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J Neurosci Methods. 2018 Jun 1;303:146-158. doi: 10.1016/j.jneumeth.2018.03.015. Epub 2018 Mar 27.

A method to assess randomness of functional connectivity matrices.

Author information

1
The Mind Research Network and Lovelace Biomedical and Environmental Research Institute, 1101 Yale Blvd. NE, Albuquerque, NM 87106, United States. Electronic address: vvergara@mrn.org.
2
The Mind Research Network and Lovelace Biomedical and Environmental Research Institute, 1101 Yale Blvd. NE, Albuquerque, NM 87106, United States. Electronic address: qyu@mrn.org.
3
The Mind Research Network and Lovelace Biomedical and Environmental Research Institute, 1101 Yale Blvd. NE, Albuquerque, NM 87106, United States; Department of Electrical and Computer Engineering, MSC01 1100, 1 University of New Mexico Albuquerque, NM 87131, United States. Electronic address: vcalhoun@mrn.org.

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.

KEYWORDS:

Functional MRI; Functional connectivity; Random matrix theory; Resting state network

PMID:
29601886
PMCID:
PMC5963882
[Available on 2019-06-01]
DOI:
10.1016/j.jneumeth.2018.03.015

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