Brain Network Analysis: A Review on Multivariate Analytical Methods

Abstract

Despite the explosive growth of neuroimaging studies aimed at analyzing the brain as a complex system, critical methodological gaps remain to be addressed. Most tools currently used for analyzing network data of the brain are univariate in nature and are based on assumptions borne out of previous techniques not directly related to the big and complex data of the brain. Although graph-based methods have shown great promise, the development of principled multivariate models to address inherent limitations of graph-based methods, such as their dependence on network size and degree distributions, and to allow assessing the effects of multiple phenotypes on the brain and simulating brain networks has largely lagged behind. Although some studies have been made in developing multivariate frameworks to fill this gap, in the absence of a "gold-standard" method or guidelines, choosing the most appropriate method for each study can be another critical challenge for investigators in this multidisciplinary field. Here, we briefly introduce important multivariate methods for brain network analyses in two main categories: data-driven and model-based methods. We discuss whether/how such methods are suited for examining connectivity (edge-level), topology (system-level), or both. This review will aid in choosing an appropriate multivariate method with respect to variables such as network type, number of subjects and brain regions included, and the interest in connectivity, topology, or both. This review is aimed to be accessible to investigators from different backgrounds, with a focus on applications in brain network studies, though the methods may be applicable in other areas too. Impact statement As the U.S. National Institute of Health notes, the rich biomedical data can greatly improve our knowledge of human health if new analytical tools are developed, and their applications are broadly disseminated. A major challenge in analyzing the brain as a complex system is about developing parsimonious multivariate methods, and particularly choosing the most appropriate one among the existing methods with respect to the study variables in this multidisciplinary field. This study provides a review on the most important multivariate methods to aid in helping the most appropriate ones with respect to the desired variables for each study.

Keywords: brain networks; connectivity; data-driven; model-based; multivariate.

FIG. 1.

Schematic of a univariate approach for analyzing brain networks. This figure illustrates the most commonly used univariate approach in comparing brain networks for two sample population studies, labeled as group 1 and group 2. Brain networks are compared via either a massive univariate comparison of individual connections or a univariate comparison of network measures across the groups. In this figure, a sample individual connection between two regions from the AAL atlas (Tzourio-Mazoyer et al, 2002) is shown for the networks of group 1 and group 2 (the connection between ROI 7: SFG and ROI 61: IP). Here, the connection strength is shown with thickness and color. Also, for ROI 7 in the AAL atlas, that is, Superior frontal gyrus, two sample network measures, including degree and clustering coefficient, are shown for the four networks above. The size and color of this node represent its degree. Degree is computed from the sum of weights of the edges connected to that node, and the clustering coefficient is computed using the number of triangles formed among neighbors of that node relative to the number of all possible triangles. The individual connection strength and nodal (/or global) network measures are then fed into averaging and univariate approaches to compare the groups. The implication of this approach has been discussed in detail in this article. Networks and the networks measures shown in this figure are generated using the BrainNet Viewer (Xia et al, 2013). AAL, automated anatomical labeling; IP, inferior parietal; ROI, region of interest; SFG, superior frontal gyrus.