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A method to assess randomness of functional connectivity matrices.

ABSTRACT: BACKGROUND:Functional magnetic resonance imaging (fMRI) allows for the measurement of functional connectivity of the brain. In this context, graph theory has revealed distinctive non-random connectivity patterns. However, the application of graph theory to fMRI often utilizes non-linear transformations (absolute value) to extract edge representations. NEW METHOD:In contrast, this work proposes a mathematical framework for the analysis of randomness directly from functional connectivity assessments. The framework applies random matrix theory to the analysis of functional connectivity matrices (FCMs). The developed randomness measure includes its probability density function and statistical testing method. RESULTS:The utilized data comes from a previous study including 603 healthy individuals. Results demonstrate the application of the proposed method, confirming that whole brain FCMs are not random matrices. On the other hand, several FCM submatrices did not significantly test out of randomness. COMPARISON WITH EXISTING METHODS:The proposed method does not replace graph theory measures; instead, it assesses a different aspect of functional connectivity. Features not included in graph theory are small numbers of nodes, testing submatrices of an FCM and handling negative as well as positive edge values. CONCLUSION:The random test not only determines randomness, but also serves as an indicator of smaller non-random patterns within a non-random FCM. Outcomes suggest that a lower order model may be sufficient as a broad description of the data, but it also indicates a loss of information. The developed randomness measure assesses a different aspect of randomness from that of graph theory.

SUBMITTER: Vergara VM

PROVIDER: S-EPMC5963882 | biostudies-literature | 2018 Jun

REPOSITORIES: biostudies-literature

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A method to assess randomness of functional connectivity matrices.

Vergara Victor M VM Yu Qingbao Q Calhoun Vince D VD

Journal of neuroscience methods 20180327

<h4>Background</h4>Functional magnetic resonance imaging (fMRI) allows for the measurement of functional connectivity of the brain. In this context, graph theory has revealed distinctive non-random connectivity patterns. However, the application of graph theory to fMRI often utilizes non-linear transformations (absolute value) to extract edge representations.<h4>New method</h4>In contrast, this work proposes a mathematical framework for the analysis of randomness directly from functional connect ...[more]

PMID: 29601886

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Project description:Understanding the correlation structure associated with multiple brain measurements informs about potential "functional groupings" and network organization. The correlation structure can be conveniently captured in a matrix format that summarizes the relationships among a set of brain measurements involving two regions, for example. Such functional connectivity matrix is an important component of many types of investigation focusing on network-level properties of the brain, including clustering brain states, characterizing dynamic functional states, performing participant identification (so-called "fingerprinting") understanding how tasks reconfigure brain networks, and inter-subject correlation analysis. In these investigations, some notion of proximity or similarity of functional connectivity matrices is employed, such as their Euclidean distance or Pearson correlation (by correlating the matrix entries). Here, we propose the use of a geodesic distance metric that reflects the underlying non-Euclidean geometry of functional correlation matrices. The approach is evaluated in the context of participant identification (fingerprinting): given a participant's functional connectivity matrix based on resting-state or task data, how effectively can the participant be identified? Using geodesic distance, identification accuracy was over 95% on resting-state data, and exceeded the Pearson correlation approach by 20%. For whole-cortex regions, accuracy improved on a range of tasks by between 2% and as much as 20%. We also investigated identification using pairs of subnetworks (say, dorsal attention plus default mode), and particular combinations improved accuracy over whole-cortex participant identification by over 10%. The geodesic distance also outperformed Pearson correlation when the former employed a fourth of the data as the latter. Finally, we suggest that low-dimensional distance visualizations based on the geodesic approach help uncover the geometry of task functional connectivity in relation to that during resting-state. We propose that the use of the geodesic distance is an effective way to compare the correlation structure of the brain across a broad range of studies.

Dataset Information

A method to assess randomness of functional connectivity matrices.

Publications

A method to assess randomness of functional connectivity matrices.

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