Principled BCI Decoder Design and Parameter Selection Using a Feedback Control Model

Abstract

Decoders optimized offline to reconstruct intended movements from neural recordings sometimes fail to achieve optimal performance online when they are used in closed-loop as part of an intracortical brain-computer interface (iBCI). This is because typical decoder calibration routines do not model the emergent interactions between the decoder, the user, and the task parameters (e.g. target size). Here, we investigated the feasibility of simulating online performance to better guide decoder parameter selection and design. Three participants in the BrainGate2 pilot clinical trial controlled a computer cursor using a linear velocity decoder under different gain (speed scaling) and temporal smoothing parameters and acquired targets with different radii and distances. We show that a user-specific iBCI feedback control model can predict how performance changes under these different decoder and task parameters in held-out data. We also used the model to optimize a nonlinear speed scaling function for the decoder. When used online with two participants, it increased the dynamic range of decoded speeds and decreased the time taken to acquire targets (compared to an optimized standard decoder). These results suggest that it is feasible to simulate iBCI performance accurately enough to be useful for quantitative decoder optimization and design.

Conflict of interest statement

K.V. Shenoy is a consultant to Neuralink Corp. and on the Scientific Advisory Boards of CTRL-Labs, Inc., MIND-X Inc., Inscopix Inc. and Heal, Inc. This work was independent of and in no way influenced or supported by these commercial entities. All other authors have no competing interests.

Figures

Figure 1

Standard calibration techniques do not always yield the optimal gain and smoothing properties for a velocity Kalman filter. Here, we define optimal as minimizing the mean movement time. (A) Simulated cursor movements using an initial decoder that was calibrated on open-loop (OL) data, using a decoder recalibrated with data from the first closed-loop (CL) block, and using a decoder with optimal gain and smoothing parameters. Average movement times are indicated in parentheses. (B) Average movement time as a function of gain and smoothing for this particular task and simulated user. Continued re-calibration of the decoder for 5 blocks (ReCal 1–5) does not cause the gain and smoothing values to converge to the optimal setting. (C,D) Same plots as in A and B except with a larger target radius; in this case, higher gain and lower smoothing values are optimal.

Figure 2

Illustration of the piecewise-linear feedback control model (PLM) used to simulate iBCI performance in this study. (A) Diagram of the feedback control model, with elements that are customized to each user shown in red. In the model, the simulated user receives delayed visual feedback of the cursor position and velocity. From the delayed feedback, the simulated user employs a forward model to estimate the current state of the cursor. The estimated cursor state and target position are then used to compute a control vector based on the user’s control policy. Finally, decoding noise, parameterized by an autoregressive model, is added to the control vector to simulate the decoder output. The decoder output is smoothed by first order smoothing dynamics and integrated to yield the cursor state. (B) Illustration of the control policy block. The user’s control vector is computed as the sum of a pushing component (a point-at-target vector weighted by the piecewise linear function ftarg) and a damping component (a heading vector weighted by the piecewise linear function fvel). The pushing component causes the cursor to move towards the target and the damping component slows down the cursor as needed to avoid overshooting the target (note that fvel is negative).

Figure 3

The PLM (piecewise-linear feedback control model) can predict the effect of gain on online performance. Results are shown for an example session with participant T6. (A) Observed cursor movements made during a single session under different gains (β, reported in units of target distances/second) are shown next to simulated trajectories predicted by the model. The model parameters were fit using data only from a single condition (β = 4.9, indicated in gray) and then used to simulate movements under different gain settings. (B) The data from (A) is quantified using four movement performance metrics (error bars represent 95% confidence intervals). Online performance is well predicted by the model (the red lines lie close to the black lines). Confidence intervals for model predictions were generated using bootstrap resampling (trials were resampled from each condition with replacement); the confidence intervals represent uncertainty in the predictions due to limited training data.

Figure 4

The PLM can predict the effect of temporal smoothing on online performance. Results are shown for an example session with participant T8. (A) Observed cursor movements made during a single session under different smoothing settings (α) are shown next to simulated trajectories predicted by the model. The model parameters were fit using data only from a single condition (α = 0.95, indicated in gray) and held fixed when simulating movements under different smoothing settings. (B) The data from (A) is quantified using four movement performance metrics (error bars represent 95% confidence intervals). Online performance is well predicted by the model (the red lines lie close to the black lines). Confidence intervals for model predictions were generated using bootstrap resampling (trials were resampled from each condition with replacement); the confidence intervals represent uncertainty in the predictions due to limited training data.

Figure 5

Assessing the ability of the PLM to predict online performance as a function of gain and smoothing across all 134 blocks included in the study. (A) The gain and smoothing settings imposed for each block are plotted as a circle. Blocks used to fit the model parameters are indicated with a black “x” inside the circle. (B) Observed vs. predicted online performance quantified using four movement performance metrics. Each circle represents the average performance for one block. Model predictions are a good quantitative match to the observed online performance (dots lie close to the solid unity line). In the top left corner of each panel, the fraction of variance accounted for by the model’s predictions (FVAF) is shown in addition to the mean absolute error of the predictions (MAE). To assess the model’s bias and statistical significance, a linear regression was performed for each panel that regressed the model’s predictions against the observed data. The regression coefficients are shown in the bottom right corner and indicate low bias (the slopes are near one and the intercepts are near zero). The regression line is plotted as a dashed black line and the unity line as a solid black line for comparison. Finally, the p-value for the slope coefficient is reported; the slope coefficients are statistically significant for all performance metrics (p < 1e-45 for all metrics), indicating that the model has statistically significant predictive power.

Figure 6

The PLM can predict online performance as a function of the task (target distance and target radius). (A) The model was fit only on movements to distant targets with small radii (indicated in gray). We illustrate observed vs. predicted performance on the random target task for an example session with T6 (left column) and T8 (right column). The model can predict how dial-in time increases as the radius becomes smaller (top row), how translation time increases as the target distance becomes greater (middle row), and how the total movement time is affected by both target distance and radius. In the bottom row, a separate index of difficulty (ID) vs. movement time line is drawn for each of the three target radii tested. The data show a departure from Fitts’ law that is predicted by the model (the departure is shown by the fact that ID does not fully predict movement time since the ID vs. movement time lines for each target radius do not lie on top of each other). (B) Observed vs. predicted online performance quantified using four movement performance metrics (same as in Fig. 5B). Each circle represents the average performance for one target distance and radius pairing. In the top left corner of each panel, the fraction of variance accounted for by the model’s predictions (FVAF) and the mean absolute error of the predictions (MAE) are shown. To assess the model’s bias and statistical significance, a linear regression was performed for each panel that regressed the model’s predictions against the observed data. The regression coefficients are shown in the bottom right corner and indicate low bias (the slopes are near one and the intercepts are near zero). The regression line is plotted as a dashed black line and the unity line as a solid black line for comparison. Finally, the p-value for the slope coefficient is reported.

Figure 7

Example simulations illustrating how the PLM can be used to find optimal gain and smoothing parameters and to optimize a typing interface. (A) Cursor movements are simulated under different gain and smoothing values to generate two-dimensional performance surfaces that describe the average predicted performance as a function of gain and smoothing. A parameter pair can then be selected to optimize a chosen metric (e.g. average movement time) or any other desired criterion. The PLM parameters were fit on one example block of data collected with T8. (B) Illustration of how the optimal gain and smoothing parameters predicted by the PLM change as a function of different factors. Three factors are depicted: decoding noise variance, the user’s visual feedback delay, and target radius. The target distance was 14 units. Parameters were selected to optimize average movement time. Error bars represent 95% confidence intervals. The simulated optimization routine was repeated 10 times for each point. (C) Example of how the PLM can be used to optimize a typing interface (in this case a 36-key keyboard in a square layout). For each possible dwell time, a separate gain and smoothing optimization routine was performed. Bit rate, optimal gain and smoothing parameters, mean acquire time and success rate are reported for the gain and smoothing parameters that maximize bit rate at each dwell time. Shaded regions represent 95% confidence intervals. The simulated optimization routine was repeated 50 times for each point.

Figure 8

The PLM finds parameters for a nonlinear speed transform function that improve performance relative to an optimized linear decoder. Results from T8 are shown on the top row and results from T5 on the bottom. (A) The optimal nonlinearity found by the PLM keep low speeds low but scale up higher speeds significantly, enabling both precise stopping and quick movements to the target. (B) Median distance from the target as a function of time when using either the standard Kalman filter (red) or the Kalman filter with the nonlinear speed transform (blue). The added nonlinearity enables the user to reach the target more quickly while maintaining a similar stopping ability (the blue line crosses the target boundary first but levels off to the same steady-state distance as the red line). Shaded regions indicate 95% confidence intervals. Movements were pooled across two sessions. (C) Median cursor speed as a function of time. The nonlinearity improves performance by enabling faster speeds while traveling to the target without causing speeds to be faster when near the target. (D) Mean success %, translation time, and dial-in time with 95% confidence intervals. Three asterisks (***) indicate a significant difference with p < 0.001 and two asterisks (**) indicate p < 0.01 (as computed with a t-test for translation time and dial-in time and fisher’s exact test for success %). (E–H) Same as (A–D) but for participant T5.