distributed model of control of saccades by superior colliculus and

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

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

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

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).


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


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


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.


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.


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.


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.


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.


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.


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.


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


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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distributed model of control of saccades by superior colliculus and

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