Automatic spike detection based on adaptive template matching for

Journal of Neuroscience Methods 165 (2007) 165–174

Automatic spike detection based on adaptive template matching for extracellular neural recordings Sunghan Kim ∗ , James McNames 1 Biomedical Signal Processing Laboratory, Electrical & Computer Engineering, Portland State University, Portland, OR, USA Received 23 January 2007; received in revised form 26 May 2007; accepted 26 May 2007

Abstract Recordings of extracellular neural activity are used in many clinical applications and scientific studies. In most cases, these signals are analyzed as a point process, and a spike detection algorithm is required to estimate the times at which action potentials occurred. Recordings from high-density microelectrode arrays (MEAs) and low-impedance microelectrodes often have a low signal-to-noise ratio (SNR < 10) and contain action potentials from more than one neuron. We describe a new detection algorithm based on template matching that only requires the user to specify the minimum and maximum firing rates of the neurons. The algorithm iteratively estimates the morphology of the most prominent action potentials. It is able to achieve a sensitivity of >90% with a false positive rate of 2.5. © 2007 Elsevier B.V. All rights reserved. Keywords: Spike detection; Spike discrimination; Extracellular neuronal recordings; Spike train; Action potential; Matched filter; Eigenfilter; Threshold selection

1. Introduction Most analysis techniques for recordings of extracellular neural activity begin with spike detection to identify the times at which action potentials occurred from one or more neurons. Until recently, spike detection was performed using simple threshold detectors or window discriminators implemented in analog hardware. These are sufficient for intracellular recordings and extracellular recordings in which the investigator can select a high-impedance electrode that can be manually placed to isolate a single neuron and reduce background noise. In many current applications it is not possible to precisely place extracellular electrodes to isolate a single neuron. Recent studies have applied one- and two-dimensional microelectrode arrays (MEAs), microwire arrays, and silicon substrate arrays

∗ Corresponding author at: Fourth Avenue Building, Room 89-02, 1900 SW 4th Avenue Portland, OR 97201, USA. Tel.: +1 503 725 5399; fax: +1 503 725 3807. E-mail addresses: [email protected] (S. Kim), [email protected] (J. McNames). 1 Present address: Fourth Avenue Building, Room 160-12, 1900 SW 4th Avenue, Portland, OR 97201, USA. Tel.: +1 503 725 5390; fax: +1 503 725 3807.

0165-0270/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2007.05.033

that generally have higher levels of background noise and do not permit microelectrodes to be positioned to isolate the activity of single neurons (Potter et al., 2005; Hasegawa et al., 2004; Branner and Normann, 2000; Bell et al., 1998; DellaSantina et al., 1997; Zhelyaskov et al., 1995). Because these recordings are obtained from many sites, it is also impractical for investigators to manually tune spike detection algorithms and select thresholds to achieve acceptable performance from their spike detectors. Similarly, in stereotactic neurosurgery microelectrodes cannot be precisely placed to isolate the activity of single neurons. Low-impedance electrodes ( di+1 . 2.3.2. Density estimator If the similarity maxima due to the most prominent action potentials are distinct from background noise and other action potentials, the probability density function (PDF) of similarity maxima should contain at least two distinct modes: a mode close to zero due to noise and a mode centered at larger amplitudes due to action potentials. If the recordings include the activity of two or more neurons with action potentials that are distinct from the noise, the PDF may contain separate modes for each neuron. This stage estimates the PDF of maxima with a kernel density estimator (Wand and Jones, 1995). The subsequent stage uses this estimate to select a threshold between the modes. Fig. 3 shows an example of the estimated PDF with two significant modes. The kernel density estimator can be expressed as,  Nk  1  d − di ˆ f (d) = b Nk σb i=1

Fig. 3. Estimated PDF of local maxima of d(n) and the threshold selected by the algorithm. The top plot uses a large vertical range to show the relative size of the primary mode due to noise. The bottom plot uses a narrow vertical range to show the shape of the estimated PDF and several local minima that serve as initial threshold candidates. The rightmost two local minima were excluded by the threshold selection stage because they were not deep enough relative to adjacent maxima.

where fˆ(d) is the estimated PDF, b(·) the kernel, and σ b is the kernel width. Our implementation uses a clipped Gaussian kernel function, ⎧  2 ⎪ ⎨ √1 exp −u −5 < u < 5 (4) b(u) = 2 2π ⎪ ⎩0 otherwise. The accuracy of the estimate is insensitive to the shape of the kernel, but is sensitive to the kernel width. We used σ b = 0.7 × IQR(D), where IQR(·) is the interquartile range of the similarity maxima D. The density only needs to be estimated over its nonzero range of (dNk − 5σb ) ≤ d ≤ (d1 + 5σb ) with a resolution sufficient to locate maxima and minima of fˆ(d) precisely. Our implementation calculates the estimated PDF fˆ(d) at 1000 uniformly spaced points over this range. 2.3.3. Threshold selector The purpose of this stage is to select a threshold that distinguishes large maxima of d(n) due to prominent action potentials from small maxima due to noise and less prominent action potentials. All of the maxima above the threshold are declared spikes from a prominent single neuron. The mode caused by maxima due to the background noise is always larger than the modes corresponding to action potential maxima because peaks due to the background noise occur more frequently than peaks due to action potentials. This mode, called the primary mode, is easily identified by locating the largest maxima in the estimated PDF. If we denote the set of ordered maxima’s abscissas in the estimated PDF as P = {p1 , . . . , pNp }, then the primary mode peak’s abscissa, pp , can be expressed as pp = argmaxfˆ(d). d ∈P

(3)

(5)

The secondary mode due to the dominant action potentials is more difficult to locate. If the noise is excessive or the action

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potentials are of small amplitude, fˆ(d) may only contain a single mode due to the noise. In this case, this stage simply selects the largest nmin maxima of d(n), where nmin is the smallest number of spikes expected in the segment given the minimum firing rate. If the recordings contain action potentials from multiple neurons, fˆ(d) may contain several modes. Since we want to detect only the most prominent action potentials in the recording, this stage selects a threshold that separates the secondary mode from the other modes due to noise and less prominent action potentials from other neurons. This is achieved by placing the threshold τ at one of the local minima of fˆ(d) between the primary mode and the rightmost mode. We represent the set of candidate ordered thresholds as N = {n1 , . . . , nNn } where n1 is the first local minimum abscissa beyond the primary mode abscissa. We also define M = {m1 , . . . , mNm } as the set of ordered maxima’s abscissas that are beyond the primary mode such that m1 < n1 < m2 < . . . < nNn < mNm . Once the ordered maxima and minima are known, this stage separates minima that are too shallow to represent a division between modes from those that separate modes, which are treated as candidate thresholds. The criterion is given by fˆ(ni ) < v · min {fˆ(mi ), fˆ(mi+1 )}

(6)

where v is a user-specified parameter. This criterion ensures that the minima is no larger than v times the smallest neighboring maximum. We used v = 0.5. If fˆ{ni ) meets this criterion, it is considered a candidate threshold and placed in the set T. If fˆ{ni ) does not meet the criterion, ni and argmin {fˆ(mi ), fˆ(mi+1 )} are eliminated from N and M, respectively. This process is repeated for all of the minima in N. To help identify the secondary mode due to dominant action potentials, we can limit the search range by using our knowledge of the maximum and minimum expected firing rates. These can be used to bound the range of the number of expected spikes, nmin = Tfmin

nmax = Tfmax

(7)

where T is the duration of the signal and fmin and fmax are the minimum and maximum firing rates provided by the user. Thus, the secondary mode should contain no more than nmax maxima of signal d(n) and no fewer than nmin maxima. Since the maxima are listed in decreasing order, the minimum and maximum thresholds can be expressed as τmin = dnmax

τmax = dnmin

(8)

The threshold, τ, selected by the automatic threshold selector should be located between these limits, τ min ≤ τ ≤ τ max . When the estimated PDF, fˆ(d), does not have any local minima within threshold limits, the threshold, τ, is equal to τ max . When the estimated PDF, fˆ(d), has only one local minimum, τ is equal to the abscissa of the local minimum. Otherwise the threshold is selected as the largest of the candidate thresholds, T, τ = max{t : t ∈ T}.

(9)

Fig. 3 shows an example of an estimated PDF and an automatically selected threshold. In this case the algorithm was able to

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exclude two local minima from the set of threshold candidates using (6). After selecting the threshold, this stage produces the indices of maxima in d(n) that are above the threshold I = {ki : d(ki ) > τ, ki ∈ K}.

(10)

Thus, the set I = {i1 , . . . , iNi } contains the time indices of the detected spikes. 2.4. Template matching 2.4.1. Template estimation The morphology of an action potential is asymmetric because repolarization requires more time than depolarization. The total duration of one cycle of polarization is approximately 1 ms (Chandra and Optican, 1997). To account for this asymmetry, the template only spans a time range starting td prior to the peak and ending tr after the peak. We used td = 0.45 ms and tr = 0.55 ms. The model template for spikes is estimated based on segments of the original signal centered at the indices of local maxima I produced by the simple threshold detector. Specifically, the template is estimated as the median of these overlapping segments, t() = med{x(i1 + ), . . . , x(iNi + )}

(11)

where med{·} represents the median operator and  is the template time index. We use a median operator instead of the sample average or first principal component because the median is more robust to outliers caused by signal artifact and false positives, which are expected in the initial iterations of the algorithm. The index of the template () ranges from κd = − fs td  samples prior to each spike index to κp = fs tr  samples after each spike index, where fs is the sample rate of the signal. Fig. 4 shows two examples of aligned signal segments after the first and third iterations, and the corresponding estimated templates. 2.4.2. Cross-correlation Cross-correlation is a traditional similarity measure between the model template and a segment of the recording. This is the most popular similarity measure in signal processing applications because it can be calculated with traditional linear filter architectures by treating the template as the impulse response of an anti-causal FIR filter. It is widely used for matched filter and eigenfilter applications (Hall et al., 1971). The cross-correlation is defined as κp

 1 r(n) = x(n + )t(). κp − κ d + 1

(12)

=κd

2.5. Final decision logic During the final threshold selection, if the estimated PDF of d(n) maxima only contains one mode, this stage declares that no spikes could be detected. Otherwise, the stage produces the time indices (I) that represent the times at which the action potential

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achieve good performance. If these are not known, the user can conservatively select a wide range of possible firing rates, as we have done. 3. Methodology 3.1. Data collection We analyzed 50 real microelectrode recordings from the globus pallidus acquired during stereotactic neurosurgery for Parkinson’s disease in 20 subjects. The recordings were obtained from a specially designed monopolar tungsten microelectrode with a tip diameter of 1–2 ␮m and impedance in the range of 1.1–1.4 M at 1 kHz. The analog signal from the microelectrode was bandpass-filtered between 300 Hz and 10 kHz to eliminate baseline drift and limit noise. A notch filter was also used to more fully eliminate the 60 Hz component of the signal. The filtered signal was sampled at a rate of fs = 22 kHz and converted into a digital signal with a 16 bit linear serial sigma-delta analog-to-digital converter (ADC). Each recording was truncated to 2.5 s in duration. We scaled the recordings to have zero mean and unit variance. Further details are given in Favre et al. (1999). 3.2. Visual annotation Fig. 4. Centered 2 ms segments and the estimated model template for spikes after (a) the first and (b) third iterations.

peaks occurred. In recordings with no discernible action potentials, this limits false positives from producing misleading results in subsequent analysis. 2.6. Summary of design parameters Table 1 lists the design parameters for the algorithm and the values selected for all of the results reported in this article. These values were selected empirically during development of the algorithm. Although these parameters could be changed to improve performance in other applications, in general the user only needs to specify the minimum and maximum firing rates to Table 1 Summary of design parameters and functions Name

Symbol

Value

Order of signal power Lowpass filter impulse response Kernel function Kernel width Template duration prior to peak Template duration after peak Minimum firing rate Maximum firing rate Number of iterations Depth parameter

p h(n) b(u) σb td tr fmin fmax η v

2 Blackman Window Clipped Gaussian 0.7 × IQR(D) 0.45 ms 0.55 ms 5 Hz 250 Hz 3 0.5

Three volunteer annotators, all graduate students in Electrical and Computer Engineering at Portland State University with a background in signal processing, independently annotated all of the microelectrode recording segments based on visual inspection. They used custom software for this task. The software initially displayed a histogram of the signal maxima amplitudes and required the user to select an initial threshold. Using the displayed signal with detected maxima, the user inspected and, if necessary, edited the detected spikes. Once the annotators had independently performed the spike detection, they reviewed recordings as a group and reached consensus on the final spike occurrences. The consensus annotations were the standard of comparison for all subsequent performance analysis. 3.3. Performance measure We used the total error as our figure of merit for the detected spikes. The total error is defined as   FP + FN TE = 100 (13) TP + FN where FP is the number of false positives, FN the number of false negatives, and TP is the number of true positives. A true positive is counted for every consensus annotation if a spike was detected within an acceptance interval of ±0.5 ms. If more than one spike was detected within this interval, the additional detections were counted as false positives. The total error represents the number of detection errors relative to the actual number of spikes contained in the recording.

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3.4. Optimal threshold benchmark Throughout our algorithm assessment we compared the performance of the template-matching (TM) algorithm to an optimal threshold (OT) detector. This is a simple threshold detector that has been optimized to minimize the total error (13). After detecting each peak above the optimal threshold, all additional maxima for the following 1 ms lockout period were ignored to prevent multiple detections of a single event. This algorithm could not be applied in practical applications because it requires knowledge of the true spike times. Rather, it should be viewed as a benchmark that represents the best performance achievable with the simple threshold detector that is still in common use. 3.5. Algorithm assessment The signal enhancement and final decision logic were assessed separately. 3.5.1. Signal enhancement To measure the performance of the signal enhancement portion of the algorithm, we compared its performance with other methods by calculating the equivalent of receiver operator characteristic (ROC) curves. Canonical ROC curves display the sensitivity on the vertical axis and the fraction of false positives (1-specificity) on the horizontal axis. These are inappropriate in signal detection applications because the number of possible false positives scales linearly with the sample rate. To indicate the frequency of false positives, we expressed the false positives on the horizontal axis as the number of occurrences per unit of time (Hz), rather than as a fraction of the samples when the event did not occur. This measure of the false positive rate is invariant to changes in the sample rate of the signal. However, the false positive rate is not limited between 0 and 1 as they are in canonical ROC curves. Nonetheless, the tradeoff between sensitivity and specificity of the algorithms can be examined in these plots in the same manner as a canonical ROC curve. We compared the output of our signal enhancement stage after each iteration of the new algorithm. The first iteration produces smoothed power maxima as the signal enhancement output, d(n), and the last three iterations produce maxima of the cross-correlation between the template and the signal. We also generated the curves for a simple threshold (ST). 3.5.2. Decision logic We considered two different signal conditions. First, we added noise to the recordings to obtain a wide range of signal-tonoise (SNR) conditions. We extracted fifty 2.5 s noise segments from fifty microelectrode recordings and each segment contained visually indiscernible action potentials. The SNR of the recordings after adding noise was estimated as ˆ = SNR

σs2 − σn2 σn2

(14)

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where σs2 is the averaged variance of spike segments in the recordings and σn2 is the sample variance of noise segments of the recordings. Spike segments are defined as the portions of the recordings between 0.5 ms prior to and 0.8 ms after each spike peak. These segments contain both the spikes and the background noise. Noise segments are defined as the remaining portions of the signal with only background noise. We created 500 signals for each desired SNR value by randomly selecting combinations of the annotated signals and scaled noise segments. We then measured the accuracy of the two detection algorithms over a range of SNR values. We want to emphasize again that those 500 signals are not synthetic ones but combinations of real neuronal recordings with and without spikes. For the second condition, we measured the performance on multi-unit recordings, which are basically combinations of two neuronal recordings containing spikes. These signals were created by randomly selecting two of the annotated signals, adding ˆ = 5, scaling each noise as described above to obtain an SNR signal to have unit power, and combining them with a specified mixing ratio α. The composite recording can be expressed as xm (n) = (1 − α)x1 (n) + αx2 (n)

(15)

where xm (n) is the composite multi-unit signal, x1 (n) the first randomly selected recording, and x2 (n) is the second randomly selected recording. When α is close to zero, xm (n) is similar to a single-unit recording. When α is close to 0.5, xm (n) is a dual-unit recording with prominent action potentials from two independent neurons. 4. Results and discussion Table 2 lists the median and range of the sensitivity, false positive rate, and total error of the three annotators, the optimal threshold (OT) detector, and the template-matching (TM) algorithm on the original recordings without any added noise. All of these recordings contained clearly discernible dominant action potentials, so we expected nearly perfect agreement among all three annotators and the two detectors. As expected, all techniques performed very well with a perfect median performance as measured by all three metrics. Fig. 5(a) shows an example of the spikes detected when the ˆ = 3. Fig. 5(b) shows the same signal without any additional SNR ˆ = 10. This noise added. This segment has an estimated SNR figure demonstrates how challenging spike detection is at low Table 2 Performance summary of annotators (A1-3), optimal threshold (OT), and template matching (TM) on original recordings Detector

Sensitivity (%)

False positive rate (Hz)

Total error (%)

A1 A2 A3 OT TM

100.0 (88.1–100.0) 100.0 (92.9–100.0) 100.0 (97.6–100.0) 100.0 (97.0–100.0) 100.0 (90.5–100.0)

0.0 (0.0–3.2) 0.0 (0.0–8.8) 0.0 (0.0–2.8) 0.0 (0.0–0.4) 0.0 (0.0–0.8)

0.0 (0.0–11.9) 0.0 (0.0–7.9) 0.0 (0.0–2.7) 0.0 (0.0–4.5) 0.0 (0.0–12.1)

Median and range (min–max) of each metric are listed.

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Fig. 6. . Mean sensitivity vs. false positive rate of several signal enhancement ˆ = 3. The simmethods applied to 100 real microelectrode recordings with SNR ilarity measure labels are OT = optimal threshold, SP = smoothed signal power, and TM 1–3 = template-matching algorithm after 1–3 iterations.

signals, but at an error rate that is unacceptable, say TE > 20%, for most practical applications. The new algorithm achieves a median total error that is less than half that of the optimal ˆ ≤ 8. threshold for 2.5 ≤ SNR 4.3. Total error of two-unit recordings

Fig. 5. Example of detected spikes on a (a) noisy recording and (b) the same recording without any added noise. Empty circles indicate the peaks of consensus spikes and dark rectangles show the times of the spikes detected in the noisy recording. There are 11 true spikes within the 0.2 s interval. The detection algorithm only failed to detect the last one and had no false positives.

SNR values and gives an example of how well the algorithm performs in these conditions.

Fig. 8 shows the total error versus the mixing ratio, α in (15), of a two-unit recording, which is a combination of two real single-unit recordings. Over a broad range of mixing ratios, 0 ≤ α ≤ 0.28, the template-matching algorithm performs significantly better than the optimized threshold algorithm. This demonstrates that the algorithm can accurately detect spikes even when the recordings contain spikes of lesser amplitude from other cells. The new algorithm achieves a median total error that is less than half that of the optimal threshold for α ≤ 0.38. This corresponds to the most prominent action potentials having

4.1. Signal detection ROC curves ˆ = Fig. 6 shows the mean sensitivity of 100 signals with SNR 3 versus the false positive rate. The template-matching algorithm was significantly more sensitive and specific after the second iteration, but there is little additional improvement after the third iteration. This suggests that a few iterations are sufficient for this algorithm to converge to a good estimate of the template and to nearly achieve its optimal performance. 4.2. Total error versus SNR Fig. 7 shows how the algorithm performs over a broad range ˆ The template-matching algorithm performs better than of SNR. the optimized threshold detection algorithm over the range of ˆ (2.5–8). At low SNR ( 0.38. In many applications the morphology of the action potentials is more sensitive to the orientation of the neuron with respect to the position of the electrode. In these cases we expect the performance of our algorithm to significantly improve, even with a mixing ratio α ≈ 0.5, while the optimized threshold algorithm would remain approximately the same since it is insensitive to differences in morphology. 5. Conclusion The template-matching algorithm described in this article has many nice properties. It is able to estimate the template morphology automatically from the signal, only requires the user to specify the minimum and maximum firing rates, is computationally efficient, and is able to decide whether it was able to accurately detect spikes in the recording. Results using real recordings with added background noise taken from other recordings show that the new algorithm has good sensitivity and specificity for recordings with low signal-to-noise ratios (SNR > 2.5) and can isolate the most prominent spikes in many multi-unit recordings. References Atiya AF. Recognition of multiunit neural signals. IEEE Trans Biomed Eng 1992;39(7):723–9. Bankman IN, Johnson KO, Schneider W. Optimal detection, classification, and superposition resolution in neural waveform recordings. IEEE Trans Biomed Eng 1993;40(8):836–41.

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