There is increasing evidence suggesting essential tremor has a central origin¹. Different structures appear to be part of the central tremorogenic network, including the motor cortex, the thalamus and the cerebellum¹. Some authors show using EEG and MEG, a linear association in the tremor frequency between the motor cortex and the contralateral tremor EMG^{2, 3}. Additionally, high thalamo-muscular 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)⁴ Despite a well-established reciprocal anatomical connection between 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 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 analysed by constructing a novel parametric nonlinear autoregressive exogenous model (NARX). 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. Under “tremor-on” state the thalamic output shows significant nonlinear interactions at the frequency of the tremor around 4 Hz and time lags exceeding 50ms, suggesting involvement of an indirect multisynaptic loop. The same analysis when the tremor is off shows interactions at much higher frequencies in the thalamic output at around 8-11Hz and associated time lags below 50ms. We provide for the first time proof-of-concept of the importance of the nonlinear interactions, between cortex and Vim thalamus in characterising this part of the central tremorogenic network in two cases with essential tremor.

We would like to acknowledge the contribution of Dr M Hadjivassiliou, Dr G Rao and Dr H Wei to this work.