A Graph Theoretical Approach to Study the Organization of the Cortical Networks during Different Mathematical Tasks

The two core systems of mathematical processing (subitizing and retrieval) as well as their functionality are already known and published. In this study we have used graph theory to compare the brain network organization of these two core systems in the cortical layer during difficult calculations. We have examined separately all the EEG frequency bands in healthy young individuals and we found that the network organization at rest, as well as during mathematical tasks has the characteristics of Small World Networks for all the bands, which is the optimum organization required for efficient information processing. The different mathematical stimuli provoked changes in the graph parameters of different frequency bands, especially the low frequency bands. More specific, in Delta band the induced network increases it’s local and global efficiency during the transition from subitizing to retrieval system, while results suggest that difficult mathematics provoke networks with higher cliquish organization due to more specific demands. The network of the Theta band follows the same pattern as before, having high nodal and remote organization during difficult mathematics. Also the spatial distribution of the network’s weights revealed more prominent connections in frontoparietal regions, revealing the working memory load due to the engagement of the retrieval system. The cortical networks of the alpha brainwaves were also more efficient, both locally and globally, during difficult mathematics, while the fact that alpha’s network was more dense on the frontparietal regions as well, reveals the engagement of the retrieval system again. Concluding, this study gives more evidences regarding the interaction of the two core systems, exploiting the produced functional networks of the cerebral cortex, especially for the difficult mathematics.

数学加工的两大核心系统——瞬时计数（subitizing）与信息提取（retrieval）——及其功能已为学界熟知并公开发表。本研究借助图论（graph theory），对比了皮层层内这两大核心系统在高难度计算过程中的脑网络组织模式。研究分别针对健康青年个体的全部脑电图（EEG）频段开展分析，结果显示：静息状态与数学任务态下的脑网络组织，在所有频段均具备小世界网络（Small World Networks）的特征，而这正是高效信息加工所需的最优组织形式。不同数学刺激可引发不同频段的图论参数发生变化，尤以低频频段最为显著。具体而言，当认知加工从瞬时计数系统切换至信息提取系统时，δ频段（Delta band）的诱发网络其局部与全局效率均有所提升；研究结果同时表明，高难度数学任务会催生具有更高团簇化组织特征的网络，这源于任务对认知加工的特异性需求。θ频段（Theta band）的脑网络呈现出一致的变化模式：在高难度数学任务中，其节点特性与远程连接特性均处于较高水平。此外，脑网络权重的空间分布显示，额顶叶区域（frontoparietal regions）的连接更为显著，这反映了信息提取系统参与过程中所带来的工作记忆负荷。α脑电波（alpha brainwaves）对应的皮层网络在高难度数学任务中，局部与全局效率同样有所提升；且该频段的脑网络在额顶叶区域同样更为密集，这再次印证了信息提取系统的参与。综上，本研究借助大脑皮层的功能网络，为两大核心系统的交互机制提供了更多实证依据，尤其针对高难度数学加工场景。