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Control of a brain–computer interface without spike sorting

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2009 J. Neural Eng. 6 055004

(http://iopscience.iop.org/1741-2552/6/5/055004)

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IOP PUBLISHING JOURNAL OF NEURAL ENGINEERING

J. Neural Eng. 6 (2009) 055004 (8pp) doi:10.1088/1741-2560/6/5/055004

Control of a brain–computer interfacewithout spike sortingGeorge W Fraser1,2,5, Steven M Chase1,2,3, Andrew Whitford2,4

and Andrew B Schwartz1,2,4

1 Department of Neurobiology, University of Pittsburgh, Pittsburgh, PA 15213, USA2 Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, USA3 Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213, USA4 Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15261, USA

E-mail: gwf2@pitt.edu

Received 16 January 2009Accepted for publication 15 July 2009Published 1 September 2009Online at stacks.iop.org/JNE/6/055004

AbstractTwo rhesus monkeys were trained to move a cursor using neural activity recorded with siliconarrays of 96 microelectrodes implanted in the primary motor cortex. We have developed amethod to extract movement information from the recorded single and multi-unit activity inthe absence of spike sorting. By setting a single threshold across all channels and fitting theresultant events with a spline tuning function, a control signal was extracted from thispopulation using a Bayesian particle-filter extraction algorithm. The animals achievedhigh-quality control comparable to the performance of decoding schemes based on sortedspikes. Our results suggest that even the simplest signal processing is sufficient forhigh-quality neuroprosthetic control.

(Some figures in this article are in colour only in the electronic version)

Introduction

This paper demonstrates an alternate strategy for processingsignals from intracortical electrodes for prosthetic control.Current brain–computer interfaces based on intracorticalelectrode arrays use extracellular action potentials processedwith spike-sorting strategies to generate a control signal(Hochberg et al 2006, Musallam et al 2004, Santhanamet al 2006, Taylor et al 2002, Velliste et al 2008, Wessberget al 2000). A threshold voltage is set for a particularelectrode, and each time the voltage potential exceeds thatthreshold, a waveform snippet of the time-varying potentialis recorded. These waveforms are divided into one ormore categories, in the hope of identifying individual cellsor separating out cell-related activity. During a typicalneuroprosthetic control experiment, a human operator willview the ongoing waveforms for a brief period on each channelat the beginning of each day’s session and attempt to identifydistinct waveforms by setting the spike-sorting parametersof a digital signal processing device. The need for human

5 Author to whom any correspondence should be addressed.

intervention is an obstacle to bringing neural prosthetics fromthe lab to the clinic, as is the complex digital signal processingemployed in current brain–computer interfaces..

A separate class of brain–computer interfaces (BCIs)use low-frequency signals from external electrodes (EEGs,for example Wolpaw et al 1991), surface macroelectrodes(ECoGs, for example Leuthardt et al 2004) or intracorticalmicroelectrodes (LFPs, for example Mehring et al 2003,Pesaran et al 2002). These techniques and those based on spikeactivity can be ordered according to their spatial resolution,with EEGs at one end and spike activity at the other. The BCIswith the highest number of degrees of freedom and accuracyhave been operated with spike activity (Taylor et al 2002,Velliste et al 2008, Wessberg et al 2000).

Recent papers have suggested other schemes forextracting a control signal from intracortical recordings. Starkand Abeles (2007) showed that multiunit activity, reflected inthe power between 300 and 6000 Hz, is a good predictor of anupcoming hand movement in macaques. Ventura (2008), usingsimulated data, extracted movement intent from the mixturesof tuned units, with an accuracy comparable to traditional

1741-2560/09/055004+08$30.00 1 © 2009 IOP Publishing Ltd Printed in the UK

J. Neural Eng. 6 (2009) 055004 G W Fraser et al

spike-sorting approaches. Both of these papers suggest thatthere is information found in relatively unprocessed signalsfrom microelectrodes in the motor cortex. In the current study,we report on the feasability of operating a brain–computerinterface without spike sorting with recordings from twomonkeys chronically implanted with microelectrode arrays.

Methods

Chronic microelectrode implant

Monkey A, a male rhesus macaque, was implanted in January2007 with a single 96-channel array (Blackrock Microsystems;Maynard et al 1997) on the convexity of the motor cortexnext to the central sulcus, with the lateral edge of the array∼2 mm medial to the genu of the arcuate sulcus. The recordingsessions reported here were done in June 2008. Monkey C, alsoa male rhesus macaque, was implanted in February 2009 in thesame location. The reported sessions were recorded 10 weekslater. Monkey A’s array gave as many as 130 distinguishablecells and multineuron combinations during the period of bestrecordings. At the time of this experiment, June 2008,there were 1–2 clear single units, 1–6 probable single units,∼40 fair neuron/multineuron combinations and 15–30 poormultineuron traces on a typical day of recording. Monkey C’sarray gave ∼75 fair neuron/multineuron combinations and ∼5probable single units on the day of this experiment.

Behavioral task

Prior to the implant, the monkey was trained to do a center-outarm movement task in a virtual environment. It sat in front ofa stereoscopic computer monitor (DTI, Rochester, NY) withone arm gently restrained, and the other free to move withan infrared marker taped slightly distal to the wrist so thatits position could be monitored with a motion capture system(Northern Digital, Waterloo, ON, Canada). The position of theinfrared marker drove the position of a green cursor displayedon the screen in a virtual environment. Blue spheres weredisplayed as targets at various points in the three-dimensionalenvironment and the monkey was rewarded with a droplet ofwater for making and holding contact with the targets. In eachcase, the monkey first made contact with a central target andtouched the target for a required time of 200–300 ms, selectedrandomly from a uniform distribution. A peripheral target wasthen randomly selected from a queue of remaining targets.In the experiments described in this paper, we used a set of16 targets, their centers arranged evenly in a circle on theplane of the monitor with a radius of 85 mm for monkey A and79 mm for monkey C. The monkey moved to the peripheraltarget within a limited time period—1600 ms in this study—and held contact for a required time of 0–200 ms. The cursorand the target had radii of 8 mm for monkey A and 9 mmfor monkey C. The variable hold period was long enoughthat the monkey could not consistently succeed by movingstraight through the target—it had to stop or drastically slowits movement as it approached the target. Once a target washit successfully, it was dequeued from the remaining targets.

After the monkey was implanted and the neural signalswere deemed large enough and stable enough to sort (about3 weeks for both monkeys), the animal began to use thebrain–computer interface. Both arms were restrained and thecursor was driven with neural activity. To decode intent, it isnecessary to determine the tuning parameters of the neuronsbeing recorded. In this study, we made a first estimate byrunning the task with null tuning parameters. In brain control,the cursor was placed on the central target at the beginningof each trial. Then the peripheral target was presented afterthe expiration of the central hold period. Initially, the monkeywas unable to move the cursor with null tuning parametersand failed each trial. Nevertheless, the monkey modulatedits neural activity consistently for each target, making itpossible to estimate tuning parameters and begin real-timeneural decoding. During this initial period where the controlparameters were adapting, we enhanced the straightness of thetrajectories by artificially reducing the deviation from the ideal,perfectly straight movement. At each timestep, the predictionof the decoding algorithm was decomposed as the sum of avector straight toward the target and a vector orthogonal to it.The orthogonal vector was then multiplied by the deviationgain: between 0.1 and 0.5 in this study. Adjusting thedeviation gain is a highly subjective process; we ramp upthe deviation gain as the model parameters are re-fit with moredata and the decoding becomes more consistent. Choosinghow much deviation gain to apply is a matter of balancing theneed for straight trajectories with the tendency of the monkeyto modulate erratically if it realizes that the trajectories comeout straight regardless of the consistency of its modulation.We need straight trajectories while the decoding parametersare being fit so that we can accurately compute the tuningfunctions of signals. At the same time, the monkeys haveshown a tendency to produce inconsistent modulation if thedeviation gain is too strong for too long. The experimenterattempts to balance these priorities. Typically the deviationgain is 0.1–0.25 for the first 16 targets, 0.5 for the next set and0 thereafter. If the trajectories are still erratic, we will keepit on longer. This procedure was used only in these adaptivesessions. Deviation gains were used only for a short period atthe beginning of a daily experimental session for calibrationpurposes. Subsequent control used no deviation gain.

Signal processing

Signals were buffered, amplified, bandpass filtered at250–8000 Hz and processed using a 96-channel PlexonMultichannel Acquisition Processor (Plexon Inc., Dallas, TX).The DSP system was configured so that it would register allevents crossing a negative threshold in the downward directionand send their times to one of the task-management computers.In monkey A, a threshold was set across all channels at−37.5 μV, except ten channels where the power of the time-varying voltage was so high that it constantly saturated the A/Dconverter. On those channels the gain was reduced until theclipping was under control, effectively putting the thresholdsin the (−)40–80 mV range. In monkey C, the signals hadhigher amplitude and the threshold was set at –60 μV for allchannels. In both animals the threshold was chosen to be as

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J. Neural Eng. 6 (2009) 055004 G W Fraser et al

low as possible without severely overloading the capacity ofthe DSP system on too many channels. There was a sufficientvariation in the signals to cross the threshold on 95/96 channelsin monkey A and 78/96 channels in monkey C. It should benoted that because of the difference in the age of the implantedarrays (10 weeks in monkey C versus 1.5 years in monkeyA), the signals are very different. In the very old array ofmonkey A, the amplitude of the sortable action potentials ismuch closer to the amplitude of the background noise. In thevery young array of monkey C, the action potentials stand outmuch more strongly from the background, but there are oftenmore active neurons observable on a given channel. Hence thethreshold had to be set higher in monkey C to avoid capturingso much activitiy that the capacity of the DSP system would beoverloaded. This higher threshold resulted in 18 channels thatobserved no threshold crossings. For the same reason monkeyC showed less of a difference in the baseline rate for sortedversus unsorted sessions, as evidenced in figure 5. It shouldbe noted that in both monkeys the resulting signals were notcomparable to single-unit recordings; the waveforms pickedup by the threshold included large amounts of backgroundactivity and noise on nearly every channel where the signalcrossed the threshold at all. This is evidenced by the fact thatthreshold crossings showed consistently higher baseline ratesand modulation depths than units sorted on the same channels(figure 5).

Decoding algorithm

We used a Bayesian–Monte Carlo estimation algorithm verysimilar to the one described by Brockwell and colleagues(2003). This algorithm, called a particle filter, solves theproblem of decoding neural intent by offering a firing-rate model for each recorded unit, and then estimating themovement intent most consistent with this forward modeland the recent history of movement. The particle filter canbe intuitively understood in terms of a hypothesis space ofmovement intents that the monkey might have at the presenttimestep. The particle filter uses modulated control signals: aneuron whose firing rate increases for a particular movementdirection, or in this study, a time-varying voltage signal whichcrosses a threshold more or less often depending on the currentintended movement direction. A single modulating signalgives the particle filter information about which regions of thehypothesis space are consistent with its current level of activity.One signal alone will leave ambiguity: a high-firing neuronindicates movement in its preferred direction, or perhapsmovement somewhat off its preferred direction at a higherspeed. These signals are noisy, so one signal may simply bewrong at the present moment. The particle filter searches thehypothesis space at several hundred points—particles—for theregion that is most likely given all the current activity levels.The distribution of particles in one timestep is generated fromtheir position in the previous timestep, which enforces ourassumption that movement in the current timestep is similar tomovement in the previous timestep. This distribution is biasedaccording to the likelihood of the hypothesis that each particlehad found. Thus the particles form a cloud that follows the

most likely region of the hypothesis space from one timestepto another. This process is diagrammed in figure 1. Using aparticle filter as an extraction algorithm is simply a matter ofidentifying a modulated signal and specifying a tuning functionfor it. Brockwell and colleagues used an exp(cosine) firing-rate model where each sorted unit had a baseline rate, a singlepreferred direction and an adjustable-width tuning function.Our new approach is based on a firing-rate model that makesfewer assumptions about the shape of the tuning function:

λi = bi,0 + s

8∑j=1

wi,j · f (θ · 4/π − j). (1)

Here, λi is the total rate of threshold crossing on channel i,bi,0 is the baseline firing rate of that channel, s is the speed ofmovement and θ is the angle of movement in the X–Y plane.f is a cubic spline basis function which is being shifted andstretched by the θ · 4/π − i formula. It has the followingmathematical definition:

f (x) =⟨

x < −2|2 < x

−2 � x < −1|1 < x � 2−1 � x � 1

∣∣∣∣∣0

(2 − |x|)3

1 + 3 (1 − |x|) + 3 (1 − |x|)2 − 3 (1 − |x|)3

⟩,

where f is a bell-shaped function spanning the range[−2, 2]. It represents a cubic spline basis function; by shiftingand spacing these basis functions at intervals of 1 and addingthem up, we get a set of basis functions that span the entirecircle of movement directions. wi,j is the weight of a particularspline basis function, fit by a regression model. The effect ofthe summation portion of the firing model is to fit a smoothingspline to the firing rate as a function of the intended movementdirection in the X–Y plane. This process is diagrammed infigure 2. Our model effectively states that the firing rate isequal to a baseline rate plus an 8-knot spline function in polarcoordinates that expands and contracts according to the speedof movement. The wi,j parameters which determine the shapeof the spline function are fit using linear regression. Ourdecoder is written in Matlab (Mathworks, Natick, MA) anduses its GLM library to fit the model with an identity linkfunction.

The empirical firing rate of cell i is taken to be Poissondistributed with mean λi . Thus, the probability of observing aspecific bin count ni given a firing rate λi from equation (1) isgiven by the following equation:

P(ni |λi) = poisspdf(ni, λi · �t),

where poisspdf gives the Poisson probability density functionwith mean λi · �t evaluated at ni (�t is the width of the bin).The particle filter also incorporates an assumption about theway velocity changes over time. In both Brockwell et al andthis paper, it is assumed that the velocity at one timepointis related to the previous timepoint according to a Gaussiandistribution. The standard deviation of this distributiondepends on the length of the time step and the assumptionsof the experimenter. In a brain-control experiment it shouldcorrespond to the distance to the target and the movement

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J. Neural Eng. 6 (2009) 055004 G W Fraser et al

X

Y

N1

N2

N3

N4

N5

Particle Filter MovementThreshold-crossings

HypothesesPDF for each unit

Figure 1. Extracellular activity-related signals are recorded from motor cortex activity (N1–N5). The number of threshold crossings iscounted on each channel for each 33 ms interval (left panel) and fed into a particle filter extraction algorithm that compares bin counts to theknown tuning functions of those channels. Each bin count points to a probable region of the hypothesis space of movement trajectories(middle panel). The particle filter maintains a set of hypotheses about movement (middle panel, small dots). At each timepoint theseparticles are moved randomly by a distance drawn from a Gaussian distribution, then resampled according to the probabilities indicated bythe counts N1–N5. In this manner the particle cloud is dragged around by the probable regions from the N1–N5 counts. An outlier bin countwhich disagrees with the rest of the population (above, N5) will have little influence over the particle cloud. To generate an estimate of theglobal movement intent we simply take the mean of all the particles.

Basis functions

Weighted bases add up to a tuning function

Figure 2. A tuning function is fit as a weighted sum of spline basisfunctions. The tuning function of one channel is shown as the thickblack line. It is fitted as a sum of shifted bell-shaped basis functions(top), each of which spans a π/4 radian section of movementdirections. The basis functions are scaled (bottom) and added toproduce the fitted function.

duration. Here, we assume that velocity changes with astandard deviation of 67 mm s−1 over 1 s. The prior probabilityof the x-component velocity at the current timestep, x, giventhe x-component of velocity at the previous timestep, x, isa function of the length of the timestep �t and the standarddeviation of movement per second σ :

P(x|x) = normpdf(x, x,√

�t · σ), (2)

where normpdf describes the normal distribution probabilitydensity function for the distribution with mean x and standarddeviation

√�t · σ , evaluated at x. The problem of decoding

an intended movement direction from the threshold-crossingactivity is then a matter of maximizing the probability

distribution defined by equations (1) and (2):

P (x, y|x, y, n1, . . . , nm) ∼ P(x|x) · P(y|y)

·P(n1|x, y) · · · · · P(nm|x, y), (3)

where x and y are set to 0 at the beginning of eachtrial (during the central hold period); n1, . . . , nm are theobserved bin counts for the m channels being used. Theabsolute probability of the left-hand side of equation (3) isscaled by additional terms, but since we are only interestedin the relative maximum we can leave them out. Theparticular filter uses a set of particles—points in the X–Yvelocity coordinate space—to estimate the maximum of thisdistribution. Each time a new set of bin counts arrives, theparticles are moved probabilistically. First, each particlemakes a random movement whose destination is chosen froma normal distribution with mean at the previous location of theparticle and standard deviation of

√�t · σ . This corresponds

to the first two terms on the right-hand side of equation (3).Second, for each particle, a probability is calculated equalto the remaining terms of equation (3). The entirepopulation of particles is then resampled from itself, withreplacement, according to these probabilities. This meansthat high-probability particles are more likely to reappearafter resampling, and that some particles will end up beingrepresented multiple times in the new population.

These steps are constructed so that the probabilitydistribution of the position of a single particle is exactly equalto the distribution being estimated. The entire population ofparticles acts as a proxy for the distribution being estimated.We generate a single estimate of movement for real-timebrain control by taking the mean of the entire population ofparticles. The accuracy of decoding increases with the numberof particles, but so does the computational complexity. Weused 400 particles, which we found to be the highest numberwhere the computation could be completed reliably in the timebetween bin counts. With a simulated population we foundthat the quality of control did not become noticeably worseuntil the number of particles dropped below 50.

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J. Neural Eng. 6 (2009) 055004 G W Fraser et al

The described decoding algorithm has a number ofparameters (the bi,0 and wi,j terms in the model) that must be fitfrom the actual tuning of the neurons. In the reported unsortedneural control session for monkey A, we used previous day’sparameters as the initial parameters for decoding. At thebeginning of the day we ran an adaptive session where were-fit the wi,j and bi,0 terms. We gave 4 sets of 16 targets,re-fitting the model to the cumulative set of data for thatday after each set. For the purposes of linear regression, theintended movement was taken as the idealized vector from thecenter of the workspace to the peripheral target. For monkeyC we set the initial parameters to 0, which means that forthe first 16 targets the cursor did not move. Nevertheless,the monkey looked at the monitor and modulated its neuralactivity sufficiently to get a set of parameters to move duringthe remainder of the adaption period.

The sorted session for monkey C was done in exactly thesame way as the unsorted session, with parameters initially setto 0. The sorted session for monkey A was done somewhatdifferently; parameters were initially 0 but the extractionalgorithm being used was a variation on the Bayesian inferencedecoder where Laplace’s method of integration is used in placeof the Monte Carlo particles of the particle filter. We havefound that the accuracy of the two methods is similar; themain difference is that the Laplacian integration method iscomputationally more efficient.

Results

Four datasets are reported here, unsorted and sorted formonkeys A and C. In all cases cursor movement was confinedto the two-dimensional plane of the monitor, though the VRsystem displayed objects in three dimensions. Monkey C didthe unsorted control session first, followed by an 80 min break,and then the sorted control session. It had less than half itsdaily water quota in the first session so its motivation levelwas still high during the second session, assessed by the factthat it engaged in the task continuously for the entirity of bothsessions. It used exactly the same decoding algorithm for bothsessions, except that the extraction algorithm was being fedcounts of threshold crossings in the first session and counts ofsorted spikes in the second. Monkey A did the unsorted session2 weeks after the sorted session. The sorted session containedtwo breaks where the decoding algorithm was seamlesslyswitched to the population vector algorithm (Taylor et al 2002)for 80 and 112 trials. These trials are excluded. This particularsorted session was chosen for comparison because it was alsodone in the middle of the week when the monkey’s motivationlevel tends to be highest, it used a Bayesian decoding algorithmvery similar to the particle filter, and it was contemporaneouswith the other session.

There is an inherent variation in the quality of brain-control decoding from one session to the next, even whenthey are performed on the same day. When the parametersare initially set to zero and then fit from a limited set ofmovements during the adaptation period, the accuracy of thefit depends on the way that the animal modulates its activityduring those particular trials. Therefore, it is not possible to

make an exacting comparison between the quality of controlin the sorted versus unsorted session. We can only evaluatewhether the unsorted scheme works approximately as well asa decoder based on sorted units. The primary metrics wehave for the quality of control are our subjective impression offigure 3; the success rate of the animal; the speed of movement;and the straightness of the trajectories.

Monkey A Monkey C

Unsorted Sorted Unsorted Sorted

Success rate 78% 93% 96% 84%Duration 815 ms 932 ms 707 ms 630 msStraightness 1.12 1.10 1.11 1.17

Success rate is simply the proportion of trials where theanimal succeeds according to the central hold, movement timeand peripheral hold criteria defined in the methods section.Speed is the time between the peripheral target being presentedand the cursor contacting it. Straightness is the total pathlength of the cursor from when it left contact with the nolonger visible central target to when it made contact with theperipheral target, divided by the length of a perfectly straightline between the endpoints of the same path. The above tablegives the median speed and straightness for all successful trials.

We can treat the threshold crossings on a particularchannel as though it were a neuron and define a tuning functionfor it—an estimate of what the threshold-crossing rate willbe when the monkey moves in a particular direction at aparticular speed. The wi,j parameters of the particle filterdecoder describe such a tuning function; figure 4 compares theassumptions of the decoder with the empirical per-target firingrates observed in the control session. The thick black lines andthe black circles in figure 4 show the comparison between themodel’s spline fit and the later activity of the channels. Thechannels shown are selected from the better-tuned half of whatwe recorded, but are representative in terms of the model’s fitand the lack of multimodality in the tuning functions. Theparticular examples shown in figure 4 are indicated on thescatterplots in figure 5.

We would also like to make a quantitative comparisonof the tuning characteristics of channels and neurons betweenunsorted and sorted sessions. In the unsorted session, wefit a cosine function to the 16-target mean threshold-crossingrates. In the sorted session, we fit a cosine function in the samemanner, except that we used the combined activity of the sortedneurons in place of the threshold-crossing event. Monkey Ahad 60 channels with sorted units where such a comparisoncould be made; monkey C had 62. Monkey A had 10 channelswith two sorted units and monkey C had 20; in these casesthe activities of the two units were simply merged together forthe purpose of fitting a cosine. In this small dataset, the meandifference in preferred directions for two units on the samechannel was 80◦. The model for the cosine fit is

ni,j = βi,0 + βi,xxj + βi,yyj ,

where ni,j is the mean firing rate for unit i and target j ;βi,0 is the baseline firing rate for neuron i; 〈xj , yj 〉 is the

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J. Neural Eng. 6 (2009) 055004 G W Fraser et al

Unsorted Sorted

Mon

key

AM

onke

y C

5 cm

Figure 3. Superimposed movement trajectories as the monkey does the center-out task for 16 targets using unsorted threshold-crossingsignals (left) or sorted activity (right). This plot shows position samples at 30 Hz and incorporates all successful trials on a single daybetween the start of the central hold period and the end of the peripheral hold period. The symbols are varied according to the targetdirection in the current trial. The upper-left plot contains 384 trials, the upper right shows 233, lower left 480, lower right 512. The trials foreach condition were done in one contiguous block, except that in the monkey A/sorted condition there were two breaks in the trials wherethe decoder was switched to the population vector algorithm (Taylor et al 2002) for 80 and 112 trials (these trials are excluded). Successrates were 78%, 93%, 96% and 84% for A/unsorted, A/sorted, C/unsorted, C/sorted. Because of the vagaries of monkey motivation andthe fact that no two adaptation sessions are the same, it is not possible to make an exacting comparison of performance here. We can onlyobserve that both algorithms produce qualitatively good control.

vector to target j ; the angle of 〈βi,x, βi,y〉 is the preferreddirection of unit i and the length of 〈βi,x, βi,y〉 is the modulationdepth of unit i. The baseline rates, modulation depths andpreferred directions are compared between sorted and unsortedconditions in figure 5. In both animals the baseline ratesand modulation depths were higher in the unsorted condition,and the preferred directions were similar between unsortedthreshold crossings and the combined sorted units recordedlater on the same channels.

Discussion

We have demonstrated that good neural control can beachieved without conventional spike sorting or careful settingof thresholds. There is intrinsic variability in the quality ofcontrol from one session to the next, so it is not possible tomake an exact quantitative comparison between sessions inthese data. An experimental paradigm that better controlsfor the quality of adaptation data and the motivation levelof the animal is clearly an avenue for future research. Thisinitial finding has demonstrated that unsorted signals can besubstituted for conventional ones without a dramatic, obviousdrop in the quality of control.

We chose an 8-knot spline to model the tuningfunction because we expected mixed neuron signals to createcomplicated, sometimes multimodal tuning functions. Wewere surprised to find that on virtually all channels, the tuningfunction of the unsorted threshold crossings was roughly uni-modal, in spite of the fact that where two units were recordedon the same channel their preferred directions did not tendto be similar. Since the tuning functions of the unsortedsignals are not multimodal, one may reasonably ask why thepopulation vector algorithm does not work well with thesesignals. We did attempt to use the population vector algorithmon these signals, but found the quality of control so poor that wecould not collect enough data to report. We speculate that thechallenging aspect of unsorted signals is not multimodality butthe background noise that is introduced. Statistical extractionalgorithms like the particle filter have the advantage of beingable to recognize when a channel is an outlier in the presenttimestep, and to effectively reduce its contribution to theinference of intent. The particle filter examines the spaceof hypothetical velocities and asks the question: what is theprobability of observing these firing rates at various points inthe hypothesis space of velocities? If a channel is momentarilyinundated with background noise, it will point to a region of

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J. Neural Eng. 6 (2009) 055004 G W Fraser et al

Firin

g ra

te

100 Hz{16 targets

0

100 Hz

0

Mon

key

AM

onke

y C

Sorted Unit 1Sorted Unit 2Sorted Unit 1+2Blind ThresholdDecoder parameters

A B

C D E

Figure 4. Five examples of 16-target tuning functions for neurons, sums of neurons and unsorted threshold crossings. Each of these fiveexamples shows various tuning functions from a single channel. The Y-axis shows the firing rate of a pseudo-unit during the movementperiod of the task. The X-axis gives the angle from the start point in the center of the monitor to the peripheral target. The multiple plottedlines illustrate how one or two identifiable neurons and background activity add up into the signal we observe with the blind thresholding weused. The thin lines are the tuning functions of sorted units. The connected-circles line is the sum of these units. The open black circlesshow the tuning function of the blind-threshold pseudo-unit used in unsorted control. The thick black line shows the fitted spline functionthat the particle filter decoder is using, which is fit from a separate dataset at the beginning of the recording session. In these five examplechannels, we can see the different relationships between the identifiable units on a channel and the signal you get when you set a blindthreshold. Unsorted activity is sometimes well-explained as the sum of units on that channel (A), (B); most often it has the same shape asthe sum of units but a higher baseline rate and modulation depth (C), (D); and sometimes a channel without sortable activity will showstrong modulation in the hash (E).

0 1000

50

100

150

AB

CD

Slope=1.56±.62R2=.31

0 500

20

40

60

80

AB

C

D

Slope=1.48±.35R2=.55

−pi 0 pi−pi

0

pi

AB

D

CSlope=1.03±.12R2=.84

Baseline Modulation depth Preferred direction

Summed sorted-unit rate (Hz) Summed PD (radians)

Uns

orte

d PD

(ra

dian

s)

Uns

orte

d ra

te (

Hz)

0 1000

50

100

150

A

B

C

DSlope=1.95±.30R2=.64

0 500

20

40

60

80

A

BCD

Slope=1.34±.26R2=.52

−pi 0 pi−pi

0

pi

A

B

C

D

Slope=1.09±.15R2=.68

Mon

key

CM

onke

y A

Figure 5. The summed activity of all the units on each channel was fit as a linear model of the X- and Y-components of target direction plusa constant. The same was done with the unsorted threshold crossings. This fit is equivalent to a cosine-tuning function with a baseline rate, amodulation depth and a preferred direction. Baseline rate is the mean firing rate across all targets. Modulation depth is the height of thecosine-tuning function, approximately the difference between the most-active target and the least-active target. Preferred direction is themovement direction which, according to the tuning function, would elicit maximum firing from the unit. The above plots show therelationship between each parameter of this model when it is fit with the unsorted threshold-crossing data, on the Y-axis, versus the sum ofthe sorted units recorded on the same channels, on the X-axis. Each channel gives a single point on the plot; the channels from figure 4 areindicated with letters. A linear fit is detailed on each plot. Unsorted control shows higher baseline rates, higher modulation depths andnearly the same preferred directions.

the hypothesis space that is inconsistent with the rest of thechannels, and it will have little weight toward the decoding ofintent. The population vector algorithm gives each signal equalweight in the computation of intent, even if that signal is highlyinconsistent with the majority of the population. We have

demonstrated that with a good choice of extraction algorithm,a simple global threshold specification can be used in placeof the spike-sorting schemes of conventional brain–computerinterfaces. These results have an immediate relevance fordesigns of self-contained spike processing circuits in the

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J. Neural Eng. 6 (2009) 055004 G W Fraser et al

next generation of neural prosthetic devices. Without theneed to set parameters of signal processing, it is possible tomake an effective neural prosthetic system without operatorintervention.

Perhaps more importantly, the kind of extractionalgorithm demonstrated in this paper is arguably better suitedto the indistinct patterns of multiunit activity that are typicalof long-term chronic multielectrode recordings. These signalsare composed of summed mixtures of signals from a numberof sources rather than action potentials of individual neurons.They are subject to high levels of baseline noise and theirtuning functions are harder to predict. We have shown thata well-chosen extraction algorithm can contend with theseissues and provide a good control signal. While we used thesame signal processing equipment that has been employed foryears in neural prosthetics, we used it in a way that simulated amuch simpler system. Our results show that a probe with fixedthresholds and one-way telemetry could be used for effectiveprosthetic control. It is easier to imagine a turn-key clinicalsystem for neural prosthetics that is based on the threshold-crossing counter used here. The elimination of elaborate signalprocessing regimes is an important step towards putting neuralprosthetics into the real world.

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