Identification of brain states, transitions, and communities using functional MRI

Brain function relies on a precisely coordinated and dynamic balance between the functional integration and segregation of distinct neural systems. Characterizing the way in which neural systems reconfigure their interactions to give rise to distinct but hidden brain states remains an open challenge. In this paper, we propose a Bayesian model-based characterization of latent brain states and showcase a novel method based on posterior predictive discrepancy using the latent block model to detect transitions between latent brain states in blood oxygen level-dependent (BOLD) time series. The set of estimated parameters in the model includes a latent label vector that assigns network nodes to communities, and also block model parameters that reflect the weighted connectivity within and between communities. Besides extensive in-silico model evaluation, we also provide empirical validation (and replication) using the Human Connectome Project (HCP) dataset of 100 healthy adults. Our results obtained through an analysis of task-fMRI data during working memory performance show appropriate lags between external task demands and change-points between brain states, with distinctive community patterns distinguishing fixation, low-demand and high-demand task conditions. I identifying changes in brain connectivity over time can provide insight into fundamental properties of human brain dynamics. However, the definition of discrete brain states and the method of identifying the states has not been commonly agreed [1]. Experiments targeting unconstrained spontaneous ‘resting-state’ neural dynamics [2, 3, 4, 5, 6, 7, 8, 9, 10] have limited ability to infer latent brain states or determine how the brain segues from one state to another because it is not clear whether changes in brain connectivity are induced by variations in neural activity (for example induced by cognitive or vigilance states) or fluctuations in non-neuronal noise [11, 12, 13]. A recent study with naturalistic movie stimuli used a hidden Markov model to explore dynamic jumps between discrete brain states and found that the variations in the sensory and narrative properties of the movie can evoke discrete brain processes [14]. Task-fMRI studies with more restrictive constraints on stimuli have demonstrated that functional connectivity exhibits variation during motor learning [15] and anxiety-inducing speech preparation [16]. Although taskbased fMRI experiments can, to some extent, delineate the external stimuli (for example, the onset and duration of stimuli in the block designed experiments), which constitute reference points against which to identify changes in the observed signal, this information does not precisely determine the timing and duration of the latent brain state relative to psychological processes or neural activity. For example, an emotional stimulus may trigger a neural response which is delayed relative to stimulus onset and which persists for some time after stimulus offset. Moreover, the dynamics of brain states and functional networks are not induced only by external stimuli, but also by unknown intrinsic latent mental processes [17]. Therefore, the development of noninvasive methods for identifying transitions of latent brain states during both task performance and task-free conditions is necessary for characterizing the spatiotemporal dynamics of brain networks. Change-point detection in multivariate time series is a statistical problem that has clear relevance to identifying transitions in brain states, particularly in the absence of knowledge regarding the experimental design. Several changepoint detection methods based on spectral clustering [18, 19] and dynamic connectivity regression (DCR) [16] have been previously developed and applied to the study of fMRI time series, and these have enhanced our understanding of brain dynamics. However, change-point detection with spectral clustering only evaluates changes to the component eigenstructures of the networks but neglects the weighted connectivity between nodes, while the DCR method only focuses on the sparse graph but ignores the modules of the brain networks Other change-point detection strategies include a frequency-specific method [20], applying a multivariate cumulative sum procedure to detect change-points using EEG data, and methods which focus on large scale network es1 ar X iv :2 10 1. 10 61 7v 1 [ qbi o. N C ] 2 6 Ja n 20 21 timation in fMRI time series [21, 22, 23, 24]. Many fMRI studies use sliding window methods for characterizing the time-varying functional connectivity in time series analysis [2, 8, 25, 26, 27, 28, 29]. Methods based on hidden Markov models (HMM) are also widely used to analyze transient brain states [30, 31, 32]. A community is defined as a collection of nodes that are densely connected in a network. The problem of community detection is a topical area of network science [33, 34]. How communities change or how the nodes in a network are assigned to specific communities is an important problem in the characterization of networks. Although many community detection problems in network neuroscience are based on modularity [15, 35, 36], recently a hidden Markov stochastic block model combined with a non-overlapping sliding window was applied to infer dynamic functional connectivity for networks, where edge weights were only binary and the candidate time points evaluated were not consecutive [37, 38]. More general weighted stochastic block models [39] have been used to infer structural connectivity for human lifespan analysis [40] and to infer functional connectivity in the mesoscale architecture of drosophila, mouse, rat, macaque, and human connectomes [41]. However, these studies using the weighted stochastic block model only explore the brain network over the whole time course of the experiment and neglect dynamic properties of networks. Weighted stochastic block models [39] are described in terms of exponential families (parameterized probability distributions), with the estimation of parameters performed using variational inference [42, 43]. Another relevant statistical approach introduces a fully Bayesian latent block model [2, 3], which includes both a binary latent block model and a Gaussian latent block model as special cases. The Gaussian latent block model is similar to the weighted stochastic block model, but different methods have been used for parameter estimation, including Markov chain Monte Carlo (MCMC) sampling. Although there is a broad literature exploring changepoint detection, and also many papers that discuss community detection, relatively few papers combine these approaches, particularly from a Bayesian perspective. In this paper, we develop Bayesian model-based methods which unify change-point detection and community detection to explore when and how the community structure of discrete brain state changes under different external task demands at different time points using functional MRI. There are several advantages of our approach compared to existing changepoint detection methods. Compared to data-driven methods like spectral clustering [18, 19] and DCR [16], which either ignore characterizing the weighted connectivity or the community patterns, the fully Bayesian framework and Markov chain Monte Carlo method provide flexible and powerful strategies that have been under-used for characterizing the latent properties of brain networks, including the dynamics of both the community memberships and weighted connectivity properties of the nodal community structures. Existing change-point detection methods based on the stochastic block model all use non-overlapping sliding windows and were applied only to binary brain networks [37, 38]. In contrast to the stochastic block model used in time-varying functional connectivity studies, the Gaussian latent block model used in our work considers the correlation matrix as an observation without imposing any arbitrary thresholds, so that all the information contained in the time series is preserved, resulting in more accurate detection of changepoints. Moreover, unlike methods based on fixed community memberships over the time course [38], our methods consider both the community memberships and parameters related to the weighted connectivity to be time varying, which results in more flexible estimation of both community structure and connectivity patterns. Furthermore, our Bayesian change-point detection method uses overlapping sliding windows that assess all of the potential candidate change-points over the time course, which increases the resolution of the detected change-points compared to methods using non-overlapping windows [37, 38]. Finally, the proposed Bayesian change-point detection method is computationally efficient, scaling to whole-brain networks potentially covering hundreds of nodes within a reasonable time frame in the order of tens of minutes. Our paper presents four main contributions, namely: (i) we quantitatively characterize discrete brain states with weighted connectivity and time-dependent community memberships, using the latent block model within a temporal interval between two consecutive change-points; (ii) we propose a new Bayesian change-point detection method called posterior predictive discrepancy (PPD) to estimate transition locations between brain states, using a Bayesian model fitness assessment; (iii) in addition to the locations of change-points, we also infer the community architecture of discrete brain states, which we show are distinctive of 2back, 0-back, and fixation conditions in a working-memory task-based fMRI experiment, and; (iv) we further empirically find that the estimated change-points between brain states show appropriate lags compared to the external working memory task conditions.