- Email: [email protected]
Multi-channel spike detection and sorting using an array processing technique
Neurocomputing 26}27 (1999) 947}956
Multi-channel spike detection and sorting using an array processing technique Steven M. Bierer, David J. Anderson* Medical Center, Department of Biomedical Engineering, University of Michigan, 1301 Ann Street, Ann Arbor, MI 48109 0506, USA Accepted 18 December 1998
Abstract In many brain regions, high levels of background activity can obscure action potentials of neurons close to a recording electrode, particularly in the presence of a stimulus. As recorded on a multi-channel electrode array, this neural noise appears to be highly correlated among the channels. We have developed an array processing technique to remove the correlated component of noise, improving the signal-to-noise ratio. In addition, we show that the weighting vector of the array algorithm can be manipulated to facilitate sorting of the action potentials. An example of the technique applied to the guinea pig cochlear nucleus is shown. 1999 Elsevier Science B.V. All rights reserved. Keywords: Spike sorting; Signal processing; Silicon micro-electrode; Tetrode; Electrophysiology
1. Introduction E!orts to record from multiple neurons within a brain region have led to a variety of multi-channel electrode systems and a subsequent need to resolve simultaneously occurring action potentials. The stereotrode and tetrode [8,9], which have closely spaced recording elements, o!er a notable advancement over single-channel sorting, particularly when combined with optimal algorithms [6,7,12]. The microelectrodes used by our laboratory at the University of Michigan are fabricated on silicon
* Corresponding author. Tel.: #1-313-763-4367; fax: #1-313-764-0014. E-mail address: [email protected] (D.J. Anderson) 0925-2312/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 2 3 1 2 ( 9 9 ) 0 0 0 9 0 - 9
948
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
substrates and have numerous recording sites arranged in a two-dimensional plane. A few of the electrode array designs have closely spaced sites, combining the improved spike discriminability of tetrodes with the "xed geometry and reproducibility of silicon machining. The layout of one such probe is illustrated in Fig. 1. Generally, both single- and multi-channel sorting methods require that each action potential, or spike, is detected before the sorting procedure. In some brain regions, however, background noise } presumably produced by neurons relatively far from the electrode } obscures the spikes from nearby neurons, preventing detection. This problem can be particularly troublesome in the mammalian dorsal cochlear nucleus (DCN), a brainstem region that receives input from the auditory nerve. A single 16-channel trace recorded from the guinea pig DCN, during a 50 ms burst of acoustic white noise, is shown in Fig. 2. The noisy `hasha appearance is caused likely by the summation of neurons in the vicinity of the probe that are activated by the auditory nerve. Some researchers have considered this multi-unit activity to be a valid representation of auditory function [14]. However, our laboratory is interested in the functional interaction of individual, distinct units in the DCN, so we need to identify isolated spikes in our recordings. The need for a robust spike-detection technique is especially important for silicon probes, which have "xed electrode sites that cannot be independently manipulated to isolate units. Recent studies with both wire [13] and silicon [2] electrodes indicate that neural noise is highly correlated among closely spaced electrode sites. A sample of such correlated activity, recorded on channels C1}4 of the probe in Fig. 1, is presented on a short time scale in Fig. 3. Note the similar structure of the noise on each channel. In contrast, the spike apparent on channel C3 is strongly attenuated on the other channels. The spatial behavior of the noise and signal components is demonstrated in
Fig. 1. 16-channel silicon-substrate recording electrode.
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
949
Fig. 2. Example of 16-channel neural activity recorded from the guinea pig DCN. Channel numbers and position correspond to the layout of Fig. 1. Stimulus is a 50 ms acoustic burst of white noise, beginning at time zero. The maximal r.m.s. voltage on channel 1 is approximately 150 lV.
Fig. 3. Sample of neural activity taken from channels C1}4. A single spike is apparent on channel C3.
950
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
Fig. 4. Normalized noise correlation coe$cient (referenced to channel C4) and spike magnitude (triggered to spikes on channel C4) as a function of distance. The channels are spaced 50 lm apart. Spike and noise measurements are made from averages of 200 sweeps, each 100 ms in duration.
Fig. 4. In this "gure, the correlation coe$cient of noise on each channel, referenced to channel C4, is plotted versus distance from channel C4, for both stimulus and no-stimulus conditions. The average spike amplitude is also plotted versus distance, for spikes from a single unit detected on channel C4. The spike amplitude rolls o! much more quickly than the noise correlation, both with and without a stimulus. This di!erence in signal and noise behavior motivates the use of the array-processing technique to remove correlated noise.
2. Array processing algorithm Fig. 5 is a schematic diagram of the array processor, described by Applebaum [1]. Each x represents one data channel, at a single point in time, and consists of a noise G component and a possible signal component. The array processing transforms and linearly combines the M channels to achieve a single output, z, with optimal signalto-noise ratio. The "rst step is to determine the noise-only spatial covariance matrix of the array, C . Care must be taken to avoid including the in#uence of spikes (the signal) in the V covariance estimate, but if the noise level is high this may not be possible. When the noise among the channels is uncorrelated and of equal power, i.e. when C is a scaled V identity matrix, the optimal weighting vector, w"[w w 2 w ]2 is given by [1] + w"s"[s s 2 s ]2, + where each s is the original signal component of x . That is, s represents the spatial G G distribution of the signal (regarded here as the voltage at the peak of a spike) across the M channels. Initially, the actual distribution of a neuron's spike } or even if a spike is present at any given time } is unknown. A spike will presumably be large at electrode sites close to the source neuron, and smaller at sites farther away. Thus, for
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
951
Fig. 5. Schematic of the array processing algorithm.
simplicity, we initially assume that each spike } when one is present } occurs only on a single channel, so s is set at 1 for the channel of interest and 0 for all other channels. G For correlated inputs, the weighting vector much be adjusted by the inverse of the covariance matrix: w "[C ]\w. V Finally, the output of the "lter z (at a single point in time) for an M-channel input x is z"x2[C ]\w. V This process is repeated for di!erent channels of interest, by changing the prior weighting. Once a neural unit has been identi"ed, the actual spike magnitude distribution can be found by taking a multi-channel average over many spike events. This distribution can then form a new prior weighting vector, w, and the noise covariance, C , can be V recalculated by excluding time points during each spike. A second iteration of the array processing algorithm using these new values should result in an improved signal-to-noise ratio.
3. Experimental methods All neural data were recorded in the dorsal cochlear nucleus of an adult guinea pig, anesthetized with a mixture of ketamine and xylazine. The basic surgical procedure has been described by Clopton and Backo! [3]. Following the craniotomy, the cochlear nucleus was exposed by aspirating the overlying cerebellum; and the probe, secured to a micro-manipulator, was lowered into the nucleus using a hydraulic microdrive (Kopf Instruments). The cavity above the brainstem was "lled with agar to reduce brain pulsation.
952
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
Acquired signals were bandpass "ltered and ampli"ed using custom built hardware. Raw data records were recorded to disk at a rate of 20 kHz/channel using a DataWave Technologies data acquisition system. These records were converted o!-line for analysis with MATLAB (Mathworks). The 16-channel silicon probe was fabricated and packaged in the University of Michigan Solid State Electronics laboratory, following the procedures detailed in Drake et al. [4], although iridium was deposited on the recording sites, instead of gold. For this study, we used the `16chan-5a design, which has the layout illustrated in Fig. 1a. The probe has four shanks separated by 100 lm, with 10;10 lm recording sites separated by 50 lm along each shank.
4. Results The result of applying the array processing algorithm to the series of data of Fig. 2 is displayed in Fig. 6. In this case, the prior weighting of 1's and 0's was employed, and all 16 channels were used as input. The noise level is much lower after processing, and isolated spikes are evident on many channels, particularly in the lower left quadrant. We have obtained signal-to-noise ratio improvements of nearly 10 dB in DCN, and the results look equally promising for recordings made in auditory cortex (not shown).
Fig. 6. Example of the same 16-channel activity as in Fig. 2 after "ltering with the array processor. The scaling has been changed to show the spikes.
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
953
Because the weighting is biased to a single channel and noise correlations decrease with distance, one might expect distant channels to have little in#uence on the output. Indeed, the results of the array processing with four neighboring channels are just as good as when using 16 channels, though better than with two. (For two channels, the array processor is equivalent to a correlation canceler, or Wiener "lter [10], in which one channel acts as a reference to subtract noise from the other.) As a further application of the array processing, we altered the prior signal weighting, w, to improve spike sorting. Consider Fig. 7. The small "lled circles represent electrode site C11 plus the four neighboring sites (compare to Fig. 1). The larger circles labeled A}D are four di!erent neuron positions surrounding the center site, re#ected in four di!erent prior weightings (the elements in each weight are ordered as channel C7, 10, 11, 12, 15; all other channel weights are zero): w "[0.4 0.8 1 0.4 0]2, w "[0.4 0.4 1 0.8 0]2, w "[0 0.8 1 0.4 0.4]2, ! w "[0 0.4 1 0.8 0.4]2. " These weight vectors are, of course, somewhat arbitrary, and the con"guration of Fig. 7 is only suggestive as to where four neurons producing such weights might lie. Nevertheless, the four outputs of the array processor, plotted in Fig. 8, are very distinct. Spikes that are apparent in one output may or may not show up in the others. In fact, at least four di!erent spike shapes can be identi"ed from this single 100 ms trace.
Fig. 7. Fine of the 16 channels (7, 10, 11, 12, and 15) used for spike sorting. The circles labeled A}D represent the approximate locations suggested by the four weighting vectors described in the text.
954
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
Fig. 8. Outcome of array processing, for one sweep, for the weighting vectors corresponding to locations A}D of Fig. 7. At least four di!erent spike waveforms are apparent, based on their shapes across the four outputs. The numbers assigned to the units are at the top of the plot. Some overlapping of spikes is noticeable.
5. Conclusion We have shown that the signal-to-noise ratio of neural activity recorded with an array of electrodes can be enhanced by taking into account the spatial correlation of the noise. Although our results were for recordings made in a brain region that often exhibits a high degree of evoked synchronous noise, the concepts of array processing should be appropriate in other regions. And the technique can be applied to any electrode system, such as tetrodes constructed from intertwined wires, in which the recording elements are close (e.g. 20}50 lm separation). The "xed geometry of silicon-substrate probes make the array-processing technique particularly well-suited to spike sorting. Because only a single neuron can occupy a given volume of brain tissue, the voltage distribution, or `signaturea, created by a spike across an electrode array (such as the one in Fig. 1) should be unique to each neuron. This is the idea behind sorting spikes with a 4-channel tetrode [8]. But unlike previous sorting methods, in which each spike is detected on only one of the channels, we use a linear combination of several channels to optimize detection. (Multi-channel detection has been utilized in some template-matching approaches [7,11], but in these cases the noise on the di!erent channels was assumed to be uncorrelated.) Moreover, the "xed geometry of the silicon probe allows one essentially to `scana the recording volume for spikes, as illustrated in Figs. 7 and 8. Extracellular neural recordings are often biased toward the detection of large action potentials produced by relatively large neurons [5]. We feel that the array processing method, which lowers the level of background noise that can overwhelm small action potentials, is a signi"cant step towards making routine recordings from small neurons.
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
955
We plan to implement the method toward the recordings of small cells in the cochlear nucleus. Another limitation of extracellular recording is the inability to identify microscopically the actual neuron that was recorded [14]. We are currently developing histological techniques, using confocal and light microscopy, to visualize the neural tissue surrounding a probe. Using the voltage pro"le of a spike across several electrode channels, we intend to estimate the position of the source neuron based on a volume conductor model; that estimate could then help us identify in a microscopic image which cell was being recorded, allowing us to compare physiological properties with cell morphology. Future improvements to the array processing technique include the development of an adaptive algorithm to account for the nonstationarity of neural noise, and implementation of the algorithm in real time for on-line spike detection and sorting. We plan also to optimize the electrode site spacing in order to maximize the signal-tonoise ratio for a given brain region.
Acknowledgements This research was supported by NIH/NCRR P41-RR09754. Probes were made available by the University of Michigan Center for Neural Communication Technology.
References [1] S.P. Applebaum, Adaptive arrays, IEEE Trans Antennas Propag AP-24 (1976) 585}598. [2] S.M. Bierer, D.J. Anderson, Analysis of dorsal cochlear nucleus activity recorded with a 16-channel microelectrode array, Abstract: Association of Researchers in Otolaryngology, Midwinter Meeting, 1998. [3] B.M. Clopton, P.M. Backo!, Spectrotemporal receptive "elds of neurons in cochlear nucleus of guinea pig, Hearing Res. 52 (1991) 329}344. [4] K.L. Drake, K.D. Wise, J. Farraye, D.J. Anderson, S.L. BeMent, Performance of planar multisite microprobes in recording extracellular single-unit intracortical activity, IEEE Trans. Biomed. 35 (9) (1988) 719}732. [5] W.E. Faller, M.W. Luttges, A method for determining individual neuron size in simultaneous single-neuron recordings, Med. Biol. Eng. Comput. 33 (1995) 121}130. [6] M.S. Fee, P.P. Mitra, D. Kleinfeld, Automatic sorting of multiple neuronal signals in the presence of anisotropic and non-Gaussian variability, J. Neurosci. Meth. 69 (1996) 175}188. [7] S.N. Gozani, J.P. Miller, Optimal discrimination and classi"cation of neuronal action potential waveforms from multiunit, multichannel recordings using software-based linear "lters, IEEE Trans. Biomed. 41 (4) (1994) 358}372. [8] C.M. Gray, P.E. Maldonado, M. Wilson, B. McNaughton, Tetrodes markedly improve the reliability and yield of multiple single-unit isolation from multi-unit recordings in cat striate cortex, J. Neurosci. Meth. 63 (1995) 43}54. [9] B.L. McNaughton, J. O'Keefe, C.A. Barnes, The stereotrode: a new technique for simultaneous isolation of several single units in the central nervous system from multiple records, J. Neurosci. Meth. 8 (1983) 391}397. [10] S. Orfanidis, Optimum Signal Processing: An Introduction, MacMillan, New York, 1988.
956
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
[11] W.M. Roberts, D.K. Hartline, Separation of multi-unit nerve impulse trains by a multi-channel linear "lter algorithm, Brain Res. 94 (1975) 141}149. [12] M. Sahani, J.P. Pezaris, R.A. Andersen, On the separation of signals from neighboring cells in tetrode recordings, in: M.I. Jordan, M.J. Kearns, S.A. Solla (Eds.), Advance in Neural Information Processing Systems 10, MIT Press, Cambridge, MA, 1998. [13] R. Sergei, B. Wright, K. Miller, Cross-channel correlations in tetrode recordings: implications for spike sorting, Abstract: Computational Neuroscience, Santa Barbara, CA, 1998. [14] R. Thompson, M. Patterson, Bioelectric Recording Techniques: Cellular Processes and Brain Potentials, Academic Press, New York, 1973.
Steven M. Bierer received a B.S. in 1992 and M.S.E. in 1995, both in Biomedical Engineering, from Johns Hopkins University. He received an M.S. in Electrical Engineering in 1997 from the University of Michigan, and is currently pursuing a doctorate in Biomedical Engineering. Mr. Bierer's "elds of interest are neurophysiology and signal processing. Currently he is studying multi-neuron processing in brainstem nuclei of the mammalian auditory system. He is a member of Tau Beta Pi.
David J Anderson received the BSEE degree from Rensselaer Polytechnic Institute, Troy, NY, and the MS and Ph.D. degrees from the University of Wisconsin, Madison. After completing a postdoctoral traineeship with the Laboratory of Neurophysiology, University of Wisconsin Medical School, he joined the University of Michigan, Ann Arbor, where he is now a professor of Electrical Engineering and Computer Science, Biomedical Engineering and Otolaryngology. He is a member of the IEEE, Neuroscience Society, Acoustical Society of America, the Association for Research in Otolaryngology, and the Barany Society.
Multi-channel spike detection and sorting using an array processing technique Steven M. Bierer, David J. Anderson* Medical Center, Department of Biomedical Engineering, University of Michigan, 1301 Ann Street, Ann Arbor, MI 48109 0506, USA Accepted 18 December 1998
Abstract In many brain regions, high levels of background activity can obscure action potentials of neurons close to a recording electrode, particularly in the presence of a stimulus. As recorded on a multi-channel electrode array, this neural noise appears to be highly correlated among the channels. We have developed an array processing technique to remove the correlated component of noise, improving the signal-to-noise ratio. In addition, we show that the weighting vector of the array algorithm can be manipulated to facilitate sorting of the action potentials. An example of the technique applied to the guinea pig cochlear nucleus is shown. 1999 Elsevier Science B.V. All rights reserved. Keywords: Spike sorting; Signal processing; Silicon micro-electrode; Tetrode; Electrophysiology
1. Introduction E!orts to record from multiple neurons within a brain region have led to a variety of multi-channel electrode systems and a subsequent need to resolve simultaneously occurring action potentials. The stereotrode and tetrode [8,9], which have closely spaced recording elements, o!er a notable advancement over single-channel sorting, particularly when combined with optimal algorithms [6,7,12]. The microelectrodes used by our laboratory at the University of Michigan are fabricated on silicon
* Corresponding author. Tel.: #1-313-763-4367; fax: #1-313-764-0014. E-mail address: [email protected] (D.J. Anderson) 0925-2312/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 2 3 1 2 ( 9 9 ) 0 0 0 9 0 - 9
948
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
substrates and have numerous recording sites arranged in a two-dimensional plane. A few of the electrode array designs have closely spaced sites, combining the improved spike discriminability of tetrodes with the "xed geometry and reproducibility of silicon machining. The layout of one such probe is illustrated in Fig. 1. Generally, both single- and multi-channel sorting methods require that each action potential, or spike, is detected before the sorting procedure. In some brain regions, however, background noise } presumably produced by neurons relatively far from the electrode } obscures the spikes from nearby neurons, preventing detection. This problem can be particularly troublesome in the mammalian dorsal cochlear nucleus (DCN), a brainstem region that receives input from the auditory nerve. A single 16-channel trace recorded from the guinea pig DCN, during a 50 ms burst of acoustic white noise, is shown in Fig. 2. The noisy `hasha appearance is caused likely by the summation of neurons in the vicinity of the probe that are activated by the auditory nerve. Some researchers have considered this multi-unit activity to be a valid representation of auditory function [14]. However, our laboratory is interested in the functional interaction of individual, distinct units in the DCN, so we need to identify isolated spikes in our recordings. The need for a robust spike-detection technique is especially important for silicon probes, which have "xed electrode sites that cannot be independently manipulated to isolate units. Recent studies with both wire [13] and silicon [2] electrodes indicate that neural noise is highly correlated among closely spaced electrode sites. A sample of such correlated activity, recorded on channels C1}4 of the probe in Fig. 1, is presented on a short time scale in Fig. 3. Note the similar structure of the noise on each channel. In contrast, the spike apparent on channel C3 is strongly attenuated on the other channels. The spatial behavior of the noise and signal components is demonstrated in
Fig. 1. 16-channel silicon-substrate recording electrode.
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
949
Fig. 2. Example of 16-channel neural activity recorded from the guinea pig DCN. Channel numbers and position correspond to the layout of Fig. 1. Stimulus is a 50 ms acoustic burst of white noise, beginning at time zero. The maximal r.m.s. voltage on channel 1 is approximately 150 lV.
Fig. 3. Sample of neural activity taken from channels C1}4. A single spike is apparent on channel C3.
950
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
Fig. 4. Normalized noise correlation coe$cient (referenced to channel C4) and spike magnitude (triggered to spikes on channel C4) as a function of distance. The channels are spaced 50 lm apart. Spike and noise measurements are made from averages of 200 sweeps, each 100 ms in duration.
Fig. 4. In this "gure, the correlation coe$cient of noise on each channel, referenced to channel C4, is plotted versus distance from channel C4, for both stimulus and no-stimulus conditions. The average spike amplitude is also plotted versus distance, for spikes from a single unit detected on channel C4. The spike amplitude rolls o! much more quickly than the noise correlation, both with and without a stimulus. This di!erence in signal and noise behavior motivates the use of the array-processing technique to remove correlated noise.
2. Array processing algorithm Fig. 5 is a schematic diagram of the array processor, described by Applebaum [1]. Each x represents one data channel, at a single point in time, and consists of a noise G component and a possible signal component. The array processing transforms and linearly combines the M channels to achieve a single output, z, with optimal signalto-noise ratio. The "rst step is to determine the noise-only spatial covariance matrix of the array, C . Care must be taken to avoid including the in#uence of spikes (the signal) in the V covariance estimate, but if the noise level is high this may not be possible. When the noise among the channels is uncorrelated and of equal power, i.e. when C is a scaled V identity matrix, the optimal weighting vector, w"[w w 2 w ]2 is given by [1] + w"s"[s s 2 s ]2, + where each s is the original signal component of x . That is, s represents the spatial G G distribution of the signal (regarded here as the voltage at the peak of a spike) across the M channels. Initially, the actual distribution of a neuron's spike } or even if a spike is present at any given time } is unknown. A spike will presumably be large at electrode sites close to the source neuron, and smaller at sites farther away. Thus, for
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
951
Fig. 5. Schematic of the array processing algorithm.
simplicity, we initially assume that each spike } when one is present } occurs only on a single channel, so s is set at 1 for the channel of interest and 0 for all other channels. G For correlated inputs, the weighting vector much be adjusted by the inverse of the covariance matrix: w "[C ]\w. V Finally, the output of the "lter z (at a single point in time) for an M-channel input x is z"x2[C ]\w. V This process is repeated for di!erent channels of interest, by changing the prior weighting. Once a neural unit has been identi"ed, the actual spike magnitude distribution can be found by taking a multi-channel average over many spike events. This distribution can then form a new prior weighting vector, w, and the noise covariance, C , can be V recalculated by excluding time points during each spike. A second iteration of the array processing algorithm using these new values should result in an improved signal-to-noise ratio.
3. Experimental methods All neural data were recorded in the dorsal cochlear nucleus of an adult guinea pig, anesthetized with a mixture of ketamine and xylazine. The basic surgical procedure has been described by Clopton and Backo! [3]. Following the craniotomy, the cochlear nucleus was exposed by aspirating the overlying cerebellum; and the probe, secured to a micro-manipulator, was lowered into the nucleus using a hydraulic microdrive (Kopf Instruments). The cavity above the brainstem was "lled with agar to reduce brain pulsation.
952
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
Acquired signals were bandpass "ltered and ampli"ed using custom built hardware. Raw data records were recorded to disk at a rate of 20 kHz/channel using a DataWave Technologies data acquisition system. These records were converted o!-line for analysis with MATLAB (Mathworks). The 16-channel silicon probe was fabricated and packaged in the University of Michigan Solid State Electronics laboratory, following the procedures detailed in Drake et al. [4], although iridium was deposited on the recording sites, instead of gold. For this study, we used the `16chan-5a design, which has the layout illustrated in Fig. 1a. The probe has four shanks separated by 100 lm, with 10;10 lm recording sites separated by 50 lm along each shank.
4. Results The result of applying the array processing algorithm to the series of data of Fig. 2 is displayed in Fig. 6. In this case, the prior weighting of 1's and 0's was employed, and all 16 channels were used as input. The noise level is much lower after processing, and isolated spikes are evident on many channels, particularly in the lower left quadrant. We have obtained signal-to-noise ratio improvements of nearly 10 dB in DCN, and the results look equally promising for recordings made in auditory cortex (not shown).
Fig. 6. Example of the same 16-channel activity as in Fig. 2 after "ltering with the array processor. The scaling has been changed to show the spikes.
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
953
Because the weighting is biased to a single channel and noise correlations decrease with distance, one might expect distant channels to have little in#uence on the output. Indeed, the results of the array processing with four neighboring channels are just as good as when using 16 channels, though better than with two. (For two channels, the array processor is equivalent to a correlation canceler, or Wiener "lter [10], in which one channel acts as a reference to subtract noise from the other.) As a further application of the array processing, we altered the prior signal weighting, w, to improve spike sorting. Consider Fig. 7. The small "lled circles represent electrode site C11 plus the four neighboring sites (compare to Fig. 1). The larger circles labeled A}D are four di!erent neuron positions surrounding the center site, re#ected in four di!erent prior weightings (the elements in each weight are ordered as channel C7, 10, 11, 12, 15; all other channel weights are zero): w "[0.4 0.8 1 0.4 0]2, w "[0.4 0.4 1 0.8 0]2, w "[0 0.8 1 0.4 0.4]2, ! w "[0 0.4 1 0.8 0.4]2. " These weight vectors are, of course, somewhat arbitrary, and the con"guration of Fig. 7 is only suggestive as to where four neurons producing such weights might lie. Nevertheless, the four outputs of the array processor, plotted in Fig. 8, are very distinct. Spikes that are apparent in one output may or may not show up in the others. In fact, at least four di!erent spike shapes can be identi"ed from this single 100 ms trace.
Fig. 7. Fine of the 16 channels (7, 10, 11, 12, and 15) used for spike sorting. The circles labeled A}D represent the approximate locations suggested by the four weighting vectors described in the text.
954
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
Fig. 8. Outcome of array processing, for one sweep, for the weighting vectors corresponding to locations A}D of Fig. 7. At least four di!erent spike waveforms are apparent, based on their shapes across the four outputs. The numbers assigned to the units are at the top of the plot. Some overlapping of spikes is noticeable.
5. Conclusion We have shown that the signal-to-noise ratio of neural activity recorded with an array of electrodes can be enhanced by taking into account the spatial correlation of the noise. Although our results were for recordings made in a brain region that often exhibits a high degree of evoked synchronous noise, the concepts of array processing should be appropriate in other regions. And the technique can be applied to any electrode system, such as tetrodes constructed from intertwined wires, in which the recording elements are close (e.g. 20}50 lm separation). The "xed geometry of silicon-substrate probes make the array-processing technique particularly well-suited to spike sorting. Because only a single neuron can occupy a given volume of brain tissue, the voltage distribution, or `signaturea, created by a spike across an electrode array (such as the one in Fig. 1) should be unique to each neuron. This is the idea behind sorting spikes with a 4-channel tetrode [8]. But unlike previous sorting methods, in which each spike is detected on only one of the channels, we use a linear combination of several channels to optimize detection. (Multi-channel detection has been utilized in some template-matching approaches [7,11], but in these cases the noise on the di!erent channels was assumed to be uncorrelated.) Moreover, the "xed geometry of the silicon probe allows one essentially to `scana the recording volume for spikes, as illustrated in Figs. 7 and 8. Extracellular neural recordings are often biased toward the detection of large action potentials produced by relatively large neurons [5]. We feel that the array processing method, which lowers the level of background noise that can overwhelm small action potentials, is a signi"cant step towards making routine recordings from small neurons.
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
955
We plan to implement the method toward the recordings of small cells in the cochlear nucleus. Another limitation of extracellular recording is the inability to identify microscopically the actual neuron that was recorded [14]. We are currently developing histological techniques, using confocal and light microscopy, to visualize the neural tissue surrounding a probe. Using the voltage pro"le of a spike across several electrode channels, we intend to estimate the position of the source neuron based on a volume conductor model; that estimate could then help us identify in a microscopic image which cell was being recorded, allowing us to compare physiological properties with cell morphology. Future improvements to the array processing technique include the development of an adaptive algorithm to account for the nonstationarity of neural noise, and implementation of the algorithm in real time for on-line spike detection and sorting. We plan also to optimize the electrode site spacing in order to maximize the signal-tonoise ratio for a given brain region.
Acknowledgements This research was supported by NIH/NCRR P41-RR09754. Probes were made available by the University of Michigan Center for Neural Communication Technology.
References [1] S.P. Applebaum, Adaptive arrays, IEEE Trans Antennas Propag AP-24 (1976) 585}598. [2] S.M. Bierer, D.J. Anderson, Analysis of dorsal cochlear nucleus activity recorded with a 16-channel microelectrode array, Abstract: Association of Researchers in Otolaryngology, Midwinter Meeting, 1998. [3] B.M. Clopton, P.M. Backo!, Spectrotemporal receptive "elds of neurons in cochlear nucleus of guinea pig, Hearing Res. 52 (1991) 329}344. [4] K.L. Drake, K.D. Wise, J. Farraye, D.J. Anderson, S.L. BeMent, Performance of planar multisite microprobes in recording extracellular single-unit intracortical activity, IEEE Trans. Biomed. 35 (9) (1988) 719}732. [5] W.E. Faller, M.W. Luttges, A method for determining individual neuron size in simultaneous single-neuron recordings, Med. Biol. Eng. Comput. 33 (1995) 121}130. [6] M.S. Fee, P.P. Mitra, D. Kleinfeld, Automatic sorting of multiple neuronal signals in the presence of anisotropic and non-Gaussian variability, J. Neurosci. Meth. 69 (1996) 175}188. [7] S.N. Gozani, J.P. Miller, Optimal discrimination and classi"cation of neuronal action potential waveforms from multiunit, multichannel recordings using software-based linear "lters, IEEE Trans. Biomed. 41 (4) (1994) 358}372. [8] C.M. Gray, P.E. Maldonado, M. Wilson, B. McNaughton, Tetrodes markedly improve the reliability and yield of multiple single-unit isolation from multi-unit recordings in cat striate cortex, J. Neurosci. Meth. 63 (1995) 43}54. [9] B.L. McNaughton, J. O'Keefe, C.A. Barnes, The stereotrode: a new technique for simultaneous isolation of several single units in the central nervous system from multiple records, J. Neurosci. Meth. 8 (1983) 391}397. [10] S. Orfanidis, Optimum Signal Processing: An Introduction, MacMillan, New York, 1988.
956
S.M. Bierer, D.J. Anderson / Neurocomputing 26}27 (1999) 947}956
[11] W.M. Roberts, D.K. Hartline, Separation of multi-unit nerve impulse trains by a multi-channel linear "lter algorithm, Brain Res. 94 (1975) 141}149. [12] M. Sahani, J.P. Pezaris, R.A. Andersen, On the separation of signals from neighboring cells in tetrode recordings, in: M.I. Jordan, M.J. Kearns, S.A. Solla (Eds.), Advance in Neural Information Processing Systems 10, MIT Press, Cambridge, MA, 1998. [13] R. Sergei, B. Wright, K. Miller, Cross-channel correlations in tetrode recordings: implications for spike sorting, Abstract: Computational Neuroscience, Santa Barbara, CA, 1998. [14] R. Thompson, M. Patterson, Bioelectric Recording Techniques: Cellular Processes and Brain Potentials, Academic Press, New York, 1973.
Steven M. Bierer received a B.S. in 1992 and M.S.E. in 1995, both in Biomedical Engineering, from Johns Hopkins University. He received an M.S. in Electrical Engineering in 1997 from the University of Michigan, and is currently pursuing a doctorate in Biomedical Engineering. Mr. Bierer's "elds of interest are neurophysiology and signal processing. Currently he is studying multi-neuron processing in brainstem nuclei of the mammalian auditory system. He is a member of Tau Beta Pi.
David J Anderson received the BSEE degree from Rensselaer Polytechnic Institute, Troy, NY, and the MS and Ph.D. degrees from the University of Wisconsin, Madison. After completing a postdoctoral traineeship with the Laboratory of Neurophysiology, University of Wisconsin Medical School, he joined the University of Michigan, Ann Arbor, where he is now a professor of Electrical Engineering and Computer Science, Biomedical Engineering and Otolaryngology. He is a member of the IEEE, Neuroscience Society, Acoustical Society of America, the Association for Research in Otolaryngology, and the Barany Society.