Decoding voluntary movements and postural tremor based on thalamic LFPs as a basis for closed-loop stimulation for essential tremor

Background High frequency Deep brain stimulation (DBS) targeting motor thalamus is an effective therapy for essential tremor (ET). However, conventional continuous stimulation may deliver unnecessary current to the brain since tremor mainly affects voluntary movements and sustained postures in ET. Objective We aim to decode both voluntary movements and the presence of postural tremor from the Local field potentials (LFPs) recorded from the electrode implanted in motor thalamus for stimulation, in order to close the loop for DBS so that stimulation could be delivered on demand, without the need for peripheral sensors or additional invasive electrodes. Methods LFPs from the motor thalamus, surface electromyographic (EMG) signals and/or behavioural measurements were simultaneously recorded in seven ET patients during temporary lead externalisation 3–5 days after the first surgery for DBS when they performed different voluntary upper limb movements. Nine different patients were recorded during the surgery, when they were asked to lift their arms to trigger postural tremor. A machine learning based binary classifier was used to detect voluntary movements and postural tremor based on features extracted from thalamic LFPs. Results Cross-validation demonstrated that both voluntary movements and postural tremor can be decoded with an average sensitivity of 0.8 and false detection rate of 0.2. Oscillatory activities in the beta frequency bands (13–23 Hz) and the theta frequency bands (4–7 Hz) contributed most to the decoding of movements and postural tremor, respectively, though incorporating features in different frequency bands using a machine learning approach increased the accuracy of decoding.

was prompted to move a joystick so that the cursor (a red dot displayed on a monitor) corresponding to the joystick position would match a target position (a green dot). For each trial, the green target jumped from the centre to one of eight potential positions, and stayed at the target position for 1 second before returning to the centre of the screen (Supplementary Fig. 1B). There were 100 trials in each session, with each movement lasting 1-1.5 seconds and an inter-trial interval of 2 -2.5 seconds.
One patient (Ox3) performed a 'cued button pressing' task, during which they were asked to press the same key on a keyboard using the index finger once they saw a cue presented on a monitor. In this task, there were 100 trials in each session with each movement lasting around 0.5 seconds and an inter-trial interval of 2.5 -3 seconds. In addition, two other patients performed self-paced continuous movements. One of them (Ox4) performed blocks of continuous finger tapping; and another (Ox5) performed blocks of continuous wrist movements (extension and flexion of the wrist).
Each block of movement lasted for 20-30 seconds with 20-30 seconds between the movement blocks.

Recording
For post-operative recordings in the Oxford cohort, ViM thalamic local field potentials were recorded using a TMSi Porti amplifier (monopolar, common average reference, anti-aliasing low-pass filtering with a cut-off frequency of 500 Hz and sampling frequency of 2048Hz, TMS International, Netherlands) in patient Ox1, 2, 6 and 7. In patient Ox3-5, bipolar derivations from adjacent contact pairs were recorded through an Analog-to-digital-converter (1401power mk-II, Cambridge Electronic Design, Cambridge, UK) after amplification (Digitimer D360, Digitimer, Welfortshire, UK). Electromyography (EMG) was simultaneously recorded from the flexor and extensor carpi radialis in gripping movements, and from the first dorsal interosseous muscle (FDI) in finger joystick or finger tapping movements. Direct behavioural measurements such as generated gripping force (Biometrics hand dynamometer) or joystick positions were also simultaneously recorded using the same amplifier.
In addition, 3D accelerometers (± 3g, TMSi, Netherlands) were attached to the hand in order to measure kinematic movements of the hand and the presence of tremor.
For intraoperative recordings in Cologne, a commercially available recording system (Inomed Micro Electrode Recording System; software: MER 2.4 beta) was used. Two to five micro-macroelectrodes were used, selected from a central electrode and four concentrically configured (anterior, medial, posterior, and lateral) further electrodes with a distance of 2mm from the central electrode. Local field potentials from the macroelectrodes were recorded while the electrodes were in the surgical target. Activity of the extensor digitorum communis (EDC) and flexor digitorum longus (FDL) muscles of the contralateral forearm were also simultaneously recorded using surface EMG electrodes.
Both LFP and EMG signals were bandpass filtered between 0.5 and 1 kHz during the recording and sampled at 2.5 KHz.

Labelling of movement states based on behavioural measurements
In the Oxford cohort, direct behavioural measurements (force or joystick position) or EMG were used to identify the period of time with or without movements. EMG activities were high-pass filtered with cut-off frequency of 1 Hz, rectified and smoothed within a moving time window of 0.2 s. All behavioural measurements were normalised: gripping force was normalised to the maximal gripping force measured before the task started; the joystick position was normalised to maximal possible displacement when the joystick was displaced to its extreme; EMG activities were normalised to the 95 th percentile value of the recording session. The mean and standard deviation of the background behavioural measurements during a 10 s time window with the patient at rest were quantified. For each recording session, time points with behavioural measurements over Mean + 4*STD relative to the resting baseline were labelled as 'Movement'. Supplementary Fig. 2 shows examples of the recordings for different tasks with labelled 'movements' shown as thin black lines. All analyses were performed in MATLAB (v. 2016a, The MathWorks Inc., Natick, Massachusetts).
In the Cologne cohort, EMG activities were used to identify periods of time with or without postural tremor. EMG activities were high pass filtered with cut-off frequency of 1 Hz and rectified. Timefrequency decomposition of the rectified EMG activities was obtained by applying continuous Morlet wavelet transforms with a linear frequency scale ranging from 1 Hz to 46 Hz and constant number (= 6) of cycles across all calculated frequencies. The mean and standard deviation of the peak power in the 3-7 Hz frequency band in the EMG activity when each patient was at rest were quantified. Time points in the forearm elevated blocks with EMG 3-7 Hz activity over Mean + 4*STD were labelled as 'Postural tremor'.

Logistic Regression based Binary Classifier
Here we adopted the logistic regression (LR) based binary (two-class) classifier. The logistic regression model predicts the probability of the presence of movements or tremor at the current time point t (p(t)) based on the linear combination of a set of predictor variables: Where K and M are the number of features and the number of time lags during which the features were taken into account for the prediction, respectively, ( − ) is the k th predictor variable with time lag relative to the current time point and , is the associated weight, 0 is an intercept constant representing the baseline probability of the occurrence of movements, and y(t) is the weighted sum of all different features. A monotonic, S-shaped continuous function (the Logistic function) was then used to map y(t) which ranges from -∞ to +∞ into a value between 0 and 1 ( ( )): A threshold was then applied to p(t) to classify the current observation as movement/tremor or not.
In this study, the ROC was plotted and the AUC was quantified to evaluate classifier performance.
The Receiver Operating Characteristics (ROC) curve plots the true positive rate (Sensitivity) against false positive rate (1-Specificity) for different thresholds. The area under the ROC curve (AUC) provides a measure of the ability of the classifier to distinguish between the two states with 0.5 indicating a chance-level accuracy and 1 suggesting perfect classification.

Training and cross-validation of the Logistic Regression based Binary Classifier
Five-fold cross-validation was applied to each recording session. In each iteration, 4 folds (80% of data) were used to train the classifier, i.e. to determine the weight , attributed to each predictor After the weight vector w was estimated based on the training data, the predictor variables extracted from the ViM thalamic LFPs recorded in the remaining 20% data were used to decode movement probability and to test the classifier performance. The training and testing were performed for five iterations so each data point is used for testing for once. The estimated weight vectors from the five iterations were averaged before evaluating the contributions of different LFP features in decoding.
For cross-task validation, the model with the averaged weight vector from the five iterations was applied to another independent dataset recorded while the patients performed voluntary movements different from those used for model training.