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Hindriks R, Broeders TAA, Schoonheim MM, Douw L, Santos F, van Wieringen W, Tewarie PKB. Higher-order functional connectivity analysis of resting-state functional magnetic resonance imaging data using multivariate cumulants. Hum Brain Mapp 2024; 45:e26663. [PMID: 38520377 PMCID: PMC10960559 DOI: 10.1002/hbm.26663] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Revised: 02/12/2024] [Accepted: 03/08/2024] [Indexed: 03/25/2024] Open
Abstract
Blood-level oxygenation-dependent (BOLD) functional magnetic resonance imaging (fMRI) is the most common modality to study functional connectivity in the human brain. Most research to date has focused on connectivity between pairs of brain regions. However, attention has recently turned towards connectivity involving more than two regions, that is, higher-order connectivity. It is not yet clear how higher-order connectivity can best be quantified. The measures that are currently in use cannot distinguish between pairwise (i.e., second-order) and higher-order connectivity. We show that genuine higher-order connectivity can be quantified by using multivariate cumulants. We explore the use of multivariate cumulants for quantifying higher-order connectivity and the performance of block bootstrapping for statistical inference. In particular, we formulate a generative model for fMRI signals exhibiting higher-order connectivity and use it to assess bias, standard errors, and detection probabilities. Application to resting-state fMRI data from the Human Connectome Project demonstrates that spontaneous fMRI signals are organized into higher-order networks that are distinct from second-order resting-state networks. Application to a clinical cohort of patients with multiple sclerosis further demonstrates that cumulants can be used to classify disease groups and explain behavioral variability. Hence, we present a novel framework to reliably estimate genuine higher-order connectivity in fMRI data which can be used for constructing hyperedges, and finally, which can readily be applied to fMRI data from populations with neuropsychiatric disease or cognitive neuroscientific experiments.
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Affiliation(s)
- Rikkert Hindriks
- Department of Mathematics, Faculty of ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands
| | - Tommy A. A. Broeders
- Department of Anatomy and Neurosciences, Amsterdam NeuroscienceAmsterdam UMC, Vrije Universiteit AmsterdamAmsterdamThe Netherlands
| | - Menno M. Schoonheim
- Department of Anatomy and Neurosciences, Amsterdam NeuroscienceAmsterdam UMC, Vrije Universiteit AmsterdamAmsterdamThe Netherlands
| | - Linda Douw
- Department of Anatomy and Neurosciences, Amsterdam NeuroscienceAmsterdam UMC, Vrije Universiteit AmsterdamAmsterdamThe Netherlands
| | - Fernando Santos
- Dutch Institute for Emergent Phenomena (DIEP)Institute for Advanced Studies, University of AmsterdamAmsterdamThe Netherlands
- Korteweg de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamthe Netherlands
| | - Wessel van Wieringen
- Department of Epidemiology and BiostatisticsAmsterdam UMC, Vrije Universiteit AmsterdamAmsterdamThe Netherlands
| | - Prejaas K. B. Tewarie
- Sir Peter Mansfield Imaging CenterSchool of Physics, University of NottinghamNottinghamUnited Kingdom
- Clinical Neurophysiology GroupUniversity of TwenteEnschedeThe Netherlands
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Hindriks R. Characterization of Second-Order Mixing Effects in Reconstructed Cross-Spectra of Random Neural Fields. Brain Topogr 2024:10.1007/s10548-024-01040-8. [PMID: 38472533 DOI: 10.1007/s10548-024-01040-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2023] [Accepted: 02/06/2024] [Indexed: 03/14/2024]
Abstract
Functional connectivity in electroencephalography (EEG) and magnetoencephalography (MEG) data is commonly assessed by using measures that are insensitive to instantaneously interacting sources and as such would not give rise to false positive interactions caused by instantaneous mixing of true source signals (first-order mixing). Recent studies, however, have drawn attention to the fact that such measures are still susceptible to instantaneous mixing from lagged sources (i.e. second-order mixing) and that this can lead to a large number of false positive interactions. In this study we relate first- and second-order mixing effects on the cross-spectra of reconstructed source activity to the properties of the resolution operators that are used for the reconstruction. We derive two identities that relate first- and second-order mixing effects to the transformation properties of measurement and source configurations and exploit them to establish several basic properties of signal mixing. First, we provide a characterization of the configurations that are maximally and minimally sensitive to second-order mixing. It turns out that second-order mixing effects are maximal when the measurement locations are far apart and the sources coincide with the measurement locations. Second, we provide a description of second-order mixing effects in the vicinity of the measurement locations in terms of the local geometry of the point-spread functions of the resolution operator. Third, we derive a version of Lagrange's identity for cross-talk functions that establishes the existence of a trade-off between the magnitude of first- and second-order mixing effects. It also shows that, whereas the magnitude of first-order mixing is determined by the inner product of cross-talk functions, the magnitude of second-order mixing is determined by a generalized cross-product of cross-talk functions (the wedge product) which leads to an intuitive geometric understanding of the trade-off. All results are derived within the general framework of random neural fields on cortical manifolds.
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Affiliation(s)
- Rikkert Hindriks
- Department of Mathematics, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.
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Tewarie PKB, Hindriks R, Lai YM, Sotiropoulos SN, Kringelbach M, Deco G. Non-reversibility outperforms functional connectivity in characterisation of brain states in MEG data. Neuroimage 2023; 276:120186. [PMID: 37268096 DOI: 10.1016/j.neuroimage.2023.120186] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Revised: 04/27/2023] [Accepted: 05/22/2023] [Indexed: 06/04/2023] Open
Abstract
Characterising brain states during tasks is common practice for many neuroscientific experiments using electrophysiological modalities such as electroencephalography (EEG) and magnetoencephalography (MEG). Brain states are often described in terms of oscillatory power and correlated brain activity, i.e. functional connectivity. It is, however, not unusual to observe weak task induced functional connectivity alterations in the presence of strong task induced power modulations using classical time-frequency representation of the data. Here, we propose that non-reversibility, or the temporal asymmetry in functional interactions, may be more sensitive to characterise task induced brain states than functional connectivity. As a second step, we explore causal mechanisms of non-reversibility in MEG data using whole brain computational models. We include working memory, motor, language tasks and resting-state data from participants of the Human Connectome Project (HCP). Non-reversibility is derived from the lagged amplitude envelope correlation (LAEC), and is based on asymmetry of the forward and reversed cross-correlations of the amplitude envelopes. Using random forests, we find that non-reversibility outperforms functional connectivity in the identification of task induced brain states. Non-reversibility shows especially better sensitivity to capture bottom-up gamma induced brain states across all tasks, but also alpha band associated brain states. Using whole brain computational models we find that asymmetry in the effective connectivity and axonal conduction delays play a major role in shaping non-reversibility across the brain. Our work paves the way for better sensitivity in characterising brain states during both bottom-up as well as top-down modulation in future neuroscientific experiments.
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Affiliation(s)
- Prejaas K B Tewarie
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Spain; Clinical Neurophysiology Group, University of Twente, Enschede, The Netherlands; Department of Neurology, Amsterdam UMC, Amsterdam, the Netherlands; Sir Peter Mansfield Imaging Centre, School of Physics, University of Nottingham, Nottingham, United Kingdom.
| | - Rikkert Hindriks
- Department of Mathematics, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam, the Netherlands
| | - Yi Ming Lai
- Sir Peter Mansfield Imaging Centre, School of Medicine, University of Nottingham, United Kingdom
| | - Stamatios N Sotiropoulos
- Sir Peter Mansfield Imaging Centre, School of Medicine, University of Nottingham, United Kingdom; NIHR Biomedical Research Centre, University of Nottingham, Nottingham University Hospitals NHS Trust, Nottingham, UK
| | - Morten Kringelbach
- Centre for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, Oxford, UK; Center for Music in the Brain, Department of Clinical Medicine, Aarhus University, Aarhus, Denmark; Department of Psychiatry, University of Oxford, Oxford, UK
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Spain; Institució Catalana de la Recerca i Estudis Avançats (ICREA), Barcelona, Spain; Department of Neuropsychology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
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Hindriks R, Tewarie PKB. Dissociation between phase and power correlation networks in the human brain is driven by co-occurrent bursts. Commun Biol 2023; 6:286. [PMID: 36934153 PMCID: PMC10024695 DOI: 10.1038/s42003-023-04648-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Accepted: 03/02/2023] [Indexed: 03/20/2023] Open
Abstract
Well-known haemodynamic resting-state networks are better mirrored in power correlation networks than phase coupling networks in electrophysiological data. However, what do these power correlation networks reflect? We address this long-outstanding question in neuroscience using rigorous mathematical analysis, biophysical simulations with ground truth and application of these mathematical concepts to empirical magnetoencephalography (MEG) data. Our mathematical derivations show that for two non-Gaussian electrophysiological signals, their power correlation depends on their coherence, cokurtosis and conjugate-coherence. Only coherence and cokurtosis contribute to power correlation networks in MEG data, but cokurtosis is less affected by artefactual signal leakage and better mirrors haemodynamic resting-state networks. Simulations and MEG data show that cokurtosis may reflect co-occurrent bursting events. Our findings shed light on the origin of the complementary nature of power correlation networks to phase coupling networks and suggests that the origin of resting-state networks is partly reflected in co-occurent bursts in neuronal activity.
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Affiliation(s)
- Rikkert Hindriks
- Department of Mathematics, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.
| | - Prejaas K B Tewarie
- Clinical Neurophysiology Group, University of Twente, Enschede, The Netherlands
- Sir Peter Mansfield Imaging Center, School of Physics, University of Nottingham, Nottingham, UK
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Aqil M, Atasoy S, Kringelbach ML, Hindriks R. Correction: Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome. PLoS Comput Biol 2022; 18:e1010224. [PMID: 35648749 PMCID: PMC9159585 DOI: 10.1371/journal.pcbi.1010224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
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Hindriks R. Relation Between the Phase-Lag Index and Lagged Coherence for Assessing Interactions in EEG and MEG Data. Int J Psychophysiol 2021. [DOI: 10.1016/j.ijpsycho.2021.07.290] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Hindriks R. Relation between the phase-lag index and lagged coherence for assessing interactions in EEG and MEG data. Neuroimage: Reports 2021. [DOI: 10.1016/j.ynirp.2021.100007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Aqil M, Atasoy S, Kringelbach ML, Hindriks R. Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome. PLoS Comput Biol 2021; 17:e1008310. [PMID: 33507899 PMCID: PMC7872285 DOI: 10.1371/journal.pcbi.1008310] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2020] [Revised: 02/09/2021] [Accepted: 12/11/2020] [Indexed: 12/22/2022] Open
Abstract
Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed "connectome harmonics", have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed graph neural fields, in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for Connectome-Harmonic Analysis Of Spatiotemporal Spectra). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.
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Affiliation(s)
- Marco Aqil
- Department of Mathematics, Vrije Universiteit, Amsterdam, The Netherlands
| | - Selen Atasoy
- Centre for Eudaimonia and Human Flourishing, University of Oxford, Oxford, United Kingdom
- Center for Music in the Brain, University of Aarhus, Aarhus, Denmark
| | - Morten L. Kringelbach
- Centre for Eudaimonia and Human Flourishing, University of Oxford, Oxford, United Kingdom
- Center for Music in the Brain, University of Aarhus, Aarhus, Denmark
| | - Rikkert Hindriks
- Department of Mathematics, Vrije Universiteit, Amsterdam, The Netherlands
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Abstract
Measurements on physical systems result from the systems' activity being converted into sensor measurements by a forward model. In a number of cases, inversion of the forward model is extremely sensitive to perturbations such as sensor noise or numerical errors in the forward model. Regularization is then required, which introduces bias in the reconstruction of the systems' activity. One domain in which this is particularly problematic is the reconstruction of interactions in spatially-extended complex systems such as the human brain. Brain interactions can be reconstructed from non-invasive measurements such as electroencephalography (EEG) or magnetoencephalography (MEG), whose forward models are linear and instantaneous, but have large null-spaces and high condition numbers. This leads to incomplete unmixing of the forward models and hence to spurious interactions. This motivated the development of interaction measures that are exclusively sensitive to lagged, i.e. delayed interactions. The drawback of such measures is that they only detect interactions that have sufficiently large lags and this introduces bias in reconstructed brain networks. We introduce three estimators for linear interactions in spatially-extended systems that are uniformly sensitive to all lags. We derive some basic properties of and relationships between the estimators and evaluate their performance using numerical simulations from a simple benchmark model.
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Affiliation(s)
- Rikkert Hindriks
- Department of Mathematics, VU University Amsterdam, Amsterdam, The Netherlands
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Hindriks R. A methodological framework for inverse-modeling of propagating cortical activity using MEG/EEG. Neuroimage 2020; 223:117345. [PMID: 32896634 DOI: 10.1016/j.neuroimage.2020.117345] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Revised: 08/18/2020] [Accepted: 09/01/2020] [Indexed: 11/16/2022] Open
Abstract
The prevailing view on the dynamics of large-scale electrical activity in the human cortex is that it constitutes a functional network of discrete and localized circuits. Within this view, a natural way to analyse magnetoencephalographic (MEG) and electroencephalographic (EEG) data is by adopting methods from network theory. Invasive recordings, however, demonstrate that cortical activity is spatially continuous, rather than discrete, and exhibits propagation behavior. Furthermore, human cortical activity is known to propagate under a variety of conditions such as non-REM sleep, general anesthesia, and coma. Although several MEG/EEG studies have investigated propagating cortical activity, not much is known about the conditions under which such activity can be successfully reconstructed from MEG/EEG sensor-data. This study provides a methodological framework for inverse-modeling of propagating cortical activity. Within this framework, cortical activity is represented in the spatial frequency domain, which is more natural than the dipole domain when dealing with spatially continuous activity. We define angular power spectra, which show how the power of cortical activity is distributed across spatial frequencies, angular gain/phase spectra, which characterize the spatial filtering properties of linear inverse operators, and angular resolution matrices, which summarize how linear inverse operators leak signal within and across spatial frequencies. We adopt the framework to provide insight into the performance of several linear inverse operators in reconstructing propagating cortical activity from MEG/EEG sensor-data. We also describe how prior spatial frequency information can be incorporated into the inverse-modeling to obtain better reconstructions.
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Affiliation(s)
- Rikkert Hindriks
- Department of Mathematics, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.
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Hindriks R, R M, N G, G D. Latency analysis of resting-state BOLD-fMRI reveals traveling waves in visual cortex linking task-positive and task-negative networks. Neuroimage 2019; 200:259-274. [DOI: 10.1016/j.neuroimage.2019.06.007] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2018] [Revised: 05/30/2019] [Accepted: 06/03/2019] [Indexed: 10/26/2022] Open
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Hindriks R, Micheli C, Bosman CA, Oostenveld R, Lewis C, Mantini D, Fries P, Deco G. Source-reconstruction of the sensorimotor network from resting-state macaque electrocorticography. Neuroimage 2018; 181:347-358. [PMID: 29886144 DOI: 10.1016/j.neuroimage.2018.06.010] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Revised: 06/01/2018] [Accepted: 06/04/2018] [Indexed: 10/28/2022] Open
Abstract
The discovery of hemodynamic (BOLD-fMRI) resting-state networks (RSNs) has brought about a fundamental shift in our thinking about the role of intrinsic brain activity. The electrophysiological underpinnings of RSNs remain largely elusive and it has been shown only recently that electric cortical rhythms are organized into the same RSNs as hemodynamic signals. Most electrophysiological studies into RSNs use magnetoencephalography (MEG) or scalp electroencephalography (EEG), which limits the spatial resolution with which electrophysiological RSNs can be observed. Due to their close proximity to the cortical surface, electrocorticographic (ECoG) recordings can potentially provide a more detailed picture of the functional organization of resting-state cortical rhythms, albeit at the expense of spatial coverage. In this study we propose using source-space spatial independent component analysis (spatial ICA) for identifying generators of resting-state cortical rhythms as recorded with ECoG and for reconstructing their functional connectivity. Network structure is assessed by two kinds of connectivity measures: instantaneous correlations between band-limited amplitude envelopes and oscillatory phase-locking. By simulating rhythmic cortical generators, we find that the reconstruction of oscillatory phase-locking is more challenging than that of amplitude correlations, particularly for low signal-to-noise levels. Specifically, phase-lags can both be over- and underestimated, which troubles the interpretation of lag-based connectivity measures. We illustrate the methodology on somatosensory beta rhythms recorded from a macaque monkey using ECoG. The methodology decomposes the resting-state sensorimotor network into three cortical generators, distributed across primary somatosensory and primary and higher-order motor areas. The generators display significant and reproducible amplitude correlations and phase-locking values with non-zero lags. Our findings illustrate the level of spatial detail attainable with source-projected ECoG and motivates wider use of the methodology for studying resting-state as well as event-related cortical dynamics in macaque and human.
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Affiliation(s)
- R Hindriks
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra (UPF), Spain; Department of Mathematics, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.
| | - C Micheli
- Institut des Sciences Cognitives Marc Jeannerod, UMR 5304, CNRS, Bron, France; Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, 6525, EN Nijmegen, the Netherlands
| | - C A Bosman
- Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, 6525, EN Nijmegen, the Netherlands; Cognitive and System Neuroscience Group, Swammerdam Institute for Life Sciences, Center for Neuroscience, University of Amsterdam, 1098, XH, Amsterdam, the Netherlands
| | - R Oostenveld
- Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, 6525, EN Nijmegen, the Netherlands
| | - C Lewis
- Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, 60528, Frankfurt, Germany
| | - D Mantini
- Research Center for Motor Control and Neuroplasticity, KU Leuven, Tervuursevest 101, 3001, Leuven, Belgium; Functional Neuroimaging Laboratory, IRCCS San Camillo Hospital, via Alberoni 70, 30126, Venice Lido, Italy
| | - P Fries
- Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, 6525, EN Nijmegen, the Netherlands; Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, 60528, Frankfurt, Germany
| | - G Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra (UPF), Spain; Instituci Catalana de la Recerca i Estudis Avanats (ICREA), Universitat Pompeu Fabra, Spain
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Hindriks R, Schmiedt J, Arsiwalla XD, Peter A, Verschure PFMJ, Fries P, Schmid MC, Deco G. Linear distributed source modeling of local field potentials recorded with intra-cortical electrode arrays. PLoS One 2017; 12:e0187490. [PMID: 29253006 PMCID: PMC5734682 DOI: 10.1371/journal.pone.0187490] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2016] [Accepted: 10/20/2017] [Indexed: 01/04/2023] Open
Abstract
Planar intra-cortical electrode (Utah) arrays provide a unique window into the spatial organization of cortical activity. Reconstruction of the current source density (CSD) underlying such recordings, however, requires “inverting” Poisson’s equation. For inter-laminar recordings, this is commonly done by the CSD method, which consists in taking the second-order spatial derivative of the recorded local field potentials (LFPs). Although the CSD method has been tremendously successful in mapping the current generators underlying inter-laminar LFPs, its application to planar recordings is more challenging. While for inter-laminar recordings the CSD method seems reasonably robust against violations of its assumptions, is it unclear as to what extent this holds for planar recordings. One of the objectives of this study is to characterize the conditions under which the CSD method can be successfully applied to Utah array data. Using forward modeling, we find that for spatially coherent CSDs, the CSD method yields inaccurate reconstructions due to volume-conducted contamination from currents in deeper cortical layers. An alternative approach is to “invert” a constructed forward model. The advantage of this approach is that any a priori knowledge about the geometrical and electrical properties of the tissue can be taken into account. Although several inverse methods have been proposed for LFP data, the applicability of existing electroencephalographic (EEG) and magnetoencephalographic (MEG) inverse methods to LFP data is largely unexplored. Another objective of our study therefore, is to assess the applicability of the most commonly used EEG/MEG inverse methods to Utah array data. Our main conclusion is that these inverse methods provide more accurate CSD reconstructions than the CSD method. We illustrate the inverse methods using event-related potentials recorded from primary visual cortex of a macaque monkey during a motion discrimination task.
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Affiliation(s)
- Rikkert Hindriks
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
| | - Joscha Schmiedt
- Ernst StrÜngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, 60528 Frankfurt, Germany
| | - Xerxes D Arsiwalla
- Synthetic Perceptive Emotive and Cognitive Systems (SPECS) Lab, Center of Autonomous Systems and Neurorobotics, Universitat Pompeu Fabra, Barcelona, Spain
| | - Alina Peter
- Ernst StrÜngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, 60528 Frankfurt, Germany
| | - Paul F M J Verschure
- Synthetic Perceptive Emotive and Cognitive Systems (SPECS) Lab, Center of Autonomous Systems and Neurorobotics, Universitat Pompeu Fabra, Barcelona, Spain.,Institucio Catalana de Recerca i Estudis Avancats (ICREA), Universitat Pompeu Fabra (UPF), Barcelona, Spain.,Institute for Bioengineering of Catalonia, 08028 Barcelona, Spain.,Barcelona Institute of Science and Technology, Barcelona, Spain
| | - Pascal Fries
- Ernst StrÜngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, 60528 Frankfurt, Germany
| | - Michael C Schmid
- Ernst StrÜngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, 60528 Frankfurt, Germany.,Institute of Neuroscience, Newcastle University, Newcastle upon Tyne, United Kingdom
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain.,Institucio Catalana de Recerca i Estudis Avancats (ICREA), Universitat Pompeu Fabra (UPF), Barcelona, Spain
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Silva Pereira S, Hindriks R, Mühlberg S, Maris E, van Ede F, Griffa A, Hagmann P, Deco G. Effect of Field Spread on Resting-State Magneto Encephalography Functional Network Analysis: A Computational Modeling Study. Brain Connect 2017; 7:541-557. [PMID: 28875718 DOI: 10.1089/brain.2017.0525] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
A popular way to analyze resting-state electroencephalography (EEG) and magneto encephalography (MEG) data is to treat them as a functional network in which sensors are identified with nodes and the interaction between channel time series and the network connections. Although conceptually appealing, the network-theoretical approach to sensor-level EEG and MEG data is challenged by the fact that EEG and MEG time series are mixtures of source activity. It is, therefore, of interest to assess the relationship between functional networks of source activity and the ensuing sensor-level networks. Since these topological features are of high interest in experimental studies, we address the question of to what extent the network topology can be reconstructed from sensor-level functional connectivity (FC) measures in case of MEG data. Simple simulations that consider only a small number of regions do not allow to assess network properties; therefore, we use a diffusion magnetic resonance imaging-constrained whole-brain computational model of resting-state activity. Our motivation lies behind the fact that still many contributions found in the literature perform network analysis at sensor level, and we aim at showing the discrepancies between source- and sensor-level network topologies by using realistic simulations of resting-state cortical activity. Our main findings are that the effect of field spread on network topology depends on the type of interaction (instantaneous or lagged) and leads to an underestimation of lagged FC at sensor level due to instantaneous mixing of cortical signals, instantaneous interaction is more sensitive to field spread than lagged interaction, and discrepancies are reduced when using planar gradiometers rather than axial gradiometers. We, therefore, recommend using lagged interaction measures on planar gradiometer data when investigating network properties of resting-state sensor-level MEG data.
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Affiliation(s)
- Silvana Silva Pereira
- 1 Computational Neuroscience Group, Center for Brain and Cognition, Universitat Pompeu Fabra, Barcelona, Spain
| | - Rikkert Hindriks
- 1 Computational Neuroscience Group, Center for Brain and Cognition, Universitat Pompeu Fabra, Barcelona, Spain
| | - Stefanie Mühlberg
- 1 Computational Neuroscience Group, Center for Brain and Cognition, Universitat Pompeu Fabra, Barcelona, Spain
| | - Eric Maris
- 2 Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, The Netherlands
| | - Freek van Ede
- 2 Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, The Netherlands
| | - Alessandra Griffa
- 3 Department of Radiology, Lausanne University Hospital (CHUV-UNIL), Lausanne, Switzerland .,4 Signal Processing Laboratory 5 , Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland
| | - Patric Hagmann
- 3 Department of Radiology, Lausanne University Hospital (CHUV-UNIL), Lausanne, Switzerland
| | - Gustavo Deco
- 1 Computational Neuroscience Group, Center for Brain and Cognition, Universitat Pompeu Fabra, Barcelona, Spain .,5 Institució Catalana de la Recerca i Estudis Avanats (ICREA), Barcelona, Spain
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15
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Pannunzi M, Hindriks R, Bettinardi RG, Wenger E, Lisofsky N, Martensson J, Butler O, Filevich E, Becker M, Lochstet M, Kühn S, Deco G. Resting-state fMRI correlations: From link-wise unreliability to whole brain stability. Neuroimage 2017; 157:250-262. [PMID: 28599964 DOI: 10.1016/j.neuroimage.2017.06.006] [Citation(s) in RCA: 55] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Revised: 05/30/2017] [Accepted: 06/01/2017] [Indexed: 12/23/2022] Open
Abstract
The functional architecture of spontaneous BOLD fluctuations has been characterized in detail by numerous studies, demonstrating its potential relevance as a biomarker. However, the systematic investigation of its consistency is still in its infancy. Here, we analyze within- and between-subject variability and test-retest reliability of resting-state functional connectivity (FC) in a unique data set comprising multiple fMRI scans (42) from 5 subjects, and 50 single scans from 50 subjects. We adopt a statistical framework that enables us to identify different sources of variability in FC. We show that the low reliability of single links can be significantly improved by using multiple scans per subject. Moreover, in contrast to earlier studies, we show that spatial heterogeneity in FC reliability is not significant. Finally, we demonstrate that despite the low reliability of individual links, the information carried by the whole-brain FC matrix is robust and can be used as a functional fingerprint to identify individual subjects from the population.
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Affiliation(s)
- Mario Pannunzi
- Universitat Pompeu Fabra, Theoretical and Computational Neuroscience, Center for Brain and Cognition, Roc Boronat, 138, 08018 Barcelona, Spain.
| | - Rikkert Hindriks
- Universitat Pompeu Fabra, Theoretical and Computational Neuroscience, Center for Brain and Cognition, Roc Boronat, 138, 08018 Barcelona, Spain
| | - Ruggero G Bettinardi
- Universitat Pompeu Fabra, Theoretical and Computational Neuroscience, Center for Brain and Cognition, Roc Boronat, 138, 08018 Barcelona, Spain
| | - Elisabeth Wenger
- Max Planck Institute for Human Development, Center for Lifespan Psychology, Lentzeallee 94, 14195 Berlin, Germany
| | - Nina Lisofsky
- Max Planck Institute for Human Development, Center for Lifespan Psychology, Lentzeallee 94, 14195 Berlin, Germany; University Clinic Hamburg-Eppendorf, Clinic and Policlinic for Psychiatry and Psychotherapy, Martinistraße 52, 20246 Hamburg, Germany
| | - Johan Martensson
- Max Planck Institute for Human Development, Center for Lifespan Psychology, Lentzeallee 94, 14195 Berlin, Germany; Department of psychology, Lund University, Box 117, 221 00 Lund, Sweden
| | - Oisin Butler
- Max Planck Institute for Human Development, Center for Lifespan Psychology, Lentzeallee 94, 14195 Berlin, Germany
| | - Elisa Filevich
- Department of Psychology, Humboldt Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany; Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13 Haus 6, 10115 Berlin, Germany
| | - Maxi Becker
- Max Planck Institute for Human Development, Center for Lifespan Psychology, Lentzeallee 94, 14195 Berlin, Germany; University Clinic Hamburg-Eppendorf, Clinic and Policlinic for Psychiatry and Psychotherapy, Martinistraße 52, 20246 Hamburg, Germany
| | - Martyna Lochstet
- Max Planck Institute for Human Development, Center for Lifespan Psychology, Lentzeallee 94, 14195 Berlin, Germany
| | - Simone Kühn
- Max Planck Institute for Human Development, Center for Lifespan Psychology, Lentzeallee 94, 14195 Berlin, Germany; University Clinic Hamburg-Eppendorf, Clinic and Policlinic for Psychiatry and Psychotherapy, Martinistraße 52, 20246 Hamburg, Germany
| | - Gustavo Deco
- Universitat Pompeu Fabra, Theoretical and Computational Neuroscience, Center for Brain and Cognition, Roc Boronat, 138, 08018 Barcelona, Spain; Institució Catalana de Recerca i Estudis Avançats (ICREA), Universitat Pompeu Fabra, Theoretical and Computational Neuroscience, Center for Brain and Cognition, Roc Boronat, 138, 08018 Barcelona, Spain
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16
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Hindriks R, Arsiwalla XD, Panagiotaropoulos T, Besserve M, Verschure PFMJ, Logothetis NK, Deco G. Discrepancies between Multi-Electrode LFP and CSD Phase-Patterns: A Forward Modeling Study. Front Neural Circuits 2016; 10:51. [PMID: 27471451 PMCID: PMC4945652 DOI: 10.3389/fncir.2016.00051] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Accepted: 06/29/2016] [Indexed: 01/05/2023] Open
Abstract
Multi-electrode recordings of local field potentials (LFPs) provide the opportunity to investigate the spatiotemporal organization of neural activity on the scale of several millimeters. In particular, the phases of oscillatory LFPs allow studying the coordination of neural oscillations in time and space and to tie it to cognitive processing. Given the computational roles of LFP phases, it is important to know how they relate to the phases of the underlying current source densities (CSDs) that generate them. Although CSDs and LFPs are distinct physical quantities, they are often (implicitly) identified when interpreting experimental observations. That this identification is problematic is clear from the fact that LFP phases change when switching to different electrode montages, while the underlying CSD phases remain unchanged. In this study we use a volume-conductor model to characterize discrepancies between LFP and CSD phase-patterns, to identify the contributing factors, and to assess the effect of different electrode montages. Although we focus on cortical LFPs recorded with two-dimensional (Utah) arrays, our findings are also relevant for other electrode configurations. We found that the main factors that determine the discrepancy between CSD and LFP phase-patterns are the frequency of the neural oscillations and the extent to which the laminar CSD profile is balanced. Furthermore, the presence of laminar phase-differences in cortical oscillations, as commonly observed in experiments, precludes identifying LFP phases with those of the CSD oscillations at a given cortical depth. This observation potentially complicates the interpretation of spike-LFP coherence and spike-triggered LFP averages. With respect to reference strategies, we found that the average-reference montage leads to larger discrepancies between LFP and CSD phases as compared with the referential montage, while the Laplacian montage reduces these discrepancies. We therefore advice to conduct analysis of two-dimensional LFP recordings using the Laplacian montage.
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Affiliation(s)
- Rikkert Hindriks
- Computational Neuroscience Group, Department of Information, Center for Brain and Cognition Barcelona, Spain
| | - Xerxes D Arsiwalla
- Synthetic Perceptive Emotive and Cognitive Systems Lab, Center of Autonomous Systems and Neurorobotics, Universitat Pompeu Fabra Barcelona, Spain
| | - Theofanis Panagiotaropoulos
- Department Physiology of Cognitive Processes, Max Planck Institute for Biological CyberneticsTubingen, Germany; Centre for Systems Neuroscience, University of LeicesterLeicester, UK; King's College London, Institute of Psychiatry, Psychology and NeuroscienceLondon, UK
| | - Michel Besserve
- Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics Tubingen, Germany
| | - Paul F M J Verschure
- Synthetic Perceptive Emotive and Cognitive Systems Lab, Center of Autonomous Systems and Neurorobotics, Universitat Pompeu FabraBarcelona, Spain; Institucio Catalana de Recerca i Estudis Avancats (ICREA), Universitat Pompeu FabraBarcelona, Spain
| | - Nikos K Logothetis
- Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics Tubingen, Germany
| | - Gustavo Deco
- Computational Neuroscience Group, Department of Information, Center for Brain and CognitionBarcelona, Spain; Institucio Catalana de Recerca i Estudis Avancats (ICREA), Universitat Pompeu FabraBarcelona, Spain
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17
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Kaplan R, Adhikari MH, Hindriks R, Mantini D, Murayama Y, Logothetis NK, Deco G. Hippocampal Sharp-Wave Ripples Influence Selective Activation of the Default Mode Network. Curr Biol 2016; 26:686-91. [PMID: 26898464 PMCID: PMC4791429 DOI: 10.1016/j.cub.2016.01.017] [Citation(s) in RCA: 61] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2015] [Revised: 12/08/2015] [Accepted: 01/05/2016] [Indexed: 11/30/2022]
Abstract
The default mode network (DMN) is a commonly observed resting-state network (RSN) that includes medial temporal, parietal, and prefrontal regions involved in episodic memory [1, 2, 3]. The behavioral relevance of endogenous DMN activity remains elusive, despite an emerging literature correlating resting fMRI fluctuations with memory performance [4, 5]—particularly in DMN regions [6, 7, 8]. Mechanistic support for the DMN’s role in memory consolidation might come from investigation of large deflections (sharp-waves) in the hippocampal local field potential that co-occur with high-frequency (>80 Hz) oscillations called ripples—both during sleep [9, 10] and awake deliberative periods [11, 12, 13]. Ripples are ideally suited for memory consolidation [14, 15], since the reactivation of hippocampal place cell ensembles occurs during ripples [16, 17, 18, 19]. Moreover, the number of ripples after learning predicts subsequent memory performance in rodents [20, 21, 22] and humans [23], whereas electrical stimulation of the hippocampus after learning interferes with memory consolidation [24, 25, 26]. A recent study in macaques showed diffuse fMRI neocortical activation and subcortical deactivation specifically after ripples [27]. Yet it is unclear whether ripples and other hippocampal neural events influence endogenous fluctuations in specific RSNs—like the DMN—unitarily. Here, we examine fMRI datasets from anesthetized monkeys with simultaneous hippocampal electrophysiology recordings, where we observe a dramatic increase in the DMN fMRI signal following ripples, but not following other hippocampal electrophysiological events. Crucially, we find increases in ongoing DMN activity after ripples, but not in other RSNs. Our results relate endogenous DMN fluctuations to hippocampal ripples, thereby linking network-level resting fMRI fluctuations with behaviorally relevant circuit-level neural dynamics. Behavioral relevance of offline fluctuations in the default mode network is unclear Hippocampal sharp-wave ripples during rest are linked with memory consolidation Default mode network signal increases after ripples, but not other hippocampal events Other neocortical resting-state networks do not show similar changes after ripples
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Affiliation(s)
- Raphael Kaplan
- Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK; Center for Brain and Cognition, Departament de Tecnologies de la Informació I les Comunicacions, Universitat Pompeu Fabra, Roc Boronat 138, 08018 Barcelona, Spain.
| | - Mohit H Adhikari
- Center for Brain and Cognition, Departament de Tecnologies de la Informació I les Comunicacions, Universitat Pompeu Fabra, Roc Boronat 138, 08018 Barcelona, Spain
| | - Rikkert Hindriks
- Center for Brain and Cognition, Departament de Tecnologies de la Informació I les Comunicacions, Universitat Pompeu Fabra, Roc Boronat 138, 08018 Barcelona, Spain
| | - Dante Mantini
- Department of Health Sciences and Technology, ETH Zurich, 8057 Zurich, Switzerland; Movement Control and Neuroplasticity Research Group, KU Leuven, 3001 Leuven, Belgium
| | - Yusuke Murayama
- Max Planck Institute for Biological Cybernetics, 72076 Tübingen, Germany
| | - Nikos K Logothetis
- Max Planck Institute for Biological Cybernetics, 72076 Tübingen, Germany; Imaging Science and Biomedical Engineering, University of Manchester, Manchester M13 9PT, UK
| | - Gustavo Deco
- Center for Brain and Cognition, Departament de Tecnologies de la Informació I les Comunicacions, Universitat Pompeu Fabra, Roc Boronat 138, 08018 Barcelona, Spain; Institució Catalana de la Recerca i Estudis Avançats (ICREA), Universitat Pompeu Fabra, Passeig Lluís Companys 23, Barcelona 08010, Spain
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18
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Hindriks R, Adhikari MH, Murayama Y, Ganzetti M, Mantini D, Logothetis NK, Deco G. Corrigendum to "Can sliding-window correlations reveal dynamic functional connectivity in resting-state fMRI?" [NeuroImage 127 (2016) 242-256]. Neuroimage 2016; 132:115. [PMID: 27131042 PMCID: PMC5603728 DOI: 10.1016/j.neuroimage.2016.02.007] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Affiliation(s)
- R Hindriks
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain.
| | - M H Adhikari
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
| | - Y Murayama
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
| | - M Ganzetti
- Department of Health Sciences and Technology, ETH Zurich, Switzerland; Department of Experimental Psychology, University of Oxford, United Kingdom
| | - D Mantini
- Department of Health Sciences and Technology, ETH Zurich, Switzerland; Department of Experimental Psychology, University of Oxford, United Kingdom
| | - N K Logothetis
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
| | - G Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain; Instituci Catalana de la Recerca i Estudis Avanats (ICREA), Universitat Pompeu Fabra, Barcelona, Spain
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19
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Hindriks R, Adhikari MH, Murayama Y, Ganzetti M, Mantini D, Logothetis NK, Deco G. Can sliding-window correlations reveal dynamic functional connectivity in resting-state fMRI? Neuroimage 2015; 127:242-256. [PMID: 26631813 PMCID: PMC4758830 DOI: 10.1016/j.neuroimage.2015.11.055] [Citation(s) in RCA: 366] [Impact Index Per Article: 40.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2015] [Revised: 10/27/2015] [Accepted: 11/23/2015] [Indexed: 11/16/2022] Open
Abstract
During the last several years, the focus of research on resting-state functional magnetic resonance imaging (fMRI) has shifted from the analysis of functional connectivity averaged over the duration of scanning sessions to the analysis of changes of functional connectivity within sessions. Although several studies have reported the presence of dynamic functional connectivity (dFC), statistical assessment of the results is not always carried out in a sound way and, in some studies, is even omitted. In this study, we explain why appropriate statistical tests are needed to detect dFC, we describe how they can be carried out and how to assess the performance of dFC measures, and we illustrate the methodology using spontaneous blood-oxygen level-dependent (BOLD) fMRI recordings of macaque monkeys under general anesthesia and in human subjects under resting-state conditions. We mainly focus on sliding-window correlations since these are most widely used in assessing dFC, but also consider a recently proposed non-linear measure. The simulations and methodology, however, are general and can be applied to any measure. The results are twofold. First, through simulations, we show that in typical resting-state sessions of 10 min, it is almost impossible to detect dFC using sliding-window correlations. This prediction is validated by both the macaque and the human data: in none of the individual recording sessions was evidence for dFC found. Second, detection power can be considerably increased by session- or subject-averaging of the measures. In doing so, we found that most of the functional connections are in fact dynamic. With this study, we hope to raise awareness of the statistical pitfalls in the assessment of dFC and how they can be avoided by using appropriate statistical methods.
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Affiliation(s)
- R Hindriks
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain.
| | - M H Adhikari
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
| | - Y Murayama
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
| | - M Ganzetti
- Department of Health Sciences and Technology, ETH Zurich, Switzerland; Department of Experimental Psychology, University of Oxford, United Kingdom
| | - D Mantini
- Department of Health Sciences and Technology, ETH Zurich, Switzerland; Department of Experimental Psychology, University of Oxford, United Kingdom
| | - N K Logothetis
- Department of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
| | - G Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain; Instituci Catalana de la Recerca i Estudis Avanats (ICREA), Universitat Pompeu Fabra, Barcelona, Spain
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20
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Hindriks R, van Putten MJAM, Deco G. Intra-cortical propagation of EEG alpha oscillations. Neuroimage 2014; 103:444-453. [PMID: 25168275 DOI: 10.1016/j.neuroimage.2014.08.027] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2014] [Revised: 08/13/2014] [Accepted: 08/17/2014] [Indexed: 11/18/2022] Open
Abstract
The most salient feature of spontaneous human brain activity as recorded with electroencephalography (EEG) are rhythmic fluctuations around 10Hz. These alpha oscillations have been reported to propagate over the scalp with velocities in the range of 5-15m/s. Since these velocities are in the range of action potential velocities through cortico-cortical axons, it has been hypothesized that the observed scalp waves reflect cortico-cortically mediated propagation of cortical oscillations. The reported scalp velocities however, appear to be inconsistent with those estimated from local field potential recordings in dogs, which are <1m/s and agree with the propagation velocity of action potentials in intra-cortical axons. In this study, we resolve these diverging findings using a combination of EEG data-analysis and biophysical modeling. In particular, we demonstrate that the observed scalp velocities can be accounted for by slow traveling oscillations, which provides support for the claim that spatial propagation of alpha oscillations is mediated by intra-cortical axons.
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Affiliation(s)
- Rikkert Hindriks
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Roc Boronat 138, Barcelona, 08018, Spain.
| | - Michel J A M van Putten
- Department of Clinical Neurophysiology, MIRA-Institute for Biomedical Technology and Technical Medicine, University of Twente, 7500 AE Enschede, The Netherlands; Department of Neurology and Clinical Neurophysiology, Medisch Spectrum Twente, Enschede, The Netherlands
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Roc Boronat 138, Barcelona, 08018, Spain; Instituci Catalana de la Recerca i Estudis Avanats (ICREA), Universitat Pompeu Fabra, Passeig Llus Companys 23, Barcelona, 08010, Spain
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21
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Tjepkema-Cloostermans MC, Hindriks R, Hofmeijer J, van Putten MJ. Generalized periodic discharges after acute cerebral ischemia: Reflection of selective synaptic failure? Clin Neurophysiol 2014; 125:255-62. [PMID: 24012049 DOI: 10.1016/j.clinph.2013.08.005] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2013] [Revised: 07/08/2013] [Accepted: 08/05/2013] [Indexed: 10/26/2022]
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Hindriks R, Meijer HGE, van Gils SA, van Putten MJAM. Phase-locking of epileptic spikes to ongoing delta oscillations in non-convulsive status epilepticus. Front Syst Neurosci 2013; 7:111. [PMID: 24379763 PMCID: PMC3863724 DOI: 10.3389/fnsys.2013.00111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2013] [Accepted: 11/26/2013] [Indexed: 12/05/2022] Open
Abstract
The EEG of patients in non-convulsive status epilepticus (NCSE) often displays delta oscillations or generalized spike-wave discharges. In some patients, these delta oscillations coexist with intermittent epileptic spikes. In this study we verify the prediction of a computational model of the thalamo-cortical system that these spikes are phase-locked to the delta oscillations. We subsequently describe the physiological mechanism underlying this observation as suggested by the model. It is suggested that the spikes reflect inhibitory stochastic fluctuations in the input to thalamo-cortical relay neurons and phase-locking is a consequence of differential excitability of relay neurons over the delta cycle. Further analysis shows that the observed phase-locking can be regarded as a stochastic precursor of generalized spike-wave discharges. This study thus provides an explanation of intermittent spikes during delta oscillations in NCSE and might be generalized to other encephathologies in which delta activity can be observed.
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Affiliation(s)
- Rikkert Hindriks
- Department of Clinical Neurophysiology, MIRA-Institute for Biomedical Technology and Technical Medicine, University of Twente Enschede, Netherlands ; Computational Neuroscience Group, Department of Information and Communication Technologies, Center for Brain and Cognition, Universitat Pompeu Fabra Barcelona, Spain
| | - Hil G E Meijer
- Department of Electrical Engineering, Mathematics and Computer Science, MIRA-Institute for Biomedical Technology and Technical Medicine, University of Twente Enschede, Netherlands
| | - Stephan A van Gils
- Department of Electrical Engineering, Mathematics and Computer Science, MIRA-Institute for Biomedical Technology and Technical Medicine, University of Twente Enschede, Netherlands
| | - Michel J A M van Putten
- Department of Clinical Neurophysiology, MIRA-Institute for Biomedical Technology and Technical Medicine, University of Twente Enschede, Netherlands ; Department of Neurology and Clinical Neurophysiology, Medisch Spectrum Twente Enschede, Netherlands
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23
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Hindriks R, Woolrich M, Kringelbach M, Luckhoo H, Joensson M, Mohseni H, Deco G. Role of anatomical pathways in shaping posterior alpha oscillations in the resting human brain. BMC Neurosci 2013. [PMCID: PMC3704852 DOI: 10.1186/1471-2202-14-s1-p98] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
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Hindriks R, van Putten MJAM. Thalamo-cortical mechanisms underlying changes in amplitude and frequency of human alpha oscillations. Neuroimage 2012; 70:150-63. [PMID: 23266701 DOI: 10.1016/j.neuroimage.2012.12.018] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2012] [Revised: 12/07/2012] [Accepted: 12/08/2012] [Indexed: 11/15/2022] Open
Abstract
Although a large number of studies have been devoted to establishing correlations between changes in amplitude and frequency of EEG alpha oscillations and cognitive processes, it is currently unclear through which physiological mechanisms such changes are brought about. In this study we use a biophysical model of EEG generation to gain a fundamental understanding of the functional changes within the thalamo-cortical system that might underly such alpha responses. The main result of this study is that, although the physiology of the thalamo-cortical system is characterized by a large number of parameters, alpha responses effectively depend on only three variables. Physiologically, these variables determine the resonance properties of feedforward, cortico-thalamo-cortical, and intra-cortical circuits. By examining the effect of modulations of these resonances on the amplitude and frequency of EEG alpha oscillations, it is established that the model can reproduce the variety of experimentally observed alpha responses, as well as the experimental finding that changes in alpha amplitude are typically an order of magnitude larger than changes in alpha frequency. The modeling results are also in line with the fact that alpha responses often correlate linearly with indices characterizing cognitive processes. By investigating the effect of synaptic and intrinsic neuronal parameters, we find that alpha responses reflect changes in cortical activation, which is consistent with the hypothesis that alpha activity serves to selectively inhibit cortical regions during cognitive processing demands. As an example of how these analyses can be applied to specific experimental protocols, we reproduce benzodiazepine-induced alpha responses and clarify the putative underlying thalamo-cortical mechanisms. The findings reported in this study provide a fundamental physiological framework within which alpha responses observed in specific experimental protocols can be understood.
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Affiliation(s)
- Rikkert Hindriks
- Department of Clinical Neurophysiology, MIRA-Institute for Biomedical Technology and Technical Medicine, University of Twente, 7500 AE Enschede, The Netherlands.
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Hindriks R, Jansen R, Bijma F, Mansvelder HD, de Gunst MCM, van der Vaart AW. Unbiased estimation of Langevin dynamics from time series with application to hippocampal field potentials in vitro. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 84:021133. [PMID: 21928975 DOI: 10.1103/physreve.84.021133] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2010] [Revised: 06/14/2011] [Indexed: 05/31/2023]
Abstract
The last decade showed an increased interest in Langevin equations for modeling time series recorded from complex dynamical systems. These equations allow to discriminate between deterministic (drift) and stochastic (diffusion) components of the recorded time series. In practice, the estimation of drift and diffusion is often based on approximations of the models' dynamics that are valid only for high sampling frequencies. Also, model assessment is not or only indirectly performed, potentially leading to false claims. In this study we compare the performance of an asymptotically unbiased estimation method with a generally used approximate method, demonstrating the necessity of using (asymptotically) unbiased estimators. Furthermore, we describe how confidence intervals for the unknown parameters can be constructed and how model assessment can be carried out. We apply the methodology to local field potentials recorded in vitro from mouse hippocampus from eight genetically different strains. The recorded field potentials turn out to be well described by linearly damped Langevin equations with parabolic diffusion. The modeling enables a dynamical interpretation of the spectral power of the field potentials. It reveals that observed spectral power differences in the field potentials across hippocampal regions are associated with differences in the deterministic component of the system, and it reveals transiently active current dipoles, which are not detectable by conventional methods. Also, all estimated parameters have significant heritabilities, which suggests that the Langevin equations capture biological relevant aspects of electrical hippocampal activity.
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Affiliation(s)
- R Hindriks
- Department of Mathematics, VU University Amsterdam, The Netherlands
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Hindriks R, Bijma F, van Dijk BW, Stam CJ, van der Werf YY, van Someren EJW, de Munck JC, van der Vaart AW. Data-driven modeling of phase interactions between spontaneous MEG oscillations. Hum Brain Mapp 2011; 32:1161-78. [PMID: 21225630 PMCID: PMC6869992 DOI: 10.1002/hbm.21099] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2008] [Revised: 03/12/2010] [Accepted: 04/23/2010] [Indexed: 11/06/2022] Open
Abstract
OBJECTIVE Synchronization between distributed rhythms in the brain is commonly assessed by estimating the synchronization strength from simultaneous measurements. This approach, however, does not elucidate the phase dynamics that underlies synchronization. For this, an explicit dynamical model is required. Based on the assumption that the recorded rhythms can be described as weakly coupled oscillators, we propose a method for characterizing their phase-interaction dynamics. METHODS We propose to model ongoing magnetoencephalographic (MEG) oscillations as weakly coupled oscillators. Based on this model, the phase interactions between simultaneously recorded signals are characterized by estimating the modulation in instantaneous frequency as a function of their phase difference. Furthermore, we mathematically derive the effect of volume conduction on the model and show how indices for strength and direction of coupling can be derived. RESULTS The methodology is tested using simulations and is applied to ongoing occipital-frontal MEG oscillations of healthy subjects in the alpha and beta bands during rest. The simulations show that the model is robust against the presence of noise, short observation times, and model violations. The application to MEG data shows that the model can reconstruct the observed occipital-frontal phase difference distributions. Furthermore, it suggests that phase locking in the alpha and beta band is established by qualitatively different mechanisms. CONCLUSION When the recorded rhythms are assumed to be weakly coupled oscillators, a dynamical model for the phase interactions can be fitted to data. The model is able to reconstruct the observed phase difference distribution, and hence, provides a dynamical explanation for observed phase locking.
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Affiliation(s)
- Rikkert Hindriks
- Department of Mathematics, Faculty of Sciences, VU University Amsterdam, Amsterdam, The Netherlands.
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Hindriks R, Bijma F, van Dijk BW, van der Werf YD, van Someren EJW, van der Vaart AW. Dynamics underlying spontaneous human alpha oscillations: a data-driven approach. Neuroimage 2011; 57:440-51. [PMID: 21558008 DOI: 10.1016/j.neuroimage.2011.04.043] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2010] [Revised: 03/18/2011] [Accepted: 04/20/2011] [Indexed: 12/01/2022] Open
Abstract
Although the cognitive and clinical correlates of spontaneous human alpha oscillations as recorded with electroencephalography (EEG) or magnetoencephalography (MEG) are well documented, the dynamics underlying these oscillations is still a matter of debate. This study proposes a data-driven method to reveal the dynamics of these oscillations. It demonstrates that spontaneous human alpha oscillations as recorded with MEG can be viewed as noise-perturbed damped harmonic oscillations. This provides evidence for the hypothesis that these oscillations reflect filtered noise and hence do not possess limit-cycle dynamics. To illustrate the use of the model, we apply it to two data-sets in which a decrease in alpha power can be observed across conditions. The associated differences in the estimated model parameters show that observed decreases in alpha power are associated with different kinds of changes in the dynamics. Thus, the model parameters are useful dynamical biomarkers for spontaneous human alpha oscillations.
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Affiliation(s)
- R Hindriks
- Department of Mathematics, Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands.
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