A state-space model for dynamic functional connectivity Sourish Chakravarty 1,5,6 , Zachary D. Threlkeld 7 , Yelena G. Bodien 6 , Brian L. Edlow 6 , Emery N. Brown 1−5 Abstract— Dynamic functional connectivity (DFC) analysis involves measuring correlated neural activity over time across multiple brain regions. Significant regional correlations among neural signals, such as those obtained from resting-state func- tional magnetic resonance imaging (fMRI), may represent neural circuits associated with rest. The conventional approach of estimating the correlation dynamics as a sequence of static correlations from sliding time-windows has statistical limita- tions. To address this issue, we propose a multivariate stochastic volatility model for estimating DFC inspired by recent work in econometrics research. This model assumes a state-space framework where the correlation dynamics of a multivariate normal observation sequence is governed by a positive-definite matrix-variate latent process. Using this statistical model within a sequential Bayesian estimation framework, we use blood oxygenation level dependent activity from multiple brain re- gions to estimate posterior distributions on the correlation trajectory. We demonstrate the utility of this DFC estimation framework by analyzing its performance on simulated data, and by estimating correlation dynamics in resting state fMRI data from a patient with a disorder of consciousness (DoC). Our work advances the state-of-the-art in DFC analysis and its principled use in DoC biomarker exploration. I. I NTRODUCTION Functional connectivity (FC) analysis can be broadly de- scribed as an analysis of “statistical dependencies among remote neuro-physiological events” [Fri11]. The FC mea- sures are considered to be representative of long-range neural coordination across brain-regions. Conventionally, they are calculated as pair-wise correlation in neural signals, e.g. This work was partially supported by NIH Award P01-GM118629 (to E.N.B), by funds from Massachusetts General Hospital (to E.N.B.), by funds from the Picower Institute for Learning and Memory (to E.N.B. and S.C.), by funds from the NIH/NINDS (DP2-HD101400, R21-NS109627, RF1- NS115268, K23-NS094538; to B.L.E.), by funds from James S. McDonnell Foundation (to B.L.E.), and by funds from the National Institute on Disability, Independent Living and Rehabilitation Research, Administration for Community Living (90DP0039, Spaulding- Harvard TBI Model System; to Y.G.B.). 1 Picower Institute for Learning and Memory, Massachusetts Institute of Technology (MIT), Cambridge, MA 2 Department of Brain and Cognitive Sciences, MIT, Cambridge, MA 3 Institute of Medical Engineering and Science, MIT, Cambridge, MA 4 Harvard-MIT Division of Health Science and Technology 5 Department of Anesthesia, Critical Care and Pain Medicine, Mas- sachusetts General Hospital (MGH), Boston, MA 6 Center for Neurotechnology and Neurorecovery, Department of Neu- rology, MGH, Boston, MA 7 Dept. of Neurology and Neurological Sciences, Stanford University School of Medicine, Stanford, CA Accepted in 53rd Annual Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA. c  2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. blood oxygen level dependent (BOLD) activation in func- tional magnetic resonance imaging (fMRI) data and or elec- trical activity in electroencephalography (EEG) data, across multiple brain regions. From a signal processing perspective, FC analysis is based upon estimation of correlation matrices from multivariate time-series data. FC analysis is widely rel- evant in basic neuroscience [AM14] as well as translational clinical neuroscience research ([BCE17], [ECS + 17]). An emerging paradigm in FC research is that of dynamic functional connectivity (DFC) [TL15]. Conventionally, FC analysis is performed on an entire session of multi-site/multi- channel neural recordings to generate a correlation map. A key assumption of such an analysis is that the true correlation remains constant across the entire sequence of a recording session. This static FC (SFC) interpretation can be generalized to DFC by assuming that the true correlation map changes over time. Therefore, DFC analysis involves estimating a time-series of pairwise correlations from mul- tivariate neural data. The DFC analysis yields information that is complementary to SFC analysis of the same dataset: SFC indicates the degree to which any two brain-regions are synchronous with each other on average, whereas DFC indicates how this degree of synchrony varies over time. Principled DFC analysis may aid translational research aimed at biomarker discovery for neurological disorders such as disorders of consciousness (DoC) [DTD + 19]. Conventionally, DFC analysis generates dynamic estimates of correlations by assuming a sliding-window (SW) ap- proach. In this approach, a sequence of instantaneous corre- lation measures is calculated by repeating the SFC analyses on a sequence of short data windows where the window-size is user-prescribed. A sub-optimal choice of window-size can lead to statistical challenges. For example, if the window size is too long, then the estimated correlation trajectory may be unable to capture faster dynamics. Conversely, if window size is too short then the estimates will be more sensitive to noise in the data. Therefore, it is preferable to use alternative DFC estimation techniques that can yield reliable estimates of cor- relation dynamics without requiring subjective windows. One such promising alternative has been proposed by Lindquist et al.[LXNC14] where the authors estimated correlation dynamics by fitting a dynamic conditional correlation model (DCC) to resting-state fMRI data. The DCC model originated in econometrics literature to estimate covariance trajectories in multivariate financial time-series data [ES01]. Motivated by this work, here we propose a novel approach based on state-space models (SSMs) to estimate DFC from neural data while avoiding data-windowing. In particular, we consider a specific class of SSMs known as Multivariate Stochastic arXiv:1912.05595v1 [stat.AP] 11 Dec 2019