Optimizing the automatic selection of spike detection thresholds using a multiple of the noise level

Abstract

Thresholding is an often-used method of spike detection for implantable neural signal processors due to its computational simplicity. A means for automatically selecting the threshold is desirable, especially for high channel count data acquisition systems. Estimating the noise level and setting the threshold to a multiple of this level is a computationally simple means of automatically selecting a threshold. We present an analysis of this method as it is commonly applied to neural waveforms. Four different operators were used to estimate the noise level in neural waveforms and set thresholds for spike detection. An optimal multiplier was identified for each noise measure using a metric appropriate for a brain-machine interface application. The commonly used root-mean-square operator was found to be least advantageous for setting the threshold. Investigators using this form of automatic threshold selection or developing new unsupervised methods can benefit from the optimization framework presented here.

Fig. 1

Spike templates used in the simulated neural waveforms. No vertical scale bar is given because the template amplitudes were scaled based on the SNR of the simulated waveform. For each template, the dotted line shows the zero-point of the vertical axis.

Fig. 2

Optimality index versus multiplier value for each of the noise measures. The firing rate was 20 Hz and the window size was 4096 samples. In each plot, each curve corresponds to a different SNR. The lower SNRs are on the bottom of the envelope; the higher SNRs are on the top of the envelope. The leftmost arrow in each plot points to the curve corresponding to an SNR of 1. The rightmost arrow in each plot points to the curve corresponding to an SNR of 15. The insets are zoomed-in views of areas of interest.

Fig. 3

(a) The maximum optimality index value achieved at each SNR. A curve is plotted for each of the four different noise measures. All four curves lie almost directly on top of each other. (b) The optimality score as a function of multiplier value for each of the four noise measures. The optimality score is a weighted average of the optimality index across all SNRs. The RMS, P84, and PA68 curves all lie almost directly on top of each other. The plots in this figure are based on the data presented in figure 2.

Fig. 4

Optimality index and optimality score for a two-unit waveform in which the first unit has an SNR of 8, each unit has a firing rate of 20 Hz, and the window size is 4096 samples. (a) Optimality index versus multiplier value for each of the noise measures. In each plot, each curve corresponds to a different SNR (1 through 8) for the second unit. The leftmost arrow in each plot points to the curve corresponding to an SNR of 1. The rightmost arrow in each plot points to the curve corresponding to an SNR of 8. (b) The maximum optimality index value achieved at each SNR of the second unit. (c) The optimality score as a function of multiplier value for each of the four noise measures. The SNR for the second unit was used when computing the optimality score.

Fig. 5

Optimality index and optimality score for a two-unit waveform in which the first unit has an SNR of 12, each unit has a firing rate of 20 Hz, and the window size is 4096 samples. (a) Optimality index versus multiplier value for each of the noise measures. In each plot, each curve corresponds to a different SNR (1 through 12) for the second unit. The leftmost arrow in each plot points to the curve corresponding to an SNR of 1. The rightmost arrow in each plot points to the curve corresponding to an SNR of 12. (b) The maximum optimality index value achieved at each SNR of the second unit. (c) The optimality score as a function of multiplier value for each of the four noise measures. The SNR for the second unit was used when computing the optimality score.

Fig. 6

Examples of real neural data along with the thresholds computed using various noise measures and multipliers. Histograms are presented showing the distribution of thresholds computed over all epochs using specific combinations of noise measures and multipliers. The multiplier is shown in parentheses next to the noise measure. The histograms show the locations of the computed negative thresholds. Zoomed-in views of the histograms are shown in the boxes below the histograms. (a) The waveform shows 2 s of neural data recorded from a rat. This waveform appears to have spikes from one discernible unit. (b) The waveform shows 2 s of neural data recorded from a rat. This waveform appears to have spikes from two discernible units of noticeably different amplitudes.