{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T00:33:32Z","timestamp":1773534812169,"version":"3.50.1"},"reference-count":43,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T00:00:00Z","timestamp":1464739200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neuroscience"],"published-print":{"date-parts":[[2016,6]]},"DOI":"10.1016\/j.neuroscience.2016.03.028","type":"journal-article","created":{"date-parts":[[2016,3,14]],"date-time":"2016-03-14T14:46:11Z","timestamp":1457966771000},"page":"377-389","source":"Crossref","is-referenced-by-count":32,"special_numbering":"C","title":["Nonlinear interactions in the thalamocortical loop in essential tremor: A model-based frequency domain analysis"],"prefix":"10.1016","volume":"324","author":[{"given":"F.","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.G.","family":"Sarrigiannis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.A.","family":"Billings","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Rowe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Romanowski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N.","family":"Hoggard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Hadjivassilliou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.G.","family":"Rao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Gr\u00fcnewald","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Yianni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.neuroscience.2016.03.028_b0005","series-title":"Nonlinear system identification: NARMAX methods in the time, frequency, and spatio-temporal domains","author":"Billings","year":"2013"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0020","doi-asserted-by":"crossref","first-page":"2157","DOI":"10.1080\/00207178908559767","article-title":"Identification of mimo non-linear systems using a forward-regression orthogonal estimator","volume":"49","author":"Billings","year":"1989","journal-title":"Int J Control"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0010","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/0888-3270(89)90042-3","article-title":"Spectral-analysis for non-linear systems. 2. Interpretation of non-linear frequency-response functions","volume":"3","author":"Billings","year":"1989","journal-title":"Mech Syst Signal Process"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0015","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1049\/ip-d.1983.0034","article-title":"Structure detection and model validity test in the identification of nonlinear systems","volume":"130","author":"Billings","year":"1983","journal-title":"IEE Proc"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0025","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.expneurol.2013.09.012","article-title":"The many roads to tremor","volume":"250","author":"Brittain","year":"2013","journal-title":"Exp Neurol"},{"issue":"Pt 2","key":"10.1016\/j.neuroscience.2016.03.028_b0030","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1016\/j.neuroimage.2013.05.084","article-title":"Oscillations and the basal ganglia: motor control and beyond","volume":"85","author":"Brittain","year":"2014","journal-title":"Neuroimage"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0035","doi-asserted-by":"crossref","first-page":"1873","DOI":"10.1080\/00207178908953472","article-title":"Orthogonal least squares methods and their application to nonlinear system identification","volume":"50","author":"Chen","year":"1989","journal-title":"Int J Control"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0040","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/S1474-4422(10)70322-7","article-title":"Treatment of patients with essential tremor","volume":"10","author":"Deuschl","year":"2011","journal-title":"Lancet Neurol"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0045","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1007\/s00422-005-0045-5","article-title":"Time delay and partial coherence analyses to identify cortical connectivities","volume":"94","author":"Govindan","year":"2006","journal-title":"Biol Cybern"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0050","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1016\/S0140-6736(00)02064-X","article-title":"Coherence between low-frequency activation of the motor cortex and tremor in patients with essential tremor","volume":"355","author":"Halliday","year":"2000","journal-title":"Lancet"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0055","doi-asserted-by":"crossref","first-page":"2233","DOI":"10.1109\/TBME.2013.2252347","article-title":"Spectral analysis for nonstationary and nonlinear systems: a discrete-time-model-based approach","volume":"60","author":"He","year":"2013","journal-title":"Biomed Eng IEEE Trans"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0060","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.jneumeth.2014.01.013","article-title":"A nonlinear causality measure in the frequency domain: nonlinear partial directed coherence with applications to EEG","volume":"225","author":"He","year":"2014","journal-title":"J Neurosci Methods"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0065","doi-asserted-by":"crossref","first-page":"2087","DOI":"10.1080\/00207721.2013.860202","article-title":"Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models","volume":"46","author":"He","year":"2015","journal-title":"Int J Syst Sci"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0070","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1016\/S1388-2457(00)00248-0","article-title":"Tremor-correlated cortical activity detected by electroencephalography","volume":"111","author":"Hellwig","year":"2000","journal-title":"Clin Neurophysiol"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0075","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/S0140-6736(00)04044-7","article-title":"Tremor-correlated cortical activity in essential tremor","volume":"357","author":"Hellwig","year":"2001","journal-title":"Lancet"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0080","doi-asserted-by":"crossref","first-page":"1462","DOI":"10.1016\/S1388-2457(03)00116-0","article-title":"Dynamic synchronisation of central oscillators in essential tremor","volume":"114","author":"Hellwig","year":"2003","journal-title":"Clin Neurophysiol"},{"issue":"Pt 4","key":"10.1016\/j.neuroscience.2016.03.028_b0085","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1093\/brain\/106.4.1001","article-title":"The correlation between tremor characteristics and the predicted volume of effective lesions in stereotaxic nucleus ventralis intermedius thalamotomy","volume":"106","author":"Hirai","year":"1983","journal-title":"Brain"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0090","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1152\/jn.00527.2004","article-title":"Posture-related oscillations in human cerebellar thalamus in essential tremor are enabled by voluntary motor circuits","volume":"93","author":"Hua","year":"2005","journal-title":"J Neurophysiol"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0095","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1212\/WNL.46.4.1150","article-title":"Deep brain stimulation for essential tremor","volume":"46","author":"Hubble","year":"1996","journal-title":"Neurology"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0100","series-title":"The thalamus","author":"Jones","year":"2007"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0105","doi-asserted-by":"crossref","first-page":"1925","DOI":"10.1080\/00207178908953474","article-title":"Recursive algorithm for computing the frequency-response of a class of non-linear difference equation models","volume":"50","author":"Jones","year":"1989","journal-title":"Int J Control"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0110","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1080\/00207179608921674","article-title":"Output frequency characteristics of nonlinear systems","volume":"64","author":"Lang","year":"1996","journal-title":"Int J Control"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0115","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s10867-008-9090-3","article-title":"Epilepsy and nonlinear dynamics","volume":"34","author":"Lehnertz","year":"2008","journal-title":"J Biol Phys"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0120","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1080\/0020718508961129","article-title":"Input-output parametric models for nonlinear systems, Part I: deterministic nonlinear systems","volume":"41","author":"Leontaritis","year":"1985","journal-title":"Int J Control"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0125","doi-asserted-by":"crossref","first-page":"6667","DOI":"10.1523\/JNEUROSCI.5459-09.2010","article-title":"Coupling between beta and high-frequency activity in the human subthalamic nucleus may be a pathophysiological mechanism in Parkinson\u2019s disease","volume":"30","author":"L\u00f3pez-Azc\u00e1rate","year":"2010","journal-title":"J Neurosci"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0130","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1097\/00004691-200401000-00002","article-title":"Deep brain stimulation and essential tremor","volume":"21","author":"Lyons","year":"2004","journal-title":"J Clin Neurophysiol"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0135","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1113\/jphysiol.2005.100271","article-title":"Dopamine-dependent non-linear correlation between subthalamic rhythms in Parkinson\u2019s disease","volume":"571","author":"Marceglia","year":"2006","journal-title":"J Physiol"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0140","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1113\/jphysiol.2005.100271","article-title":"Dopamine-dependent non-linear correlation between subthalamic rhythms in Parkinson\u2019s disease","volume":"571","author":"Marceglia","year":"2006","journal-title":"J Physiol"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0145","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1093\/brain\/123.7.1459","article-title":"Coherence between cerebellar thalamus, cortex and muscle in man: cerebellar thalamus interactions","volume":"123","author":"Marsden","year":"2000","journal-title":"Brain"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0150","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1016\/j.neuroimage.2012.01.088","article-title":"Oscillating central motor networks in pathological tremors and voluntary movements. What makes the difference?","volume":"60","author":"Muthuraman","year":"2012","journal-title":"Neuroimage"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0155","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1109\/PROC.1987.13824","article-title":"Bispectrum estimation \u2013 a digital signal-processing framework","volume":"75","author":"Nikias","year":"1987","journal-title":"Proc IEEE"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0160","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1097\/00006123-199912000-00030","article-title":"Development of a unique phantom to assess the geometric accuracy of magnetic resonance imaging for stereotactic localization","volume":"45","author":"Orth","year":"1999","journal-title":"Neurosurgery"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0165","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/S0967-5868(98)90197-7","article-title":"Use of the radionics image fusion trade mark and stereoplantrade mark programs for target localization in functional neurosurgery","volume":"5","author":"Papanastassiou","year":"1998","journal-title":"J Clin Neurosci"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0170","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.clinph.2011.09.024","article-title":"The oscillating central network of essential tremor","volume":"123","author":"Raethjen","year":"2012","journal-title":"Clin Neurophysiol"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0175","doi-asserted-by":"crossref","first-page":"3219","DOI":"10.1152\/jn.00477.2006","article-title":"Cortical involvement in the generation of essential tremor","volume":"97","author":"Raethjen","year":"2007","journal-title":"J Neurophysiol"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0180","doi-asserted-by":"crossref","first-page":"1629","DOI":"10.1002\/mds.22633","article-title":"Synchronized brain network associated with essential tremor as revealed by magnetoencephalography","volume":"24","author":"Schnitzler","year":"2009","journal-title":"Mov Disord"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0185","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1109\/TBME.2007.913418","article-title":"Statistical approach to quantify the presence of phase coupling using the bispectrum","volume":"55","author":"Siu","year":"2008","journal-title":"IEEE Trans Biomed Eng"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0190","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0167-2789(92)90102-S","article-title":"Testing for nonlinearity in time-series \u2013 the method of surrogate data","volume":"58","author":"Theiler","year":"1992","journal-title":"Physica D"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0195","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1212\/01.WNL.0000086371.78447.D2","article-title":"Deep brain stimulation of the VIM thalamic nucleus modifies several features of essential tremor","volume":"61","author":"Vaillancourt","year":"2003","journal-title":"Neurology"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0200","doi-asserted-by":"crossref","first-page":"1404","DOI":"10.1002\/mds.25137","article-title":"Short latency activation of cortex by clinically effective thalamic brain stimulation for tremor","volume":"27","author":"Walker","year":"2012","journal-title":"Mov Disord"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0205","series-title":"Biomedical Engineering and Informatics (BMEI), 2014 7th International Conference","first-page":"399","article-title":"Tremor dependant nonlinear interaction in deep brain local field potentials of Parkinson\u2019s disease","author":"Wang","year":"2014"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0210","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1006\/mssp.1998.0156","article-title":"Confidence bounds for frequency response functions from time series models","volume":"12","author":"Worden","year":"1998","journal-title":"Mech Syst Signal Process"},{"key":"10.1016\/j.neuroscience.2016.03.028_b0215","doi-asserted-by":"crossref","first-page":"1740","DOI":"10.1152\/jn.90463.2008","article-title":"Intrinsic functional relations between human cerebral cortex and thalamus","volume":"100","author":"Zhang","year":"2008","journal-title":"J Neurophysiol"}],"container-title":["Neuroscience"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0306452216002517?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0306452216002517?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T16:43:25Z","timestamp":1572367405000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0306452216002517"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6]]},"references-count":43,"alternative-id":["S0306452216002517"],"URL":"https:\/\/doi.org\/10.1016\/j.neuroscience.2016.03.028","relation":{},"ISSN":["0306-4522"],"issn-type":[{"value":"0306-4522","type":"print"}],"subject":[],"published":{"date-parts":[[2016,6]]}}}