{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T20:09:07Z","timestamp":1777320547015,"version":"3.51.4"},"reference-count":133,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T00:00:00Z","timestamp":1765756800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["101147319"],"award-info":[{"award-number":["101147319"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["101147319"],"award-info":[{"award-number":["101147319"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Electrical stimulation of nervous tissue is grounded in well-established biophysical principles, yet understanding its precise effect on neural activity remains challenging. This represents a major obstacle to both scientific and clinical applications of electrical brain stimulation.<\/jats:p>\n                  <jats:p>\n                    We here show that the reciprocity theorem of electromagnetism can be applied more broadly than previously acknowledged, providing a framework for elucidating the effects of electrical brain stimulation on neurons. Through this new perspective, we account for the observed weak frequency-dependence of extracellular electrical stimulation\u2013induced membrane potential changes, and demonstrate a 1\/\n                    <jats:italic>r<\/jats:italic>\n                    falloff for nearby and 1\/\n                    <jats:italic>r<\/jats:italic>\n                    <jats:sup>2<\/jats:sup>\n                    falloff for distant neurons.\n                  <\/jats:p>\n                  <jats:p>We also show that for transcranial electrical stimulation, the susceptibility of a neuron to the stimulation is directly proportional to the size of the current dipole moment resulting from somatic current input. The induced somatic membrane potential changes are small and exhibit weak spatial but strong orientation dependency across human neocortex.<\/jats:p>\n                  <jats:p>The reciprocity-based approach to electrical stimulation reproduces a large body of previous experimental data, and provides new insights into how ES affects neurons.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1013782","type":"journal-article","created":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T18:36:20Z","timestamp":1765823780000},"page":"e1013782","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":1,"title":["Predicting neural responses to intra- and extra-cranial electric brain stimulation by means of the reciprocity theorem"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9080-8502","authenticated-orcid":true,"given":"Torbj\u00f8rn V.","family":"Ness","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christof","family":"Koch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gaute T.","family":"Einevoll","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,12,15]]},"reference":[{"issue":"6","key":"pcbi.1013782.ref001","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1002\/andp.18531650603","article-title":"Ueber einige Gesetze der Vertheilung elektrischer Str\u00f6me in k\u00f6rperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche","volume":"165","author":"H Helmholtz","year":"1853","journal-title":"Ann Phys."},{"key":"pcbi.1013782.ref002","first-page":"012001","article-title":"Principle of reciprocity solves the most important problems in bioimpedance and in general in bioelectromagnetism","volume":"224","author":"J Malmivuo","year":"2010","journal-title":"J Phys: Conf Ser."},{"issue":"10","key":"pcbi.1013782.ref003","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1049\/piee.1974.0247","article-title":"Power reciprocity in antenna theory","volume":"121","author":"AT de Hoop","year":"1974","journal-title":"Proc Inst Electr Eng UK."},{"key":"pcbi.1013782.ref004","unstructured":"Malmivuo J. 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