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Shamsara E, Yamakou ME, Atay FM, Jost J. Dynamics of neural fields with exponential temporal kernel. Theory Biosci 2024; 143:107-122. [PMID: 38460025 PMCID: PMC11127868 DOI: 10.1007/s12064-024-00414-7] [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: 06/07/2022] [Accepted: 02/09/2024] [Indexed: 03/11/2024]
Abstract
We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which Green's function does not. Through a dynamic bifurcation analysis, we give explicit bifurcation conditions. Hopf bifurcations lead to temporally non-constant, but spatially constant solutions, but Turing-Hopf bifurcations generate spatially and temporally non-constant solutions, in particular, traveling waves. Bifurcation parameters are the coefficient of the exponential temporal kernel, the transmission speed of neural signals, the time delay rate of synapses, and the ratio of excitatory to inhibitory synaptic weights.
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Affiliation(s)
- Elham Shamsara
- Methods in Medical Informatics, Department of Computer Science, University of Tübingen, 72076, Tübingen, Germany
| | - Marius E Yamakou
- Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany.
| | - Fatihcan M Atay
- Department of Mathematics, Bilkent University, 06800, Ankara, Turkey
| | - Jürgen Jost
- Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22, 04103, Leipzig, Germany
- Santa Fe Institute for the Sciences of Complexity, Santa Fe, NM, 87501, USA
- ScaDS.AI, Dresden/Leipzig, Germany
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2
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Mitjans AG, Linares DP, Naranjo CL, Gonzalez AA, Li M, Wang Y, Reyes RG, Bringas-Vega ML, Minati L, Evans AC, Valdés-Sosa PA. Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors. Neuroimage 2023; 274:120137. [PMID: 37116767 DOI: 10.1016/j.neuroimage.2023.120137] [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: 01/18/2023] [Revised: 04/16/2023] [Accepted: 04/25/2023] [Indexed: 04/30/2023] Open
Abstract
This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass model, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen-Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since they only appear for distinct neural masses. We provide an open-source Script for the toolbox.
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Affiliation(s)
- Anisleidy González Mitjans
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China; Department of Mathematics, University of Havana, Havana, Cuba.
| | - Deirel Paz Linares
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China; Department of Neuroinformatics, Cuban Neuroscience Center, Havana, Cuba.
| | - Carlos López Naranjo
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China.
| | - Ariosky Areces Gonzalez
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China; Department of Informatics, University of Pinar del Rio, Pinar del Rio, Cuba.
| | - Min Li
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China.
| | - Ying Wang
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China.
| | | | - María L Bringas-Vega
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China; Department of Neuroinformatics, Cuban Neuroscience Center, Havana, Cuba.
| | - Ludovico Minati
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China; Center for Mind/Brain Sciences (CIMeC), University of Trento, 38100 Trento, Italy.
| | - Alan C Evans
- McGill Centre for Integrative Neuroscience, Ludmer Centre for Neuroinformatics and Mental Health, Montreal Neurological Institute, Canada.
| | - Pedro A Valdés-Sosa
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China; Department of Neuroinformatics, Cuban Neuroscience Center, Havana, Cuba.
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3
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Pinotsis DA, Miller EK. Beyond dimension reduction: Stable electric fields emerge from and allow representational drift. Neuroimage 2022; 253:119058. [PMID: 35272022 DOI: 10.1016/j.neuroimage.2022.119058] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Revised: 03/03/2022] [Accepted: 03/03/2022] [Indexed: 01/18/2023] Open
Abstract
It is known that the exact neurons maintaining a given memory (the neural ensemble) change from trial to trial. This raises the question of how the brain achieves stability in the face of this representational drift. Here, we demonstrate that this stability emerges at the level of the electric fields that arise from neural activity. We show that electric fields carry information about working memory content. The electric fields, in turn, can act as "guard rails" that funnel higher dimensional variable neural activity along stable lower dimensional routes. We obtained the latent space associated with each memory. We then confirmed the stability of the electric field by mapping the latent space to different cortical patches (that comprise a neural ensemble) and reconstructing information flow between patches. Stable electric fields can allow latent states to be transferred between brain areas, in accord with modern engram theory.
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Affiliation(s)
- Dimitris A Pinotsis
- Centre for Mathematical Neuroscience and Psychology and Department of Psychology, City-University of London, London EC1V 0HB, United Kingdom; The Picower Institute for Learning and Memory and Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
| | - Earl K Miller
- The Picower Institute for Learning and Memory and Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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4
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Lemaréchal JD, Jedynak M, Trebaul L, Boyer A, Tadel F, Bhattacharjee M, Deman P, Tuyisenge V, Ayoubian L, Hugues E, Chanteloup-Forêt B, Saubat C, Zouglech R, Reyes Mejia GC, Tourbier S, Hagmann P, Adam C, Barba C, Bartolomei F, Blauwblomme T, Curot J, Dubeau F, Francione S, Garcés M, Hirsch E, Landré E, Liu S, Maillard L, Metsähonkala EL, Mindruta I, Nica A, Pail M, Petrescu AM, Rheims S, Rocamora R, Schulze-Bonhage A, Szurhaj W, Taussig D, Valentin A, Wang H, Kahane P, George N, David O. A brain atlas of axonal and synaptic delays based on modelling of cortico-cortical evoked potentials. Brain 2021; 145:1653-1667. [PMID: 35416942 PMCID: PMC9166555 DOI: 10.1093/brain/awab362] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Revised: 08/03/2021] [Accepted: 08/14/2021] [Indexed: 11/16/2022] Open
Abstract
Epilepsy presurgical investigation may include focal intracortical single-pulse electrical stimulations with depth electrodes, which induce cortico-cortical evoked potentials at distant sites because of white matter connectivity. Cortico-cortical evoked potentials provide a unique window on functional brain networks because they contain sufficient information to infer dynamical properties of large-scale brain connectivity, such as preferred directionality and propagation latencies. Here, we developed a biologically informed modelling approach to estimate the neural physiological parameters of brain functional networks from the cortico-cortical evoked potentials recorded in a large multicentric database. Specifically, we considered each cortico-cortical evoked potential as the output of a transient stimulus entering the stimulated region, which directly propagated to the recording region. Both regions were modelled as coupled neural mass models, the parameters of which were estimated from the first cortico-cortical evoked potential component, occurring before 80 ms, using dynamic causal modelling and Bayesian model inversion. This methodology was applied to the data of 780 patients with epilepsy from the F-TRACT database, providing a total of 34 354 bipolar stimulations and 774 445 cortico-cortical evoked potentials. The cortical mapping of the local excitatory and inhibitory synaptic time constants and of the axonal conduction delays between cortical regions was obtained at the population level using anatomy-based averaging procedures, based on the Lausanne2008 and the HCP-MMP1 parcellation schemes, containing 130 and 360 parcels, respectively. To rule out brain maturation effects, a separate analysis was performed for older (>15 years) and younger patients (<15 years). In the group of older subjects, we found that the cortico-cortical axonal conduction delays between parcels were globally short (median = 10.2 ms) and only 16% were larger than 20 ms. This was associated to a median velocity of 3.9 m/s. Although a general lengthening of these delays with the distance between the stimulating and recording contacts was observed across the cortex, some regions were less affected by this rule, such as the insula for which almost all efferent and afferent connections were faster than 10 ms. Synaptic time constants were found to be shorter in the sensorimotor, medial occipital and latero-temporal regions, than in other cortical areas. Finally, we found that axonal conduction delays were significantly larger in the group of subjects younger than 15 years, which corroborates that brain maturation increases the speed of brain dynamics. To our knowledge, this study is the first to provide a local estimation of axonal conduction delays and synaptic time constants across the whole human cortex in vivo, based on intracerebral electrophysiological recordings.
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Affiliation(s)
- Jean-Didier Lemaréchal
- Sorbonne Université, Institut du Cerveau-Paris Brain Institute-ICM, Inserm, CNRS, Centre MEG-EEG and Experimental Neurosurgery Team, F-75013 Paris, France.,Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France.,Aix Marseille Université, Inserm, INS, Institut de Neurosciences des Systèmes, Marseille, France
| | - Maciej Jedynak
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | - Lena Trebaul
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | - Anthony Boyer
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | - François Tadel
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | - Manik Bhattacharjee
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | - Pierre Deman
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | - Viateur Tuyisenge
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | - Leila Ayoubian
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | - Etienne Hugues
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | | | - Carole Saubat
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | - Raouf Zouglech
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France
| | | | - Sébastien Tourbier
- Department of Radiology, Lausanne University Hospital (CHUV) and University of Lausanne (UNIL), Lausanne, Switzerland
| | - Patric Hagmann
- Department of Radiology, Lausanne University Hospital (CHUV) and University of Lausanne (UNIL), Lausanne, Switzerland
| | - Claude Adam
- Department of Neurology, Epilepsy Unit, AP-HP, Hôpital de la Pitié Salpêtrière, F-75013 Paris, France
| | - Carmen Barba
- Neuroscience Department, Children's Hospital Meyer-University of Florence, Florence, Italy
| | - Fabrice Bartolomei
- Aix Marseille Université, Inserm, INS, Institut de Neurosciences des Systèmes, Marseille, France.,Service de Neurophysiologie Clinique, APHM, Hôpitaux de la Timone, Marseille, France
| | - Thomas Blauwblomme
- Department of Pediatric Neurosurgery, Hôpital Necker-Enfants Malades, Université Paris V Descartes, Sorbonne Paris Cité, Paris, France
| | - Jonathan Curot
- Department of Neurophysiological Explorations, CerCo, CNRS, UMR5549, Centre Hospitalier Universitaire de Toulouse and University of Toulouse, Toulouse, France
| | - François Dubeau
- Montreal Neurological Institute and Hospital, Montreal, Canada
| | - Stefano Francione
- 'Claudio Munari' Centre for Epilepsy Surgery; Neuroscience Department, GOM, Niguarda, Milano, Italy
| | - Mercedes Garcés
- Multidisciplinary Epilepsy Unit, Hospital Universitario y Politécnico La Fe, Valencia, Spain
| | - Edouard Hirsch
- University Hospital, Department of Neurology, Strasbourg, France
| | | | - Sinclair Liu
- Canton Sanjiu Brain Hospital Epilepsy Center, Jinan University, Guangzhou, China
| | - Louis Maillard
- Centre Hospitalier Universitaire de Nancy, Nancy, France
| | | | - Ioana Mindruta
- Neurology Department, University Emergency Hospital, Bucharest, Romania
| | - Anca Nica
- Neurology Department, CIC 1414, Rennes University Hospital; LTSI, INSERM U 1099, F-35000 Rennes, France
| | - Martin Pail
- Brno Epilepsy Center, Department of Neurology, St. Anne's University Hospital and Medical Faculty of Masaryk University, Brno, Czech Republic
| | | | - Sylvain Rheims
- Department of Functional Neurology and Epileptology, Hospices Civils de Lyon and Lyon's Neurosciences Research Center, INSERM U1028/CNRS UMR5292/Lyon 1 University, Lyon, France
| | - Rodrigo Rocamora
- Epilepsy Monitoring Unit, Department of Neurology, Hospital del Mar-IMIM, Barcelona, Spain
| | - Andreas Schulze-Bonhage
- Epilepsy Center, Medical Center-University of Freiburg, Faculty of Medicine, University of Freiburg, Germany
| | - William Szurhaj
- Epilepsy Unit, Department of Clinical Neurophysiology, Lille University Medical Center, Lille, France
| | - Delphine Taussig
- Neurophysiology and Epilepsy Unit, Bicêtre Hospital, France.,Service de Neurochirurgie Pédiatrique, Fondation Rothschild, Paris, France
| | - Antonio Valentin
- Department of Basic and Clinical Neuroscience, Institute of Psychiatry, Psychology & Neuroscience (IoPPN), London, UK
| | - Haixiang Wang
- Yuquan Hospital Epilepsy Center, Tsinghua University, Beijing, China
| | - Philippe Kahane
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France.,Neurology Department, CHU Grenoble Alpes, Grenoble, France
| | - Nathalie George
- Sorbonne Université, Institut du Cerveau-Paris Brain Institute-ICM, Inserm, CNRS, Centre MEG-EEG and Experimental Neurosurgery Team, F-75013 Paris, France
| | - Olivier David
- Université Grenoble Alpes, Inserm, U1216, Grenoble Institut Neurosciences, 38000 Grenoble, France.,Aix Marseille Université, Inserm, INS, Institut de Neurosciences des Systèmes, Marseille, France
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5
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Ross J, Margetts M, Bojak I, Nicks R, Avitabile D, Coombes S. Brain-wave equation incorporating axodendritic connectivity. Phys Rev E 2020; 101:022411. [PMID: 32168690 DOI: 10.1103/physreve.101.022411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Accepted: 01/28/2020] [Indexed: 06/10/2023]
Abstract
We introduce an integral model of a two-dimensional neural field that includes a third dimension representing space along a dendritic tree that can incorporate realistic patterns of axodendritic connectivity. For natural choices of this connectivity we show how to construct an equivalent brain-wave partial differential equation that allows for efficient numerical simulation of the model. This is used to highlight the effects that passive dendritic properties can have on the speed and shape of large scale traveling cortical waves.
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Affiliation(s)
- James Ross
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Michelle Margetts
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Ingo Bojak
- School of Psychology and Clinical Language Sciences, University of Reading, Reading RG6 6AL, United Kingdom
| | - Rachel Nicks
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Daniele Avitabile
- Department of Mathematics, Vrije Universiteit (VU University Amsterdam), Faculteit der Exacte Wetenschappen, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
- Mathneuro Team, Inria Sophia Antipolis, 2004 Rue des Lucioles, 06902 Sophia Antipolis, Cedex, France
| | - Stephen Coombes
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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6
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Daini D, Ceccarelli G, Cataldo E, Jirsa V. Spherical-harmonics mode decomposition of neural field equations. Phys Rev E 2020; 101:012202. [PMID: 32069532 DOI: 10.1103/physreve.101.012202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Indexed: 06/10/2023]
Abstract
Large-scale neural networks can be described in the spatial continuous limit by neural field equations. For large-scale brain networks, the connectivity is typically translationally variant and imposes a large computational burden upon simulations. To reduce this burden, we take a semiquantitative approach and study the dynamics of neural fields described by a delayed integrodifferential equation. We decompose the connectivity into spatially variant and invariant contributions, which typically comprise the short- and long-range fiber systems, respectively. The neural fields are mapped on the two-dimensional spherical surface, which is choice consistent with routine mappings of cortical surfaces. Then, we perform mathematically a mode decomposition of the neural field equation into spherical harmonic basis functions. A spatial truncation of the leading orders at low wave number is consistent with the spatially coherent pattern formation of large-scale patterns observed in simulations and empirical brain imaging data and leads to a low-dimensional representation of the dynamics of the neural fields, bearing promise for an acceleration of the numerical simulations by orders of magnitude.
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Affiliation(s)
- Daniele Daini
- UMR Inserm 1106, Aix-Marseille Université, Faculté de Médecine, 27, Boulevard Jean Moulin, 13005 Marseille, France
| | - Giacomo Ceccarelli
- Physics Department, Largo B. Pontecorvo 3, University of Pisa, 56127 Pisa, Italy
| | - Enrico Cataldo
- Physics Department, Largo B. Pontecorvo 3, University of Pisa, 56127 Pisa, Italy
| | - Viktor Jirsa
- UMR Inserm 1106, Aix-Marseille Université, Faculté de Médecine, 27, Boulevard Jean Moulin, 13005 Marseille, France
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7
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Sanz-Leon P, Robinson PA, Knock SA, Drysdale PM, Abeysuriya RG, Fung FK, Rennie CJ, Zhao X. NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics. PLoS Comput Biol 2018; 14:e1006387. [PMID: 30133448 PMCID: PMC6122812 DOI: 10.1371/journal.pcbi.1006387] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2018] [Revised: 09/04/2018] [Accepted: 07/22/2018] [Indexed: 01/02/2023] Open
Abstract
A user ready, portable, documented software package, NFTsim, is presented to facilitate numerical simulations of a wide range of brain systems using continuum neural field modeling. NFTsim enables users to simulate key aspects of brain activity at multiple scales. At the microscopic scale, it incorporates characteristics of local interactions between cells, neurotransmitter effects, synaptodendritic delays and feedbacks. At the mesoscopic scale, it incorporates information about medium to large scale axonal ranges of fibers, which are essential to model dissipative wave transmission and to produce synchronous oscillations and associated cross-correlation patterns as observed in local field potential recordings of active tissue. At the scale of the whole brain, NFTsim allows for the inclusion of long range pathways, such as thalamocortical projections, when generating macroscopic activity fields. The multiscale nature of the neural activity produced by NFTsim has the potential to enable the modeling of resulting quantities measurable via various neuroimaging techniques. In this work, we give a comprehensive description of the design and implementation of the software. Due to its modularity and flexibility, NFTsim enables the systematic study of an unlimited number of neural systems with multiple neural populations under a unified framework and allows for direct comparison with analytic and experimental predictions. The code is written in C++ and bundled with Matlab routines for a rapid quantitative analysis and visualization of the outputs. The output of NFTsim is stored in plain text file enabling users to select from a broad range of tools for offline analysis. This software enables a wide and convenient use of powerful physiologically-based neural field approaches to brain modeling. NFTsim is distributed under the Apache 2.0 license.
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Affiliation(s)
- Paula Sanz-Leon
- School of Physics, University of Sydney, Sydney, Australia
- Center for Integrative Brain Function, University of Sydney, Sydney, Australia
| | - Peter A. Robinson
- School of Physics, University of Sydney, Sydney, Australia
- Center for Integrative Brain Function, University of Sydney, Sydney, Australia
| | - Stuart A. Knock
- School of Physics, University of Sydney, Sydney, Australia
- Center for Integrative Brain Function, University of Sydney, Sydney, Australia
| | | | - Romesh G. Abeysuriya
- School of Physics, University of Sydney, Sydney, Australia
- Center for Integrative Brain Function, University of Sydney, Sydney, Australia
- Oxford Centre for Human Brain Activity, Wellcome Centre for Integrative Neuroimaging, Department of Psychiatry, University of Oxford, Oxford, United Kingdom
| | - Felix K. Fung
- School of Physics, University of Sydney, Sydney, Australia
- Center for Integrative Brain Function, University of Sydney, Sydney, Australia
- Downstate Medical Center, State University of New York, Brooklyn, New York, United States of America
| | | | - Xuelong Zhao
- School of Physics, University of Sydney, Sydney, Australia
- Center for Integrative Brain Function, University of Sydney, Sydney, Australia
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8
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Wilson MT, Fulcher BD, Fung PK, Robinson P, Fornito A, Rogasch NC. Biophysical modeling of neural plasticity induced by transcranial magnetic stimulation. Clin Neurophysiol 2018; 129:1230-1241. [DOI: 10.1016/j.clinph.2018.03.018] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2017] [Revised: 02/28/2018] [Accepted: 03/14/2018] [Indexed: 10/17/2022]
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9
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Alswaihli J, Potthast R, Bojak I, Saddy D, Hutt A. Kernel Reconstruction for Delayed Neural Field Equations. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2018; 8:3. [PMID: 29399710 PMCID: PMC5797727 DOI: 10.1186/s13408-018-0058-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Accepted: 01/17/2018] [Indexed: 06/07/2023]
Abstract
Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues.In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed-point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Fréchet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience.
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Affiliation(s)
- Jehan Alswaihli
- Department of Mathematics and Statistics, University of Reading, Reading, UK
- Department of Mathematics, Faculty of Education, Misurata University, Misurata, Libya
| | - Roland Potthast
- Department of Mathematics and Statistics, University of Reading, Reading, UK
- Division for Data Assimilation (FE12), Deutscher Wetterdienst, Offenbach, Germany
| | - Ingo Bojak
- Centre for Integrative Neuroscience and Neurodynamics (CINN), Department of Psychology, University of Reading, Reading, UK
| | - Douglas Saddy
- Centre for Integrative Neuroscience and Neurodynamics (CINN), Department of Psychology, University of Reading, Reading, UK
| | - Axel Hutt
- Department of Mathematics and Statistics, University of Reading, Reading, UK
- Division for Data Assimilation (FE12), Deutscher Wetterdienst, Offenbach, Germany
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10
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Visser S, Nicks R, Faugeras O, Coombes S. Standing and travelling waves in a spherical brain model: The Nunez model revisited. PHYSICA D. NONLINEAR PHENOMENA 2017; 349:27-45. [PMID: 28626276 PMCID: PMC5421190 DOI: 10.1016/j.physd.2017.02.017] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Revised: 02/27/2017] [Accepted: 02/28/2017] [Indexed: 06/07/2023]
Abstract
The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or an integro-differential equation, have typically been studied in idealised one dimensional or planar settings. Here we revisit the original Nunez model to specifically address the role of spherical topology on spatio-temporal pattern generation. We do this using a mixture of Turing instability analysis, symmetric bifurcation theory, centre manifold reduction and direct simulations with a bespoke numerical scheme. In particular we examine standing and travelling wave solutions using normal form computation of primary and secondary bifurcations from a steady state. Interestingly, we observe spatio-temporal patterns which have counterparts seen in the EEG patterns of both epileptic and schizophrenic brain conditions.
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Affiliation(s)
- S. Visser
- School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK
- Wellcome Trust Centre for Biomedical Modelling and Analysis, RILD Building, University of Exeter, EX2 5DW, UK
| | - R. Nicks
- School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK
| | - O. Faugeras
- INRIA Sophia Antipolis Mediterannee, 2004 Route Des Lucioles, Sophia Antipolis, 06410, France
| | - S. Coombes
- School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK
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11
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Laing CR. Travelling waves in arrays of delay-coupled phase oscillators. CHAOS (WOODBURY, N.Y.) 2016; 26:094802. [PMID: 27781474 DOI: 10.1063/1.4953663] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
We consider the effects of several forms of delays on the existence and stability of travelling waves in non-locally coupled networks of Kuramoto-type phase oscillators and theta neurons. By passing to the continuum limit and using the Ott/Antonsen ansatz, we derive evolution equations for a spatially dependent order parameter. For phase oscillator networks, the travelling waves take the form of uniformly twisted waves, and these can often be characterised analytically. For networks of theta neurons, the waves are studied numerically.
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Affiliation(s)
- Carlo R Laing
- Institute of Natural and Mathematical Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand
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12
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Robinson PA, Zhao X, Aquino KM, Griffiths JD, Sarkar S, Mehta-Pandejee G. Eigenmodes of brain activity: Neural field theory predictions and comparison with experiment. Neuroimage 2016; 142:79-98. [PMID: 27157788 DOI: 10.1016/j.neuroimage.2016.04.050] [Citation(s) in RCA: 70] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2015] [Revised: 03/13/2016] [Accepted: 04/21/2016] [Indexed: 12/20/2022] Open
Abstract
Neural field theory of the corticothalamic system is applied to predict and analyze the activity eigenmodes of the bihemispheric brain, focusing particularly on their spatial structure. The eigenmodes of a single brain hemisphere are found to be close analogs of spherical harmonics, which are the natural modes of the sphere. Instead of multiple eigenvalues being equal, as in the spherical case, cortical folding splits them to have distinct values. Inclusion of interhemispheric connections between homologous regions via the corpus callosum leads to further splitting that depends on symmetry or antisymmetry of activity between brain hemispheres, and the strength and sign of the interhemispheric connections. Symmetry properties of the lowest observed eigenmodes strongly constrain the interhemispheric connectivity strengths and unihemispheric mode spectra, and it is predicted that most spontaneous brain activity will be symmetric between hemispheres, consistent with observations. Comparison with the eigenmodes of an experimental anatomical connectivity matrix confirms these results, permits the relative strengths of intrahemispheric and interhemispheric connectivities to be approximately inferred from their eigenvalues, and lays the foundation for further experimental tests. The results are consistent with brain activity being in corticothalamic eigenmodes, rather than discrete "networks" and open the way to new approaches to brain analysis.
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Affiliation(s)
- P A Robinson
- School of Physics, University of Sydney, New South Wales 2006, Australia; Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia.
| | - X Zhao
- School of Physics, University of Sydney, New South Wales 2006, Australia; Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia
| | - K M Aquino
- School of Physics, University of Sydney, New South Wales 2006, Australia; Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia; Sir Peter Mansfield Imaging Center, University of Nottingham, Nottingham NG7 2RD, UK, EU
| | - J D Griffiths
- School of Physics, University of Sydney, New South Wales 2006, Australia; Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia; Rotman Research Institute at Baycrest, 3560 Bathurst St, Toronto, Ontario, M6A 2E1, Canada
| | - S Sarkar
- Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia; Design Lab, School of Architecture, Design, and Planning, University of Sydney, New South Wales 2006, Australia
| | - Grishma Mehta-Pandejee
- School of Physics, University of Sydney, New South Wales 2006, Australia; Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia
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Freund P, Friston K, Thompson AJ, Stephan KE, Ashburner J, Bach DR, Nagy Z, Helms G, Draganski B, Mohammadi S, Schwab ME, Curt A, Weiskopf N. Embodied neurology: an integrative framework for neurological disorders. Brain 2016; 139:1855-61. [PMID: 27105896 PMCID: PMC4892755 DOI: 10.1093/brain/aww076] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2015] [Accepted: 02/26/2016] [Indexed: 12/23/2022] Open
Affiliation(s)
- Patrick Freund
- Spinal Cord Injury Centre Balgrist, University Hospital Zurich, University of Zurich, Zurich, Switzerland Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, University College London, London, UK Department of Brain Repair and Rehabilitation, UCL Institute of Neurology, University College London, London, UK Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
| | - Karl Friston
- Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, University College London, London, UK
| | - Alan J Thompson
- Department of Brain Repair and Rehabilitation, UCL Institute of Neurology, University College London, London, UK
| | - Klaas E Stephan
- Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, University College London, London, UK Translational Neuromodeling Unit (TNU), Institute of Biomedical Engineering, University of Zurich and Swiss Federal Institute of Technology (ETH Zurich), Switzerland Max Planck Institute for Metabolism Research, Cologne, Germany
| | - John Ashburner
- Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, University College London, London, UK
| | - Dominik R Bach
- Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, University College London, London, UK Department of Psychiatry, Psychotherapy, and Psychosomatics, University of Zurich, Zürich, Switzerland
| | - Zoltan Nagy
- Laboratory for Social and Neural Systems Research (SNS Lab), University of Zurich, Switzerland
| | - Gunther Helms
- Department of Clinical Sciences, Lund University, Lund, Sweden
| | - Bogdan Draganski
- Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany Laboratoire de Recherche en Neuroimagerie (LREN), University of Lausanne, Department of Clinical Neurosciences, CHUV, Lausanne, Switzerland
| | - Siawoosh Mohammadi
- Department of Systems Neuroscience, University Medical Centre Hamburg-Eppendorf Hamburg, Germany
| | - Martin E Schwab
- Brain Research Institute, University of Zurich and Dept. of Health Sciences and Technology, ETH Zurich, 8057 Zurich, Switzerland
| | - Armin Curt
- Spinal Cord Injury Centre Balgrist, University Hospital Zurich, University of Zurich, Zurich, Switzerland
| | - Nikolaus Weiskopf
- Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, University College London, London, UK Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
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14
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Sanz-Leon P, Knock SA, Spiegler A, Jirsa VK. Mathematical framework for large-scale brain network modeling in The Virtual Brain. Neuroimage 2015; 111:385-430. [PMID: 25592995 DOI: 10.1016/j.neuroimage.2015.01.002] [Citation(s) in RCA: 157] [Impact Index Per Article: 17.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2014] [Revised: 12/29/2014] [Accepted: 01/01/2015] [Indexed: 12/19/2022] Open
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15
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Bojak I, Stoyanov ZV, Liley DTJ. Emergence of spatially heterogeneous burst suppression in a neural field model of electrocortical activity. Front Syst Neurosci 2015; 9:18. [PMID: 25767438 PMCID: PMC4341547 DOI: 10.3389/fnsys.2015.00018] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2014] [Accepted: 02/02/2015] [Indexed: 11/17/2022] Open
Abstract
Burst suppression in the electroencephalogram (EEG) is a well-described phenomenon that occurs during deep anesthesia, as well as in a variety of congenital and acquired brain insults. Classically it is thought of as spatially synchronous, quasi-periodic bursts of high amplitude EEG separated by low amplitude activity. However, its characterization as a “global brain state” has been challenged by recent results obtained with intracranial electrocortigraphy. Not only does it appear that burst suppression activity is highly asynchronous across cortex, but also that it may occur in isolated regions of circumscribed spatial extent. Here we outline a realistic neural field model for burst suppression by adding a slow process of synaptic resource depletion and recovery, which is able to reproduce qualitatively the empirically observed features during general anesthesia at the whole cortex level. Simulations reveal heterogeneous bursting over the model cortex and complex spatiotemporal dynamics during simulated anesthetic action, and provide forward predictions of neuroimaging signals for subsequent empirical comparisons and more detailed characterization. Because burst suppression corresponds to a dynamical end-point of brain activity, theoretically accounting for its spatiotemporal emergence will vitally contribute to efforts aimed at clarifying whether a common physiological trajectory is induced by the actions of general anesthetic agents. We have taken a first step in this direction by showing that a neural field model can qualitatively match recent experimental data that indicate spatial differentiation of burst suppression activity across cortex.
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Affiliation(s)
- Ingo Bojak
- Systems Neuroscience Research Group, School of Systems Engineering, University of Reading Reading, UK
| | - Zhivko V Stoyanov
- Systems Neuroscience Research Group, School of Systems Engineering, University of Reading Reading, UK
| | - David T J Liley
- Brain and Psychological Sciences Research Centre, School of Health Sciences, Swinburne University of Technology Hawthorn, VIC, Australia
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16
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Jedynak M, Pons AJ, Garcia-Ojalvo J. Cross-frequency transfer in a stochastically driven mesoscopic neuronal model. Front Comput Neurosci 2015; 9:14. [PMID: 25762921 PMCID: PMC4329722 DOI: 10.3389/fncom.2015.00014] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2014] [Accepted: 01/27/2014] [Indexed: 02/05/2023] Open
Abstract
The brain is known to operate in multiple coexisting frequency bands. Increasing experimental evidence suggests that interactions between those distinct bands play a crucial role in brain processes, but the dynamical mechanisms underlying this cross-frequency coupling are still under investigation. Two approaches have been proposed to address this issue. In the first one distinct nonlinear oscillators representing the brain rhythms involved are coupled actively (bidirectionally), whereas in the second one the oscillators are coupled unidirectionally and thus the driving between them is passive. Here we elaborate the latter approach by implementing a stochastically driven network of coupled neural mass models that operate in the alpha range. This model exhibits a broadband power spectrum with 1/fb form, similar to those observed experimentally. Our results show that such a model is able to reproduce recent experimental observations on the effect of slow rocking on the alpha activity associated with sleep. This suggests that passive driving can account for cross-frequency transfer in the brain, as a result of the complex nonlinear dynamics of its underlying oscillators.
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Affiliation(s)
- Maciej Jedynak
- Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya Barcelona, Spain ; Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Parc de Recerca Biomèdica de Barcelona Barcelona, Spain
| | - Antonio J Pons
- Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya Barcelona, Spain
| | - Jordi Garcia-Ojalvo
- Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Parc de Recerca Biomèdica de Barcelona Barcelona, Spain
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17
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A Multiscale “Working Brain” Model. VALIDATING NEURO-COMPUTATIONAL MODELS OF NEUROLOGICAL AND PSYCHIATRIC DISORDERS 2015. [DOI: 10.1007/978-3-319-20037-8_5] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
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18
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Robinson PA. Determination of effective brain connectivity from functional connectivity using propagator-based interferometry and neural field theory with application to the corticothalamic system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042712. [PMID: 25375528 DOI: 10.1103/physreve.90.042712] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2014] [Indexed: 06/04/2023]
Abstract
It is shown how to compute both direct and total effective connection matrices (deCMs and teCMs), which embody the strengths of neural connections between regions, from correlation-based functional CMs using propagator-based interferometry, a method that stems from geophysics and acoustics, coupled with the recent identification of deCMs and teCMs with bare and dressed propagators, respectively. The approach incorporates excitatory and inhibitory connections, multiple structures and populations, and measurement effects. The propagator is found for a generalized scalar wave equation derived from neural field theory, and expressed in terms of neural activity correlations and covariances, and wave damping rates. It is then related to correlation matrices that are commonly used to express functional and effective connectivities in the brain. The results are illustrated in analytically tractable test cases.
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Affiliation(s)
- P A Robinson
- School of Physics, University of Sydney, New South Wales 2006, Australia; Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia; Brain Dynamics Center, Westmead Millennium Institute, Darcy Rd, Westmead, New South Wales 2145, Australia; Cooperative Research Center for Alertness, Safety, and Productivity, University of Sydney, New South Wales 2006, Australia; and Neurosleep, 431 Glebe Point Rd., Glebe, New South Wales 2037, Australia
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19
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Liewald D, Miller R, Logothetis N, Wagner HJ, Schüz A. Distribution of axon diameters in cortical white matter: an electron-microscopic study on three human brains and a macaque. BIOLOGICAL CYBERNETICS 2014; 108:541-57. [PMID: 25142940 PMCID: PMC4228120 DOI: 10.1007/s00422-014-0626-2] [Citation(s) in RCA: 188] [Impact Index Per Article: 18.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2014] [Accepted: 08/05/2014] [Indexed: 05/18/2023]
Abstract
The aim of this study was to obtain information on the axonal diameters of cortico-cortical fibres in the human brain, connecting distant regions of the same hemisphere via the white matter. Samples for electron microscopy were taken from the region of the superior longitudinal fascicle and from the transitional white matter between temporal and frontal lobe where the uncinate and inferior occipitofrontal fascicle merge. We measured the inner diameter of cross sections of myelinated axons. For comparison with data from the literature on the human corpus callosum, we also took samples from that region. For comparison with well-fixed material, we also included samples from corresponding regions of a monkey brain (Macaca mulatta). Fibre diameters in human brains ranged from 0.16 to 9 μm. Distributions of diameters were similar in the three systems of cortico-cortical fibres investigated, both in humans and the monkey, with most of the average values below 1 μm diameter and a small population of much thicker fibres. Within individual human brains, the averages were larger in the superior longitudinal fascicle than in the transitional zone between temporal and frontal lobe. An asymmetry between left and right could be found in one of the human brains, as well as in the monkey brain. A correlation was also found between the thickness of the myelin sheath and the inner axon diameter for axons whose calibre was greater than about 0.6 μm. The results are compared to white matter data in other mammals and are discussed with respect to conduction velocity, brain size, cognition, as well as diffusion weighted imaging studies.
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Affiliation(s)
- Daniel Liewald
- Max Planck Institute for Biological Cybernetics, Spemannstr. 38/41, 72076 Tübingen, Germany
| | - Robert Miller
- Department of Psychological Medicine, University of Otago, Wellington, New Zealand
| | - Nikos Logothetis
- Max Planck Institute for Biological Cybernetics, Spemannstr. 38/41, 72076 Tübingen, Germany
| | | | - Almut Schüz
- Max Planck Institute for Biological Cybernetics, Spemannstr. 38/41, 72076 Tübingen, Germany
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20
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Ross SN, Ware K. Hypothesizing the body's genius to trigger and self-organize its healing: 25 years using a standardized neurophysics therapy. Front Physiol 2013; 4:334. [PMID: 24312056 PMCID: PMC3832888 DOI: 10.3389/fphys.2013.00334] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2013] [Accepted: 10/31/2013] [Indexed: 11/13/2022] Open
Abstract
We aim for this contribution to operate bi-directionally, both as a "bedside to bench" reverse-translational fractal physiological hypothesis and as a methodological innovation to inform clinical practice. In 25 years using gym equipment therapeutically in non-research settings, the standardized therapy is consistently observed to trigger universal responses of micro to macro waves of system transition dynamics in the human nervous system. These are associated with observably desirable impacts on disorders, injuries, diseases, and athletic performance. Requisite conditions are therapeutic coaching, erect posture, extremely slow movements in mild resistance exercises, and executive control over arousal and attention. To motivate research into the physiological improvements and in validation studies, we integrate from across disciplines to hypothesize explanations for the relationships among the methods, the system dynamics, and evident results. Key hypotheses include: (1) Correctly-directed system efforts may reverse a system's heretofore misdirected efforts, restoring healthier neurophysiology. (2) The enhanced information processing accompanying good posture is an essential initial condition. (3) Behaviors accompanying exercises performed with few degrees of freedom amplify information processing, triggering destabilization and transition dynamics. (4) Executive control over arousal and attention is essential to release system constraints, amplifying and complexifying information. (5) The dynamics create necessary and in many cases evidently sufficient conditions for the body to resolve or improve its own conditions within often short time periods. Literature indicates how the human system possesses material self-awareness. A broad explanation for the nature and effects of the therapy appears rooted in the cascading recursions of the systems' dynamics, which appear to trigger health-fostering self-reorganizing processes when this therapy provides catalytic initial conditions.
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Affiliation(s)
- Sara N Ross
- Chair of Interdisciplinary Graduate Studies, Antioch University Midwest Yellow Springs, OH, USA
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21
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Wilson MT, Goodwin DP, Brownjohn PW, Shemmell J, Reynolds JNJ. Numerical modelling of plasticity induced by transcranial magnetic stimulation. J Comput Neurosci 2013; 36:499-514. [PMID: 24150916 DOI: 10.1007/s10827-013-0485-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2013] [Revised: 09/09/2013] [Accepted: 10/02/2013] [Indexed: 10/26/2022]
Abstract
We use neural field theory and spike-timing dependent plasticity to make a simple but biophysically reasonable model of long-term plasticity changes in the cortex due to transcranial magnetic stimulation (TMS). We show how common TMS protocols can be captured and studied within existing neural field theory. Specifically, we look at repetitive TMS protocols such as theta burst stimulation and paired-pulse protocols. Continuous repetitive protocols result mostly in depression, but intermittent repetitive protocols in potentiation. A paired pulse protocol results in depression at short ( < ∼ 10 ms) and long ( > ∼ 100 ms) interstimulus intervals, but potentiation for mid-range intervals. The model is sensitive to the choice of neural populations that are driven by the TMS pulses, and to the parameters that describe plasticity, which may aid interpretation of the high variability in existing experimental results. Driving excitatory populations results in greater plasticity changes than driving inhibitory populations. Modelling also shows the merit in optimizing a TMS protocol based on an individual's electroencephalogram. Moreover, the model can be used to make predictions about protocols that may lead to improvements in repetitive TMS outcomes.
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Affiliation(s)
- M T Wilson
- School of Engineering, Faculty of Science and Engineering, University of Waikato, Private Bag 3105, Hamilton, 3240, New Zealand,
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22
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Hutt A, Zhang L. Distributed nonlocal feedback delays may destabilize fronts in neural fields, distributed transmission delays do not. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2013; 3:9. [PMID: 23899051 PMCID: PMC3844455 DOI: 10.1186/2190-8567-3-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/14/2012] [Accepted: 07/10/2013] [Indexed: 06/02/2023]
Abstract
The spread of activity in neural populations is a well-known phenomenon. To understand the propagation speed and the stability of stationary fronts in neural populations, the present work considers a neural field model that involves intracortical and cortico-cortical synaptic interactions. This includes distributions of axonal transmission speeds and nonlocal feedback delays as well as general classes of synaptic interactions. The work proves the spectral stability of standing and traveling fronts subject to general transmission speeds for large classes of spatial interactions and derives conditions for the front instabilities subjected to nonlocal feedback delays. Moreover, it turns out that the uniqueness of the stationary traveling fronts guarantees its exponential stability for vanishing feedback delay. Numerical simulations complement the analytical findings.
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Affiliation(s)
- Axel Hutt
- INRIA Nancy, 615 rue du Jardin Botanique, 54600, Villers-lès-Nancy, France
| | - Linghai Zhang
- Department of Mathematics, Lehigh University, 14 East Packer Avenue, Bethlehem, PA, 18015, USA
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23
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Sanz Leon P, Knock SA, Woodman MM, Domide L, Mersmann J, McIntosh AR, Jirsa V. The Virtual Brain: a simulator of primate brain network dynamics. Front Neuroinform 2013; 7:10. [PMID: 23781198 PMCID: PMC3678125 DOI: 10.3389/fninf.2013.00010] [Citation(s) in RCA: 205] [Impact Index Per Article: 18.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2013] [Accepted: 05/22/2013] [Indexed: 01/21/2023] Open
Abstract
We present The Virtual Brain (TVB), a neuroinformatics platform for full brain network simulations using biologically realistic connectivity. This simulation environment enables the model-based inference of neurophysiological mechanisms across different brain scales that underlie the generation of macroscopic neuroimaging signals including functional MRI (fMRI), EEG and MEG. Researchers from different backgrounds can benefit from an integrative software platform including a supporting framework for data management (generation, organization, storage, integration and sharing) and a simulation core written in Python. TVB allows the reproduction and evaluation of personalized configurations of the brain by using individual subject data. This personalization facilitates an exploration of the consequences of pathological changes in the system, permitting to investigate potential ways to counteract such unfavorable processes. The architecture of TVB supports interaction with MATLAB packages, for example, the well known Brain Connectivity Toolbox. TVB can be used in a client-server configuration, such that it can be remotely accessed through the Internet thanks to its web-based HTML5, JS, and WebGL graphical user interface. TVB is also accessible as a standalone cross-platform Python library and application, and users can interact with the scientific core through the scripting interface IDLE, enabling easy modeling, development and debugging of the scientific kernel. This second interface makes TVB extensible by combining it with other libraries and modules developed by the Python scientific community. In this article, we describe the theoretical background and foundations that led to the development of TVB, the architecture and features of its major software components as well as potential neuroscience applications.
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Affiliation(s)
- Paula Sanz Leon
- Institut de Neurosciences des Systèmes, Aix Marseille Université Marseille, France
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24
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Fung P, Robinson P. Neural field theory of calcium dependent plasticity with applications to transcranial magnetic stimulation. J Theor Biol 2013; 324:72-83. [DOI: 10.1016/j.jtbi.2013.01.013] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2012] [Revised: 01/17/2013] [Accepted: 01/20/2013] [Indexed: 10/27/2022]
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25
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Bojak I, Day HC, Liley DTJ. Ketamine, Propofol, and the EEG: A Neural Field Analysis of HCN1-Mediated Interactions. Front Comput Neurosci 2013; 7:22. [PMID: 23576979 PMCID: PMC3617565 DOI: 10.3389/fncom.2013.00022] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2012] [Accepted: 03/10/2013] [Indexed: 11/18/2022] Open
Abstract
Ketamine and propofol are two well-known, powerful anesthetic agents, yet at first sight this appears to be their only commonality. Ketamine is a dissociative anesthetic agent, whose main mechanism of action is considered to be N-methyl-d-aspartate (NMDA) antagonism; whereas propofol is a general anesthetic agent, which is assumed to primarily potentiate currents gated by γ-aminobutyric acid type A (GABAA) receptors. However, several experimental observations suggest a closer relationship. First, the effect of ketamine on the electroencephalogram (EEG) is markedly changed in the presence of propofol: on its own ketamine increases θ (4–8 Hz) and decreases α (8–13 Hz) oscillations, whereas ketamine induces a significant shift to beta band frequencies (13–30 Hz) in the presence of propofol. Second, both ketamine and propofol cause inhibition of the inward pacemaker current Ih, by binding to the corresponding hyperpolarization-activated cyclic nucleotide-gated potassium channel 1 (HCN1) subunit. The resulting effect is a hyperpolarization of the neuron’s resting membrane potential. Third, the ability of both ketamine and propofol to induce hypnosis is reduced in HCN1-knockout mice. Here we show that one can theoretically understand the observed spectral changes of the EEG based on HCN1-mediated hyperpolarizations alone, without involving the supposed main mechanisms of action of these drugs through NMDA and GABAA, respectively. On the basis of our successful EEG model we conclude that ketamine and propofol should be antagonistic to each other in their interaction at HCN1 subunits. Such a prediction is in accord with the results of clinical experiment in which it is found that ketamine and propofol interact in an infra-additive manner with respect to the endpoints of hypnosis and immobility.
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Affiliation(s)
- Ingo Bojak
- Centre for Computational Neuroscience and Cognitive Robotics, School of Psychology, University of Birmingham Birmingham, UK ; Donders Centre for Neuroscience, Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen Medical Centre Nijmegen, Netherlands
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26
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Retraction - October 2011. Cereb Cortex 2013; 23:1002. [DOI: 10.1093/cercor/bhr183] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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27
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Pinotsis DA, Hansen E, Friston KJ, Jirsa VK. Anatomical connectivity and the resting state activity of large cortical networks. Neuroimage 2012; 65:127-38. [PMID: 23085498 PMCID: PMC3520011 DOI: 10.1016/j.neuroimage.2012.10.016] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2012] [Revised: 10/03/2012] [Accepted: 10/09/2012] [Indexed: 11/30/2022] Open
Abstract
This paper uses mathematical modelling and simulations to explore the dynamics that emerge in large scale cortical networks, with a particular focus on the topological properties of the structural connectivity and its relationship to functional connectivity. We exploit realistic anatomical connectivity matrices (from diffusion spectrum imaging) and investigate their capacity to generate various types of resting state activity. In particular, we study emergent patterns of activity for realistic connectivity configurations together with approximations formulated in terms of neural mass or field models. We find that homogenous connectivity matrices, of the sort of assumed in certain neural field models give rise to damped spatially periodic modes, while more localised modes reflect heterogeneous coupling topologies. When simulating resting state fluctuations under realistic connectivity, we find no evidence for a spectrum of spatially periodic patterns, even when grouping together cortical nodes into communities, using graph theory. We conclude that neural field models with translationally invariant connectivity may be best applied at the mesoscopic scale and that more general models of cortical networks that embed local neural fields, may provide appropriate models of macroscopic cortical dynamics over the whole brain.
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Affiliation(s)
- D A Pinotsis
- The Wellcome Trust Centre for Neuroimaging, University College London WC1N 3BG, UK.
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28
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Fung PK, Haber AL, Robinson PA. Neural field theory of plasticity in the cerebral cortex. J Theor Biol 2012; 318:44-57. [PMID: 23036915 DOI: 10.1016/j.jtbi.2012.09.030] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2012] [Revised: 08/20/2012] [Accepted: 09/21/2012] [Indexed: 11/25/2022]
Abstract
A generalized timing-dependent plasticity rule is incorporated into a recent neural field theory to explore synaptic plasticity in the cerebral cortex, with both excitatory and inhibitory populations included. Analysis in the time and frequency domains reveals that cortical network behavior gives rise to a saddle-node bifurcation and resonant frequencies, including a gamma-band resonance. These system resonances constrain cortical synaptic dynamics and divide it into four classes, which depend on the type of synaptic plasticity window. Depending on the dynamical class, synaptic strengths can either have a stable fixed point, or can diverge in the absence of a separate saturation mechanism. Parameter exploration shows that time-asymmetric plasticity windows, which are signatures of spike-timing dependent plasticity, enable the richest variety of synaptic dynamics to occur. In particular, we predict a zone in parameter space which may allow brains to attain the marginal stability phenomena observed experimentally, although additional regulatory mechanisms may be required to maintain these parameters.
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Affiliation(s)
- P K Fung
- School of Physics, The University of Sydney, NSW 2006, Australia.
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29
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Wilson MT, Robinson PA, O'Neill B, Steyn-Ross DA. Complementarity of spike- and rate-based dynamics of neural systems. PLoS Comput Biol 2012; 8:e1002560. [PMID: 22737064 PMCID: PMC3380910 DOI: 10.1371/journal.pcbi.1002560] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2012] [Accepted: 05/02/2012] [Indexed: 11/18/2022] Open
Abstract
Relationships between spiking-neuron and rate-based approaches to the dynamics of neural assemblies are explored by analyzing a model system that can be treated by both methods, with the rate-based method further averaged over multiple neurons to give a neural-field approach. The system consists of a chain of neurons, each with simple spiking dynamics that has a known rate-based equivalent. The neurons are linked by propagating activity that is described in terms of a spatial interaction strength with temporal delays that reflect distances between neurons; feedback via a separate delay loop is also included because such loops also exist in real brains. These interactions are described using a spatiotemporal coupling function that can carry either spikes or rates to provide coupling between neurons. Numerical simulation of corresponding spike- and rate-based methods with these compatible couplings then allows direct comparison between the dynamics arising from these approaches. The rate-based dynamics can reproduce two different forms of oscillation that are present in the spike-based model: spiking rates of individual neurons and network-induced modulations of spiking rate that occur if network interactions are sufficiently strong. Depending on conditions either mode of oscillation can dominate the spike-based dynamics and in some situations, particularly when the ratio of the frequencies of these two modes is integer or half-integer, the two can both be present and interact with each other.
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Affiliation(s)
- M T Wilson
- School of Engineering, University of Waikato, Hamilton, New Zealand.
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30
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Coombes S, Schmidt H, Bojak I. Interface dynamics in planar neural field models. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2012; 2:9. [PMID: 22655970 PMCID: PMC3478198 DOI: 10.1186/2190-8567-2-9] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/21/2011] [Accepted: 02/13/2012] [Indexed: 06/01/2023]
Abstract
Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.
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Affiliation(s)
- Stephen Coombes
- School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
| | - Helmut Schmidt
- School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
| | - Ingo Bojak
- School of Psychology (CN-CR), University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
- Centre for Neuroscience, Donders Institute for Brain, Cognition and Behaviour, Nijmegen, 6500 HB, The Netherlands
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31
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Tomasi S, Caminiti R, Innocenti GM. Areal differences in diameter and length of corticofugal projections. ACTA ACUST UNITED AC 2012; 22:1463-72. [PMID: 22302056 DOI: 10.1093/cercor/bhs011] [Citation(s) in RCA: 78] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Cortical areas differ in the size and distribution of neuronal cell bodies, density, and distribution of myelinated axons, connections, and functional properties. We find that they also differ in the diameter of long corticofugal axons, with the thickest axons originating from primary motor, somatosensory, and visual areas and the thinnest ones from prefrontal and temporal areas. Since diameter is proportional to axonal conduction velocity, it can be inferred that action potentials issued from the different areas will be relayed to their targets at different speed. Conduction delays also depend on conduction distance. By computing conduction velocity and conduction distances, we found the longest conduction delays for the primary visual and temporal areas and the shortest for the premotor, primary motor, and somatosensory areas, compatible with the available electrophysiological data. These findings seem to establish a new principle in cortical organization relevant to the pathophysiology of neurological or psychiatric illnesses as well as to the speed of information processing in cortical circuits.
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Affiliation(s)
- Simone Tomasi
- Department of Anatomy, Pharmacology and Forensic Medicine, University of Turin, Orbassano, 10126 Turin, Italy
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Robinson PA. Interrelating anatomical, effective, and functional brain connectivity using propagators and neural field theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011912. [PMID: 22400596 DOI: 10.1103/physreve.85.011912] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2011] [Revised: 12/09/2011] [Indexed: 05/31/2023]
Abstract
It is shown how to compute effective and functional connection matrices (eCMs and fCMs) from anatomical CMs (aCMs) and corresponding strength-of-connection matrices (sCMs) using propagator methods in which neural interactions play the role of scatterings. This analysis demonstrates how network effects dress the bare propagators (the sCMs) to yield effective propagators (the eCMs) that can be used to compute the covariances customarily used to define fCMs. The results incorporate excitatory and inhibitory connections, multiple structures and populations, asymmetries, time delays, and measurement effects. They can also be postprocessed in the same manner as experimental measurements for direct comparison with data and thereby give insights into the role of coarse-graining, thresholding, and other effects in determining the structure of CMs. The spatiotemporal results show how to generalize CMs to include time delays and how natural network modes give rise to long-range coherence at resonant frequencies. The results are demonstrated using tractable analytic cases via neural field theory of cortical and corticothalamic systems. These also demonstrate close connections between the structure of CMs and proximity to critical points of the system, highlight the importance of indirect links between brain regions and raise the possibility of imaging specific levels of indirect connectivity. Aside from the results presented explicitly here, the expression of the connections among aCMs, sCMs, eCMs, and fCMs in terms of propagators opens the way for propagator theory to be further applied to analysis of connectivity.
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Affiliation(s)
- P A Robinson
- School of Physics, University of Sydney, New South Wales 2006, Australia
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Spiegler A, Knösche TR, Schwab K, Haueisen J, Atay FM. Modeling brain resonance phenomena using a neural mass model. PLoS Comput Biol 2011; 7:e1002298. [PMID: 22215992 PMCID: PMC3245303 DOI: 10.1371/journal.pcbi.1002298] [Citation(s) in RCA: 92] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2011] [Accepted: 10/25/2011] [Indexed: 11/22/2022] Open
Abstract
Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect. Neuroscience aims to understand the enormously complex function of the normal and diseased brain. This, in turn, is the key to explaining human behavior and to developing novel diagnostic and therapeutic procedures. We develop and use models of mean activity in a single brain area, which provide a balance between tractability and plausibility. We use such a model to explain the resonance phenomenon in a photic driving experiment, which is routinely applied in the diagnosis of various diseases including epilepsy, migraine, schizophrenia and depression. Based on the model, we make predictions on the outcome of similar resonance experiments with periodic stimulation of the patients or participants. Our results are important for researchers and clinicians analyzing brain or behavioral data following periodic input.
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Affiliation(s)
- Andreas Spiegler
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany.
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Bojak I, Oostendorp TF, Reid AT, Kötter R. Towards a model-based integration of co-registered electroencephalography/functional magnetic resonance imaging data with realistic neural population meshes. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2011; 369:3785-3801. [PMID: 21893528 PMCID: PMC3263777 DOI: 10.1098/rsta.2011.0080] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Brain activity can be measured with several non-invasive neuroimaging modalities, but each modality has inherent limitations with respect to resolution, contrast and interpretability. It is hoped that multimodal integration will address these limitations by using the complementary features of already available data. However, purely statistical integration can prove problematic owing to the disparate signal sources. As an alternative, we propose here an advanced neural population model implemented on an anatomically sound cortical mesh with freely adjustable connectivity, which features proper signal expression through a realistic head model for the electroencephalogram (EEG), as well as a haemodynamic model for functional magnetic resonance imaging based on blood oxygen level dependent contrast (fMRI BOLD). It hence allows simultaneous and realistic predictions of EEG and fMRI BOLD from the same underlying model of neural activity. As proof of principle, we investigate here the influence on simulated brain activity of strengthening visual connectivity. In the future we plan to fit multimodal data with this neural population model. This promises novel, model-based insights into the brain's activity in sleep, rest and task conditions.
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Affiliation(s)
- I Bojak
- Centre for Computational Neuroscience and Cognitive Robotics, School of Psychology, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK.
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Valdes-Sosa PA, Roebroeck A, Daunizeau J, Friston K. Effective connectivity: influence, causality and biophysical modeling. Neuroimage 2011; 58:339-61. [PMID: 21477655 PMCID: PMC3167373 DOI: 10.1016/j.neuroimage.2011.03.058] [Citation(s) in RCA: 252] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2010] [Revised: 03/15/2011] [Accepted: 03/23/2011] [Indexed: 11/30/2022] Open
Abstract
This is the final paper in a Comments and Controversies series dedicated to "The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution". We argue that discovering effective connectivity depends critically on state-space models with biophysically informed observation and state equations. These models have to be endowed with priors on unknown parameters and afford checks for model Identifiability. We consider the similarities and differences among Dynamic Causal Modeling, Granger Causal Modeling and other approaches. We establish links between past and current statistical causal modeling, in terms of Bayesian dependency graphs and Wiener-Akaike-Granger-Schweder influence measures. We show that some of the challenges faced in this field have promising solutions and speculate on future developments.
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Affiliation(s)
- Pedro A Valdes-Sosa
- Cuban Neuroscience Center, Ave 25 #15202 esquina 158, Cubanacan, Playa, Cuba.
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Abstract
The production of genotypic and phenotypic diversity (differentiation) is the final outcome of both development and evolution, of nervous systems and of their components. Cortical axons, in particular, differentiate into a variety of phenotypes which are responsible for computational transformations of messages exchanged among neurons. One aspect of this differentiation concerns axon diameters whose diversity in development, but also within and across species, is enhanced by the addition of a relatively small proportion of thicker axons to some axonal pathways. This, combined with differences in the length of pathways and in brain volumes, has rescaled and expanded the temporal range of interneuronal communication. In both development and evolution, this and other aspects of axonal phenotypes, namely the structure and distribution of axonal arbors, differentiate by the combined action of cell intrinsic (genetic) variation, overproduction, and selection by the environment.
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Abstract
Continuing to discover how the brain works is one of the great challenges ahead of us. Although understanding the brain anatomy and its functional organization provided a first and indispensable foundation, it became clear that a static view was insufficient. To understand the complexity of neuronal communication, it is necessary to examine the chemical nature of the neurotransmission and, using the example of the acetylcholine receptors, follow the different layers of networks that can be distinguished. The natural alkaloid nicotine contained in tobacco leaves acts as an agonist with a subclass of acetylcholine receptors, and provides an interesting tool to approach brain functions. Analysis of the nicotinic acetylcholine receptors, which are ligand gated channels, revealed that these receptors are expressed at different critical locations on the neurons including the synaptic boutons, neurites, cell bodies, and even on the axons. These receptors can modulate the activity at the microcircuit synaptic level, in the cell processing of information, and, by acting on the velocity of action potential, the synchrony of communication between brain areas. These actions at multiple levels of brain organization provide an example of the complexity of brain neurocircuitry and an illustration of the relevance of this knowledge for psychiatry.
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Affiliation(s)
- Daniel Bertrand
- Dept of Neurosciences, Medical Faculty, Geneva, Switzerland; HiQScreen SARL, Geneva, Switzerland.
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Dynamics of activity fronts in a continuum mean field model of cortex. BMC Neurosci 2010. [PMCID: PMC3090913 DOI: 10.1186/1471-2202-11-s1-p28] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/04/2022] Open
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Connecting mean field models of neural activity to EEG and fMRI data. Brain Topogr 2010; 23:139-49. [PMID: 20364434 DOI: 10.1007/s10548-010-0140-3] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2009] [Accepted: 03/11/2010] [Indexed: 10/19/2022]
Abstract
Progress in functional neuroimaging of the brain increasingly relies on the integration of data from complementary imaging modalities in order to improve spatiotemporal resolution and interpretability. However, the usefulness of merely statistical combinations is limited, since neural signal sources differ between modalities and are related non-trivially. We demonstrate here that a mean field model of brain activity can simultaneously predict EEG and fMRI BOLD with proper signal generation and expression. Simulations are shown using a realistic head model based on structural MRI, which includes both dense short-range background connectivity and long-range specific connectivity between brain regions. The distribution of modeled neural masses is comparable to the spatial resolution of fMRI BOLD, and the temporal resolution of the modeled dynamics, importantly including activity conduction, matches the fastest known EEG phenomena. The creation of a cortical mean field model with anatomically sound geometry, extensive connectivity, and proper signal expression is an important first step towards the model-based integration of multimodal neuroimages.
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