Bayesian modeling of dependence in brain connectivity data

Abstract

Brain connectivity studies often refer to brain areas as graph nodes and connections between nodes as edges, and aim to identify neuropsychiatric phenotype-related connectivity patterns. When performing group-level brain connectivity alternation analyses, it is critical to model the dependence structure between multivariate connectivity edges to achieve accurate and efficient estimates of model parameters. However, specifying and estimating dependencies between connectivity edges presents formidable challenges because (i) the dimensionality of parameters in the covariance matrix is high (of the order of the fourth power of the number of nodes); (ii) the covariance between a pair of edges involves four nodes with spatial location information; and (iii) the dependence structure between edges can be related to unknown network topological structures. Existing methods for large covariance/precision matrix regularization and spatial closeness-based dependence structure specification/estimation models may not fully address the complexity and challenges. We develop a new Bayesian nonparametric model that unifies information from brain network areas (nodes), connectivity (edges), and covariance between edges by constructing the function of covariance matrix based on the underlying network topological structure. We perform parameter estimation using an efficient Markov chain Monte Carlo algorithm. We apply our method to resting-state functional magnetic resonance imaging data from 60 subjects of a schizophrenia study and simulated data to demonstrate the performance of our method.

Temporal-thalamic and cingulo-opercular connectivity in people with schizophrenia

“…Resting-state functional T2*-weighted images were obtained using a single-shot gradient-recalled, EPI pulse sequence (TR: 2000 ms, TE: 30 ms, 128 × 128 matrix, 1.72 × 1.72 mm 2 in-plane resolution, 4 mm slice thickness, 37 axial slices, and 444 volumes). Subsets of these data have been previously reported using different analytic methods ( Adhikari et al, 2019b , Chen et al, 2020b ).…”

“…However, a hybrid, analytic method may be more attractive in revealing an organized sub-network in the brain where most contained edges are differentially expressed. Here, we conduct such a hybrid analysis using network object-oriented algorithms ( Chen et al, 2020a , Chen et al, 2020b , Chen et al, 2015a , Chen et al, 2015b , Chen et al, 2018 ).…”

“…However, identifying such phenotype-related sub-networks from the whole brain connectome is challenging due to the high dimensionality and complex topological structure of connectome data and substantial noise leading to false positive errors ( Chen et al, 2020a , Chen et al, 2015b , Chen et al, 2018 ). Importantly, our approach is very robust in the face of these limitations as it simultaneously reduces network-level false positive discovery rates and improves power yielding more reliable results ( Chen et al, 2020b ). Using this approach, we aimed to examine the integrity of thalamic and cingulo-opercular rsFC between people with SZ and HCs.…”

Characterizing the Complexity of Weighted Networks via Graph Embedding and Point Pattern Analysis

“…The functional brain networks are more disturbed and less organized in male patients than female patients when comparing to healthy controls, which is associated with more severe symptoms regarding cognitive functions, anhedonia, and social functioning in male patients. We can further the location-specific edges and nodes that cause the complexity difference using recently developed network methods [ 16 , 17 , 31 ].…”

“…The network entropy has been well established for binary networks that are based on a Bernoulli distribution model [ 9 , 11 ]. However, the network entropy for the weighted network is challenging because the edge weights in W a mixture multivariate normal distributions with a large and unknown covariance matrix (the number of parameters is at the order of ) and unknown mixture component [ 17 ]. The parameter estimation is often intractable, and the computation of entropy is then challenging.…”