{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T10:42:21Z","timestamp":1778668941803,"version":"3.51.4"},"reference-count":46,"publisher":"Public Library of Science (PLoS)","issue":"2","license":[{"start":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T00:00:00Z","timestamp":1675728000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000065","name":"National Institute of Neurological Disorders and Stroke","doi-asserted-by":"publisher","award":["R01NS079533"],"award-info":[{"award-number":["R01NS079533"]}],"id":[{"id":"10.13039\/100000065","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Pablo J. Salame Goldman Sachs endowed Associate Professorship of Computational Neuroscience at Brown University;"},{"DOI":"10.13039\/100000065","name":"National Institute of Neurological Disorders and Stroke","doi-asserted-by":"publisher","award":["S10 OD025181"],"award-info":[{"award-number":["S10 OD025181"]}],"id":[{"id":"10.13039\/100000065","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 spread of seizures across brain networks is the main impairing factor, often leading to loss-of-consciousness, in people with epilepsy. Despite advances in recording and modeling brain activity, uncovering the nature of seizure spreading dynamics remains an important challenge to understanding and treating pharmacologically resistant epilepsy. To address this challenge, we introduce a new probabilistic model that captures the spreading dynamics in patient-specific complex networks. Network connectivity and interaction time delays between brain areas were estimated from white-matter tractography. The model\u2019s computational tractability allows it to play an important complementary role to more detailed models of seizure dynamics. We illustrate model fitting and predictive performance in the context of patient-specific Epileptor networks. We derive the phase diagram of spread size (order parameter) as a function of brain excitability and global connectivity strength, for different patient-specific networks. Phase diagrams allow the prediction of whether a seizure will spread depending on excitability and connectivity strength. In addition, model simulations predict the temporal order of seizure spread across network nodes. Furthermore, we show that the order parameter can exhibit both discontinuous and continuous (critical) phase transitions as neural excitability and connectivity strength are varied. Existence of a critical point, where response functions and fluctuations in spread size show power-law divergence with respect to control parameters, is supported by mean-field approximations and finite-size scaling analyses. Notably, the critical point separates two distinct regimes of spreading dynamics characterized by unimodal and bimodal spread-size distributions. Our study sheds new light on the nature of phase transitions and fluctuations in seizure spreading dynamics. We expect it to play an important role in the development of closed-loop stimulation approaches for preventing seizure spread in pharmacologically resistant epilepsy. Our findings may also be of interest to related models of spreading dynamics in epidemiology, biology, finance, and statistical physics.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010852","type":"journal-article","created":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T18:34:33Z","timestamp":1675794873000},"page":"e1010852","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["Criticality in probabilistic models of spreading dynamics in brain networks: Epileptic seizures"],"prefix":"10.1371","volume":"19","author":[{"given":"S Amin","family":"Moosavi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4444-3917","authenticated-orcid":true,"given":"Wilson","family":"Truccolo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2023,2,7]]},"reference":[{"issue":"s7","key":"pcbi.1010852.ref001","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1111\/j.1528-1167.2011.03121.x","article-title":"Standards for epidemiologic studies and surveillance of epilepsy","volume":"52","author":"DJ Thurman","year":"2011","journal-title":"Epilepsia"},{"issue":"2","key":"pcbi.1010852.ref002","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.yebeh.2012.06.016","article-title":"Epilepsy across the spectrum: Promoting health and understanding.: A summary of the Institute of Medicine report","volume":"25","author":"MJ England","year":"2012","journal-title":"Epilepsy & Behavior"},{"issue":"2","key":"pcbi.1010852.ref003","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1097\/WCO.0000000000000528","article-title":"The current place of epilepsy surgery","volume":"31","author":"J Engel Jr","year":"2018","journal-title":"Current opinion in neurology"},{"issue":"2","key":"pcbi.1010852.ref004","first-page":"536","article-title":"Surgical Treatments for epilepsy","volume":"28","author":"GW Culler IV","year":"2022","journal-title":"CONTINUUM: Lifelong Learning in Neurology"},{"key":"pcbi.1010852.ref005","doi-asserted-by":"crossref","unstructured":"Touma L, Dansereau B, Chan AY, Jett\u00e9 N, Kwon CS, Braun KP, et al. 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