{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:14:59Z","timestamp":1772172899186,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009281","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,8,30]],"date-time":"2021-08-30T00:00:00Z","timestamp":1630281600000}}],"reference-count":50,"publisher":"Public Library of Science (PLoS)","issue":"8","license":[{"start":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T00:00:00Z","timestamp":1628208000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Medical Research Council","award":["MC_UU_12024\/5"],"award-info":[{"award-number":["MC_UU_12024\/5"]}]},{"name":"Medical Research Council","award":["MC_UU_00003\/1"],"award-info":[{"award-number":["MC_UU_00003\/1"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Deep brain stimulation (DBS) is a well-established treatment option for a variety of neurological disorders, including Parkinson\u2019s disease and essential tremor. The symptoms of these disorders are known to be associated with pathological synchronous neural activity in the basal ganglia and thalamus. It is hypothesised that DBS acts to desynchronise this activity, leading to an overall reduction in symptoms. Electrodes with multiple independently controllable contacts are a recent development in DBS technology which have the potential to target one or more pathological regions with greater precision, reducing side effects and potentially increasing both the efficacy and efficiency of the treatment. The increased complexity of these systems, however, motivates the need to understand the effects of DBS when applied to multiple regions or neural populations within the brain. On the basis of a theoretical model, our paper addresses the question of how to best apply DBS to multiple neural populations to maximally desynchronise brain activity. Central to this are analytical expressions, which we derive, that predict how the symptom severity should change when stimulation is applied. Using these expressions, we construct a closed-loop DBS strategy describing how stimulation should be delivered to individual contacts using the phases and amplitudes of feedback signals. We simulate our method and compare it against two others found in the literature: coordinated reset and phase-locked stimulation. We also investigate the conditions for which our strategy is expected to yield the most benefit.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009281","type":"journal-article","created":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T13:34:23Z","timestamp":1628256863000},"page":"e1009281","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":20,"title":["Optimal closed-loop deep brain stimulation using multiple independently controlled 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University of Oxford, available at: https:\/\/data.mrc.ox.ac.uk\/data-set\/kuramoto."},{"issue":"12","key":"pcbi.1009281.ref027","doi-asserted-by":"crossref","first-page":"e3947","DOI":"10.1371\/journal.pone.0003947","article-title":"Cholinergic neuromodulation changes phase response curve shape and type in cortical pyramidal neurons","volume":"3","author":"KM Stiefel","year":"2008","journal-title":"PloS one"},{"issue":"5","key":"pcbi.1009281.ref028","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1162\/neco.1996.8.5.979","article-title":"Type I membranes, phase resetting curves, and synchrony","volume":"8","author":"B Ermentrout","year":"1996","journal-title":"Neural computation"},{"key":"pcbi.1009281.ref029","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/978-1-4614-0739-3_5","volume-title":"Phase response curves in neuroscience","author":"T Netoff","year":"2012"},{"issue":"3","key":"pcbi.1009281.ref030","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1523\/JNEUROSCI.23-03-00943.2003","article-title":"The functional consequences of changes in the strength and duration of synaptic inputs to oscillatory neurons","volume":"23","author":"AA Prinz","year":"2003","journal-title":"Journal of Neuroscience"},{"key":"pcbi.1009281.ref031","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.conb.2014.12.003","article-title":"Phase-resetting as a tool of information transmission","volume":"31","author":"CC Canavier","year":"2015","journal-title":"Current opinion in neurobiology"},{"issue":"3","key":"pcbi.1009281.ref032","doi-asserted-by":"crossref","first-page":"037113","DOI":"10.1063\/1.2930766","article-title":"Low dimensional behavior of large systems of globally coupled oscillators","volume":"18","author":"E Ott","year":"2008","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"issue":"1","key":"pcbi.1009281.ref033","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13408-020-00086-9","article-title":"Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review","volume":"10","author":"C Bick","year":"2020","journal-title":"The Journal of Mathematical Neuroscience"},{"issue":"3","key":"pcbi.1009281.ref034","doi-asserted-by":"crossref","first-page":"e59839","DOI":"10.1371\/journal.pone.0059839","article-title":"Theoretical analysis of the local field potential in deep brain stimulation applications","volume":"8","author":"SF Lempka","year":"2013","journal-title":"PloS one"},{"issue":"1","key":"pcbi.1009281.ref035","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1109\/TNSRE.2010.2081377","article-title":"Closed-loop control of deep brain stimulation: a simulation study","volume":"19","author":"S Santaniello","year":"2010","journal-title":"IEEE Transactions on Neural Systems and Rehabilitation Engineering"},{"issue":"6","key":"pcbi.1009281.ref036","doi-asserted-by":"crossref","first-page":"066009","DOI":"10.1088\/1741-2560\/7\/6\/066009","article-title":"Modeling deep brain stimulation: point source approximation versus realistic representation of the electrode","volume":"7","author":"TC Zhang","year":"2010","journal-title":"Journal of neural engineering"},{"key":"pcbi.1009281.ref037","unstructured":"Cagnan H, Weerasinghe G, Brown P. Tremor data measured from essential tremor patients subjected to phase-locked deep brain stimulation; 2019. University of Oxford, available at: https:\/\/data.mrc.ox.ac.uk\/data-set\/tremor-data-measured-essential-tremor-patients-subjected-phase-locked-deep-brain."},{"key":"pcbi.1009281.ref038","doi-asserted-by":"crossref","first-page":"e225","DOI":"10.1016\/j.wneu.2020.04.240","article-title":"Individualized Anatomy-Based Targeting for VIM-cZI DBS in Essential Tremor","volume":"140","author":"A Diaz","year":"2020","journal-title":"World neurosurgery"},{"issue":"10","key":"pcbi.1009281.ref039","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1212\/WNL.0000000000005076","article-title":"Double-target DBS for essential tremor: 8-contact lead for cZI and Vim aligned in the same trajectory","volume":"90","author":"MGDS Ghilardi","year":"2018","journal-title":"Neurology"},{"issue":"6","key":"pcbi.1009281.ref040","doi-asserted-by":"crossref","first-page":"E6","DOI":"10.3171\/2015.3.FOCUS1537","article-title":"Deep brain stimulation for vocal tremor: a comprehensive, multidisciplinary methodology","volume":"38","author":"AL Ho","year":"2015","journal-title":"Neurosurgical focus"},{"issue":"1","key":"pcbi.1009281.ref041","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1007\/s00422-005-0028-6","article-title":"Long-term anti-kindling effects of desynchronizing brain stimulation: a theoretical study","volume":"94","author":"PA Tass","year":"2006","journal-title":"Biological cybernetics"},{"issue":"11","key":"pcbi.1009281.ref042","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1038\/nrn3599","article-title":"Modelling and analysis of local field potentials for studying the function of cortical circuits","volume":"14","author":"GT Einevoll","year":"2013","journal-title":"Nature Reviews Neuroscience"},{"issue":"1","key":"pcbi.1009281.ref043","article-title":"An overview of independent component analysis and its applications","volume":"35","author":"GR Naik","year":"2011","journal-title":"Informatica"},{"issue":"12","key":"pcbi.1009281.ref044","doi-asserted-by":"crossref","first-page":"e1005881","DOI":"10.1371\/journal.pcbi.1005881","article-title":"Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks","volume":"13","author":"F Devalle","year":"2017","journal-title":"PLoS computational biology"},{"issue":"1","key":"pcbi.1009281.ref045","doi-asserted-by":"crossref","first-page":"012905","DOI":"10.1103\/PhysRevE.88.012905","article-title":"Noise-induced synchronization, desynchronization, and clustering in globally coupled nonidentical oscillators","volume":"88","author":"YM Lai","year":"2013","journal-title":"Physical Review E"},{"issue":"2","key":"pcbi.1009281.ref046","doi-asserted-by":"crossref","first-page":"026005","DOI":"10.1088\/1741-2552\/aaa14b","article-title":"Optimized programming algorithm for cylindrical and directional deep brain stimulation electrodes","volume":"15","author":"DN Anderson","year":"2018","journal-title":"Journal of neural engineering"},{"key":"pcbi.1009281.ref047","doi-asserted-by":"crossref","unstructured":"Hofmanis J, Ruiz RAS, Caspary O, Ranta R, Louis-Dorr V. 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