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This tutorial paper refers to the use of graph-theoretic concepts for analyzing brain signals. For didactic purposes it splits into two parts: theory and application. In the first part, we commence by introducing some basic elements from graph theory and stemming algorithmic tools, which can be employed for data-analytic purposes. Next, we describe how these concepts are adapted for handling evolving connectivity and gaining insights into network reorganization. Finally, the notion of signals residing on a given graph is introduced and elements from the emerging field of graph signal processing (GSP) are provided. The second part serves as a pragmatic demonstration of the tools and techniques described earlier. It is based on analyzing a multi-trial dataset containing single-trial responses from a visual ERP paradigm. The paper ends with a brief outline of the most recent trends in graph theory that are about to shape brain signal processing in the near future and a more general discussion on the relevance of graph-theoretic methodologies for analyzing continuous-mode neural recordings.
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Recent developments in graph theoretic analysis of complex networks have led to deeper understanding of brain networks. Many complex networks show similar macroscopic behaviors despite differences in the microscopic details. Probably two most often observed characteristics of complex networks are scale-free and small-world properties. In this paper, we will explore whether brain networks follow scale-free and small-worldness among other graph theory properties.
The current-source density (CSD) analysis is a widely used method in brain electrophysiology, but this method rests on a series of assumptions, namely that the surrounding extracellular medium is resistive and uniform, and in som
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Emotion perception is essential to affective and cognitive development which involves distributed brain circuits. The ability of emotion identification begins in infancy and continues to develop throughout childhood and adolescence. Understanding the development of brains emotion circuitry may help us explain the emotional changes observed during adolescence. Our previous study delineated the trajectory of brain functional connectivity (FC) from late childhood to early adulthood during emotion identification tasks. In this work, we endeavour to deepen our understanding from association to causation. We proposed a Bayesian incorporated linear non-Gaussian acyclic model (BiLiNGAM), which incorporated our previous association model into the prior estimation pipeline. In particular, it can jointly estimate multiple directed acyclic graphs (DAGs) for multiple age groups at different developmental stages. Simulation results indicated more stable and accurate performance over various settings, especially when the sample size was small (high-dimensional cases). We then applied to the analysis of real data from the Philadelphia Neurodevelopmental Cohort (PNC). This included 855 individuals aged 8-22 years who were divided into five different adolescent stages. Our network analysis revealed the development of emotion-related intra- and inter- modular connectivity and pinpointed several emotion-related hubs. We further categorized the hubs into two types: in-hubs and out-hubs, as the center of receiving and distributing information. Several unique developmental hub structures and group-specific patterns were also discovered. Our findings help provide a causal understanding of emotion development in the human brain.
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