Arjun Ramakrishnan, Snehal Chokhandre and Aditya Murthy

18 Pages·2010·0.68 MB·English

Arjun Ramakrishnan, Snehal Chokhandre and Aditya Murthy
J Neurophysiol 103:2400-2416, 2010. First published Feb 17, 2010; doi:10.1152/jn.00843.2009
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Journal of Neurophysiology publishes original articles on the function of the nervous system. It is published 12 times a year
(monthly) by the American Physiological Society, 9650 Rockville Pike, Bethesda MD 20814-3991. Copyright © 2010 by the
American Physiological Society. ISSN: 0022-3077, ESSN: 1522-1598. Visit our website at http://www.the-aps.org/.
JNeurophysiol103:2400–2416,2010.
FirstpublishedFebruary17,2010;doi:10.1152/jn.00843.2009.
Voluntary Control of Multisaccade Gaze Shifts During Movement Preparation
and Execution
Arjun Ramakrishnan, Snehal Chokhandre, and Aditya Murthy
NationalBrainResearchCentre,NainwalMore,Haryana,India
Submitted16September2009;acceptedinfinalform12February2010
RamakrishnanA,ChokhandreS,MurthyA.Voluntarycontrolof to the original target position and may then look to the final
multisaccadegazeshiftsduringmovementpreparationandexecution. position.Ifthetargetstepisearlyenough,subjectscancancel
J Neurophysiol 103: 2400–2416, 2010. First published February 17,
the first saccade and shift gaze to the new location.
2010;doi:10.1152/jn.00843.2009.Althoughthenatureofgazecontrol
Many studies have found that performance during double-
regulating single saccades is relatively well documented, how such
steptasksisstochasticandthattheprobabilityofcompensating
control is implemented to regulate multisaccade gaze shifts is not
known. We used highly eccentric targets to elicit multisaccade gaze forthetargetstepbydirectinggazetothefinaltargetlocation
shiftsandtestedtheabilityofsubjectstocontrolthesaccadesequence decreaseswiththedelayofthestep,presumablybecauseofthe
bypresentingasecondtargetonrandomtrials.Theirresponseallowed advancing commitment to shift gaze to the initial target loca-
D
us to test the nature of control at many levels: before, during, and tion.Morerecentlyithasbeenshownthatperformanceduring o
w
betweensaccades.Althoughthesaccadesequencecouldbeinhibited double-steptaskscanbeaccountedforbyaracebetweenthree n
before it began, we observed clear signs of truncation of the first lo
stochasticallyindependentprocesses:1)aGOprocessproduc- a
saccade, which confirmed that it could be inhibited in midflight as d
well.Usingaracemodelthatexplainsthecontrolofsinglesaccades, ingthesaccadetotheinitialtargetlocation,2)aSTOPprocess ed
weestimatedthatittookabout100mstoinhibitaplannedsaccadebut interrupting that GO process, and 3) an ongoing GO process fro
tookabout150mstoinhibitasaccadeduringitsexecution.Although producing the saccade to the final target location (Becker and m
thetimetakentoinhibitwasdifferent,thehighsubject-wisecorrela- Jurgens1979;Camalieretal.2007;KapoorandMurthy2008; jn.p
tion suggests a unitary inhibitory control acting at different levels Lisberger et al. 1975; Murthy et al. 2009). Using this race h
y
intheoculomotorsystem.Wealsofrequentlyobservedresponsesthat s
consistedofhypometricinitialsaccades,followedbysecondarysac- mbeoedsetli,mthaetedduarnadtiohnasrebqeueinrecdaltloedcathnecetlartgheetpsltaenpn/sewdistcahccraedaectcioann iolo
cadestotheinitialtarget.Giventheestimatesoftheinhibitoryprocess g
providedbythemodelthatalsotookintoaccountthevariancesofthe time (TSRT), which is analogous to the stop signal reaction y.o
processesaswell,thesecondarysaccades(averagelatency(cid:1)215ms) time used in the countermanding task (Hanes et al. 1998; rg
should have been inhibited. Failure to inhibit the secondary saccade LoganandCowan1984)toestimatethetimeittakestoinhibit on
suggeststhattheintersaccadicintervalinamultisaccaderesponseisa a planned saccade (Camalier et al. 2007; Joti et al. 2007; N
o
ballistic stage. Collectively, these data indicate that the oculomotor Murthy et al. 2001) Therefore in addition to studying how v
e
systemcancontrolaresponseuntilaverylatestageinitsexecution. decisions are made, the double-step task can be used to study m
However, if the response consists of multiple movements then the howcontrolisimplementedbytheoculomotorsystem,usinga be
preparationofthesecondmovementbecomesrefractorytonewvisual similar race model framework that has been successful in r 3
input, either because it is part of a preprogrammed sequence or as a modeling performance in countermanding tasks. , 2
consequenceofbeingacorrectiveresponsetoamotorerror. 0
The goal of this study was to extend behavioral predictions 1
0
arising from the race model framework that have been pro-
INTRODUCTION posed to underlie the control of single saccades to instances
involving multisaccade gaze shifts, which often occur when
Allvoluntaryactsentailadecisionprocess,whetherimplicit
subjectsmakesaccadestohighlyeccentrictargets(eccentricity
orexplicit.Sinceafundamentalgoaloftheoculomotorsystem (cid:2)15°; Becker 1972; Becker and Fuchs 1969; Henson 1978;
istochooseobjectsofinterestinthevisualscenetowhichgaze
PrablancandJeannerod1975;Prablancetal.1978;Weberand
is directed, saccadic eye movements provide a logical para-
Daroff 1972). In such instances the target is foveated by an
digm to study the decision process that precedes movement
initial hypometric saccade that undershoots the target and is
execution. A task particularly well suited to study oculomotor
thenfollowedwithasecondarysaccade.Thereforeondouble-
decisionsisthedouble-steptask(AslinandShea1987;Becker
step trials if subjects fail to inhibit the initial hypometric
and Jurgens 1979; Komoda et al. 1973; Lisberger et al. 1975;
response to the initial target, they have the opportunity to
Rayetal.2004;Westheimer1954;Wheelessetal.1966).Here
inhibit the secondary response and direct gaze to the newly
onmosttrialssubjectsareshownatargettowhichasaccadeis
specified target. Since control can manifest at multiple levels—
made. Abruptly changing the location of the target on some
either before the gaze shift begins or during the intersaccadic
random infrequent trials and measuring the ability of the
interval separating intervening saccades—we asked whether a
oculomotor system to compensate for the target shift assesses
unitarymechanismwouldsufficetoexplainoculomotorcontrol.
thetemporalevolutionofdecisionmaking.Ifthetargetstepis
In addition to understanding how our brains control multi-
toolaterelativetothedecisionprocess,subjectsshiftgazefirst
gaze shifts, we also used this paradigm to assess whether the
programming of multisaccade gaze shift might also involve a
Addressforreprintrequestsandothercorrespondence:A.Murthy,Centre
ballistic stage of processing that is refractory to voluntary
for Neuroscience, Indian Institute of Science, Bangalore, India 560012
(E-mail:[email protected]). control. Although previous behavioral (e.g., Logan 1994) and
2400 0022-3077/10Copyright©2010TheAmericanPhysiologicalSociety www.jn.org
VOLUNTARY CONTROL OF MULTISACCADE GAZE SHIFTS 2401
neurophysiological studies (Hanes and Schall 1995; Hanes et anddirectgazetothefinaltarget.Randominterleavingofthetwotrial
al.1998;Pare´ andHanes2003)supportthenotionofaraceto types prevented the subjects from delaying the initial saccade, in
a single threshold, the location of the threshold in relation to anticipationofthesecondtarget.Steptrialsinourtaskdifferedfrom
the earlier double-step studies in two main respects: the initial and
movement execution is unclear. One possibility is that the
final targets were of different colors, to ease distinction between the
thresholdoccursbeforesaccadeexecution,providingadistinct
targets, especially at shorter TSDs; further, the initial target did not
pointofnoreturninsaccadicdecisionmaking(e.g.,Osmanet
disappearwiththeappearanceofthefinaltarget.
al. 1986). Modeling countermanding behavior supports this
Trials were scored as successful, and conveyed to subjects by
model and has estimated the point of no return at 28–60 ms auditoryfeedback,ifsubjectsmadethesaccadetothegreentargetin
before saccade execution (Kornylo et al. 2003). Alternatively, a no-step trial and to the red target in a step trial, fixating the
it is possible that saccade programming has no ballistic stage respectivetargetswithinanelectronicwindowof(cid:4)5°centeredonthe
and can be controlled even during the execution of saccades. target.
Evidence in support of this derives from countermanding
studies in which hypometric saccades are generated, presum-
Data collection and analysis
ably from an interaction of the STOP process during the
execution of the noncanceled saccade (Camalier et al. 2007; ExperimentswereundercomputercontrolusingTEMPO/VIDEOSYNC
Colonius et al. 2001; Ozyurt et al. 2003; Walton and Gandhi software(ReflectiveComputing,St.Louis,MO)thatdisplayedvisual
2006). In addition, many double-step studies have provided stimuliandstoredsampledeyeposition.Eyepositionwassampledat
evidence of gaze errors being corrected very rapidly, some- 240 Hz with an infrared pupil tracker (ISCAN, Boston, MA) that
interfaced with the TEMPO software in real time. All stimuli were
timesresultingintrajectoriesthatarecurvedtowardthetarget
followinginitialerrors(BeckerandJurgens1979;Findlayand presented on a Sony Trinitron 500 GDM monitor (21 in.; 70 Hz D
refresh rate) placed 34 cm in front of the subject. Stimuli were o
Harris1984;McPeeketal.2003;Minkenetal.1993;Portand w
calibratedwithaMinoltaCA-96colorimeter. n
Wurtz 2003; Van Gisbergen et al. 1987). In this study we Tocalibrateoureyetracker(seealsoKornyloetal.2007)subjects loa
examinewhichofthesetwoalternativesexplainsperformance madesaccadeswithincreasedfixationtimes(mean(cid:5)500ms(cid:4)30%) de
during multisaccade gaze shifts. amnedaspuorsetdsatchceaSdiDctoifmtehse(emyeeatnra(cid:5)cke5r0p0omsitsio(cid:4)ns3d0u%ri)n.gFaor1t0h0esmestrfiiaxlastiwone d fro
m
period. The estimate of the inherent noise of the tracker was 0.01°.
METHODS The spatial accuracy of the tracker was estimated by measuring the jn.p
Subjects mean saccade endpoint location during 100 ms of postsaccadic fixa- h
y
tiontime.Themedianoftheseendpointsonthreedifferenttrialstothe s
Fifteennaivesubjects(agesbetween18and32yr),withnormalor io
corrected vision, performed the redirect task (see Task for details). saacmcueratcayr.get was about 0.9°, which was an estimate of saccadic log
Their eye movements were recorded with their heads stabilized by Atthebeginningofeachsession,subjectsweregivenwrittenand y.o
means of a chin and forehead rest. All subjects gave their informed verbalinstructionsfollowedbysomepracticetrials((cid:1)50).Onaver- rg
consentinaccordancewiththeinstitutionalhumanethicscommittee o
age,subjectsperformedabout500trialspersession,withbreaksevery n
of the National Brain Research Centre. Subjects were monetarily 200 trials. A typical session lasted about 1 h, with each subject N
rewardedaftereverysessiontokeepthemmotivated. o
performingfourtosixsuchsessions. v
e
All analysis and statistical tests were performed off-line using m
Task MATLAB(TheMathWorks,Natick,MA).Blinkswereremovedfrom be
the eye position data and a velocity threshold of 30°/s was used to r 3
Theredirecttask(Murthyetal.2001;Rayetal.2004)isamodified demarcate the beginning and end of saccades. The accuracy of , 2
versionoftheclassicdouble-steptask(AslinandShea1987;Becker saccadedetectionwassubsequentlyverifiedmanually. 01
andJurgens1979;Komodaetal.1973;Lisbergeretal.1975;Rayet 0

al.2004;Westheimer1954;Wheelessetal.1966).Thetaskconsists
of two kinds of trials: no-step trials in which a single target is Classification of hypometric trials
presented (i.e., target is “not stepped” to another location) and step
trialsinwhichtwotargetsarepresentedinsuccession. Anytrialinwhichtheamplitudeoftheprimarysaccadefellshort
On50%ofthetrials,referredtoasno-steptrials,followingfixation ofthetargetby(cid:1)6°wasconsideredahypometricresponse.Wehave
forarandomdurationthatrangedfrom300to800ms,asinglegreen used a fairly large amplitude cutoff to include only those trials that
target (1° (cid:3) 1°), with the International Commission on Illumination involved large corrections. Previous work has shown that when the
(CIE)chromaticitycoordinates[2736157.1],appearedonthescreen error is large, the secondary saccade is executed much faster than
onabackground,withCIEchromaticitycoordinatesof[2203000.06] whentheerrorissmall((cid:6)20%ofthetargeteccentricity,whichinour
(seeFig.1A,topleft).Thelocationofthetargetwasrandomizedsuch caseis6°;Becker1972;BeckerandFuchs1969;BeckerandJurgens
that it could appear in any one of eight locations centered on an 1979; Henson 1978; Prablanc and Jeannerod 1975; Prablanc et al.
imaginary circle with a radius of 30°. Subjects were instructed to 1978; Weber and Daroff 1972). These differences in reaction times
quicklymakeasaccadetothetarget.Theyweregivenverbalinstruc- have been suggested to arise as a consequence of the oculomotor
tionstoincreasethespeediftheirsaccadelatenciesexceeded400ms. systemusingtwodifferentalgorithmsforerrorcorrection.Inthecase
Insteptrials,afterthepresentationofthefirsttarget,asecond(1°(cid:3)1°)red oflargeerrors,fastcorrectioncanoccurwithoutwaitingfortheretinal
target,withCIEchromaticitycoordinatesof[6323307.8],appeared reafferentsignal.Ontheotherhand,whentheerrorissmalltheretinal
randomlyatanotherlocationonthescreen(seeFig.1B,topright)at informationisawaitedbecausethepredictivecorrectionislikelytobe
an angular separation equal to or (cid:2)90° to avoid averaging of the toonoisytoprepareprecisesmallcorrections.Sinceourstudyfocused
saccades to the two target locations (Ottes et al. 1984). The time of oncomparinghypometricerrorswithhypometriccorrections(seeFig.
appearanceofthefinaltargetrelativetotheinitialtarget,calledtarget 1, B3 and B4), which entailed fairly large corrections, we sought to
stepdelay(TSD),wasvariedrandomlyfromabout20to230ms.The ensurethesamefortheformersothatwecouldcontrasttheeffectof
appearanceofthesecondtargetservedasa“redirect”signalinstruct- control, independent of potential differences in the algorithms that
ingsubjectstoinhibitthepartiallyplannedsaccadetotheinitialtarget mightbeusedtopreparethecorrections.
JNeurophysiol•VOL103•MAY2010•www.jn.org
2402 A. RAMAKRISHNAN, S. CHOKHANDRE, AND A. MURTHY
A No-step trial B Step trial
FIG.1. Illustration of the temporal se-
quenceofstimuliandbehaviorintheredi-
Target step delay recttask.Thetaskconsistedofno-steptrials
(A) when a single target appeared on the
screen and step trials (B) when a second
A1 No-step B1 Successful B2 Erroneous target appeared following the first after a
variabletargetstepdelay(TSD).Inno-step
response response response trials,subjectswererequiredtofoveatethe
target. They sometimes directed their gaze
withasinglesaccade(A1)andsometimesby
making 2 saccades: an initial hypometric
saccade (primary saccade) followed by a
ef secondsaccade(secondarysaccade)tofove-
atethetarget(A2).Duringsteptrials,subjects D
o
wererequiredtocancelthepartiallyplanned w
c initial saccade and direct gaze to the final nlo
target.Sometimes,theysuccessfullycompen- a
d
Horizontal Vertical satedforthetargetstep(B1).Onotherocca- e
smioandse,atnheeyrrfoanileeodustosaincchaibdietttohethireriensiptioanlstaerganetd, d fro
following it with a corrective saccade to the m
c finaltarget(B2).Sometimes,theymadeapri- jn
ef marysaccadetowardtheinitialtargetbutcor- .p
h
0 rected midway (B3), whereas on other occa- ys
1100 ms ef c saiosnecs,onthdeayryfoslaloccwaeddetthoefporvimeaaterythseacicnaidtiealwtaitrh- iolo
g
get. This was then followed by a corrective y
saccadetothefinaltarget(B4).Thehorizontal .o
A2 Hypometric B3 Hypometric B4 Hypometric and vertical eye movement traces with re- org
response correction error spect to time are illustrated, in blue and n
black,respectively.Thetimesofappearance N
of the initial and final targets are indicated ov
by the green and red arrows, respectively. em
The alphabets (ef, erroneous first saccade; b
s p p s p pan,dprci,mcaorryrescaticvceadsea;ccsa,dese)cnoenadrarthyessaaccccaaddee; er 3
eyetraceindicatetheorderofthegazeshift. , 2
c c Forpurposesofillustration,theeyetraceshave 01
0
beensubsampledto120Hzandeachsaccade
isrepresentedbyadifferentcolor.
c p
p p s c
s
p p p
c
c
0 s s
1
100 ms
Race model and estimation of target step reaction time thethreshold.Thewinneroftheracedecidesthebehavioraloutcome.
WhentheSTOPprocesswinstherace,thesaccadetotheinitialtarget
Performance in the double-step redirect task has been recently
is inhibited. This allows the second GO process (GO ) to elicit a
modeledasaracebetweenthreestochasticallyindependentprocesses: 2
saccadetothefinaltarget,resultinginasuccessfulresponse(seeFig.
1) a GO process (GO ), producing the saccade to the initial target
1 2A).WhentheSTOPprocesslosestherace,thefirstsaccadeismade
location;2)aprocessinhibitingorinterruptingthepreparationofthis
to the initial target and is referred to as an erroneous response.
saccadetotheinitialtarget(STOP);and3)anotherGOprocess(GO ),
producing the saccade to the final target location (Camalier et a2l. Subsequently, a corrective saccade redirects gaze to the final target
2007;seeFig.2).Onsteptrials,theSTOPprocessisassumedtobe (seeFig.2B).
initiated following the appearance of the final target that attempts to The race model provides a measure of the duration of the
cancelthepartiallypreparedresponsetotheinitialtarget(GO ).The inhibitory process, which we refer to as the target step reaction
1
twoprocesses,assumedtobeindependentofeachother,racetoward time (TSRT). TSRT is analogous to the stop signal reaction time
JNeurophysiol•VOL103•MAY2010•www.jn.org
VOLUNTARY CONTROL OF MULTISACCADE GAZE SHIFTS 2403
A trialsforeachTSD(seeFig.4),andthesubject’sreactiontimesin
Successful response
the no-step trials (see Fig. 2C), are used to compute the TSRT.
Three methods of estimating the TSRT were used in the current
study.ThefirstmethodassumesthatTSRTisarandomvariableand
isbasedonthelogicdescribedbyLoganandCowan(1984;seealso
Hanes et al. 1998). Here, the mean TSRT equals the difference
betweenthemeanno-stepreactiontimeandthemeanofthecompen-
n sationfunction.Ifthecompensationfunctionrangesfromaprobabil-
o
ati STOOP ityof0to1,thenitsmeanisthedifferencebetweentheprobabilityof
v respondingattheithTSDminustheprobabilityofrespondingatthe
cti GO2 (i (cid:7) 1)th TSD multiplied by the ith TSD, summed over all TSDs
A GO1 (Logan and Cowan 1984). Since the actual compensation functions
oftenhaveaminimum(cid:2)0and/oramaximumof(cid:6)1,themeanofthe
0 100 200 300 compensationfunctionwasrescaledtoreflecttheactualrangeofthe
responseprobability.Thiswasdonebydividingthemeanofthecompensa-
B
Erroneous reesponse tionfunction by the difference between the maximum and the mini-
mum probabilities of responding (also see Idealizing compensation
functionsinthefollowingtextfordetails).Toprovideanestimatethat
was less sensitive to random variability, we fit a Weibull function,
W(t)(seeRESULTSfordetails)tothecompensationfunction(Haneset
al.1998;KapoorandMurthy2008).Anestimateofthemeanofthe
best-fitcompensationfunctionwasthengivenby D
o
n w
Activatio GO1 STTOP GO2 whereMtearannogfecsofmropmensthaetiomnifnuinmcutimont(cid:2)o t(cid:8)h(cid:10)eW(cid:9)(cid:10)Wm(cid:11)tm(cid:11)aatxx(cid:12))i(cid:3)(cid:7)muWWm((cid:11)ttmT(cid:3)iSn)D1](cid:12)(cid:13)i(cid:1)nt(cid:14)1 ms nloaded fro
intervals. m
0 100 200 300 The second method, the median method, involves calculating the jn
TSRT by subtracting the median of the compensation function from .p
C h
themedianoftheno-stepreactiontimedistribution. y
s
No-step reaction Thethirdmethod,theintegrationmethod,providesanestimateof io
time distribution Errors the TSRT at each TSD. Assuming that the duration of the STOP lo
g
Successes processisconstantacrossTSDs,inthismethodTSRTwasestimated y.o
by integrating over the no-step reaction time distribution until the rg
integralequaledtheobservedproportionoferroneoussaccadesinthe o
n
TSD TSRT compensation function (see Fig. 2C). The reaction time at the inte- N
grated value yielded the finish time of the race—i.e., the longest o
v
saccadic reaction time at which the GO process finished before the e
m
STOPprocesscouldinhibitit.Thusthetimebetweentheappearance b
0TTiimmee ff1rroo00mm tthhee oooo2nn00sseett ooff IInn3ii0tt0iiaall TTaarrgg4ee00tt ((mmss))500 oinfgTthhoeenrTtehSdeRirdeTicssttorsibibgtuanitaniolendanofdrfottmhhiesthSfieTnpOirsehPcetsidimginnegailms. TtehtoheooTdbSstaRciaTnnafvoamrrytoh,riedserTpoeSbnDuds.-t er 3, 20
estimate,wethusaveragedthethreeestimatesofTSRTtoprovidea 10
FIG.2. Theracemodelframeworkandcalculationoftargetstepreaction single composite measure, which we refer to from now on as the
time(TSRT).InAandB,followingtheappearanceofthefirsttarget(green
TSRTobtainedusingtheconventionalracemodelanalysis.
arrowonthex-axis)andavisualdelayof60ms,aGO process(greensolid
1
line)isinitiated.ExecutionofthesaccadetothetargetoccursoncetheGO
1
processcrossesthethreshold(thickhorizontalgrayline).FollowingaTSD, Race model simulations
whenasecondtargetappears(redarrowonthex-axis),theSTOPprocess(red
solidline)isinitiatedfollowingthevisualdelay,whichattemptstocancelthe We used the linear accumulation to threshold with ergodic rate
GO process. A: sometimes when the STOP process reaches the threshold
1 (LATER)model(CarpenterandWilliams1995;HanesandCarpenter
before the GO process, the initial response is successfully inhibited and a
1 1999;HanesandSchall1996;Reddietal.2003),whichhasprovided
secondGO processdirectsgazetothefinaltarget(referredtoasasuccessful
2 agooddescriptionofsaccadereactiontimes,tosimulatetheGOand
response). B: on the other hand, when the GO process wins the race, the
saccadetotheinitialtargetisexecuted(referred1toasanerroneousresponse), theSTOPprocesses.Thetwoprocessesarestochasticinnature,with
followingwhichaGO processredirectsgazetothefinaltarget.Thepanels theirrateofrisevaryingfromtrialtotrialandcanbedescribedbya
2
above A and B depict the behavior at the relevant time points. C: the finish Gaussian distribution (see Fig. 3). In all our estimations and predic-
times of the GO process give rise to a right-skewed no-step reaction time tions using the race model, the variance of the GO and STOP
1
distribution.Insteptrials,assumingthattheGOprocessisindependentofthe processes were included, in addition to the mean, to improve accu-
STOPprocess,theno-stepreactiontimedistributionwouldbepartitionedinto racy.
a faster fraction of saccades that escaped inhibition (green) and a slower
fractionthatdidnot(red).Thetimefromtheonsetoffinaltargetuntilthetime MONTE CARLO METHOD. We used MATLAB to perform Monte
of partition is the TSRT for this TSD (see calculation of TSRT by the
CarlosimulationstoestimatetheratesoftheGOandSTOPprocesses,
integrationmethodinMETHODSfordetails). asinotherstudies(Coloniusetal.2001;HanesandCarpenter1999;
(SSRT)ofthecountermandingtask(Camalieretal.2007;Kapoor Walton and Gandhi 2006). For each simulated trial, the rate of
andMurthy2008).Thereforewehaveadaptedthemethodsusedto accumulation of the GO process, denoted by rGO (in Hz), which
calculate SSRT to estimate the TSRT (Camalier et al. 2007). The defines its slope (Fig. 2, A and B), was chosen randomly from a
subject’scompensationfunction,whichisthefractionoferroneous Gaussiandistributionwithmean(cid:4) andSD(cid:5) .Thethresholdwas
go go
JNeurophysiol•VOL103•MAY2010•www.jn.org
2404 A. RAMAKRISHNAN, S. CHOKHANDRE, AND A. MURTHY
Latency of the slowest erroneous response observedcompensationfunctions.Aleastsquaresmethodwasusedto
STOP2σ determinetheerrorbetweenthepredictedandtheobservedfunctions,
whichwasminimizedintheparameterspacetoiterativelyobtainthe
TSD TSRT parametersfortheratedistributionoftheSTOPprocess(byusingthe
“fmincon” optimization routine in MATLAB). We repeated this
procedure50–75times,withdifferentsetsofinitialparametervalues,
2σ toensureconvergencetotheglobalminima.
MAXIMUM LIKELIHOOD METHOD. We also performed parameter
estimation using a maximum likelihood approach as described by
previous studies (Corneil and Elsley 2005; Kornylo et al. 2003;
n Walton and Gandhi 2006). To estimate the parameters that defined
vatio rGO rdGisOtr,ibwuteioinn.itTiahlleymcoemanpuanteddSthDeoinfvtehreseraotefsthoef tnhoe-sGteOp rperaoccteiossnwtimeree
Acti rrSTOP directly obtained running the “mle” command in MATLAB on this
inversedistribution.TheGOdistributionforsteptrialswasgenerated
usingtheabove-citedparameters.Initialvaluesfortheparametersof
rSTOPwerechosenarbitrarilyandaSTOPreactiontimedistribution
wasgenerated.ForagivenTSD,thepointofintersectionoftheGO
0IT FT150 300 450 and STOP distributions provided an estimate of the frequency of
erroneous trials (Corneil and Elsley 2005; Kornylo et al. 2003). We
TTiimmee ((mmss))
used this frequency to compute the likelihood of observing a partic- D
FIG.3. Schematicoftheracemodelrepresentingthestochasticnatureof ular number of erroneous trials based on the binomial probability ow
the GO and STOP processes. As shown in Fig. 2, the GO and the STOP distribution. Taking the negative logarithm of each likelihood value n
processes are initiated by the presentation of the initial target (IT) and final andsummingthesevaluesacrossTSDsdefinedacostfunction.This loa
target(FT),respectively,followingavisualdelayof60ms.Theratesofthe cost function was then minimized using the Nelder–Mead simplex de
GO (rGO) and STOP (rSTOP) processes that vary from trial to trial can be d
describedbyaGaussianratedistribution.The2processesrisetothethreshold mobettahiondt(hbeyupsainragmtheete“rfsmfinosreatrhceh”SoTpOtimPizraatitoendroisuttriinbeuitnioMnAthTaLtAcBo)utlod fro
(brokenhorizontalline)togiverisetotheno-stepreactiontimedistribution m
(grayhistogram)andSTOPdistribution(whitehistogram).Themethodusedto generate the best-fit compensation function. We repeated this proce- jn
calculate the latency of the slowest erroneous response based on the race dure 50–75 times, with different sets of initial parameter values, .p
model:thefinishtimeoftheslowestSTOPprocess,consideredtobeslower before choosing the best set of parameters. This was done again to hy
thanthemeanSTOPrateby2(cid:5),isdenotedbySTOP2(cid:5)andcorrespondstothe ensureconvergencetotheglobalminima. sio
endoftheSTOPreactiontimedistribution.Almostall((cid:2)97.5%)steptrials lo
gshivoeunldbybethseuscucmessoffutlhlyeiTnShDib,ittehdettaorgtheetslteefptroefacStTioOnPt2im(cid:5).eT(hTiSsRmTa)kaensdStTheOtPim2(cid:5)e, Testing the validity of the race model gy.o
equivalent to 2SDs of rSTOP, the cutoff for the latency of the slowest rg
erroneousresponse. The race model assumes that the GO and STOP processes are o
n
stochastically independent (Logan 1994)—i.e., the underlying GO N
taken as unity. Starting 60 ms after the appearance of the target, processisnotalteredbythepresenceoftheSTOPprocessinthestep o
v
correspondingtothelatencyofvisualcellresponseinthevisuomotor trials.Ifthisassumptionholds,thenforagivenTSD,thefinishtimes e
m
system (e.g., Goldberg and Wurtz 1972; Thompson et al. 1997), the oftheSTOPprocesspartitionstheno-stepreactiontimedistribution b
e
GOprocessactivationincreasedattherateofrGOeverymillisecond. suchthatonlythosesaccadesthathaveshorterlatenciesthanthesum r 3
The saccade was assumed to be executed when this process reached of the TSD and the average latency of the STOP process (TSRT), , 2
thethreshold(i.e.,at1/rGOmsafterthevisualdelay).Toestimatethe escapeinhibition(seeFig.2C).Testingthevalidityoftheracemodel 0
1
parameters(meanandSD)ofthisGaussiandistribution,wesimulated hasbeentraditionallyperformedusingthemeanlatencyoftheSTOP 0

about 2,000 no-step trials. We used the Kolmogorov–Smirnov (KS) process.However,giventhattheprocessesinvolvedarestochasticwe
statistic to compare the simulated cumulative no-step reaction time therefore included the variances for a stringent and conservative
distributionwiththeobservedone.TheKSstatisticservedasanindex methodthatwasprimarilyaimedatestablishingviolationsoftherace
of the error that was minimized in the parameter space using a model.Forthisitwasimportanttoshowthatthetimingoferroneous
nonlinear minimization procedure running in MATLAB. Conver- saccadescouldnotbeaccountedforbythesubsetofeventheslowest
gencewasdecidedbasedonparametervaluesthatminimizedtheKS STOPprocesses.InpracticethiswastestedbySTOP (seeFig.3),
2(cid:5)
statistic between the simulated and observed data. We repeated this whichisthelatencyoftheSTOPprocessthatisslowerthanthemean
procedure50–75times,withdifferentsetsofinitialparametervalues, STOPrateby2(cid:5).Since2(cid:5)accountsfor97.5%(leavingtheuppertail
whichwasdonetoensureconvergencetotheglobalminima,before of 2.5%) of the STOP distribution, we intuitively expected a 2–3%
choosingthebestsetofparameters. violationbyusingthiscriterion.However,itisimportanttonotethat
On step trials, following the appearance of the final target and a becauseofthestatisticsofsampling,thispercentageviolationrepre-
visual latency of 60 ms, a STOP process with rate of accumulation sentstheaverageexpectedviolation.Sincethepurposeoftheanalysis
rSTOPHz(chosenarbitrarilyfromaGaussiandistributionwithmean was aimed at testing the limits of the race model, it is important to
(cid:4) and SD (cid:5) ) began. Since this defines the slope of the STOP establish the upper bound of the expected violation. This number is
stop stop
process(seeFig.2,AandB)thelatencyoftheSTOPprocesswould given by Chebyshev’s theorem, which states that at most 1/k2 pro-
be1/rSTOPmsplusthevisualdelay.IftheSTOPprocessreachedthe portionoftrialscanoccurintherange(cid:4)(cid:1)k(cid:5).Thereforewhenk(cid:5)
thresholdvaluebeforetheGOprocess,thenthesaccadewassuccess- 2 we get 0.25. However, since this includes both tails of the distri-
fully inhibited. On the other hand, if the GO process reached the bution,thishastobehalvedifjusttheuppertailisconsidered.Thus
threshold before the STOP process, then the saccade was taken to values of violation (cid:2)12.5% would invalidate the race model. In
have escaped inhibition and the time of reaching the threshold was practiceatrialwasdeclaredaviolationifitslatencyexceededthesum
takenasthesimulatedlatencyoftheerroneoussaccade.Bydetermin- of the TSD, the target step reaction time, and the time equivalent to
ing the probability of erroneous saccades as a function of TSD, we 2SDsoftherateoftheSTOPprocessbyatleast15ms,thelatterbeing
plottedthesimulatedcompensationfunctionsalongwiththesubjects’ theresolutionoftheTSDbinsize.
JNeurophysiol•VOL103•MAY2010•www.jn.org
VOLUNTARY CONTROL OF MULTISACCADE GAZE SHIFTS 2405
Idealizing compensation functions subjects were asked to cancel the partially planned saccade to
thefirsttargetanddirecttheirgazetothesecondtarget.Instep
In practice, compensation functions seldom spanned the entire
trials, subjects sometimes compensated for the target step—
psychometric range (from 0 to 1). This means that at shorter TSDs
i.e., inhibited the initial saccade and directed gaze toward the
subjectssometimesfailedtocompensatewhentheyshouldhaveand,
at longer TSDs, they managed to compensate unexpectedly. Such final target (see Fig. 1B1: successful response). However, at
behaviorcansystematicallyaffectthecompensationfunctionandlead othertimes,theyfailedtoinhibitthesaccadetowardtheinitial
tobiasedparameterestimates.Wethereforecorrectedforthisbiasby target—i.e., their response was not successfully inhibited (see
making certain assumptions about the subject’s strategy. If (cid:6)(the Fig. 1B2: erroneous response). On reaching the initial target,
lower asymptote to the Weibull fit of the compensation function) is however, they made a subsequent corrective saccade toward
theproportionoftrialsasubjectfailedtoinhibitattheshortestTSD, the final target.
weconsidered(cid:6)tobetheproportionoftrialswhensubjectsignored
Thetargetsappearedat30°eccentricities.Subjectsattempting
the final target. In simulations, these trials can be incorporated by tofoveateoftenmade(onaverageacrosssubjects11.5(cid:4)2SE%)
withholdingtheSTOPprocess.Similarly,if(cid:7)(theupperasymptoteto
a set of two saccades instead of a single saccade: the primary
theWeibullfitofthecompensationfunction)isthemaximumvalueof
the compensation function, we considered (1 (cid:7) (cid:7)) to be the proportion saccade followed by a secondary saccade (see Fig. 1A2, hypo-
of trials when the subjects ignored the initial target. In simulations, metricresponseinano-steptrial).Weembeddedthisbehaviorin
thesetrialscanbeincorporatedbynotinitiatingtheGOprocess.An thecontextoftheredirecttasktoassessinhibitorycontrolduring
equivalent approach that yields the same outcome is to treat the multisaccade gaze shifts, where control can manifest at multiple
subjects’performanceintheremainingfractionoftrials((cid:7)(cid:7)(cid:6))tobe levels: either before the saccades began, during the saccade, or
ideal.Werescaledsubjects’compensationfunctionsbetween0and evenduringtheintersaccadicinterval.
1 to reflect the ideal compensation function, which was used to D
obtainbiasfreeparameterestimates.However,wealsocarriedout Performance of subjects ow
analyses without rescaling. Although this changed the parameter n
lo
values of the STOP and the GO processes and the estimated In the redirect task, the TSD was varied across trials. a
d
fraction of violations, the percentage of secondary saccades vio- Although subjects typically find it easier to inhibit at shorter ed
lnaetoinugstfihrestcsuatcocffadweass. Tnhevuesrtthheelebsassivcerreysuhlitgshd,icdomnoptacrehdanwgiethdueerroto- TSDs, they find it harder to do the same at longer TSDs, fro
presumably because they are more committed to the initial m
rescaling. response.Weplottedtheprobabilityofmakingasaccadetothe jn
.p
initial target in step trials as a function of increasing TSDs. h
RESULTS y
Onlytrialsinwhichresponseswerenonhypometricwereused s
io
We used the redirect task to understand how inhibitory for this analysis. Figure 4 shows the performance curves, lo
g
control is exerted to achieve goal directed movements. In this referred to as compensation functions (Becker and Jurgens y
.o
task, subjects were instructed to make a saccadic eye move- 1979;Camalieretal.2007),ofninetypicalsubjectsinthetask. rg
menttotheinitialtargetassoonasitappeared(no-steptrials). Superimposed are the best-fit cumulative Weibull function o
n
However,ifasecondtargetsubsequentlyappeared(steptrials), fitted to quantify performance N
o
v
e
1 1 1 m
b
e
AR JA r 3
0.5 BS 0.5 0.5 , 2
0
1
0

0 0 0
0 100 200 300 0 1000 200 300 0 100 200 300
1 1 1 FIG.4. Compensationfunctions.Plotshow-
ingtheprobabilityofmakingasaccadetothe
NC
AS JG first target as a function of TSDs calculated
or takingintoaccountthespatiallocationofthe
err 0.5 0.5 0.5 targetsandseparatedintobinsizesof(cid:4)the
of refreshrateofthemonitor(14.3ms).Datafor
y 9 representative subjects, superimposed by a
abilit 0 0 100 200 300 0 0 1000 200 300 0 0 100 200 300 tbaeislst-)fi,tshWoweibthualltftuhnecptiroonba(bseileityREoSfUmLTaSkifnogrdthee-
b
o erroneousfirstsaccadeincreaseswithincreas-
Pr 1 1 1 ingTSDs.
VI
0.5 SY 0.5 0.5 VJ
0 0 0
0 100 200 300 0 100 200 300 0 100 200 300
Target step delay (ms))
JNeurophysiol•VOL103•MAY2010•www.jn.org
2406 A. RAMAKRISHNAN, S. CHOKHANDRE, AND A. MURTHY
W(cid:11)t(cid:12)(cid:2)(cid:8)(cid:3)(cid:11)(cid:8)(cid:3)(cid:9)(cid:12)e(cid:10)(cid:3)(cid:11)t/(cid:6)(cid:12)(cid:7)(cid:13) TABLE 1. Parameter estimation based on the Monte Carlo method
wheretistheTSD,(cid:6)isthetimeatwhichthefunctionreaches Nonhypometric Hypometric STOP
64%ofitsfullgrowth,(cid:7)istheslope,(cid:8)isthemaximumvalue
of the function, and (cid:9)is the minimum value of the function. Subject GO((cid:4)) GO((cid:5)) GO((cid:4)) GO((cid:5)) STOP((cid:4)) STOP((cid:5))
Giventhenatureofthetask,(cid:8)(cid:7)(cid:9)canbeusedasanindexto
AS 5.1 2.0 7.8 2.7 16.00 0.80
assesshowthesubjectsperformed.Inalloursessions((cid:8)(cid:7)(cid:9)) BS 7.8 2.9 7.9 2.2 35.00 4.50
was (cid:2)0.5. NC 5.8 3.1 9.1 1.4 80.00 0.10
JA 7.2 3.3 8.8 1.6 48.30 7.00
CM 6.7 2.7 6.0 2.8 80.00 20.00
Race model analysis: quantifying the ability to inhibit LL 5.9 2.1 6.7 2.4 9.60 0.50
VK 7.9 2.7 10.0 3.0 29.60 0.10
We obtained the parameters of the rates of the GO process AR 5.1 1.5 6.0 3.0 25.60 7.90
DC 6.2 1.8 6.9 1.8 25.17 8.70
bysimulatingthecumulativeno-stepreactiontimedistribution
SY 7.4 2.5 8.3 1.9 28.04 0.31
using the Monte Carlo method as well as the maximum
JG 5.4 2.0 7.0 3.2 22.70 3.00
likelihoodbasedmethod(seeMETHODS).Thesimulatedandthe VI 5.6 2.0 7.2 1.4 30.00 8.70
observedcumulativeno-stepreactiontimesfortheninetypical VJ 6.3 2.1 7.5 1.8 18.60 0.60
subjects are shown in Fig. 5. The goodness-of-fit was ascer- PA 6.9 2.3 6.5 2.0 27.70 7.50
tainedbycomputingthecorrelationcoefficient(r2),whichwas TS 5.7 1.8 5.1 1.2 16.60 2.15
on average 0.98 (max (cid:5) 0.99; min (cid:5) 0.95). The r2 value was Valuesaremeans((cid:4))andSD((cid:5))forthenonhypometricGOprocess,the
used to decide the better of the estimates from the two meth- hypometricGOprocess,andtheSTOPprocessforeachsubject. D
o
ods, which was then used for all further analyses. Columns 1 w
and2ofTable1andTable2listtheparameters(meanandSD) ficient (r2), which was on average 0.89 (cid:4) 0.02 (max (cid:5) 0.95; nlo
obtained using the Monte Carlo approach and the maximum min(cid:5)0.65).Wealsoperformedthesameprocedureusingthe ad
e
likelihood based approach, respectively. maximum likelihood based procedure, which also yielded d
Step trials were simulated on the basis of the race model similar results (see Table 2, column under STOP). The good- fro
described in Fig. 2. The parameters of the GO process that ness-of-fit was on average 0.88 (cid:4) 0.02 (max (cid:5) 0.95; min (cid:5) jnm
were obtained as mentioned earlier were used to estimate the 0.64). .p
parametersoftheSTOPprocessusingtheMonteCarlomethod WeusedtheparametersoftherateofSTOPprocesstofind hy
s
(see Table 1, column under STOP), which were then used to an estimate of the latency to STOP or the target step reaction io
simulate the compensation functions (see Fig. 6). The good- time(TSRT;seeMETHODS)bycomputingthetimetakenbythe log
ness-of-fit was ascertained by computing the correlation coef- mean of the rate distribution of the STOP process ((cid:4)stop) to y.o
rg
Observed Predicted on
N
o
1 1 1 ve
m
b
e
0.5 AR 0.5 AS 0.5 r 3
BS , 2
0
1
0 0 0 0
0 200 400 600 0 2200 400 600 0 200 400 600
FIG.5. Comparisonoftheobservedand
simulated cumulative no-step reaction time
1 1 1 distributions.Parameterestimates(meanand
SD)fortheGOprocesswereobtainedfrom
boththeMonteCarlomethodandthemax-
als 0.5 JA 0.5 SY 0.5 VI iomfutmheleiksetilmihaotoeds bfraosmedtmheet2homd.etThhoedsbe(tsteeer
tri RESULTSfordetails)wasusedtosimulatethe
ofo 0 0 0 cumulative no-step reaction time distribu-
on 0 200 400 600 0 2200 400 600 0 200 400 600 tion (black) and, when compared with the
rti observed distribution (light gray), shows
po goodcorrelation.Data(binnedevery25ms)
o areshownforthe9representativesubjects.
Pr 1 1 1
0.5 JG 0.5 VJ 0.5 NC
0 0 0
0 200 400 600 0 2200 400 600 0 200 400 600
Time (ms)
JNeurophysiol•VOL103•MAY2010•www.jn.org
VOLUNTARY CONTROL OF MULTISACCADE GAZE SHIFTS 2407
TABLE 2. Parameter estimation based on the maximum s 200
m
likelihoodmethod
n
i
Nonhypometric Hypometric STOP n)
o
Subject GO((cid:4)) GO((cid:5)) GO((cid:4)) GO((cid:5)) STOP((cid:4)) STOP((cid:5)) ati 100
ul
AS 5.5 2.2 7.8 2.7 21.00 5.60 m
BS 8.1 3.1 7.9 2.2 45.20 13.50 si
NC 6.8 3.6 9.1 1.4 80.00 1.60 (
T
JA 7.3 3.1 8.8 1.6 64.00 3.20 R
CM 7.0 3.1 6.0 2.8 76.00 8.60 S 0
LL 6.1 2.2 6.7 2.4 11.90 1.00 T 0 100 200
VK 8.3 3.2 10.0 3.0 34.20 1.00
AR 5.7 4.0 6.0 3.0 19.20 2.20 TTSSRRTT ((ccoonnvveennttiioonnaall)) iinn mmss
DC 6.4 2.4 6.9 1.8 21.50 1.00
SY 7.6 2.6 8.3 1.9 80.00 0.10 FIG.7. ComparisonofTSRTobtainedbyconventionalmethodsvs.TSRT
JG 5.8 2.9 7.0 3.2 30.00 6.70 obtainedbysimulatingtheracemodel.Eachcirclerepresentsdatumfrom
VI 6.1 2.1 7.2 1.4 18.10 1.70 one subject. The broken line represents the fit derived from a linear
VJ 6.7 3.7 7.5 1.8 19.45 1.60 regressionofthedata.ThesimulatedandtheobservedTSRTsarestrongly
PA 7.8 5.3 6.5 2.0 29.08 1.33 correlated, indicating that simulation provides a good description of the
TS 5.8 2.5 5.1 1.2 17.40 1.30 behavioraldata.
D
Valuesaremeans((cid:4))andSD((cid:5))forthenonhypometricGOprocess,the We next tested the validity of the race model for all the o
hypometricGOprocess,andtheSTOPprocessforeachsubject. w
subjects by checking the percentage of erroneous saccades n
reachthethreshold(i.e.,1/(cid:4)stopmsafterthevisualdelay).The whosereactiontimesviolatedtheSTOP2(cid:5)cutoff.Thepercent- load
average TSRT across subjects calculated in this fashion age of violation for every subject is tabulated in column 1 of e
d
((110071.2(cid:4)(cid:4)5m5s.)9thmats)wawsadsercivoemdpbayracbolenvteonttihoenalTmSRetThoedsstiumsiantge Tbyabthlee3MaonndteTCabalrelo4mfoerthtohdeapnedrctehnetamgaexoifmvuimolalitkioenlishcoaoldcublaasteedd from
theracemodel(describedearlierinRacemodelandestimation method,respectively.Thepercentageoftrialsthatviolatedthe jn
of target step reaction time in METHODS). In addition, the two cutoff was on average 10.29% (min (cid:5) 3.1%; max (cid:5) 17.4%). .ph
TSRTestimateswerestronglycorrelated[Pearson’sr(cid:5)0.86, Eleven of 15 subjects are within the prescribed cutoff demar- ys
P(cid:5)0.000036]withthemeanslopeoftheregressionlineclose catedbytheSTOP2(cid:5)criterion.However,thesepercentagesare iolo
to unity (slope (cid:5) 0.94; intercept (cid:5) 0.083), indicating that our an average across TSDs. To get a better picture we separated gy
simulated parameters provided a good description of the be- these trials that violated the cutoff into three different groups .o
rg
havioral data (see Fig. 7). based on the TSDs. On closer inspection, the percentage of o
n
Observed Predicted N
o
v
e
m
1 1 1 be
r 3
AR JA , 2
0.5 BS 0.5 0.5 01
0

0 0 0
0 100 200 300 0 100 200 300 0 100 200 300
FIG.6. Comparison between simulated
and observed compensation functions. Ob-
1 1 1
served compensation functions (solid gray
NC circles) are best fit with Weibull functions
AS JG
(adaptedfromFig.4).Simulatedcompensa-
0.5 0.5 0.5 tion functions (solid black triangles) gener-
or ated for the 9 representative subjects using
rree the parameters obtained based on Monte
of 0 0 0 Carlosimulation(seeMonteCarlomethodin
y 0 100 200 300 0 1000 200 300 0 100 200 300 METHODS) show good correlation with the
bilit observeddata.
a 1 1 1
b
o
Pr
VI
0.5 SY 0.5 0.5 VJ
0 0 0
0 100 200 300 0 100 200 300 0 100 200 300
Target step delay (mms)
JNeurophysiol•VOL103•MAY2010•www.jn.org
2408 A. RAMAKRISHNAN, S. CHOKHANDRE, AND A. MURTHY
TABLE 3. Percentage of violation from the Monte Carlo method We were interested to assess the ability to inhibit the
multisaccade gaze shift at the level of the secondary saccade.
FractionofViolation Wereasonedthatthesecondarysaccade,whichwaserroneous
inthegivencontext,shouldbeinhibitedbytheSTOPprocess
FirstSaccade
and be superseded by a corrective saccade to the final target,
Subject Nonhypometric Hypometric SecondarySaccade resultinginahypometriccorrection.Althoughwedonotknow
whenthesecondarysaccadepreparationstarts,theextentofits
AS 5.7377 4.6729 70.0000
inhibitionisstillexpectedtoconformtotheparametersofthe
BS 6.2147 4.1667 100.0000
NC 12.0141 19.4828 94.4444 STOP process. Assuming the same parameters of the STOP
JA 9.8404 23.8288 97.3684 process,asintheearliercase,wedeterminedthepercentageof
CM 11.8590 19.3284 100.0000
secondarysaccadesthatoccurredbeyondthelatencypredicted
LL 8.9286 16.6667 91.6667
VK 5.6673 21.5152 83.3333 by STOP2(cid:5) and found it to consist of a large proportion
AR 15.5280 10.3704 60.4651 (average (cid:5) 78.29%; min (cid:5) 31.74%; max (cid:5) 100%) for every
DC 3.0516 3.4483 42.8571 subject examined (see column 3 of Tables 3 and 4 for results
SY 13.5897 20.1046 68.5714
using the Monte Carlo method and the maximum likelihood
JG 17.4174 17.6415 94.4444
based method, respectively). At all TSDs every subject vio-
VI 7.3620 5.8824 31.7460
VJ 16.7188 10.2041 70.5882 latedthecutoffatearly(20,50,and80ms;min(cid:5)87%;max(cid:5)
PA 8.7395 10.7692 80.0000 100%; mean (cid:5) 99%; 15/15 subjects violated the cutoff),
TS 11.7794 7.1429 88.8889 intermediate (110 and 140 ms; min (cid:5) 50%; max (cid:5) 100%;
D
mean (cid:5) 84%; 15/15 subjects violated the cutoff), and late o
Percentageofviolationforfirstsaccadesofnonhypometrictrials,hypomet- w
rictrials,andthesecondarysaccadesofhypometricerrors. ((cid:2)170 ms; min (cid:5) 0%; max (cid:5) 100%; mean (cid:5) 53%; 14/15 nlo
subjects violated the cutoff) TSDs. In contrast to the first a
violations were higher for the shorter TSDs (20, 50, and 80 d
saccades, a large percentage of secondary saccades (78%) e
ms; min (cid:5) 19%; max (cid:5) 70%; mean (cid:5) 42%; 15/15 subjects d
violated the cutoff). However, for the majority of erroneous violatedthecutoffthatcouldnotbeaccountedforbytheupper fro
tnroiaslsigtnhiafitcoacnctuvriroeldataiotnin(taetrm11e0diaanteda1n4d0lmons;gmerinTS(cid:5)D0s%th;emreaxwa(cid:5)s mcbaoodudenesdlofefasihtlaeybdploitsmoheeatdcriccboyuenrrttohfreos.rStThOePti2m(cid:5)incgritoefriothne. sTehcuosndtahrey rsaacce- jn.pm
t1mh2es%;mc;uimtnoe(cid:5)fafn).0(cid:5)%T;h5me%sae;xnr(cid:5)eos2us%ultbs;jemvcaetslaindvai(cid:5)toela0tt.e9hd%e t;rhanecoecsuumtbojofefdceatslnvdfioo(cid:2)rla1tt7eh0de quNanetxifit,edtotheunladteernsctaiensdofthtehemsaacgcnaidtuedsethoaftvtihoilsatevdiotlhaetiocnutowffe. hysiolo
Theextentofviolationoferroneousfirstsaccadesthatviolated g
erroneous first saccade of a nonhypometric response. thecutoffwas51ms(min(cid:5)20ms;max(cid:5)87ms).Likewise, y.o
rg
Inhibitory control during a hypometric response tvhieolaetxetdenthteocfutvoifoflawtiaosn3o8fmesrr(omnienou(cid:5)s 1p2rimmasr;ymsaaxcc(cid:5)ad5e2smthsa)t. on
N
PRIMARY SACCADE. Analogous to the earlier analysis, we Incontrast,thesecondarysaccadereactiontimesoccurredwell ov
testedthevalidityoftheracemodelforprimarysaccadesofthe beyond the cutoff time. The extent of violation of the second- em
hypometric response. The percentage of violation for every arysaccadesthatviolatedthecutoffwas114ms(min(cid:5)73ms; b
subject is tabulated in column 2 of Tables 3 and 4. The max (cid:5) 157 ms). To compare and contrast the extent of er 3
percentage of trials that violated the cutoff was on average , 2
13.0% (min (cid:5) 3.4%; max (cid:5) 23.8%). Eight of 15 subjects are TABLE 4. Percentage of violation from the maximum 01
within the prescribed cutoff demarcated by the STOP2(cid:5)crite- likelihood–basedmethod 0
rion. Again, on closer inspection the percentage of violations
was higher for the shorter TSDs (20, 50, and 80 ms; min (cid:5) FractionofViolation
12%; max (cid:5) 67%; mean (cid:5) 34%; 15/15 subjects violated the
FirstSaccade
cutoff). However, for the majority of erroneous trials that
occurredatintermediateandlongerTSDstherewaslittleorno Subject Nonhypometric Hypometric SecondarySaccade
significant violation (at 110 and 140 ms; min (cid:5) 0%; max (cid:5)
14%; mean (cid:5) 5%; 1/15 subjects violated the cutoff and for AS 3.2787 0.0000 70.0000
BS 3.9548 2.0833 100.0000
(cid:2)170 ms; min (cid:5) 0%; max (cid:5) 9%; mean (cid:5) 1%; no subjects NC 12.0141 16.0345 94.4444
violatedthecutoff).Theseresultsvalidatethegeneralapplica- JA 12.2340 17.4324 97.3684
bility of the race model for the primary saccade of the hypo- CM 14.4231 23.8060 100.0000
LL 11.7347 16.6667 91.6667
metric response.
VK 6.2157 23.0303 83.3333
SECONDARY SACCADE. On step trials, when subjects made an AR 19.8758 20.0000 65.1163
initialhypometricsaccadetowardthefirsttarget,twointerest- DC 9.3897 19.1379 71.4286
SY 18.5897 22.6569 81.4286
ing behavioral patterns resulted. Although on some trials they
JG 17.4174 17.6415 94.4444
managed to correct midway following the initial erroneous VI 8.3845 8.3333 34.9206
saccade(referredtoasahypometriccorrection;seeFig.1B3), VJ 16.2500 10.2041 64.7059
on others, they failed to do so and instead made a secondary PA 12.7731 24.2308 92.0000
TS 12.7820 7.1429 100.0000
saccade to the initial target, foveating the final target only in
the subsequent saccade (referred to as hypometric errors; see
Percentageofviolationforfirstsaccadesofnonhypometrictrials,hypomet-
Fig. 1B4). rictrials,andthesecondarysaccadesofhypometricerrors.
JNeurophysiol•VOL103•MAY2010•www.jn.org