Recent progress in multi-electrode spike sorting methods

Abstract

In recent years, arrays of extracellular electrodes have been developed and manufactured to record simultaneously from hundreds of electrodes packed with a high density. These recordings should allow neuroscientists to reconstruct the individual activity of the neurons spiking in the vicinity of these electrodes, with the help of signal processing algorithms. Algorithms need to solve a source separation problem, also known as spike sorting. However, these new devices challenge the classical way to do spike sorting. Here we review different methods that have been developed to sort spikes from these large-scale recordings. We describe the common properties of these algorithms, as well as their main differences. Finally, we outline the issues that remain to be solved by future spike sorting algorithms.

Keywords: Electrophysiology; Microelectrode array; Multi-electrode array; Signal processing; Spike sorting; Template matching.

Figure 1

The template matching approach. A: illustration of the iterative template matching approach. The extracellular signal (in blue, shown for 20 electrodes) is matched iteratively with a sum of templates. At each step, a template is added to the signal (red) to match better the data. At the end, all the spikes are fitted by a template, and the sum of templates (red) predict very well the data (blue). B: example of a single template over 16 electrodes. C: example of amplitude values fitted to the data for one template, as a function of time. Gray lines represent the average amplitude over time, and the minimal amplitude over time (see text for details).

Figure 2

Illustration of biased amplitudes toward 1 when minimizing the log-likelihood. A: Comparison of the error function used for the optimization of the amplitudes. Mean squared error of the residual, as described in equation 6 (blue). Penalty which comes from a regularization with a Gaussian distribution on the amplitude values (red). Log-likelihood, as described in equation 7 (green). The dotted vertical lines indicate the minimium of each of these error functions. B: Illustration of the results of the fit, with optimal scaled waveforms for each error function superimposed onto the raw data (gray), colorcoded as in A. C: Residuals (fit minus raw data) for each of those error functions, colorcoded as in A.

Figure 3

Illustrations of the assumptions of the template matching in the clustering space. A: Example of two clusters in the feature space, when assuming that they are generated by templates with no amplitude variation. B: Same than A, but now with the assumption that the template can vary in amplitude according a Gaussian distribution. C: Equivalent borders (see text) for the clusters for a template matching that chooses the template closest to the spike. D: Equivalent borders in the case where the template is chosen based on the spike shape, and that only a certain range of amplitude is allowed. See text for details.