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

Abstract

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.

Cognitive Network Neuroscience

“…During transitions from subitizing (rapid counting of small numbers of objects) to retrieval, increased local and global network efficiency were observed in the delta band. Difficult mathematics resulted in increased cliquishness in delta and theta bands (Klados et al, 2013). …”

“…Moreover, network approaches have led to the discovery of a spatiotemporal nesting of processes: cognitive control may be mediated through distributed network processes via increased modularization in dissociable frequency bands. In distinction to working memory, cognitive control may be executed across brain networks in the delta and theta bands (Klados et al, 2013). Limits to sustaining cognitive control may result from network failure to maintain difficult-to-reach states (Giessing et al, 2013).…”

Math anxiety: Brain cortical network changes in anticipation of doing mathematics

“…To overcome this problem, the cortical activity was obtained from the 57 EEG signals, by employing a realistic head model, a cortical dipole model and the inverse solutions (He, Wang, & Wu, 1999;M. A. Klados et al, 2013;Mattia et al, 2009).…”

“…MSC was used because, compared to other metrics, it produces networks closer to the brain's topology (Lithari et al, 2012). In the herein setup we have used 2 sec-long sliding windows with 50% overlap (for the mathematical formulation of MSC see (Klados et al, 2013) To investigate the impact of MA into the intrinsic networks' structure the following parameters were employed: …”

Optimized Gamma Synchronization Enhances Functional Binding of Fronto-Parietal Cortices in Mathematically Gifted Adolescents during Deductive Reasoning

“…There is a limitation that the EEG-based brain connectivity analysis was influenced by the volume conduction, which was caused by the variation of the electrical conductivity among the different head layers (Langer et al, 2012; Klados et al, 2013). To avoid this problem, the scalp-recorded EEG signals were transformed into the source space, which was performed by using the source estimation procedure of the Brainstorm Toolbox that is documented and freely available at (Tadel et al, 2011).…”