Causal functional connectivity in Alzheimer's disease computed from time series fMRI data

Abstract

Functional connectivity between brain regions is known to be altered in Alzheimer's disease and promises to be a biomarker for early diagnosis. Several approaches for functional connectivity obtain an un-directed network representing stochastic associations (correlations) between brain regions. However, association does not necessarily imply causation. In contrast, Causal Functional Connectivity (CFC) is more informative, providing a directed network representing causal relationships between brain regions. In this paper, we obtained the causal functional connectome for the whole brain from resting-state functional magnetic resonance imaging (rs-fMRI) recordings of subjects from three clinical groups: cognitively normal, mild cognitive impairment, and Alzheimer's disease. We applied the recently developed Time-aware PC (TPC) algorithm to infer the causal functional connectome for the whole brain. TPC supports model-free estimation of whole brain CFC based on directed graphical modeling in a time series setting. We compared the CFC outcome of TPC with that of other related approaches in the literature. Then, we used the CFC outcomes of TPC and performed an exploratory analysis of the difference in strengths of CFC edges between Alzheimer's and cognitively normal groups, based on edge-wise p-values obtained by Welch's t-test. The brain regions thus identified are found to be in agreement with literature on brain regions impacted by Alzheimer's disease, published by researchers from clinical/medical institutions.

Keywords: Alzheimer's disease; brain mapping; causal inference; directed graphical modeling; functional connectivity; functional magnetic resonance imaging.

Figure 1

Steps conveying the concept of the TPC algorithm to infer CFC from observed neural time series data: First the neural time series is transformed to form sequential samples with a maximum time delay of interaction, τ (here τ = 1). Then, Peter-Clark (PC) algorithm is applied on the sequential samples to obtain the unrolled DAG satisfying the Directed Markov Property. Finally the unrolled DAG is transformed to obtain the Rolled CFC between regions.

Figure 2

CFC for an example subject who is CN, estimated by TPC algorithm. (A) The estimated CFC is represented by its adjacency matrix, whose non-zero entry (i, j) represents the connection of region i→j. (B) The CFC is visualized with directed graph edges on the Frontal, Axial and Lateral brain maps (left to right). The nodes correspond to brain region centers, ranging from superficial (light gray) to deeper (darker gray) regions, in the AAL brain atlas.

Figure 3

Comparison and demonstration of FC inferred by three methods: Associative FC using SPC, and Causal FC using TPC and GC. The estimated FC is represented by its adjacency matrix with edge weights, which is symmetric for Associative FC and asymmetric for Causal FC. In the adjacency matrices, a non-zero entry in (i, j) represents the connection of region i→j.

Figure 4

Causal functional connections with edge-weights differing between clinical groups with edge-wise p-values ranging in 0 − 0.05 based on t-test. The edge-wise p-values are represented by a matrix whose entry in (i, j) corresponds to the edge i→j and also represented by graph edges on brain schematics. The brain regions are annotated by Left (L) and Right (R) hemispheres of the brain and Vermis (V).