{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T18:53:03Z","timestamp":1790189583641,"version":"4.1.0"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1012926","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T00:00:00Z","timestamp":1746748800000}}],"reference-count":135,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T00:00:00Z","timestamp":1744243200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004089","name":"Krembil Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004089","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Labatt Family Network"},{"name":"CAMH Discovery Fund"},{"DOI":"10.13039\/501100000024","name":"Canadian Institutes of Health Research","doi-asserted-by":"publisher","award":["FRN 183646_1"],"award-info":[{"award-number":["FRN 183646_1"]}],"id":[{"id":"10.13039\/501100000024","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>The electroencephalographic alpha rhythm is one of the most robustly observed and widely studied empirical phenomena in all of neuroscience. However, despite its extensive implication in a wide range of cognitive processes and clinical pathologies, the mechanisms underlying alpha generation in neural circuits remain poorly understood. In this paper we offer a renewed foundation for research on this question, by undertaking a systematic comparison and synthesis of the most prominent theoretical models of alpha rhythmogenesis in the published literature. We focus on four models, each studied intensively by multiple authors over the past three decades: (i) Jansen-Rit, (ii) Moran-David-Friston, (iii) Robinson-Rennie-Wright, and (iv) Liley-Wright. Several common elements are identified, such as the use of second-order differential equations and sigmoidal potential-to-rate operators to represent population-level neural activity. Major differences are seen in other features such as wiring topologies and conduction delays. Through a series of mathematical analyses and numerical simulations, we nevertheless demonstrate that the selected models can be meaningfully compared, by associating parameters and circuit motifs of analogous biological significance. With this established, we conduct explorations of rate constant and synaptic connectivity parameter spaces, with the aim of identifying common patterns in key behaviours, such as the role of excitatory-inhibitory interactions in the generation of oscillations. Finally, using linear stability analysis we identify two qualitatively different alpha-generating dynamical regimes across the models: (i) noise-driven fluctuations and (ii) self-sustained limit-cycle oscillations, emerging due to an Andronov-Hopf bifurcation. The comprehensive survey and synthesis developed here can, we suggest, be used to help guide future theoretical and experimental work aimed at disambiguating these and other candidate theories of alpha rhythmogenesis.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012926","type":"journal-article","created":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T16:06:35Z","timestamp":1744301195000},"page":"e1012926","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":16,"title":["A comprehensive investigation of intracortical and corticothalamic models of the alpha rhythm"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-6665-1419","authenticated-orcid":true,"given":"Sorenza P.","family":"Bastiaens","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6048-8296","authenticated-orcid":true,"given":"Davide","family":"Momi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1764-2179","authenticated-orcid":true,"given":"John D.","family":"Griffiths","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2025,4,10]]},"reference":[{"issue":"1","key":"pcbi.1012926.ref001","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/BF01797193","article-title":"\u00dcber das elektroenkephalogramm des menschen","volume":"87","author":"H Berger","year":"1929","journal-title":"Archiv f. Psychiatrie"},{"issue":"13","key":"pcbi.1012926.ref002","doi-asserted-by":"crossref","first-page":"4935","DOI":"10.1523\/JNEUROSCI.5580-10.2011","article-title":"Neuronal mechanisms and attentional modulation of corticothalamic alpha oscillations","volume":"31","author":"A Bollimunta","year":"2011","journal-title":"J Neurosci"},{"issue":"6","key":"pcbi.1012926.ref003","doi-asserted-by":"crossref","first-page":"1340","DOI":"10.1016\/j.clinph.2003.12.031","article-title":"Executive hypercontrol in obsessive\u2014compulsive disorder: electrophysiological and neuropsychological indices","volume":"115","author":"P Bucci","year":"2004","journal-title":"Clin Neurophysiol"},{"issue":"7","key":"pcbi.1012926.ref004","doi-asserted-by":"crossref","first-page":"2041","DOI":"10.1093\/brain\/awx116","article-title":"Restless \u2018rest\u2019: intrinsic sensory hyperactivity and disinhibition in post-traumatic stress disorder","volume":"140","author":"K Clancy","year":"2017","journal-title":"Brain"},{"key":"pcbi.1012926.ref005","doi-asserted-by":"crossref","first-page":"102145","DOI":"10.1016\/j.nicl.2019.102145","article-title":"Linking alpha oscillations, attention and inhibitory control in adult ADHD with EEG neurofeedback","volume":"25","author":"MP Deiber","year":"2020","journal-title":"NeuroImage Clin"},{"key":"pcbi.1012926.ref006","doi-asserted-by":"crossref","first-page":"186","DOI":"10.3389\/fnhum.2010.00186","article-title":"Shaping functional architecture by oscillatory alpha activity: gating by inhibition","volume":"4","author":"O Jensen","year":"2010","journal-title":"Front Hum Neurosci"},{"key":"pcbi.1012926.ref007","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0304-3940(77)90024-6","article-title":"The cortical source of the alpha rhythm","volume":"6","author":"F Lopes da Silva","year":"1977","journal-title":"Neurosci Lett"},{"issue":"12","key":"pcbi.1012926.ref008","doi-asserted-by":"crossref","first-page":"3052","DOI":"10.1162\/neco.2006.18.12.3052","article-title":"Bifurcation analysis of Jansen\u2019s neural mass model","volume":"18","author":"F Grimbert","year":"2006","journal-title":"Neural Comput"},{"issue":"4","key":"pcbi.1012926.ref009","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/BF00199471","article-title":"Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns","volume":"73","author":"BH Jansen","year":"1995","journal-title":"Biol Cybern"},{"issue":"1","key":"pcbi.1012926.ref010","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1080\/net.13.1.67.113","article-title":"A spatially continuous mean field theory of electrocortical activity","volume":"13","author":"DT Liley","year":"2001","journal-title":"Network"},{"issue":"6","key":"pcbi.1012926.ref011","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.neunet.2011.02.009","article-title":"A thalamo\u2013cortico\u2013thalamic neural mass model to study alpha rhythms in Alzheimer\u2019s disease","volume":"24","author":"BS Bhattacharya","year":"2011","journal-title":"Neural Netw"},{"issue":"3","key":"pcbi.1012926.ref012","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1016\/j.neuroimage.2003.07.015","article-title":"A neural mass model for MEG\/EEG:: coupling and neuronal dynamics","volume":"20","author":"O David","year":"2003","journal-title":"NeuroImage"},{"issue":"5","key":"pcbi.1012926.ref013","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1006694","article-title":"Parameter estimation and identifiability in a neural population model for electro-cortical activity","volume":"15","author":"A Hartoyo","year":"2019","journal-title":"PLoS Comput Biol"},{"issue":"1","key":"pcbi.1012926.ref014","article-title":"Neurophysical modeling of brain dynamics","volume":"28","author":"PA Robinson","year":"2003","journal-title":"Neuropsychopharmacology"},{"issue":"3","key":"pcbi.1012926.ref015","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1016\/j.neuroimage.2007.05.032","article-title":"A neural mass model of spectral responses in electrophysiology","volume":"37","author":"RJ Moran","year":"2007","journal-title":"NeuroImage"},{"key":"pcbi.1012926.ref016","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/S0925-2312(98)00149-0","article-title":"A continuum theory of electro-cortical activity","volume":"26","author":"DT Liley","year":"1999","journal-title":"Neurocomputing"},{"issue":"4","key":"pcbi.1012926.ref017","doi-asserted-by":"crossref","first-page":"041924","DOI":"10.1103\/PhysRevE.65.041924","article-title":"Dynamics of large-scale brain activity in normal arousal states and epileptic seizures","volume":"65","author":"P Robinson","year":"2002","journal-title":"Phys Rev E"},{"issue":"2","key":"pcbi.1012926.ref018","doi-asserted-by":"crossref","DOI":"10.1523\/ENEURO.0293-19.2020","article-title":"Biophysical basis of alpha rhythm disruption in Alzheimer\u2019s disease","volume":"7","author":"R Sharma","year":"2020","journal-title":"eNeuro"},{"issue":"11","key":"pcbi.1012926.ref019","doi-asserted-by":"crossref","first-page":"2980","DOI":"10.1002\/hbm.24991","article-title":"Spectral graph theory of brain oscillations","volume":"41","author":"A Raj","year":"2020","journal-title":"Hum Brain Mapp"},{"issue":"4","key":"pcbi.1012926.ref020","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1010986","article-title":"In-silico EEG biomarkers of reduced inhibition in human cortical microcircuits in depression","volume":"19","author":"F Mazza","year":"2023","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"pcbi.1012926.ref021","doi-asserted-by":"crossref","first-page":"291","DOI":"10.31887\/DCNS.2013.15.3\/ebasar","article-title":"Brain oscillations in neuropsychiatric disease","volume":"15","author":"E Ba\u015far","year":"2013","journal-title":"Dialogues Clin Neurosci"},{"key":"pcbi.1012926.ref022","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/B978-0-12-817424-1.00006-9","volume-title":"Functional and clinical neuroanatomy","author":"J Moini","year":"2020"},{"issue":"47","key":"pcbi.1012926.ref023","doi-asserted-by":"crossref","first-page":"23772","DOI":"10.1073\/pnas.1913092116","article-title":"The generation and propagation of the human alpha rhythm","volume":"116","author":"M Halgren","year":"2019","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1012926.ref024","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0165-0173(98)00056-3","article-title":"EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis","volume":"29","author":"W Klimesch","year":"1999","journal-title":"Brain Res Rev"},{"issue":"22","key":"pcbi.1012926.ref025","doi-asserted-by":"crossref","first-page":"2985","DOI":"10.1016\/j.cub.2015.10.007","article-title":"The speed of alpha-band oscillations predicts the temporal resolution of visual perception","volume":"25","author":"J Samaha","year":"2015","journal-title":"Curr Biol"},{"key":"pcbi.1012926.ref026","first-page":"154","article-title":"The role of alpha-band brain oscillations as a sensory suppression mechanism during selective attention","volume":"2","author":"JJ Foxe","year":"2011","journal-title":"Front Psychol"},{"issue":"4","key":"pcbi.1012926.ref027","doi-asserted-by":"crossref","DOI":"10.1002\/brb3.1263","article-title":"The roles of alpha oscillation in working memory retention","volume":"9","author":"E Wianda","year":"2019","journal-title":"Brain Behav"},{"issue":"12","key":"pcbi.1012926.ref028","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1016\/j.tics.2012.10.007","article-title":"\u03b1-Band oscillations, attention, and controlled access to stored information","volume":"16","author":"W Klimesch","year":"2012","journal-title":"Trends Cogn Sci"},{"key":"pcbi.1012926.ref029","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.neurobiolaging.2018.07.004","article-title":"Resting-state EEG power and connectivity are associated with alpha peak frequency slowing in healthy aging","volume":"71","author":"B Scally","year":"2018","journal-title":"Neurobiol Aging"},{"issue":"5","key":"pcbi.1012926.ref030","doi-asserted-by":"crossref","first-page":"537","DOI":"10.3390\/brainsci11050537","article-title":"Elevated and slowed EEG oscillations in patients with post-concussive syndrome and chronic pain following a motor vehicle collision","volume":"11","author":"DM Buchanan","year":"2021","journal-title":"Brain Sci"},{"issue":"2","key":"pcbi.1012926.ref031","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1002\/acn3.710","article-title":"Slower alpha rhythm associates with poorer seizure control in epilepsy","volume":"6","author":"E Abela","year":"2019","journal-title":"Ann Clin Transl Neurol"},{"issue":"2","key":"pcbi.1012926.ref032","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.neures.2006.06.006","article-title":"Composition of brain oscillations in ongoing EEG during major depression disorder","volume":"56","author":"AA Fingelkurts","year":"2006","journal-title":"Neurosci Res"},{"key":"pcbi.1012926.ref033","doi-asserted-by":"crossref","first-page":"53","DOI":"10.14196\/mjiri.31.53","article-title":"Changes of the brain\u2019s bioelectrical activity in cognition, consciousness, and some mental disorders","volume":"31","author":"M Roohi-Azizi","year":"2017","journal-title":"Med J Islam Repub Iran"},{"issue":"2","key":"pcbi.1012926.ref034","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1037\/0021-843X.113.2.324","article-title":"PTSD arousal and depression symptoms associated with increased right-sided parietal EEG asymmetry","volume":"113","author":"LJ Metzger","year":"2004","journal-title":"J Abnorm Psychol"},{"issue":"12","key":"pcbi.1012926.ref035","doi-asserted-by":"crossref","first-page":"3189","DOI":"10.3390\/biomedicines10123189","article-title":"The role of alpha oscillations among the main neuropsychiatric disorders in the adult and developing human brain: Evidence from the last 10 years of research","volume":"10","author":"G Ippolito","year":"2022","journal-title":"Biomedicines"},{"issue":"1","key":"pcbi.1012926.ref036","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.ijpsycho.2012.07.001","article-title":"A short review of alpha activity in cognitive processes and in cognitive impairment","volume":"86","author":"E Ba\u015far","year":"2012","journal-title":"Int J Psychophysiol"},{"issue":"4","key":"pcbi.1012926.ref037","first-page":"307","article-title":"Hans Berger (1873-1941)\u2014the history of electroencephalography","volume":"59","author":"M Tudor","year":"2005","journal-title":"Acta Med Croatica"},{"key":"pcbi.1012926.ref038","doi-asserted-by":"crossref","first-page":"23","DOI":"10.3389\/fncom.2018.00023","article-title":"On the physiological modulation and potential mechanisms underlying parieto-occipital alpha oscillations","volume":"12","author":"D Lozano-Soldevilla","year":"2018","journal-title":"Front Comput Neurosci"},{"issue":"2","key":"pcbi.1012926.ref039","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0013-4694(91)90044-5","article-title":"Neural mechanisms underlying brain waves: from neural membranes to networks","volume":"79","author":"F Lopes da Silva","year":"1991","journal-title":"Electroencephalogr Clin Neurophysiol"},{"key":"pcbi.1012926.ref040","article-title":"Electric fields of the brain: the neurophysics of EEG. Oxford University Press","author":"PL Nunez","year":"2006"},{"issue":"3","key":"pcbi.1012926.ref041","doi-asserted-by":"crossref","first-page":"2328","DOI":"10.1016\/j.neuroimage.2009.10.030","article-title":"White matter architecture rather than cortical surface area correlates with the EEG alpha rhythm","volume":"49","author":"PA Vald\u00e9s-Hern\u00e1ndez","year":"2010","journal-title":"Neuroimage"},{"issue":"8","key":"pcbi.1012926.ref042","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1000092","article-title":"The dynamic brain: from spiking neurons to neural masses and cortical fields","volume":"4","author":"G Deco","year":"2008","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1012926.ref043","doi-asserted-by":"crossref","first-page":"101","DOI":"10.3389\/fncir.2016.00101","article-title":"Local field potentials: myths and misunderstandings","volume":"10","author":"O Herreras","year":"2016","journal-title":"Front Neural Circuits"},{"key":"pcbi.1012926.ref044","unstructured":"Cook BJ, Peterson AD, Woldman W, Terry JR. Neural field models: historical perspectives and recent advances. arXiv. Preprint arXiv:210310554. 2021."},{"issue":"2","key":"pcbi.1012926.ref045","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1590\/S0001-37652001000200006","article-title":"Response of the brain to enrichment","volume":"73","author":"MC Diamond","year":"2001","journal-title":"An Acad Bras Cienc"},{"issue":"2","key":"pcbi.1012926.ref046","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1010915","article-title":"Global dynamics of neural mass models","volume":"19","author":"GK Cooray","year":"2023","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"pcbi.1012926.ref047","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":"Nat Neurosci"},{"key":"pcbi.1012926.ref048","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-54593-1","article-title":"Neural fields: theory and applications","author":"S Coombes","year":"2014"},{"issue":"4","key":"pcbi.1012926.ref049","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1010012","article-title":"Alpha blocking and 1\/f\u03b2 spectral scaling in resting EEG can be accounted for by a sum of damped alpha band oscillatory processes","volume":"18","author":"R Evertz","year":"2022","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1012926.ref050","volume-title":"Encyclopedia of computational neuroscience","author":"I Bojak"},{"key":"pcbi.1012926.ref051","doi-asserted-by":"crossref","first-page":"57","DOI":"10.3389\/fncom.2013.00057","article-title":"Neural masses and fields in dynamic causal modeling","volume":"7","author":"R Moran","year":"2013","journal-title":"Front Comput Neurosci"},{"key":"pcbi.1012926.ref052","doi-asserted-by":"crossref","first-page":"149","DOI":"10.3389\/fncom.2014.00149","article-title":"Neural masses and fields: modeling the dynamics of brain activity","volume":"8","author":"D Pinotsis","year":"2014","journal-title":"Front Comput Neurosci"},{"key":"pcbi.1012926.ref053","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.28927","article-title":"Inferring multi-scale neural mechanisms with brain network modelling","volume":"7","author":"M Schirner","year":"2018","journal-title":"Elife"},{"issue":"1","key":"pcbi.1012926.ref054","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/s10548-021-00828-2","article-title":"Computational models in electroencephalography","volume":"35","author":"K Glomb","year":"2021","journal-title":"Brain Topogr"},{"key":"pcbi.1012926.ref055","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.neuroimage.2016.04.050","article-title":"Eigenmodes of brain activity: Neural field theory predictions and comparison with experiment","volume":"142","author":"X Zhao","year":"2016","journal-title":"NeuroImage"},{"key":"pcbi.1012926.ref056","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.physd.2017.02.017","article-title":"Standing and travelling waves in a spherical brain model: the Nunez model revisited","volume":"349","author":"S Visser","year":"2017","journal-title":"Physica D"},{"key":"pcbi.1012926.ref057","article-title":"Whole-brain modelling: past, present, and future. In: Computational modelling of the brain. Springer","author":"JD Griffiths","year":"2022"},{"issue":"5","key":"pcbi.1012926.ref058","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1152\/jn.00404.2019","article-title":"Before and beyond the Wilson\u2013Cowan equations","volume":"123","author":"CC Chow","year":"2020","journal-title":"J Neurophysiol"},{"issue":"1","key":"pcbi.1012926.ref059","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0006-3495(72)86068-5","article-title":"Excitatory and inhibitory interactions in localized populations of model neurons","volume":"12","author":"HR Wilson","year":"1972","journal-title":"Biophys J"},{"issue":"1","key":"pcbi.1012926.ref060","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":"J Math Neurosci"},{"issue":"1","key":"pcbi.1012926.ref061","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.neuroimage.2010.01.098","article-title":"A dynamic causal model study of neuronal population dynamics","volume":"51","author":"AC Marreiros","year":"2010","journal-title":"Neuroimage"},{"key":"pcbi.1012926.ref062","doi-asserted-by":"crossref","first-page":"158","DOI":"10.3389\/fncom.2013.00158","article-title":"On conductance-based neural field models","volume":"7","author":"DA Pinotsis","year":"2013","journal-title":"Front Comput Neurosci"},{"issue":"15","key":"pcbi.1012926.ref063","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1016\/j.cub.2011.06.053","article-title":"An in vivo assay of synaptic function mediating human cognition","volume":"21","author":"RJ Moran","year":"2011","journal-title":"Curr Biol"},{"key":"pcbi.1012926.ref064","article-title":"Mass action in the nervous system","author":"WJ Freeman","year":"1975"},{"issue":"03","key":"pcbi.1012926.ref065","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1142\/S0218127492000653","article-title":"Tutorial on neurobiology: from single neurons to brain chaos","volume":"2","author":"WJ Freeman","year":"1992","journal-title":"Int J Bifurcation Chaos."},{"key":"pcbi.1012926.ref066","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"},{"key":"pcbi.1012926.ref067","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/S0006-3495(62)86953-7","article-title":"Electrophysiology of a dendritic neuron model","volume":"2","author":"W Rall","year":"1962","journal-title":"Biophys J"},{"key":"pcbi.1012926.ref068","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/BF00197607","article-title":"Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations","volume":"70","author":"C Bernard","year":"1994","journal-title":"Biol Cybern"},{"key":"pcbi.1012926.ref069","article-title":"Theoretical significance of dendritic trees for neuronal input-output relations","author":"W Rall","year":"1964","journal-title":"Neural Theor Model"},{"key":"pcbi.1012926.ref070","article-title":"Dynamics of biologically informed neural mass models of the brain","author":"A Spiegler","year":"2012"},{"key":"pcbi.1012926.ref071","first-page":"1","volume-title":"Nonlinear dynamics in computational neuroscience","author":"S Coombes","year":"2019"},{"issue":"1","key":"pcbi.1012926.ref072","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF00270757","article-title":"Model of brain rhythmic activity","volume":"15","author":"F Lopes da Silva","year":"1974","journal-title":"Kybernetik"},{"key":"pcbi.1012926.ref073","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/BF00224863","article-title":"A neurophysiologically-based mathematical model of flash visual evoked potentials","volume":"68","author":"BH Jansen","year":"1993","journal-title":"Biol Cybern"},{"issue":"1","key":"pcbi.1012926.ref074","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF00337367","article-title":"Performance of a model for a local neuron population","volume":"31","author":"LH Zetterberg","year":"1978","journal-title":"Biol Cybern"},{"key":"pcbi.1012926.ref075","first-page":"1463","volume-title":"Encyclopedia of computational neuroscience","author":"TR Kn\u00f6sche","year":"2015"},{"key":"pcbi.1012926.ref076","article-title":"Analysis of Jansen\u2019s model of a single cortical column","author":"F Grimbert","year":"2006"},{"issue":"2","key":"pcbi.1012926.ref077","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s10827-019-00727-3","article-title":"A novel neural computational model of generalized periodic discharges in acute hepatic encephalopathy","volume":"47","author":"JL Song","year":"2019","journal-title":"J Comput Neurosci"},{"issue":"1","key":"pcbi.1012926.ref078","doi-asserted-by":"crossref","first-page":"011910","DOI":"10.1103\/PhysRevE.85.011910","article-title":"Corticothalamic dynamics: structure of parameter space, spectra, instabilities, and reduced model","volume":"85","author":"J Roberts","year":"2012","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"issue":"1","key":"pcbi.1012926.ref079","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.clinph.2009.09.021","article-title":"Neurophysiological changes with age probed by inverse modeling of EEG spectra","volume":"121","author":"S Van Albada","year":"2010","journal-title":"Clin Neurophysiol"},{"key":"pcbi.1012926.ref080","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.jtbi.2013.11.013","article-title":"Prediction and verification of nonlinear sleep spindle harmonic oscillations","volume":"344","author":"RG Abeysuriya","year":"2014","journal-title":"J Theor Biol"},{"key":"pcbi.1012926.ref081","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.jneumeth.2015.06.002","article-title":"Physiologically based arousal state estimation and dynamics","volume":"253","author":"R Abeysuriya","year":"2015","journal-title":"J Neurosci Methods"},{"key":"pcbi.1012926.ref082","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.jtbi.2015.01.028","article-title":"Slow-wave oscillations in a corticothalamic model of sleep and wake","volume":"370","author":"X Zhao","year":"2015","journal-title":"J Theor Biol"},{"issue":"2","key":"pcbi.1012926.ref083","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s10827-015-0571-7","article-title":"Generalized seizures in a neural field model with bursting dynamics","volume":"39","author":"X Zhao","year":"2015","journal-title":"J Comput Neurosci"},{"issue":"2","key":"pcbi.1012926.ref084","doi-asserted-by":"crossref","first-page":"021903","DOI":"10.1103\/PhysRevE.63.021903","article-title":"Prediction of electroencephalographic spectra from neurophysiology","volume":"63","author":"PA Robinson","year":"2001","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"key":"pcbi.1012926.ref085","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.jtbi.2017.07.015","article-title":"Multistability in the corticothalamic system","volume":"432","author":"P Sanz-Leon","year":"2017","journal-title":"J Theor Biol"},{"key":"pcbi.1012926.ref086","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python","volume":"17","author":"P Virtanen","year":"2020","journal-title":"Nat Methods"},{"issue":"3","key":"pcbi.1012926.ref087","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.jtbi.2004.07.004","article-title":"Estimation of neurophysiological parameters from the waking EEG using a biophysical model of brain dynamics","volume":"231","author":"DL Rowe","year":"2004","journal-title":"J Theor Biol"},{"key":"pcbi.1012926.ref088","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1016\/j.neuroimage.2018.06.068","article-title":"1\/f electrophysiological spectra in resting and drug-induced states can be explained by the dynamics of multiple oscillatory relaxation processes","volume":"179","author":"SD Muthukumaraswamy","year":"2018","journal-title":"NeuroImage"},{"issue":"12","key":"pcbi.1012926.ref089","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1038\/s41593-020-00744-x","article-title":"Parameterizing neural power spectra into periodic and aperiodic components","volume":"23","author":"T Donoghue","year":"2020","journal-title":"Nat Neurosci"},{"key":"pcbi.1012926.ref090","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.neuroimage.2014.01.049","article-title":"Inter- and intra-individual variability in alpha peak frequency","volume":"92","author":"S Haegens","year":"2014","journal-title":"Neuroimage"},{"key":"pcbi.1012926.ref091","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0167-8760(00)00145-8","article-title":"Gamma, alpha, delta, and theta oscillations govern cognitive processes","volume":"39","author":"E Ba\u015far","year":"2001","journal-title":"Int J Psychophysiol"},{"issue":"38","key":"pcbi.1012926.ref092","doi-asserted-by":"crossref","first-page":"13257","DOI":"10.1523\/JNEUROSCI.2332-14.2015","article-title":"Age-related changes in 1\/f neural electrophysiological noise","volume":"35","author":"B Voytek","year":"2015","journal-title":"J Neurosci"},{"key":"pcbi.1012926.ref093","doi-asserted-by":"crossref","first-page":"103277","DOI":"10.1016\/j.nicl.2022.103277","article-title":"Spectral slowing in chronic stroke reflects abnormalities in both periodic and aperiodic neural dynamics","volume":"37","author":"PR Johnston","year":"2023","journal-title":"Neuroimage Clin"},{"issue":"6","key":"pcbi.1012926.ref094","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1016\/S1388-2457(03)00045-2","article-title":"Spatial spectra of scalp EEG and EMG from awake humans","volume":"114","author":"WJ Freeman","year":"2003","journal-title":"Clin Neurophysiol"},{"key":"pcbi.1012926.ref095","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s10827-010-0263-2","article-title":"Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media","volume":"29","author":"N Dehghani","year":"2010","journal-title":"J Comput Neurosci"},{"key":"pcbi.1012926.ref096","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.biopsycho.2017.09.010","article-title":"EEG differences between eyes-closed and eyes-open resting remain in healthy ageing","volume":"129","author":"RJ Barry","year":"2017","journal-title":"Biol Psychol"},{"issue":"4","key":"pcbi.1012926.ref097","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1093\/brain\/57.4.355","article-title":"The Berger rhythm: potential changes from the occipital lobes in man","volume":"57","author":"ED Adrian","year":"1934","journal-title":"Brain"},{"issue":"6","key":"pcbi.1012926.ref098","doi-asserted-by":"crossref","first-page":"858","DOI":"10.1016\/0013-4694(62)90136-0","article-title":"A quantitative survey of kappa and alpha EEG activity","volume":"14","author":"RM Chapman","year":"1962","journal-title":"Electroencephalogr Clin Neurophysiol"},{"issue":"4","key":"pcbi.1012926.ref099","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1007662","article-title":"Inferring a simple mechanism for alpha-blocking by fitting a neural population model to EEG spectra","volume":"16","author":"A Hartoyo","year":"2020","journal-title":"PLoS Comput Biol"},{"issue":"12","key":"pcbi.1012926.ref100","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0225900","article-title":"PyRates\u2014A Python framework for rate-based neural simulations","volume":"14","author":"R Gast","year":"2019","journal-title":"PLoS ONE"},{"issue":"1","key":"pcbi.1012926.ref101","doi-asserted-by":"crossref","first-page":"11825","DOI":"10.1038\/s41598-017-12140-w","article-title":"Decline of long-range temporal correlations in the human brain during sustained wakefulness","volume":"7","author":"C Meisel","year":"2017","journal-title":"Sci Rep"},{"key":"pcbi.1012926.ref102","doi-asserted-by":"crossref","first-page":"46","DOI":"10.3389\/fnins.2018.00046","article-title":"Synaptic E\u2013I balance underlies efficient neural coding","volume":"12","author":"S Zhou","year":"2018","journal-title":"Front Neurosci"},{"issue":"9","key":"pcbi.1012926.ref103","doi-asserted-by":"crossref","first-page":"1248","DOI":"10.1038\/s41380-019-0426-0","article-title":"Excitation-inhibition balance as a framework for investigating mechanisms in neuropsychiatric disorders","volume":"24","author":"VS Sohal","year":"2019","journal-title":"Mol Psychiatry"},{"issue":"4","key":"pcbi.1012926.ref104","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1093\/cercor\/bhs370","article-title":"Linking microcircuit dysfunction to cognitive impairment: effects of disinhibition associated with schizophrenia in a cortical working memory model","volume":"24","author":"JD Murray","year":"2014","journal-title":"Cereb Cortex"},{"key":"pcbi.1012926.ref105","first-page":"401","article-title":"Normal modes of the brain: neuroanatomical basis and a physiological theoretical model","author":"R Katznelson","year":"1981"},{"key":"pcbi.1012926.ref106","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/BF00317988","article-title":"Simulation of chaotic EEG patterns with a dynamic model of the olfactory system","volume":"56","author":"WJ Freeman","year":"1987","journal-title":"Biol Cybern"},{"issue":"4","key":"pcbi.1012926.ref107","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF00337412","article-title":"Nonlinear gain mediating cortical stimulus-response relations","volume":"33","author":"WJ Freeman","year":"1979","journal-title":"Biol Cybern"},{"issue":"1","key":"pcbi.1012926.ref108","first-page":"826","article-title":"Propagation and stability of waves of electrical activity in the cerebral cortex","volume":"56","author":"PA Robinson","year":"1997","journal-title":"Phys Rev A At Mol Opt Phys"},{"issue":"3","key":"pcbi.1012926.ref109","doi-asserted-by":"crossref","first-page":"3320","DOI":"10.1103\/PhysRevE.59.3320","article-title":"Effects of local feedback on dispersion of electrical waves in the cerebral cortex","volume":"59","author":"CJ Rennie","year":"1999","journal-title":"Phys Rev E."},{"key":"pcbi.1012926.ref110","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S0079-6123(08)60995-4","article-title":"Models of neuronal populations: the basic mechanisms of rhythmicity","volume":"45","author":"F Lopes da Silva","year":"1976","journal-title":"Prog Brain Res"},{"key":"pcbi.1012926.ref111","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/BF00202790","article-title":"Simulation of electrocortical waves","volume":"72","author":"JJ Wright","year":"1995","journal-title":"Biol Cybern"},{"issue":"2","key":"pcbi.1012926.ref112","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/BF02463252","article-title":"A model of the spatial-temporal characteristics of the alpha rhythm","volume":"44","author":"A van Rotterdam","year":"1982","journal-title":"Bull Math Biol"},{"issue":"5","key":"pcbi.1012926.ref113","doi-asserted-by":"crossref","first-page":"1138","DOI":"10.1152\/jn.1967.30.5.1138","article-title":"Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input","volume":"30","author":"W Rall","year":"1967","journal-title":"J Neurophysiol"},{"key":"pcbi.1012926.ref114","volume-title":"Induced rhythms of the brain","author":"WJ Freeman","year":"1991"},{"key":"pcbi.1012926.ref115","article-title":"Principles of neural science","author":"ER Kandel","year":"2000"},{"key":"pcbi.1012926.ref116","article-title":"Cortex: statistics and geometry of neuronal connectivity","author":"V Braitenberg","year":"2013"},{"issue":"2","key":"pcbi.1012926.ref117","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1002\/cne.903060209","article-title":"Dendritic morphology of pyramidal neurones of the visual cortex of the rat: III","volume":"306","author":"AU Larkman","year":"1991","journal-title":"Spine distributions. J Comp Neurol"},{"key":"pcbi.1012926.ref118","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/BF01673266","article-title":"Distribution of synapses on an intracellularly labeled small pyramidal neuron in the cat motor cortex","volume":"184","author":"XB Liu","year":"1991","journal-title":"Anat Embryol (Berl)"},{"issue":"1","key":"pcbi.1012926.ref119","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1002\/cne.902910105","article-title":"Intrinsic circuitry: synapses involving the local axon collaterals of corticocortical projection neurons in the mouse primary somatosensory cortex","volume":"291","author":"E Elhanany","year":"1990","journal-title":"J Comp Neurol"},{"issue":"2","key":"pcbi.1012926.ref120","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1088\/0954-898X_5_2_004","article-title":"Intracortical connectivity of pyramidal and stellate cells: estimates of synaptic densities and coupling symmetry","volume":"5","author":"DT Liley","year":"1994","journal-title":"Netw Comput Neural Syst"},{"key":"pcbi.1012926.ref121","doi-asserted-by":"crossref","first-page":"195","DOI":"10.3389\/neuro.02.002.2008","article-title":"E\u2013I balance and human diseases\u2014from molecules to networking","volume":"1","author":"SA Eichler","year":"2008","journal-title":"Front Mol Neurosci"},{"key":"pcbi.1012926.ref122","doi-asserted-by":"crossref","unstructured":"Li G, Hsu LM, Wu Y, Bozoki AC, Shih YYI, Yap PT. Excitation-inhibition imbalance in Alzheimer\u2019s disease using multiscale neural model inversion of resting-state fMRI. medRxiv. preprint. 2022; pp. 2022\u201310.","DOI":"10.1101\/2022.10.04.22280681"},{"key":"pcbi.1012926.ref123","doi-asserted-by":"crossref","first-page":"75","DOI":"10.3389\/fnsys.2019.00075","article-title":"Bridging single neuron dynamics to global brain states","volume":"13","author":"JS Goldman","year":"2019","journal-title":"Front Syst Neurosci"},{"key":"pcbi.1012926.ref124","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.neunet.2021.06.009","article-title":"A novel density-based neural mass model for simulating neuronal network dynamics with conductance-based synapses and membrane current adaptation","volume":"143","author":"CH Huang","year":"2021","journal-title":"Neural Netw"},{"issue":"2","key":"pcbi.1012926.ref125","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":"J Neurophysiol"},{"issue":"4","key":"pcbi.1012926.ref126","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1016\/j.neuroimage.2006.02.034","article-title":"Mechanisms of evoked and induced responses in MEG\/EEG","volume":"31","author":"O David","year":"2006","journal-title":"Neuroimage"},{"key":"pcbi.1012926.ref127","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.83232","article-title":"TMS-evoked responses are driven by recurrent large-scale network dynamics","volume":"12","author":"D Momi","year":"2023","journal-title":"Elife"},{"key":"pcbi.1012926.ref128","doi-asserted-by":"crossref","unstructured":"Kiani AA, Netoff TI, Ghose GM. Realistic alpha oscillations and transient responses in a cortical microcircuit model. bioRxiv. preprint. 2021; pp. 2021\u201311.","DOI":"10.1101\/2021.11.10.468067"},{"issue":"1","key":"pcbi.1012926.ref129","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.jtbi.2008.03.005","article-title":"Modeling absence seizure dynamics: implications for basic mechanisms and measurement of thalamocortical and corticothalamic latencies","volume":"253","author":"JA Roberts","year":"2008","journal-title":"J Theor Biol"},{"key":"pcbi.1012926.ref130","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.jtbi.2017.06.016","article-title":"Unified neural field theory of brain dynamics underlying oscillations in Parkinson\u2019s disease and generalized epilepsies","volume":"428","author":"EJ M\u00fcller","year":"2017","journal-title":"J Theor Biol"},{"issue":"10","key":"pcbi.1012926.ref131","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1016\/S1388-2457(99)00099-1","article-title":"Dynamics of the human alpha rhythm: evidence for non-linearity?","volume":"110","author":"C Stam","year":"1999","journal-title":"Clin Neurophysiol"},{"key":"pcbi.1012926.ref132","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s10827-017-0642-z","article-title":"Neural field model of seizure-like activity in isolated cortex","volume":"42","author":"X Zhao","year":"2017","journal-title":"J Comput Neurosci"},{"issue":"12","key":"pcbi.1012926.ref133","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1002298","article-title":"Modeling brain resonance phenomena using a neural mass model","volume":"7","author":"A Spiegler","year":"2011","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1012926.ref134","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13408-015-0028-3","article-title":"Extensive four-dimensional chaos in a mesoscopic model of the electroencephalogram","volume":"5","author":"MP Dafilis","year":"2015","journal-title":"J Math Neurosci"},{"issue":"3","key":"pcbi.1012926.ref135","doi-asserted-by":"crossref","first-page":"1947","DOI":"10.1016\/j.neuroimage.2012.05.054","article-title":"Quantitative theory of driven nonlinear brain dynamics","volume":"62","author":"J Roberts","year":"2012","journal-title":"Neuroimage"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1012926","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T00:00:00Z","timestamp":1746748800000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012926","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T14:15:32Z","timestamp":1746800132000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012926"}},"subtitle":[],"editor":[{"given":"Jonathan David","family":"Touboul","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2025,4,10]]},"references-count":135,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4,10]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1012926","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2024.03.01.583035","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,10]]}}}