Kerepesi Csaba, Szalkai Balázs, Varga Bálint, Grolmusz Vince
PIT Bioinformatics Group, Eötvös University, H-1117 Budapest, Hungary.
Institute for Computer Science and Control, H-1111 Budapest, Hungary.
PLoS One. 2016 Jun 30;11(6):e0158680. doi: 10.1371/journal.pone.0158680. eCollection 2016.
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.
人类脑图谱或连接组是当今一项深入研究的对象。将图论方法应用于脑科学的优势在于，图论丰富的结构、算法和定义可应用于人类大脑连接的解剖网络。在这些图中，顶点对应灰质的小区域（1 - 1.5平方厘米），如果基于扩散磁共振成像的工作流程发现轴突纤维在脑白质中的那些小灰质区域之间运行，则两个顶点由一条边相连。该领域当前的一个主要问题是发现小灰质区域之间连接的方向。在之前的一项工作中，我们报告了根据美国国立卫生研究院人类连接组计划记录的数据构建的布达佩斯参考连接组服务器http://connectome.pitgroup.org。该服务器根据可选择的参数生成第2版中96名受试者以及第3版中418名受试者的共识脑图谱。布达佩斯参考连接组服务器发布后，我们认识到该服务器一个令人惊讶且未曾预料到的特性。对于k = 1, 2, …, 418的任何值，该服务器都可以生成在418个图谱中至少k个图谱中存在的连接的脑图谱。当通过在网络服务器上从右向左移动滑块将k值从k = 418逐渐减小到1时，共识图中肯定会出现越来越多的边。令人惊讶的观察结果是，新边的出现并非随机：它类似于一棵正在生长的灌木。我们将这种现象称为共识连接组动态。我们假设在网络服务器上移动滑块的这种操作可能在以下意义上复制了人类大脑中连接的发育过程：在所有受试者中都存在的连接是最古老的，而那些仅在受试者中所占比例逐渐减少的连接在个体大脑发育中逐渐是较新的连接。关于该现象的动画可在https://youtu.be/yxlyudPaVUE上观看。基于这一观察结果和相关假设，我们可以按如下方式为连接组的某些边指定方向：设Gk + 1表示每个边至少在k + 1个图谱中存在的共识连接组，设Gk表示每个边至少在k个图谱中存在的共识连接组。假设顶点v在Gk + 1中不与任何其他顶点相连，而在Gk中与顶点u相连，其中u在Gk + 1中已经与其他顶点相连。那么我们将这条(v, u)边从v指向u。
