1
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Arinyo-I-Prats A, López-Madrona VJ, Paluš M. Lead/Lag directionality is not generally equivalent to causality in nonlinear systems: Comparison of phase slope index and conditional mutual information. Neuroimage 2024; 292:120610. [PMID: 38631615 DOI: 10.1016/j.neuroimage.2024.120610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2023] [Revised: 03/12/2024] [Accepted: 04/11/2024] [Indexed: 04/19/2024] Open
Abstract
Applications of causal techniques to neural time series have increased extensively over last decades, including a wide and diverse family of methods focusing on electroencephalogram (EEG) analysis. Besides connectivity inferred in defined frequency bands, there is a growing interest in the analysis of cross-frequency interactions, in particular phase and amplitude coupling and directionality. Some studies show contradicting results of coupling directionality from high frequency to low frequency signal components, in spite of generally considered modulation of a high-frequency amplitude by a low-frequency phase. We have compared two widely used methods to estimate the directionality in cross frequency coupling: conditional mutual information (CMI) and phase slope index (PSI). The latter, applied to infer cross-frequency phase-amplitude directionality from animal intracranial recordings, gives opposite results when comparing to CMI. Both metrics were tested in a numerically simulated example of unidirectionally coupled Rössler systems, which helped to find the explanation of the contradictory results: PSI correctly estimates the lead/lag relationship which, however, is not generally equivalent to causality in the sense of directionality of coupling in nonlinear systems, correctly inferred by using CMI with surrogate data testing.
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Affiliation(s)
- Andreu Arinyo-I-Prats
- Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, Prague, 18200, Czech Republic; Department of Archaeology and Heritage Studies, School of Culture and Society, Aarhus University, Jens Chr. Skous Vej 7, Building 1467, Aarhus, 8000, Denmark; Department of Archaeology, Simon Fraser University, Education Building 9635, 8888 University Drive, Burnaby, V5A 1S6, B.C., Canada
| | - Víctor J López-Madrona
- Institut de Neurosciences des Systèmes, Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, 27 Bd Jean Moulin, Marseille, 13005, France
| | - Milan Paluš
- Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, Prague, 18200, Czech Republic.
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2
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Shao K, Logothetis NK, Besserve M. Information theoretic measures of causal influences during transient neural events. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:1085347. [PMID: 37323237 PMCID: PMC10266490 DOI: 10.3389/fnetp.2023.1085347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Accepted: 05/11/2023] [Indexed: 06/17/2023]
Abstract
Introduction: Transient phenomena play a key role in coordinating brain activity at multiple scales, however their underlying mechanisms remain largely unknown. A key challenge for neural data science is thus to characterize the network interactions at play during these events. Methods: Using the formalism of Structural Causal Models and their graphical representation, we investigate the theoretical and empirical properties of Information Theory based causal strength measures in the context of recurring spontaneous transient events. Results: After showing the limitations of Transfer Entropy and Dynamic Causal Strength in this setting, we introduce a novel measure, relative Dynamic Causal Strength, and provide theoretical and empirical support for its benefits. Discussion: These methods are applied to simulated and experimentally recorded neural time series and provide results in agreement with our current understanding of the underlying brain circuits.
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Affiliation(s)
- Kaidi Shao
- International Center for Primate Brain Research (ICPBR), Center for Excellence in Brain Science and Intelligence Technology (CEBSIT), Chinese Academy of Sciences (CAS), Shanghai, China
- Department of Cognitive Neurophysiology, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Graduate School of Neural and Behavioral Sciences, International Max Planck Research School, Eberhard-Karls University of Tübingen, Tübingen, Germany
| | - Nikos K. Logothetis
- International Center for Primate Brain Research (ICPBR), Center for Excellence in Brain Science and Intelligence Technology (CEBSIT), Chinese Academy of Sciences (CAS), Shanghai, China
- Department of Cognitive Neurophysiology, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Centre for Imaging Sciences, Biomedical Imaging Institute, The University of Manchester, Manchester, United Kingdom
| | - Michel Besserve
- Department of Cognitive Neurophysiology, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Department of Empirical Inference, Max Planck Institute for Intelligent Systems, Tübingen, Germany
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3
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Sala A, Lizarraga A, Caminiti SP, Calhoun VD, Eickhoff SB, Habeck C, Jamadar SD, Perani D, Pereira JB, Veronese M, Yakushev I. Brain connectomics: time for a molecular imaging perspective? Trends Cogn Sci 2023; 27:353-366. [PMID: 36621368 PMCID: PMC10432882 DOI: 10.1016/j.tics.2022.11.015] [Citation(s) in RCA: 19] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Revised: 11/19/2022] [Accepted: 11/30/2022] [Indexed: 01/09/2023]
Abstract
In the past two decades brain connectomics has evolved into a major concept in neuroscience. However, the current perspective on brain connectivity and how it underpins brain function relies mainly on the hemodynamic signal of functional magnetic resonance imaging (MRI). Molecular imaging provides unique information inaccessible to MRI-based and electrophysiological techniques. Thus, positron emission tomography (PET) has been successfully applied to measure neural activity, neurotransmission, and proteinopathies in normal and pathological cognition. Here, we position molecular imaging within the brain connectivity framework from the perspective of timeliness, validity, reproducibility, and resolution. We encourage the neuroscientific community to take an integrative approach whereby MRI-based, electrophysiological techniques, and molecular imaging contribute to our understanding of the brain connectome.
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Affiliation(s)
- Arianna Sala
- Department of Nuclear Medicine, Klinikum Rechts der Isar, Technical University of Munich, School of Medicine, 81675 Munich, Germany; Coma Science Group, GIGA-Consciousness, University of Liege, 4000 Liege, Belgium; Centre du Cerveau(2), University Hospital of Liege, 4000 Liege, Belgium
| | - Aldana Lizarraga
- Department of Nuclear Medicine, Klinikum Rechts der Isar, Technical University of Munich, School of Medicine, 81675 Munich, Germany
| | - Silvia Paola Caminiti
- Vita-Salute San Raffaele University, 20132 Milan, Italy; In Vivo Human Molecular and Structural Neuroimaging Unit, Division of Neuroscience, Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS) San Raffaele Scientific Institute, 20132 Milan, Italy
| | - Vince D Calhoun
- Tri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS), Georgia State University, Georgia Institute of Technology, and Emory University, Atlanta, GA 30303, USA
| | - Simon B Eickhoff
- Institute of Neuroscience and Medicine, Brain, and Behaviour (INM-7), Research Centre Jülich, 52428 Jülich, Germany; Institute of Systems Neuroscience, Medical Faculty, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
| | - Christian Habeck
- Cognitive Neuroscience Division, Department of Neurology, Columbia University, New York, NY 10032, USA
| | - Sharna D Jamadar
- Turner Institute for Brain and Mental Health, Monash University, 3800 Melbourne, Australia; Monash Biomedical Imaging, Monash University, 3800 Melbourne, Australia
| | - Daniela Perani
- Vita-Salute San Raffaele University, 20132 Milan, Italy; In Vivo Human Molecular and Structural Neuroimaging Unit, Division of Neuroscience, Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS) San Raffaele Scientific Institute, 20132 Milan, Italy; Nuclear Medicine Unit, San Raffaele Hospital, 20132 Milan, Italy
| | - Joana B Pereira
- Department of Neurobiology, Care Sciences and Society, Karolinska Institutet, 14152 Stockholm, Sweden; Memory Research Unit, Department of Clinical Sciences, Malmö Lund University, 20502 Lund, Sweden
| | - Mattia Veronese
- Department of Neuroimaging, King's College London, London SE5 8AF, UK; Department of Information Engineering, University of Padua, 35131 Padua, Italy
| | - Igor Yakushev
- Department of Nuclear Medicine, Klinikum Rechts der Isar, Technical University of Munich, School of Medicine, 81675 Munich, Germany.
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4
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Racz FS, Czoch A, Kaposzta Z, Stylianou O, Mukli P, Eke A. Multiple-Resampling Cross-Spectral Analysis: An Unbiased Tool for Estimating Fractal Connectivity With an Application to Neurophysiological Signals. Front Physiol 2022; 13:817239. [PMID: 35321422 PMCID: PMC8936508 DOI: 10.3389/fphys.2022.817239] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 01/17/2022] [Indexed: 11/16/2022] Open
Abstract
Investigating scale-free (i.e., fractal) functional connectivity in the brain has recently attracted increasing attention. Although numerous methods have been developed to assess the fractal nature of functional coupling, these typically ignore that neurophysiological signals are assemblies of broadband, arrhythmic activities as well as oscillatory activities at characteristic frequencies such as the alpha waves. While contribution of such rhythmic components may bias estimates of fractal connectivity, they are also likely to represent neural activity and coupling emerging from distinct mechanisms. Irregular-resampling auto-spectral analysis (IRASA) was recently introduced as a tool to separate fractal and oscillatory components in the power spectrum of neurophysiological signals by statistically summarizing the power spectra obtained when resampling the original signal by several non-integer factors. Here we introduce multiple-resampling cross-spectral analysis (MRCSA) as an extension of IRASA from the univariate to the bivariate case, namely, to separate the fractal component of the cross-spectrum between two simultaneously recorded neural signals by applying the same principle. MRCSA does not only provide a theoretically unbiased estimate of the fractal cross-spectrum (and thus its spectral exponent) but also allows for computing the proportion of scale-free coupling between brain regions. As a demonstration, we apply MRCSA to human electroencephalographic recordings obtained in a word generation paradigm. We show that the cross-spectral exponent as well as the proportion of fractal coupling increases almost uniformly over the cortex during the rest-task transition, likely reflecting neural desynchronization. Our results indicate that MRCSA can be a valuable tool for scale-free connectivity studies in characterizing various cognitive states, while it also can be generalized to other applications outside the field of neuroscience.
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Affiliation(s)
- Frigyes Samuel Racz
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
- Department of Neurology, Dell Medical School, The University of Texas at Austin, Austin, TX, United States
- *Correspondence: Frigyes Samuel Racz,
| | - Akos Czoch
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
| | - Zalan Kaposzta
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
| | - Orestis Stylianou
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
- Institute of Translational Medicine, Semmelweis University, Budapest, Hungary
| | - Peter Mukli
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
- Oklahoma Center for Geroscience and Healthy Brain Aging, Department of Biochemistry & Molecular Biology, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, United States
| | - Andras Eke
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
- Department of Radiology & Biomedical Imaging, School of Medicine, Yale University, New Haven, CT, United States
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5
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Gupta K, Paluš M. Cross-Scale Causality and Information Transfer in Simulated Epileptic Seizures. ENTROPY 2021; 23:e23050526. [PMID: 33923035 PMCID: PMC8146730 DOI: 10.3390/e23050526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/05/2021] [Revised: 04/22/2021] [Accepted: 04/23/2021] [Indexed: 12/04/2022]
Abstract
An information-theoretic approach for detecting causality and information transfer was applied to phases and amplitudes of oscillatory components related to different time scales and obtained using the wavelet transform from a time series generated by the Epileptor model. Three main time scales and their causal interactions were identified in the simulated epileptic seizures, in agreement with the interactions of the model variables. An approach consisting of wavelet transform, conditional mutual information estimation, and surrogate data testing applied to a single time series generated by the model was demonstrated to be successful in the identification of all directional (causal) interactions between the three different time scales described in the model. Thus, the methodology was prepared for the identification of causal cross-frequency phase–phase and phase–amplitude interactions in experimental and clinical neural data.
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Affiliation(s)
| | - Milan Paluš
- Correspondence: ; Tel.: +420-266-053-430; Fax: +420-286-585-789
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6
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Totah NK, Logothetis NK, Eschenko O. Synchronous spiking associated with prefrontal high γ oscillations evokes a 5-Hz rhythmic modulation of spiking in locus coeruleus. J Neurophysiol 2021; 125:1191-1201. [PMID: 33566743 DOI: 10.1152/jn.00677.2020] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
The brainstem noradrenergic locus coeruleus (LC) is reciprocally connected with the prefrontal cortex (PFC). Coupling between LC spiking and the depolarizing phase of slow (1-2 Hz) waves in PFC field potentials during sleep and anesthesia suggests that LC drives cortical state transition. Reciprocal LC-PFC connectivity should also allow interactions in the opposing (top-down) direction, but prior work has only studied prefrontal control over LC activity using electrical or optogenetic stimulation. Here, we describe the physiological characteristics of spontaneously occurring top-down LC-PFC interactions. We recorded LC multiunit activity (MUA) simultaneously with PFC single-unit and local field potential (LFP) activity in urethane-anesthetized rats. We observed cross-regional coupling between the phase of 5-Hz oscillations in LC-MUA and the power of PFC LFP 60-200 Hz high γ (hγ). Transient increases in PFC hγ power preceded peaks in the 5-Hz LC-MUA oscillation. Analysis of cross-regional transfer entropy demonstrated that the PFC hγ transients were predictive of a transient increase in LC-MUA. An ∼29 ms delay between these signals was consistent with the conduction velocity from the PFC to the LC. Finally, we showed that PFC hγ transients are associated with synchronized spiking of a subset (27%) of PFC single units. Our data suggest that PFC hγ transients may indicate the timing of the top-down excitatory input to LC, at least under conditions when LC neuronal population activity fluctuates rhythmically at 5 Hz. Synchronized PFC neuronal spiking that occurs during hγ transients may provide a previously unknown mode of top-down control over the LC.NEW & NOTEWORTHY The prefrontal cortex (PFC) is thought to control activity in the noradrenergic locus coeruleus (LC). Prior anatomical and prefrontal stimulation studies demonstrated the potential for PFC-LC interactions; however, it is unknown what types of PFC activity affect the LC. Here, we show that transient increases in PFC high γ power and associated changes in PFC unit-pair synchrony are a potential sign of top-down control over the LC.
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Affiliation(s)
- Nelson K Totah
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany.,Helsinki Institute of Life Science, University of Helsinki, Helsinki, Finland.,Faculty of Pharmacy, University of Helsinki, Helsinki, Finland
| | - Nikos K Logothetis
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany.,Division of Imaging Science and Biomedical Engineering, University of Manchester, Manchester, United Kingdom
| | - Oxana Eschenko
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
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7
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Song C, Huo Y, Ma J, Ding W, Wang L, Dai J, Huang L. A Feature Tensor-Based Epileptic Detection Model Based on Improved Edge Removal Approach for Directed Brain Networks. Front Neurosci 2020; 14:557095. [PMID: 33408603 PMCID: PMC7779617 DOI: 10.3389/fnins.2020.557095] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Accepted: 11/25/2020] [Indexed: 11/13/2022] Open
Abstract
Electroencephalograph (EEG) plays a significant role in the diagnostics process of epilepsy, but the detection rate is unsatisfactory when the length of interictal EEG signals is relatively short. Although the deliberate attacking theories for undirected brain network based on node removal method can extract potential network features, the node removal method fails to sufficiently consider the directionality of brain electrical activities. To solve the problems above, this study proposes a feature tensor-based epileptic detection method of directed brain networks. First, a directed functional brain network is constructed by calculating the transfer entropy of EEG signals between different electrodes. Second, the edge removal method is used to imitate the disruptions of brain connectivity, which may be related to the disorder of brain diseases, to obtain a sequence of residual networks. After that, topological features of these residual networks are extracted based on graph theory for constructing a five-way feature tensor. To exploit the inherent interactions among multiple modes of the feature tensor, this study uses the Tucker decomposition method to get a core tensor which is finally reshaped into a vector and input into the support vectors machine (SVM) classifier. Experiment results suggest that the proposed method has better epileptic screening performance for short-term interictal EEG data.
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Affiliation(s)
- Chuancheng Song
- Bell Honors School, Nanjing University of Posts and Telecommunications, Nanjing, China
| | - Youliang Huo
- College of Electronic and Optical Engineering, College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing, China
| | - Junkai Ma
- College of Electronic and Optical Engineering, College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing, China
| | - Weiwei Ding
- College of Electronic and Optical Engineering, College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing, China
| | - Liye Wang
- College of Electronic and Optical Engineering, College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing, China
| | - Jiafei Dai
- Neurology Department, the General Hospital of Eastern Theater Command, Nanjing, China
| | - Liya Huang
- College of Electronic and Optical Engineering, College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing, China
- National and Local Joint Engineering Laboratory of RF Integration and Micro-Assembly Technology, Nanjing, China
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8
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Pinzuti E, Wollstadt P, Gutknecht A, Tüscher O, Wibral M. Measuring spectrally-resolved information transfer. PLoS Comput Biol 2020; 16:e1008526. [PMID: 33370259 PMCID: PMC7793276 DOI: 10.1371/journal.pcbi.1008526] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Revised: 01/08/2021] [Accepted: 11/12/2020] [Indexed: 12/13/2022] Open
Abstract
Information transfer, measured by transfer entropy, is a key component of distributed computation. It is therefore important to understand the pattern of information transfer in order to unravel the distributed computational algorithms of a system. Since in many natural systems distributed computation is thought to rely on rhythmic processes a frequency resolved measure of information transfer is highly desirable. Here, we present a novel algorithm, and its efficient implementation, to identify separately frequencies sending and receiving information in a network. Our approach relies on the invertible maximum overlap discrete wavelet transform (MODWT) for the creation of surrogate data in the computation of transfer entropy and entirely avoids filtering of the original signals. The approach thereby avoids well-known problems due to phase shifts or the ineffectiveness of filtering in the information theoretic setting. We also show that measuring frequency-resolved information transfer is a partial information decomposition problem that cannot be fully resolved to date and discuss the implications of this issue. Last, we evaluate the performance of our algorithm on simulated data and apply it to human magnetoencephalography (MEG) recordings and to local field potential recordings in the ferret. In human MEG we demonstrate top-down information flow in temporal cortex from very high frequencies (above 100Hz) to both similarly high frequencies and to frequencies around 20Hz, i.e. a complex spectral configuration of cortical information transmission that has not been described before. In the ferret we show that the prefrontal cortex sends information at low frequencies (4-8 Hz) to early visual cortex (V1), while V1 receives the information at high frequencies (> 125 Hz).
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Affiliation(s)
| | - Patricia Wollstadt
- MEG Unit, Brain Imaging Center, Goethe University, Frankfurt/Main, Germany
| | - Aaron Gutknecht
- Campus Institute for Dynamics of Biological Networks, Georg August University, Göttingen, Germany
| | - Oliver Tüscher
- Leibniz Institute for Resilience Research, Mainz, Germany
- Department of Psychiatry and Psychotherapy, Johannes Gutenberg University of Mainz, Mainz, Germany
| | - Michael Wibral
- MEG Unit, Brain Imaging Center, Goethe University, Frankfurt/Main, Germany
- Campus Institute for Dynamics of Biological Networks, Georg August University, Göttingen, Germany
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9
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Banaie Boroujeni K, Tiesinga P, Womelsdorf T. Adaptive spike-artifact removal from local field potentials uncovers prominent beta and gamma band neuronal synchronization. J Neurosci Methods 2019; 330:108485. [PMID: 31705936 DOI: 10.1016/j.jneumeth.2019.108485] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Revised: 10/26/2019] [Accepted: 10/29/2019] [Indexed: 01/01/2023]
Abstract
BACKGROUND Many neurons synchronize their action potentials to the phase of local field potential (LFP) fluctuations in one or more frequency bands. Analyzing this spike-to-LFP synchronization is challenging, however, when neural spikes and LFP are generated in the same local circuit, because the spike's action potential waveform leak into the LFP and distort phase synchrony estimates. Existing approaches to address this spike bleed-through artifact relied on removing the average action potential waveforms of neurons, but this leaves artifacts in the LFP and distorts synchrony estimates. NEW METHOD We describe a spike-removal method that surpasses these limitations by decomposing individual action potentials into their frequency components before their removal from the LFP. The adaptively estimated frequency components allow for variable spread, strength and temporal variation of the spike artifact. RESULTS This adaptive approach effectively removes spike bleed-through artifacts in synthetic data with known ground truth, and in single neuron and LFP recordings in nonhuman primate striatum. For a large population of neurons with both narrow and broad action potential waveforms, the use of adaptive artifact removal uncovered 20-35 Hz beta and 35-45 Hz gamma band spike-LFP synchronization that would have remained contaminated otherwise. COMPARISON WITH EXISTING METHODS We demonstrate that adaptive spike-artifact removal cleans LFP data that remained contaminated when applying existing Bayesian and non-Bayesian methods of average spike-artifact removal. CONCLUSIONS Applying adaptive spike-removal from field potentials allows to estimate the phase at which neurons synchronize and the consistency of their phase-locked firing for both beta and low gamma frequencies. These metrics may prove essential to understand cell-to-circuit neuronal interactions in multiple brain systems.
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Affiliation(s)
| | - Paul Tiesinga
- Donders Institute for Brain, Cognition and Behaviour Radboud University Nijmegen, 6525 EN Nijmegen, Netherlands
| | - Thilo Womelsdorf
- Department of Psychology, Vanderbilt University, Nashville, TN 37240, United States; Department of Biology, Centre for Vision Research, York University, 4700 Keele Street, Toronto, Ontario M6J 1P3, Canada.
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10
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Drover JD, Schiff ND. A method for decomposing multivariate time series into a causal hierarchy within specific frequency bands. J Comput Neurosci 2018; 45:59-82. [PMID: 30062615 DOI: 10.1007/s10827-018-0691-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Revised: 06/20/2018] [Accepted: 06/27/2018] [Indexed: 12/01/2022]
Abstract
We propose a method - Frequency extracted hierarchical decomposition (FEHD) - for studying multivariate time series that identifies linear combinations of its components that possess a causally hierarchical structure - the method orders the components so that those at the "top" of the hierarchy drive those below. The method shares many of the features of the "hierarchical decomposition" method of Repucci et al. (Annals of Biomedical Engineering, 29, 1135-1149, 2001) but makes a crucial advance - the proposed method is capable of determining this causal hierarchy over arbitrarily specified frequency bands. Additionally, a novel minimization strategy is used to generate the decomposition resulting in an increase in stability, reliability, and an improvement in the sensitivity to model parameters. We demonstrate the utility of the method by applying it to both artificial time series constructed to have specific causal graphs, and to the EEG of healthy volunteers and patient subjects who are recovering from a severe brain injury.
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11
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Cekic S, Grandjean D, Renaud O. Time, frequency, and time-varying Granger-causality measures in neuroscience. Stat Med 2018. [PMID: 29542141 DOI: 10.1002/sim.7621] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
This article proposes a systematic methodological review and an objective criticism of existing methods enabling the derivation of time, frequency, and time-varying Granger-causality statistics in neuroscience. The capacity to describe the causal links between signals recorded at different brain locations during a neuroscience experiment is indeed of primary interest for neuroscientists, who often have very precise prior hypotheses about the relationships between recorded brain signals. The increasing interest and the huge number of publications related to this topic calls for this systematic review, which describes the very complex methodological aspects underlying the derivation of these statistics. In this article, we first present a general framework that allows us to review and compare Granger-causality statistics in the time domain, and the link with transfer entropy. Then, the spectral and the time-varying extensions are exposed and discussed together with their estimation and distributional properties. Although not the focus of this article, partial and conditional Granger causality, dynamical causal modelling, directed transfer function, directed coherence, partial directed coherence, and their variant are also mentioned.
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Affiliation(s)
- Sezen Cekic
- Methodology and Data Analysis, Department of Psychology, University of Geneva, Geneva, Switzerland
| | - Didier Grandjean
- Neuroscience of Emotion and Affective Dynamics Lab, Department of Psychology, University of Geneva, Geneva, Switzerland
| | - Olivier Renaud
- Methodology and Data Analysis, Department of Psychology, University of Geneva, Geneva, Switzerland
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12
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Dupré la Tour T, Tallot L, Grabot L, Doyère V, van Wassenhove V, Grenier Y, Gramfort A. Non-linear auto-regressive models for cross-frequency coupling in neural time series. PLoS Comput Biol 2017; 13:e1005893. [PMID: 29227989 PMCID: PMC5739510 DOI: 10.1371/journal.pcbi.1005893] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Revised: 12/21/2017] [Accepted: 11/26/2017] [Indexed: 11/19/2022] Open
Abstract
We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling. Neural oscillations synchronize information across brain areas at various anatomical and temporal scales. Of particular relevance, slow fluctuations of brain activity have been shown to affect high frequency neural activity, by regulating the excitability level of neural populations. Such cross-frequency-coupling can take several forms. In the most frequently observed type, the power of high frequency activity is time-locked to a specific phase of slow frequency oscillations, yielding phase-amplitude-coupling (PAC). Even when readily observed in neural recordings, such non-linear coupling is particularly challenging to formally characterize. Typically, neuroscientists use band-pass filtering and Hilbert transforms with ad-hoc correlations. Here, we explicitly address current limitations and propose an alternative probabilistic signal modeling approach, for which statistical inference is fast and well-posed. To statistically model PAC, we propose to use non-linear auto-regressive models which estimate the spectral modulation of a signal conditionally to a driving signal. This conditional spectral analysis enables easy model selection and clear hypothesis-testing by using the likelihood of a given model. We demonstrate the advantage of the model-based approach on three datasets acquired in rats and in humans. We further provide novel neuroscientific insights on previously reported PAC phenomena, capturing two mechanisms in PAC: influence of amplitude and directionality estimation.
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Affiliation(s)
- Tom Dupré la Tour
- LTCI, Télécom ParisTech, Université Paris-Saclay, Paris, France
- * E-mail:
| | - Lucille Tallot
- Neuroscience Paris Seine, CNRS, INSERM, Sorbonne Universités, Université Pierre et Marie Curie, Paris, France
- Neuro-PSI, Université Paris-Sud, Université Paris Saclay, CNRS, Orsay, France
| | - Laetitia Grabot
- Cognitive Neuroimaging Unit, CEA/DRF/Joliot, INSERM, Université Paris-Sud, Université Paris-Saclay, NeuroSpin center, Gif-sur-Yvette, France
- CEA, Université Paris-Saclay, Gif-sur-Yvette, France
| | - Valérie Doyère
- Neuro-PSI, Université Paris-Sud, Université Paris Saclay, CNRS, Orsay, France
| | - Virginie van Wassenhove
- Cognitive Neuroimaging Unit, CEA/DRF/Joliot, INSERM, Université Paris-Sud, Université Paris-Saclay, NeuroSpin center, Gif-sur-Yvette, France
- CEA, Université Paris-Saclay, Gif-sur-Yvette, France
| | - Yves Grenier
- LTCI, Télécom ParisTech, Université Paris-Saclay, Paris, France
| | - Alexandre Gramfort
- LTCI, Télécom ParisTech, Université Paris-Saclay, Paris, France
- CEA, Université Paris-Saclay, Gif-sur-Yvette, France
- Inria, Université Paris-Saclay, Saclay, France
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13
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Esghaei M, Daliri MR, Treue S. Local field potentials are induced by visually evoked spiking activity in macaque cortical area MT. Sci Rep 2017; 7:17110. [PMID: 29215034 PMCID: PMC5719360 DOI: 10.1038/s41598-017-17372-4] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Accepted: 11/27/2017] [Indexed: 12/14/2022] Open
Abstract
Local field potentials (LFP) have been the focus of many recent studies in systems neuroscience. However, the exact neural basis of these signals remains unclear. To address this question, we determined the relationship between LFP signals and another, much better understood, signature of neural activity: action potentials. Specifically, we focused on the relationship between the amplitude of stimulus-induced LFPs and the magnitude of spiking activity in visual cortex of non-human primates. Our trial-by-trial correlation analyses between these two components of extracellular signals in macaque visual cortex show that the spike rate is coupled to the LFP amplitude with a surprisingly long latency, typically 50 ms. Our analysis shows that the neural spike rate is a significant predictor of the LFP amplitude. This limits the functional interpretation of LFP signals beyond that based on spiking activities.
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Affiliation(s)
- Moein Esghaei
- Cognitive Neurobiology Laboratory, School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran. .,Cognitive Neuroscience Laboratory, German Primate Center - Leibniz Institute for Primate Research, Goettingen, Germany.
| | - Mohammad Reza Daliri
- Cognitive Neurobiology Laboratory, School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.,Cognitive Neuroscience Laboratory, German Primate Center - Leibniz Institute for Primate Research, Goettingen, Germany.,Neuroscience and Neuroengineering Research Laboratory, Biomedical Engineering Department, School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran
| | - Stefan Treue
- Cognitive Neuroscience Laboratory, German Primate Center - Leibniz Institute for Primate Research, Goettingen, Germany.,Faculty of Biology and Psychology, University of Goettingen, Goettingen, Germany.,Bernstein Center for Computational Neuroscience, Goettingen, Germany.,Leibniz-ScienceCampus Primate Cognition, Goettingen, Germany
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14
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Giordano BL, Ince RAA, Gross J, Schyns PG, Panzeri S, Kayser C. Contributions of local speech encoding and functional connectivity to audio-visual speech perception. eLife 2017; 6. [PMID: 28590903 PMCID: PMC5462535 DOI: 10.7554/elife.24763] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2016] [Accepted: 05/07/2017] [Indexed: 11/13/2022] Open
Abstract
Seeing a speaker’s face enhances speech intelligibility in adverse environments. We investigated the underlying network mechanisms by quantifying local speech representations and directed connectivity in MEG data obtained while human participants listened to speech of varying acoustic SNR and visual context. During high acoustic SNR speech encoding by temporally entrained brain activity was strong in temporal and inferior frontal cortex, while during low SNR strong entrainment emerged in premotor and superior frontal cortex. These changes in local encoding were accompanied by changes in directed connectivity along the ventral stream and the auditory-premotor axis. Importantly, the behavioral benefit arising from seeing the speaker’s face was not predicted by changes in local encoding but rather by enhanced functional connectivity between temporal and inferior frontal cortex. Our results demonstrate a role of auditory-frontal interactions in visual speech representations and suggest that functional connectivity along the ventral pathway facilitates speech comprehension in multisensory environments. DOI:http://dx.doi.org/10.7554/eLife.24763.001 When listening to someone in a noisy environment, such as a cocktail party, we can understand the speaker more easily if we can also see his or her face. Movements of the lips and tongue convey additional information that helps the listener’s brain separate out syllables, words and sentences. However, exactly where in the brain this effect occurs and how it works remain unclear. To find out, Giordano et al. scanned the brains of healthy volunteers as they watched clips of people speaking. The clarity of the speech varied between clips. Furthermore, in some of the clips the lip movements of the speaker corresponded to the speech in question, whereas in others the lip movements were nonsense babble. As expected, the volunteers performed better on a word recognition task when the speech was clear and when the lips movements agreed with the spoken dialogue. Watching the video clips stimulated rhythmic activity in multiple regions of the volunteers’ brains, including areas that process sound and areas that plan movements. Speech is itself rhythmic, and the volunteers’ brain activity synchronized with the rhythms of the speech they were listening to. Seeing the speaker’s face increased this degree of synchrony. However, it also made it easier for sound-processing regions within the listeners’ brains to transfer information to one other. Notably, only the latter effect predicted improved performance on the word recognition task. This suggests that seeing a person’s face makes it easier to understand his or her speech by boosting communication between brain regions, rather than through effects on individual areas. Further work is required to determine where and how the brain encodes lip movements and speech sounds. The next challenge will be to identify where these two sets of information interact, and how the brain merges them together to generate the impression of specific words. DOI:http://dx.doi.org/10.7554/eLife.24763.002
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Affiliation(s)
- Bruno L Giordano
- Institut de Neurosciences de la Timone UMR 7289, Aix Marseille Université - Centre National de la Recherche Scientifique, Marseille, France.,Institute of Neuroscience and Psychology, University of Glasgow, Glasgow, United Kingdom
| | - Robin A A Ince
- Institute of Neuroscience and Psychology, University of Glasgow, Glasgow, United Kingdom
| | - Joachim Gross
- Institute of Neuroscience and Psychology, University of Glasgow, Glasgow, United Kingdom
| | - Philippe G Schyns
- Institute of Neuroscience and Psychology, University of Glasgow, Glasgow, United Kingdom
| | - Stefano Panzeri
- Neural Computation Laboratory, Center for Neuroscience and Cognitive Systems, Istituto Italiano di Tecnologia, Rovereto, Italy
| | - Christoph Kayser
- Institute of Neuroscience and Psychology, University of Glasgow, Glasgow, United Kingdom
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15
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Abstract
Recent work has shown that functional connectivity among cortical neurons is highly varied, with a small percentage of neurons having many more connections than others. Also, recent theoretical developments now make it possible to quantify how neurons modify information from the connections they receive. Therefore, it is now possible to investigate how information modification, or computation, depends on the number of connections a neuron receives (in-degree) or sends out (out-degree). To do this, we recorded the simultaneous spiking activity of hundreds of neurons in cortico-hippocampal slice cultures using a high-density 512-electrode array. This preparation and recording method combination produced large numbers of neurons recorded at temporal and spatial resolutions that are not currently available in any in vivo recording system. We utilized transfer entropy (a well-established method for detecting linear and nonlinear interactions in time series) and the partial information decomposition (a powerful, recently developed tool for dissecting multivariate information processing into distinct parts) to quantify computation between neurons where information flows converged. We found that computations did not occur equally in all neurons throughout the networks. Surprisingly, neurons that computed large amounts of information tended to receive connections from high out-degree neurons. However, the in-degree of a neuron was not related to the amount of information it computed. To gain insight into these findings, we developed a simple feedforward network model. We found that a degree-modified Hebbian wiring rule best reproduced the pattern of computation and degree correlation results seen in the real data. Interestingly, this rule also maximized signal propagation in the presence of network-wide correlations, suggesting a mechanism by which cortex could deal with common random background input. These are the first results to show that the extent to which a neuron modifies incoming information streams depends on its topological location in the surrounding functional network. We recorded the electrical activity of hundreds of neurons simultaneously in brain tissue from mice and we analyzed these signals using state-of-the-art tools from information theory. These tools allowed us to ascertain which neurons were transmitting information to other neurons and to characterize the computations performed by neurons using the inputs they received from two or more other neurons. We found that computations did not occur equally in all neurons throughout the networks. Surprisingly, neurons that computed large amounts of information tended to be recipients of information from neurons with a large number of outgoing connections. Interestingly, the number of incoming connections to a neuron was not related to the amount of information that neuron computed. To better understand these results, we built a network model to match the data. Unexpectedly, the model also maximized information transfer in the presence of network-wide correlations. This suggested a way that networks of cortical neurons could deal with common random background input. These results are the first to show that the amount of information computed by a neuron depends on where it is located in the surrounding network.
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16
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Huang CS, Pal NR, Chuang CH, Lin CT. Identifying changes in EEG information transfer during drowsy driving by transfer entropy. Front Hum Neurosci 2015; 9:570. [PMID: 26557069 PMCID: PMC4615826 DOI: 10.3389/fnhum.2015.00570] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Accepted: 09/28/2015] [Indexed: 11/13/2022] Open
Abstract
Drowsy driving is a major cause of automobile accidents. Previous studies used neuroimaging based approaches such as analysis of electroencephalogram (EEG) activities to understand the brain dynamics of different cortical regions during drowsy driving. However, the coupling between brain regions responding to this vigilance change is still unclear. To have a comprehensive understanding of neural mechanisms underlying drowsy driving, in this study we use transfer entropy, a model-free measure of effective connectivity based on information theory. We investigate the pattern of information transfer between brain regions when the vigilance level, which is derived from the driving performance, changes from alertness to drowsiness. Results show that the couplings between pairs of frontal, central, and parietal areas increased at the intermediate level of vigilance, which suggests that an enhancement of the cortico-cortical interaction is necessary to maintain the task performance and prevent behavioral lapses. Additionally, the occipital-related connectivity magnitudes monotonically decreases as the vigilance level declines, which further supports the cortical gating of sensory stimuli during drowsiness. Neurophysiological evidence of mutual relationships between brain regions measured by transfer entropy might enhance the understanding of cortico-cortical communication during drowsy driving.
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Affiliation(s)
- Chih-Sheng Huang
- Brain Research Center, National Chiao-Tung University Hsinchu, Taiwan ; Institute of Electrical Control Engineering, National Chiao-Tung University Hsinchu, Taiwan
| | - Nikhil R Pal
- Electronics and Communication Sciences Unit, Indian Statistical Institute Calcutta, India
| | - Chun-Hsiang Chuang
- Brain Research Center, National Chiao-Tung University Hsinchu, Taiwan ; Faculty of Engineering and Information Technology, University of Technology Sydney Sydney, NSW, Australia
| | - Chin-Teng Lin
- Brain Research Center, National Chiao-Tung University Hsinchu, Taiwan ; Institute of Electrical Control Engineering, National Chiao-Tung University Hsinchu, Taiwan ; Faculty of Engineering and Information Technology, University of Technology Sydney Sydney, NSW, Australia
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17
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Besserve M, Lowe SC, Logothetis NK, Schölkopf B, Panzeri S. Shifts of Gamma Phase across Primary Visual Cortical Sites Reflect Dynamic Stimulus-Modulated Information Transfer. PLoS Biol 2015; 13:e1002257. [PMID: 26394205 PMCID: PMC4579086 DOI: 10.1371/journal.pbio.1002257] [Citation(s) in RCA: 64] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2014] [Accepted: 08/19/2015] [Indexed: 11/19/2022] Open
Abstract
Distributed neural processing likely entails the capability of networks to reconfigure dynamically the directionality and strength of their functional connections. Yet, the neural mechanisms that may allow such dynamic routing of the information flow are not yet fully understood. We investigated the role of gamma band (50-80 Hz) oscillations in transient modulations of communication among neural populations by using measures of direction-specific causal information transfer. We found that the local phase of gamma-band rhythmic activity exerted a stimulus-modulated and spatially-asymmetric directed effect on the firing rate of spatially separated populations within the primary visual cortex. The relationships between gamma phases at different sites (phase shifts) could be described as a stimulus-modulated gamma-band wave propagating along the spatial directions with the largest information transfer. We observed transient stimulus-related changes in the spatial configuration of phases (compatible with changes in direction of gamma wave propagation) accompanied by a relative increase of the amount of information flowing along the instantaneous direction of the gamma wave. These effects were specific to the gamma-band and suggest that the time-varying relationships between gamma phases at different locations mark, and possibly causally mediate, the dynamic reconfiguration of functional connections.
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Affiliation(s)
- Michel Besserve
- Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Max Planck Institute for Intelligent Systems, Tübingen, Germany
- * E-mail:
| | - Scott C. Lowe
- Institute for Adaptive and Neural Computation, School of Informatics, University of Edinburgh, Edinburgh, United Kingdom
| | - Nikos K. Logothetis
- Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Division of Imaging Science and Biomedical Engineering, University of Manchester, Manchester, United Kingdom
| | | | - Stefano Panzeri
- Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, Rovereto, Italy
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18
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Jiang H, Bahramisharif A, van Gerven MA, Jensen O. Measuring directionality between neuronal oscillations of different frequencies. Neuroimage 2015; 118:359-67. [DOI: 10.1016/j.neuroimage.2015.05.044] [Citation(s) in RCA: 80] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2014] [Revised: 04/13/2015] [Accepted: 05/16/2015] [Indexed: 11/27/2022] Open
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19
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Amigó JM, Monetti R, Tort-Colet N, Sanchez-Vives MV. Infragranular layers lead information flow during slow oscillations according to information directionality indicators. J Comput Neurosci 2015; 39:53-62. [DOI: 10.1007/s10827-015-0563-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2015] [Revised: 04/10/2015] [Accepted: 04/15/2015] [Indexed: 11/28/2022]
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20
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Wibral M, Lizier JT, Priesemann V. Bits from Brains for Biologically Inspired Computing. Front Robot AI 2015. [DOI: 10.3389/frobt.2015.00005] [Citation(s) in RCA: 64] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
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21
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Fasoli D, Faugeras O, Panzeri S. A formalism for evaluating analytically the cross-correlation structure of a firing-rate network model. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2015; 5:6. [PMID: 25852981 PMCID: PMC4385226 DOI: 10.1186/s13408-015-0020-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2014] [Accepted: 02/21/2015] [Indexed: 06/04/2023]
Abstract
We introduce a new formalism for evaluating analytically the cross-correlation structure of a finite-size firing-rate network with recurrent connections. The analysis performs a first-order perturbative expansion of neural activity equations that include three different sources of randomness: the background noise of the membrane potentials, their initial conditions, and the distribution of the recurrent synaptic weights. This allows the analytical quantification of the relationship between anatomical and functional connectivity, i.e. of how the synaptic connections determine the statistical dependencies at any order among different neurons. The technique we develop is general, but for simplicity and clarity we demonstrate its efficacy by applying it to the case of synaptic connections described by regular graphs. The analytical equations so obtained reveal previously unknown behaviors of recurrent firing-rate networks, especially on how correlations are modified by the external input, by the finite size of the network, by the density of the anatomical connections and by correlation in sources of randomness. In particular, we show that a strong input can make the neurons almost independent, suggesting that functional connectivity does not depend only on the static anatomical connectivity, but also on the external inputs. Moreover we prove that in general it is not possible to find a mean-field description à la Sznitman of the network, if the anatomical connections are too sparse or our three sources of variability are correlated. To conclude, we show a very counterintuitive phenomenon, which we call stochastic synchronization, through which neurons become almost perfectly correlated even if the sources of randomness are independent. Due to its ability to quantify how activity of individual neurons and the correlation among them depends upon external inputs, the formalism introduced here can serve as a basis for exploring analytically the computational capability of population codes expressed by recurrent neural networks.
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Affiliation(s)
- Diego Fasoli
- NeuroMathComp Laboratory, INRIA Sophia Antipolis Méditerranée, 2004 Route des Lucioles, BP 93, 06902 Valbonne, France ; Neural Computation Laboratory, Center for Neuroscience and Cognitive Systems @Unitn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy
| | - Olivier Faugeras
- NeuroMathComp Laboratory, INRIA Sophia Antipolis Méditerranée, 2004 Route des Lucioles, BP 93, 06902 Valbonne, France
| | - Stefano Panzeri
- Neural Computation Laboratory, Center for Neuroscience and Cognitive Systems @Unitn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy
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22
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Timme N, Ito S, Myroshnychenko M, Yeh FC, Hiolski E, Hottowy P, Beggs JM. Multiplex networks of cortical and hippocampal neurons revealed at different timescales. PLoS One 2014; 9:e115764. [PMID: 25536059 PMCID: PMC4275261 DOI: 10.1371/journal.pone.0115764] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2014] [Accepted: 11/03/2014] [Indexed: 12/31/2022] Open
Abstract
Recent studies have emphasized the importance of multiplex networks--interdependent networks with shared nodes and different types of connections--in systems primarily outside of neuroscience. Though the multiplex properties of networks are frequently not considered, most networks are actually multiplex networks and the multiplex specific features of networks can greatly affect network behavior (e.g. fault tolerance). Thus, the study of networks of neurons could potentially be greatly enhanced using a multiplex perspective. Given the wide range of temporally dependent rhythms and phenomena present in neural systems, we chose to examine multiplex networks of individual neurons with time scale dependent connections. To study these networks, we used transfer entropy--an information theoretic quantity that can be used to measure linear and nonlinear interactions--to systematically measure the connectivity between individual neurons at different time scales in cortical and hippocampal slice cultures. We recorded the spiking activity of almost 12,000 neurons across 60 tissue samples using a 512-electrode array with 60 micrometer inter-electrode spacing and 50 microsecond temporal resolution. To the best of our knowledge, this preparation and recording method represents a superior combination of number of recorded neurons and temporal and spatial recording resolutions to any currently available in vivo system. We found that highly connected neurons ("hubs") were localized to certain time scales, which, we hypothesize, increases the fault tolerance of the network. Conversely, a large proportion of non-hub neurons were not localized to certain time scales. In addition, we found that long and short time scale connectivity was uncorrelated. Finally, we found that long time scale networks were significantly less modular and more disassortative than short time scale networks in both tissue types. As far as we are aware, this analysis represents the first systematic study of temporally dependent multiplex networks among individual neurons.
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Affiliation(s)
- Nicholas Timme
- Department of Physics, Indiana University, Bloomington, Indiana, 47405, United States of America
| | - Shinya Ito
- Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, California, 95064, United States of America
| | - Maxym Myroshnychenko
- Program in Neuroscience, Indiana University, Bloomington, Indiana, 47405, United States of America
| | - Fang-Chin Yeh
- Department of Physics, Indiana University, Bloomington, Indiana, 47405, United States of America
| | - Emma Hiolski
- Department of Microbiology & Environmental Toxicology, University of California Santa Cruz, Santa Cruz, California, 95064, United States of America
| | - Pawel Hottowy
- Physics and Applied Computer Science, AGH University of Science and Technology, 30–059, Krakow, Poland
| | - John M. Beggs
- Department of Physics, Indiana University, Bloomington, Indiana, 47405, United States of America
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23
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Sellers KK, Bennett DV, Fröhlich F. Frequency-band signatures of visual responses to naturalistic input in ferret primary visual cortex during free viewing. Brain Res 2014; 1598:31-45. [PMID: 25498982 DOI: 10.1016/j.brainres.2014.12.016] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2014] [Revised: 10/30/2014] [Accepted: 12/06/2014] [Indexed: 01/09/2023]
Abstract
Neuronal firing responses in visual cortex reflect the statistics of visual input and emerge from the interaction with endogenous network dynamics. Artificial visual stimuli presented to animals in which the network dynamics were constrained by anesthetic agents or trained behavioral tasks have provided fundamental understanding of how individual neurons in primary visual cortex respond to input. In contrast, very little is known about the mesoscale network dynamics and their relationship to microscopic spiking activity in the awake animal during free viewing of naturalistic visual input. To address this gap in knowledge, we recorded local field potential (LFP) and multiunit activity (MUA) simultaneously in all layers of primary visual cortex (V1) of awake, freely viewing ferrets presented with naturalistic visual input (nature movie clips). We found that naturalistic visual stimuli modulated the entire oscillation spectrum; low frequency oscillations were mostly suppressed whereas higher frequency oscillations were enhanced. In average across all cortical layers, stimulus-induced change in delta and alpha power negatively correlated with the MUA responses, whereas sensory-evoked increases in gamma power positively correlated with MUA responses. The time-course of the band-limited power in these frequency bands provided evidence for a model in which naturalistic visual input switched V1 between two distinct, endogenously present activity states defined by the power of low (delta, alpha) and high (gamma) frequency oscillatory activity. Therefore, the two mesoscale activity states delineated in this study may define the degree of engagement of the circuit with the processing of sensory input.
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Affiliation(s)
- Kristin K Sellers
- Department of Psychiatry, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States; Neurobiology Curriculum, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States
| | - Davis V Bennett
- Department of Psychiatry, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States
| | - Flavio Fröhlich
- Department of Psychiatry, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States; Neurobiology Curriculum, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States; Department of Cell Biology and Physiology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States; Department of Biomedical Engineering, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States; Neuroscience Center, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States.
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24
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Wollstadt P, Martínez-Zarzuela M, Vicente R, Díaz-Pernas FJ, Wibral M. Efficient transfer entropy analysis of non-stationary neural time series. PLoS One 2014; 9:e102833. [PMID: 25068489 PMCID: PMC4113280 DOI: 10.1371/journal.pone.0102833] [Citation(s) in RCA: 72] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2013] [Accepted: 06/24/2014] [Indexed: 11/18/2022] Open
Abstract
Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of interest in neuroscience. Estimating transfer entropy from two processes requires the observation of multiple realizations of these processes to estimate associated probability density functions. To obtain these necessary observations, available estimators typically assume stationarity of processes to allow pooling of observations over time. This assumption however, is a major obstacle to the application of these estimators in neuroscience as observed processes are often non-stationary. As a solution, Gomez-Herrero and colleagues theoretically showed that the stationarity assumption may be avoided by estimating transfer entropy from an ensemble of realizations. Such an ensemble of realizations is often readily available in neuroscience experiments in the form of experimental trials. Thus, in this work we combine the ensemble method with a recently proposed transfer entropy estimator to make transfer entropy estimation applicable to non-stationary time series. We present an efficient implementation of the approach that is suitable for the increased computational demand of the ensemble method's practical application. In particular, we use a massively parallel implementation for a graphics processing unit to handle the computationally most heavy aspects of the ensemble method for transfer entropy estimation. We test the performance and robustness of our implementation on data from numerical simulations of stochastic processes. We also demonstrate the applicability of the ensemble method to magnetoencephalographic data. While we mainly evaluate the proposed method for neuroscience data, we expect it to be applicable in a variety of fields that are concerned with the analysis of information transfer in complex biological, social, and artificial systems.
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Affiliation(s)
- Patricia Wollstadt
- MEG Unit, Brain Imaging Center, Goethe University, Frankfurt, Germany
- * E-mail:
| | - Mario Martínez-Zarzuela
- Department of Signal Theory and Communications and Telematics Engineering, University of Valladolid, Valladolid, Spain
| | - Raul Vicente
- Frankfurt Institute for Advanced Studies (FIAS), Goethe University, Frankfurt, Germany
- Max-Planck Institute for Brain Research, Frankfurt, Germany
| | - Francisco J. Díaz-Pernas
- Department of Signal Theory and Communications and Telematics Engineering, University of Valladolid, Valladolid, Spain
| | - Michael Wibral
- MEG Unit, Brain Imaging Center, Goethe University, Frankfurt, Germany
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25
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Chicharro D, Panzeri S. Algorithms of causal inference for the analysis of effective connectivity among brain regions. Front Neuroinform 2014; 8:64. [PMID: 25071541 PMCID: PMC4078745 DOI: 10.3389/fninf.2014.00064] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2014] [Accepted: 06/12/2014] [Indexed: 11/24/2022] Open
Abstract
In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl’s causality, algorithms of inductive causation (IC and IC*) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity.
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Affiliation(s)
- Daniel Chicharro
- Neural Computation Laboratory, Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia Rovereto, Italy
| | - Stefano Panzeri
- Neural Computation Laboratory, Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia Rovereto, Italy ; Institute of Neuroscience and Psychology, University of Glasgow Glasgow, UK
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26
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Orlandi JG, Stetter O, Soriano J, Geisel T, Battaglia D. Transfer entropy reconstruction and labeling of neuronal connections from simulated calcium imaging. PLoS One 2014; 9:e98842. [PMID: 24905689 PMCID: PMC4048312 DOI: 10.1371/journal.pone.0098842] [Citation(s) in RCA: 60] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2013] [Accepted: 05/08/2014] [Indexed: 11/23/2022] Open
Abstract
Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exceeds a small minimum frequency. Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter-burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network. By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.
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Affiliation(s)
- Javier G. Orlandi
- Departament d'Estructura i Consituents de la Matèria, Universitat de Barcelona, Barcelona, Spain
| | - Olav Stetter
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Georg-August-Universität, Physics Department, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
| | - Jordi Soriano
- Departament d'Estructura i Consituents de la Matèria, Universitat de Barcelona, Barcelona, Spain
| | - Theo Geisel
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Georg-August-Universität, Physics Department, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
| | - Demian Battaglia
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Institut de Neurosciences des Systèmes, Inserm UMR1106, Aix-Marseille Université, Marseille, France
- * E-mail:
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27
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Wibral M, Vicente R, Lindner M. Transfer Entropy in Neuroscience. UNDERSTANDING COMPLEX SYSTEMS 2014. [DOI: 10.1007/978-3-642-54474-3_1] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
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28
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Einevoll GT, Kayser C, Logothetis NK, Panzeri S. Modelling and analysis of local field potentials for studying the function of cortical circuits. Nat Rev Neurosci 2013; 14:770-85. [PMID: 24135696 DOI: 10.1038/nrn3599] [Citation(s) in RCA: 467] [Impact Index Per Article: 42.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
The past decade has witnessed a renewed interest in cortical local field potentials (LFPs)--that is, extracellularly recorded potentials with frequencies of up to ~500 Hz. This is due to both the advent of multielectrodes, which has enabled recording of LFPs at tens to hundreds of sites simultaneously, and the insight that LFPs offer a unique window into key integrative synaptic processes in cortical populations. However, owing to its numerous potential neural sources, the LFP is more difficult to interpret than are spikes. Careful mathematical modelling and analysis are needed to take full advantage of the opportunities that this signal offers in understanding signal processing in cortical circuits and, ultimately, the neural basis of perception and cognition.
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Affiliation(s)
- Gaute T Einevoll
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 1432 Ås, Norway
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29
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Wibral M, Pampu N, Priesemann V, Siebenhühner F, Seiwert H, Lindner M, Lizier JT, Vicente R. Measuring information-transfer delays. PLoS One 2013; 8:e55809. [PMID: 23468850 PMCID: PMC3585400 DOI: 10.1371/journal.pone.0055809] [Citation(s) in RCA: 146] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2012] [Accepted: 01/02/2013] [Indexed: 11/18/2022] Open
Abstract
In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.
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Affiliation(s)
- Michael Wibral
- MEG Unit, Brain Imaging Center, Goethe University, Frankfurt, Germany.
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30
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Ma C, Pan X, Wang R, Sakagami M. Estimating causal interaction between prefrontal cortex and striatum by transfer entropy. Cogn Neurodyn 2013; 7:253-61. [PMID: 24427205 DOI: 10.1007/s11571-012-9239-4] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2012] [Revised: 12/21/2012] [Accepted: 12/25/2012] [Indexed: 10/27/2022] Open
Abstract
Transfer entropy (TE) is an information-theoretic measure for the investigation of causal interaction between two systems without a requirement of pre-specific interaction model (such as: linear or nonlinear). We introduced an efficient algorithm to calculate TE values between two systems based on observed time signals. By this method, we demonstrated that the TE correctly estimated the coupling strength and the direction of information transmission of two nonlinearly coupled systems. We also calculated TE values of real local field potentials (LFPs) recorded simultaneously in the lateral prefrontal cortex (LPFC) and the striatum of the behavioral monkey, and observed that the TE value from the LPFC to the striatum was stronger than that from the striatum to the LPFC, consistent with anatomical structure between the two areas. Moreover, the TE value dynamically varied dependent on behavior stages of the monkey. These results from simulated and real LFPs data suggested that the TE was able to effectively estimate functional connectivity between different brain regions and characterized their dynamical properties.
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Affiliation(s)
- Chaofei Ma
- Institute for Cognitive Neurodynamics, School of Information Science and Engineering, East China University of Science and Technology, Shanghai, 200237 People's Republic of China
| | - Xiaochuan Pan
- Institute for Cognitive Neurodynamics, School of Science, East China University of Science and Technology, 200237 Shanghai, People's Republic of China
| | - Rubin Wang
- Institute for Cognitive Neurodynamics, School of Science, East China University of Science and Technology, 200237 Shanghai, People's Republic of China
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31
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Chicharro D, Ledberg A. Framework to study dynamic dependencies in networks of interacting processes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041901. [PMID: 23214609 DOI: 10.1103/physreve.86.041901] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2012] [Revised: 07/30/2012] [Indexed: 06/01/2023]
Abstract
The analysis of dynamic dependencies in complex systems such as the brain helps to understand how emerging properties arise from interactions. Here we propose an information-theoretic framework to analyze the dynamic dependencies in multivariate time-evolving systems. This framework constitutes a fully multivariate extension and unification of previous approaches based on bivariate or conditional mutual information and Granger causality or transfer entropy. We define multi-information measures that allow us to study the global statistical structure of the system as a whole, the total dependence between subsystems, and the temporal statistical structure of each subsystem. We develop a stationary and a nonstationary formulation of the framework. We then examine different decompositions of these multi-information measures. The transfer entropy naturally appears as a term in some of these decompositions. This allows us to examine its properties not as an isolated measure of interdependence but in the context of the complete framework. More generally we use causal graphs to study the specificity and sensitivity of all the measures appearing in these decompositions to different sources of statistical dependence arising from the causal connections between the subsystems. We illustrate that there is no straightforward relation between the strength of specific connections and specific terms in the decompositions. Furthermore, causal and noncausal statistical dependencies are not separable. In particular, the transfer entropy can be nonmonotonic in dependence on the connectivity strength between subsystems and is also sensitive to internal changes of the subsystems, so it should not be interpreted as a measure of connectivity strength. Altogether, in comparison to an analysis based on single isolated measures of interdependence, this framework is more powerful to analyze emergent properties in multivariate systems and to characterize functionally relevant changes in the dynamics.
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Affiliation(s)
- Daniel Chicharro
- Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia, Via Bettini 31, 38068 Rovereto (TN), Italy.
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Stetter O, Battaglia D, Soriano J, Geisel T. Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals. PLoS Comput Biol 2012; 8:e1002653. [PMID: 22927808 PMCID: PMC3426566 DOI: 10.1371/journal.pcbi.1002653] [Citation(s) in RCA: 145] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2012] [Accepted: 07/01/2012] [Indexed: 12/13/2022] Open
Abstract
A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local. Unraveling the general organizing principles of connectivity in neural circuits is a crucial step towards understanding brain function. However, even the simpler task of assessing the global excitatory connectivity of a culture in vitro, where neurons form self-organized networks in absence of external stimuli, remains challenging. Neuronal cultures undergo spontaneous switching between episodes of synchronous bursting and quieter inter-burst periods. We introduce here a novel algorithm which aims at inferring the connectivity of neuronal cultures from calcium fluorescence recordings of their network dynamics. To achieve this goal, we develop a suitable generalization of Transfer Entropy, an information-theoretic measure of causal influences between time series. Unlike previous algorithmic approaches to reconstruction, Transfer Entropy is data-driven and does not rely on specific assumptions about neuronal firing statistics or network topology. We generate simulated calcium signals from networks with controlled ground-truth topology and purely excitatory interactions and show that, by restricting the analysis to inter-bursts periods, Transfer Entropy robustly achieves a good reconstruction performance for disparate network connectivities. Finally, we apply our method to real data and find evidence of non-random features in cultured networks, such as the existence of highly connected hub excitatory neurons and of an elevated (but not extreme) level of clustering.
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Affiliation(s)
- Olav Stetter
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Georg August University, Physics Department, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
| | - Demian Battaglia
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- * E-mail:
| | - Jordi Soriano
- Departament d'ECM , Facultat de F?sica, Universitat de Barcelona, Barcelona, Spain
| | - Theo Geisel
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Georg August University, Physics Department, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
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33
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Storchi R, Zippo AG, Caramenti GC, Valente M, Biella GEM. Predicting spike occurrence and neuronal responsiveness from LFPs in primary somatosensory cortex. PLoS One 2012; 7:e35850. [PMID: 22586452 PMCID: PMC3346760 DOI: 10.1371/journal.pone.0035850] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2011] [Accepted: 03/27/2012] [Indexed: 11/18/2022] Open
Abstract
Local Field Potentials (LFPs) integrate multiple neuronal events like synaptic inputs and intracellular potentials. LFP spatiotemporal features are particularly relevant in view of their applications both in research (e.g. for understanding brain rhythms, inter-areal neural communication and neuronal coding) and in the clinics (e.g. for improving invasive Brain-Machine Interface devices). However the relation between LFPs and spikes is complex and not fully understood. As spikes represent the fundamental currency of neuronal communication this gap in knowledge strongly limits our comprehension of neuronal phenomena underlying LFPs. We investigated the LFP-spike relation during tactile stimulation in primary somatosensory (S-I) cortex in the rat. First we quantified how reliably LFPs and spikes code for a stimulus occurrence. Then we used the information obtained from our analyses to design a predictive model for spike occurrence based on LFP inputs. The model was endowed with a flexible meta-structure whose exact form, both in parameters and structure, was estimated by using a multi-objective optimization strategy. Our method provided a set of nonlinear simple equations that maximized the match between models and true neurons in terms of spike timings and Peri Stimulus Time Histograms. We found that both LFPs and spikes can code for stimulus occurrence with millisecond precision, showing, however, high variability. Spike patterns were predicted significantly above chance for 75% of the neurons analysed. Crucially, the level of prediction accuracy depended on the reliability in coding for the stimulus occurrence. The best predictions were obtained when both spikes and LFPs were highly responsive to the stimuli. Spike reliability is known to depend on neuron intrinsic properties (i.e. on channel noise) and on spontaneous local network fluctuations. Our results suggest that the latter, measured through the LFP response variability, play a dominant role.
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Affiliation(s)
- Riccardo Storchi
- Institute of Molecular Bioimaging and Physiology (IBFM), Segrate (Milan), Italy
| | - Antonio G. Zippo
- Institute of Molecular Bioimaging and Physiology (IBFM), Segrate (Milan), Italy
| | | | - Maurizio Valente
- Institute of Molecular Bioimaging and Physiology (IBFM), Segrate (Milan), Italy
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34
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Battaglia D, Witt A, Wolf F, Geisel T. Dynamic effective connectivity of inter-areal brain circuits. PLoS Comput Biol 2012; 8:e1002438. [PMID: 22457614 PMCID: PMC3310731 DOI: 10.1371/journal.pcbi.1002438] [Citation(s) in RCA: 84] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2011] [Accepted: 02/04/2012] [Indexed: 11/19/2022] Open
Abstract
Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities. The circuits of the brain must perform a daunting amount of functions. But how can “brain states” be flexibly controlled, given that anatomic inter-areal connections can be considered as fixed, on timescales relevant for behavior? We hypothesize that, thanks to the nonlinear interaction between brain rhythms, even a simple circuit involving few brain areas can originate a multitude of effective circuits, associated with alternative functions selectable “on demand”. A distinction is usually made between structural connectivity, which describes actual synaptic connections, and effective connectivity, quantifying, beyond correlation, directed inter-areal causal influences. In our study, we measure effective connectivity based on time-series of neural activity generated by model inter-areal circuits. We find that “causality follows dynamics”. We show indeed that different effective networks correspond to different dynamical states associated to a same structural network (in particular, different phase-locking patterns between local neuronal oscillations). We then find that “information follows causality” (and thus, again, dynamics). We demonstrate that different effective networks give rise to alternative modalities of information routing between brain areas wired together in a fixed structural network. In particular, we show that the self-organization of interacting “analog” rate oscillations control the flow of “digital-like” information encoded in complex spiking patterns.
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Affiliation(s)
- Demian Battaglia
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.
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35
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Chicharro D, Ledberg A. When two become one: the limits of causality analysis of brain dynamics. PLoS One 2012; 7:e32466. [PMID: 22438878 PMCID: PMC3306364 DOI: 10.1371/journal.pone.0032466] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2011] [Accepted: 01/31/2012] [Indexed: 11/19/2022] Open
Abstract
Biological systems often consist of multiple interacting subsystems, the brain being a prominent example. To understand the functions of such systems it is important to analyze if and how the subsystems interact and to describe the effect of these interactions. In this work we investigate the extent to which the cause-and-effect framework is applicable to such interacting subsystems. We base our work on a standard notion of causal effects and define a new concept called natural causal effect. This new concept takes into account that when studying interactions in biological systems, one is often not interested in the effect of perturbations that alter the dynamics. The interest is instead in how the causal connections participate in the generation of the observed natural dynamics. We identify the constraints on the structure of the causal connections that determine the existence of natural causal effects. In particular, we show that the influence of the causal connections on the natural dynamics of the system often cannot be analyzed in terms of the causal effect of one subsystem on another. Only when the causing subsystem is autonomous with respect to the rest can this interpretation be made. We note that subsystems in the brain are often bidirectionally connected, which means that interactions rarely should be quantified in terms of cause-and-effect. We furthermore introduce a framework for how natural causal effects can be characterized when they exist. Our work also has important consequences for the interpretation of other approaches commonly applied to study causality in the brain. Specifically, we discuss how the notion of natural causal effects can be combined with Granger causality and Dynamic Causal Modeling (DCM). Our results are generic and the concept of natural causal effects is relevant in all areas where the effects of interactions between subsystems are of interest.
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Affiliation(s)
- Daniel Chicharro
- Center of Brain and Cognition, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
- * E-mail: (DC); (AL)
| | - Anders Ledberg
- Center of Brain and Cognition, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
- * E-mail: (DC); (AL)
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36
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Vinck M, Battaglia FP, Womelsdorf T, Pennartz C. Improved measures of phase-coupling between spikes and the Local Field Potential. J Comput Neurosci 2011; 33:53-75. [PMID: 22187161 PMCID: PMC3394239 DOI: 10.1007/s10827-011-0374-4] [Citation(s) in RCA: 95] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2011] [Revised: 10/09/2011] [Accepted: 11/10/2011] [Indexed: 12/25/2022]
Abstract
An important tool to study rhythmic neuronal synchronization is provided by relating spiking activity to the Local Field Potential (LFP). Two types of interdependent spike-LFP measures exist. The first approach is to directly quantify the consistency of single spike-LFP phases across spikes, referred to here as point-field phase synchronization measures. We show that conventional point-field phase synchronization measures are sensitive not only to the consistency of spike-LFP phases, but are also affected by statistical dependencies between spike-LFP phases, caused by e.g. non-Poissonian history-effects within spike trains such as bursting and refractoriness. To solve this problem, we develop a new pairwise measure that is not biased by the number of spikes and not affected by statistical dependencies between spike-LFP phases. The second approach is to quantify, similar to EEG-EEG coherence, the consistency of the relative phase between spike train and LFP signals across trials instead of across spikes, referred to here as spike train to field phase synchronization measures. We demonstrate an analytical relationship between point-field and spike train to field phase synchronization measures. Based on this relationship, we prove that the spike train to field pairwise phase consistency (PPC), a quantity closely related to the squared spike-field coherence, is a monotonically increasing function of the number of spikes per trial. This derived relationship is exact and analytic, and takes a linear form for weak phase-coupling. To solve this problem, we introduce a corrected version of the spike train to field PPC that is independent of the number of spikes per trial. Finally, we address the problem that dependencies between spike-LFP phase and the number of spikes per trial can cause spike-LFP phase synchronization measures to be biased by the number of trials. We show how to modify the developed point-field and spike train to field phase synchronization measures in order to make them unbiased by the number of trials.
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Affiliation(s)
- Martin Vinck
- Cognitive and Systems Neuroscience Group, Center for Neuroscience, University of Amsterdam, Amsterdam, The Netherlands.
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37
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Chicharro D. On the spectral formulation of Granger causality. BIOLOGICAL CYBERNETICS 2011; 105:331-347. [PMID: 22249416 DOI: 10.1007/s00422-011-0469-z] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2011] [Accepted: 12/20/2011] [Indexed: 05/31/2023]
Abstract
Spectral measures of causality are used to explore the role of different rhythms in the causal connectivity between brain regions. We study several spectral measures related to Granger causality, comprising the bivariate and conditional Geweke measures, the directed transfer function, and the partial directed coherence. We derive the formulation of dependence and causality in the spectral domain from the more general formulation in the information-theory framework. We argue that the transfer entropy, the most general measure derived from the concept of Granger causality, lacks a spectral representation in terms of only the processes associated with the recorded signals. For all the spectral measures we show how they are related to mutual information rates when explicitly considering the parametric autoregressive representation of the processes. In this way we express the conditional Geweke spectral measure in terms of a multiple coherence involving innovation variables inherent to the autoregressive representation. We also link partial directed coherence with Sims' criterion of causality. Given our results, we discuss the causal interpretation of the spectral measures related to Granger causality and stress the necessity to explicitly consider their specific formulation based on modeling the signals as linear Gaussian stationary autoregressive processes.
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Affiliation(s)
- D Chicharro
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain.
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38
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Lindner M, Vicente R, Priesemann V, Wibral M. TRENTOOL: a Matlab open source toolbox to analyse information flow in time series data with transfer entropy. BMC Neurosci 2011; 12:119. [PMID: 22098775 PMCID: PMC3287134 DOI: 10.1186/1471-2202-12-119] [Citation(s) in RCA: 126] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2011] [Accepted: 11/18/2011] [Indexed: 11/10/2022] Open
Abstract
Background Transfer entropy (TE) is a measure for the detection of directed interactions. Transfer entropy is an information theoretic implementation of Wiener's principle of observational causality. It offers an approach to the detection of neuronal interactions that is free of an explicit model of the interactions. Hence, it offers the power to analyze linear and nonlinear interactions alike. This allows for example the comprehensive analysis of directed interactions in neural networks at various levels of description. Here we present the open-source MATLAB toolbox TRENTOOL that allows the user to handle the considerable complexity of this measure and to validate the obtained results using non-parametrical statistical testing. We demonstrate the use of the toolbox and the performance of the algorithm on simulated data with nonlinear (quadratic) coupling and on local field potentials (LFP) recorded from the retina and the optic tectum of the turtle (Pseudemys scripta elegans) where a neuronal one-way connection is likely present. Results In simulated data TE detected information flow in the simulated direction reliably with false positives not exceeding the rates expected under the null hypothesis. In the LFP data we found directed interactions from the retina to the tectum, despite the complicated signal transformations between these stages. No false positive interactions in the reverse directions were detected. Conclusions TRENTOOL is an implementation of transfer entropy and mutual information analysis that aims to support the user in the application of this information theoretic measure. TRENTOOL is implemented as a MATLAB toolbox and available under an open source license (GPL v3). For the use with neural data TRENTOOL seamlessly integrates with the popular FieldTrip toolbox.
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Affiliation(s)
- Michael Lindner
- MEG Unit, Brain Imaging Center, Goethe University, Frankfurt, Germany
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39
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Hahs DW, Pethel SD. Distinguishing anticipation from causality: anticipatory bias in the estimation of information flow. PHYSICAL REVIEW LETTERS 2011; 107:128701. [PMID: 22026807 DOI: 10.1103/physrevlett.107.128701] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2010] [Revised: 03/23/2011] [Indexed: 05/13/2023]
Abstract
We report that transfer entropy estimates obtained from low-resolution and/or small data sets show net information flow away from a purely anticipatory element whereas transfer entropy calculated using exact distributions show the flow towards it. This means that for real-world data sets anticipatory elements can appear to be strongly driving the network dynamics even when there is no possibility of such an influence. Furthermore, we show that in the low-resolution limit there is no statistic that can distinguish anticipatory elements from causal ones.
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Affiliation(s)
- Daniel W Hahs
- U.S. Army RDECOM, RDMR-WSS, Redstone Arsenal, Alabama 35898, USA
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40
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Besserve M, Martinerie J. Extraction of functional information from ongoing brain electrical activity. Ing Rech Biomed 2011. [DOI: 10.1016/j.irbm.2011.01.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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41
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Transfer entropy in magnetoencephalographic data: quantifying information flow in cortical and cerebellar networks. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2010; 105:80-97. [PMID: 21115029 DOI: 10.1016/j.pbiomolbio.2010.11.006] [Citation(s) in RCA: 156] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2010] [Revised: 11/18/2010] [Accepted: 11/18/2010] [Indexed: 11/24/2022]
Abstract
The analysis of cortical and subcortical networks requires the identification of their nodes, and of the topology and dynamics of their interactions. Exploratory tools for the identification of nodes are available, e.g. magnetoencephalography (MEG) in combination with beamformer source analysis. Competing network topologies and interaction models can be investigated using dynamic causal modelling. However, we lack a method for the exploratory investigation of network topologies to choose from the very large number of possible network graphs. Ideally, this method should not require a pre-specified model of the interaction. Transfer entropy--an information theoretic implementation of Wiener-type causality--is a method for the investigation of causal interactions (or information flow) that is independent of a pre-specified interaction model. We analysed MEG data from an auditory short-term memory experiment to assess whether the reconfiguration of networks implied in this task can be detected using transfer entropy. Transfer entropy analysis of MEG source-level signals detected changes in the network between the different task types. These changes prominently involved the left temporal pole and cerebellum--structures that have previously been implied in auditory short-term or working memory. Thus, the analysis of information flow with transfer entropy at the source-level may be used to derive hypotheses for further model-based testing.
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