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. 2018 Jun 12;9:439.
doi: 10.3389/fneur.2018.00439. eCollection 2018.

Network Analysis in Disorders of Consciousness: Four Problems and One Proposed Solution (Exponential Random Graph Models)

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Free PMC article

Network Analysis in Disorders of Consciousness: Four Problems and One Proposed Solution (Exponential Random Graph Models)

John Dell'Italia et al. Front Neurol. .
Free PMC article

Abstract

In recent years, the study of the neural basis of consciousness, particularly in the context of patients recovering from severe brain injury, has greatly benefited from the application of sophisticated network analysis techniques to functional brain data. Yet, current graph theoretic approaches, as employed in the neuroimaging literature, suffer from four important shortcomings. First, they require arbitrary fixing of the number of connections (i.e., density) across networks which are likely to have different "natural" (i.e., stable) density (e.g., patients vs. controls, vegetative state vs. minimally conscious state patients). Second, when describing networks, they do not control for the fact that many characteristics are interrelated, particularly some of the most popular metrics employed (e.g., nodal degree, clustering coefficient)-which can lead to spurious results. Third, in the clinical domain of disorders of consciousness, there currently are no methods for incorporating structural connectivity in the characterization of functional networks which clouds the interpretation of functional differences across groups with different underlying pathology as well as in longitudinal approaches where structural reorganization processes might be operating. Finally, current methods do not allow assessing the dynamics of network change over time. We present a different framework for network analysis, based on Exponential Random Graph Models, which overcomes the above limitations and is thus particularly well suited for clinical populations with disorders of consciousness. We demonstrate this approach in the context of the longitudinal study of recovery from coma. First, our data show that throughout recovery from coma, brain graphs vary in their natural level of connectivity (from 10.4 to 14.5%), which conflicts with the standard approach of imposing arbitrary and equal density thresholds across networks (e.g., time-points, subjects, groups). Second, we show that failure to consider the interrelation between network measures does lead to spurious characterization of both inter- and intra-regional brain connectivity. Finally, we show that Separable Temporal ERGM can be employed to describe network dynamics over time revealing the specific pattern of formation and dissolution of connectivity that accompany recovery from coma.

Keywords: coma; disorders of consciousness; exponential random graph model; functional magnetic resonance imaging; network analysis.

Figures

Figure 1
Figure 1
Florentine business ties networks. Florentine business ties data with additional grouping. Left: Network A. Right: Network B. We note that two networks are identical except for the Barbadori family being allocated to the blue group in the left graph and to the green group in the right graph.
Figure 2
Figure 2
Parcellation for structural and functional connectivity. Cortical and subcortical parcellation of the brain data (114). The imaging sessions' data sets were parcellated into 148 ROIs throughout the cortex, sub-cortical nuclei, cerebellum and brainstem. Figure from (13).
Figure 3
Figure 3
Patient recovery: network densities. Top Four Graphs are the thresholded [MANIA; (113)] structural connectivity. The first acute imaging session, second acute imaging session, third acute imaging session and chronic imaging sessions had 6.6, 6, 5.3, and 5.3% densities, respectively. Bottom Four Graphs are the thresholded functional connectivity using partial correlations [MoNeT; (116)]. The first acute imaging session, second acute imaging session, third acute imaging session and chronic imaging sessions had 10.4, 13.5, 12.9, and 14.5% densities, respectively.
Figure 4
Figure 4
Patient recovery ERGM. Comparison of results for the FM and PM for acute sessions 1 and 2. The left figures display the FM mixing term results for the Acute first and second sessions. The mixing term term accounts for the inter- and intra-regional connectivity. The legend displays tints of red for significant positive parameter estimates. The right figures display the PM mixing term results for the Acute first and second sessions. The coloring scheme is the same as the FM. These figures are symmetric within each model because the graphs are undirected.
Figure 5
Figure 5
Patient recovery ERGM. Comparison of results for the FM and PM for acute session 3 and chronic session. The left figures display the FM mixing term results for the Acute third session and Chronic session. The mixing term term accounts for the inter- and intra-regional connectivity. The legend displays tints of red for significant positive parameter estimates and the significant negative parameter estimates are colored in tints of blue. The right figures display the PM mixing term results for the Acute third session and Chronic session. The coloring scheme is the same as the FM. These figures are symmetric within each model because the graphs are undirected.
Figure 6
Figure 6
Patient recovery ERGM. Goodness of fit plots for the four FM (i.e., Acute Session 1, Acute Session 2, Acute Session 3 and Chronic Session). The black line marks the respective networks; the box-and-wiskers indicate the model data obtained from the 1000 simulations of each model (see section 2.6).
Figure 7
Figure 7
Patient Recovery STERGM. Results for the formation (left) and dissolution (right) models over 6 months. The mixing term accounts for the inter- and intra-regional connectivity that form over 6 months. The legend displays tints of red for significant positive parameter estimates and the significant negative parameter estimates are colored in tints of blue. The right figure displays the dissolution model STERGM mixing term results. The coloring scheme is the same as the formation model, but the mixing term represents the connectivity that are dissolved or preserved over 6 months. These figures are symmetric within each model because the graphs are undirected.
Figure 8
Figure 8
Patient recovery STERGM. Goodness of fit plots for the formation (top) and dissolution (bottom) models. The black line marks the formation and dissolution networks observed over time in the patient's graphs between the first Acute session and the Chronic session; the box-and-wiskers indicate the model data obtained from the 1000 simulations of each model (see section 2.6).

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