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CHAPTER 3

A dynamical systems view of motor preparation:Implications for neural prosthetic system design

Krishna V. Shenoy{,{,},k,*, Matthew T. Kaufman{, Maneesh Sahani{,} and Mark M.Churchland{,{

{ Department of Electrical Engineering, Stanford University, Stanford, California, USA{ Neurosciences Program, Stanford University, Stanford, California, USA

} Department of Bioengineering, Stanford University, Stanford, California, USA} Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom

k Department of Neurobiology, Stanford University, Stanford, California, USA

Abstract: Neural prosthetic systems aim to help disabled patients suffering from a range ofneurological injuries and disease by using neural activity from the brain to directly control assistivedevices. This approach in effect bypasses the dysfunctional neural circuitry, such as an injured spinalcord. To do so, neural prostheses depend critically on a scientific understanding of the neural activitythat drives them. We review here several recent studies aimed at understanding the neural processesin premotor cortex that precede arm movements and lead to the initiation of movement. These studieswere motivated by hypotheses and predictions conceived of within a dynamical systems perspective.This perspective concentrates on describing the neural state using as few degrees of freedom aspossible and on inferring the rules that govern the motion of that neural state. Although quite general,this perspective has led to a number of specific predictions that have been addressed experimentally. Itis hoped that the resulting picture of the dynamical role of preparatory and movement-related neuralactivity will be particularly helpful to the development of neural prostheses, which can themselves beviewed as dynamical systems under the control of the larger dynamical system to which they areattached.

Keywords: premotor cortex; motor cortex; motor preparation; state space; dynamical systems; single-trial analysis; neural prostheses; brain machine interface; brain computer interface.

Introduction

It is difficult to appreciate just how central move-ment is to everyday life until this ability is lost due

*Corresponding author.Tel.: !1-650-723-4789; Fax: !1-650-723-4659.E-mail: [email protected]

A. M. Green, C. E. Chapman, J. F. Kalaska and F. Lepore (Eds.)Progress in Brain Research, Vol. 192ISSN: 0079-6123Copyright ! 2011 Elsevier B.V. All rights reserved.

33DOI: 10.1016/B978-0-444-53355-5.00003-8

Author's personal copy

mailto:[email protected]

to neurological injury or disease. Moving is howwe interact and communicate with the world.We move our legs and feet to walk, we moveour arms and hands to manipulate the objects thatsurround us, and we move our tongues and vocalcords to speak. Movement is not only central tothese critical aspects of life, but also to self-imageand psychological well-being. In fact, the funda-mental reason that tetrapelgics wish most for therestored use of their arms is to regain somedegree of independence (Anderson, 2004).

Fortunately, it appears that a confluenceof knowledge and technology from the fields of (1)systems motor neuroscience, (2) neuroengineering,and (3) electrical engineering and computer sciencemay soon provide a new class of electronic medicalsystems (termed neural prosthetic systems, brainmachine interfaces, or brain computer interfaces)aimed at increasing the quality of life for severelydisabled patients.

First, basic neuroscience research across thepast several decades has elucidated many of thefundamental principles underlying movementgeneration and control. A substantial body ofknowledge regarding the cortical control of armmovements, particularly in rhesus macaques,now exists (e.g., Evarts, 1964; Georgopouloset al., 1982, 1986; Schwartz, 1994; Tanji andEvarts, 1976). This literature is reviewed else-where (e.g., Kalaska, 2009; Kalaska et al., 1997;Scott, 2004; Wise, 1985). As discussed below, thisunderstanding has been sufficient to help guidethe design of first generation prosthetic systems.Yet continued focus on underlying neuralmechanisms (in both monkeys and humans),how neural populations behave across timescales,and how neural populations participate in theongoing control of movement, is essential for cre-ating second generation prostheses capable ofhigher performance and a greater range ofcapabilities (e.g., Cunningham et al., 2010; Greenand Kalaska, 2010; Truccolo et al., 2008, 2010).

Second, basic neuroengineering research hasprovided proof-of-concept demonstrations of neu-ral prosthetic systems which translate the electrical

activity (action potentials and local field potentials,LFPs) from populations of intracortically recordedneurons into control signals for guiding computercursors, prosthetic arms, or stimulating theparalyzed musculature. More specifically, a seriesof designs and demonstrations across the pastdecade have produced compelling laboratory evi-dence that intracortical neural signals from rodents(e.g., Chapin et al., 1999), monkeys (e.g., Carmenaet al., 2003; Chase et al., 2009; Fetz, 1969;Fraser et al., 2009; Ganguly and Carmena, 2009;Gilja et al., 2010b,c; Heliot et al., 2009; Humphreyet al., 1970; Isaacs et al., 2000; Jackson et al., 2006;Jarosiewicz et al., 2008; Moritz et al., 2008;Mulliken et al., 2008; Musallam et al., 2004;Nuyujukian et al., 2010; Santhanam et al., 2006;Serruya et al., 2002; Shenoy et al., 2003; Tayloret al., 2002; Velliste et al., 2008; Wessberg et al.,2000; Wu et al., 2004), and humans (e.g., Hochberget al., 2006; Kim et al., 2008) can control prostheticdevices that may provide meaningful quality of lifeimprovement to paralyzed patients. This literatureis reviewed elsewhere (e.g., Andersen et al., 2010;Millan and Carmena, 2010; Donoghue, 2008;Donoghue et al., 2007; Fetz, 2007; Hatsopoulosand Donoghue, 2009; Linderman et al., 2008;Nicolelis and Lebedev, 2009; Ryu and Shenoy,2009; Scherberger, 2009; Schwartz, 2007).

Finally, the semiconductor electronics,optoelectronic telecommunications, micro-electro-mechanical systems (MEMS), and informationtechnology revolutions over the past four decadeshave produced extraordinary and relevanttechnologies. These include low-power and highcomputational-density circuits and systems, low-power wireless telemetric systems, advanced lightsources and imaging modalities, and small sensorsystems that are capable of running sophisticatedsignal processing algorithms. These technologieshave progressed extremely quickly, as describedby Moore's Law, and have been leveraged andadapted to create new neurotechnologies for basicneuroscience and neuroengineering applicationssuch as neural prosthetic systems. It is now possibleto record from hundreds of neurons simultaneously

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with bio-MEMS electrode arrays (e.g., Chesteket al., 2009a, 2011; Jackson and Fetz, 2007; Mavooriet al., 2005; Santhanam et al., 2007), filter and“spike sort” all channels in real time (e.g.,O'Driscoll et al., 2006; Santhanam et al., 2004,2006), “decode” the intended arm movement withadvanced algorithms (e.g., Achtman et al., 2007;Cunningham et al., 2008; Kemere et al., 2004,2008; Santhanam et al., 2009; Wu et al., 2006; Yuet al., 2007, 2010), wirelessly telemeter the resultingprosthetic arm control signals with just a few tens ofmilliwatts of power (e.g., Chestek et al., 2009b;Gilja et al., 2010a; Harrison et al., 2007, 2009),and soon, this will likely all be possible in fullyimplantable systems (e.g., Borton et al., 2009;Harrison, 2008; Nurmikko et al., 2010).While these laboratory proof-of-concept sys-

tems and initial FDA phase-I clinical trials areencouraging (e.g., Hochberg, 2008; Hochbergand Taylor, 2007), several barriers remain. Ifthese barriers are unaddressed, they could sub-stantially limit the prospect of intracorticallybased neural prosthetic systems having a broadand important clinical impact. We recentlyreviewed what we consider to be three of themost important neuroengineering, bioengineer-ing, electrical engineering, and computer sciencechallenges and opportunities for intracorticallybased neural prostheses (Gilja et al., 2011). Wereview here what we consider to be one of themost central and important basic systems-levelmotor neuroscience questions. The knowledgegained while investigating this question shoulddirectly advance our ability to design high-perfor-mance neural prostheses. The central question wehave been asking is: what are the neural processesthat precede movement and lead to the initiationof movement? Neural prostheses will benefitfrom a deeper and more comprehensive under-standing of the neural activity upon which theyare based (Green and Kalaska, 2010). Thisincludes activity during both movement prepara-tion and movement generation. We need tounderstand both because prostheses use both

(e.g., Yu et al., 2010), and because the two arepresumably causally linked and likely impossibleto understand fully if studied in isolation(discussed further in the final section, and Fig. 12).Prostheses should thus benefit from having a firmscientific understanding of how preparatory activ-ity relates to upcoming arm movements, and howthis preparatory activity evolves on a millisecondtimescale. These are the questions and topicsdiscussed in this review.

Preparing to move the arm

Why should one prepare and then move, asopposed to starting the movement as soon as pos-sible? In some cases, it is critical to move rightaway, such as when withdrawing a hand from aflame. Animals have evolved low-latency circuitsto help in these cases and these circuits underliea wide range of reflexive movements. However,animals have also evolved circuits to enable vol-untary movements which are intentional and pur-poseful. Voluntary movements require the abilityto change, refine, and suppress possible actionsbefore they are actually executed. A simpleexample is how we swat a fly. One approachwould be to see a fly and start moving right away.Unless the nervous system can execute perfectly,this is unlikely to be a good strategy, and if theinitial movement is not successful, the fly is likelyto depart before a correction can be made. Itwould thus be beneficial to take slightly moretime to initiate the movement, assuming that, indoing so, greater accuracy can be gained. Presum-ably, we use this slight addition of time to createand refine movement plans until the moment isright and then we initiate the movement. It is thisform of deliberate, goal-driven movement that weseek to better understand, both neurally andbehaviorally, both out of scientific curiosity andbecause it could lead to superior prostheticdesigns.

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There is indeed evidence that voluntary move-ments are prepared before they are initiated(e.g., Day et al., 1989; Ghez et al., 1997; Keele,1968; Kutas and Donchin, 1974; Riehle andRequin, 1993; Rosenbaum, 1980; Wise, 1985).An important line of evidence comes from“instructed-delay tasks” where a temporal delayseparates an instruction stimulus from asubsequent “go” cue. Figure 1 illustrates theexperimental arrangement and task timing, alongwith example hand position and electromyo-graphic (EMG) measurements. This task is widelyemployed and is the behavioral task used in therecent studies reviewed here.

At the behavioral level, reaction times (RTs),defined as the time from the go cue until move-ment onset, are shorter after an instructed-delayperiod. Figure 2 illustrates how RT decreasesand then plateaus as a function of delay period.This RT reduction with delay, largely occurringduring the first 200 ms, suggests that some time-consuming preparatory process is given a headstart by the delay (e.g., Crammond and Kalaska,2000; Riehle and Requin, 1989; Rosenbaum,1980). It is straightforward to interpret the impor-tance of this head start on preparation in the con-text of the fly swatting example offered above.There the goal was not to move instantaneouslyas soon as the fly landed or was seen. Instead,the goal was to move swiftly and accurately, at aparticular speed and along a particular path thatperhaps approaches from behind, and to be ableto start that movement as quickly as possiblewhen it is decided that the time is right. Thus, agood strategy is to prepare the desired movementas soon as possible, so that one is ready to moveas soon as possible when called upon to do so.

The ability to prepare a movement ahead oftime is presumably related to the preparatoryactivity that is widespread in cortex and subcorti-cal structures. Neurons in a number of corticalareas including dorsal premotor cortex (PMd)

(a)

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Fig. 1. Illustration of the instructed-delay task, handmeasurements, and EMG recordings. (a) Monkeys sit in aprimate chair approximately 25 cm from a fronto-paralleldisplay. Movements begin and end with the hand touchingthe display. The hand is a few millimeters from the screenwhile in flight. The white trace shows the reach trajectory forone trial. (b) Time line of the task and behavior for the sametrial. T, target onset; G, go cue; and M, movement onset.Horizontal hand (black) and target (red) position is plotted(top). The target jittered on first appearing and ceased at thego cue. Bottom: Gray trace plots hand velocity (computed inthe direction of the target), superimposed on the voltagerecorded from the medial deltoid (arbitrary vertical scale).Traces end at the time of the reward. Data are from monkeyA in a session focused on EMG recordings. Figure adaptedfrom Churchland et al. (2006b).

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and primary motor cortex (M1) show changes inactivity during the delay period (e.g., Crammondand Kalaska, 2000; Godschalk et al., 1985;Kalaska et al., 1997; Kurata, 1989; Messier andKalaska, 2000; Riehle and Requin, 1989; Snyderet al., 1997; Tanji and Evarts, 1976; Weinrichet al., 1984). Figure 3 shows four example PMdneurons. While it is typical for the average actionpotential emission (firing) rate during the delayperiod to change following target onset, the tem-poral structure is widely varying across cells: someincrease their firing rate, some decrease, somearrive at an approximate plateau level, whileothers undulate.This variety of neural responses stands in stark

contrast to the simple monotonic decline inbehavioral RT as shown in Fig. 2. The centralquestion is, therefore, how does neural activityin the first 200–300 ms of the delay period relate

to the decrease in RT? Asked in the context ofthe fly swatting example, what does this neuralactivity need to accomplish during the delay sothat we are maximally poised to generate theplanned movement and, after initiating the move-ment, successfully hit the fly?

Optimal subspace hypothesis

We have been investigating this question using adynamical systems perspective (e.g., Briggmanet al., 2005; Churchland et al., 2007; Stopferet al., 2003). What this means in essence is thatwe wish to understand (1) how the activity of aneural population evolves and achieves theneeded preparatory state, (2) how this prepara-tory state impacts the subsequent arm movement,and (3) what the underlying dynamics (rules) of

Fig. 2. Mean RT (in milliseconds) is plotted versus delay period duration. For monkeys A and B, this was for the catch trials withshort delays. Although the delay period was selected from a continuum, in practice, delay periods were integer multiples of 16 msbecause of video presentation, and this binning is used in the plots. Lines show exponential fits. For monkey G, we did not use catchtrials (the minimum delay for most experiments was already quite short, at 200 ms). The plotted data are therefore from oneexperiment using three discrete delay durations (30, 130, and 230 ms; black symbols) and another (performed the previous day)using a continuous range (200–700 ms; white symbols). For the latter, data have been binned (ranges shown in parentheses).From Churchland et al. (2006c).

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the neural circuitry are (Churchland et al., 2007;Yu et al., 2006, 2009). We start with as simplean assumption as possible: the arm movementmade (M(t)) depends upon preparatory activity(P) at the timemovement activity begins to be gen-erated (t0). In other words, M(t) depends on P(t0).

It is important to note that there are likelysources of variability that impact M(t) but arenot accounted for in P(t0), such as downstreamvariability in the state of the spinal cord ormuscles. Thus, to be strictly true, a noise sourceshould be included, or P(t0) would need to bethe initial state of the entire animal. However,for the moment, we avoid this issue and simplyconcentrate on the hypothesis that the movementyou make is in large part a function of the planthat was present just before movement began.Also, note that the above conception does notrule out a strong (or even dominant) role forfeedback. Such feedback could be part of thecausal mechanism by which the plan producesthe movement.

The central implication of our assumption thatM(t) depends on P(t0) is that motor preparation

may be the act of optimizing preparatory activity(i.e., bringing P to the state needed at t0) so thatthe generated movement has the desired pro-perties. In the case of monkeys performingreaching movements, the desired movement canbe defined as a reach that is accurate enough toresult in reward. Consider the space of all possi-ble preparatory states (all possible Ps). For agiven reach, there is presumably some small sub-region of space containing those values of P thatare adequate to produce a successful reach.Although the response of each neuron (i.e., tun-ing) may not be easily parameterized, there isnonetheless a smooth relationship between firingrate and movement. Therefore, the small subre-gion of space is conceived of as being contiguous.

Figure 4 illustrates this idea. We conceive of allpossible preparatory states as forming a space,with the firing rate of each neuron contributingan axis. Each possible state—each vector of possi-ble firing rates—is then a point in this space. Fora given reach (e.g., rightwards), there will besome subset of states (gray region in Fig. 4,referred to as the optimal subspace) that will

Cell B29

Cell B46

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Fig. 3. Examples of typical delay-period responses in PMd. (a) Mean"SE firing rates for four example neurons. Three of theseshowed increases in firing rate after target onset, whereas one showed a decrease. Data are from experiments using a continuousrange of delay periods (500–900 for monkey B and 400–800 for monkey A). For each time point, mean firing rate was computedfrom only those trials with a delay period at least that long. Labels give the monkey initial and cell number. Details (direction,distance, instructed speed, and trials/condition) were as follows: cell B29, 45#, 85 mm, fast, 23 trials; cell B16, 135#, 60 mm, fast,20 trials; cell B46, 335#, 85 mm, fast, 41 trials; cell A2, 185#, 120 mm, slow, 42 trials. From Churchland et al. (2006c).

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result in a successful reach that garners a reward.Under this optimal subspace hypothesis, the cen-tral goal of motor preparation is to bring the neu-ral state within this subspace before themovement is triggered. This may occur in differ-ent ways on different trials (trial 1 and trial 2 inFig. 4). This framework, though rather general,has provided us with a number of specific andtestable predictions, which we review below.Before doing so, it is worth considering that an

almost-trivial prediction of the optimal subspacehypothesis is that different movements requiredifferent initial states. If preparatory activity hasa strong role in determining movement, thenmaking different movements will require differentpatterns of preparatory activity. The overall

neural state, and thus the state of individualneurons, should therefore vary with differentmovements. This is of course consistent with theobservation that preparatory activity is tuned forreach parameters such as direction and distance(e.g., Messier and Kalaska, 2000). In fact, underthe optimal subspace hypothesis, neural activityshould appear tuned for essentially every control-lable aspect of the upcoming reach (a predictionwe will return to shortly).

As a brief aside on the topic of tuning, we notethat one could conceive of each axis in Fig. 4 ascapturing not the activity of a single neuron, butrather the activity of a population of neurons thatare all tuned for the same thing. Thus, the threeaxes might capture, respectively, the averageactivity of neurons tuned for direction, distance,and speed. If so, the preparatory state could bethought of as an explicit representation of direc-tion, distance, and speed. However, it has beenargued that few individual neurons appear tunedfor reach parameters in the straightforward andinvariant way that one might hope (e.g.,Churchland et al., 2006b; Churchland and Shenoy,2007b; Cisek, 2006; Fetz, 1992; Scott, 2004, 2008;Todorov, 2000). The optimal subspace hypothesisis largely agnostic to this debate. So long as thereis a systematic relationship between preparatoryactivity and movement, the optimal subspace con-ception remains viable. Put another way, the spaceillustrated in Fig. 4 could have axes that capturewell-defined parameters, but it need not, and thereare reasons to suspect that it does not.

A related and critical point is that the space inwhich neural activity evolves is certainly larger thanthe three dimensions illustrated in Fig. 4. Move-ments vary from one another inmore than three dif-ferent ways. Similarly, neural activity varies acrossmovements in more than three different ways(Churchland and Shenoy, 2007b). Thus, care shouldbe taken when gleaning intuition from illustrationssuch as that in Fig. 4, to keep in mind that what isillustrated is a projection of a larger and richer space(Churchland et al., 2007; Yu et al., 2009).

Neuron 3

Right reach

Left reach

Trial 1

Trial 2

Neuron 2

Firing rate,neuron 1

Fig. 4. Illustration of the optimal subspace hypothesis. Theconfiguration of firing rates is represented in a state space,with the firing rate of each neuron contributing an axis, onlythree of which are drawn. For each possible movement, wehypothesize that there exists a subspace of states that areoptimal in the sense that they will produce the desired resultwhen the movement is triggered. Different movements willhave different optimal subspaces (shaded areas). The goal ofmotor preparation would be to optimize the configuration offiring rates so that it lies within the optimal subspace for thedesired movement. For different trials (arrows), this processmay take place at different rates, along different paths, andfrom different starting points. From Churchland et al. (2006c).

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We now review a number of specific andtestable predictions of the optimal subspacehypothesis.

Prediction 1: Reach-speed modulation

Figure 5a illustrates in state space our first predic-tion under the optimal subspace hypothesis: pre-paratory activity should covary with othermeaningful aspects of movement, including peakreach speed. Confirming this would be consistentwith our assumption above, whereas failing tofind this would be consistent with preparatoryactivity having a higher-level, perhaps more sen-sory role reflecting the target location but notthe more detailed aspects of movement.

To test this prediction, we trained monkeys toreach to targets in a variant of the instructed-delaytask. Reaches must be made somewhat faster($1.5 m/s peak speed) when the target was redand somewhat slower ($1.0 m/s peak speed) whenthe target was green (Churchland et al., 2006b).All other movement metrics such as reach pathremained similar. Delay-period activity was sub-stantially different ahead of fast and slow armmovements to the same target location. Figure 5bshows the average response of an example neuron,ahead of reaches to a particular target, where thedelay-period activity was greater ahead of fastreaches (red) than ahead of slow reaches (green).Figure 5c and d show two more example neuronswhere this difference in preparatory activity aheadof fast (red) and slow (green) reaches isemphasized by collapsing across all reach targetlocations. Some neurons had higher average firingrates ahead of fast movements (Fig. 5c), whileother neurons had higher average rates ahead ofslow movements (Fig. 5d).

In sum, prediction 1 as illustrated in Fig. 5aappears to be correct.

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Fig. 5. Predicted and measured relationships between neuralactivity and reach velocity. (a) The prediction thatpreparatory activity should covary with instructed reachspeed (prediction 1) is visualized in the state-spaceframework. Two optimal subspaces are illustrated: oneshaded red for the fast instruction and another shaded greenfor the slow instruction. The prediction that preparatoryactivity should correlate, on a trial-by-trial basis, with peakreach speed (prediction 2) can also be visualized in this statespace. For example, an instructed-fast trial with a slower-than-typical actual reach speed should have a preparatorystate toward one end of the “fast” optimal subspace, nearerto the “slow” optimal subspace. (b) Examination of the firstprediction: the mean firing rate is plotted as a function oftime for one neuron, one target location, and both instructedspeeds. For this neuron, the mean firing rate was highestwhen preparing a fast reach. Other neurons showed theopposite pattern. “T,” “G,” and “M” indicate target onset,

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Prediction 2: Reach-speed (trial-by-trial)correlation

Figure 5a also illustrates in state space our secondprediction under the optimal subspace hypothesis:preparatory activity should correlate, on a trial-by-trial basis, with the peak reach speed.Our assumption that M(t) depends on P(t0)predicts that even a slightly different P(t0) valueshould lead to a different M(t). If P(t0)reflects the result of a difficult optimization,then variability in P(t0) is likely. Therefore,it should be possible to observe a trial-by-trialcorrelation between P(t0) and movement metricsM(t).To test this prediction, we again employed the

reach-speed variant of the instructed-delay task.We found trial-by-trial correlations between thefiring rate of individual neurons before the gocue and peak reach speed (Churchland et al.,2006a). Consider the instructed-fast condition(red) in Fig. 5c. The horizontal spread of points(one point per trial) reflects the trial-to-trial vari-ance in peak reach speed. The vertical spread ofpoints largely reflects the trial-to-trial variance in

estimated firing rate, which is the inevitable resultof it being difficult to assess the firing rate of asingle neuron on a single trial from a handful ofstochastically occurring spikes. Nevertheless a sta-tistically significant correlation was found formost neurons and for both instructed speeds.

Importantly, the state-space illustration(Fig. 5a) further predicts that within theinstructed-fast condition, for example, a trial witha slightly slower peak reach speed should have apreparatory state slightly closer to those foundin the instructed-slow condition. In other words,if we assume that movement parameters aremapped smoothly from firing rate, the slope ofthe within-condition correlation (black lines)should agree with the slope of the across-condi-tion mean line fit (gray line) both when theinstructed-fast condition had a higher average fir-ing rate (Fig. 5c) and when it had a lower averagefiring rate (Fig. 5d). We found this to be the casein the majority of neurons (Churchland et al.,2006a).

In sum, prediction 2 as illustrated in Fig. 5aappears to be correct.

Prediction 3: Across-trial firing-rate variance(Fano factor) reduces through time

Figure 6a illustrates in state space our third pre-diction under the optimal subspace hypothesis:preparatory activity should become, throughtime, quite accurate and therefore quite similaracross trials. Before the target appears, “base-line” neural activity can be somewhat differentfrom trial to trial, leading to some amount ofacross-trial firing-rate variance (black circles inpanel labeled “before target onset” in Fig. 6a,top). After target onset, and for the coming200–300 ms, preparatory activity on each trial isnominally being optimized and brought to residewithin the optimal subspace. The optimal sub-space is presumably rather restricted by virtue ofthe behavioral task constraints and thus shouldhave less across-trial firing-rate variance (black

the go cue, and the median time of movement onset. (c) Trial-by-trial correlation between preparatory firing rate and peakreach speed. Data are from one neuron (B24). Each dotplots the mean delay-period firing rate versus peak reachspeed for one trial. Trials have been pooled across targetlocations (for this neuron all locations involved a preferencefor the fast instruction). To allow pooling, firing rates andpeak speeds are expressed relative to the mean for therelevant condition. The offset between the left subpanel(instructed-slow reaches) and the right subpanel (instructed-fast reaches) indicates the degree to which firing rates wereon average higher for the instructed-fast condition. Thisdefines a “predicted slope” (gray line) with which one cancompare the slopes computed from the trial-by-trialvariability (black lines). (d) Similar plot but for a secondneuron (A06) for which the average firing rate was higherfor instructed-slow reaches. In agreement, the trial-by-trialcorrelations show negative slopes. Figure adapted fromChurchland et al. (2006a).

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circles within the optimal subspace shaded gray,in the panel labeled “$200 ms after target onset’in Fig. 6a, bottom).

To test this prediction, we analyzed data froman instructed-delay task using the Fano factor:the across-trial spike-count variance divided bythe mean (Churchland et al., 2006c, 2007,2010c). Normalization, and an additional set ofcontrols, is necessary to ensure that the measuredchanges in variance are not simply due to thewell-known scaling of spike-count variance withspike-count mean (as happens, e.g., for a Poisson

process; Churchland et al., 2007, 2010c; Rickertet al., 2009). As shown in Figure 6b, we foundthat the Fano factor declines over the course ofapproximately 200 ms and then approximatelyplateaus (Churchland et al., 2006c). This is some-what remarkable, as it so closely resembles thedecline and plateau seen in the behavioral curves(RT versus delay, Fig. 2).

In sum, prediction 3 as illustrated in Fig. 6aappears to be correct. Moreover, it appears thatthe across-trial firing-rate variance (as measuredby the Fano factor) parallels the reduction in

Fano

fact

or

(b)

(c) (d)

Fano factor aroundtime of go cue

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30 ms

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Neuron 2

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Target

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n R

T (m

s)

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Hand speed

~200 ms aftertarget onset

Fig. 6. State-space viewof prediction 3, andFano factor relationshipwithRT in the instructed-delay task. (a) State-space illustration, as inFig. 4, showing the state of several trials (black circles) frombefore target onset until convergingwithin the optimal subspace (gray shadedregion) approximately 200 ms later. (b) Fano factor reduces from the time of target onset, approximately holds at a plateau levelthroughout delay periods longer than 200 ms, and then reduces further following the go cue. (c) By employing shorter delay periods,where the go cue comes at 30, 130, or 230 ms after target onset (colored arrows), it is possible to ask if the resulting RTs are longerwhen the Fano factor is higher (prediction 4-I). (d) Mean"SEM measured RT plotted against mean"measured Fano factor for thethree delay durations (monkey G). A clear correlation is observed, with longer delay durations leading to both lower Fano factors andlower RTs as predicted. As a technical aside, when measuring across-trial variability our later publications (e.g., Churchland et al. 2007,Churchland et al. 2010c) employed the Fano factor while our original publication (Churchland et al. 2006c) employed the closelyrelated 'normalized variance'. The above plots are reproduced from that original manuscript, and it should thus be kept in mindthat the vertical axis is not technically the Fano factor, because spiking was assessed in a Gaussian window rather than a squarecounting window. That said, results are very similar regardless of the exact window shape (e.g., Churchland et al. 2007, Fig. 4).

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11

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es p

er s

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Fig. 7. Changes in firing-rate variability for 10 datasets (one per panel). Insets indicate stimulus type. Data are aligned on stimulusonset (arrow). For the two bottom panels (MT area/direction and MT speed), the dot pattern appeared at time zero (first arrow)and began moving at the second arrow. The mean rate (gray) and the Fano factor (black with flanking SEM) were computedusing a 50-ms sliding window. For OFC, where response amplitudes were small, a 100-ms window was used to gain statisticalpower. Analysis included all conditions, including nonpreferred. The Fano factor was computed after mean matching(Churchland et al., 2010c). The resulting stabilized means are shown in black. The mean number of trials per condition was 100(V1), 24 (V4), 15 (MT plaids), 88 (MT dots), 35 (LIP), 10 (PRR), 31 (PMd), 106 (OFC), 125 (MT direction and area), and 14(MT speed). Figure from Churchland et al. (2010c).


RT: both drop over the course of approximately200 ms and then hold at that level. This possibilityis explored below, as predictions 4-I and 4-II.

As a brief aside, it could be the case that thisreduction in across-trial firing-rate variance isprincipally a motor phenomenon and is specificto the preparation of arm movements. However,we found that this same general structure of areduction in across-trial firing-rate variance fol-lowing a stimulus onset is present across much ifnot all of cerebral cortex (Churchland et al.,2010c). Figure 7 shows a substantial reduction inFano factor following stimulus onset in numerousareas, across all four cortical lobes, and in a vari-ety of behaviors. This reduction seems to be ageneral property of the nervous systemresponding to an input, much as the mean(across-trial) firing-rate changing is a generalproperty of cortical neurons. This reduction inacross-trial firing-rate variance in each area maybe correlated with the relevant functions per-formed therein (e.g., sensation, cognition, behav-ior), again just as the mean firing rate is wellknown to correlate with the function of each area.

Predictions 4-I and 4-II: Lower Fano factor andlower RTs

Figure 6c illustrates the first part of our fourthprediction (prediction 4-I) under the optimal sub-space hypothesis: the lower the across-trial firing-rate variance at the time of the go cue, the lowertoo should be the RT. Having seen the similaritybetween how the Fano factor descends and holdsas a function of delay duration (Fig. 6b), and howRT descends and holds as a function of RT(Fig. 2), it is natural to predict that there shouldexist a positive correlation between Fano factorand RT. For example, one expects that shortdelays should lead to high Fano factors and highRTs, while long delays should lead to low Fanofactors and low RTs.

To test this prediction, we analyzed short delay-duration trials from the instructed-delay task.

Figure 2 shows representative RT data from mon-key G when 30, 130, and 230 ms delay durationswere used. Figure 6c shows the Fano factor atthe three critical times: 30, 130, and 230 ms aftertarget onset. Figure 6d shows RT data plottedagainst Fano factor data, from the same trials inMonkey G, and a clear relationship is seen. Thelower the across-trial firing-rate variance at thetime of the go cue (as measured by the Fano fac-tor), the lower the RT (Churchland et al., 2006c).

!"#$%&"'($)

(a)

(b)

Long RT¢s

Long RT¢s

Short RT¢s

Short RT¢s

Go

Target

Fig. 8. State-space view of prediction 4-II, and relationship ofthe Fano factor to natural RT variability. (a) State-spaceview of prediction 4-II. The shaded area represents theoptimal subspace for the movement being prepared, as inFig. 4. Each dot corresponds to one trial and represents theconfiguration of firing rates around the time of the go cue.For some trials, that configuration may lie within the optimalsubspace (green dots), leading to a short RT. For other trials,the configuration may lie outside (red dots), leading to alonger RT. (b) Red and green traces show the Fano factor,around the time of the go cue, for trials with RTs longer andshorter than the median. Data were pooled across therecordings from 7 days (monkey G), including all trials withdelay periods >200 ms. Figure adapted from Churchlandet al. (2006c).

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Figure 8a illustrates in state space the secondpart of our fourth prediction (prediction 4-II)under the optimal subspace hypothesis: the lowerthe across-trial firing-rate variance at the time ofthe go cue, the lower too should be the RT, evenin long delay-duration trials where sufficient timehas elapsed for “complete” motor preparation toresult. For long delay durations (e.g.,>200–300 ms), the Fano factor has nominallyplateaued, as has the RT, at a low level. But, asdepicted in Fig. 8a, there could still remain somevariability. On trials that “wander outside” theoptimal subspace (red circles), some additionaltime (i.e., increased RT) should be required tocomplete preparatory optimization following ago cue. In contrast, on trials where the prepara-tory state is within the optimal subspace (greendots) and therefore motor preparation is com-plete and ready for execution, movement canbegin with a minimum of latency following thego cue (i.e., low RT).To test this prediction, we started with all trials

with 200 ms or longer delay durations, across7 days of experiments using a 96-channel electrodearray. This helped assure sufficient data. Second,we sorted trials according to whether the RT wasshorter than or longer than the median RT. Third,we calculated the across-trial firing-rate variance(Fano factor) for the half of trials with shorter thanmedian RT, and the same for the half of trials withlonger than median RT. We did so for times rang-ing from 200 ms before the go cue until 200 msafter the go cue in order to assess the robustnessof the result. Figure 8b plots the Fano factor curvefor shorter than median trials (green curve) andlonger thanmedian trials (red curve). These curvesare statistically significantly different (not shown),and as predicted, the lower across-trial firing-ratevariance trials (green curve) are associated withlower RTs (Churchland et al., 2006c).In sum, prediction 4-II as illustrated in Fig. 8a

appears to be correct. When combined with theexperiments and results associated with predic-tion 4-I, it appears clear that there is a close rela-tionship between the across-trial firing-rate

variability at the time of the go cue and theresulting RT. Recently, similar results have beenfound in area V4 ahead of saccadic eye move-ments, suggesting that this relationship is not lim-ited to the arm movement system alone(Steinmetz and Moore, 2010).

Prediction 5: Perturbing neural activityincreases RT

The inset of Fig. 9 illustrates in state space thefifth prediction under the optimal subspacehypothesis: perturbing the preparatory state outof the optimal subspace should result in anincreased RT. But it should not reduce movementaccuracy.

The first four predictions of the optimal sub-space hypothesis were correlative, and their affir-mation provides important evidence supportingthe optimal subspace hypothesis. The inset ofFig. 9 illustrates a causal prediction, wherein apreparatory state within the optimal subspace isdeliberately perturbed (curly line with displacedpreparatory state, black circle) and it is pre-dicted that the RT should increase. This followsfrom the reasoning that if the goal of motor prep-aration is to help make accurate movements, thenthe brain must somehow be able to monitor pre-paratory activity and determine when it is accu-rate enough to initiate movement. If preparatoryactivity were optimized and within the optimalsubspace, but were then perturbed away fromthe optimal subspace, the brain should wait forthe plan to reoptimize to the optimal subspace(i.e., recover) before initiating movement (reddashed arrow labeled “reoptimization”). Impor-tantly, after taking time to reoptimize preparatoryactivity, the resulting movements should be asaccurate as on nonstimulated trials.

To test this prediction, we delivered subthresh-old electrical microstimulation to PMd on a sub-set of trials and did so at various times relativeto the go cue (Churchland and Shenoy, 2007a).Figure 9 plots experimental results from all (30)

45


stimulation sites in PMd in one monkey. RTs areincreased when microstimulation is deliveredaround the time of the go cue. This is seen as arightward shift in the red hand-speed curve (stim-ulation around time of go cue, as indicated by thered bar) relative to the black hand-speed curve(no stimulation). This is consistent with time hav-ing been consumed (increased RT) to reoptimizepreparatory activity. Importantly, aside fromdelaying the onset of movement, all other move-ment metrics were extremely similar to the non-stimulated trials (consistent with prediction 5).Note that the red and green averaged curves inFig. 9 have lower peak hand speed due to stag-gered RTs, but individual trials do achieve thesame, higher peak hand speed (see Churchlandand Shenoy, 2007a for details).

As it is critical to establish effect specificity whenconducting causal perturbation experiments, weperformed several additional control experiments(Churchland and Shenoy, 2007a). Four are briefly

summarized here. First, we found that stimulatingwell before the go cue (Fig. 9, green bar) had littleimpact on the RT. This can be seen in Fig. 9 by not-ing that the green curve largely overlaps with theblack curve. This result is consistent with therebeing sufficient time for reoptimization to occurbefore the go cue appears. This is an importanttemporal control and indicates that the effect ofsubthreshold microstimulation exerts its influencejust when the preparatory state is most needed(consistent with prediction 5). Second, stimulatingon zero delay-duration trials where there was pre-sumably no optimized preparatory activity presentto perturb did not alter RT. This is an importantcontrol as it confirms the necessity of there firstexisting a preparatory state near the optimal sub-space (consistent with prediction 5). Third,stimulating inM1 where there is relatively less pre-paratory activity resulted in little RT increase. Theimportance of this control is twofold. (i) It confirmsthat perturbing motor preparation is easier in an

Han

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Fig. 9. State-space view of prediction 5 and influence of subthreshold microstimulation in PMd on arm movement RT. Inset: State-space view of the predicted effect of subthreshold microstimulation on the preparatory state (curly arrow displacing the state, shownas a black circle), and the time consuming process of reoptimizing the preparatory state so that it is returned to within the optimalsubspace (red dashed line). Black curve: nonstimulated trials. Red curve: microstimulation occurring just after the go cue, whenpreparatory activity is most needed. Green curve: stimulation occurring well before the go cue, when time exists followingstimulation offset for preparatory activity to recover before the go cue appears. Red and green bars indicate when stimulationwas delivered. Data are from 30 experiments in PMd, and curves plot mean"SE.

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area where preparatory activity is prevalent (PMd)than in an area where it is not (M1). (ii) It confirmsarea specificity. M1 is just a few millimeters fromPMd, but the effect is dramatically reduced andthereby helps assure that subthresholdmicrostimulation is not just a generalized distrac-tion. Both findings are consistent with prediction5. Fourth and finally, the effect of microstimulationwas specific to arm movements and produced littleincrease in saccadic eye movement RT. This is animportant control for the possibility thatmicrostimulation is altering attention, whichshould impact both effectors equivalently.In sum, prediction 5 as illustrated in Fig. 9 is

borne out. This contributes causal supportive evi-dence for the optimal subspace hypothesis, whichcomplements predictions 1–4 as well as 6 and 7(below).

Prediction 6: Single-trial neural trajectories

The conceptual sketch in Fig. 4 illustrates in statespace the sixth prediction under the optimal sub-space hypothesis: it should be possible to con-struct single-trial state-space neural trajectoriesand use them to directly confirm that across-trialfiring-rate variability decreases through time.To test this prediction, we must begin by mea-

suring many neurons simultaneously. This isessential as we seek an accurate estimate of thepreparatory state on each individual trial and ona fine time scale. Both require data from manyneurons, instead of the more traditional tech-nique of trial averaging, in order to mathemati-cally reduce the deleterious effects of spikingnoise (Churchland et al., 2007; Yu et al., 2009).These measurements can be made with electrodearrays, which have been developed substantiallyas part of neural prosthesis research. The analysescan be performed using modern dimensionalityreduction and visualization methods such asGaussian Process Factor Analysis (GPFA; Yuet al., 2009). Dimensionality reduction is neededfor two reasons. First, reducing the dimensionality

of the data from its original $100 D space (e.g.,100 neurons measured simultaneously constitutesa 100 D space) down to 10–15 D appears to bepossible without significant loss of informationand has the benefit of effectively denoising thedata (Yu et al., 2009). This can be thought of asessentially performing a weighted average tocombine the responses of neurons that sharesome important aspect of their response. Second,while reducing the dimensionality further (below10–15 D) does result in a loss of information, itcan be quite useful for visualization purposes.This is because the two or three dimensions usedin drawings can be the two or three dimensionsthat capture the greatest variance in the data,and the resulting plots are still sufficient to spuron hypotheses and predictions as describedabove.

Figure 10a shows multiple single-trial neuraltrajectories in a 2D state space created withGPFA (Churchland et al., 2010c; Yu et al.,2009). This is the first time that true single-trialneural trajectories (gray lines in Fig. 10a), asopposed to the cartoon depictions in Fig. 4, areplotted in this review. It is reassuring to see inFig. 10a that the scatter in across-trial preparatorystates at each point in time (black dots) reduces asthe trial progresses. As the trial progresses frombefore target onset (100 ms pretarget) to just aftertarget onset when the preparatory state isevolving toward the optimal subspace (100 mspost-target), and on to when the neural state oneach trial is presumably within the optimal sub-space (200 ms post-target), the variance (scatter)of the preparatory state reduces. This is consistentwith the results presented above, inferred withFano factor analyses.

Figure 10b again shows multiple single-trialneural trajectories in a 2D state space createdwith GPFA but now goes on to show data untilthe time of movement onset (Churchland et al.,2010c). This reveals for the first time that neuraltrajectories (gray lines) follow a largely stereo-typed path through state space, after the initialconvergence following target onset. They start in

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the baseline pretarget state (blue circles), prog-ress, and slow-down (if an extended delay period)in the optimal subspace until the time of the gocue (green), and then arch around and arrive ata small region where the arm movement is firstdetected (black). Highlighted in red is one outliertrial which had a substantially longer RT thantypical. With single-trial visualization of even(entirely) internal neural processing, it is nowpossible to ask, for the first time, what the reasonmight be. On this trial, the preparatory processappears to have completed normally. The green

circle is within the (presumed) optimal subspaceand surrounded by other trials that had normalRTs. While we cannot conclude what the causewas from this data alone, we appear to be ableto rule out incomplete motor preparation. Fig-ure 10c plots data from a different data set.Again, one trial with a particularly long RT ishighlighted in red. This trial's neural trajectoryundergoes an entire loop between the go cueand movement onset.

In sum, prediction 6 as illustrated in Fig. 4 isborne out. It is possible to construct single-trial

100 ms pretarget 100 ms posttarget

Movementonset

Pretarget

Go cue

200 ms posttarget

(a)

(b) (c)

Fig. 10. Single-trial neural trajectories computed using GPFA. (a) Projections of PMd activity into a two-dimensional state space.Each black point represents the location of neural activity on one trial. Gray traces show trajectories from 200 ms before targetonset until the indicated time. The stimulus was a reach target (135, 60 mm distant), with no reach allowed until a subsequent gocue. Fifteen (of 47) randomly selected trials are shown. (b) Trajectories were plotted until movement onset. Blue dots indicate100 ms before stimulus (reach target) onset. No reach was allowed until after the go cue (green dots), 400–900 ms later. Activitybetween the blue and green dots thus relates to movement planning. Movement onset (black dots) was approximately 300 msafter the go cue. For display, 18 randomly selected trials are plotted, plus one hand-selected trial (red, trialID 211). Covarianceellipses were computed across all 47 trials. This is a two-dimensional projection of a 10-dimensional latent space. In the fullspace, the black ellipse is far from the edge of the blue ellipse. This projection was chosen to accurately preserve the relativesizes (on a per-dimension basis) of the true 10-dimensional volumes of the ellipsoids. Data are from the G20040123 dataset. (c)Data are presented as in (b), with the same target location, but for data from another day's dataset (G20040122; red trial, trialID793). From Churchland et al. (2010c).

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neural trajectories and use these trajectories todirectly see key features that can only be inferredless directly with single-neuron recordings. It alsoappears to now be possible to begin to investigatethe reasons for outlier and other types of uniquetrials. Intriguingly, it should now also be possibleto design experiments aimed at creatinginherently single-trial phenomenon such as sin-gle-trial decision making, which could shed con-siderable insight on internal cognitive processingand neural dynamics (Kalmar et al., 2010;Rivera-Alvidrez et al., 2008). Further, as tasksbecome more complex (e.g., Churchland et al.,2008) and naturalistic (e.g., Chestek et al.,2009b; Gilja et al., 2010a; Jackson et al., 2006;Santhanam et al., 2007), both behavior and thepreceding neural processes will likely become lessstereotyped and may therefore often require sin-gle-trial analyses.

Prediction 7: Farther and faster along loopreduces RT

We have posited that the preparatory state has alarge impact on the subsequent movement. Wehave also seen several predictions that stem fromthe optimal subspace hypothesis along with evi-dence supporting these predictions. It does seemto be the case that the preparatory state at the timeof the go cue has a substantial influence on thesubsequent movement. But why should this be?One possibility is illustrated in Fig. 11a. It could

be that the preparatory state at the time of the gocue (green circle) acts as the initial state of asubsequent dynamical system that serves to gen-erate muscle activity and create movement (greenand blue arrows; Churchland et al., 2010a). Assuch, it is important that the preparatory statebe within the optimal subspace in order to helpcreate the desired movement. Thus some regionor regions of the brain appear to monitor andwait for this to be true before “pulling the trig-ger” to initiate movement. After the movementtrigger has been pulled, if the preparatory state

happens to be farther along the “loop” andmoving in the standard direction around the loop(see arrows), then RT may be further lowered.

Neuron 3

Neuron 3

Neuron 2

Neuron 2

Trial 2Trial 1

LongerRT

ShorterRT



(a)

(b)

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Go cue

Movementonset

Fig. 11. Low-dimensional state space (as in Fig. 4) illustratingprediction 7. (a) A single-trial neural trajectory is illustratedwith activity from the time of target onset (red circle) shownin red, from the time the go cue is presented (green circle)shown in green, and from the time of movement onset (bluecircle) shown in blue. One or more regions of the brainappear to monitor the preparatory state and initiatemovement (“pull the movement trigger”) only if it is withinthe optimal subspace, so as to assure that the desiredmovement results. (b) Illustration of prediction 7. After themovement trigger is pulled, a preparatory state that happensto be farther along the loop in the standard direction shouldhave a shorter RT. Trial 1 should have a shorter RT thantrial 2. Not shown is the related prediction that a preparatorystate that is moving faster in the standard direction of looptravel should also have a shorter RT.

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Figure 11b illustrates in state space the seventhprediction under the optimal subspace hypothesis:the farther the preparatory state is along the loopwhen the movement trigger is pulled, and thefaster it is moving along the loop in the standarddirection (not shown in Fig. 11b), the shorter theRT should be. Figure 11b depicts the “loop”structure seen in Fig. 10b, where most individualtrials follow a stereotyped path in state space.The two single-trial neural trajectories in Fig. 11bexit the optimal subspace in a particular direction,as was the case for all single-trial neuraltrajectories (gray lines) in Fig. 10b and c. Predic-tion 7 states that a trial like trial 1 in Fig. 11bshould have a shorter RT than trial 2, because(i) the preparatory state at the time of the gocue is within the optimal subspace for both trials(and thus the movement trigger is presumablypulled at the same time) and (ii) the preparatorystate for trial 1 (green circle) is nearer the exit-edge of the optimal subspace and is thus fartheralong the stereotyped path that it will need totake to generate movement. If the preparatorystate also happened to be moving along the ste-reotyped path in the standard direction, asopposed to not moving or moving in the oppositedirection, then the RT ought to be shorter still.

To test this hypothesis, we correlated, on atrial-by-trial basis, how far along the loop the pre-paratory state was (at the time of the go cue) withRT. As predicted, we found a statistically signifi-cant negative correlation, and primarily in justthe exit-edge direction (Afshar et al., 2011). Alsoas predicted, we found a statistically significantcorrelation between the direction of movementof the preparatory state at the time of the gocue and RT: preparatory states that were movingin the direction of (subsequent) loop travel hadlower RTs than comparably positioned prepara-tory states moving in the opposite direction(Afshar et al., 2011).

This appears to suggest that a trial with prepa-ratory activity at the time of the go cue (green cir-cle) that is (i) within the optimal subspace and (ii)farther along, and moving in, the standard “loop”

direction is in some sense “doubly advantaged”because it is both (i) a well-optimized preparatorystate (i.e., within the optimal subspace so themovement trigger can be pulled straight away)and (ii) fortuitously positioned and alreadyheaded along the path it will need to take to gen-erate movement. In sum, prediction 7 asillustrated in Fig. 11b is borne out.

Future directions

The above predictions were derived from adynamical systems perspective, and to somedegree their confirmation argues for that perspec-tive. Yet the most central questions remain largelyunaddressed. What is the nature of the relevantdynamics (e.g., Yu et al., 2006)? Do they relateto the dynamics of movement-generating circuitsin simpler organisms (e.g., Grillner, 2006; Kristanand Calabrese, 1976)? How and why do dynamicschange as a function of overall state (e.g., restingvs. planning vs. moving)? What is the nature ofthe circuitry, both local and feedback, that pro-duces those dynamics? Answering such questionswill likely depend on progress in three domains:(1) the ability to better perturb and probe dynam-ics, (2) the ability to resolve dynamical structure inneural data, and (3) the ability to relate therecorded “neural trajectories” to externally mea-surable parameters such as muscle activity andhand movement. We consider these in turn.

First, when reverse-engineering any system, theability to perturb and observe is critical. Asdescribed above, we used intracortical electricalmicrostimulation to ask how a perturbation ofneural activity influenced RT. Pharmacologicalmanipulations are also possible and would offercell-type specific manipulation of the system.Recent advances in optogenetic stimulation ofneurons in rhesus monkeys may also provideimportant new insights due to the ability to exciteand inhibit neurons in a cell-type specific manner(unlike electrical microstimulation), do so on amillisecond timescale (unlike pharmacological

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manipulations), and not interfere with simulta-neous electrical recordings (unlike electricalmicrostimulation; Diester et al., 2011; Han et al.,2009). This could enable the direct visualizationof neural trajectories throughout trials where theneural state is optically perturbed at varioustimes. Recall the Fig. 9 inset, where the curlyblack line and dashed red line could only illus-trate our speculation about how the neural trajec-tory might evolve during and directly followingstimulation, because electrical microstimulationinterferes with electrical array recordings. Also,while permanently altering the underlying neuralcircuitry transgenically is not currently possible inrhesus monkeys, it is possible to reversibly lesionbrain regions, cell-types, and neuronal projectionspharmacologically and optogenetically. Under-standing how the subsequent alteration of neuraltrajectories relates to altered behavior woulddeepen our understanding of motor preparationand generation, and the role of specific cells andconnectivity (Kaufman et al., 2009, 2010a; Lerchneret al., 2011).Second, any real understanding of dynamics will

hinge upon the ability to go beyond merely plottingstate-space trajectories. One wishes to take thoseseemingly complex neural trajectories, which evolveinmanydimensions, and infermeaningful and parsi-monious underlying dynamics (Yu et al., 2006).Indeed, if this cannot be done—if the proposeddynamics are not simpler than the data they seekto explain—then the dynamical systems perspectivemay have little to offer. Fortunately, it appears thatsimple dynamics may well be able to explain a con-siderable amount of the structure of the data(Churchland et al., 2010b, 2011; Cunningham et al.,2011; Macke et al., 2011; Petreska et al., 2011), butfurther progress in this realm will depend on thecontinued development of analysis methods thatcan capture how one neural state leads to the next.Finally, while the observed state-space

trajectories often appear rather abstract, theymust exist for a concrete purpose: producingmovement. That is, there must be some directand causal relationship between the neural

trajectory and some externally measurable quan-tity such as muscle activation or arm kinematics.Historically, the relationship between move-ment-period activity and the parameters of move-ment has been contentious (e.g., Kalaska, 2009).The dynamical systems perspective will not onits own resolve this debate, but there are a num-ber of contributions it can make. The dimension-ality-reduction techniques that produce the state-space trajectories force the experimenter to focuson those patterns that are most strongly presentin the data (e.g., Rivera-Alvidrez et al., 2009,2010a,b). Also, the relatively high dimensionalityof the state space makes it clear that not allaspects of neural activity can or should be relateddirectly to external factors: some dimensions maybe important to the overall dynamics but may notexert any direct influence on the periphery(Kaufman et al., 2010b, 2011).

Progress in the above domains should alsoincrease the breadth of questions addressableunder the dynamical systems perspective. Alreadyit has been possible to ask whether neuralvariability decreases during learning (Mandelblat-Cerf et al., 2009). More generally, we wish to knowwhat the “state-space” correlate of motor learningmight look like. For example, does the location ofthe optimal subspace change following learning?Or does learning change the dynamics that deter-mine the trajectory away from that planned state?Of course, one suspects that both such mechanismsmight be at play, perhaps depending on the type oflearning (e.g., the former strategy might be morerapid but less flexible). The further developmentof critical tools, as described above, could openthe door to many experiments of this type.

Importance to neural prosthetic system design

Neural prosthetic system design depends criticallyon a fundamental and comprehensive scientificunderstanding of how populations of neuronsprepare and generate natural movements (Greenand Kalaska, 2010). How neural populations

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evolve on a fast timescale is of particular interest,as neural prostheses must operate rapidly toensure accurate and stable control. Figure 12highlights perhaps the most fundamental problemthat basic neuroscience (reviewed above) and neu-ral prosthetic systems have in common: how tounderstand noisy electrical activity from a popula-tion of neurons on a millisecond timescale and ona single-trial basis. Figure 12 shows the now

familiar instructed-delay reach task and, for thefirst time in this review, reasonably raw and unpro-cessed electrode-array neural data. The moststriking feature is how noisy spiking data reallyare. Staring at this figure for a fewmoments revealsthe subtle difference in response pattern betweenthe preparatory period following target onset andthe baseline period preceding it. More obvious isthe difference between the movement period and

Touch, fixate

Neuron 1Neuron 2

Neuron 97

200 msTrial G20040508.118

1 m

/s

Target onset Go cue Movement onset

Hand speed

Fig. 12. Instructed-delay reach task and neural activity from a single trial, highlighting the need to understand all phases ofvolitional arm movement (holding, preparing, and moving) on a trial-by-trial basis as this is the fundamental information sourceand (millisecond) timescale on which neural prosthetic systems depend. Top: Schematic illustration and timeline of theinstructed-delay reach task introduced in Fig. 1 and discussed throughout this review. Middle: measured hand speed. Photo: 100electrode array used to record from many tens of neurons simultaneously. Bottom: action potential (spike) raster from 97simultaneously recorded single and multi-units, with the time of an action potential indicated by a black tick mark. Red verticallines indicate the time of target onset, go cue presentation, and movement onset.

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preparatory period. While the eye is often poor atdiscerning signal from noise, particularly withoutthe visual benefit of trial averaging, this is a usefulexercise as it helps one appreciate the challengebefore us as neuroscientists and neuroengineers.We seek to understand how these neural responsesarise, how they support behavior, and how we canuse these volitional signals as an informationsource for controlling neural prostheses. Whileseveral important design insights for prostheseshave already resulted from a deeper scientificunderstanding, some of which are discussed brieflybelow, there is little doubt that the most importantleaps forward in prostheses will result from futurescientific discovery. This has historically been thecase, with science deeply informing engineering.In addition to how the basic scientific under-

standing of brain organization and movement con-trol has already informed neural prosthetic systemdesign, as described in the Introduction, there aretwo additional points to briefly note here. First,communication prostheses rely on preparatoryactivity, as can motor prostheses (e.g., Musallamet al., 2004; Santhanam et al., 2006; Shenoy et al.,2003; Yu et al., 2007, 2010). These systems canmake use of new discoveries such as preparatoryactivity in PMd reflecting the speed of the upcom-ing movement. Second, at the heart of the dynam-ical systems perspective and the associated questfor single-trial neural trajectories is time. How longdoes it take for the neural trajectory to actually tra-verse from baseline to the optimal subspace where,once there, the neural activity can be fruitfullydecoded and used to guide a prosthesis? This isprecisely the “transit time” we needed to know aspart of our recent prosthesis research, so that wecould skip this transition period to avoid inadver-tently decoding neural activity that is still in flux.This time (Tskip; Santhanam et al., 2006) is approx-imately 200 ms as measured with single-trial neuraltrajectories in scientific experiments (as describedabove) and agrees with measurements from neuralprosthetic experiments. Similarly, for prostheticsdesigns, it is important to know how long neuralactivity should be integrated (Tint), so as to best

estimate the parameters of interest, and this isrelated to how stable preparatory neural activityis while in and around the optimal subspace. Sin-gle-trial neural trajectories can, and have, revealedimportant features which will continue to informthe design of neural prosthetic systems.

Summary

The ability to move voluntarily is central to thehuman experience. By pursuing a deeper scien-tific understanding of the neural control of natu-ral movement, it should be possible to advancethe design of neural prostheses, with the goal ofhelping patients who have lost their ability tomove. A potentially underappreciated part ofcontrolling movement is preparing movement.Preparation is, after all, how each movementbegins. Motor preparation can be studied in manydifferent ways. We have elected to adopt adynamical systems perspective in order to facili-tate the construction of hypotheses, and setabout testing their predictions. The optimal sub-space hypothesis has led to seven tested pre-dictions. It appears that this dynamical systemsperspective, and closely associated state-spacediagrams, is helping to generate an ongoing seriesof testable predictions. As a result of the recentstudies reviewed above, numerous questions arenow more apparent and remain to be addressedas described in the Future Directions. We believethat the dynamical systems perspective shouldcontinue to help generate new and testable ideasand lead to deeper insights for both basic andapplied neuroscience.

Acknowledgment

This work was supported by Burroughs WellcomeFund Career Awards in the Biomedical Sciences(K. V. S and M. M. C.), DARPA REPAIRN66001-10-C-2010 and NIH-NINDS CRCNSR01-NS-054283 (K. V. S. and M. S.), an NIH

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Director's Pioneer Award 1DP1OD006409 (K. V.S.), a National Science Foundation graduateresearch fellowship (M. T. K.), and the GatsbyCharitable Foundation (M. S.).

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A dynamical systems view of motor preparation ...shenoy/GroupPublications/... · Abstract: Neural prosthetic systems aim to help disabled patients suffering from a range of neurological