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A model-based spike sorting algorithm for removing correlation artifacts in multi-neuron recordings.

Pillow JW, Shlens J, Chichilnisky EJ, Simoncelli EP - PLoS ONE (2013)

Bottom Line: Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data.We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit".The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate.

View Article: PubMed Central - PubMed

Affiliation: Center for Perceptual Systems, Department of Psychology and Section of Neurobiology, The University of Texas at Austin, Austin, Texas, USA. pillow@mail.utexas.edu

ABSTRACT
We examine the problem of estimating the spike trains of multiple neurons from voltage traces recorded on one or more extracellular electrodes. Traditional spike-sorting methods rely on thresholding or clustering of recorded signals to identify spikes. While these methods can detect a large fraction of the spikes from a recording, they generally fail to identify synchronous or near-synchronous spikes: cases in which multiple spikes overlap. Here we investigate the geometry of failures in traditional sorting algorithms, and document the prevalence of such errors in multi-electrode recordings from primate retina. We then develop a method for multi-neuron spike sorting using a model that explicitly accounts for the superposition of spike waveforms. We model the recorded voltage traces as a linear combination of spike waveforms plus a stochastic background component of correlated Gaussian noise. Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data. We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit". The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate. This method substantially corrects cross-correlation artifacts that arise with conventional methods, and substantially outperforms clustering methods on both real and simulated data. Finally, we develop diagnostic tools that can be used to assess errors in spike sorting in the absence of ground truth.

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Cross-correlation artifacts induced by failure of clustering method for temporally overlapping spikes.(A) The cross-correlation function (CCF), which expresses the firing rate of one neuron relative to the spike times of another neuron. The CCF shows a substantial elevation in the firing of the primary cell in a time window extending roughly ± 5 ms around the spike of the secondary cell, as well as a sharp notch at the origin (width roughly ± 1 ms). The timescale of this notch matches the range of times over which the waveforms interfere with each other, as shown in Figure 1. (B) Summary of pairwise cross-correlations for all adjacent ON retinal ganglion cells within a simultaneously recorded population (338 pairs). Each row of the image represents the CCF between a pair of cells (shade of grey represents firing rate relative to the mean). Rows are sorted according to the value of the center time bin. (C) For pairs of neurons with significant synchronized firing, the magnitude of the secondary spike waveform (corresponding to the length of the red vector in Figure 1 ) provides a strong prediction of the strength of the CCF artifact (). We quantify the strength of the CCF artifact (index on vertical axis) as the difference between the average firing rate during the intervals of  ms and  ms, divided by the baseline firing rate.
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pone-0062123-g002: Cross-correlation artifacts induced by failure of clustering method for temporally overlapping spikes.(A) The cross-correlation function (CCF), which expresses the firing rate of one neuron relative to the spike times of another neuron. The CCF shows a substantial elevation in the firing of the primary cell in a time window extending roughly ± 5 ms around the spike of the secondary cell, as well as a sharp notch at the origin (width roughly ± 1 ms). The timescale of this notch matches the range of times over which the waveforms interfere with each other, as shown in Figure 1. (B) Summary of pairwise cross-correlations for all adjacent ON retinal ganglion cells within a simultaneously recorded population (338 pairs). Each row of the image represents the CCF between a pair of cells (shade of grey represents firing rate relative to the mean). Rows are sorted according to the value of the center time bin. (C) For pairs of neurons with significant synchronized firing, the magnitude of the secondary spike waveform (corresponding to the length of the red vector in Figure 1 ) provides a strong prediction of the strength of the CCF artifact (). We quantify the strength of the CCF artifact (index on vertical axis) as the difference between the average firing rate during the intervals of ms and ms, divided by the baseline firing rate.

Mentions: The failure to correctly identify near-synchronous spikes in a pair of neurons leads to an artifact that can be observed directly. Figure 2 A shows the cross-correlation function (CCF) between recovered spike trains of an adjacent pair of ON parasol retinal ganglion cells (RGCs), which are known to exhibit some synchrony in their spiking. The cross-correlation function provides an estimate of the instantaneous spike rate of the second cell relative to the time of a spike in the first cell. The plot in Figure 2 A shows an increase in rate over the interval ms, which is typical for the timescale of synchrony in these cells [33]–[35]. But one can also see a pronounced CCF notch in the interval ms, which corresponds to the most highly synchronized spikes. This notch has been observed in extracellular but not intracellular recordings [34], [36], and its duration is matched to the interval over which the clustering failures identified in Figure 1 occur. These two facts suggest that the notch is an artifact that corresponds to spikes that the clustering method has failed to identify.


A model-based spike sorting algorithm for removing correlation artifacts in multi-neuron recordings.

Pillow JW, Shlens J, Chichilnisky EJ, Simoncelli EP - PLoS ONE (2013)

Cross-correlation artifacts induced by failure of clustering method for temporally overlapping spikes.(A) The cross-correlation function (CCF), which expresses the firing rate of one neuron relative to the spike times of another neuron. The CCF shows a substantial elevation in the firing of the primary cell in a time window extending roughly ± 5 ms around the spike of the secondary cell, as well as a sharp notch at the origin (width roughly ± 1 ms). The timescale of this notch matches the range of times over which the waveforms interfere with each other, as shown in Figure 1. (B) Summary of pairwise cross-correlations for all adjacent ON retinal ganglion cells within a simultaneously recorded population (338 pairs). Each row of the image represents the CCF between a pair of cells (shade of grey represents firing rate relative to the mean). Rows are sorted according to the value of the center time bin. (C) For pairs of neurons with significant synchronized firing, the magnitude of the secondary spike waveform (corresponding to the length of the red vector in Figure 1 ) provides a strong prediction of the strength of the CCF artifact (). We quantify the strength of the CCF artifact (index on vertical axis) as the difference between the average firing rate during the intervals of  ms and  ms, divided by the baseline firing rate.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3643981&req=5

pone-0062123-g002: Cross-correlation artifacts induced by failure of clustering method for temporally overlapping spikes.(A) The cross-correlation function (CCF), which expresses the firing rate of one neuron relative to the spike times of another neuron. The CCF shows a substantial elevation in the firing of the primary cell in a time window extending roughly ± 5 ms around the spike of the secondary cell, as well as a sharp notch at the origin (width roughly ± 1 ms). The timescale of this notch matches the range of times over which the waveforms interfere with each other, as shown in Figure 1. (B) Summary of pairwise cross-correlations for all adjacent ON retinal ganglion cells within a simultaneously recorded population (338 pairs). Each row of the image represents the CCF between a pair of cells (shade of grey represents firing rate relative to the mean). Rows are sorted according to the value of the center time bin. (C) For pairs of neurons with significant synchronized firing, the magnitude of the secondary spike waveform (corresponding to the length of the red vector in Figure 1 ) provides a strong prediction of the strength of the CCF artifact (). We quantify the strength of the CCF artifact (index on vertical axis) as the difference between the average firing rate during the intervals of ms and ms, divided by the baseline firing rate.
Mentions: The failure to correctly identify near-synchronous spikes in a pair of neurons leads to an artifact that can be observed directly. Figure 2 A shows the cross-correlation function (CCF) between recovered spike trains of an adjacent pair of ON parasol retinal ganglion cells (RGCs), which are known to exhibit some synchrony in their spiking. The cross-correlation function provides an estimate of the instantaneous spike rate of the second cell relative to the time of a spike in the first cell. The plot in Figure 2 A shows an increase in rate over the interval ms, which is typical for the timescale of synchrony in these cells [33]–[35]. But one can also see a pronounced CCF notch in the interval ms, which corresponds to the most highly synchronized spikes. This notch has been observed in extracellular but not intracellular recordings [34], [36], and its duration is matched to the interval over which the clustering failures identified in Figure 1 occur. These two facts suggest that the notch is an artifact that corresponds to spikes that the clustering method has failed to identify.

Bottom Line: Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data.We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit".The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate.

View Article: PubMed Central - PubMed

Affiliation: Center for Perceptual Systems, Department of Psychology and Section of Neurobiology, The University of Texas at Austin, Austin, Texas, USA. pillow@mail.utexas.edu

ABSTRACT
We examine the problem of estimating the spike trains of multiple neurons from voltage traces recorded on one or more extracellular electrodes. Traditional spike-sorting methods rely on thresholding or clustering of recorded signals to identify spikes. While these methods can detect a large fraction of the spikes from a recording, they generally fail to identify synchronous or near-synchronous spikes: cases in which multiple spikes overlap. Here we investigate the geometry of failures in traditional sorting algorithms, and document the prevalence of such errors in multi-electrode recordings from primate retina. We then develop a method for multi-neuron spike sorting using a model that explicitly accounts for the superposition of spike waveforms. We model the recorded voltage traces as a linear combination of spike waveforms plus a stochastic background component of correlated Gaussian noise. Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data. We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit". The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate. This method substantially corrects cross-correlation artifacts that arise with conventional methods, and substantially outperforms clustering methods on both real and simulated data. Finally, we develop diagnostic tools that can be used to assess errors in spike sorting in the absence of ground truth.

Show MeSH
Related in: MedlinePlus