title: Nonlinear interactions in the thalamocortical loop in essential tremor: A model-based frequency domain analysis.
abstract: There is increasing evidence to suggest that essential tremor has a central origin. Different structures appear to be part of the central tremorogenic network, including the motor cortex, the thalamus and the cerebellum. Some studies using electroencephalogram (EEG) and magnetoencephalography (MEG) show linear association in the tremor frequency between the motor cortex and the contralateral tremor electromyography (EMG). Additionally, high thalamomuscular coherence is found with the use of thalamic local field potential (LFP) recordings and tremulous EMG in patients undergoing surgery for deep brain stimulation (DBS). Despite a well-established reciprocal anatomical connection between the thalamus and cortex, the functional association between the two structures during "tremor-on" periods remains elusive. Thalamic (Vim) LFPs, ipsilateral scalp EEG from the sensorimotor cortex and contralateral tremor arm EMG recordings were obtained from two patients with essential tremor who had undergone successful surgery for DBS. Coherence analysis shows a strong linear association between thalamic LFPs and contralateral tremor EMG, but the relationship between the EEG and the thalamus is much less clear. These measurements were then analyzed by constructing a novel parametric nonlinear autoregressive with exogenous input (NARX) model. This new approach uncovered two distinct and not overlapping frequency "channels" of communication between Vim thalamus and the ipsilateral motor cortex, defining robustly "tremor-on" versus "tremor-off" states. The associated estimated nonlinear time lags also showed non-overlapping values between the two states, with longer corticothalamic lags (exceeding 50ms) in the tremor active state, suggesting involvement of an indirect multisynaptic loop. The results reveal the importance of the nonlinear interactions between cortical and subcortical areas in the central motor network of essential tremor. This work is important because it demonstrates for the first time that in essential tremor the functional interrelationships between the cortex and thalamus should not be sought exclusively within individual frequencies but more importantly between cross-frequency nonlinear interactions. Should our results be successfully reproduced on a bigger cohort of patients with essential tremor, our approach could be used to create an on-demand closed-loop DBS device, able to automatically activate when the tremor is on.
authors.affiliation: Department of Automatic Control and Systems Engineering, University of Sheffield, S1 3JD, United Kingdom. Electronic address: f.he@sheffield.ac.uk.
authors.forename: F
authors.initials: F
authors.lastname: He
authors.affiliation: Department of Clinical Neurophysiology, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, Sheffield S10 2JF, United Kingdom. Electronic address: ptolemaios.sarrigiannis@sth.nhs.uk.
authors.forename: P G
authors.initials: PG
authors.lastname: Sarrigiannis
authors.affiliation: Department of Automatic Control and Systems Engineering, University of Sheffield, S1 3JD, United Kingdom. Electronic address: s.billings@sheffield.ac.uk.
authors.forename: S A
authors.initials: SA
authors.lastname: Billings
authors.affiliation: Department of Automatic Control and Systems Engineering, University of Sheffield, S1 3JD, United Kingdom. Electronic address: w.hualiang@sheffield.ac.uk.
authors.forename: H
authors.initials: H
authors.lastname: Wei
authors.affiliation: Department of Neurosurgery, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, Sheffield S10 2JF, United Kingdom. Electronic address: Jeremy.Rowe@sth.nhs.uk.
authors.forename: J
authors.initials: J
authors.lastname: Rowe
authors.affiliation: Department of Radiology, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, Sheffield S10 2JF, United Kingdom. Electronic address: Charles.Romanowski@sth.nhs.uk.
authors.forename: C
authors.initials: C
authors.lastname: Romanowski
authors.affiliation: Department of Radiology, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, Sheffield S10 2JF, United Kingdom. Electronic address: Nigel.Hoggard@sth.nhs.uk.
authors.forename: N
authors.initials: N
authors.lastname: Hoggard
authors.affiliation: Department of Neurology, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, Sheffield S10 2JF, United Kingdom. Electronic address: Marios.Hadjivassiliou@sth.nhs.uk.
authors.forename: M
authors.initials: M
authors.lastname: Hadjivassilliou
authors.affiliation: Department of Clinical Neurophysiology, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, Sheffield S10 2JF, United Kingdom. Electronic address: Ganesh.Rao@sth.nhs.uk.
authors.forename: D G
authors.initials: DG
authors.lastname: Rao
authors.affiliation: Department of Neurology, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, Sheffield S10 2JF, United Kingdom. Electronic address: Richard.Grunewald@sth.nhs.uk.
authors.forename: R
authors.initials: R
authors.lastname: Grünewald
authors.affiliation: Department of Neurology, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, Sheffield S10 2JF, United Kingdom. Electronic address: Aijaz.Khan@sth.nhs.uk.
authors.forename: A
authors.initials: A
authors.lastname: Khan
authors.affiliation: Department of Neurosurgery, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, Sheffield S10 2JF, United Kingdom. Electronic address: John.Yianni@sth.nhs.uk.
authors.forename: J
authors.initials: J
authors.lastname: Yianni
mesh_terms: D001132:Arm / Q000503:physiopathology; D002540:Cerebral Cortex / Q000503:physiopathology*; D046690:Deep Brain Stimulation; D004569:Electroencephalography; D004576:Electromyography; D020329:Essential Tremor / Q000503:physiopathology* / Q000628:therapy; D005260:Female; D007839:Functional Laterality; D006801:Humans; D008875:Middle Aged; D008959:Models, Neurological; D009068:Movement / Q000502:physiology; D018482:Muscle, Skeletal / Q000503:physiopathology; D009434:Neural Pathways / Q000503:physiopathology; D017711:Nonlinear Dynamics; D012146:Rest; D012815:Signal Processing, Computer-Assisted; D013788:Thalamus / Q000503:physiopathology*
keywords: EEG; coherence; essential tremor; local field potentials; nonlinear modeling; spectral analysis