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Are Heptodes Better than Tetrodes for Spike Sorting?
9th onBerlin, Biological and Medical Systems Aug.IFAC 31 - Symposium Sept. 2, 2015. Germany 9th IFAC Symposium on Biological and Medical Systems Aug. 31 - Symposium Sept. 2, 2015. Germany 9th IFAC onBerlin, Biological and Medicalonline Systems Aug. 31 - Sept. 2, 2015. Berlin, Germany Available at www.sciencedirect.com Aug. 31 - Sept. 2, 2015. Berlin, Germany
ScienceDirect IFAC-PapersOnLine 48-20 Tetrodes (2015) 094–099 for Spike Sorting? Are Heptodes Better than Are Heptodes Better than Tetrodes Are Heptodes Better than Tetrodes for for Spike Spike Sorting? Sorting? Are Heptodes Better than Tetrodes Spike Sorting? Christopher Doerr*. Thomasfor Schanze*
Christopher Christopher Doerr*. Doerr*. Thomas Thomas Schanze* Schanze* Christopher Doerr*. Thomas Schanze* *Technische Hochschule Mittelhessen (THM) – University of Applied Sciences, *Technische Hochschule Mittelhessen of 35390 Giessen, Germany (e-mail: [email protected], *Technische Hochschule Mittelhessen (THM) (THM) –– University [email protected]) of Applied Applied Sciences, Sciences, 35390 Giessen, Germany (e-mail: [email protected], [email protected]) *Technische Hochschule Mittelhessen (THM) – [email protected]) of Applied Sciences, 35390 Giessen, Germany (e-mail: [email protected], 35390 Giessen, Germany (e-mail: [email protected], [email protected]) Abstract: Multi-neuron extracellular recordings with multichannel microelectrodes, like tetrodes or Abstract: Multi-neuron extracellular with like tetrodes or heptodes, used to get insights in the recordings neuronal information processingmicroelectrodes, in the brain. Spike is the Abstract:are Multi-neuron extracellular recordings with multichannel multichannel microelectrodes, likesorting tetrodes or heptodes, are used to get insights in the neuronal information processing in the brain. Spike sorting is the Abstract: Multi-neuron extracellular with multichannel microelectrodes, like tetrodes or detection classification of extracellular actioninformation potentials (spikes) recorded these electrodes. heptodes, and are used to get insights in the recordings neuronal processing in thewith brain. Spike sorting isHere the detection classification of action potentials recorded these electrodes. heptodes, are used to get insights the sorting neuronal information processing in thewith brain. Spike isHere the we report and on the improvement of in spike performance when using heptodes rather thansorting tetrodes by detection and classification of extracellular extracellular action potentials (spikes) (spikes) recorded with these electrodes. Here we on the improvement of sorting performance when heptodes rather than by detection classification of extracellular action potentials (spikes) recorded withspike thesesorting electrodes. Here simulating tetrode/heptode recordings analysing them automatically with our algorithm. we report report and on the improvement of spike spikeand sorting performance when using using heptodes rather than tetrodes tetrodes by simulating tetrode/heptode recordings and analysing them automatically with our spike sorting algorithm. we report on the improvement of spike sorting performance when using heptodes rather than tetrodes by Simulation of signals is performed via a simple model of neurons and electrodes that has the ability to simulating tetrode/heptode recordings and analysing them automatically with our spike sorting algorithm. Simulation of signals is performed via a simple model of neurons and electrodes that has the ability simulating tetrode/heptode recordings and analysing them automatically with our spike sorting algorithm. emulate preferably realistic recording conditions without too much complexity. Results indicate that Simulation of signals is performed via a simple model of neurons and electrodes that has the ability to to emulate preferably realistic conditions without too much Results indicate that Simulation of performance signals is performed a simple model of neurons andcomplexity. electrodes has the ability to spike sorting isrecording better via when heptodes instead of tetrodes are used tothat record from highly emulate preferably realistic recording conditions without too much complexity. Results indicate that spike sorting performance is better when heptodes instead of tetrodes are used to record from highly emulate preferably realistic recording conditions without too much complexity. Results indicate that active local clusters consisting of many neurons and when the signals have a low signal-to-noise ratio. spike sorting performance is better when heptodes instead of tetrodes are used to record from highly active local clusters consisting of neurons and when the signals haveare aa low ratio. spike sorting performance is better when heptodes instead of tetrodes usedsignal-to-noise to record from highly active clusters consisting of many many and Control) when theHosting signals low signal-to-noise ratio. © 2015,local IFAC (International Federation ofneurons Automatic byhave Elsevier Ltd. Allactivity, rights reserved. Keywords: classification, electrodes, modelling, multisensor integration, neuronal recording, active local clusters consisting of many neurons and when the signals have a low signal-to-noise ratio. Keywords: classification, electrodes, modelling, multisensor multisensor integration, integration, neuronal neuronal activity, activity, recording, recording, signal processing, simulation, spike sorting. Keywords: classification, electrodes, modelling, signal processing, simulation, spike sorting. Keywords: classification, electrodes, modelling, multisensor integration, neuronal activity, recording, signal processing, simulation, spike sorting. signal processing, simulation, spike sorting. 1. INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION Multi-neuron recordings with multichannel microelectrodes, 1. INTRODUCTION Multi-neuron recordings microelectrodes, like tetrodes (four channels) or multichannel heptodes (seven channels), are Multi-neuron recordings with with multichannel microelectrodes, like tetrodes (four channels) or heptodes (seven Multi-neuron recordings with multichannel microelectrodes, increasingly used to get insights in the neuronal processingare of like tetrodes (four channels) or heptodes (seven channels), channels), are increasingly used to get insights in the neuronal processing like tetrodes (four channels) or heptodes (seven channels), are information in the brain. The extracellular action potentials increasingly used to get insights in the neuronal processing of of information in the brain. The extracellular potentials increasingly used get the insights in the neuronal processing of (spikes) captured recordings ariseaction from multiple information in thetoby brain. The extracellular action potentials (spikes) by the recordings arise from multiple information in thedistances brain. extracellular action neurons several to the electrode are potentials generally (spikes) atcaptured captured by theThe recordings ariseand from multiple neurons several distances to the are (spikes) by theand recordings ariseand multiple superimposed by artefacts noise. neurons at atcaptured several distances to the electrode electrode andfrom are generally generally superimposed by artefacts and noise. neurons at several distances to the electrode and are generally superimposed by artefacts and noise. The detection by of artefacts spikes and superimposed and their noise.classification in clusters, The of spikes and their in which correspond different is called spike sorting. The detection detection of to spikes and neurons, their classification classification in clusters, clusters, which correspond to different neurons, is called spike The detection of spikes and their classification in clusters, which correspond to different neurons, is called spike sorting. sorting. Fig. 1 correspond shows on the left side neurons, an illustration of spike a heptode, as which to different is called sorting. Fig. 1 shows on the left side an illustration of a heptode, manufactured by Thomas RECORDING GmbH, Gießen, Fig. 1 shows on the left side an illustration of a heptode, as as manufactured GmbH, Gießen, Fig. 1 shows theThomas leftofside an illustration of awith heptode, as 100 µm Germany and on aby a RECORDING recording situation several manufactured bysketch Thomas RECORDING GmbH, Gießen, Germany and a sketch of a recording situation with several manufactured by Thomas RECORDING GmbH, Gießen, neurons. Spikes recorded with these electrodes, have different Germany and a sketch of a recording situation with several 100 100 µm µm neurons. recorded with these different Germany and sketch a channels recording with several amplitudes on aeach of of the assituation can behave seen in the 100 Fig. µm 1. Sketch of an extracellular recording with a fibreneurons. Spikes Spikes recorded with these electrodes, electrodes, have different amplitudes on each of channels as seen in the Fig. of aa fibreneurons. Spikes recorded with these electrodes, different signal sketch 1). the This is due thebe fact that and several neurons. Left:recording Heptodewith geometry and amplitudes on (Fig. each of the channels astocan can behave seen in the the heptode Fig. 1. 1. Sketch Sketch of an an extracellular extracellular recording with fibresignal sketch (Fig. 1). This is due to the fact that the heptode and several neurons. Left: Heptode geometry and amplitudes on each of the channels as can be seen in amplitude of a (Fig. spike 1). on This a channel depends the that distance Fig. 1. Sketch of an extracellular recording with fibreof neurons relative to the electrode. Thea diameter signal sketch is due to theonfact the positions heptode and several neurons. Left: Heptode geometry and of amplitude of a spike on a channel depends on the distance positions of neurons relative to the electrode. The diameter of signal sketch (Fig. 1). This is due to the fact that the between this channel’s contact, i.e. conductor/tissue interface, and several Left: geometry andthree the heptode’s shaft isneurons. about 100 µm.Heptode Tetrodes onlydiameter have amplitude of a spike on a channel depends on the distance heptode positions of neurons relative to the electrode. The of between this channel’s contact, i.e. conductor/tissue interface, the heptode’s shaft is about 100 µm. Tetrodes only have three amplitude of a spike on a channel depends on the distance and the signal generating neuron. The distribution of the positions of neurons relative to the electrode. The diameter of of six electrodes on the ring (e.g.only no electrodes between this channel’s contact, i.e. conductor/tissue interface, instead the heptode’s shaft is about 100outer µm. Tetrodes have three and signal generating The distribution of instead of electrodes the outer ring no between this channel’s i.e. conductor/tissue spike’s overcontact, the neuron. channels encodes the interface, neuron’s the heptode’s shaft is about 100The µm.distant, Tetrodes only have three positions two, four andon indifferent and the the amplitude signal generating neuron. The distribution of the the at instead of six six electrodes onsix). the outer ring (e.g. (e.g. no electrodes electrodes spike’s amplitude over the channels encodes the neuron’s at positions two, four and six). The distant, indifferent and the signal generating neuron. The distribution of the position relative to the electrode distinctly. This heptode or instead of six electrodes on the outer ring (e.g. no electrodes reference electrode is not shown here. Right: Signals spike’s amplitude over the channels encodes the neuron’s at positions two, four and six). The distant, indifferent position relative to the distinctly. This or electrode is not here. Right: Signals spike’s theknown channels encodes neuron’s tetrode effect, as the stereotrode effect at positions two, six). distant, indifferent recorded with thefour heptode. NoteThe that the amplitude position amplitude relativeoriginally to over the electrode electrode distinctly. Thistheheptode heptode or reference reference electrode is and not shown shown here. Right: Signals tetrode effect, originally known as the stereotrode effect with the heptode. Note that the amplitude position relativeO'Keefe to the and electrode distinctly. This heptode or recorded (McNaughton, Barnes, provides a useful reference electrode is not shown here. Right: Signals distribution of the spikes depends on the position of the tetrode effect, originally known as1983), the stereotrode effect recorded with the heptode. Note that the amplitude (McNaughton, O'Keefe and Barnes, 1983), provides aa useful of the spikes depends on the position tetrode effect, originally the et stereotrode effect feature for spike classification asasGray al. (1995) and distribution recorded with the heptode. Note that amplitude neurons relative to the contacts of the heptode’s recording (McNaughton, O'Keefe andknown Barnes, 1983), provides useful distribution of the spikes depends on the position of of the the feature for spike classification as Gray et al. (1995) and neurons relative to the contacts of the heptode’s recording (McNaughton, O'Keefe and Barnes, 1983), provides a useful Harris al. (2000) found for tetrodes. distribution of the depends on position of the Also note thatcontacts almost simultaneously active featureetfor spike classification as Gray et al. (1995) and channels. neurons relative tospikes the of thethe heptode’s recording Harris al. found Also note that almost simultaneously feature spike classification as Gray et al. (1995) and channels. neurons totothe of the heptode’sactive recording can lead waveform Harris et etfor al. (2000) (2000) found for for tetrodes. tetrodes. channels.relative Also note thatcontacts almostinterferences. simultaneously active The of (2000) heptodes instead of tetrodes for extracellular channels. neurons can lead to waveform interferences. Harrisuse et al. found for tetrodes. Also note that almost simultaneously active neurons can lead to waveform interferences. The instead tetrodes extracellular recordings expected to furtherof performance of neurons can lead to waveform interferences. The use use of ofis heptodes heptodes instead ofincrease tetrodesthefor for extracellular To verify this assumption we developed a heptode signal recordings is expected to further increase the performance The use of heptodes instead of tetrodes for extracellular spike sorting. This should be due to the fact that with an recordings is expected to further increase the performance of of To this we developed aa heptode signal simulation based on model of neurons and To verify verify algorithm this assumption assumption wea simple developed heptode signal spike sorting. This should be due to the fact that with an recordings isnumber expected to further increase performance of simulation increasing of recording the with signal spike sorting. This should be due to channels thethe fact that an algorithm based on a simple model of neurons To verify this assumption we developed a heptode signal electrodes and a spike sorting algorithm with which the simulation algorithm based on a simple model of neurons and and increasing number of recording the signal spike sorting. This should bethe dueinfluence to channels the fact that with an electrodes redundancy increases or that of the noise and increasing number of recording channels the signal and a spike sorting algorithm with which simulation algorithm based on a simple model of neurons and signals can be analysed automatically. As an example for electrodes and a spike sorting algorithm with which the the redundancy increases or the of noise and increasing number of recording channels signal artefacts decreases. redundancy increases or that that the influence influence of the thethe noise and signals can be analysed automatically. As an example electrodes and a spike sorting algorithm with which the tetrodes and heptodes, we use the electrode arrangement of signals can be analysed automatically. As an example for for artefacts redundancy increases or that the influence of the noise and tetrodes artefacts decreases. decreases. and heptodes, we use the electrode arrangement signals can be analysed automatically. As an example for tetrodes and heptodes, we use the electrode arrangement of of artefacts decreases. Copyright © 2015 IFAC 94 tetrodes and heptodes, we use the electrode arrangement of 2405-8963©©2015 2015,IFAC IFAC (International Federation of Automatic Control) Copyright 94 Hosting by Elsevier Ltd. All rights reserved. Copyright © 2015 94 Control. Peer review underIFAC responsibility of International Federation of Automatic Copyright © 2015 IFAC 94 10.1016/j.ifacol.2015.10.121
9th IFAC BMS Aug. 31 - Sept. 2, 2015. Berlin, Germany Christopher Doerr et al. / IFAC-PapersOnLine 48-20 (2015) 094–099
heptodes and tetrodes RECORDING GmbH.
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different neurons may overlap and produce a “corrupted” spike waveform, which is a linear superposition of the original spike waveforms (Figs. 1 and 2). The fire-rates of the neurons are approximately 12 spikes per second. This leads to a high amount of overlapping spikes and means a challenge for the spike sorting algorithm, especially for the clustering.
The focus of this work lies on the spike sorting performance with tetrode and heptode signals depending on the number of units present in the signal and the amount of noise contamination. 2. METHODS 2.1 Signal simulation algorithm To simulate heptode and tetrode signals we use a simple model of neurons and electrodes. The heptode is simulated with point sinks as electrode contacts. This makes it easy to compute the distance to neurons and therefore the amplitude of the spikes on the channels. The electrode contacts two to seven are equally spaced on a circle with a diameter of 43 µm and each have a distance of 60.8 µm to the first electrode contact. Neurons are simulated as point sources that are placed at arbitrary positions relative to the electrode’s tip. The positions of the neurons are limited to a maximum radial distance to the heptode’s surface of 15 µm. The minimum distance between two neurons is set to 20 µm to avoid neurons with highly similar amplitude distributions and, thus, to take into account their spatial extension of about 10 µm in diameter. The spikes fired by a neuron are modelled as biphasic spikes by superimposing two time-shifted and weighted Gaussian curves (see spikes in Fig. 1 or Fig. 2), which is assumed to be a realistic approximation of extracellularly recorded action potentials (Roh, Choi and Kim, 2008). The spikes of a single neuron are modelled as uniform events with amplitude 1 at the neuron's position. The duration of the spikes of a neuron is generated by a uniformly distributed one-off random selection process over [0.8 ms, 2.8 ms]. The amplitude of a spike on one channel of the heptode depends on the distance between neuron and the respective electrode contact via the exponential model developed by Gray et al. (1995). Here the amplitude V(x) at distance x obeys
V ( x) = V (0) ⋅ exp(− x / λ ),
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(1)
with λ = 28.42 µm. λ is the decay constant of the model, which has been determined by Gray et al. (1995) via in vivo recordings with tetrodes. The occurrences of spikes, i.e. spike times, are computed for every neuron by an individual interspike interval distribution. These are simulated by an exponential distribution, modified by a Gaussian distribution to incorporate an absolute and a relative refractory period (Dayan and Abbott, 2005). From this distribution, quite natural interspike intervals are obtained for every neuron. Spike times are computed by concatenating subsequent interspike intervals. Since the spike times of every neuron are computed individually, spikes of
Fig. 2. Segment taken from a simulated heptode signal. Note the channel related amplitude distributions of the spikes indicate the spatial resolution of the heptode. The signal to noise ratio can be seen as similar to real recordings (Uwe Thomas, Thomas RECORDING GmbH, Giessen, Germany, personal communication). Observe the overlapping spikes at t = 16 ms. 95
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Noise is simulated by adjusting the amplitude distribution and the spectrum of Gaussian white noise according to the noise of a neuronal signal that has been recorded by the group of Frank Bremmer at the Department of Neurophysics, Philipps-Universität Marburg, Germany with Thomas RECORDING electrodes in the area V4 of a macaca mulatta. The artificial noise is then added with an arbitrary amplitude on the simulated spike signal.
Compared to cubic spline interpolation our analyses indicated no clear difference in spike classification performance. In the multichannel recording case we use the concatenated spike waveforms for alignment, except for the pre-alignment, were the mean shift over the channels is computed. The spikes si[n] of channel i consist of 50 samples. The concatenated waveforms s therefore consist, in the heptode case, of 350 samples, i.e. s=[s0, …, s6].
Signals are simulated as heptode signals. By turning off the signals on channels three, five and seven a tetrode signal is obtained (see Fig. 1).
For feature extraction we use a standard PCA. In the multichannel recording case we use again the concatenated waveforms of the spikes. Therefore, we can combine the spike’s amplitude distribution over the signal channels and its waveform in the feature extraction. PCA should be capable of finding the optimal energy related combination of waveform and amplitude distribution to separate spikes from different neurons under different, undetermined signal conditions.
Fig. 2 shows a segment of a simulated heptode signal. Observe the various spike time courses and the apparent channel and neuron related amplitude distributions. To calculate signal-to-noise ratio, we compute the maximum amplitudes of the recorded spikes of all neurons. The amplitudes have the range 0.01 to 0.93. The mean maximum amplitude is 0.13, its standard deviation is 0.13. Then we calculated the mean signal-to-noise ratio by 0.13/stdev(noise). 2.2 Spike sorting We adopted and refined parts of a spike sorting algorithm developed by Franke et al. (2010) that has been developed for analysis of multichannel signals. To detect spikes we initially compute the instantaneous energy of the signal. In improvement to Franke et al. (2010), this is done by a multiresolution energy filter (MEF) (Doerr and Schanze, 2013). The MEF is based on an analytic signal approach and consists of multiple, spectral overlapping, constant Q Hilbert bandpass filters. Instantaneous energy calculation of noisy, wideband signals via the analytic signal is superior to teager energy operator (TEO) based approaches, which also give poor results for a wide range of signals (Vakman, 1996). Therefore an analytic signal based approach is more suitable for spike detection than a TEO based one.
Fig. 3. Spike sorting performance for heptode signals and tetrode signals as a function of the number of neurons. The noise level was set to 0.05. For signals with more neurons (i.e. 14) the heptode performance significantly better as the tetrode. The standard error of the mean (SEM) is displayed by dashed lines, indicating the significance of the performance benefit. The number of analysed signals was 20 for each simulated lot of neurons.
The spike detection threshold is set by a fixed multiple of the median of the computed energy. The median serves as an estimation for the noise level (Quiroga, Nadasdy and BenShaul, 2004). An automatic selection of the spike detection threshold is necessary for automatic evaluation of simulated signals. For spike alignment we compare the interpolated and squared spike waveforms to a mean waveform, computed from all squared spike waveforms, via correlation. The shifted spike waveform which is best correlated to the mean waveform is taken as the best aligned waveform. After all spikes have been processed a new mean spike is computed and all spikes are tested again (Franke et al., 2010). This procedure is repeated until a convergence criterion is reached.
The number of principal components used for spike classification is hard to set automatically. It can be left as a parameter manually to set. A scree plot with the variance explained by the principal components can support the user in choosing an appropriate value (Jolliffe, 2002). Spikes are then classified via a heteroscedastic Gaussian mixture model (McLachlan and Peel, 2000), in contrast to a homoscedastic Gaussian mixture model (GMM) that was used by Franke et al. (2010), into several clusters. The
For a precise computation of an initial mean waveform, we initially align every spike according to its centre of mass. We use linear interpolation due to performance reasons. 96
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number of clusters is automatically determined via searching the minimum of the Bayesian information criterion (Schwarz, 1978). An interesting feature is that this clustering scales with the numbers of channels used for spike sorting. Here we use the GMM object of the python scikit-learn library (Pedregosa et al., 2011).
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The performance of heptodes and tetrodes for different numbers of neurons present in the signal is shown in Fig. 3. The performance of the heptode for few neurons is virtually equal to the tetrode’s performance. With more neurons present (i.e. 14), the heptode performs significantly better than the tetrode (0.72 to 0.66). Fig. 4 shows the performance of heptodes and tetrodes for different noise amplitudes. Here, the heptode’s performance is significantly higher for noise levels from 0.05 to 0.09. At a noise level of 0.09 it is about 50 percent better.
2.3 Evaluation of classification results Simulated signals are analysed automatically by the spike sorting algorithm with comparable or similar parameterisation. Classification results are evaluated automatically and quantitatively. As a measure for the spike sorting performance, the fraction of correctly classified spikes of all spikes in the signal is computed.
For less noise, both heptodes and tetrodes perform similarly. Since in these signals are 14 neurons present (the maximum in Fig. 3) it gets clear that heptodes perform better than tetrodes when many neurons are active and when the noise level is high.
To find correctly classified spikes, we assign every neuron to the cluster where the majority of spikes of this neuron is classified to. Every spike of this neuron that is assigned to this cluster is counted as correctly classified. The spikes of a neuron that has been classified to other clusters are not counted. 3. RESULTS Heptode and tetrode signals are simulated and analysed with our spike sorting algorithm. All analysed signals have a length of 100 seconds with a sampling rate of 25 kHz and contain about 1200 spikes per neuron.
Fig. 5. Spike sorting performance for heptode and tetrode signals, consisting of non-overlapping spikes, as a function of the noise amplitude. The overall performance is clearly better as in Fig. 4 indicating that overlapping spikes infer spike sorting. 14 neurons were simulated. The standard error of the mean (SEM) is displayed by dashed lines, indicating the significance of the performance benefit. The number of analysed signals was 20 for each simulated lot of neurons. In comparison to the results in Fig. 3 one can see the maximum performance of both, heptodes and tetrodes, is clearly lower in Fig. 4. This may be due to the fact, that the number of neurons in the signals in Fig. 4 is high and therefore the number of overlapping spikes, which cannot be separated properly by our algorithm, is considerably higher. To support this finding, we simulated signals where overlapping of spikes is precluded. The results are shown in Fig. 5. Here the maximum performance for heptodes and tetrodes is clearly higher. E. g. for heptodes and with a noise
Fig. 4. Spike sorting performance for heptode signals and tetrode signals as a function of the noise amplitude. 14 neurons were simulated. The standard error of the mean (SEM) is displayed by dashed lines, indicating the significance of the performance benefit. The number of analysed signals was 20 for each simulated lot of neurons. 97
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amplitude of 0.05 the performance without overlapping spikes is 36 percent better than with overlapping spikes.
that demanding, both, heptodes and tetrodes, perform equally for spike sorting.
The dependence on the number of principal components is shown in Fig. 6. It can be seen that heptode and tetrode based spike sorting results are similarly depending on the number of principal components used for analysis. Both yield maximum performance for five principal components.
The neuron model as a point source is, obviously, a simplification. Other simulation algorithms include the morphology of different neurons (Lindén et al., 2013), (Gold et al., 2006). Using such a model would lead to a considerably more realistic generation of spike waveforms and amplitudes on the different recording channels. On the other hand, such an appproach may not yield general results. However, it is not clear if a general or if a situational modelling of neuronal sources and tissues is reasonable, especially with respect to computational burdens.
The performance decrease with lower noise level (see Fig. 4 and 5) is caused by false negative errors of the spike detection algorithm due to a, for this noise level, inappropriate detection threshold. The effect of overlapping spikes is neglected in Fig. 5, thus the effect of inappropriate spike detection threshold setting can be seen. For noise levels 0.03 and 0.05 the threshold is well set. For a noise level of 0.01 the false negative errors lead, as expected, to a decrease in spike sorting performance.
Recent studies have suggested that a neuron could be simulated via an electrical monopole or a dipole model (Mechler and Victor, 2012), (Gratiy et al., 2013), (Destexhe and Bedard, 2012). This would also lead to a different spatial decay of the signal’s amplitude. The simulation of the electrode contacts as point sinks is also a simplification. A simulation of these contacts as planes would lead to more realistic computations of the signal amplitudes on the heptode channels. Using this, insights in the spatial resolution of the electrodes could be gained and more reliable conclusions on the spike sorting performance for different electrode geometries could be obtained. A further improvement is expected when the electric properties of electrode’s glass substrate are taken into account. All these suggestions for improvement may be used as a basis for future research concerning the optimal multichannel electrode for best possible extracellular recordings of neuronal activities. The number of principal components used for classification strongly influences the spike sorting performance. Fig. 6 indicates that the performance loss for heptodes due to using three instead of five principal components is 12 percent. We will work on ways to improve the estimation of the appropriate number of principal components. The automatic selection of spike detection thresholds is not a trivial task, especially for low signal-to-noise ratios. Here, a better threshold estimation method for simulation experiments as well as for analysis of real signals has to be found.
Fig. 6. Spike sorting performance for heptode signals and tetrode signals as a function of the number of principal components. 14 neurons where simulated with noise amplitude 0.05. The standard error of the mean (SEM) is displayed by dashed lines, indicating the significance of the performance benefit. The number of analysed heptode and tetrode signals was 20.
When the spikes of many highly acitve neurons are present in a recording, the problem of overlapping spikes gets relevant for the spike sorting performance. In data simulated in this work, where the number of active neurons was limited to 14, each firing with a rate of 12 spikes per second, the performance decrease is approximately 25 percent. We are currently working on this issue by finding an algorithm that is capable of classifying and separating overlapping spikes. Here heptodes may perform better due to their better spatial resolution.
4. DISCUSSION Heptode and tetrode signals have been simulated with different signal conditions via a novel signal simulation algorithm based on a simple model of neurons and electrodes and have been analysed by our spike sorting algorithm.
To verify our findings evaluations of real heptode signals has to be performed. Especially to verify whether the number of active neurons from which heptodes perform significantly better than tetrodes is truly approximatively 14.
Our results indicate that heptode outperform tetrode recordings when many neurons are present in a signal with a poor signal-to-noise ratio. In signal conditions that are not
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5. ACKNOWLEDGMENTS
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multiple unit records', Journal of neuroscience methods 8(4), 391--397. Mechler, F. & Victor, J. D. (2012), 'Dipole characterization of single neurons from their extracellular action potentials', Journal of computational neuroscience 32(1), 73--100. Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V. & others (2011), 'Scikit-learn: Machine learning in Python', The Journal of Machine Learning Research 12, 2825--2830. Quiroga, R.; Nadasdy, Z. & Ben-Shaul, Y. (2004), 'Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering', Neural computation 16(8), 1661--1687. Roh, S.-e.; Choi, J. H. & Kim, T. (2008), 'A new action potential classifier using 3-Gaussian model fitting', Neurocomputing 71(16), 3631--3634. Schwarz, G. (1978), 'Estimating the dimension of a model', The annals of statistics 6(2), 461--464. Vakman, D. (1996), 'On the analytic signal, the TeagerKaiser energy algorithm, and other methods for defining amplitude and frequency', IEEE Transactions on Signal Processing 44(4), 791--797.
This work is partly funded by BMWi ZIM KF2268909AK2. Thanks to F. Franke and his colleagues for providing us with their spike sorting program and F. Bremmer for neuronal noise data. Special thanks to U. Thomas and D. Höhl for helpful discussions. 5. REFERENCES Dayan, P. & Abbott, L. F. (2005), Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, The MIT Press. Destexhe, A. & Bedard, C. (2012), 'Do neurons generate monopolar current sources?', Journal of neurophysiology 108(4), 953--955. Doerr, C. & Schanze, T. (2013), 'Analytic Signal Based Detection of Extracellular Action Potentials', Biomedical Engineering/Biomedizinische Technik. Franke, F.; Natora, M.; Boucsein, C.; Munk, M. H. & Obermayer, K. (2010), 'An online spike detection and spike classification algorithm capable of instantaneous resolution of overlapping spikes', Journal of computational neuroscience 29(1-2), 127--148. Gold, C.; Henze, D. A.; Koch, C. & Buzsáki, G. (2006), 'On the origin of the extracellular action potential waveform: a modeling study', Journal of neurophysiology 95(5), 3113--3128. Gratiy, S. L.; Pettersen, K. H.; Einevoll, G. T. & Dale, A. M. (2013), 'Pitfalls in the interpretation of multielectrode data: on the infeasibility of the neuronal current-source monopoles', Journal of neurophysiology 109(6), 1681-1682. Gray, C. M.; Maldonado, P. E.; Wilson, M. & McNaughton, B. (1995), 'Tetrodes markedly improve the reliability and yield of multiple single-unit isolation from multi-unit recordings in cat striate cortex', Journal of neuroscience methods 63(1), 43--54. Harris, K. D.; Henze, D. A.; Csicsvari, J.; Hirase, H. & Buzsáki, G. (2000), 'Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements', Journal of neurophysiology 84(1), 401--414. Jolliffe, I. (2002), Principal component analysis, Wiley Online Library. Lewicki, M. S. (1998), 'A review of methods for spike sorting: the detection and classification of neural action potentials', Network: Computation in Neural Systems 9(4), R53--R78. Lindén, H.; Hagen, E.; Łeski, S.; Norheim, E. S.; Pettersen, K. H. & Einevoll, G. T. (2013), 'LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons', Frontiers in neuroinformatics 7. McLachlan, G. & Peel, D. (2000), Finite mixture models, John Wiley & Sons. McNaughton, B. L.; O'Keefe, J. & Barnes, C. A. (1983), 'The stereotrode: a new technique for simultaneous isolation of several single units in the central nervous system from 99
ScienceDirect IFAC-PapersOnLine 48-20 Tetrodes (2015) 094–099 for Spike Sorting? Are Heptodes Better than Are Heptodes Better than Tetrodes Are Heptodes Better than Tetrodes for for Spike Spike Sorting? Sorting? Are Heptodes Better than Tetrodes Spike Sorting? Christopher Doerr*. Thomasfor Schanze*
Christopher Christopher Doerr*. Doerr*. Thomas Thomas Schanze* Schanze* Christopher Doerr*. Thomas Schanze* *Technische Hochschule Mittelhessen (THM) – University of Applied Sciences, *Technische Hochschule Mittelhessen of 35390 Giessen, Germany (e-mail: [email protected], *Technische Hochschule Mittelhessen (THM) (THM) –– University [email protected]) of Applied Applied Sciences, Sciences, 35390 Giessen, Germany (e-mail: [email protected], [email protected]) *Technische Hochschule Mittelhessen (THM) – [email protected]) of Applied Sciences, 35390 Giessen, Germany (e-mail: [email protected], 35390 Giessen, Germany (e-mail: [email protected], [email protected]) Abstract: Multi-neuron extracellular recordings with multichannel microelectrodes, like tetrodes or Abstract: Multi-neuron extracellular with like tetrodes or heptodes, used to get insights in the recordings neuronal information processingmicroelectrodes, in the brain. Spike is the Abstract:are Multi-neuron extracellular recordings with multichannel multichannel microelectrodes, likesorting tetrodes or heptodes, are used to get insights in the neuronal information processing in the brain. Spike sorting is the Abstract: Multi-neuron extracellular with multichannel microelectrodes, like tetrodes or detection classification of extracellular actioninformation potentials (spikes) recorded these electrodes. heptodes, and are used to get insights in the recordings neuronal processing in thewith brain. Spike sorting isHere the detection classification of action potentials recorded these electrodes. heptodes, are used to get insights the sorting neuronal information processing in thewith brain. Spike isHere the we report and on the improvement of in spike performance when using heptodes rather thansorting tetrodes by detection and classification of extracellular extracellular action potentials (spikes) (spikes) recorded with these electrodes. Here we on the improvement of sorting performance when heptodes rather than by detection classification of extracellular action potentials (spikes) recorded withspike thesesorting electrodes. Here simulating tetrode/heptode recordings analysing them automatically with our algorithm. we report report and on the improvement of spike spikeand sorting performance when using using heptodes rather than tetrodes tetrodes by simulating tetrode/heptode recordings and analysing them automatically with our spike sorting algorithm. we report on the improvement of spike sorting performance when using heptodes rather than tetrodes by Simulation of signals is performed via a simple model of neurons and electrodes that has the ability to simulating tetrode/heptode recordings and analysing them automatically with our spike sorting algorithm. Simulation of signals is performed via a simple model of neurons and electrodes that has the ability simulating tetrode/heptode recordings and analysing them automatically with our spike sorting algorithm. emulate preferably realistic recording conditions without too much complexity. Results indicate that Simulation of signals is performed via a simple model of neurons and electrodes that has the ability to to emulate preferably realistic conditions without too much Results indicate that Simulation of performance signals is performed a simple model of neurons andcomplexity. electrodes has the ability to spike sorting isrecording better via when heptodes instead of tetrodes are used tothat record from highly emulate preferably realistic recording conditions without too much complexity. Results indicate that spike sorting performance is better when heptodes instead of tetrodes are used to record from highly emulate preferably realistic recording conditions without too much complexity. Results indicate that active local clusters consisting of many neurons and when the signals have a low signal-to-noise ratio. spike sorting performance is better when heptodes instead of tetrodes are used to record from highly active local clusters consisting of neurons and when the signals haveare aa low ratio. spike sorting performance is better when heptodes instead of tetrodes usedsignal-to-noise to record from highly active clusters consisting of many many and Control) when theHosting signals low signal-to-noise ratio. © 2015,local IFAC (International Federation ofneurons Automatic byhave Elsevier Ltd. Allactivity, rights reserved. Keywords: classification, electrodes, modelling, multisensor integration, neuronal recording, active local clusters consisting of many neurons and when the signals have a low signal-to-noise ratio. Keywords: classification, electrodes, modelling, multisensor multisensor integration, integration, neuronal neuronal activity, activity, recording, recording, signal processing, simulation, spike sorting. Keywords: classification, electrodes, modelling, signal processing, simulation, spike sorting. Keywords: classification, electrodes, modelling, multisensor integration, neuronal activity, recording, signal processing, simulation, spike sorting. signal processing, simulation, spike sorting. 1. INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION Multi-neuron recordings with multichannel microelectrodes, 1. INTRODUCTION Multi-neuron recordings microelectrodes, like tetrodes (four channels) or multichannel heptodes (seven channels), are Multi-neuron recordings with with multichannel microelectrodes, like tetrodes (four channels) or heptodes (seven Multi-neuron recordings with multichannel microelectrodes, increasingly used to get insights in the neuronal processingare of like tetrodes (four channels) or heptodes (seven channels), channels), are increasingly used to get insights in the neuronal processing like tetrodes (four channels) or heptodes (seven channels), are information in the brain. The extracellular action potentials increasingly used to get insights in the neuronal processing of of information in the brain. The extracellular potentials increasingly used get the insights in the neuronal processing of (spikes) captured recordings ariseaction from multiple information in thetoby brain. The extracellular action potentials (spikes) by the recordings arise from multiple information in thedistances brain. extracellular action neurons several to the electrode are potentials generally (spikes) atcaptured captured by theThe recordings ariseand from multiple neurons several distances to the are (spikes) by theand recordings ariseand multiple superimposed by artefacts noise. neurons at atcaptured several distances to the electrode electrode andfrom are generally generally superimposed by artefacts and noise. neurons at several distances to the electrode and are generally superimposed by artefacts and noise. The detection by of artefacts spikes and superimposed and their noise.classification in clusters, The of spikes and their in which correspond different is called spike sorting. The detection detection of to spikes and neurons, their classification classification in clusters, clusters, which correspond to different neurons, is called spike The detection of spikes and their classification in clusters, which correspond to different neurons, is called spike sorting. sorting. Fig. 1 correspond shows on the left side neurons, an illustration of spike a heptode, as which to different is called sorting. Fig. 1 shows on the left side an illustration of a heptode, manufactured by Thomas RECORDING GmbH, Gießen, Fig. 1 shows on the left side an illustration of a heptode, as as manufactured GmbH, Gießen, Fig. 1 shows theThomas leftofside an illustration of awith heptode, as 100 µm Germany and on aby a RECORDING recording situation several manufactured bysketch Thomas RECORDING GmbH, Gießen, Germany and a sketch of a recording situation with several manufactured by Thomas RECORDING GmbH, Gießen, neurons. Spikes recorded with these electrodes, have different Germany and a sketch of a recording situation with several 100 100 µm µm neurons. recorded with these different Germany and sketch a channels recording with several amplitudes on aeach of of the assituation can behave seen in the 100 Fig. µm 1. Sketch of an extracellular recording with a fibreneurons. Spikes Spikes recorded with these electrodes, electrodes, have different amplitudes on each of channels as seen in the Fig. of aa fibreneurons. Spikes recorded with these electrodes, different signal sketch 1). the This is due thebe fact that and several neurons. Left:recording Heptodewith geometry and amplitudes on (Fig. each of the channels astocan can behave seen in the the heptode Fig. 1. 1. Sketch Sketch of an an extracellular extracellular recording with fibresignal sketch (Fig. 1). This is due to the fact that the heptode and several neurons. Left: Heptode geometry and amplitudes on each of the channels as can be seen in amplitude of a (Fig. spike 1). on This a channel depends the that distance Fig. 1. Sketch of an extracellular recording with fibreof neurons relative to the electrode. Thea diameter signal sketch is due to theonfact the positions heptode and several neurons. Left: Heptode geometry and of amplitude of a spike on a channel depends on the distance positions of neurons relative to the electrode. The diameter of signal sketch (Fig. 1). This is due to the fact that the between this channel’s contact, i.e. conductor/tissue interface, and several Left: geometry andthree the heptode’s shaft isneurons. about 100 µm.Heptode Tetrodes onlydiameter have amplitude of a spike on a channel depends on the distance heptode positions of neurons relative to the electrode. The of between this channel’s contact, i.e. conductor/tissue interface, the heptode’s shaft is about 100 µm. Tetrodes only have three amplitude of a spike on a channel depends on the distance and the signal generating neuron. The distribution of the positions of neurons relative to the electrode. The diameter of of six electrodes on the ring (e.g.only no electrodes between this channel’s contact, i.e. conductor/tissue interface, instead the heptode’s shaft is about 100outer µm. Tetrodes have three and signal generating The distribution of instead of electrodes the outer ring no between this channel’s i.e. conductor/tissue spike’s overcontact, the neuron. channels encodes the interface, neuron’s the heptode’s shaft is about 100The µm.distant, Tetrodes only have three positions two, four andon indifferent and the the amplitude signal generating neuron. The distribution of the the at instead of six six electrodes onsix). the outer ring (e.g. (e.g. no electrodes electrodes spike’s amplitude over the channels encodes the neuron’s at positions two, four and six). The distant, indifferent and the signal generating neuron. The distribution of the position relative to the electrode distinctly. This heptode or instead of six electrodes on the outer ring (e.g. no electrodes reference electrode is not shown here. Right: Signals spike’s amplitude over the channels encodes the neuron’s at positions two, four and six). The distant, indifferent position relative to the distinctly. This or electrode is not here. Right: Signals spike’s theknown channels encodes neuron’s tetrode effect, as the stereotrode effect at positions two, six). distant, indifferent recorded with thefour heptode. NoteThe that the amplitude position amplitude relativeoriginally to over the electrode electrode distinctly. Thistheheptode heptode or reference reference electrode is and not shown shown here. Right: Signals tetrode effect, originally known as the stereotrode effect with the heptode. Note that the amplitude position relativeO'Keefe to the and electrode distinctly. This heptode or recorded (McNaughton, Barnes, provides a useful reference electrode is not shown here. Right: Signals distribution of the spikes depends on the position of the tetrode effect, originally known as1983), the stereotrode effect recorded with the heptode. Note that the amplitude (McNaughton, O'Keefe and Barnes, 1983), provides aa useful of the spikes depends on the position tetrode effect, originally the et stereotrode effect feature for spike classification asasGray al. (1995) and distribution recorded with the heptode. Note that amplitude neurons relative to the contacts of the heptode’s recording (McNaughton, O'Keefe andknown Barnes, 1983), provides useful distribution of the spikes depends on the position of of the the feature for spike classification as Gray et al. (1995) and neurons relative to the contacts of the heptode’s recording (McNaughton, O'Keefe and Barnes, 1983), provides a useful Harris al. (2000) found for tetrodes. distribution of the depends on position of the Also note thatcontacts almost simultaneously active featureetfor spike classification as Gray et al. (1995) and channels. neurons relative tospikes the of thethe heptode’s recording Harris al. found Also note that almost simultaneously feature spike classification as Gray et al. (1995) and channels. neurons totothe of the heptode’sactive recording can lead waveform Harris et etfor al. (2000) (2000) found for for tetrodes. tetrodes. channels.relative Also note thatcontacts almostinterferences. simultaneously active The of (2000) heptodes instead of tetrodes for extracellular channels. neurons can lead to waveform interferences. Harrisuse et al. found for tetrodes. Also note that almost simultaneously active neurons can lead to waveform interferences. The instead tetrodes extracellular recordings expected to furtherof performance of neurons can lead to waveform interferences. The use use of ofis heptodes heptodes instead ofincrease tetrodesthefor for extracellular To verify this assumption we developed a heptode signal recordings is expected to further increase the performance The use of heptodes instead of tetrodes for extracellular spike sorting. This should be due to the fact that with an recordings is expected to further increase the performance of of To this we developed aa heptode signal simulation based on model of neurons and To verify verify algorithm this assumption assumption wea simple developed heptode signal spike sorting. This should be due to the fact that with an recordings isnumber expected to further increase performance of simulation increasing of recording the with signal spike sorting. This should be due to channels thethe fact that an algorithm based on a simple model of neurons To verify this assumption we developed a heptode signal electrodes and a spike sorting algorithm with which the simulation algorithm based on a simple model of neurons and and increasing number of recording the signal spike sorting. This should bethe dueinfluence to channels the fact that with an electrodes redundancy increases or that of the noise and increasing number of recording channels the signal and a spike sorting algorithm with which simulation algorithm based on a simple model of neurons and signals can be analysed automatically. As an example for electrodes and a spike sorting algorithm with which the the redundancy increases or the of noise and increasing number of recording channels signal artefacts decreases. redundancy increases or that that the influence influence of the thethe noise and signals can be analysed automatically. As an example electrodes and a spike sorting algorithm with which the tetrodes and heptodes, we use the electrode arrangement of signals can be analysed automatically. As an example for for artefacts redundancy increases or that the influence of the noise and tetrodes artefacts decreases. decreases. and heptodes, we use the electrode arrangement signals can be analysed automatically. As an example for tetrodes and heptodes, we use the electrode arrangement of of artefacts decreases. Copyright © 2015 IFAC 94 tetrodes and heptodes, we use the electrode arrangement of 2405-8963©©2015 2015,IFAC IFAC (International Federation of Automatic Control) Copyright 94 Hosting by Elsevier Ltd. All rights reserved. Copyright © 2015 94 Control. Peer review underIFAC responsibility of International Federation of Automatic Copyright © 2015 IFAC 94 10.1016/j.ifacol.2015.10.121
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heptodes and tetrodes RECORDING GmbH.
as
manufactured
by
Thomas
different neurons may overlap and produce a “corrupted” spike waveform, which is a linear superposition of the original spike waveforms (Figs. 1 and 2). The fire-rates of the neurons are approximately 12 spikes per second. This leads to a high amount of overlapping spikes and means a challenge for the spike sorting algorithm, especially for the clustering.
The focus of this work lies on the spike sorting performance with tetrode and heptode signals depending on the number of units present in the signal and the amount of noise contamination. 2. METHODS 2.1 Signal simulation algorithm To simulate heptode and tetrode signals we use a simple model of neurons and electrodes. The heptode is simulated with point sinks as electrode contacts. This makes it easy to compute the distance to neurons and therefore the amplitude of the spikes on the channels. The electrode contacts two to seven are equally spaced on a circle with a diameter of 43 µm and each have a distance of 60.8 µm to the first electrode contact. Neurons are simulated as point sources that are placed at arbitrary positions relative to the electrode’s tip. The positions of the neurons are limited to a maximum radial distance to the heptode’s surface of 15 µm. The minimum distance between two neurons is set to 20 µm to avoid neurons with highly similar amplitude distributions and, thus, to take into account their spatial extension of about 10 µm in diameter. The spikes fired by a neuron are modelled as biphasic spikes by superimposing two time-shifted and weighted Gaussian curves (see spikes in Fig. 1 or Fig. 2), which is assumed to be a realistic approximation of extracellularly recorded action potentials (Roh, Choi and Kim, 2008). The spikes of a single neuron are modelled as uniform events with amplitude 1 at the neuron's position. The duration of the spikes of a neuron is generated by a uniformly distributed one-off random selection process over [0.8 ms, 2.8 ms]. The amplitude of a spike on one channel of the heptode depends on the distance between neuron and the respective electrode contact via the exponential model developed by Gray et al. (1995). Here the amplitude V(x) at distance x obeys
V ( x) = V (0) ⋅ exp(− x / λ ),
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(1)
with λ = 28.42 µm. λ is the decay constant of the model, which has been determined by Gray et al. (1995) via in vivo recordings with tetrodes. The occurrences of spikes, i.e. spike times, are computed for every neuron by an individual interspike interval distribution. These are simulated by an exponential distribution, modified by a Gaussian distribution to incorporate an absolute and a relative refractory period (Dayan and Abbott, 2005). From this distribution, quite natural interspike intervals are obtained for every neuron. Spike times are computed by concatenating subsequent interspike intervals. Since the spike times of every neuron are computed individually, spikes of
Fig. 2. Segment taken from a simulated heptode signal. Note the channel related amplitude distributions of the spikes indicate the spatial resolution of the heptode. The signal to noise ratio can be seen as similar to real recordings (Uwe Thomas, Thomas RECORDING GmbH, Giessen, Germany, personal communication). Observe the overlapping spikes at t = 16 ms. 95
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Noise is simulated by adjusting the amplitude distribution and the spectrum of Gaussian white noise according to the noise of a neuronal signal that has been recorded by the group of Frank Bremmer at the Department of Neurophysics, Philipps-Universität Marburg, Germany with Thomas RECORDING electrodes in the area V4 of a macaca mulatta. The artificial noise is then added with an arbitrary amplitude on the simulated spike signal.
Compared to cubic spline interpolation our analyses indicated no clear difference in spike classification performance. In the multichannel recording case we use the concatenated spike waveforms for alignment, except for the pre-alignment, were the mean shift over the channels is computed. The spikes si[n] of channel i consist of 50 samples. The concatenated waveforms s therefore consist, in the heptode case, of 350 samples, i.e. s=[s0, …, s6].
Signals are simulated as heptode signals. By turning off the signals on channels three, five and seven a tetrode signal is obtained (see Fig. 1).
For feature extraction we use a standard PCA. In the multichannel recording case we use again the concatenated waveforms of the spikes. Therefore, we can combine the spike’s amplitude distribution over the signal channels and its waveform in the feature extraction. PCA should be capable of finding the optimal energy related combination of waveform and amplitude distribution to separate spikes from different neurons under different, undetermined signal conditions.
Fig. 2 shows a segment of a simulated heptode signal. Observe the various spike time courses and the apparent channel and neuron related amplitude distributions. To calculate signal-to-noise ratio, we compute the maximum amplitudes of the recorded spikes of all neurons. The amplitudes have the range 0.01 to 0.93. The mean maximum amplitude is 0.13, its standard deviation is 0.13. Then we calculated the mean signal-to-noise ratio by 0.13/stdev(noise). 2.2 Spike sorting We adopted and refined parts of a spike sorting algorithm developed by Franke et al. (2010) that has been developed for analysis of multichannel signals. To detect spikes we initially compute the instantaneous energy of the signal. In improvement to Franke et al. (2010), this is done by a multiresolution energy filter (MEF) (Doerr and Schanze, 2013). The MEF is based on an analytic signal approach and consists of multiple, spectral overlapping, constant Q Hilbert bandpass filters. Instantaneous energy calculation of noisy, wideband signals via the analytic signal is superior to teager energy operator (TEO) based approaches, which also give poor results for a wide range of signals (Vakman, 1996). Therefore an analytic signal based approach is more suitable for spike detection than a TEO based one.
Fig. 3. Spike sorting performance for heptode signals and tetrode signals as a function of the number of neurons. The noise level was set to 0.05. For signals with more neurons (i.e. 14) the heptode performance significantly better as the tetrode. The standard error of the mean (SEM) is displayed by dashed lines, indicating the significance of the performance benefit. The number of analysed signals was 20 for each simulated lot of neurons.
The spike detection threshold is set by a fixed multiple of the median of the computed energy. The median serves as an estimation for the noise level (Quiroga, Nadasdy and BenShaul, 2004). An automatic selection of the spike detection threshold is necessary for automatic evaluation of simulated signals. For spike alignment we compare the interpolated and squared spike waveforms to a mean waveform, computed from all squared spike waveforms, via correlation. The shifted spike waveform which is best correlated to the mean waveform is taken as the best aligned waveform. After all spikes have been processed a new mean spike is computed and all spikes are tested again (Franke et al., 2010). This procedure is repeated until a convergence criterion is reached.
The number of principal components used for spike classification is hard to set automatically. It can be left as a parameter manually to set. A scree plot with the variance explained by the principal components can support the user in choosing an appropriate value (Jolliffe, 2002). Spikes are then classified via a heteroscedastic Gaussian mixture model (McLachlan and Peel, 2000), in contrast to a homoscedastic Gaussian mixture model (GMM) that was used by Franke et al. (2010), into several clusters. The
For a precise computation of an initial mean waveform, we initially align every spike according to its centre of mass. We use linear interpolation due to performance reasons. 96
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number of clusters is automatically determined via searching the minimum of the Bayesian information criterion (Schwarz, 1978). An interesting feature is that this clustering scales with the numbers of channels used for spike sorting. Here we use the GMM object of the python scikit-learn library (Pedregosa et al., 2011).
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The performance of heptodes and tetrodes for different numbers of neurons present in the signal is shown in Fig. 3. The performance of the heptode for few neurons is virtually equal to the tetrode’s performance. With more neurons present (i.e. 14), the heptode performs significantly better than the tetrode (0.72 to 0.66). Fig. 4 shows the performance of heptodes and tetrodes for different noise amplitudes. Here, the heptode’s performance is significantly higher for noise levels from 0.05 to 0.09. At a noise level of 0.09 it is about 50 percent better.
2.3 Evaluation of classification results Simulated signals are analysed automatically by the spike sorting algorithm with comparable or similar parameterisation. Classification results are evaluated automatically and quantitatively. As a measure for the spike sorting performance, the fraction of correctly classified spikes of all spikes in the signal is computed.
For less noise, both heptodes and tetrodes perform similarly. Since in these signals are 14 neurons present (the maximum in Fig. 3) it gets clear that heptodes perform better than tetrodes when many neurons are active and when the noise level is high.
To find correctly classified spikes, we assign every neuron to the cluster where the majority of spikes of this neuron is classified to. Every spike of this neuron that is assigned to this cluster is counted as correctly classified. The spikes of a neuron that has been classified to other clusters are not counted. 3. RESULTS Heptode and tetrode signals are simulated and analysed with our spike sorting algorithm. All analysed signals have a length of 100 seconds with a sampling rate of 25 kHz and contain about 1200 spikes per neuron.
Fig. 5. Spike sorting performance for heptode and tetrode signals, consisting of non-overlapping spikes, as a function of the noise amplitude. The overall performance is clearly better as in Fig. 4 indicating that overlapping spikes infer spike sorting. 14 neurons were simulated. The standard error of the mean (SEM) is displayed by dashed lines, indicating the significance of the performance benefit. The number of analysed signals was 20 for each simulated lot of neurons. In comparison to the results in Fig. 3 one can see the maximum performance of both, heptodes and tetrodes, is clearly lower in Fig. 4. This may be due to the fact, that the number of neurons in the signals in Fig. 4 is high and therefore the number of overlapping spikes, which cannot be separated properly by our algorithm, is considerably higher. To support this finding, we simulated signals where overlapping of spikes is precluded. The results are shown in Fig. 5. Here the maximum performance for heptodes and tetrodes is clearly higher. E. g. for heptodes and with a noise
Fig. 4. Spike sorting performance for heptode signals and tetrode signals as a function of the noise amplitude. 14 neurons were simulated. The standard error of the mean (SEM) is displayed by dashed lines, indicating the significance of the performance benefit. The number of analysed signals was 20 for each simulated lot of neurons. 97
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amplitude of 0.05 the performance without overlapping spikes is 36 percent better than with overlapping spikes.
that demanding, both, heptodes and tetrodes, perform equally for spike sorting.
The dependence on the number of principal components is shown in Fig. 6. It can be seen that heptode and tetrode based spike sorting results are similarly depending on the number of principal components used for analysis. Both yield maximum performance for five principal components.
The neuron model as a point source is, obviously, a simplification. Other simulation algorithms include the morphology of different neurons (Lindén et al., 2013), (Gold et al., 2006). Using such a model would lead to a considerably more realistic generation of spike waveforms and amplitudes on the different recording channels. On the other hand, such an appproach may not yield general results. However, it is not clear if a general or if a situational modelling of neuronal sources and tissues is reasonable, especially with respect to computational burdens.
The performance decrease with lower noise level (see Fig. 4 and 5) is caused by false negative errors of the spike detection algorithm due to a, for this noise level, inappropriate detection threshold. The effect of overlapping spikes is neglected in Fig. 5, thus the effect of inappropriate spike detection threshold setting can be seen. For noise levels 0.03 and 0.05 the threshold is well set. For a noise level of 0.01 the false negative errors lead, as expected, to a decrease in spike sorting performance.
Recent studies have suggested that a neuron could be simulated via an electrical monopole or a dipole model (Mechler and Victor, 2012), (Gratiy et al., 2013), (Destexhe and Bedard, 2012). This would also lead to a different spatial decay of the signal’s amplitude. The simulation of the electrode contacts as point sinks is also a simplification. A simulation of these contacts as planes would lead to more realistic computations of the signal amplitudes on the heptode channels. Using this, insights in the spatial resolution of the electrodes could be gained and more reliable conclusions on the spike sorting performance for different electrode geometries could be obtained. A further improvement is expected when the electric properties of electrode’s glass substrate are taken into account. All these suggestions for improvement may be used as a basis for future research concerning the optimal multichannel electrode for best possible extracellular recordings of neuronal activities. The number of principal components used for classification strongly influences the spike sorting performance. Fig. 6 indicates that the performance loss for heptodes due to using three instead of five principal components is 12 percent. We will work on ways to improve the estimation of the appropriate number of principal components. The automatic selection of spike detection thresholds is not a trivial task, especially for low signal-to-noise ratios. Here, a better threshold estimation method for simulation experiments as well as for analysis of real signals has to be found.
Fig. 6. Spike sorting performance for heptode signals and tetrode signals as a function of the number of principal components. 14 neurons where simulated with noise amplitude 0.05. The standard error of the mean (SEM) is displayed by dashed lines, indicating the significance of the performance benefit. The number of analysed heptode and tetrode signals was 20.
When the spikes of many highly acitve neurons are present in a recording, the problem of overlapping spikes gets relevant for the spike sorting performance. In data simulated in this work, where the number of active neurons was limited to 14, each firing with a rate of 12 spikes per second, the performance decrease is approximately 25 percent. We are currently working on this issue by finding an algorithm that is capable of classifying and separating overlapping spikes. Here heptodes may perform better due to their better spatial resolution.
4. DISCUSSION Heptode and tetrode signals have been simulated with different signal conditions via a novel signal simulation algorithm based on a simple model of neurons and electrodes and have been analysed by our spike sorting algorithm.
To verify our findings evaluations of real heptode signals has to be performed. Especially to verify whether the number of active neurons from which heptodes perform significantly better than tetrodes is truly approximatively 14.
Our results indicate that heptode outperform tetrode recordings when many neurons are present in a signal with a poor signal-to-noise ratio. In signal conditions that are not
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5. ACKNOWLEDGMENTS
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