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Case Reports
. 2017 Apr;14(2):026010.
doi: 10.1088/1741-2552/aa5990. Epub 2017 Feb 8.

Signal-independent Noise in Intracortical Brain-Computer Interfaces Causes Movement Time Properties Inconsistent With Fitts' Law

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Case Reports

Signal-independent Noise in Intracortical Brain-Computer Interfaces Causes Movement Time Properties Inconsistent With Fitts' Law

Francis R Willett et al. J Neural Eng. .
Free PMC article

Abstract

Objective: Do movements made with an intracortical BCI (iBCI) have the same movement time properties as able-bodied movements? Able-bodied movement times typically obey Fitts' law: [Formula: see text] (where MT is movement time, D is target distance, R is target radius, and [Formula: see text] are parameters). Fitts' law expresses two properties of natural movement that would be ideal for iBCIs to restore: (1) that movement times are insensitive to the absolute scale of the task (since movement time depends only on the ratio [Formula: see text]) and (2) that movements have a large dynamic range of accuracy (since movement time is logarithmically proportional to [Formula: see text]).

Approach: Two participants in the BrainGate2 pilot clinical trial made cortically controlled cursor movements with a linear velocity decoder and acquired targets by dwelling on them. We investigated whether the movement times were well described by Fitts' law.

Main results: We found that movement times were better described by the equation [Formula: see text], which captures how movement time increases sharply as the target radius becomes smaller, independently of distance. In contrast to able-bodied movements, the iBCI movements we studied had a low dynamic range of accuracy (absence of logarithmic proportionality) and were sensitive to the absolute scale of the task (small targets had long movement times regardless of the [Formula: see text] ratio). We argue that this relationship emerges due to noise in the decoder output whose magnitude is largely independent of the user's motor command (signal-independent noise). Signal-independent noise creates a baseline level of variability that cannot be decreased by trying to move slowly or hold still, making targets below a certain size very hard to acquire with a standard decoder.

Significance: The results give new insight into how iBCI movements currently differ from able-bodied movements and suggest that restoring a Fitts' law-like relationship to iBCI movements may require non-linear decoding strategies.

Figures

Figure 1
Figure 1
Diagram illustrating how increasing (decreasing) the cursor gain is equivalent to shrinking (expanding) both the target distance and radius. We study the effect of cursor gain on iBCI movement times as a way of testing the scale invariance predicted by Fitts’ law.
Figure 2
Figure 2
Effect of cursor gain on iBCI movements. (A) Cursor trajectories (colored by target) made by T8 under four different cursor gains. Cursor movements made at higher gains are faster but lack accuracy; the cursor takes curved paths towards the target and circles around it instead of coming to a complete stop on top of it. (B) Dial-in Time, Translation Time, and Movement Time as a function of cursor gain (reported in workspace widths per second at terminal speed) for three sessions (2 with T6, 1 with T8). Error regions are 95% confidence intervals for the mean. Cursor gain has a large effect on movement time, in contrast to the scale invariance predicted by Fitts’ law.
Figure 3
Figure 3
(A) Example cursor movements made by T8 in the random target task under three different gain conditions. (B) Index of difficulty (ID) vs. movement time plots for 6 example conditions (3 from T6 on the top row, 3 from T8 on the bottom row). One “ID vs. movement time” line is plotted for each target radius and illustrates the average movement time for four target distance bins. If Fitts’ law holds, all three radius lines should lie on top of one another. Divergent lines (left and right columns) indicate that index of difficulty alone cannot describe how movement time varies as a function of target distance and radius. Error regions represent 95% confidence intervals. Each line contains data from four distinct target distance bins (with bin edges at 0.15, 0.3, 0.45, 0.6, and 0.75 workspace widths).
Figure 4
Figure 4
Main effect of target distance (left column) and target radius (right column) on translation time (top row) and dial-in time (bottom row) across all sessions and conditions. Each circle indicates the average dial-in time or translation time for movements corresponding to a single “dataset” (a unique session date and dwell time setting). Variables have been normalized (z-score) to enable comparison across data with different absolute levels of performance and target characteristics. The thick black lines with gray 95% CI regions were generated by fitting a third-order polynomial for visualization purposes. They indicate that translation time is a linear function of target distance and that dial-in time is a power law function of target radius.
Figure 5
Figure 5
A highly simplified computer model of iBCI cursor movements featuring signal-independent decoding noise reproduces all of the movement time relationships we empirically observed in figures 2–4. One hundred movements were simulated for each condition and the shaded regions indicate 95% confidence intervals. (A) Simulated gain vs. movement time curves are U-shaped, as in figure 2. (B) The simulated ID vs. movement time curves diverge for low and high gains, as in figure 3. (C) Simulated dial-in time is a power law function of radius (independently of distance) and simulated translation time is a linear function of distance (independently of radius), as in figure 4.
Figure 6
Figure 6
Verifying that the participants’ neural modulation and decoding noise is consistent with the computer model of iBCI cursor movements. (A–C) Before analysis can be done, the output of the decoder must first be decomposed into a volitional modulation component and a noise component. Panel A shows an example cursor movement from a random target session with T8, illustrating the trajectory (black line) plus the pre-smoothed output of the decoder at each time step along the trajectory (red vectors). Panel B shows the same decoder output (u) as a time series plotted against what we estimated to be the volitional component (c, which we call the “encoded control vector”). Panel C shows the noise component (e) obtained by subtracting c from u. Gray regions indicate when the cursor is on top of the target. (D,E) Size of the control vector as a function of target distance and radius for T6 and T8. Each line is estimated from a different session of the random target task. Consistent with the computer model, modulation is independent of target radius and is relatively flat when not near the target. (F) Magnitude of the noise (characterized by standard deviation) for each block of the random target task included in the study (blocks from the same session are connected with a line). The noise magnitude is comparable to that of the volitional modulation. (G) Normalized noise magnitude as a function of control vector magnitude for each block of data. Each curve was normalized by dividing by its mean value. Consistent with our hypothesis, the noise is largely signal-independent.
Figure 7
Figure 7
Decoding from a simulated ensemble of Poisson-distributed neural features. (A, B) Thin colored lines illustrate the mean firing rate of example features as a function of the encoded control vector. The thick black lines show the mean firing rate across the entire ensemble. The features in (A) are tuned only to the control vector (b2=0), while those in (B) are tuned to the control vector and its magnitude independently (b2=b0), causing the mean firing rate of the ensemble to increase with the control vector magnitude. (C) A linear decoding matrix was calibrated with the same mathematical methods used with our participants and then applied to the neural ensemble. The standard deviation of the decoding noise is plotted as a function of control vector magnitude, showing that the noise is purely signal-independent (model A, blue line) or predominantly signal-independent (model B, red line).
Figure 8
Figure 8
Movement time data from participant A (1 of 3 able-bodied volunteers) using a joystick to complete the random target task under different gain and artificial noise conditions. The cursor’s velocity is smoothed and integrated in the same way as it is under iBCI control, but the output of the decoder is determined by the joystick position instead of neural activity. Performance is relatively robust to gain under the no noise and signal-dependent noise (SDN) conditions, but rapidly deteriorates as gain is increased under the signal-independent noise (SIN) condition. Consequently, Fitts’ law is a good descriptor of movement times in the no noise and signal-dependent noise conditions, but breaks down when signal-independent noise is added (the radius-specific lines do not overlap). Note that failed trials (where movement time exceeded 8 seconds) are reported as 8 second movement times.
Figure 9
Figure 9
Signal-to-noise ratio (signal strength divided by noise standard deviation) of our iBCI compared to the able-bodied motor system. iBCI and able-bodied SNRs are computed using a small time window of movement (100 ms to 300 ms) representing the “ballistic” phase of motion. (A) The decoding noise of iBCI cursor movements is compared to the variability of able-bodied motion. The standard deviation of the noise at different movement magnitudes is illustrated with a Gaussian probability density function (normalized to unit height). Movement magnitudes have been normalized so that 1 corresponds to the largest movement studied in a given experiment. (B) The signal-to-noise ratios implied by the data shown in A, plotted as a function of signal strength. (C) The same SNR curves as in B, but normalized to the SNR at full signal strength, revealing the relative fall-off of SNR as the signal strength declines. For purely signal-independent noise, the curve would lie on the unity line. (D) How many more recording electrodes would be needed for iBCI movements to approach the SNR of able-bodied movements using the decoder studied here? To answer this, we plot the signal to noise ratio as a logarithmic function of the number of recording channels included in the decoder (computed offline). One line is drawn for each session, and linear extrapolations are drawn as dashed lines (a linear model was fit to the session-specific lines using least squares regression and then extrapolated).

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