Inferring firing rates from local field potentials in the human subthalamic nucleus

Neurons in the subthalamic nucleus (STN) spontaneously fire rhythmically in vivo due to intrinsic membrane properties. In patients with Parkinson’s disease, intranuclear local field potentials (LFPs) recorded from deep brain stimulation (DBS) electrodes show increased power in the beta band (13–30 Hz), and STN DBS has been shown to decrease aberrant STN LFP beta power. As many current models of basal ganglia employ a rate code, it is natural to ask to what extent STN firing rates can be inferred from simultaneously recorded LFPs, and further, to understand when such predictive relationships arise.

We applied online linear decoding methods to STN LFP and unit data recorded from 11 human parkinsonian patients (236 one to three minute recordings; spike-sorted single and multiunits). Using 10-fold cross validation and several voltage, power, and instantaneous phase features (with delays), we attempted to predict the presence or absence of spikes in a given time bin (e.g. 5 ms) using an online linear filter. The full linear model contained 88 features. We trained our algorithms on an equal number of positive and negative examples for each cross validation fold. We measured prediction accuracy by correlating Gaussian-convolved target spike trains with Gaussian-convolved predicted spike trains.

Units displayed a wide range of spike phase and power relationships. Beta power was not always a good predictor of firing rate. The number of units with decoding prediction accuracy above 0.1 was relatively small (16%). Units exhibited large variation in their ability to be decoded over the course of a recording session, with some cross validation test sets >0.6 correlation. Using the full linear model, mean prediction accuracy was significantly above chance.