Minimum requirements for accurate and efficient real-time on-chip spike sorting

Abstract

Background: Extracellular recordings are performed by inserting electrodes in the brain, relaying the signals to external power-demanding devices, where spikes are detected and sorted in order to identify the firing activity of different putative neurons. A main caveat of these recordings is the necessity of wires passing through the scalp and skin in order to connect intracortical electrodes to external amplifiers. The aim of this paper is to evaluate the feasibility of an implantable platform (i.e., a chip) with the capability to wirelessly transmit the neural signals and perform real-time on-site spike sorting.

New method: We computationally modelled a two-stage implementation for online, robust, and efficient spike sorting. In the first stage, spikes are detected on-chip and streamed to an external computer where mean templates are created and sent back to the chip. In the second stage, spikes are sorted in real-time through template matching.

Results: We evaluated this procedure using realistic simulations of extracellular recordings and describe a set of specifications that optimise performance while keeping to a minimum the signal requirements and the complexity of the calculations.

Comparison with existing methods: A key bottleneck for the development of long-term BMIs is to find an inexpensive method for real-time spike sorting. Here, we simulated a solution to this problem that uses both offline and online processing of the data.

Conclusions: Hardware implementations of this method therefore enable low-power long-term wireless transmission of multiple site extracellular recordings, with application to wireless BMIs or closed-loop stimulation designs.

Keywords: BMIs; Extracellular recordings; On-chip; On-line; Real-time; Spike sorting; Template matching.

Figure 1. Simulation and processing of extracellular recordings.

Recordings were created considering three zones. Zone 1 models the neurons located close to the tip of the electrode, generating single-unit activity. In Zone 2, neurons produce spikes that cannot be clustered due to their small amplitude, leading to multi-unit activity. Zone 3 represents the activity of further away neurons that give rise to the background noise. Extracellular recordings were generated by adding the activity in these three zones (step 1). Signals were then filtered using different specifications (step 2). Virtual Analog-to-digital conversion (ADC) was simulated by downsampling the data and quantizing the signal to a lower resolution (step 3). Spikes were then detected and sorted (steps 4 and 5).

Figure 2. Effect of filtering on spike detection.

A) For different high-pass cut-off frequencies, non-causal filters (black line) lead to better spike detection performance than causal filters (red line) for the Elliptic (left panel), Butterworth (center panel), and Bessel (right panel) filters. These results are based on the simulations with low SNR. B) Illustration of phase distortion effects introduced by causal filters. For a given threshold value, the spike obtained with the non-causal filter is detected (top-right panel) whereas the spike obtained with the causal filter is not (low-right panel). C) For different SNRs, higher cut-off frequencies of the high-pass filter lead to worse spike detection for the Elliptic (left panel), Butterworth (center panel), and Bessel (right panel) filters.

Figure 3. Effect of sampling rate and signal resolution on spike detection.

A-B) Spike detection performance for different sampling rates (A) or signal resolutions (B) for high (green), medium (yellow), and low (red) SNRs.

Figure 4. Effect of sampling rate and signal resolution on spike sorting and template building.

A-B) Spike sorting performance for different sampling rates (A) and signal resolutions (B) for high (green), medium (yellow), and low (red) SNRs. C) Illustration of how different clusters (single-unit #2 and #3) are mixed up due to sampling limitations. For this example, a sampling rate of 7 kHz and a signal resolution of 10 bits allow correct identification of the three clusters.

Figure 5. Hybrid strategy for real-time spike sorting.

A) In the Template Building Stage, spikes are detected in real time after filtering and ADC of the signal. Unsorted spike events are streamed to a power-demanding computer where templates are built and sent to the low-power platform. B) In the Template Matching Stage, spikes are detected in real time after filtering and ADC. Detected spikes are then compared to the templates via template matching. This method allows streaming only binary spike events with a label indicating which neuron fired at each time.

Figure 6. Effect of sampling rate and signal resolution on real-time template matching for different metrics.

A-B) For simulations with Medium SNR, template matching performance for different sampling rates (A), signal resolutions (B) and different metrics: Norm 1 (red), Mahalanobis (cyan), Norm Infinite (green), Squared Euclidean (blue), and Nearest Neighbors (black). C-D) Template matching performance for different sampling rates (C) and signal resolutions (D) for the Squared Euclidean distance and for high (green), medium (yellow), and low (red) SNRs. E) Relative complexity of each metric for signals with 28 kHz and 16-bit resolution. Values are normalized to the metric with least complexity (Squared Euclidean distance). F) Relative complexity of the Squared Euclidean distance for different sampling rates and signal resolutions. Values are normalized to the condition with highest complexity (28 kHz and 16-bit resolution).

Figure 7. Effect of misalignment and window size on template matching.

A) Template matching performance for different metrics and different jitter values in the peak alignment of the spikes. B) Template matching performance for different metrics and for spikes with different window sizes. For both cases, data was sampled at 28 kHz with a 16-bit resolution.

Figure 8. Validating minimum requirements with real data.

A) Clusters detected in one real extracellular recording, obtained from the human medial temporal lobe, using highest specifications (28 kHz and 16-bit resolution) and offline data processing (i.e. non-causal filters). The blue cluster represents multi-unit activity whereas the red and green clusters represent two different single units. B) Same as A) but using the minimum signal requirements found in this study (7 kHz and 10-bit resolution) and real-time data processing (i.e. causal filters). C) Spike detection, spike sorting, and template matching performance obtained with real extracellular recordings.