{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:29:38Z","timestamp":1760239778681,"version":"build-2065373602"},"reference-count":60,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T00:00:00Z","timestamp":1608508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61971374","61603327"],"award-info":[{"award-number":["61971374","61603327"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Neural oscillations reflect rhythmic fluctuations in the synchronization of neuronal populations and play a significant role in neural processing. To further understand the dynamic interactions between different regions in the brain, it is necessary to estimate the coupling direction between neural oscillations. Here, we developed a novel method, termed weighted symbolic transfer entropy (WSTE), that combines symbolic transfer entropy (STE) and weighted probability distribution to measure the directionality between two neuronal populations. The traditional STE ignores the degree of difference between the amplitude values of a time series. In our proposed WSTE method, this information is picked up by utilizing a weighted probability distribution. The simulation analysis shows that the WSTE method can effectively estimate the coupling direction between two neural oscillations. In comparison with STE, the new method is more sensitive to the coupling strength and is more robust against noise. When applied to epileptic electrocorticography data, a significant coupling direction from the anterior nucleus of thalamus (ANT) to the seizure onset zone (SOZ) was detected during seizures. Considering the superiorities of the WSTE method, it is greatly advantageous to measure the coupling direction between neural oscillations and consequently characterize the information flow between different brain regions.<\/jats:p>","DOI":"10.3390\/e22121442","type":"journal-article","created":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T09:41:41Z","timestamp":1608543701000},"page":"1442","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Measuring the Coupling Direction between Neural Oscillations with Weighted Symbolic Transfer Entropy"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4009-4374","authenticated-orcid":false,"given":"Zhaohui","family":"Li","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering (School of Software), Yanshan University, Qinhuangdao 066004, China"},{"name":"Hebei Key Laboratory of Information Transmission and Signal Processing, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuaifei","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering (School of Software), Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Yu","sequence":"additional","affiliation":[{"name":"Beijing Institute of Functional Neurosurgery, Capital Medical University, Beijing 100053, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoli","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1126\/science.1099745","article-title":"Neuronal oscillations in cortical networks","volume":"304","author":"Buzsaki","year":"2004","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"013138","DOI":"10.1063\/1.4794793","article-title":"Short desynchronization episodes prevail in synchronous dynamics of human brain rhythms","volume":"23","author":"Ahn","year":"2013","journal-title":"Chaos"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1146\/annurev.neuro.051508.135603","article-title":"Neuronal gamma-band synchronization as a fundamental process in cortical computation","volume":"32","author":"Fries","year":"2009","journal-title":"Annu. 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