人类脑图或连接体是当今深入研究的对象。脑科学图解法的优势在于丰富的结构,图论的算法和定义可以应用于人类大脑连接的解剖网络。在这些图表中,顶点对应于灰质的小(1-1.5cm2)区域,两个顶点通过一条边连接,如果基于扩散磁共振成像的工作流程发现了轴突纤维,在大脑白质的那些小灰质区域之间运行。今天,该领域的一个主要问题是发现小灰质区域之间的连接方向。在以前的工作中,我们已经报告了布达佩斯参考Connectome服务器http://connectome的构建。pitgroup.org来自NIHHumanConnectome项目中记录的数据。服务器根据可选择的参数生成版本2中的96个受试者和版本3中的418个受试者的共识脑图。布达佩斯参考Connectome服务器发布后,我们认识到服务器的一个令人惊讶和不可预见的属性。对于k=1,2,...的任何值,服务器可以生成418中至少k个图形中存在的连接的脑图,418.当通过从右到左移动Web服务器上的滑块将k值从k=418更改为1时,当然,越来越多的边出现在共识图中。令人惊讶的观察是,新边缘的外观不是随机的:它类似于生长的灌木。我们将这种现象称为共识连接组动态。我们假设Web服务器中滑块的这种运动可能会从以下意义上复制人脑中连接的发展:所有主题中存在的连接都是最古老的连接,那些只存在于逐渐减少的受试者中的个体大脑发育中的新联系。有关该现象的动画可在https://youtu获得。是/yxlyudPaVUE。基于这一观察和相关假设,我们可以为连接体的某些边缘分配方向,如下所示:令Gk+1表示共识连接体,其中每个边缘至少存在于k+1个图形中,让Gk表示一致性连接体,其中每个边存在于至少k个图中。假设顶点v不连接到Gk+1中的任何其他顶点,并且连接到Gk中的顶点u,其中u连接到已经在Gk+1中的其他顶点。然后我们指导这个(v,u)从v到u的边。
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.