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A computational approach to the control of voluntary saccadic eye movements.
Jérémy Fix
To cite this version:
Jérémy Fix. A computational approach to the control of voluntary saccadic eye movements.. The 1st International Conference on Cognitive Neurodynamics : ICCN 2007, 2007, Shanghai, China. �inria- 00166540�
voluntary saadi eye movements
JeremyFix
Loria,CampusSientique,BP239
54506Vandoeuvre-les-Nany,Frane
Abstrat. We present a omputational model of how the several ar-
eas involvedinthe ontrol of voluntarysaadieyemovementsmight
ooperate. This modelis based on anatomial onsiderations and lays
theemphasisonthetemporalevolutionoftheativitiesineahofthese
areas,andtheirpotentialfuntionalroleintheontrolofsaades.
1 Introdution
Fromthe early work of [1℄,re-examinedby [2℄, we knowthat the visual infor-
mation is proessed along two pathways : the ventral stream provides visual
information forobjetreognitionwhereasthedorsal streamprovidesinforma-
tion neessary for the the ontrol of ation. In the rest of the artile, we will
exlusivelyfousontheontrolof voluntarysaadi eyemovementsinvolving
aortial pathway throughout severalbrain areas. A subortial pathwayalso
existandmightbeinvolvedinreexivesaades.Ifwefollowthepathwayfrom
avisualstimulationtotheprodutionofasaade,weanidentifyseveralstru-
tures involveddiretly orindiretly in the ontrol of these movements.In the
aseof voluntary saadieyemovements, themain areasinlude thesuperior
olliulus(SC),thefrontaleyeelds(FEF),thesupplementaryeyeelds(SEF),
thedorsolateralprefrontalortex(dlPFC),thelateralintraparietalsulus(LIP)
andthevisualortex([3,4℄).
Inthe last few years, several studies haveled to a better understanding of
the representation of the spatial representation of visual information in LIP.
Bothexperimentalmeasurementsandomputationalmodelshaveshedthelight
onaneyeentered representation([5,6℄).Theneuronsin LIParealsostrongly
modulated bythe position of theeye,headand bodyparts.Andersen et al[5℄
haveshown,forexample,thattheativityoftheneuronsinthisareadependson
theeentriityoftheeye,whilealwaysexhibitingamaximalresponseatagiven
retinalposition.Computationalmodelings[7℄haveprovidedstrongresultsthat
indiate that the representation of the information in a ommon eye-entered
representation,modulatedbythepositionoftheeye,headandbodyparts,an
bedeodedinseveralframesofreferene,namelyeye-,head-andbody-entered.
The neurons in FEF reeive strong topographially organized projetions
ation of asaade.On theopposite, movement related neurons rebefore and
duringsaades,whetherornotthesaadeistriggeredbyavisualstimulus.Vi-
suomovement neurons havebothvisualandmovement-relatedativity.Among
thesethreetypesofells,onlyonesrelatedtomovementprojettothesuperior
olliulusandto theaudatenuleus[3℄.Therstprojetionarriesthetarget
ofthesaadewhiletheseonddetermineswhenthemovementisexeuted.
Anenhanedativityinthesupplementaryeyeeld(SEF)isreordedwhen
theseletionofatarget(amongseveralpossiblestimuli)forasaadieyemove-
mentisbasedoninternalfatorssuhasmotivationorrewardexpetation[9,10℄.
TheSEFhasbeenthoughttorepresentthetargetsofsaadieyemovementsin
aranioentriframeof referene[11℄.Morereently,[12℄ haveshownthat the
enodinginSEFismuhmoreomplexthanasimpleranioentrirepresenta-
tionandthatthereoexistsaontinuumofeye-,head-andspae/body-entered
representationsforgazeoding.Finally,[13℄haveprovidedevidenesfortherole
ofthedorsolateralprefrontalortexinspatialworkingmemory.
While more and more is known about the dierent strutures involved in
theontrolof saadieyemovements,the waythese areasooperateto selet
the relevant stimuli, to deide whih of them is the next target to fous on,
to memorize these targets when the task at hand requires it is still unlear.
We propose in the next setion a neural network arhiteture relying on the
previously introdued anatomial onsiderations and illustrate its funtioning
withalassialdouble-steptask.
2 Arhiteture of the model
Themodelwepropose,depitedongure1,isbasedontheContinuumNeural
Field Theory([14,15℄), aframework of dynamiallateralinterationswithin a
neural map. It onsists in several two dimensional sets of units, eah of them
haraterised by an ativitydenoted u
M
(x;t) (for aunit at position x, in the
mapM)that followstheordinarydierentialequation1.
u
M
(x;t+1)=u
M
(x;t)+:Æu
M (x;t)
Æu
M
(x;t)= X
y2M w
xy :u
M
(y;t)+I(u
M 0
(y;t);y2M 0
;M 0
6=M) (1)
whereM andM 0
aremapsofunits,w
xy
amexian-hat lateral-weightfuntion
andI(u
M
0(y;t);M 0
6=M)afuntionomputingtheinueneofinputunits.We
distinguishtwokindsoffuntion fortheintegrationoftheinputs:thelassial
weightedsum and aweightedsum of theprodut of inputs' ativity. Wehave
shownin[16℄that thesesigma-piintegrationsprovideaneÆientwaytoremap
avisualinformationarosssaadieyemovements.
After this brief introdution of the omputational bases, we will desribe
the global arhiteture of the model and thefuntional roleof eah map. The
FEFvm FEFv LIP
FEFm
Visual input Fixation
Eye movement SC
Eye Position SEF
dlPFC
Fig.1.Apossiblearhitetureofhowthemajorbrainareasinvolvedintheontrolof
voluntarysaadieyemovementsmightooperate.(Refertothetextfordetails)
aneye-enteredframeofreferene,itsunitsbeingmodulatedbythepositionof
the eye. The lipmap then projetsto thefefv and sef maps. The pathway
from fefv to fefm selets onetargetfor asaadi eyemovementamong the
presentedstimuli.Thesemapsrepresentthevisualinformationinaneyeentered
frameof referene(FR). Whilefefvm representsallthepotentialtargetsfora
saadi eyemovement,aloal exitatory- globalinhibitory pattern oflateral
onnetionsin fefm providesaompetition amongthese targets, so that only
onestimulusanemergeinfefm:thetargetofthenextsaade.Thistargetthen
reenterslip;thisreentrysignalrepresentsthespatialattentionbiasobservedin
physiologial reordings. The sef map enodesthe positions of the eye in the
orbit(inaranioentriorhead-enteredFR) thatentereah stimulusonthe
retina. As detailed in the introdution, the distributed representation in lip
(inaneyeenteredFR,modulatedbytheproprioeption)allowstodeodethe
informationinsuhaframeofreferene.Thereurentiruitformedbysefand
dlpfformsaranioentrimemoryofthestimuli,usedwhenthetaskrequires
to memorizetheirposition.Thismemoryhastheadvantageto beindependent
on the position of the eye and provides the fefvm map with the positions of
thestimulirelativetotheurrentposition oftheeye,thistransformationbeing
realised by the sigma-pi ombination of the sef and eye position maps (we
annotexplainindetailthistransformationbutthesameprinipleisdetailedin
[16℄). Theprojetionsfrom fefm to sarrytheposition ofthetarget forthe
eye movement.s is stronglyinhibited by fixation units so that the saade
is exeutedonlyifthese neuronsreleasetheirinhibition. This inhibitionmight
representtheinhibitoryprojetionsfromtheFEFtoSC,goingthroughthebasal
ganglia,reportedin anatomialstudies.
3 Disussion
The presented arhiteture was suessfully applied to a lassial double-step
task 1
. The aim of the model was notto reprodue all the physiologial prop-
1
A video showing the temporal evolution of the model is avalaible at
movements.Rather,wewantedtotestapossiblewayinwhihtheseareasmight
ooperateemphasizing the funtional role of eah of them. One of the limita-
tionsofthismodelisthattheseletionofthetargetofthesaadeemergesfrom
lateralompetition in thefefm map, givingtheopportunity to allthe poten-
tial stimuli to be seletedwhile onemaydesire toavoid seletingapreviously
fousedone.Abias towardnonpreviouslyfousedstimulimaybe ahievedby
adjoiningaworkingmemorytotheFEFmapsasillustratedin[16℄.
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