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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5815_Библиотеки_им_академика_М_И_Перельмана
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Complex Decisions: Multiple LATER Units 71
Figure 4.25 Comparison between a fixed and moving background. (a) The target moves but the background
does not. (b) The target and background move equally. (c) A moving background (blue) slows the distribution,
moving it rightward in a self-parallel fashion; this is characteristic of the effect of lateral inhibition (see
Figure 4.11). Modified, after Roos, Calandrini et al. (2008).
4.8.6 The Increase in Early Responses
The other major differen ce between evoked and spontaneous saccades is that the latter
show a greatly increased early population. Why might this be? One characteristic of early
saccades is that they become much more frequent when stimuli are predictable. This is in
keeping with the sense that the early population represents relatively automatic, reflexive
responses, probably associated with a relatively low-level structure such as the superior
colliculus, normally tonically inhibited by higher-level, probably cortical, decision mechanisms. A functional dichotomy of this kind seems first to have been proposed by Harris
(Harris 1989), and an equivalent process of procrastination is an intrinsic feature of
LATER (Carpenter 1981). A systematic study of altering the prior probability of saccadic
step targets (Carpenter and Williams 1995) showed a systematic increase in the size of
this population from 0.5% to 10% as the stimulus probability increased from 0.05 to 0.95,
their distributions appearing to fall on a straight line swivelling about the origin k.
If we think of a spontaneous saccade as being, in effect, evoked by the preceding
saccade and the new retinal image that it creates, then one important characteristic of
this stimulus is that it is exceptionally easy to predict. We could scarcely have more
information in advance about its timing (since we caused it!), and its amplitude and
direction are similarly known almost perfectly before it happen s. So, it would not be
surprising for spontaneous saccades to display the increased proportion of aberrantly
fast early saccades characteristic of highly predictable stimuli. To test this, we again
arranged for the target to move randomly as described for the fixed background above.
However, after a 250 ms delay, it returned to its original central position (Figure 4.26).
Thus, the same target and background were presented first when timing and direction
72 LATER
Figure 4.26 (a) Effect of extreme predictability on incidence of early response. The target and background
moved together: (b) after a random delay from the start of the trial; (c) with a fixed delay and amplitude. As a
result, the probability of an early saccade increased from about 3% to about 20%. Modified, after Roos, Calandrini
et al. (2008).
were completely unpredictable, and then when they were completely certain. The
resulting distributions were dramatically different: when the target was predictable, there
was a large early component that was absent when it was unpredictable (Figure 4.26).
When lateral inhibition and expectation were both increased, the simulation could fully
account for the distribution of ISIs (Roos, Calandrini et al. 2005, figure 5B).
4.8.7 The LATEST Model
LATER is primarily a model of the timing of saccades: as a consequence, it can also
predict choices between alternative targets. What it does not claim to do is predict the
amplitude and direction metrics of the resultant saccade. However, it turns out that a
small modification to LATER does in fact enable it to make quite a good job of
predicting metrics in static scanning tasks, as well as timing and choice. This modified
version is called LATEST (Tatler, Brockmole et al. 2017) (Linear Approach to Threshold
Explaining Space and Time).
The concept underlying LATEST is that when scanning a static pattern, apart from
interactions between possible targets, at a more fundamental level there is competition
between the targets and the possibility of not moving at all: ‘Go’ versus ‘Stay’ . If there is
still information to be extracted from the current fixation, that will favour ‘Stay’. On the
other hand, if a new potential target seems likely to provide more information, that will
bias the decision favour of ‘Go’. Competition of this kind seems first to have been
suggested by Beintema, (Beintema, van Loon et al. 2003) with a choice between ‘make
saccade’ and ‘keep fixating’; by framing this concept within LATER, it is possible to
generate quantitative predictions concerning saccadic amplitude and direction. As would
be expected, the decision rate (i.e., μ) for the Stay unit is influenced by factors describing
the current fixation and also the preceding saccade (Figure 4.27(a)), whereas for the Go
unit it is determined by factors relating to the destination of the proposed saccade (for
instance, ‘semantics’, the likely amount of information at that location), together with
Complex Decisions: Multiple LATER Units 73
Figure 4.27 The LATEST model. (a) The overall μ for a given saccade (in this case, from fixation 1 to 2) can be
regarded as the result of two competing processes: μ
current fixation in order to complete the processing of information, and μ
information from the next fixation. In addition, μ
do with the new saccade. (b) Examples of how the overall μ is influenced by these various aspects. Modified, after
Tatler, Brockmole et al. (2017).
, representing the tendency to wish to remain at the
Stay
is influenced by the preceding saccade, and μGoby factors to
Stay
, the tendency to want to obtain new
Go
factors relating to the trajectory of the saccade about to be made, such as its direction and
amplitude. As can be seen in Figure 4.27(b), ‘semantics’ works in opposite directions for
Stay and Go. Increased information at the proposed location increases the decision rate,
but reduces it at the current fixation. Taking all these factors together, it is then possible
to make better predictions of both the temporal and spatial aspects of individual
saccades.
74 LATER
(b)
3.75
Decision rate µ
3
(1)
(2) (3)
0
Edge information at fixation
Decision rate µ
Figure 4.27 (cont.)
3.75
3×10
3
–6
Semantics at fixation
003×10
Edge information at next location Salience at fixation
(4) (5)
–6
2.6×10
–6
00
Semantics at next location
2.6×10
–6
1.1×10
–6
4.9 Stop Signals and Cancellation
So far, we have considered only situations where a target triggers the generation of a
corresponding eye movement. But there are several situations in which the response to a
target is suppression rather than generation of a response. They fall into two categories:
extrinsic and intrinsic. Extrinsic means that the suppression is the result of prior
instructions to the subject telling them to suppress a movement they would otherwise
make; intrinsic implies a situation where the subject is given no particular instructions
about suppressing a response, but where the logic of the proto col – for instance, a change
in the ultimate destination of the saccade – means that the previously planned response is
no longer appropriate.
In both cases, responses can be modelled with considerable precision by designating
certain LATER units as ‘Stop units’, whose output inhibits or abolishes the ‘Go units’ that
would otherwise generate an eye movement. Focused discussions on this topic are
provided in reviews elsewhere (Carpenter and Nooran i 2017, Noorani 2017, Noorani
and Carpenter 2017), but here we discuss the salient points behind our understanding of
stop mechanisms in the brain and how we study them experimentally.
4.9.1 Countermanding
The simplest and most thoroughly studied example of extrinsic suppression is the
countermanding task (Logan and Cowan 1984, Hanes and Schall 1995, Patterson and
Schall 1997, Hanes and Carpenter 1999, Asrress and Carpenter 2001, Ozyurt, Colonius
et al. 2003, Walton and Gandhi 2006, Boucher, Palmieri et al. 2007, Emeric, Brown et al.
2007, Salinas and Stanford 2013, Schmidt, Leventhal et al. 2013). Here the subject is told
that if a second target (the Stop signal) appears on some trials, they are required to
Complex Decisions: Multiple LATER Units 75
Figure 4.28 Countermanding task. (a) The protocol. It begins like a conventional step task, but on some trials a
Stop signal appears after a delay d that instructs the subject to withhold the impending saccade. (b) Results from
a countermanding experiment. Depending on d, countermanding may or may not be successful: the larger the
d, the less likely that the saccade is withheld; the black bars are the control trials, the red are trials with Stop
signals at 100 ms, only 28% of which resulted in successful cancellation. (c) The corresponding distribution of
responses (unpublished data).
Figure 4.29 Modelling countermanding. (a) After the Stop-signal delay, the Stop unit is activated. If it reaches
its criterion threshold before the Go unit, the movement is aborted. (b) Observed and simulated percentages of
trials where the cancellation is successful, as a function of the Stop-signal delay. Modified from Hanes and
Carpenter (1999).
withhold the movement that would otherwise have been made. The behaviour is
stochastic, with the movement successfully cancelled on some trials but not others.
The longer the period between presentation of the primary target and presentation of
the Stop signal – the Stop-signal delay, d – the less likely it is that the movement will be
successfully cancelle d (Figure 4.28(c)). The behaviour can be modelled in terms of a race
between ‘Go’ and ‘Stop’ processes (Hanes and Carpenter 1999, Boucher, Palmieri et al.
2007, Schall, Palmieri et al. 2017), Figure 4.29. An important difference with the
precedence task (which is intrinsic rather than extrinsic) is that – perhaps because
cancellation is a simpler operation than selecting a different target – the Stop process
is more rapid than the Go, so that reliable cancellation can occur even with relatively
large values of d.
4.9.2 Wheeless
In the Wheeless task (Wheeless, Boynton et al. 1966, Noorani and Carpenter 2015),
which is special case of the double-step task (Becker and Jürgens 1975, Becker and
Jürgens 1979, Camalier, Gotier et al. 2007), we present the subject with a series of trials
of which some are simple step tasks and act as controls. But in the remaining experimental trials, after a delay d the target jumps to the alternative target position. The
76 LATER
Figure 4.30 The Wheeless task. (a) The protocol begins like a step task, but in some trials (as shown here), after
a delay d, the target steps across to the opposite side; sometimes the subsequent saccade is in the same
direction as the original step (an A response), otherwise in the opposite direction (a B response). (b) Data from a
single subject performing this task, with a delay d of 100 ms; at first the A responses follow the same distribution
as in the controls, but then cease as the B responses begin to appear. (c) Observed and simulated data from one
subject for four different values of d. Modified from Noorani and Carpenter (2015).
subject is not given any explicit instructions but simply told to follow the target. The
behaviour is then stochastic: on some experimental trials, the subject saccades to the first
target and then jumps to the second (an A response: see Figure 4.30), in the remainder
they jump straight to the second (a B response), ignoring the original target. The larger
the d, the more likely is an A response. Behaviour in this task can be modelled by LATER
using a similar arrangement to the model for the Go / NoGo task, predicting latency
distributions for all responses in this task remarkably well. In the model, an A response
unit is triggered by the stimulus; after a delay d, the Stop unit is activated, which cancels
the original A response if it has not already occurred; at the same time as triggering the
Stop unit, the B unit is activated and rises toward threshold.
In many ways, this is a better task than countermanding (Noorani and Carpenter
2015). It saves time, since it generates data on every trial, whereas successful cancellation
in countermanding means that there is nothing to measure. It also means that we do not
have to give the subject prior instruction about what to do (and that the subject does not
have to remember those instructions!), making it feel like a simpler task for a subject
to perform.
4.9.3 Go / NoGo and Errors
Another situation that calls for an intrinsic Stop signal is the Go / NoGo task, where the
subject is instructed before the run to make saccades to one class of target but not others.
In this scenario, subjects often make saccades to the ‘wrong’ target, generating errors. For
instance (Figure 4.31), they may be told to make a saccade to a green target (appearing
on either side, the correct response) but not to red (the error). The reason why a Stop
signal is needed in this case is that it takes longer for the brain (Schall and Hanes 1993,
Thompson, Hanes et al. 1996, Thompson, Bichot et al. 1997) to respond to the colour of
a target than to its existence and position (here we take this extra delay as 60 ms). In this
way, there is a close analogy with the countermanding task, where colour information
needs accounting for before a. correct response can be given with confidence. As a result,
Go units will at first be activated on both sides, before the red unit is suppressed by a
Stop signal originati ng from the colour of the red target. As a result of this intrinsic delay
from colour information processing, mistakes will be made (some 40% in Figure 4.31(c))
if a decision is made by the brain before colour information arrives. A race-to-threshold
Complex Decisions: Multiple LATER Units 77
Figure 4.31 Go / NoGo task. (a) Protocol. After the foreperiod, a target appears either on the left or right, and
may be red or green. The subject is instructed to make saccades to green targets but not red. (b) A model for this
task, using two Go units (for red and green) and one Stop unit (for red). (c) Observed and simulated distributions
for this task in one subject. Modified from Noorani, Gao et al. (2011).
model of this nature, with a Go unit triggered on appearance of a visual target followed
by a Stop unit and another, more refined Go unit initiating when colour information is
evaluated in the brain, accurately predicts the quite complex response time distribution
from human subjects performing this task, emphasising the power of such a model in
explaining behaviour (Noo rani, Gao et al. 2011). In comparison with the Wheeless task
where a response is generated in every trial, the Go / NoGo task has some inefficiency as
an experimental system because a large proportion of trials (those with no responses, i.e.,
correctly stopping of saccades) do not contribute to the reaction time distributions.
It is an interesting notion that errors are made when the brain responds to a stimulus
before all the necessary information arrives, and although this is exemplified well here in
the Go / NoGo task with colour information, this is by no means the only situation in
which this occurs. For example, we discussed earl ier that when we are distracted, we tend
to make more errors: an experiment with a Go / NoGo task where a subject had to make
saccades to a specific colour but not others whilst simultaneously talking on a mobile
phone (designed to distract them) led to many errors and also some responses that
occurred much earlier than would otherwise occur if the subject had not been so
distracted. Response time distributions in this scenario can be accurately recapitulated
with incorporation of an ‘early’ Go LATER unit, suggesting that when extra cognitive
loading distracts the cerebral cortex, then more primitive brain regions (likely the
superior colliculus) can instead make saccadic decisions when they would otherwise be
tonically inhibited by the higher cortical areas (Halliday and Carpenter 2010).
4.9.4 Antisaccades
Especially amongst clinicians, the antisaccade task is extremely popular, in some ways
more than it merits (Hallett and Adams 1980). Here the subject is required to do
something rather complex and extremely unnatural: when the target appears on the
right, they are to make a saccade to the left, and when it is on the left, to the right
(Figure 4.32). There may or may not be some kind of marker permanently visible to
indicate more exactly where the saccade is meant to end up, but more commonly we
don’t mind very much how large the antisaccade is, only that it is in the ‘right’ (i.e.,
wrong) direction. As we shall see in Appendix 2, the reason for the clinical popularity of
antisaccades is that they are difficult to execute without making mistakes. There is a
powerful tendency to look at the target rather than away from it (a ‘prosaccad e’ ), so that
the task requires a very strong and natural response to be inhibited, while generating
78 LATER
Figure 4.32 Antisaccade task. The protocol is as for a conventional step task, but the subject is instructed to
make a saccade in the opposite direction to that of the target.
another response that is unnatural and slow because it is only slightly related to the
stimulus and requires an additional stage of remapping to be performed. As a result,
even ‘normal’ people make many mistakes, and a wide variety of clinical conditions of
various kinds (Hutton, Joyce et al. 2002, Condy, Rivaud-Péchoux et al. 2004, Hutton and
Ettinger 2006) cause significant and obvious impairment of performance (see Appendix
2). Of note, from an experimental point of view, there has historically been great
variability between laboratories and clinics in the protocols employed for the antisaccade
task, which can of course greatly affect interpretation of results and make it difficult to
compare conclusions from different studies. A useful ‘harmonised’ protocol for antisaccades has therefore been suggested to help solve this issue, with some success to date
(Antoniades, Ettinger et al. 2013).
Despite the complexity of the task, it turns out to be relatively easy to predict both
the number of errors and the distribution of both antisaccade and prosaccade latencies
by building on the kind of economical assemblies of small numbers of LATER units
that are so successful in the case of tasks such as countermanding, W heeless, or Go/
NoGo, where similar mistakes are frequently made. The key feature in a ll these cases is
once again the Stop unit that cancels an ongoing decision process that has not yet
reached its threshold (Figure 4.33(c)), whose existence is proved by the substantial
gap between the distribution for error prosaccades and correct antisaccades
(Figure 4.33(b), though this has been denied (Cutsuridis, Smyrnis et al. 2007). This
gap between distributions is n ot explained simply by a time delay between two LATER
units initiating, and hence implies the existence of another active (Stop) decision
process. In the case of antisaccades, two other LATER units are responsible respectively
for triggering the c orrect antisaccade (an Anti unit) and the incorrect prosaccade (a
Pro unit). As can be seen in Figure 4.33(a), the appearance of the stimulus initiates
both these units. The Anti unit is triggered after a delay representing the time needed to
make the necessary spatial transformation from the actual location of the stimulus to
the intended destination on the other side. The Stop unit is triggered at the same time:
if it is fast enough, it cancels the Pro unit (Noorani and Carpenter 2013). Prior
probability can be seen to have a large effect on the distributions. Another feature of
Complex Decisions: Multiple LATER Units 79
Figure 4.33 Modelling antisaccades. (a) A model for antisaccades, using two Go units for (correct) antisaccades
and (erroneous) prosaccades. (b) Splined raw distributions from one subject (shown also as cumulative
distributions in Figure 4.30(a)), emphasising the rightward shift of the antisaccade distribution relative to both the
controls and error prosaccades. (c) Splined raw distributions for 80% prior probability and for 20%. Modified, after
Noorani and Carpenter (2013).
Figure 4.34 Distributions for the antisaccade task. (a) One subject’s responses in a control (prosaccade) task
(black), and for correct antisaccades and incorrect prosaccades. (b and c) Observed and simulated distributions
for correct and incorrect responses, with different prior probabilities (20% and 80%), which can be seen to have a
big effect, particularly on the final error rate. Note that these are incomplete distributions, showing cumulative
probability as a fraction of all the trials. Modified from Noorani and Carpenter (2013).
this task is that subjects typically correct themselves after an error: that is, they look in
the correct direction after initially lookingthewrongway.Thereactiontimesofthese
later correct responses can be easily modelled by employing a LATER Go unit that is
onlytriggeredoncompletionofanerrorbythe first Go unit (Noorani and Carpenter
2014). In this way, the LATER model accurately recapitulates all major behaviours in
the antisaccade task with remarkable simplicity, Figure 4.34.
Chapter
LATER and the Brain
5
An act which may seem simple even to banality is the dire cting of the gaze. Yet its factors
engage the roof- brain far and wide ...
Charles Sherrington, Man on his Nature (1940)
Structurally, the human brain is a mess. The problem is the way in which it has evolved:
the bulk of what fills our skulls – the telencephalon, and especially the cerebral cortex – is
relatively new, but it has not displaced the older and simpler structures seen in reptiles.
Rather, the brain has evolved through accretion (Sarnat and Netsky 1974)(Figure 5.1):
the older areas are still functional – indeed they are much the more important – but they
have come to be supplemented and regulated by the newer areas, which provide
improved overall integration and prediction through the massive bands of associational
fibres that link every part of cerebral cortex to every other. In addition, these newer and
‘higher’ areas send and receive huge nerve tracts that have elbowed the older structures
aside and distorted their shapes, making the relationships between their parts hard to
discern. The key to understanding the structur e of the brain is to think comparatively
(Kaas 2009) – trying to identify in the human brain the fundamental components seen in
simpler animals – and from a functional point of view to think hierarchically (Hughlings
Jackson 1884), recognising the different roles played by the successive layers that have
been laid down in the course of evolution.
In the case of saccades, this approach is particularly successful, as there is an obvious
correlation between the anatomical levels (of which there are essentially three: hindbrain,
midbrain, and cerebral cortex) and the intrinsic functional hierarchy that follows from
the logic of what is needed to create eye movements to look at objects of importance
Figure 5.1 Evolution by accretion. (a) Schematic diagram of the motor system of a lower vertebrate. (b) Motor
system of a typical mammal. The older system is essentially still present (grey area), but under the overall control
of newer areas, particularly the cerebral cortex. Based on Sarnat and Netsky (1974).
80
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