Non-Linear Adaptive Bayesian Filtering for Brain Machine Interfaces
Brain-machine interfaces (BMI) are systems which connect brains directly to machines or computers for communication. BMI-controlled prosthetic devices use algorithms to decode neuronal recordings into movement commands. These algorithms operate using models of how recorded neuronal signals relate to desired movements, called models of tuning. Models of tuning have typically been linear in prior work, due to the simplicity and speed of the algorithms used with them. Neuronal tuning has been shown to slowly change over time, but most prior work do not adapt tuning models to these changes. Furthermore, extracellular electrical recordings of neurons' action potentials slowly change over time, impairing the preprocessing step of spike-sorting, during which the neurons responsible for recorded action potentials are identified.
This dissertation presents a non-linear adaptive Bayesian filter and an adaptive spike-sorting method for BMI decoding. The adaptive filter consists of the n-th order unscented Kalman filter and Bayesian regression self-training updates. The unscented Kalman filter estimates desired prosthetic movements using a non-linear model of tuning as its observation model. The model is quadratic with terms for position, velocity, distance from center of workspace, and velocity magnitude. The tuning model relates neuronal activity to movements at multiple time offsets simultaneously, and the movement model of the filter is an order n autoregressive model.
To adapt the tuning model parameters to changes in the brain, Bayesian regression self-training updates are performed periodically. Tuning model parameters are stored as probability distributions instead of point estimates. Bayesian regression uses the previous model parameters as priors and calculates the posteriors of the regression between filter outputs, which are assumed to be the desired movements, and neuronal recordings. Before each update, filter outputs are smoothed using a Kalman smoother, and tuning model parameters are passed through a transition model describing how parameters change over time. Two variants of Bayesian regression are presented: one uses a joint distribution for the model parameters which allows analytical inference, and the other uses a more flexible factorized distribution that requires approximate inference using variational Bayes.
To adapt spike-sorting parameters to changes in spike waveforms, variational Bayesian Gaussian mixture clustering updates are used to update the waveform clustering used to calculate these parameters. This Bayesian extension of expectation-maximization clustering uses the previous clustering parameters as priors and computes the new parameters as posteriors. The use of priors allows tracking of clustering parameters over time and facilitates fast convergence.
To evaluate the proposed methods, experiments were performed with 3 Rhesus monkeys implanted with micro-wire electrode arrays in arm-related areas of the cortex. Off-line reconstructions and on-line, closed-loop experiments with brain-control show that the n-th order unscented Kalman filter is more accurate than previous linear methods. Closed-loop experiments over 29 days show that Bayesian regression self-training helps maintain control accuracy. Experiments on synthetic data show that Bayesian regression self-training can be applied to other tracking problems with changing observation models. Bayesian clustering updates on synthetic and neuronal data demonstrate tracking of cluster and waveform changes. These results indicate the proposed methods improve the accuracy and robustness of BMIs for prosthetic devices, bringing BMI-controlled prosthetics closer to clinical use.
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