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      Modeling time-varying brain networks with a self-tuning optimized Kalman filter

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          Abstract

          Brain networks are complex dynamical systems in which directed interactions between different areas evolve at the sub-second scale of sensory, cognitive and motor processes. Due to the highly non-stationary nature of neural signals and their unknown noise components, however, modeling dynamic brain networks has remained one of the major challenges in contemporary neuroscience. Here, we present a new algorithm based on an innovative formulation of the Kalman filter that is optimized for tracking rapidly evolving patterns of directed functional connectivity under unknown noise conditions. The Self-Tuning Optimized Kalman filter (STOK) is a novel adaptive filter that embeds a self-tuning memory decay and a recursive regularization to guarantee high network tracking accuracy, temporal precision and robustness to noise. To validate the proposed algorithm, we performed an extensive comparison against the classical Kalman filter, in both realistic surrogate networks and real electroencephalography (EEG) data. In both simulations and real data, we show that the STOK filter estimates time-frequency patterns of directed connectivity with significantly superior performance. The advantages of the STOK filter were even clearer in real EEG data, where the algorithm recovered latent structures of dynamic connectivity from epicranial EEG recordings in rats and human visual evoked potentials, in excellent agreement with known physiology. These results establish the STOK filter as a powerful tool for modeling dynamic network structures in biological systems, with the potential to yield new insights into the rapid evolution of network states from which brain functions emerge.

          Author summary

          During normal behavior, brains transition between functional network states several times per second. This allows humans to quickly read a sentence, and a frog to catch a fly. Understanding these fast network dynamics is fundamental to understanding how brains work, but up to now it has proven very difficult to model fast brain dynamics for various methodological reasons. To overcome these difficulties, we designed a new Kalman filter (STOK) by innovating on previous solutions from control theory and state-space modelling. We show that STOK accurately models fast network changes in simulations and real neural data, making it an essential new tool for modelling fast brain networks in the time and frequency domain.

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          Most cited references84

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          Partial directed coherence: a new concept in neural structure determination.

          This paper introduces a new frequency-domain approach to describe the relationships (direction of information flow) between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models. We discuss its application and compare its performance to other approaches to the problem of determining neural structure relations from the simultaneous measurement of neural electrophysiological signals. The new concept is shown to reflect a frequency-domain representation of the concept of Granger causality.
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            BOLD correlates of EEG topography reveal rapid resting-state network dynamics.

            Resting-state functional connectivity studies with fMRI showed that the brain is intrinsically organized into large-scale functional networks for which the hemodynamic signature is stable for about 10s. Spatial analyses of the topography of the spontaneous EEG also show discrete epochs of stable global brain states (so-called microstates), but they remain quasi-stationary for only about 100 ms. In order to test the relationship between the rapidly fluctuating EEG-defined microstates and the slowly oscillating fMRI-defined resting states, we recorded 64-channel EEG in the scanner while subjects were at rest with their eyes closed. Conventional EEG-microstate analysis determined the typical four EEG topographies that dominated across all subjects. The convolution of the time course of these maps with the hemodynamic response function allowed to fit a linear model to the fMRI BOLD responses and revealed four distinct distributed networks. These networks were spatially correlated with four of the resting-state networks (RSNs) that were found by the conventional fMRI group-level independent component analysis (ICA). These RSNs have previously been attributed to phonological processing, visual imagery, attention reorientation, and subjective interoceptive-autonomic processing. We found no EEG-correlate of the default mode network. Thus, the four typical microstates of the spontaneous EEG seem to represent the neurophysiological correlate of four of the RSNs and show that they are fluctuating much more rapidly than fMRI alone suggests. Copyright 2010 Elsevier Inc. All rights reserved.
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              EEG and MEG: relevance to neuroscience.

              To understand dynamic cognitive processes, the high time resolution of EEG/MEG is invaluable. EEG/MEG signals can play an important role in providing measures of functional and effective connectivity in the brain. After a brief description of the foundations and basic methodological aspects of EEG/MEG signals, the relevance of the signals to obtain novel insights into the neuronal mechanisms underlying cognitive processes is surveyed, with emphasis on neuronal oscillations (ultra-slow, theta, alpha, beta, gamma, and HFOs) and combinations of oscillations. Three main functional roles of brain oscillations are put in evidence: (1) coding specific information, (2) setting and modulating brain attentional states, and (3) assuring the communication between neuronal populations such that specific dynamic workspaces may be created. The latter form the material core of cognitive functions. Copyright © 2013 Elsevier Inc. All rights reserved.
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                Author and article information

                Contributors
                Role: ConceptualizationRole: Data curationRole: Formal analysisRole: InvestigationRole: MethodologyRole: SoftwareRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: ConceptualizationRole: Formal analysisRole: InvestigationRole: MethodologyRole: SoftwareRole: ValidationRole: Writing – review & editing
                Role: ConceptualizationRole: Funding acquisitionRole: InvestigationRole: Project administrationRole: ResourcesRole: SupervisionRole: Writing – original draftRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, CA USA )
                1553-734X
                1553-7358
                17 August 2020
                August 2020
                : 16
                : 8
                : e1007566
                Affiliations
                [1 ] Perceptual Networks Group, University of Fribourg, Fribourg, Switzerland
                [2 ] Laboratory of Psychophysics, Brain Mind Institute, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
                [3 ] Functional Brain Mapping Lab, Department of Fundamental Neurosciences, University of Geneva, Geneva, Switzerland
                [4 ] Department of Neurosciences, University of Padova, Padova, Italy
                Radboud Universiteit Nijmegen, NETHERLANDS
                Author notes

                The authors have declared that no competing interests exist.

                Author information
                http://orcid.org/0000-0002-1139-2586
                http://orcid.org/0000-0002-9883-3371
                Article
                PCOMPBIOL-D-19-02025
                10.1371/journal.pcbi.1007566
                7451990
                32804971
                f0b4a92d-958e-4cc5-a462-c1cfb8182ee9
                © 2020 Pascucci et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 20 November 2019
                : 3 July 2020
                Page count
                Figures: 4, Tables: 0, Pages: 29
                Funding
                Funded by: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (CH)
                Award ID: PZ00P3_131731
                Award Recipient :
                Funded by: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (CH)
                Award ID: PP00P1_157420
                Award Recipient :
                Funded by: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (CH)
                Award ID: CRSII5-170873
                Award Recipient :
                Funded by: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (CH)
                Award ID: CRSII5-170873
                Award Recipient :
                This study was supported by the Swiss National Science Foundation grants to GP (PZ00P3_131731, PP00P1_157420 and CRSII5-170873), and to MR (CRSII5-170873). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Physical Sciences
                Mathematics
                Applied Mathematics
                Algorithms
                Kalman Filter
                Research and Analysis Methods
                Simulation and Modeling
                Algorithms
                Kalman Filter
                Research and Analysis Methods
                Bioassays and Physiological Analysis
                Electrophysiological Techniques
                Brain Electrophysiology
                Electroencephalography
                Biology and Life Sciences
                Physiology
                Electrophysiology
                Neurophysiology
                Brain Electrophysiology
                Electroencephalography
                Biology and Life Sciences
                Neuroscience
                Neurophysiology
                Brain Electrophysiology
                Electroencephalography
                Biology and Life Sciences
                Neuroscience
                Brain Mapping
                Electroencephalography
                Medicine and Health Sciences
                Clinical Medicine
                Clinical Neurophysiology
                Electroencephalography
                Research and Analysis Methods
                Imaging Techniques
                Neuroimaging
                Electroencephalography
                Biology and Life Sciences
                Neuroscience
                Neuroimaging
                Electroencephalography
                Physical Sciences
                Mathematics
                Probability Theory
                Random Variables
                Covariance
                Computer and Information Sciences
                Neural Networks
                Biology and Life Sciences
                Neuroscience
                Neural Networks
                Computer and Information Sciences
                Systems Science
                Dynamical Systems
                Physical Sciences
                Mathematics
                Systems Science
                Dynamical Systems
                Biology and Life Sciences
                Neuroscience
                Cognitive Science
                Cognition
                Memory
                Biology and Life Sciences
                Neuroscience
                Learning and Memory
                Memory
                Physical Sciences
                Mathematics
                Statistics
                Statistical Noise
                Computer and Information Sciences
                Network Analysis
                Custom metadata
                vor-update-to-uncorrected-proof
                2020-08-27
                Matlab and Python code for STOK, KF and the simulation framework are available on GitHub ( https://github.com/PscDavid/dynet_toolbox; https://github.com/joanrue/pydynet).

                Quantitative & Systems biology
                Quantitative & Systems biology

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