Graph analysis and modularity of brain functional connectivity networks: searching for the optimal threshold

Neuroimaging data can be represented as networks of nodes and edges that capture the topological organization of the brain connectivity. Graph theory provides a general and powerful framework to study these networks and their structure at various scales. By way of example, community detection methods have been widely applied to investigate the modular structure of many natural networks, including brain functional connectivity networks. Sparsification procedures are often applied to remove the weakest edges, which are the most affected by experimental noise, and to reduce the density of the graph, thus making it theoretically and computationally more tractable. However, weak links may also contain significant structural information, and procedures to identify the optimal tradeoff are the subject of active research. Here, we explore the use of percolation analysis, a method grounded in statistical physics, to identify the optimal sparsification threshold for community detection in brain connectivity networks. By using synthetic networks endowed with a ground-truth modular structure and realistic topological features typical of human brain functional connectivity networks, we show that percolation analysis can be applied to identify the optimal sparsification threshold that maximizes information on the networks' community structure. We validate this approach using three different community detection methods widely applied to the analysis of brain connectivity networks: Newman's modularity, InfoMap and Asymptotical Surprise. Importantly, we test the effects of noise and data variability, which are critical factors to determine the optimal threshold. This data-driven method should prove particularly useful in the analysis of the community structure of brain networks in populations characterized by different connectivity strengths, such as patients and controls.Comment: 15 pages, 7 figure

A Monte Carlo Evaluation of Weighted Community Detection Algorithms

The past decade has been marked with a proliferation of community detection algorithms that aim to organize nodes (e.g., individuals, brain regions, variables) into modular structures that indicate subgroups, clusters, or communities. Motivated by the emergence of big data across many fields of inquiry, these methodological developments have primarily focused on the detection of communities of nodes from matrices that are very large. However, it remains unknown if the algorithms can reliably detect communities in smaller graph sizes (i.e., 1000 nodes and fewer) which are commonly used in brain research. More importantly, these algorithms have predominantly been tested only on binary or sparse count matrices and it remains unclear the degree to which the algorithms can recover community structure for different types of matrices, such as the often used cross-correlation matrices representing functional connectivity across predefined brain regions. Of the publicly available approaches for weighted graphs that can detect communities in graph sizes of at least 1000, prior research has demonstrated that Newman's spectral approach (i.e., Leading Eigenvalue), Walktrap, Fast Modularity, the Louvain method (i.e., multilevel community method), Label Propagation, and Infomap all recover communities exceptionally well in certain circumstances. The purpose of the present Monte Carlo simulation study is to test these methods across a large number of conditions, including varied graph sizes and types of matrix (sparse count, correlation, and reflected Euclidean distance), to identify which algorithm is optimal for specific types of data matrices. The results indicate that when the data are in the form of sparse count networks (such as those seen in diffusion tensor imaging), Label Propagation and Walktrap surfaced as the most reliable methods for community detection. For dense, weighted networks such as correlation matrices capturing functional connectivity, Walktrap consistently outperformed the other approaches for recovering communities

Multivariate functional network connectivity for disorders of consciousness

Recent evidence suggests that healthy brain is organized on large-scale spatially distant brain regions, which are temporally synchronized. These regions are known as resting state networks (RSNs). The level of interaction among these functional entities has been studied in the so called functional network connectivity (FNC). FNC aims to quantify the level of interaction between pairs of RSNs, which commonly emerge at similar spatial scale. Nevertheless, the human brain is a complex functional structure which is partitioned into functional regions that emerge at multiple spatial scales. In this work, we propose a novel multivariate FNC strategy to study interactions among communities of RSNs, these communities may emerge at different spatial scales. For this, first a community or hyperedge detection strategy was used to conform groups of RSNs with a similar behavior. Following, a distance correlation measurement was employed to quantify the level of interaction between these communities. The proposed strategy was evaluated in the characterization of patients with disorders of consciousness, a highly challenging problem in the clinical setting. The results suggest that the proposed strategy may improve the capacity of characterization of these brain altered conditions

Interpretation of the Precision Matrix and Its Application in Estimating Sparse Brain Connectivity during Sleep Spindles from Human Electrocorticography Recordings

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an 8 x 8 electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present

Fronto-parietal subnetworks flexibility compensates for cognitive decline due to mental fatigue

Fronto‐parietal subnetworks were revealed to compensate for cognitive decline due to mental fatigue by community structure analysis. Here, we investigate changes in topology of subnetworks of resting‐state fMRI networks due to mental fatigue induced by prolonged performance of a cognitively demanding task, and their associations with cognitive decline. As it is well established that brain networks have modular organization, community structure analyses can provide valuable information about mesoscale network organization and serve as a bridge between standard fMRI approaches and brain connectomics that quantify the topology of whole brain networks. We developed inter‐ and intramodule network metrics to quantify topological characteristics of subnetworks, based on our hypothesis that mental fatigue would impact on functional relationships of subnetworks. Functional networks were constructed with wavelet correlation and a data‐driven thresholding scheme based on orthogonal minimum spanning trees, which allowed detection of communities with weak connections. A change from pre‐ to posttask runs was found for the intermodule density between the frontal and the temporal subnetworks. Seven inter‐ or intramodule network metrics, mostly at the frontal or the parietal subnetworks, showed significant predictive power of individual cognitive decline, while the network metrics for the whole network were less effective in the predictions. Our results suggest that the control‐type fronto‐parietal networks have a flexible topological architecture to compensate for declining cognitive ability due to mental fatigue. This community structure analysis provides valuable insight into connectivity dynamics under different cognitive states including mental fatigue

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we explore the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.Comment: Main Text: 19 pages, 4 figures Supplementary Materials: 34 pages, 4 figures, 3 table