-
1998 Special Issue
Distributed model of control of saccades by superiorcolliculus
and cerebellum
Philippe Lefevrea,b, Christian Quaiaa,c, Lance M.
Opticana,*aLaboratory of Sensorimotor Research, National Eye
Institute, Bethesda, MD 20892, USA
bLaboratory of Neurophysiology and CESAME, UCL,
Louvain-La-Neuve, BelgiumcDEEIUniversita degli Studi di Trieste,
Trieste, Italy
Received and accepted 5 May 1998
Abstract
We investigate the role that superior colliculus (SC) and
cerebellum (CBLM) might play in controlling saccadic eye movements.
Eventhough strong experimental evidence argues for an important
role for the CBLM, the most recent models of the saccadic system
have reliedmostly on the SC for the dynamic control of saccades. In
this study, we propose that saccades are controlled by two parallel
pathways, oneincluding the SC and the other including the CBLM. In
this model, both SC and CBLM provide part of the drive to the
saccade. Furthermore,the CBLM receives direct feedback from the
brain stem and keeps track of the residual motor error, so that it
can issue appropriate commandsto compensate for incorrect heading
and to end the movement when the target has been foveated. We
present here a distributed model thatproduces realistic saccades
and accounts for a great deal of neurophysiological data. Published
by Elsevier Science Ltd.
Keywords: Saccade; Eye movements; Superior colliculus;
Cerebellum; Frontal eye fields; Parietal cortex; Modeling
1. Introduction
The neural system that generates the voluntary, rapid
eyerotations called saccades is probably the most studied
motorcontroller in the brain. The wealth of data available aboutthe
physiology and anatomy of the many brain areasinvolved in
controlling saccades, and about the effects oflesions and
electrical stimulation in those areas, hasprompted the development
of many models of the saccadicsystem. The forerunner of these
models was Robinsonsimplementation of a lumped model with an
internal, orlocal, feedback loop (Robinson, 1975; Zee et al.,
1976).Robinsons key idea was that a local feedback loop com-pares
the desired position of the eyes in space with an inter-nal
estimate of their actual position, thus producing anestimate of the
instantaneous (or dynamic) motor error. Sub-sequent work suggested
that the saccadic system did notdepend on absolute signals, such as
eye position in space,but rather on relative signals, such as the
desired change ineye position (i.e. displacement). Thus, most
models follow avariant of the Robinson model, due to Jurgens et al.
(1981),
that replaces the absolute eye and target position signalswith
relative signals. Subsequent efforts to extend saccadicmodels have
focused on interpreting the local feedback loopin terms of brain
activity and structure.
Although physiological and anatomical observationshave shown
that several brain structures cooperate to pro-duce saccades,
models were usually restricted to a subset ofthese structures.
Typically, models focused on the roleplayed by the superior
colliculus (SC) in controlling sac-cades and in determining the
firing pattern observed in brainstem motor and premotor neurons
(e.g. Droulez andBerthoz, 1988; Waitzman et al., 1991; Lefevre and
Galiana,1992; Van Opstal and Kappen, 1993; Arai et al.,
1994;Optican, 1994).
However, it has been known for a long time that
collicularablations disrupt saccades only for a brief period
(Schiller etal., 1980) and, even in the acute phase of a collicular
lesion,the trajectory and speed of saccades can be affected
withouta striking loss of accuracy (Quaia et al., 1998; Aizawa
andWurtz, 1998). Thus, one of the major problems with
colli-culocentric models is that they do not explain why lesions
ofthe SC do not result in large and enduring deficits.
Even though the saccadic system seems to be able tocompensate,
at least partially, for impairments of itscollicular pathway,
cerebellar lesions (e.g. Optican and
* Corresponding author. Bldg. 49, Rm. 2A50, National Eye
Institute, NIH,Bethesda, MD 20892-4435, USA. Tel: +1 301 4963549;
fax: +1 3014020511; e-mail: [email protected]
08936080/98/$19.00 Published by Elsevier Science Ltd.PII:
S0893-6080(98)00071-9
Neural Networks 11 (1998) 11751190PERGAMON
NeuralNetworks
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Robinson, 1980) induce permanent deficits, affecting
dra-matically the accuracy and consistency of saccades.
None-theless, the vast majority of saccadic system models do
notincorporate the cerebellum (CBLM). Furthermore, the fewmodels of
the saccadic system with a CBLM (e.g. Opticanand Miles, 1985;
Grossberg, 1986; Optican, 1986), pro-posed that its role is to
compensate for alterations of theoculomotor plant due to age or
injury, and to adjust thesaccadic command as a function of the
orbital position(compensating for plant nonlinearities). In other
words, inthose schemes the commands generated by both the SC andthe
CBLM were a stereotyped function of the desired dis-placement of
the eyes. Such models could account for sev-eral observations, such
as the impairment of the ability tocompensate for changes in the
oculomotor plant (Opticanand Robinson, 1980) and the persistent
saccadic dysmetria(e.g. Ritchie, 1976; Optican and Robinson, 1980;
Sato andNoda, 1992; Robinson et al., 1993; Takagi et al.,
1998),often as a function of orbital position, induced by
cerebellarlesions. However, they cannot account for one of the
moststriking effects of cerebellar lesions: the increased
variabil-ity of both amplitude and direction of saccades
(e.g.Robinson et al., 1993; Robinson, 1995; Takagi et al.,
1998).
We propose that this last observation, which has beenreported
following both permanent and temporary lesions,is compatible with a
cerebellar contribution that is carefullytailored, for each
saccade, to compensate for the variabilitypresent in the rest of
the saccadic system during the prepara-tion and execution of the
movement. In other words, thecerebellum is, in our view, within the
local feedback loop
that has been proposed by Robinson as the key element ofthe
saccadic system.
The model of the saccadic system that we propose here isbased on
the concept that saccades are controlled by twoparallel pathways,
one including the SC and the otherincluding the CBLM, which are
both affected by feedbackinformation. In another paper (Quaia et
al., 1998), we haveshown how this model can account for many of the
proper-ties of the saccadic system, for a great deal of
anatomicaland physiological data, and for the effects of lesions.
Herewe focus on a detailed analysis of the computational issuesof a
distributed implementation of this model, comparingthe activity of
our simulated cells with that of real neurons.
2. Model
The general structure of our model is very similar toothers that
include a main pathway from the cortex to themotoneurons and a side
loop including the CBLM (e.g.Albus, 1971; Grossberg and Kuperstein,
1989; Dean,1995; Contreras-Vidal et al., 1997). In our model the
mainpathway (collicular pathway) originates in the motor cellsof
the Frontal Eye Fields (FEF) (Fig. 1), where desired dis-placement
of the eyes is encoded, and includes the inter-mediate layers of
the SC and the Medium Lead BurstNeurons (MLBNs) in the brain stem,
which in turn projectto the extraocular motoneurons (MNs). The
other pathway(cerebellar pathway) originates in the FEF and in the
SC,goes through the Nucleus Reticularis Tegmenti Pontis(NRTP), and
activates the CBLM (lobuli VI and VII ofthe vermis and caudal
fastigial nuclei), which then drivesthe MLBNs.
In our scheme, the activity in both pathways is instanta-neously
influenced by the efference copy of the signal thatthe MLBNs send
to the MNs. The fact that the cerebellarcontribution to the control
of the movement is determinedusing on-line feedback information (as
opposed to usingonly long-term adaptation) is a major departure
from earlierapproaches, and is the major novelty introduced by
ourmodel.
We will now describe how the different sections of ourmodel
cooperate to produce saccadic eye movements; sub-sequently we will
present a distributed implementation ofthe model. Finally, to
illustrate the behavior of the model,several simulations of this
distributed implementation willbe shown.
2.1. Overview
The main building blocks of our model are FEF, SC,NRTP, CBLM and
the brain stem circuitry. Before analyz-ing each one of these
blocks in detail, it is important tounderstand their contribution
to saccadic execution. As pre-viously explained, in our model the
role of the FEF is toprovide the desired displacement signal
directly to the SC
Fig. 1. Overview of the different brain structures included in
our model,with their inter-connections. The saccadic goal is
provided by the frontaleye fields (FEF) in the oculomotor cortex.
This structure projects to thesuperior colliculus (SC) and nucleus
reticularis tegmenti pontis (NRTP).The SC also projects to the NRTP
which activates the cerebellum (CBLM).Both SC and CBLM participate
in the drive to the saccade and activatebrain stem medium lead
burst neurons (MLBNs) that in turn recruit theextraocular
motoneurons of the eye plant (MNs).
1176 P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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and, indirectly through the NRTP, to the CBLM. It is wellknown
that the DE signal is encoded in cortex, as well as inthe SC and
NRTP, in spatial coordinates (i.e. different dis-placements are
associated with different, albeit possiblyoverlapping, populations
of neurons, and not just with dif-ferent levels of activation of a
group of neurons); we pro-pose that such a spatial code is also
maintained in theCBLM. Under these conditions, topographically
organizedprojections from FEF to SC and NRTP and from NRTP tothe
CBLM are sufficient to distribute the DE signal acrossthe
network.
The FEF motor cells project to two classes of neurons inthe SC
(Fig. 2): the burst neurons (BNs) and the buildupneurons (BUNs),
which in turn send excitatory projectionsto the contralateral brain
stem MLBNs (Fig. 3). In additionto this signal, the BUNs also
receive another input from thelateral intraparietal area (LIP)
(Pare and Wurtz, 1997). Thisinput reflects the saccadic plan that
indicates which saccadeshould be generated next in re-mapping
experiments(Duhamel et al., 1992). This second input to the BUNs
isactive well before the saccade, and has a weaker influenceon BUN
activity than the input coming from the FEF. Thereare two other
major differences between these two corticalinputs: first, the FEF
input is necessary to produce a saccade,whereas the LIP input is
neither sufficient nor necessary.Second, the spatial distribution
of the LIP input changesduring the saccade, inducing a sort of
spread of activityfrom caudal BUNs (corresponding to the desired
displace-ment DE) toward rostral BUNs (encoding smaller
move-ments); in contrast, the FEF input is approximatelyconstant,
both spatially and temporally, throughout themovement.
In addition to the BNs and the BUNs, we have modeled a
third class of collicular neurons, the so-called fixation
neu-rons (FNs). These neurons receive a cortical fixation
signal(which represents a command to maintain fixation) and
havereciprocal inhibitory connections with the BNs (Fig. 2).During
periods of fixation, the FNs are tonically active,preventing the
BNs from firing, but allowing the BUNs tofire in response to input
from LIP. However, when the FEFsupplies a DE command to the
BNs/BUNs, and the corticalfixation command is withdrawn, this
balance of activitychanges and the equilibrium is reversed, with
the BN/BUN complex firing intensely while the FNs are silent.The
silencing of the FNs has the effect of removing anexcitatory input
to the brain stem omnipause neurons(OPNs), which tonically inhibit
(or gate) MLBNs inbetween saccades, thus determining the onset of
the sac-cade. To capture this important event we say that the
SCissues a GO signal (Fig. 3), which depends on the timecourse of
the DE and fixation cortical inputs and on theintrinsic dynamics of
the collicular network.
Once the OPN gate is open, the MLBNs start firing, thusinducing
activity in the MNs and causing the eye to movetoward the target.
At the same time, the CBLM provides anadditional drive, which
contributes to the acceleration of themovement. Thus, at the
beginning of the saccade both theSC and the CBLM drive the eyes
toward the target. Once theeyes start moving, the CBLM starts
receiving the efferencecopy of the signal that the MLBNs send to
the MNs, and wepropose that it integrates this signal to keep track
of thedisplacement of the eyes since the beginning of the
saccade.In other words, the CBLM performs the function
classicallyascribed (Jurgens et al., 1981) to the displacement
integrator(DI). However, we propose that this integration is
per-formed not in time but in space (i.e. the displacement is
Fig. 2. Organization of the SC connections. Excitatory
connections are solid lines and inhibitory are dashed. The SC
(dotted box) contains three different typesof cells: burst neurons
(BNs), buildup neurons (BUNs) and fixation neurons (FNs). FEF
provides the DE signal to both BNs and BUNs. LIP provides
anadditional input to BUNs. Collicular FNs have an inhibitory
shunting effect on the input provided by the FEF. A similar action
is performed by the feedbacksignal provided by the cerebellum
(CBLM). In turn FNs are inhibited by BNs and receive an excitatory
fixation input (FIX) from the cortex. These interactionsbetween
BNs/BUNs and FNs determine the onset of the saccade through their
action on the brain stem saccadic gate element (OPN) and on the
premotormedium lead burst neurons (MLBNs).
1177P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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encoded by a change in the spatial distribution of thecerebellar
activity, and not by a monotonic change in theactivity of some
cerebellar neurons).
As the saccade progresses, the CBLM sends, directly
orindirectly, an inhibitory signal to the SC, thus making theburst
of activity in BN/BUN neurons decay approximatelyas a function of
the residual motor error (Waitzman et al.,1991). Finally, when the
eyes approach the target, theCBLM starts driving the MLBNs
contralateral to the move-ment, interrupting the movement. However,
the stopping ofthe movement is not achieved by activating the
antagonistmuscle, as in models of limb control (e.g.
Contreras-Vidalet al., 1997) but by activating contralateral
inhibitoryMLBNs (IBNs) which then choke off, at the level of
theMNs, the drive provided by ipsilateral excitatory MLBNs(EBNs).
We suggest that for eye movements a choke issufficient because the
inertia of the ocular globe is muchsmaller than the inertial forces
involved in limb movements.Thus, we say that the CBLM provides a
choke, as opposedto a brake, to stop the saccade. When the choke is
applied,the eyes stop, although the excitatory drive from theMLBNs
to the MNs is still active. However, because the
choke signal is only temporary, the OPNs must be reacti-vated to
ensure the stability of the system.
2.2. The cortex
We have modeled the motor layers of the FEF as a latticeof 33 by
33 neurons, covering desired displacementsranging from 408 to 408
horizontally and verticallyand uniformly distributed. All the other
areas implementedin our model (LIP, SC, NRTP and CBLM) are
organized inthe same way. This is of course a simplification of the
actualorganization of neural maps and it does not account for
theirwell known logarithmic warping (Robinson, 1972;
Schwartz,1980). However, this assumption simplifies the
implemen-tation of the model, without affecting its
functionality.
The FEF motor map, which encodes the desired displace-ment DE,
projects, in a topographically organized fashion,to both the SC and
the NRTP, and contributes to the peri-saccadic burst of activity
observed in both these areas. Wemodeled the activity (xFEF(i, j,
t)) on this map as a Gaussianprofile centered around the cell (iDE,
jDE) that encodes thedesired displacement DE:
xFEF(i, j, t) I(t)exp (i iDE)2 (j jDE)2
j2
To fit the experimental data we chose j2 5; I(t) becomesactive
some time during the simulation, and is maintainedconstant (150
spikes/s) until after the end of the saccade [itmust be removed, or
at least weakened, around 50 ms afterthe end of the saccade,
otherwise it could induce a secondsaccade; however, such a time
course is compatible withexperimental evidence (Segraves and Park,
1993)].
In addition to the FEF we have modeled another corticalarea, the
LIP. In our model this area projects to the BUNs inthe SC and is
responsible for their early activation and forthe spread of
activity across the collicular BUN layer. It isimportant to note
that this spread of activity (which startswell before saccade
onset, i.e. it is predictive) plays nofunctional role in our model,
which only focuses on saccadeexecution, but may play a role in the
preparation of thesaccade and can affect the balance between
collicular BNsand FNs.
To simulate the long prelude of activity in the BUNs, yetkeep
the simulation time as short as possible, in our modelthe LIP
output that is associated with the displacement DEbecomes active at
the very beginning of the simulation.When the FEF output starts,
the LIP activity spreads tocells that encode smaller movements in
the same direction.This spread starts and continues throughout the
saccade witha time constant (Ts) of 50 ms. More precisely, the
output ofthis layer is described by
x0LIP(t) xLIP(t)
Ts
ILIPTs
ILIP represents the input from neighboring LIP cells, and it
isused to make the activity spread. This input is obtained by
Fig. 3. Overview of the interactions between the different
components ofthe model. Two pathways can be identified, one going
through the superiorcolliculus (SC) and the other including the
cerebellum. The SC exerts twofunctions: first, it determines the
onset of the saccade (Go), by causing theomnipause neurons (OPNs)
to release their inhibitory action (Gate) on themedium lead burst
neurons (MLBNs). Second, the SC provides an excita-tory input
(Drive) to the MLBNs. The cerebellum performs three functions:(1)
it provides an additional drive to the MLBNs, (2) it monitors the
pro-gress of the saccade by acting as a displacement integrator
(DI), and (3) itchokes off the drive to the MLBNs, ending the
movement. The differencebetween the sum of the two drives and the
choke is passed on to themotoneurons (MNs), and determines the
velocity of the eyes. Note thatfor clarity on the figure we have
omitted the NRTP (which merely relaysthe collicular signals to the
cerebellum) and LIP (which plays no function incontrolling the
execution of the saccade).
1178 P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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convolving the parietal activity (xLIP) with a matrix K that isa
function of the direction of the planned saccade DE:
K (cos( ~DE)MH sin( ~DE)MV)
2p
1
2
p1 1 1
2p
1
2
p2664
3775where the division indicates element-by-element division,and
MH and MV are defined below (see Section 2.4). TheLIP output is
normalized to have a peak of 75 spikes/s forthe whole duration of
the simulation; furthermore, it cannotcross the midline.
2.3. Superior colliculus
As we have already pointed out, we have modeled threeclasses of
collicular cells: BNs, BUNs and FNs. We nowdefine the equations
that determine the firing patterns ofthese classes of cells. The
burst neurons receive anexcitatory input from the FEF just before
and during thesaccade, an inhibitory input from the CBLM which
growsduring the saccade and is an approximate function of
theresidual error, and an inhibitory input from the FNs. Toavoid
the need for different connectivity for BNs and BUNs,we hypothesize
that the inhibitory signals act by shuntingthe dendritic FEF input,
and not directly on the soma of thecell. Then, we can represent the
BNs by the equation:
x0BN(t) xBN(t)TBN
IBNTBN
where
IBN kFEFxFEF(1 kFBxFB) kFNxFN
[x] x if x $ 0
0 otherwise
(where xFEF represents the activity of the FEF map, xFB
thefeedback cerebellar input (defined as the ratio between thenorm
of displacement since the beginning of the saccadeand the norm of
DE), and xFN the activity of the fixationneurons; kFEF 4, kFB 0.85
and kFN 3.
In addition to the three inputs we have just described, theBUNs
also receive an input from LIP. However, this input isapplied
directly to the soma and is not affected by the twoinhibitory
signals described above. The need for having anearly activation of
the BUNs, even when the FNs are stillstrongly activated, is what
has induced us to use the inhibi-tion to shunt the dendritic FEF
input to the SC as opposed todirectly inhibiting the SC cells.
Then, the activity of theBUNs can be described by:
x0BUN(t) xBUN(t)TBUN
IBUNTBUN
where
IBUN kFEFxFEF(1 kFBxFB) kFNxFN
xLIP
Thus, except for the input from LIP, the BNs and the BUNsare
governed by the same equation.
The FNs receive different inputs: first, they are inhibitedby
the BNs; second, they receive a cortical fixation inputFIX; and
third, they receive an excitatory input from theoculomotor region
of the fastigial nucleus (FOR) (Mayet al., 1990). They are
described by:
x0FN(t) xFN(t)TFN
IFNTFN
where
IFN FIX kFORxFOR kBNmax(xBN)
and where kBN 0:001k ~DEk2 0:6 is used to simulate a
stronger inhibition from BNs and BUNs encoding
largerdisplacements; kFOR 0.0073. FIX is set to 150 spikes/sduring
periods of fixation, it is set to zero just before theonset of the
movement and it is reactivated at the end of themovement. However,
this input plays no role in determiningthe end of the movement, but
it is used only to stabilize thesystem after the saccade. This
input is present all the timeduring simulations of electrical
stimulation.
The time constant of BNs (TBN) and BUNs (TBUN) is set to7.5 ms,
whereas for FNs (TFN) it is set to 20 ms.
2.4. Cerebellum
Our major goal in modeling the cerebellum was to repro-duce the
pattern of activation that is observed in FOR neu-rons during
saccades. Thus, we have built a circuit thatgenerates a burst of
activity synchronized with saccadeonset in the FOR contralateral to
the direction of the sac-cade (for horizontal saccades) and a burst
synchronized withsaccade end in the FOR ipsilateral to the saccade.
Further-more, the duration of the contralateral (early) burst
shouldbe correlated with the duration of the movement. In ourmodel
such signals are generated imposing a burst of activ-ity in the
contralateral FOR and causing the activity tospread, with a speed
proportional to the velocity of theeyes, from the contralateral to
the ipsilateral FOR.
To generate the initial burst we connected the NRTP(which in
turn receives topographically organized projec-tions from the SC
and the cortex) to the FOR in a topogra-phically organized manner.
The FOR cells, which aremodeled as a low pass filter with
saturation of their inputs,are connected to each other, and the
strength of these pro-jections is linearly modulated by the
efference copy of thephasic input provided to the motoneurons. More
precisely,the output of the FOR neurons is generated using the
fol-lowing equation:
x0FOR(t) xFOR(t)
TC
(kNRTPINRTP kCBLMICBLM)TC
1179P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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where INRTP represents the input from the NRTP, that is
afunction of FEF, BN and BUN activation (kFEF 0.8,kBUN 0.4, kBN
0.4; INRTP is greater than zero and smallerthan 600 spikes/s):
INRTP kFEFXFEF kBUNXBUN kBNXBN
TC is the time constant of the cells (20 ms during saccades,40
ms during fixation), ICBLM is the input from neighboringcells;
these two inputs are multiplied by two constants.ICBLM is obtained
by convolving the FOR activity with amatrix M that is a function of
the efference copy of thehorizontal and vertical phasic signals (PH
and PV,respectively):
M lPHlMH lPVlMV
2p
1
2
p1 1 1
2p
1
2
p2664
3775where the division indicates element-by-element
divisionand
MH
0:707 0 0
1 0 0
0:707 0 0
26643775 if PH $ 0
0 0 0:707
0 0 1
0 0 0:707
26643775 if PH , 0
8>>>>>>>>>>>>>>>>>>>>>:
MV
0:707 1 0:707
0 0 0
0 0 0
26643775 if PV $ 0
0 0 0
0 0 0
0:707 1 0:707
26643775 if PV , 0
8>>>>>>>>>>>>>>>>>>>>>:With
the strength of the connections chosen in such a waythat the FOR
cells never reach saturation (kNRTP 0.7 andkCBLM 0.0032),
simulations (see Section 3) show that sucha simple scheme is
sufficient to implement a very accuratespatial integrator.
Because the integration is performed spatially, the
initiallocation of the activated FOR area plays a major role
indetermining the amplitude of the movement. However,note that the
central region is reached when the eyes arestill a few degrees away
from the fovea. Consequently, if weproduce a movement of amplitude
x by imposing the activ-ity y cells away from the central cell, to
obtain a movementof amplitude 2x we cannot simply impose the
activity 2ycells away from the central cell. To avoid a complex
remap-ping from the NRTP to the CBLM, and given that the
exactlocation of the activated zone in the SC does not have a
strong effect on the amplitude of the movement (which
isdetermined by the CBLM), we decided to simply impose thetarget on
the cortical map (and thus on all the maps) at alocation
appropriate for the cerebellum. So, given the targetlocation
(eccentricity and direction), we find a correctedeccentricity, and
we center the cortical activity aroundthe cell that encodes that
eccentricity. The equation thatdescribes this corrected
eccentricity is
1 0:3 1 4p
abs v%p
4
p
4
(1:7kDEk 12:7)
where % indicates the modulus operation.We emphasize that such a
mechanism is not necessarily
implemented physiologically; all we are interested in
isreproducing a pattern of activation that closely resemblesneural
recordings, so that we can study the effects of suchactivities and
make predictions regarding the function of thecerebellum.
2.5. Brain stem network
The two parallel pathways from SC and CBLM convergeat the level
of brain stem MLBNs and provide inputs toexcitatory and inhibitory
burst neurons (EBNs and IBNs).We simulated the activity of eight
neurons, one excitatory(EBN) and one inhibitory (IBN) for each of
the four cardinaldirections: right, left, up and down. For
simplicity wedescribe here what determines the activity of the
rightwardEBN and IBN. The activity of the six other neurons
arecomputed similarly.
All MLBN cells have a time constant of 1 ms; their dis-charge
cannot be negative and saturates at 1000 spikes/s.Right EBNs and
IBNs receive four inputs: from the BNs,BUNs, FOR and OPNs. The
input from the SC is such thatneurons that are active before a
rightward saccade exciterightward MLBNs; similarly neurons that are
active beforean upward saccade excite upward MLBNs. The weight
ofthe projections from the SC to the MLBNs is a function ofthe
location of the cell on the SC, with cells encoding largermovements
having stronger weights.
The projections from the OPNs is inhibitory, and isequally
applied to all MLBNs. Like the one from the SC,also the input from
the FOR is characterized by differentweights depending on the
position of each cell on the FORmap. For example, the leftward FOR
excites rightwardMLBNs, and the weights of this projection are
larger forcells that are far away from the midline. However, in
thiscase the weights to the IBNs are five times stronger thanthose
to the EBNs.
We did not introduce any dynamical element to modelOPNs; their
output is the sum of their inputs, it cannot benegative and
saturates at 300 spikes/s. They receive twoexcitatory inputs: a
constant bias input (100 spikes/s) andan input from FNs (gain 15).
They also receive threeinhibitory inputs: the sum of the activity
of all BNs andBUNs weighted by 0.05 (which mimics the
inhibitory
1180 P. Lefevre et al. / Neural Networks 11 (1998) 11751190
-
input that they receive from long lead burst neurons) and thesum
of the activity of all EBNs.
The eye plant was modeled as a second order system,with time
constants of 150 ms and 5 ms. The phasic inputto the plant was
represented by the output of the MLBNs,defined as the difference
between ipsilateral EBNs and con-tralateral IBNs. This phasic
signal is a good approximationof eye velocity, and is also used in
the feedback pathway tothe CBLM.
3. Simulations
3.1. Characteristics of saccadic eye movements
We have simulated saccadic eye movements by driving
asecond-order model of the oculomotor plant (see Section 2.5)with a
distributed network that encompasses the SC, theCBLM and several
brain stem structures. As we have pre-viously pointed out (see
Section 2), this model departs
considerably from earlier approaches; in particular, herethe
phasic input to the motoneurons is not determined bya local
feedback loop that continuously reduces an estimateof the motor
error to zero. Consequently, it is not evenobvious, a priori, that
our model can produce accurate sac-cadic eye movements for saccades
of different amplitudes orfor saccades having the same amplitude
but differentspeeds. Clearly, a model unable to reproduce these
basiccharacteristics of saccades (using a fixed set of
connectionsbetween its elements) would be worthless.
Consequently, we started by simulating saccades of dif-ferent
amplitudes, setting the weights of the connections sothat the
movements produced fall on the so called mainsequence (Bahill et
al., 1975) for monkeys (whose saccadesare faster than humans
saccades). In Fig. 4 we show velo-city (A) and position (B)
profiles of three horizontal sacca-dic eye movements (10, 20 and
308). The saccades producedare accurate and have a peak speed which
is compatible withthe speed of monkey saccades. The velocity
profiles areslightly skewed, especially for large saccades, but
this canbe accounted for by our use of a first-order controller
todrive a second-order plant.
Next, we simulated a family of saccades to the sametarget (208
to the right) but with different speeds (peakspeed varying from
8008/s to 1608/s). To produce move-ments of different speeds we
used different levels of corticalactivation (100, 80, 60, 40 and
20% of maximum). A lowerlevel of cortical activation resulted in a
lower collicularactivation and thus in a reduced drive to the
motoneurons.In Fig. 5 we show the results of these simulations.
Panel Ashows the velocity profiles of the saccades obtained; it
isclear that slower saccades are stretched, i.e. their duration
isincreased. This is due to the different feedback signals
thataffected both the decay of the collicular drive and the
timingof the cerebellar choke signal. Because of this stretching,
theamplitude of the saccades is essentially constant (panel
B)despite the large variation in the dynamics of the move-ments.
These simulations demonstrate that the scheme wehave proposed, even
though it does not embed a classicmotor error feedback loop, shares
one of its important prop-erties.
Note that only the slowest saccade simulated is appreci-ably
dysmetric (hypometric); interestingly, such hypometriais not due to
an untimely application of the choke but to theearly reactivation
of the OPNs. In this case the signals thatare supposed to keep the
OPNs off (i.e. the caudal SC andthe EBNs) are not strongly
activated and cannot keep theOPNs off long enough for the eye to
get on target. Interest-ingly, this is the same mechanism that has
been recentlyproposed (Quaia et al., 1998) to account for the
widespreadhypometria observed following collicular
inactivation(Aizawa and Wurtz, 1998).
To produce these movements we have manipulated twoparameters:
the weight that determines the speed of thecerebellar spread as a
function of the speed of the movementand the mapping of connections
from the NRTP to the
Fig. 4. Simulation of three saccadic eye movements of different
amplitudes.(A) Velocity profiles (in deg/s) of three saccades
simulated by the model.Solid line 208, dashed line 308 and dotted
line 108. (B) Positionprofiles (in deg) for the same three
rightward movements. These move-ments are compatible with the main
sequence of monkey saccadic eyemovements. Time zero is saccade
onset.
1181P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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CBLM (see above). However, once we found the desired setof
parameters they stayed fixed. Thus, all the saccadesshown here were
obtained using the same set of parameters.Furthermore, the behavior
reported above holds for verticaland oblique saccades as well (one
example of an obliquemovement will be shown later), as long as the
saccades werenot so large that edge effects (because of the limited
size ofour maps) became a problem.
3.2. Collicular activity
The perisaccadic time course of collicular activity is
illus-trated in Fig. 6. This simulation corresponds to a 208
right-ward saccade. We represent the SC (in this case the left
SC,which controls rightward saccades) as a two-dimensionalmap; for
the sake of simplicity (see Section 2.2) we haveused a linear map,
as opposed to a more realistic logarith-mically warped map
(Robinson, 1972; Ottes et al., 1986;Optican, 1995). Each panel in
Fig. 6 represents the spatial
distribution of the BUNs activity at different times: 100
msbefore saccade onset, 50 ms before saccade onset, at sac-cade
onset (0 ms) and 50 ms after saccade onset. The FNsare located at
the rostral pole of the left SC, on the right ofeach panel. The
level of activation is represented using agrayscale image; to
emphasize the prelude of activity(which is much weaker than the
saccadic burst) we haveused a quadratic mapping between activity
levels and graylevels.
The first two panels reveal the prelude of activityobserved in
BUNs. During that time, the FNs are still active(on the right of
the panels), inhibiting the BNs andexciting the OPNs to keep a
saccade from occurring. Initi-ally (time 100 ms) the prelude is
localized around thesite that corresponds to the saccadic target
(i.e. the sitewhere the burst will occur), but before the onset of
thesaccade (time 50 ms) it starts spreading towards therostral pole
of the SC. At saccade onset (time 0 ms), thisongoing spread of
activity is supplemented by a strong burstof activity, which occurs
at the site corresponding to thetarget and does not spread. Around
saccade end (time 50 ms), the residual unclipped activity of the
burst iscombined with the late spread near the rostral pole, andthe
FNs are slowly reactivated by the large amount of activ-ity present
in the fastigial nucleus (see below).
The pattern of activity in the burst neuron layer is verysimilar
to the one reported in Fig. 6, except that BNs do notexhibit a
prelude of activity. Thus, the activity in the BNlayer is simply a
spatially localized burst of activity thatstarts just before
saccade onset and decays during the sac-cade, without any rostral
spread.
To better illustrate the evolution of the collicular activityin
the different classes of cells modeled, we have plotted thetime
course of activation of some collicular cells (all locatedalong the
horizontal meridian) during the same saccade(Fig. 7). In panel A we
show the time course of the firingrate of four different BNs, the
one that discharges maxi-mally for a 208 rightward saccade, and
three other cellslocated more rostrally. The burst of activity
starts around50 ms before saccade onset, peaks around saccade onset
andis almost over by saccade end (the net drive to the moto-neurons
is over around time 40 ms, even though the saccadeends
approximately 10 ms later). Neurons that dischargeoptimally for
different saccades start discharging later andstop discharging
earlier. These characteristics are in agree-ment with
neurophysiological recordings in the SC of mon-keys (Sparks et al.,
1976). The decay of activity during themovement is due to an
inhibitory feedback from the CBLM,and is also in agreement with
neurophysiological recordingsin the SC of monkeys (Waitzman et al.,
1991).
In panel B we report the activity of three buildup neuronsand
one fixation neuron (dotted line). We show one buildupneuron
(dashed line) that discharges maximally for the sac-cade simulated.
The activity of this neuron is characterizedby a prelude of
activity that starts more than 100 ms beforesaccade onset, and by a
burst of activity essentially identical
Fig. 5. Simulation of a family of saccades to the same target
(208 to theright) with different speeds. (A) Velocity profiles
(deg/s). (B) Positionprofiles (deg). Solid line: nominal FEF
activation (150 spikes/s), dashedline: 80% FEF activation, long
dashed line: 60%, dotted line: 40%, dotteddashed: 20%. Saccadic
peak velocity varies from 8008/s (normal, solid line)to 1608/s
(slowest, dotteddashed line). Note the high accuracy despitelarge
variations in saccade dynamics.
1182 P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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to the one carried by the burst neurons. The prelude ofactivity
is initially localized at the site where the burstwill later
emerge, but around 80 ms before the onset ofthe saccade it starts
spreading toward the rostral pole(dashdotted line), and some time
during the saccade itreaches the most rostral cells (solid line).
In our modelthis spread is not due to intracollicular mechanisms,
but toan external cortical input, which has predictive
properties(see above).
The fixation neurons (dotted line) are tonically active
inbetween saccades, and stop discharging just before saccadeonset.
The time course of the decay in FN activity beforesaccades is
determined by two factors: first, the removalof a cortical tonic
input, which simulates the removal of acognitive fixation command;
second, the rise of the burstof activity in the caudal SC (which
inhibits FNs). Aroundthe end of the saccade the FNs start
discharging again.This reactivation is due to several factors:
first, theincreased excitation from the fastigial neurons;
secondthe decreased inhibition from the collicular BNs; andthird,
the reactivation of the cortical fixation command.When FNs are
tonically active again, the system reentersfixation mode.
Note that in our model we simulate only the saccade-related
activity of distributed SC and CBLM networks.Accordingly, all the
activity that is not directly related tosaccades (e.g. visual
signals in the SC) are ignored.
3.3. Fastigial activities
The FOR plays a central role in our model. In Fig. 8 weplot the
pattern of activation of FOR neurons at four differ-ent instants
during a 208 rightward saccade (the same move-ment used to
illustrate the collicular activity). Thecontralateral FOR starts
firing first, with a weak prelude ofactivity (time 100 ms). At
saccade onset (time 0 ms),a strong burst of activity is present in
the contralateral FOR,complementing the collicular drive for the
saccade.
Initially, the FOR burst is centered in the contralateralFOR at
a location that is a function of the amplitude anddirection of the
desired movement. Once the saccade starts,the burst of activity
spreads across the FOR with a speed anddirection that is
proportional to the velocity of the move-ment, estimated using an
efference copy of the phasic signalsent by the EBNs and IBNs to the
motoneurons. When theactivity reaches the other side, which occurs
around 30 msbefore saccade end, the FOR starts driving the
IBNs/EBNscontralateral to the direction of the movement, with
strongerweights to the IBNs than to the EBNs. Because
thecontralateral EBNs are inhibited by the ipsilateralIBNs, the
only important effect of the ipsilateral FORfiring is that the
contralateral IBNs turn on. These con-tralateral IBNs choke off the
residual drive input pro-vided to the ipsilateral IBNs by the
contralateral SC andFOR. By the time the saccade is over (time 50
ms),
Fig. 6. Spatial distribution of BUN activity during a 208
rightward saccade (illustrated in Fig. 4, solid line). FNs are
represented on the right side of each panel(dark spot on the first
panel). (A) 100 ms before saccade onset the prelude of activity,
due to the input from LIP, is present and the FNs are tonically
active. (B)50 ms before saccade onset the spread of the prelude has
started, while the FNs are still active. (C) At saccade onset a
strong burst of activity occurs and the FNsare silent. (D) 50 ms
after saccade onset some activity is still present on BUNs and the
FNs are being reactivated. Time zero refers to saccade onset.
Toemphasize the low levels of activity we used a quadratic mapping
between gray levels and activity levels.
1183P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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a large part of the ipsilateral FOR is activated, so the
eyeswill always stop.
As we did previously for the SC, we now plot the timecourse of
the activity of four FOR cells, all located along thehorizontal
meridian, during the same saccade (Fig. 9). Thedasheddotted line
corresponds to the activity of the opti-mal cell for this movement
(i.e. the cell that gets activatedfirst). This cell starts
discharging weakly well before sac-cade onset, and essentially
reflects the activity of the SC cellthat is maximally activated.
The dotted line corresponds to
the activity of a cell that is located in between the
optimalcell and the midline. This cell is characterized by a burst
thatstarts around saccade onset and peaks some time later. Thethird
cell illustrated (dashed line) is located near the mid-line,
whereas the last one (solid line) is located in the ipsi-lateral
FOR. It is apparent that these cells discharge later andlater, so
that the front of the spreading activity on the FORmap is
correlated with the residual motor error.
3.4. Control of saccade trajectory
We will now show that the model presented here is alsoable to
compensate, at least partially, for trajectory pertur-bations. This
kind of correction is necessary if the initialheading does not
correspond to the desired direction. Errorsin initial saccade
direction and subsequent compensationsgive saccades a curved
trajectory, and are a characteristic ofnormal saccades (Erkelens
and Vogels, 1995). In Fig. 10 weshow an example of two simulations
of saccades toward thesame target (approximately 148 up and 148 to
the right).
In the normal case (i.e. no perturbations) the eyes
goessentially straight to the target (dashed line). We causeda
perturbation in saccade trajectory by transiently decreas-ing the
gain of the horizontal EBNs (gain 0.8; duration 10 ms), which made
the initial saccade direction incorrect.As a result of the
perturbation, the eyes initially moved morequickly up than to the
right, so that the initial direction (thinline a) deviates from the
normal trajectory (dashed line).However, the eyes then steer back
toward the target, eventhough the final overall direction (thin
line b) does not coin-cide with the desired overall direction
(dashed line). Notethat if there were no compensating mechanism
built into themodel, once the perturbation was over the eyes would
pro-ceed parallel to the normal direction (thin line c). This
com-pensation, which is due to the cerebellar contribution to
thegeneration of the saccade, is highlighted in the inset
figurewhich enlarges the final part of the two saccades. The
resi-dual error in eye orientation (i.e. the difference between
theactual and the desired eye orientation) is represented by
thesegment Dr, whereas Dc corresponds to the correction
intrajectory due to the cerebellar contribution (i.e. the
differ-ence between the final position and the position that
wouldhave been achieved without a compensation mechanism).
Even though a partial compensation is achieved by themodel, such
compensation is not perfect (i.e. Dr is not zero).A perfect
compensation (which would be produced by anymodel based on a
closed-loop feedback mechanism) cannotbe achieved because our model
is not an end-point control-ler in the strict sense. Furthermore,
in our implementationonly a small fraction of the drive is
controllable in direction.Thus, partial compensation is a
prediction of our model.This suggests a limit to the maximum
compensation forerrors in initial saccade direction. Furthermore,
perturba-tions near the end of the movement, or for small
saccades,should be compensated less, because there will not
beenough time to redistribute activity on the FOR map.
Fig. 7. Time profile of BNs (panel A) and BUNs (panel B) during
thesimulation of the same saccade as illustrated above (Fig. 4,
solid line;Fig. 6). (A) Activity of BN cells. The dashed line
corresponds to the activityof the cell carrying the peak of
activity for that particular movement; itpeaks around saccade onset
and still carries some unclipped activity atsaccade end (40 ms in
this case). The three other curves in the figurecorrespond to the
activity of three other BN cells located more rostrally;the onset
of their discharge is later and their peak is weaker. (B) Activity
ofBUN cells. The dashed line corresponds to the cell carrying the
peak of theburst; it has a long prelude of activity; the dotted
line corresponds to theactivity of FNs which are characterized by a
tonic discharge during fixationand pause during the execution of
saccades. The two other curves corre-spond to the activity of cells
located between the peak and the rostral pole;these two last cells
do not carry any burst, but only the spreading compo-nent of BUN
cells. The solid line corresponds to the cell located the
mostrostrally which receives the spread later in the simulation.
Time zero issaccade onset.
1184 P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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Fig. 11 illustrates the activity in the FOR map during thesame
perturbed saccade as shown above. The center of grav-ity of FOR
activities is represented by the white spot; it isclear on the
third panel (FOR activities at time 10 ms) that
there is a shift of FOR activities due to the feedback. TheCBLM
is aware of the wrong trajectory of the eye and canproduce a drive
that compensates for it. The eye can thuschange its direction
in-flight, as illustrated in Fig. 10.
Fig. 8. Spatial distribution of bilateral FOR activities during
a 208 rightward saccade (solid line, Fig. 4). (A) 100 ms before
saccade onset the contralateral FOR(vertical line midline) is only
mildly active. (B) At saccade onset a burst is present on the
contralateral (left) FOR. (C) The activity quickly spreads across
theFOR map under the action of the velocity feedback. (D) Near the
end of the saccade the ipsilateral FOR is activated, engages the
choke and stops the saccade.The same conventions are used as in
Fig. 6 for the levels of activity.
Fig. 9. Time profile of FOR activities during a 208 rightward
saccade (Fig. 4, solid line). These profiles correspond to the
activity of four FOR cells during thesame simulation as in Fig. 8.
The dasheddotted line corresponds to the activity of the optimal
cell for this movement; its discharge leads saccade onset and
itpeaks shortly after saccade onset. The dotted line plots the
activity of a cell located closer to the midline which starts
discharging later. The dashed linecorresponds to a cell located
near the midline and the solid one is located in the ipsilateral
FOR. The activation of the ipsilateral FOR triggers the end of
thesaccade. Time zero is saccade onset.
1185P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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Fig. 10. Comparison of two saccades to the same target, located
148 up and 148 right. Solid line: straight saccade to the target.
Dashed line: a perturbation wasintroduced at the level of the gain
of the EBNs (gain 0.8, duration 10 ms). This perturbation causes an
initial misdirection of the eye (direction a).However, during the
movement the trajectory is partially corrected and the eye lands
near the target. Direction c corresponds to the direction of the
normalsaccade, whereas direction b corresponds to the overall
direction of the curved saccade after correction. The inset focuses
on the residual error after correction:Dr is the residual error and
Dc is the correction introduced by the model.
Fig. 11. Spatial distribution of FOR activities during the
curved saccade represented in Fig. 10 (dashed line). The white spot
represents the center of activity onthe FOR map. The dashed oblique
line is where this spot lies during a normal straight saccade. It
is particularly clear 10 ms after saccade onset that the center
ofgravity deviates from its normal trajectory under the influence
of the feedback on the FOR. This deviation induces the correction
observed in Fig. 10. Time zerois saccade onset.
1186 P. Lefevre et al. / Neural Networks 11 (1998) 11751190
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3.5. Electrical stimulation of the SC
The first experimental evidence for the role of the SC inthe
control of saccades comes from early stimulation studiesof this
structure (Adamuk, 1872; Apter, 1946). Robinson(1972) first
described in quantitative detail the retinotopicorganization of the
SC motor map. The similarity betweensaccades electrically evoked
and natural movements ofthe eyes has led many investigators to
conclude that elec-trical stimulation of the SC mimics natural SC
activationand provides downstream structures with an identical
motorcommand (DE). This view has been reinforced by the
tightcorrespondence between the movement field of SC cells
asrecorded during natural saccades and the characteristics
ofsaccades evoked by electrical stimulation of the same col-licular
site (Van Opstal et al., 1990; Pare et al., 1994; Pareand Guitton,
1994).
During sustained stimulation of the SC, the first saccadeof a
stair case is approximately the same size as that evoked
by a brief stimulation from that site. Subsequent saccadesbecome
smaller. The simulations that we present show thatour model
simulates staircases of saccades when the CBLMplays the central
role in saccadic control (Fig. 12). In allcases the same collicular
site was activated; panel A corre-sponds to the case where no
delays are included in thecircuit, whereas panel B shows the
results obtained by intro-ducing a 6 ms delay in the feedback
pathway that providesthe eye velocity signal to the CBLM. Different
positiontraces correspond to different intensities in collicular
activ-ity (SC peak discharge K*600 spikes/s. Dashed line, K 1
(0.9); solid, K 0.675 (0.7); long dashed, K 0.6 (0.6);dotted, K 0.5
(0.5); dasheddotted, K 0.475 (0.475)).To simulate sustained
electrical stimulation of the SC, wemade the assumption that the
cerebellar inhibitory feedbackhad no effect on SC drive as long as
the SC was stimulated(i.e. the SC burst does not decay during the
saccade); theonly significant effect of cerebellar feedback was on
the FNsthat receive a direct input from the FOR. Furthermore,
dur-ing electrical SC stimulation, the spreading cortical input
tothe SC was absent (no signal in the brain could predict theonset
of electrical stimulation, and even if it were to occurlater it
would have a small effect). Similarly, the corticalfixation input
to the FNs is not withdrawn, but is kept con-stant during the whole
duration of the stimulation. Thisinduces an effect of stimulation
strength on saccade latencythat is very clear on both panels of
Fig. 12: the stronger thestimulation, the shorter the saccade
latency. Furthermore,whereas strong stimulations yielded saccades
that had anamplitude corresponding roughly to the site
activated,weak stimulations were cut short because of an early
reac-tivation of the OPNs (due to the persistent cortical
fixationinput provided to the FNs). Another aspect of these
stimula-tions that is in good agreement with neurophysiological
datais modulation of the inter-saccadic interval with the
inten-sity of the stimulation (Stryker and Schiller, 1975).
In the case of very strong stimulations, the first saccade
isfollowed by a smooth eye movement (dashed line in panelA), or by
a series of very small saccades in the case wherethe 6 ms delay is
introduced (dashed line in panel B).
It is worth noting that the model neither contains amechanical
limit to the displacement of the eye in theorbit, nor takes into
account the well known effects of orbi-tal eye position on the
dynamics of eye saccades. These twocharacteristics, though
important, are beyond the scope ofthis paper.
4. Discussion
We have developed a model in which the accuracy ofsaccades is
not assured by the reduction of a temporallyencoded motor error,
but by monitoring the residual motorerror. This error, where the
eye is relative to where it needsto be, is represented by the
distribution of activity in thecerebellum. In this sense, our model
is a major departure
Fig. 12. Simulations of electrical stimulation of the SC. SC
peak discharge K*600 spikes/s. Time zero is stimulation onset.
Different position tracescorrespond to different intensities of SC
stimulation. (A) No delays areconsidered. Dashed line, K 1; solid,
K 0.675; long dashed, K 0.6;dotted, K 0.5; dasheddotted, K 0.475.
(B) A 6 ms delay is introducedin the feedback pathway. Dashed line,
K 0.9; solid, K 0.7; long dashed,K 0.6; dotted, K 0.5;
dasheddotted, K 0.475.
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from the control system schemes that have dominated sac-cadic
modeling for the last 20 years, which computed motorerror as the
difference between two temporal signals(desired eye displacement
and current eye displacement).The main concepts that characterize
our scheme are: (1)the saccade ends because the motor drive is
actively chokedoff by the cerebellum; (2) only the cerebellar part
of thedrive can be controlled in direction; (3) the activity of
thecerebellum is carefully tailored for each movement, becauseit is
inside the velocity feedback loop; (4) the displacementintegrator
is implemented in the spatial domain in thecerebellum.
In another paper, we have examined the behavior of ourparallel
pathway model using an implementation withlumped versions of
cerebral, collicular and cerebellarregions (Quaia et al., 1998). In
this paper, we have examinedthe computational aspects of our model
using an implemen-tation with distributed representations of those
regions. Theadvantage of using a distributed implementation of
themodel is that it allows a direct comparison of simulationsof the
activity of cells, within large populations, withrecordings from
individual neurons. The success of ourmodel in reproducing saccadic
behavior and neurophysio-logical observations suggests that the
anatomical connec-tions and neurophysiological cell types used in
our modelare almost sufficient to reproduce most of the
propertiesassociated with the generation of visually guided
saccades.Thus, the model suggests that future work designed
toextend our understanding of saccade generation shouldfocus on the
role of the cerebellar vermis in determiningthe accuracy of
saccades, and on the connections betweencerebellum and brain
stem.
4.1. Comparison with other models of the saccadic system
Early models of the saccadic system were based on alocal
feedback loop located in the brain stem (Robinson,1975; Zee et al.,
1976). In an attempt to merge the localfeedback loop hypothesis
with neurophysiological findings,recent models embedded the SC in
the feedback loop. Thesemodels can be divided into two classes. The
first class pos-tulates the temporal coding of dynamic motor error
by theactivity of SC cells (Van Opstal and Kappen, 1993; Araiet
al., 1994), and it was inspired by the report that duringsaccades
the activity of BN cells is proportional to dynamicmotor error
(Waitzman et al., 1991). In contrast, the secondclass postulates
the spatial coding of dynamic motor erroron the SC map (Droulez and
Berthoz, 1988; Lefevre andGaliana, 1992; Optican, 1994; Wurtz and
Optican, 1994),and it stemmed from reports that the activity of SC
cellsappears to encode dynamic motor error by the spatial
dis-tribution of BUN activity on the motor map (Munoz et al.,1991;
Munoz and Wurtz, 1995). Both types of colliculo-centric models can
reproduce accurate saccades regardlessof dynamics, because they
rely on the local feedbackscheme. However, when the control of
oblique saccades is
considered, there is a big difference between temporal
andspatial coding schemes. In fact, the temporal coding modelsdo
not allow the saccadic system to exert any control on thetrajectory
of saccades; BN activity codes the magnitude ofthe dynamic motor
error whereas the locus of SC activitycodes the direction of the
planned movement. If the direc-tion of the eye movement is
inaccurate, the system cannotcorrect for it. On the other hand,
this does not hold true forspatial coding models, because dynamic
motor error isencoded spatially on the SC map, thus encoding also
thedirection of the error. This second class of models can
thusreproduce curved saccades.
A major problem of all colliculocentric models is theirinability
to account for lesion studies involving the SC andthe CBLM. Because
in these models the output of the SC isthe residual motor error,
lesions of this structure shouldresult in dramatic effects on the
accuracy of saccades. Incontrast, experiments reveal only minor
deficits after SClesions (Aizawa and Wurtz, 1998), whereas large
deficitsare seen after cerebellar lesions (Ritchie, 1976;
Opticanand Robinson, 1980; Robinson et al., 1993).
Our model can be characterized by the cooperation of SCand CBLM
in saccadic control. Both structures provide partof the saccadic
drive, but it is the cerebellum that keepstrack of the residual
motor error. Because the cerebellumperforms a spatial integration
it encodes the amplitude anddirection of motor error, as in spatial
coding models.Accordingly, the model can control the trajectory of
curvedsaccades because the cerebellar part of the drive can
correctfor heading errors. Furthermore, this control of
trajectorycan take place despite lesions of the SC, which was
impos-sible for colliculocentric models.
4.2. Limitations of the model
We have proposed a mechanism that can reproduce theobserved
pattern of activity in the FOR. However, thatmechanism depends upon
our speculation that spatial inte-gration is somehow carried out in
the vermis, and conveyedto the FOR. Thus, additional data,
especially about thevermis, are necessary before a detailed
analysis of the func-tion of the cerebellum can be carried out.
Another conjecture raised here is that the FOR exerts
itsinfluence on saccades by activating IBNs. These IBNs inturn
choke off the drive to the motor neurons. This possiblerole for the
IBNs needs to be examined further.
4.3. Conclusions
We have presented a model that, using two parallel path-ways,
explains many of the observed saccadic and neuronalbehaviors. One
of the most important innovations of themodel that we present here
is that the cerebellum carriesout the function ascribed to the
displacement integrator, i.e.monitoring the dynamic motor error.
Thus, the cerebellumguarantees the accuracy of saccades. This role
is
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accomplished by compensating for directional errors byproviding
an appropriate directional drive to the brainstem and by choking
off the collicular drive at the appro-priate time.
Furthermore, in our model the SC plays a smaller rolethan that
proposed in many recent models; in our view, theSC simply provides
a directional drive that starts movingthe eyes in approximately the
right direction. It is up to thecerebellum to guarantee that the
overall drive is appropriateto accurately foveate the target.
We propose that the burst and buildup neurons are, as faras
movement execution is concerned, functionally indis-tinguishable.
Nonetheless it is possible that they exert dif-ferent roles for
other aspects of eye movements, like targetselection (Optican,
1994), learning of consistent maps fordifferent modalities
(Grossberg et al., 1997) and determina-tion of reaction time
(Dorris et al., 1997).
The distributed nature of our model should make it simpleto
extend it when new experimental evidence is accumu-lated. Thus, our
model can act as a framework for under-standing how new anatomical
regions and new cell typescan interact with those previously
studied, to produce sac-cadic eye movements.
Acknowledgements
C.Q. was partially supported by a grant (Sistemi naturalied
artificiali nei problemi cognitivi e dellapprendimento)from
Ministero dellUniversita e della Ricerca Scientifica eTecnologica
to Paolo Inchingolo.
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