1Laboratory of Sensorimotor Research, National Eye Institute, Bethesda, Maryland 20892-4435; 2Dipartimento di Elettronica, Elettrotecnica ed Informatica, Università degli Studi di Trieste, 34100 Trieste, Italy; 3Laboratory of Neurophysiology and Center for Systems Engineering and Applied Mechanics, Universitè Catholique de Louvain, B-1348 Louvain-La-Neuve, Belgium
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ABSTRACT |
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Quaia, Christian, Philippe Lefèvre, and Lance M. Optican. Model of the Control of Saccades by Superior Colliculus and Cerebellum. J. Neurophysiol. 82: 999-1018, 1999. Experimental evidence indicates that the superior colliculus (SC) is important but neither necessary nor sufficient to produce accurate saccadic eye movements. Furthermore both clinical and experimental evidence points to the cerebellum as an indispensable component of the saccadic system. Accordingly, we have devised a new model of the saccadic system in which the characteristics of saccades are determined by the cooperation of two pathways, one through the SC and the other through the cerebellum. Both pathways are influenced by feedback information: the feedback determines the decay of activity for collicular neurons and the timing of the activation for cerebellar neurons. We have modeled three types of cells (burst, buildup, and fixation neurons) found in the intermediate layers of the superior colliculus. We propose that, from the point of view of motor execution, the burst neurons and the buildup neurons are not functionally distinct with both providing a directional drive to the brain stem circuitry. The fixation neurons determine the onset of the saccade by disfacilitating the omnipause neurons in the brain stem. Excluding noise-related variations, the ratio of the horizontal to the vertical components of the collicular drive is fixed throughout the saccade (i.e., its direction is fixed); the duration of the drive is such that it always would produce hypermetric movements. The cerebellum plays three roles: first, it provides an additional directional drive, which improves the acceleration of the eyes; second, it keeps track of the progress of the saccade toward the target; and third, it ends the saccade by choking off the collicular drive. The drive provided by the cerebellum can be adjusted in direction to exert a directional control over the saccadic trajectory. We propose here a control mechanism that incorporates a spatial displacement integrator in the cerebellum; under such conditions, we show that a partial directional control arises automatically. Our scheme preserves the advantages of several previous models of the saccadic system (e.g., the lack of a spatial-to-temporal transformation between the SC and the brain stem; the use of efference copy feedback to control the saccade), without incurring many of their drawbacks, and it accounts for a large amount of experimental data.
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INTRODUCTION |
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The saccadic system (i.e., the neural system that controls the rapid eye movements called saccades) has attracted the attention of many investigators during the last 40 years. Thanks to the combined efforts of so many researchers, a great deal of data are now available about the pattern of neural activity, the anatomy of functional connections, and the effects of lesions and electrical stimulation in several brain areas involved in controlling saccades. The availability of such a large database and the relative simplicity of the mechanical system to be controlled (the eye plant), has prompted models of the saccadic system to spring up like mushrooms on a damp forest floor.
In 1975, a milestone in the history of saccadic modeling, the Robinson
model, was published (Robinson 1975; Zee et al.
1976
). The central idea of that model, inherited by almost all
subsequent models of the saccadic system, was that saccades are
controlled by a local feedback loop, which in Robinson's model was
used to compare the desired position of the eyes with an internal
estimate of their actual position, thus producing an estimate of the
instantaneous (or dynamic) motor error. This model, as well as others
derived from it, was mainly conceptual, and many of its building blocks were not closely associated with anatomic structures. However, the
growth of anatomic and physiological knowledge, due to the large number
of experiments carried out after 1975 (largely prompted by the many
predictions of Robinson's model), impelled modelers to identify the
different parts of their models with specific regions of the brain.
Why a new model of the saccadic system?
Although the concept that several brain structures cooperate to
produce fast and accurate saccadic eye movements has long been widely
accepted, models necessarily concentrate on a restricted subset of
these structures. Initially models included only the brain stem
circuitry, but soon the great amount of data available about the
superior colliculus (SC) made it essential to find a role for this
midbrain structure. Accordingly, models focused on the role played by
the SC in controlling saccades and in determining the firing pattern
observed in brain stem neurons. However, during the last 10 years, new
experimental evidence has induced modelers to attribute an increasing
importance to the SC. This trend has lead to the development of a
fairly large family of models that impute to the SC a dominant role in
determining saccade metrics, and that thus could be dubbed
"colliculocentric" (Arai et al. 1994;
Droulez and Berthoz 1988
; Lefèvre and
Galiana 1992
; Optican 1994
; Van Opstal
and Kappen 1993
; Waitzman et al. 1991
).
One of the major problems with colliculocentric models is that they
have difficulties in explaining why lesions of the SC do not result in
large and enduring deficits. In particular, it is well known
(Schiller et al. 1980) that collicular ablations impair
the ability to make saccades only for a brief time. Furthermore even in
the acute phase of a collicular lesion, the trajectory and speed of
saccades can be affected without a striking loss of accuracy
(Aizawa and Wurtz 1998
; Quaia et al.
1998a
). Conversely, it has been shown that cerebellar lesions
(e.g., Optican and Robinson 1980
) induce permanent
deficits, affecting dramatically the accuracy and consistency of
saccades. Thus we feel that a model is needed that gives less import to
the SC and gives more relevance to the role of the cerebellum in
controlling saccades.
What is the role of the cerebellum in controlling saccades?
For decades, the role attributed to the cerebellum by the few
models of the saccadic system that considered it (e.g., Dean et
al. 1994; Grossberg and Kuperstein 1989
;
Optican 1986
; Optican and Miles 1985
) has
been to compensate for alterations of the oculomotor plant due to age
or injury and to adjust the saccadic command as a function of the
orbital position, compensating for plant nonlinearities. Such an
approach was justified on the basis that cerebellar lesions impair the
ability of the system to compensate for changes in the oculomotor plant
(Optican and Robinson 1980
) and induce saccadic
dysmetria (e.g., Optican and Robinson 1980
; Ritchie 1976
; Robinson et al. 1993
;
Sato and Noda 1992b
; Takagi et al. 1998
),
often as a function of orbital position. In all those schemes, the
assumption was made (implicitly or explicitly) that the extracerebellar
pathway generates, using a feedback loop controller, a command that is
a fixed function of the desired displacement of the eyes; that command
then is supplemented by a fixed (but adaptable over the long term)
command produced by the cerebellum. Thus in those schemes the
extracerebellar pathway guarantees the consistency of saccades, whereas
the cerebellum is responsible for their accuracy. The major failure of
this scheme is that it does not account for one of the most striking
effects of cerebellar lesions: the increased variability of saccades. In fact, after cerebellar impairment, saccades not only loose their
characteristic accuracy, becoming dysmetric (hypermetric or hypometric
depending on the cerebellar areas affected by the lesion), but they
also become subject to a conspicuous trial-to-trial variability,
affecting both amplitude and direction (e.g., Robinson 1995
; Robinson et al. 1993
; Takagi et al.
1998
).
This last observation, which has been reported after both permanent and temporary lesions, clearly is inconsistent with the cerebellar output being simply an adaptive function of the starting orbital position and the desired displacement of the eyes. Accordingly, we propose that the cerebellar contribution is carefully tailored during each saccade to compensate for both the characteristics of the oculomotor plant and the variability present in the rest of the saccadic system during the preparation and execution of the movement. In our model the cerebellar output is tailored in flight, because it is part of a feedback loop, functionally similar to that proposed by Robinson as the core component of the saccadic system. Thus in our scheme the cerebellum is responsible for both the accuracy and the consistency of saccades. The increased variability observed after cerebellar lesions is simply due to the unmasking of variability inherently present in the rest of the saccadic system. Unmasking occurs because the mechanism (i.e., the feedback loop) that normally compensates (at least partially) for the variability is itself impaired. Previous models did not include the cerebellum in the feedback path and thus could not account for the increased variability.
We will show here how the presence of two separate pathways, one
through the superior colliculus and the other through the cerebellum,
can account for many of the properties of the saccadic system and for a
great deal of anatomic and physiological data as well as for the
effects of lesions and electrical stimulation. In another paper
(Lefèvre et al. 1998), we presented a distributed implementation of the model described here. In that paper, we used
simulations to demonstrate that this model 1) produces
normal saccades that lie on the so-called main sequence (Bahill
et al. 1975
), 2) guarantees the accuracy of saccades
regardless of their speed, 3) replicates the patterns of
activation observed in collicular burst, buildup, and fixation neurons
as well as in fastigial oculomotor region (FOR) neurons, 4)
exerts a partial trajectory control, and 5) replicates the
effects of sustained electrical stimulation of the SC (i.e., it
generates staircases of saccades). The decision to present the
distributed implementation of the model as a separate paper was
motivated by our desire to focus here on the neurophysiological basis
of the model in a paper of reasonable length. Nonetheless, we will
present here some additional simulations of that model, mainly to show
how it can account for the effects of collicular and cerebellar
lesions. We also will discuss the implications and the advantages that
this organization has for controlling eye movements, as well as its
limits and possible extensions. Finally particular care will be devoted
to illustrating the predictions of the model and describing
experimental tests that could corroborate or refute it.
Earlier accounts of this model appeared in abstract form
(Lefèvre et al. 1996; Optican et al.
1996
; Quaia et al. 1996
).
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BACKGROUND |
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To justify our choices in attributing roles to the large number of cell types and anatomic interconnections that we are modeling, we now briefly describe a subset of the relevant literature, pointing out inconsistencies in the data, some of the previous modeling studies, and alternative interpretations. Because this analysis is not a complete review of the pertinent literature, we will refer to existing reviews for all the topics on which there is general agreement, concentrating our efforts on the most controversial or least explored subjects.
Intermediate layers of the SC
Since the early 1970s, single-unit recordings (Schiller and
Stryker 1972; Wurtz and Goldberg 1971
, 1972
) and
electrical stimulation experiments (Robinson 1972
;
Schiller and Stryker 1972
) indicated that the
intermediate layers of the SC must play an important role in producing
saccades. Cells in the SC (from now on we always refer implicitly to
the intermediate layers of the SC) are characterized by fairly large
movement fields (i.e., the range of movements associated with
activation of a neuron) (Sparks et al. 1976
), which are
organized topographically (i.e., cells close together have similar
movement fields). Neurons that discharge in correspondence with small
saccades are located rostrally, whereas large movements are encoded in
more caudal sites. Accordingly, electrical stimulation at rostral sites
results in small saccades, whereas at more caudal sites larger saccades
are evoked. These results indicate that the saccadic (or target) vector
is spatially, and not temporally, encoded on the SC; movements toward
targets in the left visual hemifield are encoded in the right SC and
vice-versa (for a review, see Guitton 1991
;
Sparks and Hartwich-Young 1989
; Wurtz
1996
).
Recently saccade-related neurons in the SC have been divided into three
classes according to their pattern of activity and location: burst,
buildup, and fixation neurons (Munoz and Wurtz 1992, 1993a
,
1995a
; Wurtz and Optican 1994
). The burst
neurons, as classified by Munoz and Wurtz (1995a)
, are
characterized by a brisk discharge synchronized with saccade onset,
have a closed movement field (i.e., they discharge only for saccades
around an optimal vector), and are probably the same cells described by
Sparks and colleagues as saccade-related burst neurons (SRBNs) (Sparks 1978
; Sparks and Mays 1980
).
Fixation neurons, located in the rostral pole of the SC, behave in an
opposite manner, i.e., they discharge during active fixation and pause
during saccades in any direction (except sometimes they do not pause,
or even burst, for small, contraversive saccades). These cells pause
immediately before the onset of a saccade and resume firing at the time
of saccade termination (Munoz and Wurtz 1993a
). The
third class of cells is represented by the so-called buildup neurons
(located among and just below the burst neurons), which are
characterized by a small buildup of activity preceding saccades (hence
their name) and have an open movement field (i.e., they discharge,
albeit with different intensities, for all saccades in one direction larger than a certain amplitude). Some, but not all, buildup cells are
characterized by a burst occurring at saccade onset, similar to that of
the burst cells. In the majority of buildup cells, this burst component
has a closed movement field, similar to that of the burst neurons (see
Munoz and Wurtz 1995a
, their Figs. 7B and 8).
One striking characteristic of the buildup neurons is that some of the
activity (but not the burst component) in the buildup layer seems to
spread rostrally across the SC during a saccade (Munoz and Wurtz
1995b
). This observation, based on the analysis of the time
course of cells' discharge during saccades of different amplitude, is
reminiscent of the finding that in the cat the locus of collicular
activation appears to move rostrally during a saccade (Munoz et
al. 1991a
), possibly encoding instantaneous gaze error
spatially (Guitton et al. 1993
; Munoz et al.
1991b
).
Role of the SC in current models of the saccadic system
The function classically attributed to the SC is to provide the
desired displacement signal to the brain stem circuitry (e.g., Grossberg and Kuperstein 1989; Scudder
1988
; Tweed and Vilis 1990
). Thus in these
schemes, the SC is outside the local feedback loop that has been
postulated to control saccades. In many of these models, the collicular
output is processed by a spatial-to-temporal transformation (STT, a
process or mechanism used to transform information from a spatial
encoding to a temporal encoding), which converts the location of the
activated locus on the collicular map into a temporal signal encoding
the desired displacement of the eyes.
Recently the finding that there is a fairly good correlation between
the level of activity of some collicular neurons and the residual motor
error prompted the development of a model (Waitzman et al.
1991) in which the burst neurons encode motor error with their
temporal discharge. In this case, as well as in similar models
(Arai et al. 1994
; Van Opstal and Kappen
1993
), the SC becomes part of the local feedback loop. One of
the major advantages of these schemes is that they do not require an
STT because the information that is encoded spatially on the SC (i.e.,
the desired displacement) is never converted into a temporal code and
the dynamic motor error is encoded temporally in the brain stem as well
as in the SC. The lack of an STT, which is a feature of several other
models as well as the model presented here (see following text), is
very important, because it simplifies considerably the connectivity
from the SC to the brain stem (Quaia and Optican 1997
).
Unfortunately there are some major problems with the scheme proposed by
Waitzman and colleagues: first of all, because it posits that only the
level of collicular activation, but not its spatial distribution, is
under feedback control, it cannot account for the purposeful curvature
of saccades [which is such that when the eyes are not headed in the
correct direction they are brought back toward the target
(Becker and Jürgens 1990; Erkelens and Sloot 1995
; Erkelens and Vogels 1995
). This
behavior is particularly prominent after collicular reversible
inactivation (Aizawa and Wurtz 1998
)]. Another problem
with this scheme is that it does not explain why sustained electrical
stimulation of the colliculus produces movements the amplitude of which
is a function of the rostrocaudal position of the electrode on the SC
map (Paré et al. 1994
; Robinson
1972
; Stanford et al. 1996
).
Because of these problems, we think it is unlikely that the collicular
burst neurons are part of a feedback loop used to tightly control
saccade amplitude. Nonetheless we think that the correlation between
burst neuron discharge and dynamic motor error is not just an
epiphenomenon. In fact, when saccades are interrupted in midflight by
electrical stimulation of the region containing omnipause neurons
(OPNs), the burst neurons' activity goes temporarily to zero
(supposedly because of antidromic stimulation of collicular fixation
neurons) and then resumes a level of activity that is again compatible
with the encoding of dynamic motor error (Keller and Edelman
1994). This last finding makes the hypothesis that the burst
neurons' discharge simply is preprogrammed very unlikely.
The peculiar characteristics of the buildup neurons' discharge, and
particularly the rostral spread of activity during a saccade, makes it
tempting to ascribe to this class of neurons a distinct function (e.g.,
Wurtz and Optican 1994). In particular, it has been
proposed (Optican 1994
) that the displacement of the
center of activity on the buildup layer could represent an internal
estimate of the progress of the saccade toward the target (i.e.,
functionally represent the output of a displacement integrator). This
role for the spread of activity is similar to the role attributed to the SC by models based on cat data (Droulez and Berthoz
1988
; Lefèvre and Galiana 1992
).
Unfortunately, a close inspection of the pattern of activity of monkey
buildup neurons reveals that an interpretation of the spread of
activity as functionally important in controlling the movement is
problematic. For example, to have a significant effect, the change of
spatial distribution of activity during a saccade should be quite
dramatic. However, the activity that spreads across the buildup layer
during a saccade is only a small fraction of the activity that is
produced at the site corresponding to the target (often characterized
by a burst, see preceding text). Thus the center of gravity of the
activated area in the buildup layer does not change much during the
movement (Anderson et al. 1998). One could argue that
the spread of activity over the SC map could have an effect by inducing
a timely reactivation of the fixation neurons, contributing to stopping
the movement. However, under this hypothesis, lesions of the rostral
pole of the colliculus are expected to induce dysmetria (in particular
hypermetria), whereas such lesions do not seem to affect saccade
amplitude (Munoz and Wurtz 1993b
). Thus even though it
is certainly possible that the reactivation of the fixation zone plays
a role in stabilizing the system, we think that it is unwarranted to
attribute to it a dominant role in the determination of saccade
amplitude. Finally it should be noted that this spread of activity
begins well before saccade onset (e.g., during a 50° saccade the 3°
buildup cell gets activated between 100 and 50 ms before saccade onset
and reaches its maximal activation
20 ms before saccade onset)
(Munoz and Wurtz 1995b
, Fig. 3). This observation makes
the hypothesis that the spread is controlled by feedback information
tightly related to the movement pretty unlikely even though it does not rule out less tight feedback schemes.
One final problem common to all colliculocentric models is that they
cannot easily account for some recent findings that suggest a
dissociation between saccade metrics and the collicular locus activated. For example, it has been shown that the collicular movement
fields are different when comparing visually guided movements with
saccades to remembered targets (Stanford and Sparks
1994). Analogous results have been obtained using the averaging
saccade task (Edelman and Keller 1998
), after adaptation
induced with the double step paradigm (Frens and Van Opstal
1997
; Goldberg et al. 1993
), and when saccades
to moving targets are considered (Keller et al. 1996
).
In all these cases, the collicular locus activated appears to be a
function of the location of the target and not of the movement evoked.
As will become clear later, these results, which challenge the various
colliculocentric models, are perfectly compatible with our model; in
fact, in our scheme the actual displacement of the eyes is determined
by the cerebellum, which decides when to stop the movement.
Cerebellum
A great deal of evidence points toward lobuli VIc and VII of the
cerebellar vermis as being involved in the control of saccadic eye
movements. First of all, only very small currents are needed to evoke
saccades from this region (Noda and Fujikado 1987),
whereas much higher currents are needed to evoke saccades from nearby lobuli (Keller et al. 1983
; Ron and Robinson
1973
). Second, ablations of this area result in dysmetric
movements (Ritchie 1976
; Takagi et al.
1998
). Finally, neurons in this area present saccade-related activity (Helmchen and Buttner 1995
; Ohtsuka and
Noda 1995
; Sato and Noda 1992a
), whereas
activity in neurons belonging to other vermal lobuli is not modulated
during saccades (Sato and Noda 1992a
). Unfortunately,
there is not much agreement regarding the pattern of saccade-related
activity of these neurons. Whereas Ohtsuka and Noda
(1995)
reported that neurons in the oculomotor vermis produce
an early burst for ipsilateral saccades and a late burst for
contralateral movements, Helmchen and Büttner
(1995)
reported that the preferred direction (i.e., the
direction associated with the early burst) is ipsilateral for half the
cells and contralateral for the other half.
In turn the oculomotor vermis projects to an ellipsoidal region in the
caudal fastigial nucleus (Yamada and Noda 1987), the so-called FOR. These projections are strictly ipsilateral and topographically organized (Carpenter and Batton 1982
;
Courville and Diakiw 1976
; Noda et al.
1990
). Because the vermis does not project directly outside the
cerebellum, the signals present in the FOR determine the effect of the
cerebellar vermis on saccades. Consequently any model that is concerned
with the control of saccades by the cerebellum has to give strong
import to the saccade-related discharge of the FOR neurons. Fortunately
there is general agreement on the pattern of discharge of these neurons
(Fuchs et al. 1993
; Helmchen et al. 1994
;
Ohtsuka and Noda 1990
, 1991
). They produce an early
burst of activity for movements in one direction (preferred direction)
and a late burst, time-locked with the end of the movement, for
saccades in the opposite direction. The preferred direction always has
a contralateral horizontal component.
Model
In this section, we describe our model in detail. We first outline the structure of the model to provide a general idea of the role that the various areas play in the overall picture. To avoid any misunderstanding, we stress that all the connections and patterns of activity described hereafter refer to our model, and we will indicate, by means of citations to the relevant literature, when they are supported by experimental findings. Similarly, when we make assertions relative to the role played by brain areas in controlling saccades, we refer to our model of the saccadic system not to the saccadic system itself, even when this is not explicitly stated.
Overall structure of the model
In designing this model, we gave primary significance to the patterns of saccade-related activity recorded from single cells in the SC, in the cerebellum (especially the fastigial nuclei, which contain the cerebellar neurons that project to the brain stem saccadic circuitry), and in the brain stem. Using many of the known anatomic connections between these different areas, we have created a model in which the metric and dynamic characteristics of saccades are determined by the cooperation of two parallel pathways (Fig. 1). The first pathway (collicular pathway) involves the cerebral cortex (which provides the target location in retinotopic coordinates), the SC, the premotor medium-lead burst neurons (MLBNs) [which are divided into excitatory (EBN) and inhibitory (IBN) burst neurons] and the motoneurons (MNs) that innervate the extraocular muscles. The core structure of this pathway is the SC, which plays two roles: first, it determines the onset of the saccade, by releasing the excitation provided to the OPNs, which tonically inhibit (gate) the MLBNs in between saccades. Second, it drives the eyes toward the target. Thus this pathway provides a go signal and what we call a directional drive.
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The second pathway (cerebellar pathway) involves the cerebral cortex, the SC (which just relays the target information), the cerebellum (vermis lobuli VIc and VII and FOR), MLBNs, and MNs. The cerebellum, which is the central structure of this second pathway, plays three roles: 1) it provides an additional directional drive, 2) it monitors the progress of the saccade toward the target (acting as a displacement integrator, DI), adjusting its output to compensate for directional errors, and, when the eyes approach the target, and 3) it chokes off the drive provided by these two pathways to the motoneurons, ending the saccade. Thus this pathway also provides two signals to the brain stem circuitry: a directional drive and a choke signal.
As will become clear further on, there is a fundamental difference in our model between the collicular and the cerebellar drives: whereas the first cannot change direction during a saccade (i.e., the ratio between the horizontal and vertical components of the collicular drive is fixed throughout the movement), the second is adjustable in direction.
Brain stem circuitry
The brain stem network that we use in our model is supported by a
great deal of experimental evidence and is essentially identical to
that used in several other models. Thus here we just briefly describe
its fundamental aspects. Several reviews describing the evidence for
the connections we use have been published (e.g., Büttner-Ennever and Büttner 1988;
Fuchs et al. 1985
; Hepp et al. 1989
;
Moschovakis et al. 1991
).
The basic structure of the horizontal channel of the brain stem
circuitry implemented in our model is represented in Fig. 2. The muscles innervated to move the
eyes in the horizontal plane (i.e., to rotate the eye ball around the
vertical axis) are the lateral recti (LR), which rotate the left eye to
the left and the right eye to the right (i.e., they rotate the eyes
temporally), and the medial recti (MR), which exert opposite effects
(i.e., they rotate the eyes nasally). When a conjugate movement of the eyes is produced, the LR of one eye and the MR of the other eye act as
agonists (i.e., their tension is increased), whereas the other two
muscles act as antagonists (i.e., their tension is decreased). The
innervation to the lateral recti is provided by motoneurons (MN)
located in the ipsilateral abducens (VI) nucleus; intermixed with these
motoneurons are interneurons (IN), which presumably receive the same
inputs and project to the motoneurons of the contralateral MR, located
in the contralateral oculomotor (III) nucleus. We modeled the eye plant
as a second-order system, with time constants of 0.15 and 0.005 s
(Keller and Robinson 1972; Robinson
1973
), and because the tension exerted by a pair of muscles is
a linear function of the difference in innervation between the agonist
and the antagonist (Haustein 1989
), we lumped the two
muscles into one equivalent muscle.
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Each side of the brain stem contains two populations of MLBNs, one
(EBNs) that excites the ipsilateral MNs and INs and another (IBNs) that
inhibits contralateral MNs and INs. These populations of MLBNs are
inhibited by OPNs (located across the midline), which fire tonically
during periods of fixation and pause during saccades, thus acting as a
gate. In turn, MLBNs inhibit the OPNs, helping to keep them inactive
during saccades. Because no direct projections from the IBNs to the
OPNs have been found (Büttner-Ennever and Büttner
1988), we assume that the EBNs inhibit the OPNs through an interneuron.
The difference between the signal carried by the ipsilateral EBNs and that carried by the contralateral IBNs determines the velocity of the horizontal component of the movement. This velocity signal then is integrated by neurons located in the nucleus prepositus hypoglossi and in the vestibular nuclei (for clarity this pathway has been omitted in Fig. 2); the output of this neural integrator, which is fed to the motoneurons, is used to hold the eyes in an eccentric position at the end of the saccade.
The scheme for the vertical channel is organized similarly (e.g.,
Crawford and Vilis 1992), even though two pairs of
muscles for each eye (vertical recti and obliques) are activated during vertical movements. For the sake of simplicity and because we consider
only movements in Listing's plane, we modeled the vertical channel in
the same way as the horizontal channel (which is reasonable under the
hypothesis described in Quaia and Optican 1998
).
Superior colliculus
INPUTS TO BURST NEURONS.
We have modeled four inputs to the collicular burst neurons: the first
input comes from the frontal eye fields (FEF), and it encodes the
location of the target for the impending saccade in retinotopic
coordinates (saccadic command) by providing a
topographically organized excitatory input to the SC. Each input fiber
discharges maximally for one saccade vector; its discharge decreases
following a Gaussian function as the direction of the movement deviates from the preferred vector and following a log-Gaussian function as the
amplitude of the movement deviates from the preferred vector. This is
in agreement with recordings from movement cells in FEF (Bruce
and Goldberg 1985). The width of the FEF movement fields is
larger than that of collicular burst neurons, and we assume that they
are narrowed by intracollicular on-center-off-surround connections
(Grossberg 1973
, 1988
), which determine the size of the
burst neurons' movement fields.
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ACTIVITY OF SC BURST NEURONS.
We modeled the output of the burst neurons as a burst of activity that
starts just before the beginning of the saccade and is almost over by
the end of the saccade (Fig. 3D). Thus in our model, the
burst neurons are only partially clipped, i.e., the neurons are still
active at the end of the movement, even though at a fairly low level
(~20% of maximum activation). The choice of keeping this residual
activity at the end of the movement is due to the experimental finding
that, even though some burst cells are clipped (i.e., the activity is
over by saccade end), most burst cells (probably as many as 70%) are
only partially clipped (Munoz and Wurtz 1995a;
Waitzman et al. 1991
). The presence of unclipped
activity is not a problem because, as stated above, in our model the
collicular output does not encode dynamic motor error, which has to be
zero at the end of the saccade. In fact, later on it will become clear
that the presence of unclipped activity is an indispensable feature of
the model.
OUTPUTS OF BURST NEURONS.
In our model, the burst cells excite the contralateral MLBNs (both EBNs
and IBNs) (see Chimoto et al. 1996), with weights that
are a function of the position of the cell on the collicular map
(caudal sites have stronger projections than rostral sites), as
originally proposed by Edwards and Henkel (1978)
. Cells
in the lateral and medial part of the SC project preferentially to vertical MLBNs, whereas cells along the central meridian project preferentially to horizontal MLBNs (see Grantyn et al.
1997
). However, the input provided by the SC to the MLBNs is a
directional drive signal and no spatial-to-temporal transformation (see
Role of the SC in current models of the saccadic system) is
performed. Thus the input provided to the MLBNs by the SC can be the
same even if two different collicular loci are activated at different levels (e.g., a 20° locus weakly activated compared with a 10° locus strongly activated). In contrast, by definition the output of an
STT always must be different when different loci are activated regardless of the level of activity.
INPUTS TO BUILDUP NEURONS.
In our model, the second cortical input to the SC, which we call the
saccadic plan input and briefly introduced in the previous section, is the source of the early activation and of the rostral spread of activity in buildup neurons. We call this signal the saccadic
plan because it indicates the presence and location of an area of
interest in the visual scene. Any such location is a potential target
for a saccade, but a saccade to it is not necessarily generated. In our
model, this signal starts exciting buildup neurons soon after the
target has been designated and is characterized by a perisaccadic
spread (i.e., a particular input fiber is activated later for larger
saccades in one direction). Recordings from lateral intraparietal
cortex (LIP) neurons projecting to the SC (Paré and Wurtz
1997) revealed the presence of a signal that could be compatible with these requirements. Actually, because of the breadth of
the cortical movement fields, there is no need for the input to spread:
all that is needed is a step-like remapping of the target from its
initial eccentric position to a foveal position (Fig.
4, left).
|
|
ACTIVITY OF THE BUILDUP NEURONS. In Fig. 5 we show how, in our scheme, the spatial distribution of neuronal activity across the SC changes before and during the movement. Here the case of a horizontal saccade having a duration of ~60 ms is illustrated. As already pointed out, only the burst neurons around the optimal vector are activated during a saccade (Fig. 5, left). The activation starts just before, and it peaks around, saccade onset (see also Fig. 3D); no change in the spatial distribution of the activity occurs. The fixation neurons (Fig. 5, right, rostral neurons) are inactive during the saccade and are otherwise firing tonically (see also Fig. 3B). Buildup neurons are instead characterized by the superposition of the burst and of the input described in Fig. 4, which produces a pattern of activation that resembles a rostrally directed spread of activity. It is important to note that because, in our model, feedback information controls the strength of the burst input but not the spread (or remapping) of activity toward the rostral pole, the buildup neurons cannot contribute to the goal-directed curvature of saccades (i.e., even if there is a change in spatial distribution, it does not depend on the trajectory of the eyes and thus is not part of a trajectory control mechanism).
OUTPUTS OF THE BUILDUP NEURONS. In our scheme, the buildup neurons project to the same recipients as the burst neurons. Thus they provide an excitatory input to MLBNs (directional drive), an inhibitory input to the collicular fixation neurons, and topographically organized inputs to NRTP and pontine nuclei. Thus we propose that, as far as movement execution is concerned, buildup neurons are not functionally different from burst neurons.
FIXATION NEURONS.
In our model, the fixation neurons receive five inputs: an excitatory
visual input from targets on the fovea, an excitatory input that is
related to the desire to keep the eyes steady (active fixation), an
excitatory input from the caudal fastigial nucleus, an inhibitory input
from the ipsilateral caudal SC (burst and buildup neurons), and an
excitatory input from the contralateral rostral pole of the SC. Several
investigators have provided experimental evidence that supports this
scheme (e.g., May et al. 1990; Munoz and Istvan
1998
; Munoz and Wurtz 1993a
).
DIFFERENCE BETWEEN BURST AND BUILDUP NEURONS.
Physiological recordings indicate that the early activity observed in
collicular neurons can vary, in the same cell, from a significant level
to essentially zero activity, depending on the experimental conditions,
such as likelihood of appearance of a target in the response field or
initial eye position (Basso and Wurtz 1997;
Dorris et al. 1997
; Paré and Munoz
1996
). Thus if, as we propose here, this same low level
component confers to the buildup neurons their open-movement field
characteristics, the same neuron could be classified as burst or
buildup depending on the conditions under which it is observed.
|
INHIBITORY CONNECTIONS IN OUR MODEL OF THE SC.
It must be noted (see Fig. 6) that in our scheme the inhibition
from the fixation neurons acts on the saccadic command input at the
dendritic level, shunting that signal, and not (or only weakly) on the
soma of the burst/buildup neurons. This arrangement allows our buildup
neurons to be active long before the saccade (when the fixation neurons
are active) and to have a burst closely synchronized with the saccade.
Such connections have not been shown experimentally, but under these
conditions, it should be possible to find a frequency of stimulation in
the fixation zone that would prevent the occurrence of the burst but
not the early activity in the buildup cells. Lower frequencies would
not be sufficient to prevent the occurrence of the burst, and higher frequencies also might inhibit the early activity if a fraction of the
inhibition acts at the level of the soma. In fact, such a finding has
been reported recently (Munoz and Istvan 1998).
Cerebellum
INPUTS.
To keep track of how far the eyes have turned since the beginning of
the saccade, the cerebellum needs accurate information about eye
movements. In our model, the cerebellum obtains this information by
monitoring the output of the MLBNs (i.e., velocity efference copy). In
support of this hypothesis, bilateral projections from regions
containing MLBNs to the cerebellum have been reported (Noda et
al. 1990; Thielert and Thier 1993
; Yamada
and Noda 1987
), and MLBN-like activity has been recorded in
mossy fibers (Kase et al. 1980
; Ohtsuka and Noda
1992
). However, in one study no direct projections from the
MLBNs to the cerebellum have been reported (Strassman et al.
1986a
,b
), thus an alternative would be to extract the velocity
signal from the burst-tonic signal provided (presumably by the nucleus
prepositus hypoglossi) to the cerebellum, which also has been
documented (Kase et al. 1980
).
ACTIVITY.
The discharge characteristics of fastigial neurons have played a
significant role in guiding our modeling effort. In our model, each
fastigial neuron produces an early burst for saccades in one direction
(having a contralateral horizontal component) and a late burst for
saccades in the opposite direction. The early burst occurring in the
contralateral FOR provides, through crossing connections from the FOR
to the MLBNs, an additional directional drive. Thus the sum of the FOR
and the collicular inputs to MLBNs determines the initial direction and
speed of the saccade (Fig. 7). However,
because of the relatively mild effects on initial acceleration of
muscimol injections in the FOR (Robinson et al. 1993),
we posit that, at the very beginning of the saccade, the cerebellar
contribution to the overall directional drive is not very intense
(~20-30% of the total drive). Accordingly, in our model the
collicular pathway is stronger than the cerebellar pathway.
|
|
OUTPUTS.
As indicated in the previous section, in our model the FOR projects to
the contralateral MLBNs, stronger to the IBNs than to the EBNs.
Experimental evidence supports this hypothesis (Gonzalo-Ruiz et
al. 1988; Noda et al. 1990
).
Action of the vermis
As we already pointed out, in our scheme the desired displacement
signal is delivered to the cerebellum by connections from the NRTP,
which is characterized by a retinotopic organization (i.e., cells have
retinotopic response fields) (Crandall and Keller 1985).
So, the earliest burst on the FOR is imposed by topographic inputs from
NRTP (or from DMPN). However, in our scheme, the connections from NRTP
(or from DMPN) to the FOR need to be bilateral; this aspect, which is
supported by experimental evidence (Noda et al. 1990
),
is extremely important. In fact during small saccades, there is no time
for the ipsilateral burst to be generated by making the contralateral
burst spread across the FOR under the effect of velocity feedback. Thus
in these conditions, the ipsilateral FOR, which in our model provides
the choke, should start discharging before the onset of the saccade
(this is in agreement with experimental findings) (see Fuchs et
al. 1993
, their Fig. 1).
Another reason for having bilateral projections from the NRTP to the
FOR is related to the fact that the vermis, which in our model controls
the spread, can only disinhibit the FOR neurons. So it is conceivable
that the burst of the FOR neurons is determined by a widespread
excitatory input from the NRTP, controlled by a selective inhibition of
FOR cells by the vermis (Fig. 9). At the
beginning of the movement, the activity is localized in the contralateral FOR (Fig. 9, solid annulus), whereas by the end of the
movement the activity has spread to the other FOR (Fig. 9, dashed
annulus). The only relationship to be learned to produce accurate
saccades is the relationship between the velocity of the movement
[which is a function of the output of the MLBNs and the orbital
position of the eyes (Collins 1975)] and the speed and
direction of the spread. It also should be noted that because in our
model the SC encodes (spatially) the location of the target and not the
desired displacement, eye position information also could be used by
the cerebellum to implement the visuomotor transformation needed to
convert a target location from retinotopic coordinates into the
displacement of the eyes required to foveate it (Klier and
Crawford 1998
).
|
Simulations
As pointed out in the INTRODUCTION, in another paper
(Lefèvre et al. 1998) we presented a distributed
implementation of the model described here. Now we briefly indicate how
sensitive the model is to changes in its various parameters, and we
present some additional simulations, showing how it can account for the effects of collicular and cerebellar lesions. The simulations reported
here were performed using MATLAB/SIMULINK (The Mathworks, Natick, MA)
running on a Challenge-L computer (Silicon Graphics, Mountain View,
CA). All the details of the implementation are presented elsewhere
(Lefèvre et al. 1998
); unless the contrary is
stated explicitly, the simulations in both papers have been obtained
using the same values for the various parameters of the model.
Sensitivity of the model to changes in its parameters
As expected, our model is very sensitive to the relationship between the MLBNs' activity, which determines the speed of the eyes, and the speed of the spread of activity in the FOR. If this relationship is not precise, saccades will not be accurate. A second important factor is the mapping from NRTP/DMPN to the cerebellum. This mapping determines the area of the FOR that bursts at the beginning of the movement; the location of this area is also very important to ensure the accuracy of the movement.
On the other hand, the model's saccade accuracy turned out to be fairly insensitive to changes in the speed of the movement and thus to the weight of the connections between the SC and the MLBNs; furthermore altering the feedback inhibition signal to the SC has little effect on the metric of saccades. Similarly the weight of the connections between the FOR and the MLBNs is not very important as long as the input to the IBNs (the choke) is strong enough to overcome the collicular input to the EBNs (otherwise the movement would not stop).
Finally the OPNs deserve a special note: we have noticed that even though under normal circumstances they play essentially no role in determining the characteristics of saccades, they can become very important when abnormal conditions are considered. For example, they can have important effects after lesions or during electrical stimulation. Thus we suggest that it would be interesting to study their behavior under these conditions or, for example, to study how a lesion of the OPNs effects electrically evoked saccades.
Effects of cerebellar lesions
Lesions of the oculomotor cerebellum have a large impact on the characteristics of saccades. Because in our implementation we have focused on the role of the FOR and we have not directly addressed the issue of how the cerebellar cortex carries out its function, we will describe here simulations of lesions of the FOR. All the simulations we show refer to the effects of FOR lesions on a saccade to a target located 20° to the right of the center. In all figures the prelesion (control) saccades are indicated with a dashed line, whereas the postlesion saccades are indicated with a solid line.
It has been shown (Robinson et al. 1993) that when the
fastigial nuclei are lesioned bilaterally saccades become hypermetric regardless of their direction. Furthermore their speed is lower than
expected for saccades of their size and even lower than the speed of
normal (i.e., prelesion) saccades to the same target. To simulate these
conditions with our model, we have assumed that the effect of a lesion
of the FOR is to attenuate its output (because some of the FOR possibly
is spared). For example, when we impose an attenuation of 60%, we
obtain saccades that are hypermetric (Fig.
10A) and slower (Fig.
10B) than normal just as reported in the literature. Effects
on latency by actual lesions seem to be very inconsistent; in our
simulations, we observe a very small latency decrease due to a decrease
in the excitatory drive provided by the FOR to the collicular fixation
neurons.
|
With unilateral lesions of the FOR, it is possible to evoke a much
larger range of effects (Ohtsuka et al. 1994;
Robinson et al. 1993
). First of all, ipsilateral
saccades become hypermetric, while their velocity (at least for 20°
saccades) slightly increases. Our simulations (performed by attenuating
by 60% the output of the right FOR for a 20° rightward movement) are
in agreement with such findings (Fig. 10, C and
D). Conversely after contralateral lesions, saccades become
hypometric and slower. However, when we simulate this condition with
our model (using the same attenuation as before), we can reproduce the
slowing down,but not the hypometria (Fig. 10, E and
F). This is due to the fact that we are assuming that
altering the activity in the contralateral FOR (the one that is active
at the beginning of the movement) does not affect in any way
the functioning of the spatial integrator. Thus even though the
saccade starts slower, the choking signal supplied by the ipsilateral
FOR is delivered later and the eyes land on target. However, it should
be noted that the FOR projects to the NRTP (Noda et al.
1990
), which in turn projects to the vermis, possibly disrupting the mechanism underlying the spatial integration of the
velocity signal and inducing an early activation of the choke (in our
simulations, we only attenuated the output of the cells). To clarify
this issue, a better understanding of the NRTP-vermis interaction is needed.
Unilateral lesions of the FOR also affect vertical saccades, which
become slightly hypermetric and bend toward the side of the injection
(Robinson et al. 1993). Because of a large edge effect
(due to the need to activate both collicular maps), the current
implementation of our model is not very well suited to simulate
vertical saccades. However, because of our model's structure, the
effects of a lesion of the left FOR on an upward saccade are equivalent
to the effects of a lesion of the upper half of the FOR (see Fig. 8) on
a rightward saccade. This allows a vertical saccade to be simulated by
interchanging of horizontal and vertical in our model. The results of
such a simulation (Fig. 11) are very similar to what has been reported in the literature (see
Robinson et al. 1993
, their Fig. 2). In particular, note
that the saccade starts in the correct direction and then starts
bending away from the target. Furthermore the saccade is also slower
(not shown), as reported by Robinson and colleagues
(1993)
.
|
Another study of unilateral injections of muscimol in the fastigial
nuclei of the head-free cat (Goffart and Pelisson 1994) showed that ipsilateral saccadic deficits were compatible with a
remapping of the target rather than with a generalized hypermetria. In
contrast, contralateral saccades were hypometric, as expected. Our
model, in its present form, does not predict such results; this could
be due to the disruption of some additional mechanism (perhaps related
to the removal of the tonic level of activity that is normally present
in fastigial neurons, which we have not modeled here). Nonetheless it
should be noted that the effect of unilateral FOR lesions on vertical
saccades, which is reproduced very well by our model, would be very
difficult to explain with a theory that posits a role for the FOR in
specifying the target.
Finally we previously pointed out that when the FOR is lesioned the variability of saccades is considerably increased, both in amplitude and in direction. As pointed out in the preceding text, this increased variability is incompatible with classic models of cerebellar contribution that use only long-term adapted control signals. On the other hand, the increased variability is compatible with our model, where the cerebellum is the structure that accounts for both the accuracy and consistency of saccades. Because noise sources have not been included in this implementation of our model, we did not use simulations to demonstrate this property. However, because without a cerebellum our model of the saccadic system would simply be a feed-forward controller, the results are obvious.
Effects of collicular lesions
Even though the SC is not necessary to produce saccadic eye
movements (Schiller et al. 1980), it is well known that
its partial chemical inactivation causes, at least in the acute phase
of the lesion, changes in all saccadic parameters. Typical effects of reversible partial deactivation of the SC are increased latency, decreased peak velocity, and dysmetria of the movements (Aizawa and Wurtz 1998
; Hikosaka and Wurtz 1985
, 1986
;
Lee et al. 1988
; Quaia et al. 1998a
).
Furthermore it has been reported recently that the trajectory
(Aizawa and Wurtz 1998
) and the initial velocity and
direction (Quaia et al. 1998a
) also can be affected systematically.
We have simulated a collicular lesion by attenuating the output of a
region of the SC. We have reduced the activity of one cell by 70%, of
its 8 neighbors by 60%, and of the successive 12 neighbors by 50%
(both buildup and burst neurons were affected in the same way) with the
central cell corresponding to a 15° saccade at 45° of elevation.
Then we have looked at the effect of this lesion on a 10° and a 20°
saccade, both at 45° of elevation. In another paper (Quaia et
al. 1998a), we suggested that the effects of SC lesions on the
initial direction of saccades can be accounted for if it is assumed
that the lesion always causes a change in the horizontal drive larger
than what would be expected given the location of the lesion. To
include this assumption in our simulations, we also have reduced the
drive of the SC to the horizontal MLBNs by 30%.
When, under the above mentioned conditions, a saccade to a 20° target is simulated (Fig. 12, A and B), the eyes deviate upward and then curve back toward the target. However, the compensation is only partial so that the saccade falls short of the target. The speed (both initial and peak) of the movement is considerably lower than in the control situation, even though the amplitude of the movement is not much different. When a 10° saccade is simulated (Fig. 12, C and D), a similar pattern of curvature is observed, and again both peak and initial speed are considerably affected. However, in this case the eyes fall considerably short of the target.
|
All these characteristics are in agreement (at least qualitatively)
with the results presented by Aizawa and Wurtz (1998); however, our simulations clearly fail to show the large change in
latency which is a trademark of collicular lesions. This failure is due
principally to the fact that the cortical fixation input provided to
the collicular fixation neurons (see preceding text) is, in our current
implementation, removed abruptly and not gradually. A more gradual
removal of this input would make the timing of the saccade onset more
sensitive to the balance between the activity of the burst/buildup
neurons and that of the fixation neurons, thus allowing a much larger
spread of latencies.
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DISCUSSION |
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We have presented a model in which saccades are generated by the cooperation of two pathways, both influenced by feedback information. In this sense, our model departs from the Robinsonian scheme that has dominated saccadic modeling for the last 20 years, where the saccadic drive was generated by a single feedback loop. The main concepts that characterize our scheme are as follows: 1) the saccade ends not because the MNs run out of drive from the EBNs but because that drive is actively choked off; 2) only one part of the drive can be controlled in direction; 3) the cerebellar contribution depends on feedback information, and it is tailored carefully for each movement; 4) no classical spatial-to-temporal transformation (which would produce a temporally coded dynamic motor error) is performed; and 5) the displacement integrator is implemented in the spatial domain in the cerebellum.
Even though we have left out many other structures, both cortical and subcortical, which certainly are involved in controlling saccadic eye movement, we think that the areas we have modeled are sufficient to reproduce at least the simplest saccadic behavior. In the next few sections, we will compare the model presented here with other models recently proposed; because in previous sections we already have described at length other models of the collicular involvement in saccadic control, we will now focus on the role of the cerebellum. Finally we will indicate some experiments that could be used to test our scheme and to shed further light on the saccadic system.
Types of cerebellar models
Models of cerebellar function can be divided into two groups:
those that are inspired by theories of learning in neural networks and
those that are inspired by principles of control theory. Models of the
first group stem from the early work by Marr (1969),
Grossberg (1969)
, and Albus (1971)
; two
of the most influential theories in this group are those of Houk,
Barto, and colleagues (Barto et al. 1998
;
Berthier et al. 1993
; Houk 1989
;
Houk et al. 1996
) and of Grossberg and colleagues
(Contreras-Vidal et al. 1997
; Grossberg and
Kuperstein 1989
). On the other hand, cerebellar models inspired
by principles of control theory propose that the cerebellum functions
as a model of the controlled system and usually do not deal with
adaptation and learning in the cerebellum. Some of these models (e.g.,
Jordan and Rumelhart 1992
; Miall and Wolpert 1996
; Miall et al. 1993
) suggest that the
cerebellum computes an estimate of the effect that an outgoing motor
signal will have on the controlled plant (direct, or forward, models),
whereas others (e.g., Gomi and Kawato 1992
;
Kawato and Gomi 1992
) estimate the motor outputs needed
to generate a desired movement (inverse models).
Even though we took special care in reproducing the pattern of
activation of FOR neurons, our model is clearly more inspired by
principles of control theory than by theories of network learning. More
precisely, we think that our scheme could be regarded as a forward
model because the spatial integration process (which we hypothesize
takes place in the cerebellum) is used to predict when the eyes are
approaching the target, given the efference copy of the motor command.
However, this signal is not fed back to the main controller, and thus
it is different from classical control schemes. In this sense, it is
closer to models like the one proposed by Grossberg and
Kuperstein (1989), where the cerebellum is embedded in a side
loop. One important advantage of learning theory models is that,
especially in their most recent versions (Barto et al.
1998
; Contreras-Vidal et al. 1997
), they make
testable predictions about the pattern of activities in Purkinje cells and interneurons (especially basket cells) in the cerebellar cortex. This is certainly a most desirable feature; unfortunately at this stage, our model lacks this. However, we think that our model has
certain advantages (which will be outlined next) over existing models
that justify our decision to take another approach and to propose a
different model.
Comparison with other models of cerebellar involvement in saccadic control
Recently some models that address the role of the cerebellum in
the in-flight control of saccades have appeared; however, in only one
of those models (Houk et al. 1992, 1996
) is the
cerebellum part of the feedback loop. The theory proposed by Houk and
colleagues posits that the Purkinje cells in the cerebellar cortex are
trained to recognize particular configurations of the proprioceptive
inputs (carried by the mossy fibers), and when these patterns occur, they fire to stop an ongoing movement. Thus one of the roles that we
propose here for the cerebellum is similar to the one proposed by Houk
and colleagues (i.e., to terminate the saccade when the eyes approach
the target), even though the mechanism used by the cerebellum to
achieve this goal is very different in the two models. The
pattern-recognition mechanism proposed by Houk and colleagues works
well to control limb movement, where the delays in the system are
shorter than the duration of the movement and proprioceptive feedback
can be used to track (and even predict) the ongoing movement (Barto et al. 1998
). However, we think there are some
fundamental problems in extending their model to the control of
saccadic eye movements. First of all in Houk's model, the movement is
interrupted when a given final position, and not displacement, is
attained. Thus the cerebellar cortex should work in head coordinates;
however, it has been shown recently that saccadic adaptation, which
almost certainly is controlled by the cerebellum (Goldberg et
al. 1993
; Optican and Robinson 1980
), occurs in
oculocentric coordinates (Frens and van Opstal 1994
).
Furthermore it is known that proprioceptive feedback plays no role in
the in-flight control of saccades (Guthrie et al. 1983
);
one could argue that an internal estimate of the position of the eyes
could be used instead, but no signal encoding the position of the eyes
during saccades has been found in the mossy fibers [in our model (Fig.
9), the eye position signal is used only before the movement to
determine the displacement of the eyes required to foveate the
target]. One could overcome these problems by postulating the presence
of a displacement integrator in the brain stem, whose output then could
be fed to the cerebellum. However, to the best of our knowledge, such a
signal has not been observed in the mossy fibers. Finally in its
present form, the scheme proposed by Houk predicts a pattern of
activity for the FOR that mirrors the activity in the SC, i.e., a burst
of activity only for saccades in one direction, that is not compatible
with what is reported in the cerebellar literature. For these reasons, we think that even though Houk's scheme is consistent with data on
limb control, it is at odds with some crucial data regarding the
saccadic system.
Another theory of cerebellar function is the one proposed by Grossberg
and colleagues, both for saccadic (Grossberg and Kuperstein 1989) and limb control (Contreras-Vidal et al.
1997
). One of the major differences between Houk's and
Grossberg's models is that Grossberg proposes an extracerebellar loop
to compute the residual motor error and to generate a desired velocity
signal, which then is fed to the cerebellum. Thus the cerebellum is
part of a side loop, and it works with velocity (as opposed to
position) signals. We believe that our model has two main advantages
over the one proposed by Grossberg and colleagues: first, it does not
require a spatial-to-temporal transformation, which is part of the
extracerebellar loop in Grossberg's model. Second, our model can
account more readily for the large increase in variability observed
after cerebellar lesions.
Recently, Dean (1995) proposed a model of the saccadic
system that deals with the role played by the fastigial nuclei in
on-line control of saccades, taking particular care in reproducing the pattern of FOR activation. There are several similarities between Dean's models and ours, including the connectivity between the FOR and
the MLBNs. The role attributed by Dean to the FOR is to ensure saccadic
accuracy; because of the timing of the FOR bursts, this is achieved by
contributing to the acceleration of the eyes at the beginning of
saccades and to their deceleration at the end of the movement. This
role, which also has been proposed in other studies (Fuchs et
al. 1993
; Helmchen et al. 1994
; Noda
1991
; Robinson 1995
; Sparks and Barton
1993
), is similar to the one that we propose here, i.e., to
provide a directional drive and to choke off the collicular output at
the end of the movement. However, in our model, there are not two
distinct bursts, one in the ipsilateral and the other in the
contralateral FOR, but one single burst that spreads across the
fastigial nuclei. Accordingly the FOR does not play a role only at the
beginning and at the end of the saccade but also during the saccade,
exerting a trajectory control. Furthermore the role played in our
scheme by the late part of the burst is not just to slow the movement
but to stop it when the eyes reach the target. Importantly in our
scheme the cerebellum determines when the movement should end. In
Dean's model, the cerebellum only makes a preprogrammed contribution to a saccade the end of which is controlled by the local feedback loop
in the brain stem.
Another, fundamental, difference between Dean's model and ours is that in his scheme the brain stem circuit (extracerebellar pathway) consists of a feedback loop with a gain lower than one. Consequently, Dean's model does not predict the increased variability in saccades observed after cerebellar lesions because it is the brain stem that guarantees the consistency of saccades. In contrast, in our model the loop is closed through the cerebellum, which is the structure that guarantees both the consistency and accuracy of saccades. Nonetheless, the two schemes would be in good agreement if the feedback loop proposed by Dean was affected by large and unpredictable changes in gain due to an unreliable feedback integrator. However, it is not clear whether the presence of an unreliable integrator would affect the accuracy of the saccades produced by Dean's scheme even when the cerebellum is working properly.
Predictions and experimental tests
FOR NEURONS' ACTIVITY. We have conjectured that the FOR is organized topographically and that a spatial integration is performed in the vermis and represented on the fastigial map. We have shown that all the input/output connections needed are in place; furthermore this hypothesis makes some testable predictions about the pattern of activity in FOR neurons.
First, the burst should occur later and later for larger and larger ipsilateral saccades. Second, for contralateral saccades, the timing of the burst should depend on both the saccadic vector and the location of the cell on the fastigial map. Third, there should be cells that burst only for contralateral saccades larger than a given amplitude. Fourth, adaptive alteration of saccadic size should alter the time of occurrence of the ipsilateral burst, which should remain time-locked to the end of the movement. Finally, in analogy with what has been done in the SC (Keller and Edelman 1994MLBN ACTIVITY.
The discharge and connectivity of FOR neurons raise some expectations
regarding the activity present in MLBNs during saccades. More
specifically, the late burst present in the ipsilateral FOR should
induce, toward the end of a saccade, a discharge in the contralateral
EBNs and IBNs. In fact evidence for a late burst in at least some EBNs
for contralateral movements has been reported (Keller
1974; Strassman et al. 1986a
; Van
Gisbergen et al. 1981
). This burst is pretty weak, but that is
in line with our prediction: we do not expect these neurons to
discharge >200 spikes/s, and for no more than ~20 ms [because of
the reactivation of the OPNs (Everling et al. 1998
;
Fuchs et al. 1991
; Paré and Guitton
1998
)]. Thus only three or four spikes are expected.
Conclusions
We have presented a model that, using two parallel pathways, preserves the advantages of many previous models (e.g., the lack of a spatial-to-temporal transformation between the SC and the brain stem, and thus a much simplified connectivity) without incurring many of their drawbacks.
In our model, the SC plays a lesser role than in many recent models; we
propose that the SC helps determine the target and provides a
directional drive that moves the eyes approximately in the right
direction. It is up to the cerebellum to guarantee that the overall
drive is appropriate to accurately foveate the target. Moreover, we
propose that the burst and buildup neurons are, as far as movement
execution is concerned, functionally indistinguishable [but it is
possible that they exert different roles for other aspects of eye
movements, like target selection (Optican 1994), learning of consistent maps for different modalities (Grossberg et al. 1997
) and determination of reaction time (Dorris
et al. 1997
)].
One of the most important innovations of the model that we presented here is that in this scheme the cerebellum carries out the function that in previous models was ascribed to the displacement integrator and feedback summing junction, i.e., monitoring the dynamic motor error. Here the cerebellum plays a pivotal role in guaranteeing both the accuracy and the consistency of saccades. This role is accomplished by choking off the collicular drive at the appropriate time and by compensating for directional errors by providing an appropriate directional drive to the brain stem circuitry. Thus the signal provided by the cerebellum is subject not only to long-term adaptation, as often suggested, but is adjusted during each saccade to compensate for the instantaneous behavior of the rest of the system.
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ACKNOWLEDGMENTS |
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We thank Dr. Martin Paré for many clarifying discussions and for helpful comments about the manuscript. We also thank Drs. Paul Dean, David A. Robinson, and R. John Leigh and three anonymous reviewers for helpful comments on the manuscript.
C. Quaia was supported partially by a grant (Sistemi naturali ed artificiali nei problemi cognitivi e dell'apprendimento) from the Ministero dell' Università e della Ricerca Scientifica e Tecnologica to Paolo Inchingolo. P. Lefèvre was supported partially by the Fonds National de la Recherche Scientifique and Belgian Program on Inter-university Poles of Attraction, initiated by the Belgian State, Prime Minister's Office for Science, Technology and Culture.
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FOOTNOTES |
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Address for reprint requests: L. M. Optican, Bldg. 49, Rm. 2A50, National Eye Institute, NIH, Bethesda, MD 20892-4435.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 20 November 1998; accepted in final form 22 February 1999.
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REFERENCES |
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