An information network flow approach for measuring functional connectivity and predicting behavior

Abstract

Introduction: Connectome-based predictive modeling (CPM) is a recently developed machine-learning-based framework to predict individual differences in behavior from functional brain connectivity (FC). In these models, FC was operationalized as Pearson's correlation between brain regions' fMRI time courses. However, Pearson's correlation is limited since it only captures linear relationships. We developed a more generalized metric of FC based on information flow. This measure represents FC by abstracting the brain as a flow network of nodes that send bits of information to each other, where bits are quantified through an information theory statistic called transfer entropy.

Methods: With a sample of individuals performing a sustained attention task and resting during functional magnetic resonance imaging (fMRI) (n = 25), we use the CPM framework to build machine-learning models that predict attention from FC patterns measured with information flow. Models trained on n - 1 participants' task-based patterns were applied to an unseen individual's resting-state pattern to predict task performance. For further validation, we applied our model to two independent datasets that included resting-state fMRI data and a measure of attention (Attention Network Task performance [n = 41] and stop-signal task performance [n = 72]).

Results: Our model significantly predicted individual differences in attention task performance across three different datasets.

Conclusions: Information flow may be a useful complement to Pearson's correlation as a measure of FC because of its advantages for nonlinear analysis and network structure characterization.

Keywords: functional connectivity; information flow; predictive model; resting-state fMRI connectivity; sustained attention.

Figure 1

Simple example of the maximum flow problem: a directed graph where each edge's weight represents the edge's capacity, which is the greatest amount of flow that can go through that edge. Although one can only flow two units directly from A to C, one can also flow three units using the alternative path from A to B and then from B to C, which means the maximum flow from A to C is equal to 5

Figure 2

Steps used to construct an individual's information flow connectivity matrix. (a) Each individual's fMRI data are parcellated into n ROI time series, depending on the parcellation used (see Step 1: parcellation). (b) A full transfer entropy matrix (TE^full) is populated with all pairwise transfer entropies among the ROI time series. (c) Negative transfer entropy values are set to 0 to create TE^sparse (see Step 2: measuring functional connectivity with transfer entropy). (d) Cells in the TE^sparse matrix are used to construct graphs in which edges are defined as the maximum flow between each pair of nodes. (e) These graphs are represented as a new maximum flow matrix (see Step 3: computing higher‐order connectivity features with maximum flow). (f) The maximum flow matrix is then reduced over the anatomical lobe groups (see Step 3: computing higher‐order connectivity features with maximum flow)

Figure 3

Overview of our predictive modeling pipeline. Task‐based information flow matrices are used to train a linear model that can predict a subject's behavior score using his/her resting‐state information flow connectome

Figure 4

Group averaged resting‐state information flow connectivity matrices across datasets. The scale of the color bar is in bits

Figure 5

Results from three different types of flows: full flow matrix with no anatomical restriction (described in Methods), full flow matrix with anatomical restriction (described in Methods), and the reduced flow matrix (described in Methods). Here, we see that models based on the reduced information flow matrix significantly predict individual differences in attentional performance in the gradCPT sample, whereas the models based on the other two flow matrices did not yield significant predictions

Figure 6

Internal validation results. Predicted and actual d′ results were correlated using Spearman's rank correlation. Statistical significance was determined by randomly permuting subjects’ d′ scores for 10,000 iterations, repeating the prediction analysis, and determining the fraction of correlations between predicted and actual scores that were as extreme as the original data. The relationship between observed and predicted d′ scores remains significant in permutation testing if the two lowest predicted d′ scores are excluded (ρ = 0.568, p = 0.0048)

Figure 7

External validation results for Attention Network Task (ANT) and methylphenidate (MPH). Both ANT and MPH predictions were statistically significant. All relationships between observed and predicted behavioral scores are in the expected direction, as gradCPT d′ and stop‐signal go rate scores correspond to better attention but higher ANT RT variability scores correspond to worse attention

Figure 8

Distribution of flows included in the final predictive model in external testing. The connections are colored by their relative contribution to the model. A flow's contribution was calculated by summing the absolute value of its weight in a principal component across all components

Figure 9

Comparison of our results with those of previous studies. We compared our model to other models that, like our model, were trained on task‐based fMRI and applied to resting‐state fMRI data. Yoo et al. (2018) compare different models, so just as we used the model that performed best in internal validation, and we compared the model in Yoo et al. (2018) that performed best in internal validation when trained on task‐based fMRI and applied to resting‐state fMRI. Note that we previously evaluated predictions based on Spearman's correlation. However, since previous publications were evaluated based on Pearson's correlation, all the results reported here are with Pearson's correlation