some of the edges of the connectome as follows: Let Gk + 1 denote the consensus connectome where each edge is present in at least k+1 graphs, and let Gk denote the consensus connectome where each edge is present in at least k graphs. Suppose that vertex v is not connected to any other vertices in Gk+1, and becomes connected to a vertex u in Gk, where u was connected to other vertices already in Gk+1. Then we direct this (v, u) edge from v to u.

The dorsal striatum and the dynamics of the consensus connectomes in the frontal lobe of the human brain

“…We hypothesize that -similarly as in the whole braingraph, observed in [26] -the edges whose frequencies are higher were developed in an earlier stage of the brain development than those with lower frequencies. We think that our videos at https://youtu.be/wBciB2eW6_8 for the frontal lobe and https://youtu.be/yxlyudPaVUE for the whole brain approximately reconstruct this development.…”

“…Since the difference from the random appearances of the edges is very clear on the visualization and also in Figure 2 in [26], we have presented a hypothesis in [26] as follows: we think that the CCD phenomenon copies the individual development of the cerebral connections in a way that the oldest connections are those that are present in all or almost all connectomes, and gradually the younger connections are appearing as new edges in k-consensus connectomes, by decreasing the value of k one-by-one.…”

“…The astonishing observation is that the growing number of edges build up a developing, tree-like graph; that is, the edges do not appear randomly, but they appear as the branches of a growing tree. For the whole braingraph we have reported this phenomenon in [26] and have visualized that on a video at https://youtu.be/yxlyudPaVUE.…”

Parameterizable consensus connectomes from the Human Connectome Project: the Budapest Reference Connectome Server v3.0

“…Version 2.0 of the webserver (Szalkai et al 2015) was compiled from 96 connectomes, computed from the Human Connectome Project's (McNab et al 2013) 500-subjects release. We have reported a surprising and unforeseen discovery, found by changing the parameters of the version 2.0 of the webserver in Kerepesi et al (2016).…”

The Frequent Network Neighborhood Mapping of the human hippocampus shows much more frequent neighbor sets in males than in females

“…While it seems to be clear for all brain scientists that the complex connection patterns of the neurons play a fundamental role in brain function [1,2,3], when the large-scale, macroscopic description of these connections has become available by the development of diffusion MRI techniques, it turned out that novel methods are needed to handle these large graphs [1,2]. MRI-mapped human connectomes have only several hundred or at most one thousand vertices today [4], and, therefore, more complex, more refined graph theoretical algorithms [5,6,7] can be applied for their analysis than the widely followed network science approach, originally developed for tens of millions of vertices of the web graph [8].…”