{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T11:56:25Z","timestamp":1790510185797,"version":"4.1.0"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1008310","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T00:00:00Z","timestamp":1612828800000}}],"reference-count":68,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:00:00Z","timestamp":1611792000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed \u201cconnectome harmonics\u201d, have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed\n                    <jats:italic>graph neural fields<\/jats:italic>\n                    , in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for\n                    <jats:italic>Connectome-Harmonic Analysis Of Spatiotemporal Spectra<\/jats:italic>\n                    ). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1008310","type":"journal-article","created":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T14:48:19Z","timestamp":1611845299000},"page":"e1008310","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":24,"title":["Graph neural fields: A framework for spatiotemporal dynamical models on the human 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Deco","year":"2011","journal-title":"Nature Reviews Neuroscience"},{"key":"pcbi.1008310.ref003","first-page":"273136","article-title":"Discordant attributes of structural and functional connectivity in a two-layer multiplex network","author":"S Lim","year":"2018","journal-title":"bioRxiv"},{"issue":"1","key":"pcbi.1008310.ref004","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-019-12765-7","article-title":"Decoupling of brain function from structure reveals regional behavioral specialization in humans","volume":"10","author":"MG Preti","year":"2019","journal-title":"Nature communications"},{"issue":"871-898","key":"pcbi.1008310.ref005","first-page":"12","article-title":"The Laplacian spectrum of graphs","volume":"2","author":"B Mohar","year":"1991","journal-title":"Graph theory, combinatorics, and applications"},{"issue":"7","key":"pcbi.1008310.ref006","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1109\/TSP.2013.2238935","article-title":"Discrete 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A Graph Signal Processing Perspective on Functional Brain Imaging. Proceedings of the IEEE. 2018;.","DOI":"10.1109\/JPROC.2018.2798928"},{"issue":"8","key":"pcbi.1008310.ref014","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/j.cagd.2004.07.007","article-title":"Discrete Laplace\u2013Beltrami operators and their convergence","volume":"21","author":"G Xu","year":"2004","journal-title":"Computer aided geometric design"},{"key":"pcbi.1008310.ref015","doi-asserted-by":"crossref","unstructured":"Belkin M, Sun J, Wang Y. Discrete laplace operator on meshed surfaces. In: Proceedings of the twenty-fourth annual symposium on Computational geometry; 2008. p. 278\u2013287.","DOI":"10.1145\/1377676.1377725"},{"key":"pcbi.1008310.ref016","doi-asserted-by":"crossref","first-page":"116805","DOI":"10.1016\/j.neuroimage.2020.116805","article-title":"Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches","author":"P Tewarie","year":"2020","journal-title":"NeuroImage"},{"issue":"6","key":"pcbi.1008310.ref017","doi-asserted-by":"crossref","first-page":"e1005550","DOI":"10.1371\/journal.pcbi.1005550","article-title":"Brain network eigenmodes provide a robust and compact representation of the structural connectome in health and disease","volume":"13","author":"MB Wang","year":"2017","journal-title":"PLoS computational biology"},{"key":"pcbi.1008310.ref018","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.neuroimage.2018.10.079","article-title":"How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes","volume":"186","author":"P Tewarie","year":"2019","journal-title":"NeuroImage"},{"key":"pcbi.1008310.ref019","article-title":"Spectral graph theory of brain oscillations","author":"A Raj","year":"2020","journal-title":"Human Brain Mapping"},{"key":"pcbi.1008310.ref020","doi-asserted-by":"crossref","first-page":"117137","DOI":"10.1016\/j.neuroimage.2020.117137","article-title":"Connectome spectral analysis to track EEG task dynamics on a subsecond scale","volume":"221","author":"K Glomb","year":"2020","journal-title":"NeuroImage"},{"issue":"3","key":"pcbi.1008310.ref021","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1038\/nn.4497","article-title":"Dynamic models of large-scale brain activity","volume":"20","author":"M Breakspear","year":"2017","journal-title":"Nature neuroscience"},{"issue":"3","key":"pcbi.1008310.ref022","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1162\/netn_a_00084","article-title":"Guided graph spectral embedding: Application to the C. elegans connectome","volume":"3","author":"M Petrovic","year":"2019","journal-title":"Network Neuroscience"},{"issue":"1","key":"pcbi.1008310.ref023","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13408-015-0034-5","article-title":"Wilson\u2013Cowan equations for neocortical dynamics","volume":"6","author":"JD Cowan","year":"2016","journal-title":"The Journal of Mathematical Neuroscience"},{"issue":"3","key":"pcbi.1008310.ref024","doi-asserted-by":"crossref","first-page":"3557","DOI":"10.1103\/PhysRevE.58.3557","article-title":"Steady states and global dynamics of electrical activity in the cerebral cortex","volume":"58","author":"P Robinson","year":"1998","journal-title":"Physical Review E"},{"key":"pcbi.1008310.ref025","article-title":"Increased conduction velocity as a result of myelination","author":"D Purves","year":"2001","journal-title":"Neuroscience"},{"issue":"1","key":"pcbi.1008310.ref026","doi-asserted-by":"crossref","first-page":"17661","DOI":"10.1038\/s41598-017-17546-0","article-title":"Connectome-harmonic decomposition of human brain activity reveals dynamical repertoire re-organization under LSD","volume":"7","author":"S Atasoy","year":"2017","journal-title":"Scientific reports"},{"issue":"28","key":"pcbi.1008310.ref027","doi-asserted-by":"crossref","first-page":"5111","DOI":"10.1021\/jp970984n","article-title":"Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms","volume":"101","author":"DJ Wales","year":"1997","journal-title":"The Journal of Physical Chemistry A"},{"issue":"11","key":"pcbi.1008310.ref028","doi-asserted-by":"crossref","first-page":"2114","DOI":"10.1038\/npp.2017.86","article-title":"Modern clinical research on LSD","volume":"42","author":"ME Liechti","year":"2017","journal-title":"Neuropsychopharmacology"},{"issue":"11","key":"pcbi.1008310.ref029","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1038\/s41583-020-0367-2","article-title":"Psychedelic drugs: neurobiology and potential for treatment of psychiatric disorders","volume":"21","author":"FX Vollenweider","year":"2020","journal-title":"Nature Reviews Neuroscience"},{"issue":"10","key":"pcbi.1008310.ref030","doi-asserted-by":"crossref","first-page":"2331","DOI":"10.1021\/acschemneuro.8b00043","article-title":"Dark classics in chemical neuroscience: lysergic acid diethylamide (LSD)","volume":"9","author":"DE Nichols","year":"2018","journal-title":"ACS chemical neuroscience"},{"key":"pcbi.1008310.ref031","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.neuroimage.2016.06.016","article-title":"How do parcellation size and short-range connectivity affect dynamics in large-scale brain network models?","volume":"142","author":"T Proix","year":"2016","journal-title":"NeuroImage"},{"issue":"3","key":"pcbi.1008310.ref032","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/j.neuroimage.2010.01.045","article-title":"Large-scale neural dynamics: simple and complex","volume":"52","author":"S Coombes","year":"2010","journal-title":"NeuroImage"},{"key":"pcbi.1008310.ref033","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.neuroimage.2015.01.002","article-title":"Mathematical framework for large-scale brain network modeling in The Virtual Brain","volume":"111","author":"P Sanz-Leon","year":"2015","journal-title":"Neuroimage"},{"issue":"2","key":"pcbi.1008310.ref034","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1152\/jn.00406.2019","article-title":"Next-generation neural mass and field modeling","volume":"123","author":"\u00c1 Byrne","year":"2020","journal-title":"Journal of 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Kuehn","year":"2018","journal-title":"Trends in cognitive sciences"},{"issue":"1","key":"pcbi.1008310.ref048","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1186\/s13408-018-0058-8","article-title":"Kernel reconstruction for delayed neural field equations","volume":"8","author":"J Alswaihli","year":"2018","journal-title":"The Journal of Mathematical Neuroscience"},{"issue":"25","key":"pcbi.1008310.ref049","doi-asserted-by":"crossref","first-page":"10302","DOI":"10.1073\/pnas.0901831106","article-title":"Key role of coupling, delay, and noise in resting brain fluctuations","volume":"106","author":"G Deco","year":"2009","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"2","key":"pcbi.1008310.ref050","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1137\/S0036139903430884","article-title":"Stability and bifurcations in neural fields with finite propagation speed and general connectivity","volume":"65","author":"FM Atay","year":"2004","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"1-2","key":"pcbi.1008310.ref051","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.physd.2005.03.002","article-title":"Analysis of nonlocal neural fields for both general and gamma-distributed connectivities","volume":"203","author":"A Hutt","year":"2005","journal-title":"Physica D: Nonlinear Phenomena"},{"key":"pcbi.1008310.ref052","unstructured":"Shamsara E, Yamakou ME, Atay FM, Jost J. Dynamics of neural fields with exponential temporal kernel. arXiv preprint arXiv:190806324. 2019;."},{"issue":"2","key":"pcbi.1008310.ref053","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s00422-005-0574-y","article-title":"Waves, bumps, and patterns in neural field theories","volume":"93","author":"S Coombes","year":"2005","journal-title":"Biological cybernetics"},{"issue":"19","key":"pcbi.1008310.ref054","doi-asserted-by":"crossref","first-page":"3065","DOI":"10.1016\/j.cub.2018.07.083","article-title":"Whole-brain multimodal neuroimaging model using serotonin receptor maps explains non-linear functional effects of LSD","volume":"28","author":"G Deco","year":"2018","journal-title":"Current Biology"},{"issue":"17","key":"pcbi.1008310.ref055","doi-asserted-by":"crossref","first-page":"9566","DOI":"10.1073\/pnas.1921475117","article-title":"Dynamic coupling of whole-brain neuronal and neurotransmitter systems","volume":"117","author":"ML Kringelbach","year":"2020","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"pcbi.1008310.ref056","article-title":"A mechanistic model of the neural entropy increase elicited by psychedelic drugs","author":"R Herzog","year":"2020","journal-title":"bioRxiv"},{"issue":"2","key":"pcbi.1008310.ref057","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1016\/j.neuroimage.2007.09.034","article-title":"Population receptive field estimates in human visual cortex","volume":"39","author":"SO Dumoulin","year":"2008","journal-title":"Neuroimage"},{"issue":"10","key":"pcbi.1008310.ref058","doi-asserted-by":"crossref","first-page":"1952","DOI":"10.1109\/TMI.2013.2271486","article-title":"Cortical graph smoothing: a novel method for exploiting DWI-derived anatomical brain connectivity to improve EEG source estimation","volume":"32","author":"DK Hammond","year":"2013","journal-title":"IEEE transactions on medical 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Sciences"},{"issue":"4","key":"pcbi.1008310.ref065","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1137\/S0036144596301390","article-title":"On the Gibbs phenomenon and its resolution","volume":"39","author":"D Gottlieb","year":"1997","journal-title":"SIAM review"},{"issue":"6","key":"pcbi.1008310.ref066","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/MSP.2020.3015024","article-title":"Localized spectral graph filter frames: A unifying framework, survey of design considerations, and numerical comparison","volume":"37","author":"DI Shuman","year":"2020","journal-title":"IEEE Signal Processing Magazine"},{"issue":"37","key":"pcbi.1008310.ref067","doi-asserted-by":"crossref","first-page":"375101","DOI":"10.1088\/1751-8121\/aa7fd8","article-title":"Periodic orbits in nonlinear wave equations on networks","volume":"50","author":"JG Caputo","year":"2017","journal-title":"Journal of Physics A: Mathematical and 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