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From: Arjun Ramakrishnan and Aditya Murthy, Brain mechanisms controlling decision making and motor planning. In V.S. Chandrasekhar Pammi and

Narayanan Srinivasan, editors: Progress in Brain Research, Vol. 202, Amsterdam: The Netherlands, 2013, pp. 321-345.

ISBN: 978-0-444-62604-2 © Copyright 2013 Elsevier B.V.

Elsevier

Author's personal copy

CHAPTER

7
Brain mechanismscontrolling decision makingand motor planning
1
Arjun Ramakrishnan*, Aditya Murthy{,1
⁎National Brain Research Centre, Nainwal Mode, Manesar, Haryana, India{Centre for Neuroscience, Indian Institute of Science, Bangalore, Karnataka, India

1Corresponding author. Tel.: þ91-80-22933433, Fax: þ91-80-23603323,

e-mail address: [email protected]

AbstractAccumulator models of decision making provide a unified framework to understand decision

making and motor planning. In these models, the evolution of a decision is reflected in the

accumulation of sensory information into a motor plan that reaches a threshold, leading to

choice behavior. While these models provide an elegant framework to understand perfor-

mance and reaction times, their ability to explain complex behaviors such as decision making

and motor control of sequential movements in dynamic environments is unclear. To examine

and probe the limits of online modification of decision making and motor planning, an ocu-

lomotor “redirect” task was used. Here, subjects were expected to change their eye movement

plan when a new saccade target appeared. Based on task performance, saccade reaction time

distributions, computational models of behavior, and intracortical microstimulation of

monkey frontal eye fields, we show how accumulator models can be tested and extended

to study dynamic aspects of decision making and motor control.

Keywordssaccade, plan change, redirect, double step, countermanding, oculomotor

1 INTRODUCTIONAn issue of central interest to cognitive neuroscience is to understand how sensory

information is transformed into a motor response. Even the simple act of making a

saccadic eye movement to a stimulus, which should take around 60–150 ms (Schall

et al., 1995)—considering the sum of transduction delays and neural transmission

times alone (Donders, 1868; Luce, 1986; Posner, 1978)—is much longer and

variable, ranging from 100 to 500 ms. This implies that a significant component

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322 CHAPTER 17 Brain mechanisms controlling decision making


of the reaction time (RT) may be required for decision making that entails determin-

ing where and when to shift the eyes. Since the time of Yarbus (1967), it has been

known that eye movements are modulated by a host of factors, such as the nature of

the scene being viewed, as well as the viewer’s mindset.

For example, when volunteers were asked to view a picture, saccadic eye move-

ments were not directed to arbitrary locations but to salient, feature-rich locations,

suggesting that saccades were modulated by bottom-up saliency (Cave and

Wolfe, 1990; Itti and Koch, 2001; Koch and Ullman, 1985; Olshausen et al.,

1993; Treisman, 1988; Wolfe, 1994; Yarbus, 1967). This notwithstanding, when

the volunteers were instructed to pay attention to some aspect of the picture, say,

the clothes of the people in the picture, the pattern of eye movements changed to

dwell more on the clothing, suggesting that saccades were modulated in a top-down

manner by the goal of the task.

It is also known that cognitive factors can modulate RTs (Posner, 1978). Saccadic

RTs, for example, reduce when a cue is presented signaling the appearance of a

saccade-target (Niemi and Naatanen, 1981). The appearance of the target more fre-

quently in a particular location, as compared to another, also reduces the RT to make

a saccade to the chosen location (e.g., Bichot and Schall, 2002; Dorris et al., 1999). RTs

are longer when subjects are asked to be more accurate. In contrast, RTs are shorter

when the subjects are asked to speed up their response, which, however, results in

more errors (Chittka et al., 2009; Schouten and Bekker, 1967; Wickelgren, 1977).

These observations point to a framework in which saccadic decision making and

response preparation may be envisioned as a signal that represents the likelihood of

the response, which accumulates to reach a threshold, at which point the saccade is

triggered. In this framework, the warning signal and repetitive appearance of a target

at a particular location serve to increase the likelihood of a response, thus decreasing

the RT, whereas the trade-off that is observed between speed and accuracy may be

explained by a shift in the threshold for responding (Reddi and Carpenter, 2000). Thus,

taken together, the study of saccadic eye movements affords a simple but effective

model to study how our brains make decisions leading to actions.

Using saccadic eye movements as a model system, in the first part of the review,

we present evidence from recent neurophysiological studies that have provided a

neural basis for accumulator models. We then present evidence from our work show-

ing that electrical microstimulation can be used in a causal manner to test the

involvement of brain areas implicated in saccade planning, as predicted by the

accumulator model, and in turn validating the model. The next part of the review

focuses on the ability to adapt decisions to suit the dynamic environment, a hallmark

of executive control. To test the ability to rapidly modify saccadic eye movement

plans, we used a paradigm called the “redirect task.” In this section, we present

results from our work where we have examined the saccade planning stage, the

execution stage, and finally sequences of saccades to determine whether they can

be modified in the context of the redirect task. Further, we have also estimated

the time taken to modify the plan/action at these various stages. Finally, we present

the results from a recent microstimulation experiment performed in monkeys where

the changing saccade plan was tracked in real time.

3232 Evidence for accumulator models


2 EVIDENCE FOR ACCUMULATOR MODELS2.1 RTs and the LATER modelA particularly simplistic model that accounts for saccadic RTs is the LATER (Linear

Approach to Threshold with Ergodic Rates) model developed by Carpenter (1981).

According to this model (Fig. 1A), RT is a result of a decision signal—representing the

accumulation of information that starts at a baseline and then rises at a constant rate “r”until it reaches a threshold value, at which time a saccade is triggered. “r” varies

randomly from trial to trial according to a Gaussian distribution, which accounts

for the variability in RTs across trials. The LATER model has only two variables,

the distance and slope, whereas the baseline and threshold are considered fixed within

a block of trials in the experiment. Increase in neuronal firing rate, in a LATER-like

accumulation-to-threshold fashion, was initially observed in neurons in the primary

motor and premotor cortical areas, prior to a wrist movement response (Riehle and

Requin, 1993). LATER-like buildup in firing rate was observed prior to saccadic

eye movements as well as in the superior colliculus (SC) and the frontal eye fields

(FEF; Fig. 1B) in a subset of neurons (Figs. 2 and 3; Dorris et al., 1999; Hanes and

Schall, 1996; Munoz and Schall, 2004).

2.2 Neural evidence for accumulation-to-thresholdHanes and Schall (1996) provided the first clear evidence from single cells in the

FEF, referred to as movement neurons, showing an increasing neuronal activity

during the RT indicative of accumulation-to-threshold, which was subsequently

verified by Brown et al. (2008). The saccade was triggered when the discharge rate

of the movement neuron reached a threshold, which was unique for the neuron, and

did not vary with RT (Fig. 3). Furthermore, most of the variability in the RT was

accounted for by the variability in the rate of increase in the movement-related neu-

ronal activity to threshold. This finding is consistent with observations from pre-

saccadic neuronal activity in SC (Dorris et al., 1997) and lateralized readiness

potentials measured from primary motor areas prior to forelimb movements

(Gratton et al., 1988).

To determine whether the accumulating activity was necessary for the impending

saccade, Hanes and Schall (1996) randomly interleaved a few catch trials into

the simple saccade RT task, in which a signal was given to “stop” the saccade being

planned. If the accumulating neuronal activity was related to saccade preparation,

they reasoned that the activity of these cells would not reach the threshold on trials

in which the monkey withheld the saccade successfully. Consistent with this predic-

tion, they observed that the activity of movement neurons did not rise to threshold in

trials in which the monkey successfully withheld the saccade, suggesting that the

accumulating activity of movement neurons is indeed necessary for saccade

generation.

LATER model

Stimulus

Response

Decision signal

0 100

Time (ms)

(A)

(B)

Midsaggital view

Cortex

Thalamus

Cerebellum

V1

PS

AS

CS

IPSMT

LuS

LaS

STS

Cerebellum

Brainstem

Spinal cord

IT

V1

V2

V4

LIP

SC

Ventral pathway

DorsalpathwayBasal ganglia

FEF

Midbrain

VV

H

Brainstem

Spinal cord

HPons

Optic nerve

LGN

SC

Dorsal view

200

r

300

BaselineA

ctiv

atio

n

Threshold

Reaction time

FIGURE 1

(A) LATER model. On presentation of a stimulus, the decision signal (in green) rises

linearly from the baseline at the rate r. On reaching the threshold, the saccade is initiated.

On different trials, r varies randomly about a mean according to a Gaussian distribution,

which gives rise to a right skewed reaction time distribution. (B) Schematic representation of

the visuo-saccadic circuitry in the monkey brain. In the midsagittal view, the visual signal

from the eye is shown going through the optic nerve (in yellow) to the lateral geniculate

nucleus (LGN) and then to the primary cortical visual area (V1). In the dorsal view, signal from

V1 is shown feeding into ventral pathway visual areas (orange arrows) and dorsal pathway

visual areas (green arrows). Signals from both the pathways reach LIP and FEF, which project

to the SC both directly and via the basal ganglia. FEF, LIP, and SC control saccade generation

(where and when to shift gaze) via a saccade generator circuitry (red and green patches) in

the midbrain and pons, seen in the midsagittal view. Excitatory burst neurons (red patches)

and inhibitory burst neurons (green patches) for horizontal (H) and vertical/torsional (V)

components of eyemovements are served by independent nuclei. Final motor commands are

carried to extraocular muscles via three cranial nerves (III, IV, VI), represented by red–green

lines. Patches with broken boundaries depict nuclei that are not at surface level. AS, arcuate

sulcus; PS, principle sulcus; CS, central sulcus; IPS, intraparietal sulcus; LaS, lateral sulcus;

STS, superior temporal; LuS, lunate sulcus.

Figure adapted with permission from Reddi et al. (2003).


FIGURE 2

Responses of a visuo-movement FEF neuron during a memory-guided delayed saccade task.

The sequence of events within this task is illustrated in the upper part of the panel. The

monkey foveates the fixation point (small white square) and a visual stimulus (red square) is

transiently displayed shortly thereafter (gray band depicts how long the stimulus is on) in the

RF of the cell (area on screen demarcated by white arc) being recorded from. The monkey

continues to hold his gaze on the fixation point for a variable delay period (hold time). After

the fixation point disappears, the monkey has to execute a saccade (white arrow) to the

remembered location of the visual target to earn a juice reward. The lower part of the panel

depicts the recorded neuronal response, aligned to stimulus onset time (left) and saccade

onset (right). The gray band at saccade onset indicates the average saccade duration. Each

row in the panel corresponds to a trial and the ticks mark the presence of a neuronal spike.

The histogram of the neuronal firing rate is depicted by the thick black line. The small red

triangles depict the termination of the hold time period with respect to the saccade onset.

This neuron responds to the visual stimulus prior to the saccadic eye movement.



2.3 Accumulation represents accrual of informationAlthough the variable rate of increase in neuronal activity accounts for the variability

in RTs, whether this accumulating activity represents accrual of sensory information

is not clear from simple RT tasks per se. To test this hypothesis, Roitman and

Shadlen (2002) trained monkeys to view a random-dot stimulus (Fig. 4; Britten

et al., 1992) in which a fraction of the dots moved coherently—either toward or away

from the response field (RF) of the neuron that was being recorded from. The fraction

Reaction time (ms)

Act

iva

tion

Sac

cade

RT

0 150

FEF movement cell activation

300

FIGURE 3

Evidence of accumulation-to-threshold. Following the appearance of the stimulus (at 0 ms),

the activity of FEF movement-related neuron rises (e.g., shown in blue) to a fixed threshold

firing rate (dashed horizontal line) at which point the saccade is initiated. Trial-to-trial

variability in the time of initiation of the saccade originates from the variable time taken for

the activity to reach threshold. To illustrate this, trials were subdivided into fast (green part of

the reaction time distribution histogram), medium (blue), and slow (yellow) reaction time

groups and the average buildup activity of the movement neuron for each of these groups is

shown in the corresponding color.

Figure modified with permission from Schall and Thompson (1999).



of coherently moving dots could be varied to vary the motion signal strength over

noise. Two peripheral targets were presented: one placed in the neuron’s RF and

the other in the diametrically opposite location. The monkey had to discriminate

the net direction of motion and indicate the decision bymaking a saccade to the target

presented in that direction.By recording fromsingle neurons in the lateral intraparietal

area (LIP), a progressive increase in firing ratewas observed following the appearance

of the stimulus, and the rate of increase in firing rate was modulated by the strength of

the motion signal. Furthermore, when the firing rate reached a threshold level of ac-

tivity, the saccade was initiated. In other words, when the motion strength was stron-

ger, these neurons showed a faster increase in neuronal activity, so the threshold was

attained sooner resulting in shorter RTs, whereas, when the motion strength was

weaker, the increase in the neuronal activity was slower, so the threshold was attained

later resulting in longer RTs. These observations are consistent with the notion that LIP

neurons accumulate sensory evidence up to a threshold following which the saccade

results. Similar results were obtained from other sensorimotor brain regions, like

the SC (Horwitz and Newsome, 2001) and the FEF (Kim and Shadlen, 1999) that

Time (ms)

Select T2

51.2

25.6

12.8

6.4

3.2

0

Select T1

(A)

(B)

Fixation

Targets

Motion

Time

SaccadeRT

RF

Motionstrength

Firi

ng r

ate

(sp

/s)

200 400 600 800 -800 -600 -400 -200 0020

25

30

35

40

45

50

55

60

65

70

FIGURE 4

Accumulation represents accrual of sensory evidence. (A) Motion direction discrimination

task. In this task, following a fixation period, two targets appear (black-filled circles), one in the

RF (gray patch) and the other opposite to it. Subsequently, the random-dot stimulus appears

at the center. The monkey has to indicate the direction of the moving dots by making a

saccade to one of the filled circles. RT, reaction time. (B) The response of LIP neurons when

the monkey is discriminating the direction of motion. The average firing rate of 54 neurons is

shown for six different motion strength conditions (in different colors). Left: the responses are

aligned to the onset of random-dot stimulus. Right: the responses are aligned to the saccade





are also involved in oculomotor control. Further, in order to causally test whether this

accumulating activity, seen in the LIP and the FEF, etc., determines choice or merely

reflects it, Gold and Shadlen (2000, 2003) administered microampere currents strong

enough to evoke a saccade reliably in the FEF, when the monkeys were discerning

motion direction. The arrangement of stimuli was changed such that the saccade

evoked by microstimulation was perpendicular to the choice saccades (Fig. 5A).

It is known from earlier studies that the direction of the electrically evoked saccade

is influenced by the eyemovement being planned (Sparks andMays, 1983). In other

words, if the monkey were to initiate an upward saccade to signal upward motion

(Saccade “2” in Fig. 5B), then the horizontal saccade evoked by the electrical stim-

ulation (Saccade “1” in Fig. 5B) would deviate away from the horizontal direction,

the RF at the site of stimulation, to land slightly upward (Saccade “3” in Fig. 5B). If

the accumulating activity is indicative of the evolving saccade plan, which is

reflected by the deviation of the saccade away from the RF, then the extent of devi-

ation should be modulated by factors that affect the state of the saccade plan like the

stimulus-viewingduration and the stimulusmotion strength.Consistentwith this hy-

pothesis, it was observed that the saccade deviation in fact increasedwith increase in

stimulus-viewing duration as well as motion strength, suggesting that the accumu-

lating activity represents accrual of information, on the basis of which the saccade

choice is made.

Ramakrishnan et al. (2012) verified the validity of the accumulator model in the

context of a simple RT task in which monkeys were trained to make a saccadic eye

movement to the stimulus that appeared on a computer monitor. The saccade target

was in the direction orthogonal to the stimulation-evoked saccade, like in the previ-

ously described experiment (Fig. 6A); however, stimulation pulses were adminis-

tered at various time points on different trials (at 30, 60, 90, 120, 150, or 180 ms

following target onset) to sample the RT period (200 ms on average). If the accumu-

lating activity is causally linked to response preparation, then the stimulation-evoked

saccade is expected to interact with the formative saccade at various stages of

response preparation. Thus, the direction of the resultant averaged saccade is

expected to change systematically. In other words, if the stimulation pulse was

administered early during saccade preparation, the resultant saccade is expected

to land close to the RF at the site of stimulation, whereas if the stimulation was

administered at a later stage of saccade preparation, the resultant saccade is expected

onset. Bold lines indicate the neuronal response when the saccade target is in the RF (T1),

and dashed lines indicate the neuronal response when the saccade target (red-filled circles)

is outside the RF (T2). It can be seen that the average firing rate of LIP neurons increases

following stimulus onset and reaches a threshold level of activation at which time the saccade

is initiated. More importantly, when the motion strength was increased, the firing rate

increased to threshold faster, suggesting that increase in firing rate, a form of accumulation,

may represent accrual of sensory evidence in favor of the saccade to the right direction.

Figure taken with permission from Roitman and Shadlen, (2002).

x position (°)

y po

sitio

n (°

)

Viewing duration (ms)

(A)

(B) (C)

Time

FixationMotion

Evokedsaccade

Voluntarysaccade

Dev

iatio

n (°

)

1000

0.5

1.0

1.5

300

0.0%

6.4%

25.6%

51.2%

500-5

-5

0

23

15

0 5 10

FIGURE 5

The evolving saccadic decision is seen in the oculomotor system. (A) Microstimulation-

interrupted direction discrimination task. In this task, the monkey has to decide the net

direction of motion like in the direction discrimination task (refer Fig. 4). However, while the

monkey is discriminating, a microstimulation pulse is administered to the FEF to evoke a

saccade in the orthogonal direction (rightward in this case). Following the evoked saccade, the

monkey initiates a voluntary saccade to the saccade target. (B) Eye movement trajectories.

When the monkey is stimulated while fixating at the center (0, 0), an evoked saccade results

(shown by trajectory 1). However, if the monkey is viewing upward motion and therefore

planning theupward saccade (shownby trajectory2), then stimulation results in a saccade that

deviates in the upward direction (shown by trajectory 3). (C) Extent of deviation. The average

amountofdeviation, representative of accumulatingactivity, dependedonmotionstrengthand

viewing time. This shows that oculomotor system is causally involved in decision making and,

more importantly, the accumulating activity may represent the evolving decision.

Figure taken with permission from Gold and Shadlen (2000).



to land further away from the RF, closer to the target. Consistent with the predic-

tions from the accumulator model, it was observed that stimulation early in the RT

resulted in saccades that landed close to the RF. The saccade deviation increased

with the time of stimulation, monotonically, till the maximum was attained close to

the time of the voluntary saccade onset (Fig. 6E). Additionally, if the rate of

Stimulation after target onset (ms)

(A) (B)

(C) (D)

(E) (F)

Reaction time (ms)

Slo

pe o

f th

eno

–ste

p de

via

tion

100

0

q2

q1

q1

q2

90

Dev

iatio

n (°

)

Stimulation after target onset (ms)Tim

e (m

s)

Reaction time (ms)

Act

iva

tion

00

500

1000

150 300

RF

RF

x-axis (°)

RF

-5° 0°-5°

0°

y-ax

is (°)

0

0.2

0.4

150 200 250 300

Dev

iatio

n fr

om R

F (°)

0-5

0

5

10

15

20

25

50 100 150 200

FIGURE 6

Evoked saccade deviation in no-step trials. (A) The plot shows the evoked saccade endpoint

locations when the monkey is fixating (on the black-filled square) but planning a saccade

to the target (green-filled square) and the stimulation is administered early (<100 ms

after target onset; black dots) and late (>100 ms after target onset; purple dots).



3313 Extending accumulator models to account for saccade plan


increase in saccade deviation was indicative of the rate of response preparation,

then sessions with faster increase in saccade deviation are expected to be associ-

ated with shorter average saccade RT and vice versa. Since the stimulation pulse

was administered in random 50% of the trials in every session, the saccade devi-

ation profile and the average saccade RT could be obtained from the stimulated

and nonstimulated trials, respectively. Further, since the mean RT varied across

sessions, the session-wise mean RT and the rate of increase in saccade deviation

could be compared across sessions. This comparison showed that the RT was in-

versely correlated with the rate of increase in saccade deviation (Fig. 6F), estab-

lishing a causal relationship between saccadic response preparation and the

accumulating activity in the oculomotor network, as assessed by microstimulation

in the FEF.

3 EXTENDING ACCUMULATOR MODELS TO ACCOUNTFOR SACCADE PLAN MODIFICATION

3.1 Countermanding paradigm: Canceling a saccadic responseIn these experiments, while subjects are preparing a saccade to a peripheral stimulus,

a second, centrally appearing stimulus instructs them to cancel the saccade plan on

random catch trials (Fig. 7A). In general, if the second stimulus appears after a

shorter interval called the stop signal delay, subjects cancel the saccade plan more

(B) An accumulator model of saccade initiation where accumulation (blue-noisy signal) to

threshold (dashed-black line) begins following a visual delay period of 60 ms after target

onset. Panels above indicate the task-related events. (C) Vector addition model of saccade

deviation. The target is represented by the green square. The black arrow that increases

in magnitude across panels represents the population vector of the saccade being planned

towards the target. The magnitude of the vector represents the extent of the evolving plan.

The blue circle on the left represents the evoked saccade RF and the blue arrow the evoked

saccade. The resultant saccade (red arrow) is the vector addition of the evoked saccade

(blue arrow) and the saccade being planned (black arrow). (D) The evoked saccade

deviations seen in (C) are now represented on a deviation versus time axis. (E) Systematic

changes in the deviation of the evoked saccade with respect to the RF are shown as a function

of time of stimulation. The mean deviation (red-filled circles) is fit by a weighted-smoothing

spline (solid black line). The dashed blue lines represent the 95% confidence interval. In (D)

and (E), RF—0�; Target—90�. (F) The relation between median of the first saccade reaction

time distribution from the nonstimulation trials and the slope of no-step deviation profile

(N¼51 sites). Each cyan-filled circle represents datum from a session. Linear regression of

the data is shown by the black-dashed line.

Figure adapted with permission from Ramakrishnan et al. (2012).

No-stop trial

a

b

a

b

Stop trial

Noncanceled

Canceled

Stop signal delay

(A)

(B)

(C)Stop signal delay (ms)

Canceled

Act

iva

tion

STOP

GO

0 100 200 300

Noncanceled

Act

iva

tion

STOP

GO

0 100 200 300

00

0.5

1

100 200

Pro

babi

lity

of e

rror

Reaction time





often than when it appears after a longer interval (Fig. 7B). A race model framework

has often been used to understand the basis for performance in the countermanding

task. The model involves a LATER-like GO process that accumulates to threshold

following the appearance of the peripheral target. The GO process initiates a sac-

cade upon reaching a threshold level of activation. However, on trials in which

the saccade is to be canceled, a STOP process accumulates to threshold. Trials

in which the STOP process reaches the threshold before the GO process are trials

in which the saccade is successfully withheld (Fig. 7C), whereas trials in which the

GO process reaches threshold are error trials. Such a race model can successfully

account for performance of subjects, as assessed by the probability of error trials,

which are the catch trials in which the saccade was initiated, as a function of the

stop signal delay. Note, however, that the race model assumes that the STOP pro-

cess can stop the GO process anytime until the GO process reaches threshold. In

other words, the model assumes that the impending saccade can be canceled any-

time during the planning stage. This may not be possible if part of the response prep-

aration period includes a ballistic stage, which is a response processing stage that is

not amenable to modification (De Jong et al., 1990; Logan, 1981; McGarry and

Franks, 1997; McGarry et al., 2000). To test this, Kornylo et al. (2003) modified

the race model to include a terminal ballistic stage. In other words, in this race

model, after a certain time point, the GO process was deemed unstoppable. The op-

timal duration of such a ballistic stage that was needed to fit the performance pro-

files was assessed by simulating the modified race model. The duration of the

ballistic stage estimated in this way was found to be very short (9–25 ms in monkeys

and 28–60 ms in humans). This time period is, interestingly, equivalent to the

FIGURE 7

(A) Countermanding task. Trials begin with the presentation of a central fixation box, which

disappears after a variable fixation time. Simultaneously, a target appears at an eccentric

location.Ona fractionof trials, after a delay, referred to as stop signal delay (SSD), the fixation box

(shown in red) reappears (in (b)). In these trials, the saccade to the target is required to be

withheld (stop signal trials). During trials when the stop signal is not presented (no-stop trial;

in (a)), a saccade is required to be initiated to the target (represented by an arrow to the target).

In stop trials, subjects sometimes withheld the saccadic response successfully (canceled trials)

and sometimes did not (noncanceled trials). (B) Inhibition functions. Plots showing the

probability of making a saccade to the first target a function of SSD. (C) Race model of

countermanding behavior. Following the appearance of the target (green box), a GO process

(green line) rises to threshold (gray horizontal bar), triggering off a saccade to the target. In stop

trials, a stop signal is presented (red box) which gives rise to a STOPprocess (red line) that races

to threshold. If the STOP process reaches threshold before the GO process, then the saccade is

canceled successfully (upper panel), whereas if the GOprocess reaches threshold first, then the

saccade is not canceled (lower panel).



experimentally estimated neural transmission delays of the final efferent pathways

from the FEF/SC. These observations suggest that saccade plans can be canceled

anytime up to the final efferent delay period.

3.2 The double-step task: Modifying a saccade planThe double-step task is another paradigm that is used to study how saccadic re-

sponse preparation can be modified. In this task, a peripheral saccade target is

stepped to a new position, while the saccade to the initial location is being prepared

but not yet executed. The correct response involves modifying the current saccade

plan to make a saccade to the new target. Such behavior allows the assessment of the

subject’s control over the saccade under preparation by measuring the probability of

trials in which the response is modified successfully, much like in the countermand-

ing task. Initially, it was observed that saccades to each of the targets were executed

in tandem even if the target had stepped to the new location before the first saccade

began, which spurred the debate on whether saccade programming is ballistic

(Westheimer, 1954). However, a number of studies have challenged this view by

showing that the saccade to the first stimulus can be modified (e.g., Komoda

et al., 1973; Lisberger et al., 1975; Wheeless et al., 1966). The redirect task, which

is a modified version of the double-step task, has also been successfully used to

probe the ability to modify saccade plans (Ramakrishnan et al., 2010; Ray et al.,

2004). In this task, the initial target stays on, instead of shifting to a new

location, even after the new peripheral stimulus appears (Fig. 8A and B). Subjects

have to modify the saccade plan to the initial target to make one to the new target,

like in the double-step task. However, in some trials, subjects are unable to modify

the saccade plan to the initial target leading to an erroneous response. The proba-

bility of error trials, which is an index of the ability to modify the initial response,

increases with the delay in the appearance of the new stimulus, which is called the

target step delay (Fig. 8C). This suggests that subjects find it harder to modify the

initial saccade plan when the new target appears later, a trend that is consistent with

the countermanding task. In general, these observations suggest that a saccade plan

can be modified or canceled during the response preparation stage; however, it gets

progressively harder to do so later in time, presumably because of advancing

commitment to the initial response.

3.3 Race model approachGO–GO model: Theoretically, the simplest model that can account for performance

in a redirect task involves the use of two independent LATER-like accumulators—

GO1 and GO2, which represent saccade preparation to the initial and final target,

respectively (Becker and Jurgens, 1979). However, GO–GO models fail to explain

the compensation function in the redirect task (Ramakrishnan et al., 2012). This

result is because such a model does not allow for the cancelation of the saccade

No-step trial

No-stepresponse

00

0.5

1

100 200

BS

300 00

0.5

1

100 200

AR

300 00

0.5

1

100 200

JA

300

00

0.5

1

100 200

AS

300 00

0.5

1

100 200

JG

300 00

0.5

1

100 200

NC

300

00

0.5

1

100 200

SY

300 00

0.5

1

100 200

VI

300

Target step delay (ms)

(A) (B)

(A1) (B1) (B2)

(C)

Pro

babi

lity

of e

rror

00

0.5

1

100 200

VJ

300

Successfulresponse

Erroneousresponse

Target step delay

Step trial





preparation to the first target, and therefore, the proportion of error trials is much

more than expected.

GO–STOP–GOmodel: One way to modify the race model is by including a STOP

process, developed to account for performance in the countermanding task, to inhibit

the GO1 process, to allow the GO2 process to initiate the saccade to the final target

(Ramakrishnan et al., 2010). In other words, the competition between the GO1 pro-

cess and the STOP process will decide whether the first response is canceled or not.

Following successful cancelation of the GO1 process, the GO2 process sets off the

saccade to the new target (see Fig. 9A). Error trials are those in which the saccade to

the first target is initiated. In these trials, according to the race model, the GO1 pro-

cess reached the threshold before the STOP process (Fig. 9A, green part of the dis-

tribution). Success trials are the ones in which the STOP process beat the GO1

process to the threshold (Fig. 9A; red part of the distribution). The inherent variabil-

ity in the rate of accumulation of the GO1 process, from trial to trial, gives rise to a

fraction of trials that are successfully modified at every target step delay. Implemen-

tation of such a race model allows one to arrive at the rate of accumulation of the

STOP process, in order to predict the fraction of error trials as a function of the target

step delay.

The race model, however, assumes that the STOP process does not have any var-

iability. This assumption is unwarranted since the STOP process too is a biological

process and may be subject to variability. In other words, the rate of accumulation of

the STOP process may vary across trials as well. Therefore, in the modified race

model, the rates of the STOP process were also modeled as a Gaussian distribution,

like that of the GO process (Fig. 9B). Knowledge of both distributions enable the

estimation of the fraction of error trials for a given target step delay. In practice,

however, given the limited number of trials per subject, it may not be possible to

sample the entire distribution of the STOP process, especially at the extremities,

whereas it may be easier to sample the central part of the distribution (two standard

FIGURE 8

Illustration of the temporal sequence of stimuli and behavior in the redirect task. The task

comprises (A) no-step trials, when a single target (green square) appeared on the screen, and

(B) step trials, when a second target (red square) appeared after a target step delay (TSD).

In no-step trials, subjects were required to foveate the target by making a saccade, shown

in yellow, to the target (A1). In step trials, subjects were required to modify the saccade

plan and initiate a saccade to the final target. Sometimes, they successfully compensated

for the target step (yellow) (B1). On other occasions, they failed to compensate, which

resulted in an erroneous saccade to the initial target (yellow) followed by a corrective saccade

to the final target (magenta) (B2). (C) Compensation functions. Plots showing the probability of

making a saccade to the first target as a function of TSD. Data for nine representative subjects,

superimposed by the best-fit Weibull function, show that the probability of making an

erroneous first saccade increases with increasing TSD.

Figure taken with permission from Ramakrishnan et al. (2010).

No-step reactiontime distribution Error

TSD

GO1GO2

TSRT

STOP

Time from initial target onset (ms)

Time from initial target onset (ms)

(A)

(B)

(C)

Act

iva

tion

Act

iva

tion

Latency of the slowest erroneous response

Multi saccadegaze shift

100 ms

pp

p p

ppp

pc

s

s

c

c

cc

s

cs

s

10 °

Midflightmodification

Hypometricerror

TSD TSRT

STOP2s

STOP

GO

0 150

a b c

300 450IT FT

2s

0 100 200 300

Success





deviations on either side of the mean, Fig. 9B). The estimate of the probability of

error trials is, therefore, underestimated. The underestimation is, however, only

due to the right tail of the STOP distribution, because the trials with slower STOP

process rates are the ones that result in errors, which is about 2.5%. However, it

may be possible that the distribution of the STOP process is non-Gaussian. Never-

theless, based on Chebyshev’s theorem, the upper limit of the underestimation of the

percentage of error trials is not expected to exceed 12.5% (Ramakrishnan et al.,

2010). In summary, even if the rates of GO and STOP processes are both variable

across trials, the proportion of error trials can be found with the upper limit of the

underestimation being limited to 12.5%.

The race model, as mentioned earlier, assumes that the STOP process can inhibit

the GO process anytime during planning stage. However, if parts of the saccade plan-

ning stage are not amenable to inhibitory control, that is, if the preparatory stage

involves a ballistic stage, the proportion of error trials should increase and, as a result,

the underestimation should be more than 12.5%. This criterion, which is robust to the

inherent variability of the GO and STOP processes and to the unavoidable sampling

FIGURE 9

(A)Racemodel framework for the redirect task. Themodel is adapted from theoneused for the

countermanding task (see Fig. 7). However, in thismodel, following successful inhibition of the

GO1process, theGO2processdirects gaze to thenew target. As the rate of accumulation of the

GO1 process can vary from trial to trial, slower GO1 processes are successfully inhibited (red

part of theno-step reaction timedistribution in theupperpanel),whereas fasterGO1processes

arenot inhibited (greenpart of the distribution). The average time takenby theSTOPprocess to

reach threshold (TSRT) can be estimated using the racemodel under the assumption that the

STOP process has a constant rate of accumulation across trials. (B) Race model with variable

STOPprocessaccumulation rates.As shown in (A), theGOandSTOPprocessesare initiatedby

the presentation of the initial (IT) and final target (FT), respectively, following a visual delay of

60 ms. The rates of the GO and STOP processes on a trial are drawn from a Gaussian

distribution. The two processes rise to the threshold (broken horizontal line) to give rise to the

no-step reaction time distribution (green histogram) and STOP distribution (red histogram).

The fraction of error trials for a given TSD is decided by the finish time of the slowest STOP

process. Inpractice, STOP2s,whichdenotes the rateof theSTOPprocess slower than themean

STOP rate by 2s, was considered the slowest STOP process. (C) Behavior during redirect task

with increased target eccentricity. In no-step trials, subjects sometimes make a set of two

saccades, a multisaccade gaze shift, to foveate the target: an initial hypometric saccade

(primary saccade) followed by a second saccade (secondary saccade) (see (a)). During step

trials, subjects sometimesmodify the first saccademidflight to direct gaze to the new target (see

(b)).Onotheroccasions, they follow theprimary saccadewithasecondarysaccade to foveate the

initial target, followed by a corrective saccade to the final target (see (c)). The horizontal and

vertical eye movement traces with respect to time are illustrated in blue and black, respectively.

The time of appearance of the initial and final targets are indicated by green and red arrows,

respectively. p, the primary saccade; s, the secondary saccade; and c, the corrective saccade.

Figure taken with permission from Ramakrishnan et al. (2010).



errors, was used to detect the presence of a ballistic stage during saccade planning

and execution. Using this method, Ramakrishnan et al. (2010) tested for the presence

of a ballistic stage in the saccade planning phase and found the underestimation of the

error trial probability to be limited to 10 %, less than 12.5%, which meant that sac-

cade planning phase may not involve a ballistic stage. Or, in race model terms, the

STOP process can inhibit the GO process till it reached threshold. This result is con-

gruent with earlier work based on the countermanding task that reported the ballistic

stage to be limited, perhaps, to the final efferent pathway (Kornylo et al., 2003).

Having tested the planning stage, Ramakrishnan et al. (2010) probed the saccade

execution stage for the presence of a ballistic stage, that is, whether the saccade can

be modified midflight or not. Large amplitude saccades provide a longer saccade

execution duration, which is beneficial in testing whether the saccade can be inter-

rupted during this late stage. Therefore, subjects were made to perform a version of

the redirect task in which the target eccentricity from the center was increased to 30�,

which increased the saccade duration to about 70 ms. The long saccade duration

sometimes allowed subjects to interrupt the saccade midflight and make a compen-

satory saccade to the new target (see panel (b) in Fig. 9C). Using the race model-

based framework, the probability of error trials, trials in which they could not change

the saccade plan midflight, could be estimated and the underestimation in this case

was found to be �13%, suggesting that saccade execution stage, like the saccade

planning stage, did not, perhaps, involve a ballistic stage. In other words, saccades

could be modified anytime during movement execution as well.

In about 13% of the trials, on average across subjects, subjects made a sequence

of two saccades, a multisaccade gaze shift (panel (a) in Fig. 9C), to foveate the

eccentrically located target. These multisaccade gaze shifts provided Ramakrishnan

et al. (2010) the opportunity to test for the ability of the oculomotor system to modify

a saccade plan in redirect trials during saccade sequences. In other words, the saccade

sequence allowed the authors to test whether the saccade plan could be modified fol-

lowing the primary saccade (p) in a multisaccade sequence. The error trials in this case

comprised trials in which the primary saccade was followed by a secondary saccade (s)

to foveate the initial target (panel (c) in Fig. 9C) despite the appearance of the final

target before the primary saccade was initiated. Even though the parameters of the rate

of accumulation of the secondary saccade are not known, because, presumably, the

parameters of the STOP process remain the same, the probability of error trials can,

nevertheless, be estimated. When this analysis was carried out, it was found that a sur-

prisingly large fraction of trials turned out to be error trials, almost 78% on average

across subjects, which was about six times more than expected. In other words, sec-

ondary saccades of a large fraction of trials involving multisaccades could not be com-

pensated despite there being enough time to modify the plan. This strongly indicated

the presence of a ballistic stage in the programming of multisaccade sequences, sug-

gesting that the response preparation stage of the secondary saccade involved stages of

processing that were not amenable to modification.

By providing a computational basis for the behavior in the redirect task, the race

model allowed the estimation of the time taken to modify the saccade plan, called the

target step reaction time (TSRT; Ramakrishnan et al., 2010), analogous to the stop



signal reaction time (SSRT) of the countermanding task (Logan and Cowan, 1994)

which was 107 ms on average, across subjects. However, the TSRT to modify the

saccade during execution was significantly higher at 152 ms across subjects, on

average. Nevertheless, a significant subject-wise correlation (r¼0.77; p¼0.0008)

between the two TSRT estimates suggested that inhibitory control might engage sim-

ilar mechanisms even though it took more time to modify the saccade during execu-

tion. In contrast, subjects failed to modify the secondary saccade even when they had

about 215 ms, on average. In other words, even though the saccade control processes

could effectively modify the saccade plan in about 107 ms, more than double that

time was insufficient to modify the secondary saccade, rendering it opaque to control

processes. Thus, the intersaccadic interval before the secondary saccade onset in

multisaccade gaze shifts may be a potential point of no return in saccadic response

preparation, which may be the first clear demonstration of it in sensorimotor

response preparation. Although it is puzzling that the secondary saccade is refractive

to the new stimulus, stopping the secondary saccade may be a lot harder because they

may be programmed as a package along with the primary saccade of multisaccade

gaze shifts. Alternately, the primary hypometric saccade of multisaccade gaze shifts

may also be a consequence of the motor command not fully specifying the goal.

In such a scenario, it is possible that the error correction system might, by priority,

engage the oculomotor circuitry to correct the hypometric saccade, which might

prevent new visual input from modifying the saccadic response. Knowing whether

this observation is applicable to saccade sequences, in general, or is limited to multi-

saccade gaze shifts may shed some light on the basis for the point of no return.

3.4 Time course of the change of plan as assessedwith microstimulation

It is known from earlier work that electrical microstimulation administered to the

FEF to evoke a saccade orthogonal in direction to the one being planned results

in an averaged saccade whose direction indicates the state of the saccade being

planned (Gold and Shadlen, 2000, 2003; see also Kustov and Robinson, 1996;

Sparks andMays, 1983; Fig. 6E). Ramakrishnan et al. (2012) extended this technique

to assess the state of the saccade plan while it was being modified. For this,

the authors trained two monkeys to perform the redirect task. During a step trial,

while the monkey was changing the saccade plan, they administered stimulation cur-

rents to the FEF at six different time points, spaced by 30 ms, following the final

target onset. The experimental design was such that stimulation alone would produce

an electrically evoked saccade in the direction orthogonal to both the initial and final

targets. If microstimulation could reveal the state of the saccade plan, they reasoned

that stimulation administered soon after the final target onset would evoke a saccade

that should interact with the saccade plan to the initial target, to produce a saccade

that lands in between the initial target and RF (Fig. 10A, middle row of panels), since

saccade preparation to the initial target is yet to be modified. However, when the

monkey is stimulated long after final target onset, the stimulation-evoked saccade

0 50 100

Time (ms)

(A)

(B)

(D)

(C)TSD = 80 ms All TSDs

Time of stimulation afterfinal target onset (ms)

Time of stimulation afterfinal target onset (ms)

Dev

iatio

n fr

om R

F (°)

0

-24

-12

0

12

Dev

iatio

n fr

om R

F (°)

-24

-12

0

1224

30 60 90 120

00

60

120

180

60 120

Crossover time (ms)

Obs

erve

d T

SR

T (

ms)

180

0 50 100 150 200

CT = 91 ms CT = 102 ms

150 200





should interact with the saccade plan to the final target to produce a saccade that

lands in between the final target and the RF (Fig. 10A, bottom row of panels), as

the saccade preparation to the initial target should be modified by then. As predicted,

the evoked saccade direction, as indicated by saccade deviation from the RF,

gradually shifted from the initial target direction to the final target direction

(Fig. 10B and C). The time when the deviation profile crossed the RF– the crossover

time– an estimate of the time when the plan changed, was about 100 ms, on average.

Furthermore, session-wise comparisons of crossover time with TSRT, which was es-

timated from the nonstimulated trials of the session, was reasonably well correlated

(r¼0.45; p<0.003; 43 sites, two monkeys; Fig. 10D). Taken together, these data

suggest that microstimulation is a powerful tool to visualize the time course of covert

cognitive processes changes plans in real time.

4 CONCLUSIONThe body of work reviewed in this chapter suggests that saccadic decision making

and motor planning can be envisioned as an accumulation of activity within a selec-

tive population of neurons distributed within the oculomotor system. These plans

may be modified anytime during the planning and execution stage. Successful plan

modification takes about 107 ms on average and the time course of this process can

be tracked by electrical microstimulation as well as single unit recordings. The

FIGURE 10

Evoked saccade deviation in step trials. (A) In the first row of panels, when a stimulation pulse

(blue oscillations) is delivered, a saccade (blue arrow) is evoked. The middle and bottom rows

represent a short TSD (16 ms) trial that is microstimulated by either a short latency (10 ms) or

a long latency (140 ms) pulse. The subsequent panel shows the evoked saccade, the

saccade under preparation, and the averaged saccade as blue, black, and red arrows,

respectively. The black arrows are drawn short of the target to represent saccades under

preparation. The rightmost panels show the observed saccade. The dots forming the saccade

represent the eye position samples. At early stimulation times, the resultant averaged saccade

deviates toward the initial target, but at later stimulation times, it deviates toward the final

target. (B) The evoked saccade deviation profile in a typical session for TSD¼80 ms is shown.

(C) The averaged saccade deviation profile from three TSDs (16, 80, 144 ms) is shown after

aligning each of them to the onset of the final target. In (B) and (C), themedian of the deviation

(red circles) is fit by a weighted-smoothing spline (solid black line). The dashed blue lines

represent 95% confidence limits. Crossover time (CT) represents the time when the deviation

profile crosses the RF (denoted by the red arrow), as estimated from the fit. In (D), the TSRT

obtained from the race model-based analysis is plotted against the crossover time obtained

from the observed evoked saccade deviation profile as a scatter plot (N¼43 sites). Each gray-

filled circle represents data from a session. Dashed-black line represents the line of unity

slope.

Figure adapted with permission from Ramakrishnan et al. (2012).

343References


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(DST) and the Department of Biotechnology (DBT), Government of India, and core

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