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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
17
Brain mechanisms
controlling decision making
and motor planning
Arjun Ramakrishnan*, Aditya Murthy{,1
⁎
National Brain Research Centre, Nainwal Mode, Manesar, Haryana, India
Centre for Neuroscience, Indian Institute of Science, Bangalore, Karnataka, India
1
Corresponding author. Tel.: þ91-80-22933433, Fax: þ91-80-23603323,
e-mail address: aditya@cns.iisc.ernet.in
{
Abstract
Accumulator 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 performance 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 oculomotor “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.
Keywords
saccade, plan change, redirect, double step, countermanding, oculomotor
1 INTRODUCTION
An 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
Progress in Brain Research, Volume 202, ISSN 0079-6123, http://dx.doi.org/10.1016/B978-0-444-62604-2.00017-4
© 2013 Elsevier B.V. All rights reserved.
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CHAPTER 17 Brain mechanisms controlling decision making
of the reaction time (RT) may be required for decision making that entails determining 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 movements 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 frequently 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 showing 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.
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2 Evidence for accumulator models
2 EVIDENCE FOR ACCUMULATOR MODELS
2.1 RTs and the LATER model
A 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-threshold
Hanes 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 neuronal activity to threshold. This finding is consistent with observations from presaccadic 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 prediction, 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.
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LATER model
(A)
Stimulus
Reaction time
Response
Threshold
Activation
Decision signal
r
Baseline
0
100
200
300
Time (ms)
(B)
Midsaggital view
Dorsal view
Cortex
LIP
CS
FEF
Dors
MT
IPS
alpa
thw
ay
V2
Basal ganglia
PS
LuS
LGN
Thalamus
V1
SC
Optic
e
nerv
V1
AS
SC
Midbrain
V4
V
V
LaS
l
tra
Cerebellum
H
H
Po
n
s
IT
Br
ain
pa
ay
thw
n
Ve
STS
Cerebellum
ste
m
Br
ain
ste
m
Sp
ina
lc
Sp
or
d
ina
lc
or
d
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 eye movements 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).
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2 Evidence for accumulator models
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 information
Although 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
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CHAPTER 17 Brain mechanisms controlling decision making
Saccade RT
FEF movement cell activation
Activation
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0
150
300
Reaction time (ms)
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 by making a saccade to the target
presented in that direction. By recording from single neurons in the lateral intraparietal
area (LIP), a progressive increase in firing rate was 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 activity, the saccade was initiated. In other words, when the motion strength was stronger, 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
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2 Evidence for accumulator models
(A)
RT
Saccade
Motion
Targets
Fixation
RF
e
Tim
(B)
Motion
strength
51.2
70
Select T1
65
25.6
12.8
60
6.4
3.2
Firing rate (sp/s)
55
0
50
45
40
Select T2
35
30
25
20
0
200
400
600
800
-800 -600 -400 -200
0
Time (ms)
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
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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 eye movement being planned (Sparks and Mays, 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 stimulation (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 deviation should be modulated by factors that affect the state of the saccade plan like the
stimulus-viewing duration and the stimulus motion strength. Consistent with this hypothesis, it was observed that the saccade deviation in fact increased with increase in
stimulus-viewing duration as well as motion strength, suggesting that the accumulating 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 previously described experiment (Fig. 6A); however, stimulation pulses were administered 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 accumulating 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).
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2 Evidence for accumulator models
(A)
Evoked
saccade
Motion
Fixation
Voluntary
saccade
Time
(B)
(C)
1.5
51.2%
2
3
1
0
Deviation (°)
y position (°)
25.6%
5
1.0
6.4%
0.0%
0.5
-5
-5
0
5
10
x position (°)
0
100
300
500
Viewing duration (ms)
FIGURE 5
The evolving saccadic decision is seen in the oculomotor system. (A) Microstimulationinterrupted 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 the upward saccade (shown by trajectory 2), then stimulation results in a saccade that
deviates in the upward direction (shown by trajectory 3). (C) Extent of deviation. The average
amount of deviation, representative of accumulating activity, depended on motion strength and
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 predictions 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
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CHAPTER 17 Brain mechanisms controlling decision making
(A)
(B)
y-axis (°)
0°
Activation
1000
RF
-5°
-5°
500
0°
0
x-axis (°)
0
(C)
150
300
Reaction time (ms)
(D)
90
Deviation (°)
q2
q1
0
s)
q1
Tim
RF
q2
e (m
RF
(E)
Stimulation after target onset (ms)
(F)
25
0.4
20
Slope of the
no–step deviation
Deviation from RF (°)
330
15
10
5
0
-5
50
100
150
200
0
Stimulation after target onset (ms)
0.2
0
100
150
200
250
300
Reaction time (ms)
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).
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3 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 associated 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 deviation 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 inversely correlated with the rate of increase in saccade deviation (Fig. 6F), establishing 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 ACCOUNT
FOR SACCADE PLAN MODIFICATION
3.1 Countermanding paradigm: Canceling a saccadic response
In 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
(N ¼ 51 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).
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CHAPTER 17 Brain mechanisms controlling decision making
(A)
a
Reaction time
No-stop trial
Noncanceled
b
Stop trial
Canceled
Stop signal delay
Probability of error
(B)
1
0.5
0
0
100
200
Stop signal delay (ms)
(C)
Activation
a
Canceled
GO
STOP
0
100
200
300
b
Activation
332
Noncanceled
GO
STOP
0
100
200
300
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3 Extending accumulator models to account for saccade plan
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 saccade 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 process 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 anytime during the planning stage. This may not be possible if part of the response preparation 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 optimal duration of such a ballistic stage that was needed to fit the performance profiles 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. On a fraction of 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 STOP process (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 GO process reaches threshold first, then the
saccade is not canceled (lower panel).
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CHAPTER 17 Brain mechanisms controlling decision making
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 plan
The double-step task is another paradigm that is used to study how saccadic response 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 countermanding 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 probability 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 approach
GO–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
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3 Extending accumulator models to account for saccade plan
(A)
(B)
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(A1)
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response
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response
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response
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CHAPTER 17 Brain mechanisms controlling decision making
preparation to the first target, and therefore, the proportion of error trials is much
more than expected.
GO–STOP–GO model: 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 process 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 process reached the threshold before the STOP process (Fig. 9A, green part of the distribution). 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 variability 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. Implementation 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 variability. 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).
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3 Extending accumulator models to account for saccade plan
(A)
No-step reaction
time distribution
Activation
TSD
Error
Success
TSRT
STOP
GO2
GO1
0
100
200
300
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(B)
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STOP2s
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2s
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STOP
0 IT
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300
450
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a
b
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gaze shift
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modification
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error
p
p
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c
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s
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CHAPTER 17 Brain mechanisms controlling decision making
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. Nevertheless, 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 planning 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) Race model framework for the redirect task. The model is adapted from the one used for the
countermanding task (see Fig. 7). However, in this model, following successful inhibition of the
GO1 process, the GO2 process directs gaze to the new 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 the no-step reaction time distribution in the upper panel), whereas faster GO1 processes
are not inhibited (green part of the distribution). The average time taken by the STOP process to
reach threshold (TSRT) can be estimated using the race model under the assumption that the
STOP process has a constant rate of accumulation across trials. (B) Race model with variable
STOP process accumulation rates. As shown in (A), the GO and STOP processes are initiated by
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. In practice, STOP2s, which denotes the rate of the STOP process slower than the mean
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 sometimes modify the first saccade midflight to direct gaze to the new target (see
(b)). On other occasions, they follow the primary saccade with a secondary saccade 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).
Author's personal copy
3 Extending accumulator models to account for saccade plan
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 saccade 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 congruent 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 interrupted 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 compensatory saccade to the new target (see panel (b) in Fig. 9C). Using the race modelbased 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 following 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 surprisingly 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, secondary saccades of a large fraction of trials involving multisaccades could not be compensated despite there being enough time to modify the plan. This strongly indicated
the presence of a ballistic stage in the programming of multisaccade sequences, suggesting 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
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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 (r ¼ 0.77; p ¼ 0.0008)
between the two TSRT estimates suggested that inhibitory control might engage similar mechanisms even though it took more time to modify the saccade during execution. 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 multisaccade 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 assessed
with 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 and Mays, 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 currents 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
Author's personal copy
3 Extending accumulator models to account for saccade plan
(A)
0
50
150
100
200
Time (ms)
(B)
(C)
All TSDs
CT = 91 ms
24
Deviation from RF (°)
Deviation from RF (°)
TSD = 80 ms
12
0
-12
-24
0
30
60
90
120
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final target onset (ms)
Observed TSRT (ms)
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60
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0
-12
-24
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100
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final target onset (ms)
(D)
0
CT = 102 ms
12
180
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CHAPTER 17 Brain mechanisms controlling decision making
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 estimated from the nonstimulated trials of the session, was reasonably well correlated
(r ¼ 0.45; 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 CONCLUSION
The 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 selective 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 TSD ¼ 80 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), the median 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 (N ¼ 43 sites). Each grayfilled circle represents data from a session. Dashed-black line represents the line of unity
slope.
Figure adapted with permission from Ramakrishnan et al. (2012).
Author's personal copy
References
congruence between patterns of activity obtained from electrophysiological measurements in single neurons, physiological perturbations of the oculomotor network by
microstimulation, and computational modeling provide firm grounding to the belief
that race models are a logical framework to understand how motor plans and decisions
are prepared or modified by the brain. On the other hand, the failure of the race model
to explain secondary saccades of multisaccade gaze shifts suggest a genuine failure of
inhibitory control and provides the necessary evidence of a ballistic stage that intervenes during more complex movements involving multiple saccades. Although,
why and how such ballistic stages are implemented by the brain remain a matter of
speculation, we hope that the success of accumulator and race models in the domain
of oculomotor control can be extended to the study of motor control involving other
effectors such as hand movements, as well as in the study of natural movements that
require temporal coordination between multiple independent effectors.
Acknowledgments
This work was supported by grants from the Department of Science and Technology
(DST) and the Department of Biotechnology (DBT), Government of India, and core
funding from the National Brain Research Centre.
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