At present, the practicality of experimental Brain Machine Interface (BMI) hardware

Transcription

1 Chapter Spike Detection.1 Introduction At present, the practicality of experimental Brain Machine Interface (BMI) hardware is limited by the transcutaneous cortical electrodes and the omnipresent cables between the electrodes and data processors. The advent of wireless data acquisition hardware promises to facilitate fully implantable BMIs, bringing brain controlled prostheses from the realm of the experimental into that of the practical. Incorporating spike detection will allow the BMI to transmit only the action potential (AP) waveforms and their respective arrival times instead of the sparse, raw signal in its entirety. This compression reduces the transmitted data rate per channel, and thus increases the number of channels that may be monitored simultaneously []. Spike detection can further reduce the data rate if spike counts are transmitted instead of spike waveforms. Spike detection will also be a necessary first step for any future hardware implementation of an autonomous spike sorter [3]. This chapter evaluates a number of known spike detection algorithms and determines which are best suited for hardware implementation in an application specific integrated circuit (ASIC) with limited computational resources. 17

2 Neither the study of spike detection nor is its application to neural signals is new [75]; the implementation of spike detection in the real-time BMI, however, presents novel problems. The hardware realization of a spike detector in a wireless BMI must operate in real-time and function at realistic signal to noise ratios (SNRs). Furthermore, BMI based spike detectors must work with limited computational resources that are divided among dozens of channels. Finally, spike detection must be fully autonomous; as the number of channels in a system scales, it will become unreasonable for a user to manually determine threshold levels or create spike templates. Spike detection can be broken down into two separate problems. The first involves preprocessing the signal to accentuate the spike relative to the noise. The second involves determining which threshold to apply to the processed signal. This chapter only addresses the preprocessor question; algorithms for autonomously determining the optimal threshold have not been evaluated. The findings of this study have been incorporated into the spike detection hardware in the Backpack (Section 3..1). For the purposes of the study in this chapter, it is assumed that spikes transmitted from the BMI will be spike sorted by a host computer before being used to drive a neuroprosthetic limb. Since false positive detections will be rejected by the spike sorter, they are undesirable only in terms of the telemetry bandwidth that they consume. Spike detectors must therefore maximize the number of correctly detected action potentials while limiting the number of false positive spikes that would otherwise reduce the effective system bandwidth.. Methods..1 Overview This study compares 17 preprocessor algorithms for their applicability to neural spike detection in a real-time BMI. The study was conducted in two phases. In the first 1

3 phase, all 17 preprocessors were applied to each of one-second long artificial neural signals. In the second phase, the best five preprocessors from the first phase were applied to each of 5 experimentally obtained in vivo signals. The results from both phases were analyzed to determine which preprocessor to implement in the Backpack. The following procedure was established to quantify the performance of a preprocessor on a particular test signal. First, the preprocessor was applied to the test signal. Then, a series of threshold values were applied to the resulting signal. Positive threshold crossings were identified at each threshold level, and labeled as detected events. Detections were evaluated both with and without a refractory period (RP) check that rejected positive threshold crossings occurring fewer than samples (.msec) apart. Each qualifying positive threshold crossing was classified as either a true or a false detection depending on whether it occurred within ± samples of an actual spike. The actual spike times are known a priori for the artificial data signals (see Section..), but must be determined empirically for the in vivo data. The tally of correct detections and false alarms is fed into a cost function which was developed specifically for analyzing spike detection results in the context of the wireless BMI. Cost function scores were grouped according to signal SNR, averaged, and then plotted versus threshold values expressed as a percentage of the range of the preprocessed input signal. In order for threshold values to be normalized, it was necessary that all test signals have the same RMS noise level. Therefore, each of the in vivo signals was scaled appropriately. This scaling was not necessary for the artificial test signals, as they were all created with equal RMS noise levels. 19

4 .. Test Data Signals Artificial Data Two sets of 3 artificial test signals (duration 1 sec, F S = 31.5kHz) were created using a bank of 3 action potential (AP) waveforms isolated from in vivo motor cortex recordings from a rat, an owl monkey, and a macaque (1 APs per species) aligned at their minimum points (see Figure.1). Signals in the first test set consisted of one near-field signal neuron and 5 noise neurons. Each of the 3 APs was used as the signal neuron for a family of ten signals, with the signal neuron amplitudes being varied to achieve ten signal to noise ratios ranging linearly from 1. to.. In every signal, the near-field neuron fired 5 times, once every 5 samples (1msec). The firing times of the 5 noise neurons were determined according to the Poisson distribution; firing rates were uniformly distributed between 5 9Hz. The number of noise neurons is an approximation based on the assumptions that (a) only neurons within 1µm of the electrode are detectable [3] (b) the density of motor cortex neurons in primates is 3, /mm 3 [37] (c) AP amplitudes are inversely proportional to their distance from the electrode, and (d) a portion of the detectable neurons may be silent during a particular task [3]. The combination of 5 noise neurons with the distribution of their firing rates produces an average of 5 noise samples per time step, sufficient to create a realistic background signal. The calculated thermal noise contributions from a 1M Ω recording electrode and an analog front end amplification circuit (V th = 1µV rms ) were added to the signals. All signals were bandpass filtered with a linear phase FIR filter (5.5kHz). A single family of signals from the first test data set is shown in Figure.. The second test set consisted of signals with pairs of overlapping signal spikes and 5 noise neurons. Fifty pairs of spikes were located every 5 samples, with the interspike interval of each pair selected at random between and 5 samples. The

5 rat owl monkey macaque..9 t (msec) (a) generic alternate (3) alternate (1)..9 time (msec) (b) Figure.1: (a) The 3 action potential waveforms used to generate the test data set. These were isolated from in vivo recordings of a rat, owl monkey, and macaque. (b) The three matched filter templates used to analyze the data. The generic template is averaged over all 3 base APs. The two alternate templates represent averages over three and one base AP, chosen at random from the original 3. 1

6 Time (seconds) (a) Time (seconds) (b) Figure.: (a) A family of ten test signals generated using the same action potential waveform as the sole near-field neuron. The amplitude of the near-field neuron is varied to create signals with 1 evenly spaced SNRs. The SNR values for each signal are shown to the left. (b) Zoomed in view of the same signals. The first spike waveforms in each signal is seen in detail.

7 Table.1: SNR statistics of the spike detection in vivo test signals Species Mean SNR Std SNR Min SNR Min SNR Rat Owl Monkey Macaque spike waveforms for both spikes in each pair were chosen at random from the bank of 3 in vivo waveforms. As before, 3 test signals were generated at ten signal to noise ratios varying linearly from 1. to.. In Vivo Data A second class of test data was created from actual cortical signals recorded in vivo. This class is comprised of 5 ten-second signals taken from five different animals (two macaques, two rats, one owl monkey), each under different recording conditions. The data was sorted manually using the Offline Spike Sorter software package (Plexon, Inc) yielding 113 individual units whose signal to noise ratios (SNRs) varied from 1. to 7.. SNR statistics are summarized by species in Table.1. All signals were resampled to F s = 31.5ksamples/sec and scaled to a constant background noise RMS level. Samples of data from this class are shown in Figure.3. The in vivo signals were comprised, on average, of.1 units per signal, and each unit fired at an average rate of 1.1 times per second...3 Preprocessors The 17 preprocessors considered in this study can be broken down into three classes. Simple Threshold 1. Null : No preprocessor is applied: Ψ{x[n]} = x[n]. 3

8 Time (msec) Figure.3: Sample data from three of the signals in the in vivo set of test data. From top to bottom, the signals were recorded from an owl monkey, a macaque, and a rat, respectively. The signals have been normalized so that RMS background noise level is constant.

9 . Negation : Signal is inverted: Ψ{x[n]} = x[n]; equivalent to applying a negative threshold 3. Absolute Value (Abs) : Absolute value of the signal: Ψ{x[n]} = x[n] ; equivalent to applying both positive and negative thresholds simultaneously. Energy Based 1. NEO(δ) : Non-linear energy operator: Ψ{x[n]} = x [n] x[n+δ]x[n δ], where 1 δ.. SNEO(δ) : Smoothed non-linear energy operator: convolution of NEO(δ) with a six point Bartlett window [9]; 1 δ Matched Filter Based 1. Matched Filter (MF) : Convolution of the raw signal with a template that is the average of the 3 APs used to generate the in vivo test data.. NEO(δ) w/ MF : Convolution of the NEO(δ) signal with a template that is the average of the action potential waveforms after being processed by NEO(δ). 3. Absolute Value w/ MF : Convolution of the Abs signal with a template that is the average of the action potential waveforms after being processed by Abs. The matched filter template was created by averaging together the 5 AP events in each of the 3 largest signals from the non-overlapping artificial data set. Since the AP times were known precisely, there was no alignment error associated with averaging the APs from the artificial signals. Note that the same matched filter template created from the artificial data set was used when applying the matched filter to signals from the in vivo data set. 5

10 .. Cost Function A cost function was developed to evaluate the relative benefits of implementing any particular preprocessor in a generic BMI. The cost function comprises three terms, each normalized to one and weighted according to its perceived relevance. CF (P D, nf a, pp) = w 1 P D w (r ms m P D + nf a) n b BW w 3 C(pp) F s n F c (.1) where: P D is the probability of correctly detecting a spike; nf a is the number of false alarm detections per second; pp is the preprocessor; w 1,,3 are the weights; r ms is the maximum expected sustained firing rate per neuron; m is the maximum expected number of neurons per channel; n is the number of channels in the BMI; b is the number of bytes per spike transmitted by the BMI; BW is the available wireless data rate of the BMI; C(pp) is the number of clock cycles required by preprocessor pp to compute one value; F s is the BMI sampling rate; and F c is the system clock frequency. The values for C(pp) are shown in Table. and are based on the assumption that each multiply and accumulate (MAC) operation in an ASIC requires ten clock cycles [7], while negations and squarings (which can be realized with look-up tables) require only one clock cycle each. The three terms of Equation.1 reflect the fact that an effective BMI must (a) detect as many APs as possible, (b) not exceed its maximum wireless data rate, and (c) operate in real-time. The second term applies the bandwidth limit by forcing the maximum number of detected spikes per channel per second (both correct detections and false alarms) times the number of channels times the number of bytes per spike to be less than the available wireless data rate: (r ms m P D +nf a) n b BW, or equivalently, (rms m P D+nF a) n b BW 1. The third term reflects the real-time implementation constraint by requiring that the total number of clock cycles per second (C(pp) F s n) be less than the clock frequency, or equivalently, C(pp) F s n F c 1. The second and third terms in Equation.1 are

11 Table.: Estimated number of clock cycles required per sample to perform spike detection using each of the preprocessors. Preprocessor Req d Computation Req d Clock Cycles Null N/A Negation 1 neg 1 NEO(δ) 1 sq. & 1 MAC 11 SNEO(δ) NEO(δ) & 5 MACs 1 Abs 1 neg. 1 Matched Filter 51 MACs 51 NEO(δ) w/ MF NEO(δ) & 51 MACs 51 Abs w/ MF 1 neg. & 51 MACs 511 Table.3: Constant terms used to evaluate the cost function (Equation.1). Constant Value Units n 9 channels b 7 bytes/spike r ms 5 spikes/sec m 3 neurons/channel F s k samples/sec F c 9 1 clock cycles/sec BW 3k bytes/sec w 1 1 w 1 w 3 1 subtracted so that the score is reduced as the system s available wireless bandwidth and clock cycles are consumed. The cost function was evaluated using constants that reflect the specific requirements of the Backpack (Table.3). The value for the bandwidth, BW, is the Backpack s net data throughput, measured in the laboratory, across an IEEE.11b wireless UDP network. The weights w 1,,3 were selected to reflect a subjective interpretation of the relative importance of detecting as many APs as possible since it has been shown that even small numbers of missed spikes 7

12 can greatly deteriorate the information content of a spike train [77]..3 Results.3.1 Artificial Data The cost function (Equation.1) was computed for each of the artificial test signals, and the scores were grouped according to SNR and averaged. Figure. shows typical families of cost function curves arranged by preprocessor with each trace representing signals of different SNRs. Input signals are swept from minimum to maximum SNR. The x-axis for each graph has been normalized to the maximum range of the preprocessed signal. The shapes of the cost function curves are as expected. At low threshold values there is a high incidence rate of false positive detections which lower the cost function score accordingly. As the threshold values increase, fewer false detections occur, and the cost function scores increase. The scores reach a plateau when the thresholds are so high that almost all action potentials are detected while almost no false positives occur. Finally, as the thresholds increase beyond the peak signal values, the number of correct detections falls to zero. The cost function scores are reduced to the third term of Equation.1, which is constant for each preprocessor. For any given preprocessor, signals with low SNRs score relatively poorly and have a limited range of optimal threshold values. Signals with bigger SNRs result in greater scores over a larger range of threshold values. Abs produces the greatest cost function scores; scores for the Negation and NEO operators are slightly lower than those for Abs and are maximized over a smaller range of threshold values. The matched filter works over the widest range of threshold values but produces a substantially lower cost function score due to its computationally intensive nature. Table. ranks the maximum scores achieved by each preprocessor. For brevity, only the top five scores in each category (overlapping vs. non-overlapping spikes;

13 1 Absolute Value SNR 5 1 Negation SNR 5 Cost Function Score Cost Function Score Threshold (Pct. of Input Range) 1 1 Threshold (Pct. of Input Range) 1 1 NEO() SNR 5 1 Matched Filter SNR 5 Cost Function Score Cost Function Score Threshold (Pct. of Input Range) 1 1 Threshold (Pct. of Input Range) 1 Figure.: Families of cost function score curves for four preprocessors. Each of the ten curves within a family are color-coded according to the test signal SNR. All curves were taken from data generated with non-overlapping spikes and using a sample refractory period to qualify positive threshold crossings as valid spikes. Abs, Negation, and NEO() are the best three preprocessors in this category (see Table.). The matched filter curves are included for comparison. Note that the y-axis for the matched filter plot does not match those of the other three. Cost function scores for the matched filter are lower than for the other preprocessors due to the large number of MAC operations required for computation. 9

14 Table.: The five overall highest scoring preprocessors in each of four categories. Cost function scores are computed using Equation.1 and the constants in Table.3. with Refr. Per. w/o Refr. Per. No Overlap Overlap Preprocessor Score Preprocessor Score Abs 5. Abs. Negation 5.31 Negation.33 NEO() 5. NEO().9 NEO(3) 5.1 NEO(). Null.9 NEO(1).19 Negation 5.3 Abs.59 NEO(3).9 Negation.5 Abs.9 Null. NEO().9 NEO(3).31 NEO(1).3 NEO().3 detection with RP vs. without) are shown. For both overlapping and non-overlapping data, the Abs preprocessor, used with an RP, was the best overall detector. The necessity of pairing Abs with an RP is as expected; without an RP, both phases of a biphasic AP would produce a valid positive threshold crossing, incurring one false alarm for every correct detection. Excluding the RP improved scores slightly for overlapping spikes. Table. also shows that the performances of the simple threshold and energy based preprocessors were almost identical. To quantify whether certain preprocessors perform better at different SNRs, the cost function scores for the five best preprocessors (determined by Table.) were grouped by SNR (Figure.5). At SN R = 1., Abs marginally outscored both Negation and Null, and operated over a wider percentage of the input range. At its peak cost function score, Abs correctly detected % of the APs with a false positive rate of per second. By comparison, the Null detector correctly identified 5% of the APs with a false positive rate of 13 per second. Negation detected 3% correctly with 9 false alarms per second. The differences in performance between the 3

15 1 SNR = Abs SNR =. NEO() 1 NEO(3) 1 Cost Function Score SNR =. Negation Null Threshold (Pct. of Input Range) Figure.5: Cost function scores for the top five preprocessors at three different SNR levels. The insets at the right show close-up detail of their corresponding plots at the left. 31

16 Table.5: The five highest scoring preprocessors when computational complexity is disregarded in computing the cost function score (i.e. w 3 = in Equation.1). with Refr. Per. w/o Refr. Per. No Overlap Overlap Preprocessor Score Preprocessor Score MF 5.5 Abs. Abs 5.5 NEO().73 NEO() 5.5 NEO() w/ MF. SNEO() 5.7 NEO(3) w/ MF. NEO(3) 5.5 Abs w/ MF. MF 5.53 SNEO().7 NEO() w/ MF 5. NEO(3).75 NEO(3) w/ MF 5.3 NEO().7 SNEO(3) 5. NEO(1).73 SNEO() 5.1 SNEO(3).7 preprocessors became less pronounced at the higher SNRs (SN R =.,.). The generic matched filter template was compared with two others: one that was derived from only three of the 3 APs, and another derived from only one (Figure.1(b)). These were applied to the signals from the data sets that were based on the same AP waveforms as the ones included in the respective template. Only negligible differences in performance were found between the alternate templates and the generic one. To assess preprocessors in systems that are not computationally limited, the data were reanalyzed by setting w 3 = in Equation.1 (see Table.5). For nonoverlapping APs, matched filter based operators perform comparably with energy based operators despite the non-specific nature of the generic matched filter template. The matched filter didn t perform as effectively for signals with overlapping spikes (score =.39 with RP;. without RP). When a preprocessor is applied to a signal, the SNR between the spikes and the background noise is changed. One interesting question is whether this SNR gain 3

17 Table.: Signal to noise ratio gain (in db). The gains for NEO(δ), SNEO(δ), and NEO(δ)wMF were very similar, and so they were averaged for brevity. Preprocessor Raw Signal SNR Simple Threshold..... NEO SNEO MF NEO w/ MF Abs w/ MF is a good predictor of how well a given preprocessor detects spikes. SNR gains were measured for each of the preprocessors in this study, and are listed in Table.. The gains are shown for each category of preprocessors over a range of raw signal SNRs. Comparing Table. with Table. shows that a preprocessor s SNR gain does not accurately predict its cost function score. For example the simple threshold preprocessors (N ull, N egation, Abs) provide no SNR gain (.db), yet score comparably to energy based operators that have SNR gains of up to 1.3dB. The matched filter showed slightly negative gains as a result of the non-specific nature of the generic template. SNR gain is therefore a poor predictor of a preprocessor s ability to detect spikes..3. In Vivo Data The five best preprocessors identified in Section.3.1 were applied to the 5 in vivo test signals. The cost function scores were computed as before, averaged by SNR, and then plotted versus the input range (Figure.). These data reflect the same basic trends as with the artificial data set. In general, either the Negation or Abs operators scored highest and over the broadest range of threshold values. Below SNR =, the null operator scored below Abs and Negation. NEO(3) and NEO() 33

18 SNR = 1 SNR = Cost Function Score 1 SNR = 3 1 SNR = 5 1 SNR = 7 1 Threshold (Pct. of Input Range) 1 SNR = 1 SNR = 1 Abs Negation NEO() NEO(3) Null Figure.: Cost function scores for preprocessors applied to the in vivo test data signals. The scores for individual signals have been grouped together with signals of similar SNR and averaged. Scores are plotted versus threshold values expressed as a percentage of the input range. 3

19 achieved the same maximum cost function score at each SNR, but NEO() tended to work over a broader range of threshold values. The maximum cost function scores were uniform at each SNR, indicating that the best way to improve spike detection is not to use any particular preprocessor, but rather to improve the SNR of the neural data. The in vivo data was also tested with the five best preprocessors for use when computational complexity is disregarded. From Table.5, these are the Matched Filter, Abs, NEO(), SNEO(), and NEO(3). The M F was computed using the same generic template used with the artificial test data and was therefore not specific to any of the particular action potential waveforms in the in vivo data set. The data in Figure.7 demonstrate that the M F was the optimal preprocessor, especially at lower SNRs. The Abs operator performed comparably, and over approximately the same range of threshold values. These results are significant because they demonstrate that the matched filter, which is theoretically the optimal preprocessor if the spike waveform is well-defined a priori, is still the best technique even when a non-specific template is used. As before, the differences between cost function scores are salient only at the lower SNRS; for signals above SNR = 3, all five preprocessors performed equivalently.. Discussion The purpose of the study presented in this Chapter is to compare a number of common spike detection algorithms to determine which is best suited for detecting neural action potentials in a wireless BMI. The results indicate that the Absolute Value is as effective a preprocessor as any energy or matched filter based operator, which is consistent with Fang s findings [75]. The data suggest that the best way of improving spike detection is not to employ an elaborate preprocessor, but rather to maximize 35

20 SNR = 1 SNR = Cost Function Score 1 SNR = 3 1 SNR = 5 1 SNR = 7 1 Threshold (Pct. of Input Range) 1 SNR = 1 SNR = 1 MF Abs NEO() SNEO() NEO(3) Figure.7: Cost function scores for preprocessors applied to the in vivo test data signals with w 3 = in Equation.1. These plots predict that the matched filter is the optimal preprocessor when the BMI is not limited by its computational speed. 3

21 the SNR of the neural signal before it is spike detected. This finding underscores the importance of minimizing circuit noise in the analog electronics that condition the neural signals before they are detected. One ramification of this work is that, since Abs is relatively simple to implement, an efficient spike detector can be realized in both the analog and digital domains, provided that there exists a realistic method for setting the threshold voltage autonomously...1 Simple Threshold Preprocessors Preprocessor performance was found to depend largely on the shape of the action potential waveform under detection. For example, consider the class of Simple Threshold preprocessors being used to detect a unit with a biphasic spike waveform. If the positive aspect of the spike is larger than the negative one, the Null operator can be expected to outperform the Negation operator since it is detecting the larger of the spike s two phases. Conversely, the Negation operator will be better suited for detecting spikes whose negative aspects dominate their positive ones. The typical biphasic waveform can be characterized with two signal to noise ratios, one each for measuring the ratios of the positive and negative phases to the background noise. If it is known a priori which of the two SNRs is larger, the corresponding detector (Null or Neg) can be used. However, in general it is safer to use the Abs preprocessor, since it is equivalent to applying both a positive and a negative threshold, thus allowing the larger of the two phases to be detected. This effectively guarantees that the spike detector operates on signals at the larger of the two SNRs. Thus it is not necessary to know ahead of time the details of the waveform shapes or to manually select, channel by channel, the ideal detector based on the observed waveform morphologies. This analysis predicts that the Abs cost function score will essentially be the maximum score of Null and Neg; this trend is seen in Figures.5 and.. 37

22 Time (msec) Time (msec) Figure.: Action potentials from one in vivo unit are shown before (a) and after (b) transformation by the NEO(1) preprocessor. Small variations in the raw signal waveforms can substantially affect the NEO output. Red traces denote signals whose NEO transform does not exceed a set threshold... Energy Based Preprocessors Waveform analysis can also rationalize the observation that the NEO operators were often outperformed by Simple Threshold preprocessors. Figure. shows all spike events from a single in vivo data file. The upper trace shows the raw AP waveforms while the lower trace shows the waveforms after being transformed by the NEO(1) preprocessor; red traces denote spikes whose NEO(1) transforms do not exceed a certain threshold value. Due to typical variations between spikes, the largest of the raw spikes is approximately three times larger than the smallest, and the fastest spike has a maximum slope three times larger than the slowest. These relatively small variations produce profound differences in the NEO signals. The NEO operator computes an estimate of (AΩ) where x[n] = Asin[Ωn] + B is the sinusoid uniquely 3

23 described by the three samples included in the NEO calculation (see Appendix B). Therefore, if two APs differ in both amplitude (A) and frequency (Ω) by only 1%, the difference in their NEO responses can be as great as 35%. The NEO signals in Figure. differ in amplitude by as much as a factor of eight. A well known energy based preprocessor that has not been discussed in this study is the instantaneous square of the signal, ψ {x[n]} = x [n]. Since there is a oneto-one mapping between the absolute value and signal squared operators, there is theoretically no difference between the two for enhancing spike detectability. This was verified by simulation, and so these redundant results were omitted...3 Matched Filter Preprocessor The matched filter was the best preprocessor when computation time was removed from the cost function (i.e. w 3 = in Equation.1), despite the fact that the template was not specific to the APs under detection. The generic template was no better at detecting spikes than the two specific ones that were tested. This indicates that, at least for this data set, the waveform variation between units is roughly equal to the variation between successive firings of any single unit. Since performance did not depend on the precise shape of the template, it may be possible to design an autonomous matched filter spike detector that does not require user input to generate templates for individual channels. This finding is consistent with published results demonstrating the viability of wavelet-based spike detection [55, 7]. The matched filter performed poorly when detecting overlapping spikes. The shape of the waveform resulting from overlapping spikes depends on the shapes of the component spikes and their degree of overlap. This often results in a waveform bearing little resemblance to the matched filter template. The Abs operator (with refractory period) was the best preprocessor for detecting overlapping spikes (see Table.5). 39

24 .. Cost Function The width of the cost function s plateau region indicates the range of threshold values that can be used to achieve optimal spike detection. In general, wider plateaus must be considered to be more favorable, since autonomous threshold selection algorithms will be able to operate with a larger margin of error. This will in turn lead to better cost function scores and more efficient spike detection. The cost function plateau width can also be used to explain why a preprocessor s SNR gain does not accurately predict its peak cost function score. Figures. and. show that, beyond a certain point, increasing the SNR of the neural signal does not improve the maximum cost function score, but rather widens the cost function s plateau region. Therefore, it follows that simply because a preprocessor improves SNR, it does not automatically increase the maximum cost function score. The relationship between SNR gain and cost function score is further weakened by the fact that SNR is not always a robust metric of a fixed-point arithmetic system such as the Backpack. For example, squaring a signal in a fixed-point system is precisely equivalent to taking its absolute value, since there is a one-to-one, monotonically increasing map between the two transforms. Yet, arithmetically, there is more SNR gain associated with the squaring transform than with the absolute value transform...5 Limitations This work is limited by the degree to which the test data signals are representative of extracellular cortical recordings on the whole. The artificial data set is limited by how realistically the background noise represents true neural noise. The artificial data was created using the assumption that neural background noise is comprised almost exclusively from far field neurons whose frequency content is identical to that of the near field neurons. An assumption has also been made regarding the number of

25 Power (db) Frequency Hz Figure.9: Average power spectrum densities for the artificial data set (blue) and in vivo data set (red). far field neurons and the relative amplitudes of their contributed signals. Figure.9 compares the average power spectral density (PSD) from all 3 of the non-overlapping artificial data signals with SNR = 3. to the average PSD of the in vivo data signals. Below the signal passband (< 3Hz), the energy of the artificial data at any given frequency exceeds that of the in vivo data by as much as 15dB. A more realistic technique for creating artificial neural signals would have been to model a collection of interconnected neurons in free space and then to calculate the extracellular potential recorded by an electrode in response to their membrane voltages [79, ]. However, creating enough signals for a diverse spike detection study such as this one would be computationally prohibitive. The nature of the in vivo data makes it difficult to compare the detection results at different SNRs. Each SNR level of in vivo data includes different units with different waveform morphologies. Since waveform morphology can greatly influence preprocessor performance, it is not appropriate to compare the performances of the preprocessors between SNR levels. This restriction does not apply to the artificial data, since the same base of 3 action potential waveforms was used to create signals at each of the 1 SNR levels. The results from the in vivo data are also skewed 1

26 because the actual spike times were determined by hand, thus introducing an element of human bias. A detected spike may be classified as either a correct detection or a false alarm depending on whether the person who sorted the data decided that the event in question was due to a firing neuron or to noise..5 Conclusion This study in this chapter has concluded that it is the quality of the neural signal that mainly determines the spike detector s performance, not the choice of preprocessor. It is therefore logical to choose the simplest preprocessor. Of the three simplest preprocessors analyzed in this study, Abs is as fast to compute as Null and Negation while slightly better at detecting spikes; it is therefore ideally suited for the Backpack. However, in systems not limited by computational power, a matched filter with a nonspecific template will be best. A robust and versatile cost function has been developed to compare detection results from different preprocessors.