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. 2018 Nov;30(11):2986-3008.
doi: 10.1162/neco_a_01129. Epub 2018 Sep 14.

Robust Closed-Loop Control of a Cursor in a Person With Tetraplegia Using Gaussian Process Regression

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Robust Closed-Loop Control of a Cursor in a Person With Tetraplegia Using Gaussian Process Regression

David M Brandman et al. Neural Comput. .
Free PMC article

Abstract

Intracortical brain computer interfaces can enable individuals with paralysis to control external devices through voluntarily modulated brain activity. Decoding quality has been previously shown to degrade with signal nonstationarities-specifically, the changes in the statistics of the data between training and testing data sets. This includes changes to the neural tuning profiles and baseline shifts in firing rates of recorded neurons, as well as nonphysiological noise. While progress has been made toward providing long-term user control via decoder recalibration, relatively little work has been dedicated to making the decoding algorithm more resilient to signal nonstationarities. Here, we describe how principled kernel selection with gaussian process regression can be used within a Bayesian filtering framework to mitigate the effects of commonly encountered nonstationarities. Given a supervised training set of (neural features, intention to move in a direction)-pairs, we use gaussian process regression to predict the intention given the neural data. We apply kernel embedding for each neural feature with the standard radial basis function. The multiple kernels are then summed together across each neural dimension, which allows the kernel to effectively ignore large differences that occur only in a single feature. The summed kernel is used for real-time predictions of the posterior mean and variance under a gaussian process framework. The predictions are then filtered using the discriminative Kalman filter to produce an estimate of the neural intention given the history of neural data. We refer to the multiple kernel approach combined with the discriminative Kalman filter as the MK-DKF. We found that the MK-DKF decoder was more resilient to nonstationarities frequently encountered in-real world settings yet provided similar performance to the currently used Kalman decoder. These results demonstrate a method by which neural decoding can be made more resistant to nonstationarities.

Figures

Figure 1:
Figure 1:
Schematic demonstrating the effect of kernel selection on the measure of similarity for two-dimensional neural features. Since kernel similarity between two points depends on only their coordinate-wise differences, we let p1 = (0, 0) be a point at the origin and consider the kernel-determined similarity between p1 and a second point p2 = (x, y). For each plot, the color at (x, y) represents the measure of similarity according to the selected kernel K˜θ˜(p1,p2). Traveling along the red line illustrates the effect of increasing the difference in measurements for a single neuron. For the RBF kernel (A), moving along the arrow results in the kernel becoming arbitrarily small. By contrast, the MK kernel (B) never falls below half of the value at the origin as it moves along the arrow. For 40 dimensions, the MK kernel would never fall below 39/40 of its maximal value. Hence, when the RBF kernel is used for closed-loop decoding, nonstationarities from a single neural feature would result in no similarity between the current neural feature and any of the training data. By contrast, the MK kernel will remain relatively unaffected by even a drastic change in a single neuron and continue to effectively use the information from the remaining neurons.
Figure 2:
Figure 2:
(A) Radial-8 task. Eight targets are presented on the screen (blue circle). T10 was instructed to move the cursor (white circle) to the goal (red circle). Targets were acquired when the cursor overlapped the target for 300 ms. (B) Grid task. Square targets were arranged in a grid. T10 was instructed to move the cursor (white circle) to the target (green square). A target was acquired when T10 held the cursor within any square for 1 second. Note that unlike the radial-8 task, incorrect targets were scored.
Figure 3:
Figure 3:
(A) Change in angular error as a function of z-score offset for the Kalman filter, the Kalman filter with feature saturation, and MK-DKF decoders. We identified 96 research sessions where T10 performed closed-loop neural control. For each session, we performed a 50–50 split of the data and used the training data to compute the coefficients for the decoders; then we predicted the angular error on the testing data. Next, we added a z-score offset to a single channel (standardized for each decoder). The shaded areas represent the standard error of measurement for each decoder. (B) Change in angular error as a function of feature thresholding. During the bootstrapping procedure, we saturated features for both the training and testing data sets and computed the change in angular error compared to no saturation. The shaded area represents the standard error of measurement. (C) Examining the frequency of noise events. For each of the bootstrapped simulations, we counted the frequency at which each feature was incorporated into the decoder (m = 40), as well as the frequency at which the feature was observed to deviate by more than two z-scores.
Figure 4:
Figure 4:
(A) Percentage of targets acquired during closed-loop cursor control by T10 in the radial-8 task. On research days 259, 265, 272, and 300, T10 acquired targets wherein the decoder (Kalman and MK-DKF) and the amount of noise (no noise, one z-score, five z-scores) were randomly selected. There was no statistically significant difference in performance across the noise injection trials for the MK-DKF decoder (χ2, p = 0.81) There was a statistically significant difference across conditions for the Kalman decoder (χ 2, p < 10–37). To ensure that T10 could not distinguish between which decoder was being used, the kinematic parameters of the MK-DKF matched to the Kalman decoder. (B) Performance of both the MK-DKF and Kalman decoders with optimal kinematic parameters. There was no statistically significant difference in bit rate between the two decoders (trial days 272 and 300, Wilcoxon rank-sum test p = 0.48).

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