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Fast, scalable, Bayesian spike identification for multi-electrode arrays.

Prentice JS, Homann J, Simmons KD, Tkačik G, Balasubramanian V, Nelson PC - PLoS ONE (2011)

Bottom Line: Our method can distinguish large numbers of distinct neural units, even when spikes overlap, and accounts for intrinsic variability of spikes from each unit.Human interaction plays a key role in our method; but effort is minimized and streamlined via a graphical interface.We illustrate our method on data from guinea pig retinal ganglion cells and document its performance on simulated data consisting of spikes added to experimentally measured background noise.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America. jprentic@sas.upenn.edu

ABSTRACT
We present an algorithm to identify individual neural spikes observed on high-density multi-electrode arrays (MEAs). Our method can distinguish large numbers of distinct neural units, even when spikes overlap, and accounts for intrinsic variability of spikes from each unit. As MEAs grow larger, it is important to find spike-identification methods that are scalable, that is, the computational cost of spike fitting should scale well with the number of units observed. Our algorithm accomplishes this goal, and is fast, because it exploits the spatial locality of each unit and the basic biophysics of extracellular signal propagation. Human interaction plays a key role in our method; but effort is minimized and streamlined via a graphical interface. We illustrate our method on data from guinea pig retinal ganglion cells and document its performance on simulated data consisting of spikes added to experimentally measured background noise. We present several tests demonstrating that the algorithm is highly accurate: it exhibits low error rates on fits to synthetic data, low refractory violation rates, good receptive field coverage, and consistency across users.

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After fitting spikes, only noise remains.(A) Noise covariance after spatial whitening. Subpanels: spacetime covariance  between the central channel and its neighbors as a function of , for various fixed  (colored curves). Central panel (dotted line): the function . (The various  lines and the dotted line are too similar to discriminate visually.) Horizontal axes:  in ; Vertical axes:  in . (B) Blue curve, Semilog plot of the one point marginal probability density function of decorrelated noise samples. Red curve, same quantity, evaluated on residuals after spikes have been removed from spike events. Dotted curve, The Gaussian chosen to represent this distribution. (C) Green, detail of the same template waveform shown in Fig. 5. Red, pointwise mean of the residuals after the fit spike is subtracted from 4,906 one-spike events of this type is nearly flat. This validates our assumption that spikes vary only in overall amplitude, and that noise is independent of spiking. Blue, pointwise standard deviation of the residuals, again evidence that only noise remains after fitting and subtracting spikes. (D, top) Histogram of fit values of the scale factor  for a template with peak amplitude  (well above noise) obtained without a prior on , superposed with a Gaussian of the same mean and variance. (D, bottom) Similar histogram for a low amplitude template. A secondary bump appears, due to noise-fits, but is well separated from the main peak; a cutoff is shown as a dashed green line. The superposed Gaussian has mean and variance computed from the part of the empirical distribution lying above the cutoff.
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pone-0019884-g006: After fitting spikes, only noise remains.(A) Noise covariance after spatial whitening. Subpanels: spacetime covariance between the central channel and its neighbors as a function of , for various fixed (colored curves). Central panel (dotted line): the function . (The various lines and the dotted line are too similar to discriminate visually.) Horizontal axes: in ; Vertical axes: in . (B) Blue curve, Semilog plot of the one point marginal probability density function of decorrelated noise samples. Red curve, same quantity, evaluated on residuals after spikes have been removed from spike events. Dotted curve, The Gaussian chosen to represent this distribution. (C) Green, detail of the same template waveform shown in Fig. 5. Red, pointwise mean of the residuals after the fit spike is subtracted from 4,906 one-spike events of this type is nearly flat. This validates our assumption that spikes vary only in overall amplitude, and that noise is independent of spiking. Blue, pointwise standard deviation of the residuals, again evidence that only noise remains after fitting and subtracting spikes. (D, top) Histogram of fit values of the scale factor for a template with peak amplitude (well above noise) obtained without a prior on , superposed with a Gaussian of the same mean and variance. (D, bottom) Similar histogram for a low amplitude template. A secondary bump appears, due to noise-fits, but is well separated from the main peak; a cutoff is shown as a dashed green line. The superposed Gaussian has mean and variance computed from the part of the empirical distribution lying above the cutoff.

Mentions: The goal of spike fitting is to identify, for each spike event, all the units which contribute to the event and their firing times irrespective of their amplitudes . Thus we assumed a probabilistic generative model of the data [8], [21]–[23] and computed the posterior probability of given the observed data. We assumed that a spike event could be explained by a linear combination of templates with variable amplitudes and correlated, zero-mean Gaussian noise :(1)Here is the (a priori unknown) number of units contributing to the event. Given this model, to obtain the posterior probability that a firing event consists of a particular set of templates, we need to specify the prior probability of , , and . We chose a Gaussian prior for the amplitude , a Poisson prior for , and a uniform prior for . Although is a strictly positive quantity, we modeled its distribution with a Gaussian for analytical tractability. In practice, the distribution of was tightly concentrated around its mean of approximately and the Gaussian approximation had negligible weight at negative values (Fig. 6D).


Fast, scalable, Bayesian spike identification for multi-electrode arrays.

Prentice JS, Homann J, Simmons KD, Tkačik G, Balasubramanian V, Nelson PC - PLoS ONE (2011)

After fitting spikes, only noise remains.(A) Noise covariance after spatial whitening. Subpanels: spacetime covariance  between the central channel and its neighbors as a function of , for various fixed  (colored curves). Central panel (dotted line): the function . (The various  lines and the dotted line are too similar to discriminate visually.) Horizontal axes:  in ; Vertical axes:  in . (B) Blue curve, Semilog plot of the one point marginal probability density function of decorrelated noise samples. Red curve, same quantity, evaluated on residuals after spikes have been removed from spike events. Dotted curve, The Gaussian chosen to represent this distribution. (C) Green, detail of the same template waveform shown in Fig. 5. Red, pointwise mean of the residuals after the fit spike is subtracted from 4,906 one-spike events of this type is nearly flat. This validates our assumption that spikes vary only in overall amplitude, and that noise is independent of spiking. Blue, pointwise standard deviation of the residuals, again evidence that only noise remains after fitting and subtracting spikes. (D, top) Histogram of fit values of the scale factor  for a template with peak amplitude  (well above noise) obtained without a prior on , superposed with a Gaussian of the same mean and variance. (D, bottom) Similar histogram for a low amplitude template. A secondary bump appears, due to noise-fits, but is well separated from the main peak; a cutoff is shown as a dashed green line. The superposed Gaussian has mean and variance computed from the part of the empirical distribution lying above the cutoff.
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Related In: Results  -  Collection

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pone-0019884-g006: After fitting spikes, only noise remains.(A) Noise covariance after spatial whitening. Subpanels: spacetime covariance between the central channel and its neighbors as a function of , for various fixed (colored curves). Central panel (dotted line): the function . (The various lines and the dotted line are too similar to discriminate visually.) Horizontal axes: in ; Vertical axes: in . (B) Blue curve, Semilog plot of the one point marginal probability density function of decorrelated noise samples. Red curve, same quantity, evaluated on residuals after spikes have been removed from spike events. Dotted curve, The Gaussian chosen to represent this distribution. (C) Green, detail of the same template waveform shown in Fig. 5. Red, pointwise mean of the residuals after the fit spike is subtracted from 4,906 one-spike events of this type is nearly flat. This validates our assumption that spikes vary only in overall amplitude, and that noise is independent of spiking. Blue, pointwise standard deviation of the residuals, again evidence that only noise remains after fitting and subtracting spikes. (D, top) Histogram of fit values of the scale factor for a template with peak amplitude (well above noise) obtained without a prior on , superposed with a Gaussian of the same mean and variance. (D, bottom) Similar histogram for a low amplitude template. A secondary bump appears, due to noise-fits, but is well separated from the main peak; a cutoff is shown as a dashed green line. The superposed Gaussian has mean and variance computed from the part of the empirical distribution lying above the cutoff.
Mentions: The goal of spike fitting is to identify, for each spike event, all the units which contribute to the event and their firing times irrespective of their amplitudes . Thus we assumed a probabilistic generative model of the data [8], [21]–[23] and computed the posterior probability of given the observed data. We assumed that a spike event could be explained by a linear combination of templates with variable amplitudes and correlated, zero-mean Gaussian noise :(1)Here is the (a priori unknown) number of units contributing to the event. Given this model, to obtain the posterior probability that a firing event consists of a particular set of templates, we need to specify the prior probability of , , and . We chose a Gaussian prior for the amplitude , a Poisson prior for , and a uniform prior for . Although is a strictly positive quantity, we modeled its distribution with a Gaussian for analytical tractability. In practice, the distribution of was tightly concentrated around its mean of approximately and the Gaussian approximation had negligible weight at negative values (Fig. 6D).

Bottom Line: Our method can distinguish large numbers of distinct neural units, even when spikes overlap, and accounts for intrinsic variability of spikes from each unit.Human interaction plays a key role in our method; but effort is minimized and streamlined via a graphical interface.We illustrate our method on data from guinea pig retinal ganglion cells and document its performance on simulated data consisting of spikes added to experimentally measured background noise.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America. jprentic@sas.upenn.edu

ABSTRACT
We present an algorithm to identify individual neural spikes observed on high-density multi-electrode arrays (MEAs). Our method can distinguish large numbers of distinct neural units, even when spikes overlap, and accounts for intrinsic variability of spikes from each unit. As MEAs grow larger, it is important to find spike-identification methods that are scalable, that is, the computational cost of spike fitting should scale well with the number of units observed. Our algorithm accomplishes this goal, and is fast, because it exploits the spatial locality of each unit and the basic biophysics of extracellular signal propagation. Human interaction plays a key role in our method; but effort is minimized and streamlined via a graphical interface. We illustrate our method on data from guinea pig retinal ganglion cells and document its performance on simulated data consisting of spikes added to experimentally measured background noise. We present several tests demonstrating that the algorithm is highly accurate: it exhibits low error rates on fits to synthetic data, low refractory violation rates, good receptive field coverage, and consistency across users.

Show MeSH
Related in: MedlinePlus