High-pass filtering an average CA1 spike waveform.

<p>The figure shows the effect of passing the spike waveform from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082141#pone-0082141-g001" target="_blank">Figure 1B</a> through various high-pass filters, after inserting it into the recorded hippocampal local field potential. The red trace indicates the inserted waveform (and thus the desired output), the blue trace indicates the average of the filtered signal with standard deviation in the error bars. High-pass filtering frequencies increase from 12.5 Hz (top) to 800 Hz (bottom). An order-2 Butterworth filter is used for the left column, a single-pole (RC) filter is used for the right column. The filter-types were chosen because they correspond to common filter designs used for extracellular multi-unit recording. The gradual development of the waveform distortion is evident from the upper to the lower panels, with significant distortion already ad 12.5 Hz for order-2 Butterworth and 12 Hz for RC. The waveform distortion includes narrowing of the spike, depression of the amplitude, and positive over-shoot after the spike. The red and blue arrows indicate the peak amplitude of the inserted signal (red traces) and the average filtered signals (blue traces). The distance between the blue and red arrow indicate the bias in the amplitude estimate. The development of the amplitude bias in the left column is also shown in greater detail by the dotted lines in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082141#pone-0082141-g005" target="_blank">Figure 5A–E</a>.</p

Waveform estimation with spike-triggered average and multiple regression.

<p>(<b>A–F</b>) Estimation of a biphasic square-wave pulse phase-locked to different theta phases with spike-triggered average (A–C) and multiple regression (D–F). The red line corresponds to a dummy signal inserted into the hippocampal LFP. The blue line shows the average regression or filter estimates with standard deviations in the error bars. (<b>G–L</b>) Estimation of an extracellular spike phase-locked to different theta phases with spike-triggered average (G–I) and multiple regression (J–L). The full depth profile from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082141#pone-0082141-g001" target="_blank">Figure 1A</a> was inserted into the hippocampal LFP. Spike-triggered average produces larger standard deviation and phase-dependent systematic error.</p

Depth profile and wavelet spectrum of the spike triggered hippocampal LFP.

<p>(<b>A</b>) Depth profile of the local field potential (LFP) in the mouse hippocampus, subfields CA1 and DG. The plotted signals are average LFP traces triggered on the action potentials from an isolated CA1 pyramidal cell. The LFP was recorded using a 16-site laminar electrode array, with 50 µm between the recording sites. The LFP traces are broad-band filtered between 0.5 Hz and 6 kHz. (<b>B</b>) Wavelet spectrum (Paul mother wavelet, m = 4) of the fourth LFP trace in panel A, counting from the top, <i>i.e.</i> the one with the strongest spike amplitude in the CA1 LFP. The relative signal power is color coded from red (highest) to blue (no signal). Common high-pass filtering frequencies used for extracellular multi-unit recording (300 Hz and 600 Hz) intersects the bulk of the wavelet spectrum. The waveform corresponding to the wavelet spectrum is shown in white. The Paul wavelet was chosen because its asymmetric shape and high temporal resolution and makes it well suited for analyzing spike waveforms.</p

LFP predictions from linear filters and multiple regression.

<p>(<b>A</b>) Prediction of LFP (blue) and spikes (black) using order-2 Butterworth filters at 600 Hz. The original broad-band signal is shown in red. The distortion of the spike waveform can be seen in the expanded traces in B. (<b>B</b>) Example of an extracellular spike in the original signal (red) and the corresponding high-pass (black) and low-pass (blue) filtered traces using an order-2 Butterworth filter. (<b>C</b>) Prediction of LFP and spikes using linear regression, with a sliding time-window of 100 ms. There is higher noise in the LFP estimate (blue in B) and the spike estimate (black in B) than in the original broad-band signal (red in A) and the filtered spike trace (black in A). (<b>D</b>) The same spike with original broad-band signal (red) residual from multiple regression (black) and LFP prediction from multiple regression (blue).</p

Principle for modelling and subtracting the LFP.

<p>(<b>A</b>) Rostrocaudal localization of the laminar electrode array used to record the local field potential (LFP) in the mouse hippocampus. (<b>B</b>) Localization of the laminar electrode array in the coronal plane of the mouse brain (lateromedial and dorsoventral localization). (<b>C</b>) The panel shows the time windows used to model the LFP. The dashed red line is a tricube window (here: 100 ms wide) used to get a local estimate around the spike in the center (0 ms). The dashed green line is flipped tricube windows used to remove the influence of the spike waveform from the fitted LFP model. Three spikes are edited out. The solid red line is the weight function actually used to estimate the regression model, computed as the product of the dashed red and green lines. The corresponding LFP signal is shown in blue. The dashed black line is the DC level. (<b>D</b>) Depth profile of temporally weighted LFP traces recorded from the mouse hippocampus. A microscope image of the tip of the laminar electrode array is shown in the background. The 16 light spots in the center of the probe are the recording sites. The electrode array can be seen to cover the full depth profile trough the hippocampal layers from CA1 to DG. Recording from a set of reference channels in a laminar electrode can give an estimate of the local field potential on a different channel with spikes, thus allowing the estimated LFP to be subtracted in order to recover the spike waveforms from the LFP. The recovered waveforms are expressed as the prediction errors. The illustrations of the mouse brain (<b>A</b>, <b>B</b> and <b>D</b>) are adapted from Paxinos and Franklin <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082141#pone.0082141-Paxinos1" target="_blank">[56]</a>.</p

Waveform estimation with high-pass filtering and multiple regression.

<p>(<b>A–C</b>) Estimation of a biphasic square-wave pulse using (A) multiple regression, (B) on-line high-pass filter, or (C) anti-causal high-pass filter. The red line corresponds to a dummy signal inserted into the hippocampal LFP. The blue line shows the average regression or filter estimates with standard deviations in the error bars. (<b>D–F</b>) Estimation of an extracellular spike with the same methods as in A–F. The full depth profile from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082141#pone-0082141-g001" target="_blank">Figure 1A</a> was inserted into the hippocampal LFP.</p

Estimating Extracellular Spike Waveforms from CA1 Pyramidal Cells with Multichannel Electrodes

<div><p>Extracellular (EC) recordings of action potentials from the intact brain are embedded in background voltage fluctuations known as the “local field potential” (LFP). In order to use EC spike recordings for studying biophysical properties of neurons, the spike waveforms must be separated from the LFP. Linear low-pass and high-pass filters are usually insufficient to separate spike waveforms from LFP, because they have overlapping frequency bands. Broad-band recordings of LFP and spikes were obtained with a 16-channel laminar electrode array (silicone probe). We developed an algorithm whereby local LFP signals from spike-containing channel were modeled using locally weighted polynomial regression analysis of adjoining channels without spikes. The modeled LFP signal was subtracted from the recording to estimate the embedded spike waveforms. We tested the method both on defined spike waveforms added to LFP recordings, and on in vivo-recorded extracellular spikes from hippocampal CA1 pyramidal cells in anaesthetized mice. We show that the algorithm can correctly extract the spike waveforms embedded in the LFP. In contrast, traditional high-pass filters failed to recover correct spike shapes, albeit produceing smaller standard errors. We found that high-pass RC or 2-pole Butterworth filters with cut-off frequencies below 12.5 Hz, are required to retrieve waveforms comparable to our method. The method was also compared to spike-triggered averages of the broad-band signal, and yielded waveforms with smaller standard errors and less distortion before and after the spike.</p></div

Amplitude distribution and clustering-cutting scatter-plots.

<p>(<b>A</b>) Predicted amplitudes of EC spikes with variable amplitudes using high-pass filtering (open circles) or multiple regression (filled dots). The dashed diagonal indicates perfect estimate. The amplitude estimated from high-pass filtering is negatively biased, whereas regression produces an unbiased estimate. (<b>B</b>) Average waveforms with standard deviation from the cell isolated in A and B. It can be seen how high-pass filtering delays the waveform, depresses the amplitude, and adds a trailing “bump”. (<b>C–D</b>) Scatter-plot of the amplitudes of recorded EC spikes from CA1 cells on three channels (range 0–350 µV) on a laminar electrode using high-pass filtering (C) and multiple regression (D). The shape of the cluster of amplitudes produced by an isolated cell (red dots) is indicated with a transparent red surface. It can be seen how high-pass filtering and multiple regression produce different ranges and correlation structures for spike amplitudes of the cell.</p

Effect of filtering frequency and time window size on the prediction error and variability.

<p>(<b>A–D</b>) Quantification of the frequency dependent spike-waveform distortion from an order-2 Butterworth high-pass filter. The red and green lines show the root mean square (RMS) errors in the 1.5 ms before and after the spike. The solid black line shows the standard deviation of the filtered amplitude at the peak of the spike. The dashed black line shows the bias (absolute error) in the spike amplitude. (<b>E</b>) The effect of time window size on the waveform distortion from the regression estimator. (<b>F</b>) The effect of time window size on the variability in the LFP regression estimate. The standard deviation is smallest around 100 ms, which corresponds to half the period of a theta cycle (5 Hz) in the hippocampal LFP under these recording conditions (urethane anesthesia).</p