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Khanra P, Nakuci J, Muldoon S, Watanabe T, Masuda N. Reliability of energy landscape analysis of resting-state functional MRI data. Eur J Neurosci 2024. [PMID: 38837814 DOI: 10.1111/ejn.16390] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Revised: 04/05/2024] [Accepted: 04/25/2024] [Indexed: 06/07/2024]
Abstract
Energy landscape analysis is a data-driven method to analyse multidimensional time series, including functional magnetic resonance imaging (fMRI) data. It has been shown to be a useful characterization of fMRI data in health and disease. It fits an Ising model to the data and captures the dynamics of the data as movement of a noisy ball constrained on the energy landscape derived from the estimated Ising model. In the present study, we examine test-retest reliability of the energy landscape analysis. To this end, we construct a permutation test that assesses whether or not indices characterizing the energy landscape are more consistent across different sets of scanning sessions from the same participant (i.e. within-participant reliability) than across different sets of sessions from different participants (i.e. between-participant reliability). We show that the energy landscape analysis has significantly higher within-participant than between-participant test-retest reliability with respect to four commonly used indices. We also show that a variational Bayesian method, which enables us to estimate energy landscapes tailored to each participant, displays comparable test-retest reliability to that using the conventional likelihood maximization method. The proposed methodology paves the way to perform individual-level energy landscape analysis for given data sets with a statistically controlled reliability.
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Affiliation(s)
- Pitambar Khanra
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York, USA
| | - Johan Nakuci
- School of Psychology, Georgia Institute of Technology, Atlanta, Georgia, USA
| | - Sarah Muldoon
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York, USA
- Institute for Artificial Intelligence and Data Science, State University of New York at Buffalo, Buffalo, New York, USA
| | - Takamitsu Watanabe
- International Research Centre for Neurointelligence, The University of Tokyo, Tokyo, Japan
| | - Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York, USA
- Institute for Artificial Intelligence and Data Science, State University of New York at Buffalo, Buffalo, New York, USA
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2
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Mohan UR, Zhang H, Ermentrout B, Jacobs J. The direction of theta and alpha travelling waves modulates human memory processing. Nat Hum Behav 2024; 8:1124-1135. [PMID: 38459263 DOI: 10.1038/s41562-024-01838-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Accepted: 01/24/2024] [Indexed: 03/10/2024]
Abstract
To support a range of behaviours, the brain must flexibly coordinate neural activity across widespread brain regions. One potential mechanism for this coordination is a travelling wave, in which a neural oscillation propagates across the brain while organizing the order and timing of activity across regions. Although travelling waves are present across the brain in various species, their potential functional relevance has remained unknown. Here, using rare direct human brain recordings, we demonstrate a distinct functional role for travelling waves of theta- and alpha-band (2-13 Hz) oscillations in the cortex. Travelling waves propagate in different directions during separate cognitive processes. In episodic memory, travelling waves tended to propagate in a posterior-to-anterior direction during successful memory encoding and in an anterior-to-posterior direction during recall. Because travelling waves of oscillations correspond to local neuronal spiking, these patterns indicate that rhythmic pulses of activity move across the brain in different directions for separate behaviours. More broadly, our results suggest a fundamental role for travelling waves and oscillations in dynamically coordinating neural connectivity, by flexibly organizing the timing and directionality of network interactions across the cortex to support cognition and behaviour.
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Affiliation(s)
- Uma R Mohan
- Surgical Neurology Branch, NINDS, National Institutes of Health, Bethesda, MD, USA
| | | | - Bard Ermentrout
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
| | - Joshua Jacobs
- Department of Biomedical Engineering, Columbia University, New York City, NY, USA.
- Department of Neurological Surgery, Columbia University, New York City, NY, USA.
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3
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Xie M, Khan SU, Sumelka W, Alamri AM, AlQahtani SA. Advanced stability analysis of a fractional delay differential system with stochastic phenomena using spectral collocation method. Sci Rep 2024; 14:12047. [PMID: 38802447 PMCID: PMC11130344 DOI: 10.1038/s41598-024-62851-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Accepted: 05/22/2024] [Indexed: 05/29/2024] Open
Abstract
In recent years, there has been a growing interest in incorporating fractional calculus into stochastic delay systems due to its ability to model complex phenomena with uncertainties and memory effects. The fractional stochastic delay differential equations are conventional in modeling such complex dynamical systems around various applied fields. The present study addresses a novel spectral approach to demonstrate the stability behavior and numerical solution of the systems characterized by stochasticity along with fractional derivatives and time delay. By bridging the gap between fractional calculus, stochastic processes, and spectral analysis, this work contributes to the field of fractional dynamics and enriches the toolbox of analytical tools available for investigating the stability of systems with delays and uncertainties. To illustrate the practical implications and validate the theoretical findings of our approach, some numerical simulations are presented.
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Affiliation(s)
- Mengqi Xie
- Department of Electronic Information Engineering, Xi'an Technological University, Xi'an, 710021, China
| | - Sami Ullah Khan
- Department of Mathematics, City University of Science and Information Technology, Peshawar, KP, 2500, Pakistan.
| | - Wojciech Sumelka
- Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5 Street, 60-965, Poznan, Poland
| | - Atif M Alamri
- Software Engineering Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia
| | - Salman A AlQahtani
- Computer Engineering Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia
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4
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Potratzki M, Bröhl T, Rings T, Lehnertz K. Synchronization dynamics of phase oscillators on power grid models. CHAOS (WOODBURY, N.Y.) 2024; 34:043131. [PMID: 38598675 DOI: 10.1063/5.0197930] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 03/25/2024] [Indexed: 04/12/2024]
Abstract
We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous natural frequencies. We employ the complex-valued order parameter-a widely used indicator for phase ordering-to assess the synchronization dynamics and observe the order parameter to exhibit either constant or periodic or non-periodic, possibly chaotic temporal evolutions for a given coupling strength but depending on initial conditions and the systems' disorder. Interestingly, both topological and spectral characteristics of the power grids point to a diminished capability of these networks to support a temporarily stable synchronization dynamics. We find non-trivial commonalities between the synchronization dynamics of oscillators on seemingly opposing topologies.
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Affiliation(s)
- Max Potratzki
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
| | - Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
- Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany
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5
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Rosa LAS, Brugnago EL, Delben GJ, Rost JM, Beims MW. The influence of hyperchaoticity, synchronization, and Shannon entropy on the performance of a physical reservoir computer. CHAOS (WOODBURY, N.Y.) 2024; 34:043120. [PMID: 38579146 DOI: 10.1063/5.0175001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 03/21/2024] [Indexed: 04/07/2024]
Abstract
In this paper, we analyze the dynamic effect of a reservoir computer (RC) on its performance. Modified Kuramoto's coupled oscillators are used to model the RC, and synchronization, Lyapunov spectrum (and dimension), Shannon entropy, and the upper bound of the Kolmogorov-Sinai entropy are employed to characterize the dynamics of the RC. The performance of the RC is analyzed by reproducing the distribution of random, Gaussian, and quantum jumps series (shelved states) since a replica of the time evolution of a completely random series is not possible to generate. We demonstrate that hyperchaotic motion, moderate Shannon entropy, and a higher degree of synchronization of Kuramoto's oscillators lead to the best performance of the RC. Therefore, an appropriate balance of irregularity and order in the oscillator's dynamics leads to better performances.
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Affiliation(s)
- Lucas A S Rosa
- Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Paraná, Brazil
| | - Eduardo L Brugnago
- Instituto de Fí sica, Universidade de São Paulo, 05508-090 São Paulo, SP, Brazil
| | - Guilherme J Delben
- Departamento de Ciências Naturais e Sociais, Universidade Federal de Santa Catarina, 89520-000 Curitibanos, SC, Brazil
| | - Jan-Michael Rost
- Max-Planck Institute for the Physics of Complex Systems, Nöthnitzerstr.38, 01187 Dresden, Germany
| | - Marcus W Beims
- Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Paraná, Brazil
- Max-Planck Institute for the Physics of Complex Systems, Nöthnitzerstr.38, 01187 Dresden, Germany
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6
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von Wegner F, Wiemers M, Hermann G, Tödt I, Tagliazucchi E, Laufs H. Complexity Measures for EEG Microstate Sequences: Concepts and Algorithms. Brain Topogr 2024; 37:296-311. [PMID: 37751054 PMCID: PMC10884068 DOI: 10.1007/s10548-023-01006-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2023] [Accepted: 08/31/2023] [Indexed: 09/27/2023]
Abstract
EEG microstate sequence analysis quantifies properties of ongoing brain electrical activity which is known to exhibit complex dynamics across many time scales. In this report we review recent developments in quantifying microstate sequence complexity, we classify these approaches with regard to different complexity concepts, and we evaluate excess entropy as a yet unexplored quantity in microstate research. We determined the quantities entropy rate, excess entropy, Lempel-Ziv complexity (LZC), and Hurst exponents on Potts model data, a discrete statistical mechanics model with a temperature-controlled phase transition. We then applied the same techniques to EEG microstate sequences from wakefulness and non-REM sleep stages and used first-order Markov surrogate data to determine which time scales contributed to the different complexity measures. We demonstrate that entropy rate and LZC measure the Kolmogorov complexity (randomness) of microstate sequences, whereas excess entropy and Hurst exponents describe statistical complexity which attains its maximum at intermediate levels of randomness. We confirmed the equivalence of entropy rate and LZC when the LZ-76 algorithm is used, a result previously reported for neural spike train analysis (Amigó et al., Neural Comput 16:717-736, https://doi.org/10.1162/089976604322860677 , 2004). Surrogate data analyses prove that entropy-based quantities and LZC focus on short-range temporal correlations, whereas Hurst exponents include short and long time scales. Sleep data analysis reveals that deeper sleep stages are accompanied by a decrease in Kolmogorov complexity and an increase in statistical complexity. Microstate jump sequences, where duplicate states have been removed, show higher randomness, lower statistical complexity, and no long-range correlations. Regarding the practical use of these methods, we suggest that LZC can be used as an efficient entropy rate estimator that avoids the estimation of joint entropies, whereas entropy rate estimation via joint entropies has the advantage of providing excess entropy as the second parameter of the same linear fit. We conclude that metrics of statistical complexity are a useful addition to microstate analysis and address a complexity concept that is not yet covered by existing microstate algorithms while being actively explored in other areas of brain research.
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Affiliation(s)
- Frederic von Wegner
- School of Biomedical Sciences, University of New South Wales (UNSW), Wallace Wurth, Kensington, NSW, 2052, Australia.
| | - Milena Wiemers
- Department of Neurology and Clinical Neurophysiology, Lüneburg Hospital, Bögelstrasse 1, 21339, Lüneburg, Germany
| | - Gesine Hermann
- Department of Neurology, Christian-Albrechts University, Arnold-Heller-Strasse 3, 24105, Kiel, Germany
| | - Inken Tödt
- Institute of Sexual Medicine & Forensic Psychiatry and Psychotherapy, Christian-Albrechts University, Schwanenweg 24, 24105, Kiel, Germany
| | - Enzo Tagliazucchi
- Department of Physics, University of Buenos Aires, 1428, Buenos Aires, Argentina
| | - Helmut Laufs
- Department of Neurology, Christian-Albrechts University, Arnold-Heller-Strasse 3, 24105, Kiel, Germany
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7
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Díaz M, Lucchetti F, Avan P, Giraudet F, Deltenre P, Nonclercq A. Preserved Auditory Steady State Response and Envelope-Following Response in Severe Brainstem Dysfunction Highlight the Need for Cross-Checking. Ear Hear 2024; 45:400-410. [PMID: 37828657 DOI: 10.1097/aud.0000000000001437] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2023]
Abstract
OBJECTIVES Commercially available auditory steady state response (ASSR) systems are widely used to obtain hearing thresholds in the pediatric population objectively. Children are often examined during natural or induced sleep so that the recorded ASSRs are of subcortical origin, the inferior colliculus being often designated as the main ASSR contributor in these conditions. This report presents data from a battery of auditory neurophysiological objective tests obtained in 3 cases of severe brainstem dysfunction in sleeping children. In addition to ASSRs, envelope-following response (EFR) recordings designed to distinguish peripheral (cochlear nerve) from central (brainstem) were recorded to document the effect of brainstem dysfunction on the two types of phase-locked responses. DESIGN Results obtained in the 3 children with severe brainstem dysfunctions were compared with those of age-matched controls. The cases were identified as posterior fossa tumor, undiagnosed (UD), and Pelizaeus-Merzbacher-Like Disease. The standard audiological objective tests comprised tympanograms, distortion product otoacoustic emissions, click-evoked auditory brainstem responses (ABRs), and ASSRs. EFRs were recorded using horizontal (EFR-H) and vertical (EFR-V) channels and a stimulus phase rotation technique allowing isolation of the EFR waveforms in the time domain to obtain direct latency measurements. RESULTS The brainstem dysfunctions of the 3 children were revealed as abnormal (weak, absent, or delayed) ABRs central waves with a normal wave I. In addition, they all presented a summating and cochlear microphonic potential in their ABRs, coupled with a normal wave I, which implies normal cochlear and cochlear nerve function. EFR-H and EFR-V waveforms were identified in the two cases in whom they were recorded. The EFR-Hs onset latencies, response durations, and phase-locking values did not differ from their respective age-matched control values, indicating normal cochlear nerve EFRs. In contrast, the EFR-V phase-locking value and onset latency varied from their control values. Both patients had abnormal but identifiable and significantly phase-locked brainstem EFRs, even in a case with severely distorted ABR central waves. ASSR objective audiograms were recorded in two cases. They showed normal or slightly elevated (explained by a slight transmission loss) thresholds that do not yield any clue about their brainstem dysfunction, revealing the method's lack of sensitivity to severe brainstem dysfunction. CONCLUSIONS The present study, performed on 3 sleeping children with severe brainstem dysfunction but normal cochlear responses (cochlear microphonic potential, summating potential, and ABR wave I), revealed the differential sensitivity of three auditory electrophysiological techniques. Estimated thresholds obtained by standard ASSR recordings (cases UD and Pelizaeus-Merzbacher-Like Disease) provided no clue to the brainstem dysfunction clearly revealed by the click-evoked ABR. EFR recordings (cases posterior fossa tumor and UD) showed preserved central responses with abnormal latencies and low phase-locking values, whereas the peripheral EFR attributed to the cochlear nerve was normal. The one case (UD) for which the three techniques could be performed confirms this sensitivity gradient, emphasizing the need for applying the Cross-Check Principle by avoiding resorting to ASSR recording alone. The entirely normal EFR-H recordings observed in two cases further strengthen the hypothesis of its cochlear nerve origin in sleeping children.
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Affiliation(s)
- Macarena Díaz
- Bio-, Electro- and Mechanical Systems Department, Université Libre de Bruxelles, Brussels, Belgium
| | - Federico Lucchetti
- Critical and Extreme Security and Dependability Group (CritiX), Interdisciplinary Centre for Security, Reliability and Trust, Université du Luxembourg, Esch-sur-Alzette, Luxembourg
| | - Paul Avan
- Department of Neurosensory Biophysics, Institut national de la santé et de la recherche médicale, Université Clermont Auvergne, Clermont-Ferrand, France
| | - Fabrice Giraudet
- Department of Neurosensory Biophysics, Institut national de la santé et de la recherche médicale, Université Clermont Auvergne, Clermont-Ferrand, France
| | - Paul Deltenre
- Laboratoire de Neurophysiologie Sensorielle et Cognitive, Department of Neurology, Brugmann Hospital, Brussels, Belgium
| | - Antoine Nonclercq
- Bio-, Electro- and Mechanical Systems Department, Université Libre de Bruxelles, Brussels, Belgium
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8
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Papo D, Buldú JM. Does the brain behave like a (complex) network? I. Dynamics. Phys Life Rev 2024; 48:47-98. [PMID: 38145591 DOI: 10.1016/j.plrev.2023.12.006] [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: 12/08/2023] [Accepted: 12/10/2023] [Indexed: 12/27/2023]
Abstract
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.
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Affiliation(s)
- D Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, Ferrara, Italy; Center for Translational Neurophysiology, Fondazione Istituto Italiano di Tecnologia, Ferrara, Italy.
| | - J M Buldú
- Complex Systems Group & G.I.S.C., Universidad Rey Juan Carlos, Madrid, Spain
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9
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Vardalakis N, Aussel A, Rougier NP, Wagner FB. A dynamical computational model of theta generation in hippocampal circuits to study theta-gamma oscillations during neurostimulation. eLife 2024; 12:RP87356. [PMID: 38354040 PMCID: PMC10942594 DOI: 10.7554/elife.87356] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2024] Open
Abstract
Neurostimulation of the hippocampal formation has shown promising results for modulating memory but the underlying mechanisms remain unclear. In particular, the effects on hippocampal theta-nested gamma oscillations and theta phase reset, which are both crucial for memory processes, are unknown. Moreover, these effects cannot be investigated using current computational models, which consider theta oscillations with a fixed amplitude and phase velocity. Here, we developed a novel computational model that includes the medial septum, represented as a set of abstract Kuramoto oscillators producing a dynamical theta rhythm with phase reset, and the hippocampal formation, composed of biophysically realistic neurons and able to generate theta-nested gamma oscillations under theta drive. We showed that, for theta inputs just below the threshold to induce self-sustained theta-nested gamma oscillations, a single stimulation pulse could switch the network behavior from non-oscillatory to a state producing sustained oscillations. Next, we demonstrated that, for a weaker theta input, pulse train stimulation at the theta frequency could transiently restore seemingly physiological oscillations. Importantly, the presence of phase reset influenced whether these two effects depended on the phase at which stimulation onset was delivered, which has practical implications for designing neurostimulation protocols that are triggered by the phase of ongoing theta oscillations. This novel model opens new avenues for studying the effects of neurostimulation on the hippocampal formation. Furthermore, our hybrid approach that combines different levels of abstraction could be extended in future work to other neural circuits that produce dynamical brain rhythms.
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Affiliation(s)
- Nikolaos Vardalakis
- University of Bordeaux, CNRS, IMNBordeauxFrance
- University of Bordeaux, INRIA, IMNBordeauxFrance
| | - Amélie Aussel
- University of Bordeaux, CNRS, IMNBordeauxFrance
- University of Bordeaux, INRIA, IMNBordeauxFrance
- University of Bordeaux, CNRS, Bordeaux INPTalenceFrance
| | - Nicolas P Rougier
- University of Bordeaux, CNRS, IMNBordeauxFrance
- University of Bordeaux, INRIA, IMNBordeauxFrance
- University of Bordeaux, CNRS, Bordeaux INPTalenceFrance
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10
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Kuzmina E, Kriukov D, Lebedev M. Neuronal travelling waves explain rotational dynamics in experimental datasets and modelling. Sci Rep 2024; 14:3566. [PMID: 38347042 PMCID: PMC10861525 DOI: 10.1038/s41598-024-53907-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2023] [Accepted: 02/06/2024] [Indexed: 02/15/2024] Open
Abstract
Spatiotemporal properties of neuronal population activity in cortical motor areas have been subjects of experimental and theoretical investigations, generating numerous interpretations regarding mechanisms for preparing and executing limb movements. Two competing models, representational and dynamical, strive to explain the relationship between movement parameters and neuronal activity. A dynamical model uses the jPCA method that holistically characterizes oscillatory activity in neuron populations by maximizing the data rotational dynamics. Different rotational dynamics interpretations revealed by the jPCA approach have been proposed. Yet, the nature of such dynamics remains poorly understood. We comprehensively analyzed several neuronal-population datasets and found rotational dynamics consistently accounted for by a traveling wave pattern. For quantifying rotation strength, we developed a complex-valued measure, the gyration number. Additionally, we identified parameters influencing rotation extent in the data. Our findings suggest that rotational dynamics and traveling waves are typically the same phenomena, so reevaluation of the previous interpretations where they were considered separate entities is needed.
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Affiliation(s)
- Ekaterina Kuzmina
- Skolkovo Institute of Science and Technology, Vladimir Zelman Center for Neurobiology and Brain Rehabilitation, Moscow, Russia, 121205.
- Artificial Intelligence Research Institute (AIRI), Moscow, Russia.
| | - Dmitrii Kriukov
- Artificial Intelligence Research Institute (AIRI), Moscow, Russia
- Skolkovo Institute of Science and Technology, Center for Molecular and Cellular Biology, Moscow, Russia, 121205
| | - Mikhail Lebedev
- Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia, 119992
- Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint-Petersburg, Russia, 194223
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11
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Ponce-Alvarez A, Deco G. The Hopf whole-brain model and its linear approximation. Sci Rep 2024; 14:2615. [PMID: 38297071 PMCID: PMC10831083 DOI: 10.1038/s41598-024-53105-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2023] [Accepted: 01/27/2024] [Indexed: 02/02/2024] Open
Abstract
Whole-brain models have proven to be useful to understand the emergence of collective activity among neural populations or brain regions. These models combine connectivity matrices, or connectomes, with local node dynamics, noise, and, eventually, transmission delays. Multiple choices for the local dynamics have been proposed. Among them, nonlinear oscillators corresponding to a supercritical Hopf bifurcation have been used to link brain connectivity and collective phase and amplitude dynamics in different brain states. Here, we studied the linear fluctuations of this model to estimate its stationary statistics, i.e., the instantaneous and lagged covariances and the power spectral densities. This linear approximation-that holds in the case of heterogeneous parameters and time-delays-allows analytical estimation of the statistics and it can be used for fast parameter explorations to study changes in brain state, changes in brain activity due to alterations in structural connectivity, and modulations of parameter due to non-equilibrium dynamics.
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Affiliation(s)
- Adrián Ponce-Alvarez
- Departament de Matemàtiques, Universitat Politècnica de Catalunya, 08028, Barcelona, Spain.
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08005, Barcelona, Spain
- Institució Catalana de la Recerca i Estudis Avançats (ICREA), 08010, Barcelona, Spain
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12
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Vidaurre D. A generative model of electrophysiological brain responses to stimulation. eLife 2024; 12:RP87729. [PMID: 38231034 PMCID: PMC10945576 DOI: 10.7554/elife.87729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2024] Open
Abstract
Each brain response to a stimulus is, to a large extent, unique. However this variability, our perceptual experience feels stable. Standard decoding models, which utilise information across several areas to tap into stimuli representation and processing, are fundamentally based on averages. Therefore, they can focus precisely on the features that are most stable across stimulus presentations. But which are these features exactly is difficult to address in the absence of a generative model of the signal. Here, I introduce genephys, a generative model of brain responses to stimulation publicly available as a Python package that, when confronted with a decoding algorithm, can reproduce the structured patterns of decoding accuracy that we observe in real data. Using this approach, I characterise how these patterns may be brought about by the different aspects of the signal, which in turn may translate into distinct putative neural mechanisms. In particular, the model shows that the features in the data that support successful decoding-and, therefore, likely reflect stable mechanisms of stimulus representation-have an oscillatory component that spans multiple channels, frequencies, and latencies of response; and an additive, slower response with a specific (cross-frequency) relation to the phase of the oscillatory component. At the individual trial level, still, responses are found to be highly variable, which can be due to various factors including phase noise and probabilistic activations.
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Affiliation(s)
- Diego Vidaurre
- Center for Functionally Integrative Neuroscience, Department of Clinical Medicine, Aarhus UniversityAarhusDenmark
- Department of Psychiatry, Oxford UniversityOxfordUnited Kingdom
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13
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Wang SH, Siebenhühner F, Arnulfo G, Myrov V, Nobili L, Breakspear M, Palva S, Palva JM. Critical-like Brain Dynamics in a Continuum from Second- to First-Order Phase Transition. J Neurosci 2023; 43:7642-7656. [PMID: 37816599 PMCID: PMC10634584 DOI: 10.1523/jneurosci.1889-22.2023] [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: 10/05/2022] [Revised: 06/07/2023] [Accepted: 09/25/2023] [Indexed: 10/12/2023] Open
Abstract
The classic brain criticality hypothesis postulates that the brain benefits from operating near a continuous second-order phase transition. Slow feedback regulation of neuronal activity could, however, lead to a discontinuous first-order transition and thereby bistable activity. Observations of bistability in awake brain activity have nonetheless remained scarce and its functional significance unclear. Moreover, there is no empirical evidence to support the hypothesis that the human brain could flexibly operate near either a first- or second-order phase transition despite such a continuum being common in models. Here, using computational modeling, we found bistable synchronization dynamics to emerge through elevated positive feedback and occur exclusively in a regimen of critical-like dynamics. We then assessed bistability in vivo with resting-state MEG in healthy adults (7 females, 11 males) and stereo-electroencephalography in epilepsy patients (28 females, 36 males). This analysis revealed that a large fraction of the neocortices exhibited varying degrees of bistability in neuronal oscillations from 3 to 200 Hz. In line with our modeling results, the neuronal bistability was positively correlated with classic assessment of brain criticality across narrow-band frequencies. Excessive bistability was predictive of epileptic pathophysiology in the patients, whereas moderate bistability was positively correlated with task performance in the healthy subjects. These empirical findings thus reveal the human brain as a one-of-a-kind complex system that exhibits critical-like dynamics in a continuum between continuous and discontinuous phase transitions.SIGNIFICANCE STATEMENT In the model, while synchrony per se was controlled by connectivity, increasing positive local feedback led to gradually emerging bistable synchrony with scale-free dynamics, suggesting a continuum between second- and first-order phase transitions in synchrony dynamics inside a critical-like regimen. In resting-state MEG and SEEG, bistability of ongoing neuronal oscillations was pervasive across brain areas and frequency bands and was observed only with concurring critical-like dynamics as the modeling predicted. As evidence for functional relevance, moderate bistability was positively correlated with executive functioning in the healthy subjects, and excessive bistability was associated with epileptic pathophysiology. These findings show that critical-like neuronal dynamics in vivo involves both continuous and discontinuous phase transitions in a frequency-, neuroanatomy-, and state-dependent manner.
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Affiliation(s)
- Sheng H Wang
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Doctoral Programme Brain & Mind, University of Helsinki, 00014 Helsinki, Finland
- BioMag Laboratory, HUS Medical Imaging Center, 00290 Helsinki, Finland
- Department of Neuroscience and Biomedical Engineering, Aalto University, 00076 Espoo, Finland
| | - Felix Siebenhühner
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- BioMag Laboratory, HUS Medical Imaging Center, 00290 Helsinki, Finland
| | - Gabriele Arnulfo
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Department of Informatics, Bioengineering, Robotics and System Engineering, University of Genoa, 16136 Genoa, Italy
| | - Vladislav Myrov
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Department of Neuroscience and Biomedical Engineering, Aalto University, 00076 Espoo, Finland
| | - Lino Nobili
- Department of Neurosciences, Rehabilitation, Ophthalmology, Genetics and Maternal and Children's Sciences, University of Genoa, 16136 Genoa, Italy
- Child Neuropsychiatry Unit, Istituto Di Ricovero e Cura a Carattere Scientifico Istituto Giannina Gaslini, 16147 Genoa, Italy
- Centre of Epilepsy Surgery "C. Munari," Department of Neuroscience, Niguarda Hospital, 20162 Milan, Italy
| | - Michael Breakspear
- College of Engineering, Science and Environment, College of Health and Medicine, University of Newcastle, Callaghan, 2308 Australia
| | - Satu Palva
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Centre for Cognitive Neuroimaging, Institute of Neuroscience & Psychology, University of Glasgow, Glasgow G12 8QB, United Kingdom
| | - J Matias Palva
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, 00014 Helsinki, Finland
- Department of Neuroscience and Biomedical Engineering, Aalto University, 00076 Espoo, Finland
- Centre for Cognitive Neuroimaging, Institute of Neuroscience & Psychology, University of Glasgow, Glasgow G12 8QB, United Kingdom
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14
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Williams N, Ojanperä A, Siebenhühner F, Toselli B, Palva S, Arnulfo G, Kaski S, Palva JM. The influence of inter-regional delays in generating large-scale brain networks of phase synchronization. Neuroimage 2023; 279:120318. [PMID: 37572765 DOI: 10.1016/j.neuroimage.2023.120318] [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: 03/15/2023] [Revised: 07/14/2023] [Accepted: 08/10/2023] [Indexed: 08/14/2023] Open
Abstract
Large-scale networks of phase synchronization are considered to regulate the communication between brain regions fundamental to cognitive function, but the mapping to their structural substrates, i.e., the structure-function relationship, remains poorly understood. Biophysical Network Models (BNMs) have demonstrated the influences of local oscillatory activity and inter-regional anatomical connections in generating alpha-band (8-12 Hz) networks of phase synchronization observed with Electroencephalography (EEG) and Magnetoencephalography (MEG). Yet, the influence of inter-regional conduction delays remains unknown. In this study, we compared a BNM with standard "distance-dependent delays", which assumes constant conduction velocity, to BNMs with delays specified by two alternative methods accounting for spatially varying conduction velocities, "isochronous delays" and "mixed delays". We followed the Approximate Bayesian Computation (ABC) workflow, i) specifying neurophysiologically informed prior distributions of BNM parameters, ii) verifying the suitability of the prior distributions with Prior Predictive Checks, iii) fitting each of the three BNMs to alpha-band MEG resting-state data (N = 75) with Bayesian optimization for Likelihood-Free Inference (BOLFI), and iv) choosing between the fitted BNMs with ABC model comparison on a separate MEG dataset (N = 30). Prior Predictive Checks revealed the range of dynamics generated by each of the BNMs to encompass those seen in the MEG data, suggesting the suitability of the prior distributions. Fitting the models to MEG data yielded reliable posterior distributions of the parameters of each of the BNMs. Finally, model comparison revealed the BNM with "distance-dependent delays", as the most probable to describe the generation of alpha-band networks of phase synchronization seen in MEG. These findings suggest that distance-dependent delays might contribute to the neocortical architecture of human alpha-band networks of phase synchronization. Hence, our study illuminates the role of inter-regional delays in generating the large-scale networks of phase synchronization that might subserve the communication between regions vital to cognition.
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Affiliation(s)
- N Williams
- Helsinki Institute of Information Technology, Department of Computer Science, Aalto University, Finland; Department of Neuroscience and Biomedical Engineering, Aalto University, Finland.
| | - A Ojanperä
- Department of Computer Science, Aalto University, Finland
| | - F Siebenhühner
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, Finland; BioMag laboratory, HUS Medical Imaging Center, Helsinki, Finland
| | - B Toselli
- Department of Informatics, Bioengineering, Robotics & Systems Engineering, University of Genoa, Italy
| | - S Palva
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, Finland; Centre for Cognitive Neuroimaging, School of Neuroscience & Psychology, University of Glasgow, United Kingdom
| | - G Arnulfo
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, Finland; Department of Informatics, Bioengineering, Robotics & Systems Engineering, University of Genoa, Italy
| | - S Kaski
- Helsinki Institute of Information Technology, Department of Computer Science, Aalto University, Finland; Department of Computer Science, Aalto University, Finland; Department of Computer Science, University of Manchester, United Kingdom
| | - J M Palva
- Department of Neuroscience and Biomedical Engineering, Aalto University, Finland; Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, Finland; Centre for Cognitive Neuroimaging, School of Neuroscience & Psychology, University of Glasgow, United Kingdom
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15
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Arenas A, Garijo A, Gómez S, Villadelprat J. On the number of stable solutions in the Kuramoto model. CHAOS (WOODBURY, N.Y.) 2023; 33:093127. [PMID: 37729100 DOI: 10.1063/5.0161977] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 08/25/2023] [Indexed: 09/22/2023]
Abstract
We consider a system of n coupled oscillators described by the Kuramoto model with the dynamics given by θ˙=ω+Kf(θ). In this system, an equilibrium solution θ∗ is considered stable when ω+Kf(θ∗)=0, and the Jacobian matrix Df(θ∗) has a simple eigenvalue of zero, indicating the presence of a direction in which the oscillators can adjust their phases. Additionally, the remaining eigenvalues of Df(θ∗) are negative, indicating stability in orthogonal directions. A crucial constraint imposed on the equilibrium solution is that |Γ(θ∗)|≤π, where |Γ(θ∗)| represents the length of the shortest arc on the unit circle that contains the equilibrium solution θ∗. We provide a proof that there exists a unique solution satisfying the aforementioned stability criteria. This analysis enhances our understanding of the stability and uniqueness of these solutions, offering valuable insights into the dynamics of coupled oscillators in this system.
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Affiliation(s)
- Alex Arenas
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
- Pacific Northwest National Laboratory, 902 Battelle Blvd, Richland, Washington 99354, USA
| | - Antonio Garijo
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - Sergio Gómez
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - Jordi Villadelprat
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
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16
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Scirè A, Annovazzi-Lodi V. The emergence of dynamic networks from many coupled polar oscillators: a paradigm for artificial life. Theory Biosci 2023; 142:291-299. [PMID: 37516712 DOI: 10.1007/s12064-023-00401-4] [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: 02/20/2023] [Accepted: 07/19/2023] [Indexed: 07/31/2023]
Abstract
This work concerns a many-body deterministic model that displays life-like properties such as emergence, complexity, self-organization, self-regulation, excitability and spontaneous compartmentalization. The model portraits the dynamics of an ensemble of locally coupled polar phase oscillators, moving in a two-dimensional space, that under certain conditions exhibit emergent superstructures. Those superstructures are self-organized dynamic networks, resulting from a synchronization process of many units, over length scales much greater than the interaction range. Such networks compartmentalize the two-dimensional space with no a priori constraints, due to the formation of porous transport walls, and represent a highly complex and novel non-linear behavior. The analysis is numerically carried out as a function of a control parameter showing distinct regimes: static pattern formation, dynamic excitable networks formation, intermittency and chaos. A statistical analysis is drawn to determine the control parameter ranges for the various behaviors to appear. The model and the results shown in this work are expected to contribute to the field of artificial life.
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Affiliation(s)
- Alessandro Scirè
- Dipartimento Di Ingegneria Industriale E Dell'Informazione, Università Di Pavia, 27100, Pavia, Italy.
| | - Valerio Annovazzi-Lodi
- Dipartimento Di Ingegneria Industriale E Dell'Informazione, Università Di Pavia, 27100, Pavia, Italy
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17
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Duchet B, Bick C, Byrne Á. Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity. Neural Comput 2023; 35:1481-1528. [PMID: 37437202 PMCID: PMC10422128 DOI: 10.1162/neco_a_01601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2022] [Accepted: 04/26/2023] [Indexed: 07/14/2023]
Abstract
Understanding the effect of spike-timing-dependent plasticity (STDP) is key to elucidating how neural networks change over long timescales and to design interventions aimed at modulating such networks in neurological disorders. However, progress is restricted by the significant computational cost associated with simulating neural network models with STDP and by the lack of low-dimensional description that could provide analytical insights. Phase-difference-dependent plasticity (PDDP) rules approximate STDP in phase oscillator networks, which prescribe synaptic changes based on phase differences of neuron pairs rather than differences in spike timing. Here we construct mean-field approximations for phase oscillator networks with STDP to describe part of the phase space for this very high-dimensional system. We first show that single-harmonic PDDP rules can approximate a simple form of symmetric STDP, while multiharmonic rules are required to accurately approximate causal STDP. We then derive exact expressions for the evolution of the average PDDP coupling weight in terms of network synchrony. For adaptive networks of Kuramoto oscillators that form clusters, we formulate a family of low-dimensional descriptions based on the mean-field dynamics of each cluster and average coupling weights between and within clusters. Finally, we show that such a two-cluster mean-field model can be fitted to synthetic data to provide a low-dimensional approximation of a full adaptive network with symmetric STDP. Our framework represents a step toward a low-dimensional description of adaptive networks with STDP, and could for example inform the development of new therapies aimed at maximizing the long-lasting effects of brain stimulation.
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Affiliation(s)
- Benoit Duchet
- Nuffield Department of Clinical Neuroscience, University of Oxford, Oxford X3 9DU, U.K
- MRC Brain Network Dynamics Unit, University of Oxford, Oxford X1 3TH, U.K.
| | - Christian Bick
- Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam 1081 HV, the Netherlands
- Amsterdam Neuroscience-Systems and Network Neuroscience, Amsterdam 1081 HV, the Netherlands
- Mathematical Institute, University of Oxford, Oxford X2 6GG, U.K.
| | - Áine Byrne
- School of Mathematics and Statistics, University College Dublin, Dublin D04 V1W8, Ireland
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18
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Fuscà M, Siebenhühner F, Wang SH, Myrov V, Arnulfo G, Nobili L, Palva JM, Palva S. Brain criticality predicts individual levels of inter-areal synchronization in human electrophysiological data. Nat Commun 2023; 14:4736. [PMID: 37550300 PMCID: PMC10406818 DOI: 10.1038/s41467-023-40056-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Accepted: 07/10/2023] [Indexed: 08/09/2023] Open
Abstract
Neuronal oscillations and their synchronization between brain areas are fundamental for healthy brain function. Yet, synchronization levels exhibit large inter-individual variability that is associated with behavioral variability. We test whether individual synchronization levels are predicted by individual brain states along an extended regime of critical-like dynamics - the Griffiths phase (GP). We use computational modelling to assess how synchronization is dependent on brain criticality indexed by long-range temporal correlations (LRTCs). We analyze LRTCs and synchronization of oscillations from resting-state magnetoencephalography and stereo-electroencephalography data. Synchronization and LRTCs are both positively linearly and quadratically correlated among healthy subjects, while in epileptogenic areas they are negatively linearly correlated. These results show that variability in synchronization levels is explained by the individual position along the GP with healthy brain areas operating in its subcritical and epileptogenic areas in its supercritical side. We suggest that the GP is fundamental for brain function allowing individual variability while retaining functional advantages of criticality.
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Affiliation(s)
- Marco Fuscà
- Centre for Cognitive Neuroimaging, School of Psychology and Neuroscience, University of Glasgow, Glasgow, UK
- Neuroscience Center, HiLIFE-Helsinki Institute of Life Science, University of Helsinki, Helsinki, Finland
| | - Felix Siebenhühner
- Neuroscience Center, HiLIFE-Helsinki Institute of Life Science, University of Helsinki, Helsinki, Finland
- BioMag Laboratory, HUS Medical Imaging Center, University of Helsinki, Aalto University, and Helsinki University Hospital, Helsinki, Finland
| | - Sheng H Wang
- Neuroscience Center, HiLIFE-Helsinki Institute of Life Science, University of Helsinki, Helsinki, Finland
- Department of Neuroscience and Biomedical Engineering, Aalto University, Espoo, Finland
- CEA, NeuroSpin, Gif-sur-Yvette, France
- MIND team, Inria, Université Paris-Saclay, Bures-sur-Yvette, France
| | - Vladislav Myrov
- Department of Neuroscience and Biomedical Engineering, Aalto University, Espoo, Finland
| | - Gabriele Arnulfo
- Neuroscience Center, HiLIFE-Helsinki Institute of Life Science, University of Helsinki, Helsinki, Finland
- Dept. of Informatics, Bioengineering, Robotics and System engineering, University of Genoa, Genoa, Italy
| | - Lino Nobili
- Child Neuropsychiatry Unit, IRCCS, Istituto G. Gaslini, Department of Neuroscience (DINOGMI), University of Genoa, Genoa, Italy
- "Claudio Munari" Epilepsy Surgery Centre, Niguarda Hospital, Milan, Italy
| | - J Matias Palva
- Centre for Cognitive Neuroimaging, School of Psychology and Neuroscience, University of Glasgow, Glasgow, UK
- Neuroscience Center, HiLIFE-Helsinki Institute of Life Science, University of Helsinki, Helsinki, Finland
- Department of Neuroscience and Biomedical Engineering, Aalto University, Espoo, Finland
| | - Satu Palva
- Centre for Cognitive Neuroimaging, School of Psychology and Neuroscience, University of Glasgow, Glasgow, UK.
- Neuroscience Center, HiLIFE-Helsinki Institute of Life Science, University of Helsinki, Helsinki, Finland.
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19
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Mackay M, Huo S, Kaiser M. Spatial organisation of the mesoscale connectome: A feature influencing synchrony and metastability of network dynamics. PLoS Comput Biol 2023; 19:e1011349. [PMID: 37552650 PMCID: PMC10437862 DOI: 10.1371/journal.pcbi.1011349] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2022] [Revised: 08/18/2023] [Accepted: 07/12/2023] [Indexed: 08/10/2023] Open
Abstract
Significant research has investigated synchronisation in brain networks, but the bulk of this work has explored the contribution of brain networks at the macroscale. Here we explore the effects of changing network topology on functional dynamics in spatially constrained random networks representing mesoscale neocortex. We use the Kuramoto model to simulate network dynamics and explore synchronisation and critical dynamics of the system as a function of topology in randomly generated networks with a distance-related wiring probability and no preferential attachment term. We show networks which predominantly make short-distance connections smooth out the critical coupling point and show much greater metastability, resulting in a wider range of coupling strengths demonstrating critical dynamics and metastability. We show the emergence of cluster synchronisation in these geometrically-constrained networks with functional organisation occurring along structural connections that minimise the participation coefficient of the cluster. We show that these cohorts of internally synchronised nodes also behave en masse as weakly coupled nodes and show intra-cluster desynchronisation and resynchronisation events related to inter-cluster interaction. While cluster synchronisation appears crucial to healthy brain function, it may also be pathological if it leads to unbreakable local synchronisation which may happen at extreme topologies, with implications for epilepsy research, wider brain function and other domains such as social networks.
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Affiliation(s)
- Michael Mackay
- Newcastle University, School of Computing, Newcastle upon Tyne, United Kingdom
| | - Siyu Huo
- East China Normal University, School of Physics and Electronic Science, Shanghai, China
- University of Nottingham, NIHR Nottingham Biomedical Research Centre, School of Medicine, Nottingham, United Kingdom
| | - Marcus Kaiser
- University of Nottingham, NIHR Nottingham Biomedical Research Centre, School of Medicine, Nottingham, United Kingdom
- University of Nottingham, Sir Peter Mansfield Imaging Centre, School of Medicine, Nottingham, United Kingdom
- Shanghai Jiao Tong University, School of Medicine, Shanghai, China
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20
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Jain R, Sharma J, Tiwari I, Gadre SD, Kumarasamy S, Parmananda P, Prasad A. In-phase and mixed-phase measure synchronization of camphor rotors. Phys Rev E 2023; 108:024217. [PMID: 37723774 DOI: 10.1103/physreve.108.024217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2023] [Accepted: 08/03/2023] [Indexed: 09/20/2023]
Abstract
The numerical, analytical, and experimental analyses are presented for synchronizing two rotors under the Yukawa interaction. We report that the rotors exhibit in-phase and mixed-phase measure synchronizations for a pair of coupled rotors. Here, the analytical condition for synchronization is derived, tested numerically, and confirmed experimentally using coupled camphor infused rotors as a test bed. Moreover, the concept of measure synchronization is discussed. We report that, in conservative systems, not only the critical coupling parameter but initial conditions also play an essential role for estimating the measure synchronization region.
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Affiliation(s)
- Rishabh Jain
- Kirori Mal College, University of Delhi, Delhi 110007, India
| | - Jyoti Sharma
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Ishant Tiwari
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | | | - Suresh Kumarasamy
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Awadhesh Prasad
- Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India
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21
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Yang L, Lu J, Li D, Xiang J, Yan T, Sun J, Wang B. Alzheimer's Disease: Insights from Large-Scale Brain Dynamics Models. Brain Sci 2023; 13:1133. [PMID: 37626490 PMCID: PMC10452161 DOI: 10.3390/brainsci13081133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Revised: 07/21/2023] [Accepted: 07/25/2023] [Indexed: 08/27/2023] Open
Abstract
Alzheimer's disease (AD) is a degenerative brain disease, and the condition is difficult to assess. In the past, numerous brain dynamics models have made remarkable contributions to neuroscience and the brain from the microcosmic to the macroscopic scale. Recently, large-scale brain dynamics models have been developed based on dual-driven multimodal neuroimaging data and neurodynamics theory. These models bridge the gap between anatomical structure and functional dynamics and have played an important role in assisting the understanding of the brain mechanism. Large-scale brain dynamics have been widely used to explain how macroscale neuroimaging biomarkers emerge from potential neuronal population level disturbances associated with AD. In this review, we describe this emerging approach to studying AD that utilizes a biophysically large-scale brain dynamics model. In particular, we focus on the application of the model to AD and discuss important directions for the future development and analysis of AD models. This will facilitate the development of virtual brain models in the field of AD diagnosis and treatment and add new opportunities for advancing clinical neuroscience.
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Affiliation(s)
- Lan Yang
- College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan 030024, China; (L.Y.); (J.L.); (D.L.); (J.X.); (J.S.)
| | - Jiayu Lu
- College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan 030024, China; (L.Y.); (J.L.); (D.L.); (J.X.); (J.S.)
| | - Dandan Li
- College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan 030024, China; (L.Y.); (J.L.); (D.L.); (J.X.); (J.S.)
| | - Jie Xiang
- College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan 030024, China; (L.Y.); (J.L.); (D.L.); (J.X.); (J.S.)
| | - Ting Yan
- Teranslational Medicine Research Center, Shanxi Medical University, Taiyuan 030001, China;
| | - Jie Sun
- College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan 030024, China; (L.Y.); (J.L.); (D.L.); (J.X.); (J.S.)
| | - Bin Wang
- College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan 030024, China; (L.Y.); (J.L.); (D.L.); (J.X.); (J.S.)
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22
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Hipólito I, Mago J, Rosas FE, Carhart-Harris R. Pattern breaking: a complex systems approach to psychedelic medicine. Neurosci Conscious 2023; 2023:niad017. [PMID: 37424966 PMCID: PMC10325487 DOI: 10.1093/nc/niad017] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Revised: 05/19/2023] [Accepted: 06/08/2023] [Indexed: 07/11/2023] Open
Abstract
Recent research has demonstrated the potential of psychedelic therapy for mental health care. However, the psychological experience underlying its therapeutic effects remains poorly understood. This paper proposes a framework that suggests psychedelics act as destabilizers, both psychologically and neurophysiologically. Drawing on the 'entropic brain' hypothesis and the 'RElaxed Beliefs Under pSychedelics' model, this paper focuses on the richness of psychological experience. Through a complex systems theory perspective, we suggest that psychedelics destabilize fixed points or attractors, breaking reinforced patterns of thinking and behaving. Our approach explains how psychedelic-induced increases in brain entropy destabilize neurophysiological set points and lead to new conceptualizations of psychedelic psychotherapy. These insights have important implications for risk mitigation and treatment optimization in psychedelic medicine, both during the peak psychedelic experience and during the subacute period of potential recovery.
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Affiliation(s)
- Inês Hipólito
- Berlin School of Mind and Brain, Humboldt-Universität zu Berlin, Berlin 10117, Germany
- Department of Philosophy, Macquarie University, New South Wales 2109, Australia
| | - Jonas Mago
- Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, United Kingdom
- Integrative Program in Neuroscience, McGill University, Montreal, Quebec QC H3A, Canada
| | - Fernando E Rosas
- Department of Brain Sciences, Centre for Psychedelic Research, Imperial College London, London SW7 2BX, United Kingdom
- Centre for Complexity Science, Imperial College London, London SW7 2BX, United Kingdom
- Data Science Institute, Imperial College London, London SW7 2BX, United Kingdom
- Department of Informatics, University of Sussex, Brighton BN1 9RH, United Kingdom
- Centre for Eudaimonia and Human Flourishing, University of Oxford, Oxford OX3 9BX, United Kingdom
| | - Robin Carhart-Harris
- Department of Brain Sciences, Centre for Psychedelic Research, Imperial College London, London SW7 2BX, United Kingdom
- Psychedelics Division, University of California San Francisco, San Francisco, CA 92521, United States
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23
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Bomela W, Singhal B, Li JS. Engineering spatiotemporal patterns: information encoding, processing, and controllability in oscillator ensembles. Biomed Phys Eng Express 2023; 9:045033. [PMID: 37348467 PMCID: PMC10486008 DOI: 10.1088/2057-1976/ace0c9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Revised: 04/21/2023] [Accepted: 06/22/2023] [Indexed: 06/24/2023]
Abstract
The ability to finely manipulate spatiotemporal patterns displayed in neuronal populations is critical for understanding and influencing brain functions, sleep cycles, and neurological pathologies. However, such control tasks are challenged not only by the immense scale but also by the lack of real-time state measurements of neurons in the population, which deteriorates the control performance. In this paper, we formulate the control of dynamic structures in an ensemble of neuron oscillators as a tracking problem and propose a principled control technique for designing optimal stimuli that produce desired spatiotemporal patterns in a network of interacting neurons without requiring feedback information. We further reveal an interesting presentation of information encoding and processing in a neuron ensemble in terms of its controllability property. The performance of the presented technique in creating complex spatiotemporal spiking patterns is demonstrated on neural populations described by mathematically ideal and biophysical models, including the Kuramoto and Hodgkin-Huxley models, as well as real-time experiments on Wein bridge oscillators.
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Affiliation(s)
- Walter Bomela
- Department of Electrical and Systems Engineering, Washington University in St. Louis,
United States of America
| | - Bharat Singhal
- Department of Electrical and Systems Engineering, Washington University in St. Louis,
United States of America
| | - Jr-Shin Li
- Department of Electrical and Systems Engineering, Washington University in St. Louis,
United States of America
- Division of Biology & and Biomedical Sciences, Washington University in St. Louis,
United States of America
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Berner R, Lu A, Sokolov IM. Synchronization transitions in Kuramoto networks with higher-mode interaction. CHAOS (WOODBURY, N.Y.) 2023; 33:073138. [PMID: 37463093 DOI: 10.1063/5.0151038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 06/21/2023] [Indexed: 07/20/2023]
Abstract
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is still elusive for real-world systems in particular. We study the synchronization transition in a phase oscillator system with two nonvanishing Fourier-modes in the interaction function, hence going beyond the Kuramoto paradigm. We show that the transition scenarios crucially depend on the interplay of the two coupling modes. We describe the multistability induced by the presence of a second coupling mode. By extending the collective coordinate approach, we describe the emergence of various states observed in the transition from incoherence to coherence. Remarkably, our analysis suggests that, in essence, the two-mode coupling gives rise to states characterized by two independent but interacting groups of oscillators. We believe that these findings will stimulate future research on dynamical systems, including complex interaction functions beyond the Kuramoto-type.
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Affiliation(s)
- Rico Berner
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Annie Lu
- Department of Mathematics, Washington State University, Pullman, Washington 99164-3113, USA
| | - Igor M Sokolov
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
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25
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Benigno GB, Budzinski RC, Davis ZW, Reynolds JH, Muller L. Waves traveling over a map of visual space can ignite short-term predictions of sensory input. Nat Commun 2023; 14:3409. [PMID: 37296131 PMCID: PMC10256723 DOI: 10.1038/s41467-023-39076-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Accepted: 05/25/2023] [Indexed: 06/12/2023] Open
Abstract
Recent analyses have found waves of neural activity traveling across entire visual cortical areas in awake animals. These traveling waves modulate the excitability of local networks and perceptual sensitivity. The general computational role of these spatiotemporal patterns in the visual system, however, remains unclear. Here, we hypothesize that traveling waves endow the visual system with the capacity to predict complex and naturalistic inputs. We present a network model whose connections can be rapidly and efficiently trained to predict individual natural movies. After training, a few input frames from a movie trigger complex wave patterns that drive accurate predictions many frames into the future solely from the network's connections. When the recurrent connections that drive waves are randomly shuffled, both traveling waves and the ability to predict are eliminated. These results suggest traveling waves may play an essential computational role in the visual system by embedding continuous spatiotemporal structures over spatial maps.
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Affiliation(s)
- Gabriel B Benigno
- Department of Mathematics, Western University, London, ON, Canada
- Brain and Mind Institute, Western University, London, ON, Canada
- Western Academy for Advanced Research, Western University, London, ON, Canada
| | - Roberto C Budzinski
- Department of Mathematics, Western University, London, ON, Canada
- Brain and Mind Institute, Western University, London, ON, Canada
- Western Academy for Advanced Research, Western University, London, ON, Canada
| | - Zachary W Davis
- The Salk Institute for Biological Studies, La Jolla, CA, USA
| | - John H Reynolds
- The Salk Institute for Biological Studies, La Jolla, CA, USA
| | - Lyle Muller
- Department of Mathematics, Western University, London, ON, Canada.
- Brain and Mind Institute, Western University, London, ON, Canada.
- Western Academy for Advanced Research, Western University, London, ON, Canada.
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26
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Pang JC, Aquino KM, Oldehinkel M, Robinson PA, Fulcher BD, Breakspear M, Fornito A. Geometric constraints on human brain function. Nature 2023; 618:566-574. [PMID: 37258669 PMCID: PMC10266981 DOI: 10.1038/s41586-023-06098-1] [Citation(s) in RCA: 68] [Impact Index Per Article: 68.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 04/18/2023] [Indexed: 06/02/2023]
Abstract
The anatomy of the brain necessarily constrains its function, but precisely how remains unclear. The classical and dominant paradigm in neuroscience is that neuronal dynamics are driven by interactions between discrete, functionally specialized cell populations connected by a complex array of axonal fibres1-3. However, predictions from neural field theory, an established mathematical framework for modelling large-scale brain activity4-6, suggest that the geometry of the brain may represent a more fundamental constraint on dynamics than complex interregional connectivity7,8. Here, we confirm these theoretical predictions by analysing human magnetic resonance imaging data acquired under spontaneous and diverse task-evoked conditions. Specifically, we show that cortical and subcortical activity can be parsimoniously understood as resulting from excitations of fundamental, resonant modes of the brain's geometry (that is, its shape) rather than from modes of complex interregional connectivity, as classically assumed. We then use these geometric modes to show that task-evoked activations across over 10,000 brain maps are not confined to focal areas, as widely believed, but instead excite brain-wide modes with wavelengths spanning over 60 mm. Finally, we confirm predictions that the close link between geometry and function is explained by a dominant role for wave-like activity, showing that wave dynamics can reproduce numerous canonical spatiotemporal properties of spontaneous and evoked recordings. Our findings challenge prevailing views and identify a previously underappreciated role of geometry in shaping function, as predicted by a unifying and physically principled model of brain-wide dynamics.
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Affiliation(s)
- James C Pang
- The Turner Institute for Brain and Mental Health, School of Psychological Sciences and Monash Biomedical Imaging, Monash University, Clayton, Victoria, Australia.
| | - Kevin M Aquino
- School of Physics, University of Sydney, Camperdown, New South Wales, Australia
- BrainKey Inc., San Francisco, CA, USA
| | - Marianne Oldehinkel
- Donders Institute for Brain, Cognition, and Behaviour, Radboud University Medical Centre, Nijmegen, the Netherlands
| | - Peter A Robinson
- School of Physics, University of Sydney, Camperdown, New South Wales, Australia
| | - Ben D Fulcher
- School of Physics, University of Sydney, Camperdown, New South Wales, Australia
| | - Michael Breakspear
- School of Psychological Sciences, College of Engineering, Science and the Environment, University of Newcastle, Callaghan, New South Wales, Australia
- School of Medicine and Public Health, College of Health, Medicine and Wellbeing, University of Newcastle, Callaghan, New South Wales, Australia
| | - Alex Fornito
- The Turner Institute for Brain and Mental Health, School of Psychological Sciences and Monash Biomedical Imaging, Monash University, Clayton, Victoria, Australia
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27
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Molnár L, Ferando I, Liu B, Mokhtar P, Domokos J, Mody I. Capturing the power of seizures: an empirical mode decomposition analysis of epileptic activity in the mouse hippocampus. Front Mol Neurosci 2023; 16:1121479. [PMID: 37256078 PMCID: PMC10225690 DOI: 10.3389/fnmol.2023.1121479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 04/28/2023] [Indexed: 06/01/2023] Open
Abstract
Introduction Various methods have been used to determine the frequency components of seizures in scalp electroencephalography (EEG) and in intracortical recordings. Most of these methods rely on subjective or trial-and-error criteria for choosing the appropriate bandwidth for filtering the EEG or local field potential (LFP) signals to establish the frequency components that contribute most to the initiation and maintenance of seizure activity. The empirical mode decomposition (EMD) with the Hilbert-Huang transform is an unbiased method to decompose a time and frequency variant signal into its component non-stationary frequencies. The resulting components, i.e., the intrinsic mode functions (IMFs) objectively reflect the various non-stationary frequencies making up the original signal. Materials and methods We employed the EMD method to analyze the frequency components and relative power of spontaneous electrographic seizures recorded in the dentate gyri of mice during the epileptogenic period. Epilepsy was induced in mice following status epilepticus induced by suprahippocampal injection of kainic acid. The seizures were recorded as local field potentials (LFP) with electrodes implanted in the dentate gyrus. We analyzed recording segments that included a seizure (mean duration 28 s) and an equivalent time period both before and after the seizure. Each segment was divided into non-overlapping 1 s long epochs which were then analyzed to obtain their IMFs (usually 8-10), the center frequencies of the respective IMF and their spectral root-mean-squared (RMS) power. Results Our analysis yielded unbiased identification of the spectral components of seizures, and the relative power of these components during this pathological brain activity. During seizures, the power of the mid frequency components increased while the center frequency of the first IMF (with the highest frequency) dramatically decreased, providing mechanistic insights into how local seizures are generated. Discussion We expect this type of analysis to provide further insights into the mechanisms of seizure generation and potentially better seizure detection.
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Affiliation(s)
- László Molnár
- Department of Electrical Engineering, Sapientia Hungarian University of Transylvania, Târgu-Mures, Romania
| | - Isabella Ferando
- Department of Neurology, The David Geffen School of Medicine at UCLA, Los Angeles, CA, United States
- Department of Neurology, School of Medicine at University of Florida, Miami, FL, United States
| | - Benjamin Liu
- Department of Neurology, The David Geffen School of Medicine at UCLA, Los Angeles, CA, United States
| | - Parsa Mokhtar
- Department of Neurology, The David Geffen School of Medicine at UCLA, Los Angeles, CA, United States
| | - József Domokos
- Department of Electrical Engineering, Sapientia Hungarian University of Transylvania, Târgu-Mures, Romania
| | - Istvan Mody
- Department of Neurology, The David Geffen School of Medicine at UCLA, Los Angeles, CA, United States
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28
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Kora Y, Salhi S, Davidsen J, Simon C. Global excitability and network structure in the human brain. Phys Rev E 2023; 107:054308. [PMID: 37328981 DOI: 10.1103/physreve.107.054308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Accepted: 04/07/2023] [Indexed: 06/18/2023]
Abstract
We utilize a model of Wilson-Cowan oscillators to investigate structure-function relationships in the human brain by means of simulations of the spontaneous dynamics of brain networks generated through human connectome data. This allows us to establish relationships between the global excitability of such networks and global structural network quantities for connectomes of two different sizes for a number of individual subjects. We compare the qualitative behavior of such correlations between biological networks and shuffled networks, the latter generated by shuffling the pairwise connectivities of the former while preserving their distribution. Our results point towards a remarkable propensity of the brain to achieve a trade-off between low network wiring cost and strong functionality, and highlight the unique capacity of brain network topologies to exhibit a strong transition from an inactive state to a globally excited one.
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Affiliation(s)
- Youssef Kora
- Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada and Hotchkiss Brain Institute, University of Calgary, T2N 4N1 Calgary, Canada
| | - Salma Salhi
- Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada and Hotchkiss Brain Institute, University of Calgary, T2N 4N1 Calgary, Canada
| | - Jörn Davidsen
- Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada and Hotchkiss Brain Institute, University of Calgary, T2N 4N1 Calgary, Canada
| | - Christoph Simon
- Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada and Hotchkiss Brain Institute, University of Calgary, T2N 4N1 Calgary, Canada
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29
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Calmon L, Krishnagopal S, Bianconi G. Local Dirac Synchronization on networks. CHAOS (WOODBURY, N.Y.) 2023; 33:033117. [PMID: 37003807 DOI: 10.1063/5.0132468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 02/13/2023] [Indexed: 06/19/2023]
Abstract
We propose Local Dirac Synchronization that uses the Dirac operator to capture the dynamics of coupled nodes and link signals on an arbitrary network. In Local Dirac Synchronization, the harmonic modes of the dynamics oscillate freely while the other modes are interacting non-linearly, leading to a collectively synchronized state when the coupling constant of the model is increased. Local Dirac Synchronization is characterized by discontinuous transitions and the emergence of a rhythmic coherent phase. In this rhythmic phase, one of the two complex order parameters oscillates in the complex plane at a slow frequency (called emergent frequency) in the frame in which the intrinsic frequencies have zero average. Our theoretical results obtained within the annealed approximation are validated by extensive numerical results on fully connected networks and sparse Poisson and scale-free networks. Local Dirac Synchronization on both random and real networks, such as the connectome of Caenorhabditis Elegans, reveals the interplay between topology (Betti numbers and harmonic modes) and non-linear dynamics. This unveils how topology might play a role in the onset of brain rhythms.
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Affiliation(s)
- Lucille Calmon
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Sanjukta Krishnagopal
- Department of Electrical Engineering and Computer Science, University of California Berkeley, California 94720, USA
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
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30
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Ceron S, O’Keeffe K, Petersen K. Diverse behaviors in non-uniform chiral and non-chiral swarmalators. Nat Commun 2023; 14:940. [PMID: 36806287 PMCID: PMC9941214 DOI: 10.1038/s41467-023-36563-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Accepted: 02/06/2023] [Indexed: 02/22/2023] Open
Abstract
We study the emergent behaviors of a population of swarming coupled oscillators, dubbed swarmalators. Previous work considered the simplest, idealized case: identical swarmalators with global coupling. Here we expand this work by adding more realistic features: local coupling, non-identical natural frequencies, and chirality. This more realistic model generates a variety of new behaviors including lattices of vortices, beating clusters, and interacting phase waves. Similar behaviors are found across natural and artificial micro-scale collective systems, including social slime mold, spermatozoa vortex arrays, and Quincke rollers. Our results indicate a wide range of future use cases, both to aid characterization and understanding of natural swarms, and to design complex interactions in collective systems from soft and active matter to micro-robotics.
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Affiliation(s)
- Steven Ceron
- grid.5386.8000000041936877XSibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853 USA ,grid.116068.80000 0001 2341 2786Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA 02139 USA
| | - Kevin O’Keeffe
- grid.116068.80000 0001 2341 2786Senseable City Lab, Massachusetts Institute of Technology, Cambridge, MA 02139 USA
| | - Kirstin Petersen
- Electrical and Computer Engineering, Cornell University, 136 Hoy Road, Ithaca, NY, 14853, USA.
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31
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Fialkowski J, Yanchuk S, Sokolov IM, Schöll E, Gottwald GA, Berner R. Heterogeneous Nucleation in Finite-Size Adaptive Dynamical Networks. PHYSICAL REVIEW LETTERS 2023; 130:067402. [PMID: 36827552 DOI: 10.1103/physrevlett.130.067402] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 10/17/2022] [Accepted: 01/10/2023] [Indexed: 06/18/2023]
Abstract
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive dynamical networks feature a connectivity structure that changes over time, coevolving with the nodes' dynamical state. In this Letter, we show the emergence of two distinct first-order nonequilibrium phase transitions in a finite-size adaptive network of heterogeneous phase oscillators. Depending on the nature of defects in the internal frequency distribution, we observe either an abrupt single-step transition to full synchronization or a more gradual multistep transition. This observation has a striking resemblance to heterogeneous nucleation. We develop a mean-field approach to study the interplay between adaptivity and nodal heterogeneity and describe the dynamics of multicluster states and their role in determining the character of the phase transition. Our work provides a theoretical framework for studying the interplay between adaptivity and nodal heterogeneity.
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Affiliation(s)
- Jan Fialkowski
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Serhiy Yanchuk
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany
- Institute of Mathematics, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
| | - Igor M Sokolov
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
- IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin, Germany
| | - Eckehard Schöll
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, 10115 Berlin, Germany
| | - Georg A Gottwald
- School of Mathematics and Statistics, University of Sydney, Camperdown New South Wales 2006, Australia
| | - Rico Berner
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
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32
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Petkoski S, Ritter P, Jirsa VK. White-matter degradation and dynamical compensation support age-related functional alterations in human brain. Cereb Cortex 2023; 33:6241-6256. [PMID: 36611231 PMCID: PMC10183745 DOI: 10.1093/cercor/bhac500] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Revised: 11/02/2022] [Accepted: 11/03/2022] [Indexed: 01/09/2023] Open
Abstract
Structural connectivity of the brain at different ages is analyzed using diffusion-weighted magnetic resonance imaging (MRI) data. The largest decrease of streamlines is found in frontal regions and for long inter-hemispheric links. The average length of the tracts also decreases, but the clustering is unaffected. From functional MRI we identify age-related changes of dynamic functional connectivity (dFC) and spatial covariation features of functional connectivity (FC) links captured by metaconnectivity. They indicate more stable dFC, but wider range and variance of MC, whereas static features of FC did not show any significant differences with age. We implement individual connectivity in whole-brain models and test several hypotheses for the mechanisms of operation among underlying neural system. We demonstrate that age-related functional fingerprints are only supported if the model accounts for: (i) compensation of the individual brains for the overall loss of structural connectivity and (ii) decrease of propagation velocity due to the loss of myelination. We also show that with these 2 conditions, it is sufficient to decompose the time-delays as bimodal distribution that only distinguishes between intra- and inter-hemispheric delays, and that the same working point also captures the static FC the best, and produces the largest variability at slow time-scales.
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Affiliation(s)
- Spase Petkoski
- Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, Marseille, France
| | - Petra Ritter
- Berlin Institute of Health at Charité - Universitätsmedizin Berlin, Berlin, Germany.,Department of Neurology with Experimental Neurology, Brain Simulation Section, Charité - Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany.,Bernstein Focus State Dependencies of Learning, Bernstein Center for Computational Neuroscience, Berlin, Germany
| | - Viktor K Jirsa
- Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, Marseille, France
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33
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Portoles O, Qin Y, Hadida J, Woolrich M, Cao M, van Vugt M. Modulations of local synchrony over time lead to resting-state functional connectivity in a parsimonious large-scale brain model. PLoS One 2022; 17:e0275819. [PMID: 36288273 PMCID: PMC9604991 DOI: 10.1371/journal.pone.0275819] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2020] [Accepted: 09/24/2022] [Indexed: 11/30/2022] Open
Abstract
Biophysical models of large-scale brain activity are a fundamental tool for understanding the mechanisms underlying the patterns observed with neuroimaging. These models combine a macroscopic description of the within- and between-ensemble dynamics of neurons within a single architecture. A challenge for these models is accounting for modulations of within-ensemble synchrony over time. Such modulations in local synchrony are fundamental for modeling behavioral tasks and resting-state activity. Another challenge comes from the difficulty in parametrizing large scale brain models which hinders researching principles related with between-ensembles differences. Here we derive a parsimonious large scale brain model that can describe fluctuations of local synchrony. Crucially, we do not reduce within-ensemble dynamics to macroscopic variables first, instead we consider within and between-ensemble interactions similarly while preserving their physiological differences. The dynamics of within-ensemble synchrony can be tuned with a parameter which manipulates local connectivity strength. We simulated resting-state static and time-resolved functional connectivity of alpha band envelopes in models with identical and dissimilar local connectivities. We show that functional connectivity emerges when there are high fluctuations of local and global synchrony simultaneously (i.e. metastable dynamics). We also show that for most ensembles, leaning towards local asynchrony or synchrony correlates with the functional connectivity with other ensembles, with the exception of some regions belonging to the default-mode network.
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Affiliation(s)
- Oscar Portoles
- Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
- * E-mail:
| | - Yuzhen Qin
- Department of Mechanical Engineering, University of California, Riverside, California, United States of America
| | - Jonathan Hadida
- Wellcome Centre for Integrative Neuroimaging, University of Oxford, Oxford, United Kingdom
| | - Mark Woolrich
- Wellcome Centre for Integrative Neuroimaging, University of Oxford, Oxford, United Kingdom
| | - Ming Cao
- Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
| | - Marieke van Vugt
- Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
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34
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John YJ, Sawyer KS, Srinivasan K, Müller EJ, Munn BR, Shine JM. It's about time: Linking dynamical systems with human neuroimaging to understand the brain. Netw Neurosci 2022; 6:960-979. [PMID: 36875012 PMCID: PMC9976648 DOI: 10.1162/netn_a_00230] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Accepted: 01/04/2022] [Indexed: 11/04/2022] Open
Abstract
Most human neuroscience research to date has focused on statistical approaches that describe stationary patterns of localized neural activity or blood flow. While these patterns are often interpreted in light of dynamic, information-processing concepts, the static, local, and inferential nature of the statistical approach makes it challenging to directly link neuroimaging results to plausible underlying neural mechanisms. Here, we argue that dynamical systems theory provides the crucial mechanistic framework for characterizing both the brain's time-varying quality and its partial stability in the face of perturbations, and hence, that this perspective can have a profound impact on the interpretation of human neuroimaging results and their relationship with behavior. After briefly reviewing some key terminology, we identify three key ways in which neuroimaging analyses can embrace a dynamical systems perspective: by shifting from a local to a more global perspective, by focusing on dynamics instead of static snapshots of neural activity, and by embracing modeling approaches that map neural dynamics using "forward" models. Through this approach, we envisage ample opportunities for neuroimaging researchers to enrich their understanding of the dynamic neural mechanisms that support a wide array of brain functions, both in health and in the setting of psychopathology.
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Affiliation(s)
- Yohan J. John
- Neural Systems Laboratory, Department of Health Sciences, Boston University, Boston, MA, USA
| | - Kayle S. Sawyer
- Departments of Anatomy and Neurobiology, Boston University, Boston University, Boston, MA, USA
- Department of Radiology, Massachusetts General Hospital, Boston, MA, USA
- Boston VA Healthcare System, Boston, MA, USA
- Sawyer Scientific, LLC, Boston, MA, USA
| | - Karthik Srinivasan
- McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Eli J. Müller
- Brain and Mind Center, University of Sydney, Sydney, NSW, Australia
| | - Brandon R. Munn
- Brain and Mind Center, University of Sydney, Sydney, NSW, Australia
| | - James M. Shine
- Brain and Mind Center, University of Sydney, Sydney, NSW, Australia
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35
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O'Byrne J, Jerbi K. How critical is brain criticality? Trends Neurosci 2022; 45:820-837. [PMID: 36096888 DOI: 10.1016/j.tins.2022.08.007] [Citation(s) in RCA: 49] [Impact Index Per Article: 24.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Revised: 07/27/2022] [Accepted: 08/10/2022] [Indexed: 10/31/2022]
Abstract
Criticality is the singular state of complex systems poised at the brink of a phase transition between order and randomness. Such systems display remarkable information-processing capabilities, evoking the compelling hypothesis that the brain may itself be critical. This foundational idea is now drawing renewed interest thanks to high-density data and converging cross-disciplinary knowledge. Together, these lines of inquiry have shed light on the intimate link between criticality, computation, and cognition. Here, we review these emerging trends in criticality neuroscience, highlighting new data pertaining to the edge of chaos and near-criticality, and making a case for the distance to criticality as a useful metric for probing cognitive states and mental illness. This unfolding progress in the field contributes to establishing criticality theory as a powerful mechanistic framework for studying emergent function and its efficiency in both biological and artificial neural networks.
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Affiliation(s)
- Jordan O'Byrne
- Cognitive and Computational Neuroscience Lab, Psychology Department, University of Montreal, Montreal, Quebec, Canada
| | - Karim Jerbi
- Cognitive and Computational Neuroscience Lab, Psychology Department, University of Montreal, Montreal, Quebec, Canada; MILA (Quebec Artificial Intelligence Institute), Montreal, Quebec, Canada; UNIQUE Center (Quebec Neuro-AI Research Center), Montreal, Quebec, Canada.
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36
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Beecroft D, Restrepo JG, Angulo-Garcia D. Greedy optimization for growing spatially embedded oscillatory networks. Phys Rev E 2022; 106:034304. [PMID: 36266840 DOI: 10.1103/physreve.106.034304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2021] [Accepted: 08/12/2022] [Indexed: 06/16/2023]
Abstract
The coupling of some types of oscillators requires the mediation of a physical link between them, rendering the distance between oscillators a critical factor to achieve synchronization. In this paper, we propose and explore a greedy algorithm to grow spatially embedded oscillator networks. The algorithm is constructed in such a way that nodes are sequentially added seeking to minimize the cost of the added links' length and optimize the linear stability of the growing network. We show that, for appropriate parameters, the stability of the resulting network, measured in terms of the dynamics of small perturbations and the correlation length of the disturbances, can be significantly improved with a minimal added length cost. In addition, we analyze numerically the topological properties of the resulting networks, and we find that, while being more stable, their degree distribution is approximately exponential and independent of the algorithm parameters. Moreover, we find that other topological parameters related with network resilience and efficiency are also affected by the proposed algorithm. Finally, we extend our findings to more general classes of networks with different sources of heterogeneity. Our results are a step in the development of algorithms for the directed growth of oscillatory networks with desirable stability, dynamical and topological properties.
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Affiliation(s)
- Damien Beecroft
- Department of Applied Mathematics, University of Washington, Washington 98195, USA
| | - Juan G Restrepo
- Department of Applied Mathematics, University of Colorado at Boulder, Colorado 80309, USA
| | - David Angulo-Garcia
- Universidad de Cartagena, Instituto de Matemáticas Aplicadas, Grupo de Modelado Computacional-Dinámica y Complejidad de Sistemas, Carrera 6 no. 36-100, Cartagena de Indias, Bolívar, Colombia
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Buzanello GL, Barioni AED, de Aguiar MAM. Matrix coupling and generalized frustration in Kuramoto oscillators. CHAOS (WOODBURY, N.Y.) 2022; 32:093130. [PMID: 36182358 DOI: 10.1063/5.0108672] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2022] [Accepted: 08/29/2022] [Indexed: 06/16/2023]
Abstract
The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a frustrated version that resulted in dynamic behavior of the order parameter, even when the average natural frequency of the oscillators is zero. Here, we consider a generalization of the frustrated KS model that exhibits new transitions to synchronization. The model is identical in form to the original Kuramoto model but written in terms of unit vectors and with the coupling constant replaced by a coupling matrix. The matrix breaks the rotational symmetry and forces the order parameter to point in the direction of the eigenvector with the highest eigenvalue, when the eigenvalues are real. For complex eigenvalues, the module of order parameter oscillates while it rotates around the unit circle, creating active states. We derive the complete phase diagram for the Lorentzian distribution of frequencies using the Ott-Antonsen ansatz. We also show that changing the average value of the natural frequencies leads to further phase transitions where the module of the order parameter goes from oscillatory to static.
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Affiliation(s)
- Guilhermo L Buzanello
- Instituto de Física "Gleb Wataghin," Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, SP, Brazil
| | - Ana Elisa D Barioni
- Instituto de Física "Gleb Wataghin," Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, SP, Brazil
| | - Marcus A M de Aguiar
- Instituto de Física "Gleb Wataghin," Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, SP, Brazil
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Jain R, Sharma J, Tiwari I, Gadre SD, Kumarasamy S, Parmananda P, Prasad A. Generation of aperiodic motion due to sporadic collisions of camphor ribbons. Phys Rev E 2022; 106:024201. [PMID: 36109890 DOI: 10.1103/physreve.106.024201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 07/13/2022] [Indexed: 06/15/2023]
Abstract
We present numerical and experimental results for the generation of aperiodic motion in coupled active rotators. The numerical analysis is presented for two point particles constrained to move on a unit circle under the Yukawa-like interaction. Simulations exhibit that the collision among the rotors results in chaotic motion of the rotating point particles. Furthermore, the numerical model predicts a route to chaotic motion. Subsequently, we explore the effect of separation between the rotors on their chaotic dynamics. The numerically calculated fraction of initial conditions which led to chaotic motion shed light on the observed effects. We reproduce a subset of the numerical observations with two self-propelled ribbons rotating at the air-water interface. A pinned camphor rotor moves at the interface due to the Marangoni forces generated by surface tension imbalance around it. The camphor layer present at the common water surface acts as chemical coupling between two ribbons. The separation distance of ribbons (L) determines the nature of coupled dynamics. Below a critical distance (L_{T}), rotors can potentially, by virtue of collisions, exhibit aperiodic oscillations characterized via a mixture of co- and counterrotating oscillations. These aperiodic dynamics qualitatively matched the chaotic motion observed in the numerical model.
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Affiliation(s)
- Rishabh Jain
- Kirori Mal College, University of Delhi, Delhi 110007, India
| | - Jyoti Sharma
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Ishant Tiwari
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | | | - Suresh Kumarasamy
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India
| | - Awadhesh Prasad
- Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India
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Ramezanian-Panahi M, Abrevaya G, Gagnon-Audet JC, Voleti V, Rish I, Dumas G. Generative Models of Brain Dynamics. Front Artif Intell 2022; 5:807406. [PMID: 35910192 PMCID: PMC9335006 DOI: 10.3389/frai.2022.807406] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Accepted: 06/10/2022] [Indexed: 01/28/2023] Open
Abstract
This review article gives a high-level overview of the approaches across different scales of organization and levels of abstraction. The studies covered in this paper include fundamental models in computational neuroscience, nonlinear dynamics, data-driven methods, as well as emergent practices. While not all of these models span the intersection of neuroscience, AI, and system dynamics, all of them do or can work in tandem as generative models, which, as we argue, provide superior properties for the analysis of neuroscientific data. We discuss the limitations and unique dynamical traits of brain data and the complementary need for hypothesis- and data-driven modeling. By way of conclusion, we present several hybrid generative models from recent literature in scientific machine learning, which can be efficiently deployed to yield interpretable models of neural dynamics.
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Affiliation(s)
| | - Germán Abrevaya
- Mila-Quebec AI Institute, Montréal, QC, Canada
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Instituto de Física de Buenos Aires (IFIBA), CONICET, Universidad de Buenos Aires, Buenos Aires, Argentina
| | | | - Vikram Voleti
- Mila-Quebec AI Institute, Montréal, QC, Canada
- Université de Montréal, Montréal, QC, Canada
| | - Irina Rish
- Mila-Quebec AI Institute, Montréal, QC, Canada
- Université de Montréal, Montréal, QC, Canada
| | - Guillaume Dumas
- Mila-Quebec AI Institute, Montréal, QC, Canada
- Université de Montréal, Montréal, QC, Canada
- Department of Psychiatry, CHU Sainte-Justine Research Center, Mila-Quebec AI Institute, Université de Montréal, Montréal, QC, Canada
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Buendía V, Villegas P, Burioni R, Muñoz MA. The broad edge of synchronization: Griffiths effects and collective phenomena in brain networks. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200424. [PMID: 35599563 DOI: 10.1098/rsta.2020.0424] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Many of the amazing functional capabilities of the brain are collective properties stemming from the interactions of large sets of individual neurons. In particular, the most salient collective phenomena in brain activity are oscillations, which require the synchronous activation of many neurons. Here, we analyse parsimonious dynamical models of neural synchronization running on top of synthetic networks that capture essential aspects of the actual brain anatomical connectivity such as a hierarchical-modular and core-periphery structure. These models reveal the emergence of complex collective states with intermediate and flexible levels of synchronization, halfway in the synchronous-asynchronous spectrum. These states are best described as broad Griffiths-like phases, i.e. an extension of standard critical points that emerge in structurally heterogeneous systems. We analyse different routes (bifurcations) to synchronization and stress the relevance of 'hybrid-type transitions' to generate rich dynamical patterns. Overall, our results illustrate the complex interplay between structure and dynamics, underlining key aspects leading to rich collective states needed to sustain brain functionality. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- Victor Buendía
- Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Department of Computer Science, University of Tübingen, Tübingen, Germany
| | - Pablo Villegas
- IMT Institute for Advanced Studies, Piazza San Ponziano 6 55100 Lucca, Italy
| | - Raffaella Burioni
- Dipartimento di Matematica, Fisica e Informatica, Università di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy
- INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy
| | - Miguel A Muñoz
- Departamento de Electromagnetismo y Física de la Materia e Instituto Carlos I de Física Teórica y Computacional. Universidad de Granada, E-18071 Granada, Spain
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Petkoski S, Jirsa VK. Normalizing the brain connectome for communication through synchronization. Netw Neurosci 2022; 6:722-744. [PMID: 36607179 PMCID: PMC9810372 DOI: 10.1162/netn_a_00231] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Accepted: 01/10/2022] [Indexed: 01/10/2023] Open
Abstract
Networks in neuroscience determine how brain function unfolds, and their perturbations lead to psychiatric disorders and brain disease. Brain networks are characterized by their connectomes, which comprise the totality of all connections, and are commonly described by graph theory. This approach is deeply rooted in a particle view of information processing, based on the quantification of informational bits such as firing rates. Oscillations and brain rhythms demand, however, a wave perspective of information processing based on synchronization. We extend traditional graph theory to a dual, particle-wave, perspective, integrate time delays due to finite transmission speeds, and derive a normalization of the connectome. When applied to the database of the Human Connectome Project, it explains the emergence of frequency-specific network cores including the visual and default mode networks. These findings are robust across human subjects (N = 100) and are a fundamental network property within the wave picture. The normalized connectome comprises the particle view in the limit of infinite transmission speeds and opens the applicability of graph theory to a wide range of novel network phenomena, including physiological and pathological brain rhythms. These two perspectives are orthogonal, but not incommensurable, when understood within the novel, here-proposed, generalized framework of structural connectivity.
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Affiliation(s)
- Spase Petkoski
- Aix-Marseille University, Inserm, INS, Institut de Neurosciences des Systèmes, Marseille, France,* Corresponding Authors: ;
| | - Viktor K. Jirsa
- Aix-Marseille University, Inserm, INS, Institut de Neurosciences des Systèmes, Marseille, France,* Corresponding Authors: ;
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Hancock F, Cabral J, Luppi AI, Rosas FE, Mediano PAM, Dipasquale O, Turkheimer FE. Metastability, fractal scaling, and synergistic information processing: what phase relationships reveal about intrinsic brain activity. Neuroimage 2022; 259:119433. [PMID: 35781077 PMCID: PMC9339663 DOI: 10.1016/j.neuroimage.2022.119433] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Revised: 06/25/2022] [Accepted: 06/29/2022] [Indexed: 12/21/2022] Open
Abstract
Spatiotemporal patterns of phase-locking tend to be time-invariant. Global metastability is representative and stable in a cohort of heathy young adults. dFC characteristics are in general unique to any fMRI acquisition. Dynamical and informational complexity are interrelated. Complexity science contributes to a coherent description of brain dynamics.
Dynamic functional connectivity (dFC) in resting-state fMRI holds promise to deliver candidate biomarkers for clinical applications. However, the reliability and interpretability of dFC metrics remain contested. Despite a myriad of methodologies and resulting measures, few studies have combined metrics derived from different conceptualizations of brain functioning within the same analysis - perhaps missing an opportunity for improved interpretability. Using a complexity-science approach, we assessed the reliability and interrelationships of a battery of phase-based dFC metrics including tools originating from dynamical systems, stochastic processes, and information dynamics approaches. Our analysis revealed novel relationships between these metrics, which allowed us to build a predictive model for integrated information using metrics from dynamical systems and information theory. Furthermore, global metastability - a metric reflecting simultaneous tendencies for coupling and decoupling - was found to be the most representative and stable metric in brain parcellations that included cerebellar regions. Additionally, spatiotemporal patterns of phase-locking were found to change in a slow, non-random, continuous manner over time. Taken together, our findings show that the majority of characteristics of resting-state fMRI dynamics reflect an interrelated dynamical and informational complexity profile, which is unique to each acquisition. This finding challenges the interpretation of results from cross-sectional designs for brain neuromarker discovery, suggesting that individual life-trajectories may be more informative than sample means.
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Affiliation(s)
- Fran Hancock
- Department of Neuroimaging, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK.
| | - Joana Cabral
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Portugal
| | - Andrea I Luppi
- Division of Anaesthesia, School of Clinical Medicine, University of Cambridge; Department of Clinical Neurosciences, University of Cambridge; Leverhulme Centre for the Future of Intelligence, University of Cambridge; Alan Turing Institute, London, UK
| | - Fernando E Rosas
- Centre for Psychedelic Research, Department of Brain Science, Imperial College London, London SW7 2DD; Data Science Institute, Imperial College London, London SW7 2AZ; Centre for Complexity Science, Imperial College London, London SW7 2AZ
| | - Pedro A M Mediano
- Department of Psychology, University of Cambridge, Cambridge CB2 3EB; Department of Psychology, Queen Mary University of London, London E1 4NS
| | - Ottavia Dipasquale
- Department of Neuroimaging, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - Federico E Turkheimer
- Department of Neuroimaging, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
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Nasr K, Haslacher D, Dayan E, Censor N, Cohen LG, Soekadar SR. Breaking the boundaries of interacting with the human brain using adaptive closed-loop stimulation. Prog Neurobiol 2022; 216:102311. [PMID: 35750290 DOI: 10.1016/j.pneurobio.2022.102311] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2022] [Accepted: 06/20/2022] [Indexed: 11/18/2022]
Abstract
The human brain is arguably one of the most complex systems in nature. To understand how it operates, it is essential to understand the link between neural activity and behavior. Experimental investigation of that link requires tools to interact with neural activity during behavior. Human neuroscience, however, has been severely bottlenecked by the limitations of these tools. While invasive methods can support highly specific interaction with brain activity during behavior, their applicability in human neuroscience is limited. Despite extensive development in the last decades, noninvasive alternatives have lacked spatial specificity and yielded results that are commonly fraught with variability and replicability issues, along with relatively limited understanding of the neural mechanisms involved. Here we provide a comprehensive review of the state-of-the-art in interacting with human brain activity and highlight current limitations and recent efforts to overcome these limitations. Beyond crucial technical and scientific advancements in electromagnetic brain stimulation, new frontiers in interacting with human brain activity such as task-irrelevant sensory stimulation and focal ultrasound stimulation are introduced. Finally, we argue that, along with technological improvements and breakthroughs in noninvasive methods, a paradigm shift towards adaptive closed-loop stimulation will be a critical step for advancing human neuroscience.
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Affiliation(s)
- Khaled Nasr
- Clinical Neurotechnology Laboratory & Center for Translational Neuromodulation, Department of Psychiatry and Neurosciences, Charité Campus Mitte (CCM), Charité - Universitätsmedizin Berlin, Berlin, Germany
| | - David Haslacher
- Clinical Neurotechnology Laboratory & Center for Translational Neuromodulation, Department of Psychiatry and Neurosciences, Charité Campus Mitte (CCM), Charité - Universitätsmedizin Berlin, Berlin, Germany
| | - Eran Dayan
- Department of Radiology and Biomedical Research Imaging Center, School of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Nitzan Censor
- School of Psychological Sciences and Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel
| | - Leonardo G Cohen
- Human Cortical Physiology and Neurorehabilitation Section, National Institutes of Neurological Disorders and Stroke (NINDS), Bethesda, MD, USA
| | - Surjo R Soekadar
- Clinical Neurotechnology Laboratory & Center for Translational Neuromodulation, Department of Psychiatry and Neurosciences, Charité Campus Mitte (CCM), Charité - Universitätsmedizin Berlin, Berlin, Germany.
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Biophysical mechanism underlying compensatory preservation of neural synchrony over the adult lifespan. Commun Biol 2022; 5:567. [PMID: 35681107 PMCID: PMC9184644 DOI: 10.1038/s42003-022-03489-4] [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: 11/19/2021] [Accepted: 05/12/2022] [Indexed: 11/17/2022] Open
Abstract
We propose that the preservation of functional integration, estimated from measures of neural synchrony, is a key objective of neurocompensatory mechanisms associated with healthy human ageing. To support this proposal, we demonstrate how phase-locking at the peak alpha frequency in Magnetoencephalography recordings remains invariant over the lifespan in a large cohort of human participants, aged 18-88 years. Using empirically derived connection topologies from diffusion tensor imaging data, we create an in-silico model of whole-brain alpha dynamics. We show that enhancing inter-areal coupling can cancel the effect of increased axonal transmission delays associated with age-related degeneration of white matter tracts, albeit at slower network frequencies. By deriving analytical solutions for simplified connection topologies, we further establish the theoretical principles underlying compensatory network re-organization. Our findings suggest that frequency slowing with age- frequently observed in the alpha band in diverse populations- may be viewed as an epiphenomenon of the underlying compensatory mechanism. Analysis of MEG data from healthy participants and whole-brain network modeling suggests that the brain compensates for age-related disruptions in connectivity by slowing down the frequency of neural synchronization.
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45
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Das S, Puthankattil SD. Functional Connectivity and Complexity in the Phenomenological Model of Mild Cognitive-Impaired Alzheimer's Disease. Front Comput Neurosci 2022; 16:877912. [PMID: 35733555 PMCID: PMC9207343 DOI: 10.3389/fncom.2022.877912] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Accepted: 04/26/2022] [Indexed: 11/13/2022] Open
Abstract
BackgroundFunctional connectivity and complexity analysis has been discretely studied to understand intricate brain dynamics. The current study investigates the interplay between functional connectivity and complexity using the Kuramoto mean-field model.MethodFunctional connectivity matrices are estimated using the weighted phase lag index and complexity measures through popularly used complexity estimators such as Lempel-Ziv complexity (LZC), Higuchi's fractal dimension (HFD), and fluctuation-based dispersion entropy (FDispEn). Complexity measures are estimated on real and simulated electroencephalogram (EEG) signals of patients with mild cognitive-impaired Alzheimer's disease (MCI-AD) and controls. Complexity measures are further applied to simulated signals generated from lesion-induced connectivity matrix and studied its impact. It is a novel attempt to study the relation between functional connectivity and complexity using a neurocomputational model.ResultsReal EEG signals from patients with MCI-AD exhibited reduced functional connectivity and complexity in anterior and central regions. A simulation study has also displayed significantly reduced regional complexity in the patient group with respect to control. A similar reduction in complexity was further evident in simulation studies with lesion-induced control groups compared with non-lesion-induced control groups.ConclusionTaken together, simulation studies demonstrate a positive influence of reduced connectivity in the model imparting a reduced complexity in the EEG signal. The study revealed the presence of a direct relation between functional connectivity and complexity with reduced connectivity, yielding a decreased EEG complexity.
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46
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Li Y, Shi J, Aihara K. Mean-field analysis of Stuart-Landau oscillator networks with symmetric coupling and dynamical noise. CHAOS (WOODBURY, N.Y.) 2022; 32:063114. [PMID: 35778116 DOI: 10.1063/5.0081295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 05/09/2022] [Indexed: 06/15/2023]
Abstract
This paper presents analyses of networks composed of homogeneous Stuart-Landau oscillators with symmetric linear coupling and dynamical Gaussian noise. With a simple mean-field approximation, the original system is transformed into a surrogate system that describes uncorrelated oscillation/fluctuation modes of the original system. The steady-state probability distribution for these modes is described using an exponential family, and the dynamics of the system are mainly determined by the eigenvalue spectrum of the coupling matrix and the noise level. The variances of the modes can be expressed as functions of the eigenvalues and noise level, yielding the relation between the covariance matrix and the coupling matrix of the oscillators. With decreasing noise, the leading mode changes from fluctuation to oscillation, generating apparent synchrony of the coupled oscillators, and the condition for such a transition is derived. Finally, the approximate analyses are examined via numerical simulation of the oscillator networks with weak coupling to verify the utility of the approximation in outlining the basic properties of the considered coupled oscillator networks. These results are potentially useful for the modeling and analysis of indirectly measured data of neurodynamics, e.g., via functional magnetic resonance imaging and electroencephalography, as a counterpart of the frequently used Ising model.
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Affiliation(s)
- Yang Li
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Jifan Shi
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Kazuyuki Aihara
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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Pathak A, Roy D, Banerjee A. Whole-Brain Network Models: From Physics to Bedside. Front Comput Neurosci 2022; 16:866517. [PMID: 35694610 PMCID: PMC9180729 DOI: 10.3389/fncom.2022.866517] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Accepted: 05/02/2022] [Indexed: 11/13/2022] Open
Abstract
Computational neuroscience has come a long way from its humble origins in the pioneering work of Hodgkin and Huxley. Contemporary computational models of the brain span multiple spatiotemporal scales, from single neuronal compartments to models of social cognition. Each spatial scale comes with its own unique set of promises and challenges. Here, we review models of large-scale neural communication facilitated by white matter tracts, also known as whole-brain models (WBMs). Whole-brain approaches employ inputs from neuroimaging data and insights from graph theory and non-linear systems theory to model brain-wide dynamics. Over the years, WBM models have shown promise in providing predictive insights into various facets of neuropathologies such as Alzheimer's disease, Schizophrenia, Epilepsy, Traumatic brain injury, while also offering mechanistic insights into large-scale cortical communication. First, we briefly trace the history of WBMs, leading up to the state-of-the-art. We discuss various methodological considerations for implementing a whole-brain modeling pipeline, such as choice of node dynamics, model fitting and appropriate parcellations. We then demonstrate the applicability of WBMs toward understanding various neuropathologies. We conclude by discussing ways of augmenting the biological and clinical validity of whole-brain models.
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Affiliation(s)
| | - Dipanjan Roy
- Centre for Brain Science and Applications, School of Artificial Intelligence and Data Science, Indian Institute of Technology, Jodhpur, India
| | - Arpan Banerjee
- National Brain Research Centre, Gurgaon, India
- *Correspondence: Arpan Banerjee
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48
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Portoles O, Blesa M, van Vugt M, Cao M, Borst JP. Thalamic bursts modulate cortical synchrony locally to switch between states of global functional connectivity in a cognitive task. PLoS Comput Biol 2022; 18:e1009407. [PMID: 35263318 PMCID: PMC8936493 DOI: 10.1371/journal.pcbi.1009407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Revised: 03/21/2022] [Accepted: 02/16/2022] [Indexed: 11/23/2022] Open
Abstract
Performing a cognitive task requires going through a sequence of functionally diverse stages. Although it is typically assumed that these stages are characterized by distinct states of cortical synchrony that are triggered by sub-cortical events, little reported evidence supports this hypothesis. To test this hypothesis, we first identified cognitive stages in single-trial MEG data of an associative recognition task, showing with a novel method that each stage begins with local modulations of synchrony followed by a state of directed functional connectivity. Second, we developed the first whole-brain model that can simulate cortical synchrony throughout a task. The model suggests that the observed synchrony is caused by thalamocortical bursts at the onset of each stage, targeted at cortical synapses and interacting with the structural anatomical connectivity. These findings confirm that cognitive stages are defined by distinct states of cortical synchrony and explains the network-level mechanisms necessary for reaching stage-dependent synchrony states. A novel machine-learning method was applied to unveil the dynamics of local and cortex-wide neural coordination underlying the fundamental cognitive processes involved in a memory task. To explain how neural activity–and ultimately behavior–was coordinated throughout the task, we developed a whole-brain model that incorporates cognitive mechanisms, anatomy, and neural biophysics. Similar models are regularly used with resting state data, but simulating a cognitive task remained elusive. By using hidden semi-Markov models to divide the task into stages with separate connectivity patterns, we were able to generalize the whole brain model from resting state to cognitive task data. The model showed that sub-cortical pulses at the onset of cognitive processes–as hypothesized by cognitive and neurophysiological theories–were sufficient to switch between the states of neural coordination observed. These findings have implications for understanding goal-directed cognitive processing and the mechanisms needed to reach states of neural coordination.
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Affiliation(s)
- Oscar Portoles
- Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
- Engineering and Technology Institute Groningen, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
- * E-mail: (OP); (JP)
| | - Manuel Blesa
- MRC Centre for Reproductive Health, University of Edinburgh, Edinburgh, United Kingdom
| | - Marieke van Vugt
- Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
| | - Ming Cao
- Engineering and Technology Institute Groningen, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
| | - Jelmer P. Borst
- Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
- * E-mail: (OP); (JP)
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49
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Aquino KM, Fulcher B, Oldham S, Parkes L, Gollo L, Deco G, Fornito A. On the intersection between data quality and dynamical modelling of large-scale fMRI signals. Neuroimage 2022; 256:119051. [PMID: 35276367 DOI: 10.1016/j.neuroimage.2022.119051] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Revised: 01/23/2022] [Accepted: 03/01/2022] [Indexed: 12/25/2022] Open
Abstract
Large-scale dynamics of the brain are routinely modelled using systems of nonlinear dynamical equations that describe the evolution of population-level activity, with distinct neural populations often coupled according to an empirically measured structural connectivity matrix. This modelling approach has been used to generate insights into the neural underpinnings of spontaneous brain dynamics, as recorded with techniques such as resting state functional MRI (fMRI). In fMRI, researchers have many degrees of freedom in the way that they can process the data and recent evidence indicates that the choice of pre-processing steps can have a major effect on empirical estimates of functional connectivity. However, the potential influence of such variations on modelling results are seldom considered. Here we show, using three popular whole-brain dynamical models, that different choices during fMRI preprocessing can dramatically affect model fits and interpretations of findings. Critically, we show that the ability of these models to accurately capture patterns in fMRI dynamics is mostly driven by the degree to which they fit global signals rather than interesting sources of coordinated neural dynamics. We show that widespread deflections can arise from simple global synchronisation. We introduce a simple two-parameter model that captures these fluctuations and performs just as well as more complex, multi-parameter biophysical models. From our combined analyses of data and simulations, we describe benchmarks to evaluate model fit and validity. Although most models are not resilient to denoising, we show that relaxing the approximation of homogeneous neural populations by more explicitly modelling inter-regional effective connectivity can improve model accuracy at the expense of increased model complexity. Our results suggest that many complex biophysical models may be fitting relatively trivial properties of the data, and underscore a need for tighter integration between data quality assurance and model development.
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Affiliation(s)
- Kevin M Aquino
- The Turner Institute for Brain and Mental Health, School of Psychological Sciences, and Monash Biomedical Imaging, Monash University, Victoria 3168, Australia; School of Physics, University of Sydney, New South Wales, 2006 Australia.
| | - Ben Fulcher
- School of Physics, University of Sydney, New South Wales, 2006 Australia
| | - Stuart Oldham
- The Turner Institute for Brain and Mental Health, School of Psychological Sciences, and Monash Biomedical Imaging, Monash University, Victoria 3168, Australia
| | - Linden Parkes
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA, 19104 USA
| | - Leonardo Gollo
- The Turner Institute for Brain and Mental Health, School of Psychological Sciences, and Monash Biomedical Imaging, Monash University, Victoria 3168, Australia
| | - Gustavo Deco
- The Turner Institute for Brain and Mental Health, School of Psychological Sciences, and Monash Biomedical Imaging, Monash University, Victoria 3168, Australia; Center for Brain and Cognition, Universitat Pompeu Fabra, Barcelona 08010, Spain; Institució Catalana de la Recerca i Estudis Avançats (ICREA), Universitat Pompeu Fabra, Barcelona 08010, Spain
| | - Alex Fornito
- The Turner Institute for Brain and Mental Health, School of Psychological Sciences, and Monash Biomedical Imaging, Monash University, Victoria 3168, Australia
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Bauer LG, Hirsch F, Jones C, Hollander M, Grohs P, Anand A, Plant C, Wohlschläger A. Quantification of Kuramoto Coupling Between Intrinsic Brain Networks Applied to fMRI Data in Major Depressive Disorder. Front Comput Neurosci 2022; 16:729556. [PMID: 35311219 PMCID: PMC8929174 DOI: 10.3389/fncom.2022.729556] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2021] [Accepted: 01/28/2022] [Indexed: 11/13/2022] Open
Abstract
Organized patterns of system-wide neural activity adapt fluently within the brain to adjust behavioral performance to environmental demands. In major depressive disorder (MD), markedly different co-activation patterns across the brain emerge from a rather similar structural substrate. Despite the application of advanced methods to describe the functional architecture, e.g., between intrinsic brain networks (IBNs), the underlying mechanisms mediating these differences remain elusive. Here we propose a novel complementary approach for quantifying the functional relations between IBNs based on the Kuramoto model. We directly estimate the Kuramoto coupling parameters (K) from IBN time courses derived from empirical fMRI data in 24 MD patients and 24 healthy controls. We find a large pattern with a significant number of Ks depending on the disease severity score Hamilton D, as assessed by permutation testing. We successfully reproduced the dependency in an independent test data set of 44 MD patients and 37 healthy controls. Comparing the results to functional connectivity from partial correlations (FC), to phase synchrony (PS) as well as to first order auto-regressive measures (AR) between the same IBNs did not show similar correlations. In subsequent validation experiments with artificial data we find that a ground truth of parametric dependencies on artificial regressors can be recovered. The results indicate that the calculation of Ks can be a useful addition to standard methods of quantifying the brain's functional architecture.
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Affiliation(s)
- Lena G. Bauer
- Research Network Data Science, University of Vienna, Vienna, Austria
| | - Fabian Hirsch
- Departement of Neuroradiology, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
- TUMNIC, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
| | - Corey Jones
- Departement of Neuroradiology, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
- TUMNIC, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
| | - Matthew Hollander
- Departement of Neuroradiology, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
- TUMNIC, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
| | - Philipp Grohs
- Research Network Data Science, University of Vienna, Vienna, Austria
- Faculty of Mathematics, University of Vienna, Vienna, Austria
| | - Amit Anand
- Center for Behavioral Health, Cleveland Clinic, Cleveland, OH, United States
| | - Claudia Plant
- Research Network Data Science, University of Vienna, Vienna, Austria
- Faculty of Computer Science, University of Vienna, Vienna, Austria
| | - Afra Wohlschläger
- Departement of Neuroradiology, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
- TUMNIC, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
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