A Novel Joint Brain Network Analysis Using Longitudinal Alzheimer’s Disease Data

There is well-documented evidence of brain network differences between individuals with Alzheimer’s disease (AD) and healthy controls (HC). To date, imaging studies investigating brain networks in these populations have typically been cross-sectional, and the reproducibility of such findings is somewhat unclear. In a novel study, we use the longitudinal ADNI data on the whole brain to jointly compute the brain network at baseline and one-year using a state of the art approach that pools information across both time points to yield distinct visit-specific networks for the AD and HC cohorts, resulting in more accurate inferences. We perform a multiscale comparison of the AD and HC networks in terms of global network metrics as well as at the more granular level of resting state networks defined under a whole brain parcellation. Our analysis illustrates a decrease in small-worldedness in the AD group at both the time points and also identifies more local network features and hub nodes that are disrupted due to the progression of AD. We also obtain high reproducibility of the HC network across visits. On the other hand, a separate estimation of the networks at each visit using standard graphical approaches reveals fewer meaningful differences and lower reproducibility.

Mean Clustering Coefficient (MCC) A measure of the interconnectedness of the brain network calculated by counting how many of a brain node's neighbors are also neighbors of each other, averaged over all nodes.
Small-Worldedness A measure of whether or not the brain exhibits small world properties calculated by examining the ratio of normalized mean clustering coefficient to normalized characteristic path length, SW = MCC/MCC 0 CPL/CPL 0 . Here MCC 0 ,CPL 0 , refer to the metrics corresponding to a baseline distribution for each cohort and visit by generating 1000 surrogate random networks with the same connection density as the estimated graph for the cohort/visit and then calculating the average CPL and MCC for these surrogate graphs. The ratio of each metric to the average over the surrogate graphs is then taken as the normalized metric. A ratio SW > 1 indicates that the estimated brain network exhibits more small-worldedness than a random network.
Betweenness A node-specific measure of importance, betweenness examines how frequently a node is a part of the shortest path between two other nodes. High values of betweenness suggest that a node may be a hub node, as a large number of the optimal paths of information transmission pass through it. We calculated a normalized betweeenness metric by dividing by the average betwenness within each cohort/visit [4].
Participation Coefficient Another node-specific measure of importance, participation examines the proportion of a node's connections that are to RSNs other than the one the node is a member of. Large values of the participation coefficient indicate that a significant amount of the node's communication is with other RSNs of the brain. For this metric, only the 232 nodes belonging to a known RSN were used.

Description of Bayesian Joint Network Learning
Suppose y g,it denotes the p-dimensional vector of prewhitened fMRI measurements over p brain regions (p = 264 for the Power atlas) for the t-th brain volume at baseline (g = 0) and one year follow-up (g = 1) for the i-th subject (i = 1, . . . , n). Our analysis jointly estimates the networks at baseline and one-year follow-up for AD subjects and then performs the analysis separately for HC subjects. We model where N p denotes a p-dimensional Gaussian distribution, M + p denotes the space of all symmetric and positive definite matrices, and Ω g captures the sparse inverse covariance or precision matrix encoding the network at longitudinal visit g = 0, 1. The BJNL approach specifies spike and slab graphical lasso priors on the inverse covariance off-diagonal elements, and Exponential type priors on the diagonal elements of the precision matrix. The prior specification is designed to ensure that the precision matrices are drawn from M + p , the space of all positive-definite precision matrices. The spike and slab graphical lasso priors on the precision off-diagonals ensure that these elements are assigned small absolute values close to zero corresponding to unimportant edges (under a Laplace type specification) with some probability π, and large absolute values corresponding to significant edges in the network with probability 1 − π. These edge inclusion probabilities are edge-specific and network-specific, and are constructed as flexible functions of a shared component that is common across networks and differential components that are network-specific. Each edge inclusion probability is jointly estimated by pooling information across the baseline and one-year follow-up, which results in the joint estimation of the longitudinal networks. Once these inclusion probabilities are estimated, the elements of the precision matrices can be sampled using closed form posterior distributions. The edge-inclusion probabilities are thresholded in a systematic manner in order to infer important connections, which is designed to control the false discovery rate and yield meaningful estimates for the network. Figure S1. Locations of the nodes with the top 10 largest percent change in GE upon removal in HC and AD identified using the graphical lasso. The nodes are colored by resting state network. These nodes exhibited very small changes in the magnitude of the percent change between AD and HC at baseline and one-year and in several cases there were no differences identified at all.

MCI Analysis
We analyzed the early MCI (EMCI) and late MCI (LMCI) patients using the same procedure as for the HC and AD patients. Only MCI patients who were amyloid positive were included in the analysis. There were 14 EMCI (9 males, average age 71.0, average education = 15.6 years) and 14 LMCI subjects (7 males, average age =72.1, average education = 16.7 years). We present some select results of the BJNL analysis below. Table S1 displays the number of edges in each group at baseline and one-year follow up. Figure S3 displays the corresponding adjacency matrices. Graph metric densities for each group and time point are presented in Figure S4. We see that, in general, the MCI patients are more similar to the HC subjects than to the AD patients.