Research Article Evaluating the Influence of Motor Control ...downloads.hindawi.com/journals/bmri/2014/162423.pdf · motor programming and focuses on the saccade goal, covert attention

Research ArticleEvaluating the Influence of Motor Control on SelectiveAttention through a Stochastic Model The Paradigm ofMotor Control Dysfunction in Cerebellar Patient

Giacomo Veneri1 Antonio Federico2 and Alessandra Rufa12

1 Eye Tracking amp Visual Application Lab University of Siena Viale Bracci 2 53100 Siena Italy2 Department of Neurological Sciences and Behavior University of Siena Viale Bracci 2 53100 Siena Italy

Correspondence should be addressed to Giacomo Veneri gveneriieeeorg

Received 29 April 2013 Revised 3 November 2013 Accepted 7 November 2013 Published 9 February 2014

Academic Editor Hitoshi Mochizuki

Copyright copy 2014 Giacomo Veneri et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Attention allows us to selectively process the vast amount of information with which we are confronted prioritizing some aspectsof information and ignoring others by focusing on a certain location or aspect of the visual scene Selective attention is guided bytwo cognitive mechanisms saliency of the image (bottom up) and endogenous mechanisms (top down) These two mechanismsinteract to direct attention and plan eye movements then the movement profile is sent to the motor system which must constantlyupdate the command needed to produce the desired eye movement A new approach is described here to study how the eye motorcontrol could influence this selection mechanism in clinical behavior two groups of patients (SCA2 and late onset cerebellar ataxiaLOCA) with well-known problems of motor control were studied patients performed a cognitively demanding task the resultswere compared to a stochastic model based on Monte Carlo simulations and a group of healthy subjects The analytical procedureevaluated some energy functions for understanding the process The implemented model suggested that patients performed anoptimal visual search reducing intrinsic noise sourcesOur findings theorize a strict correlation between the ldquooptimalmotor systemrdquoand the ldquooptimal stimulus encodersrdquo

1 Introduction

The human vision system is a foveocentric structure reflect-ing the specific anatomical distribution of photoreceptorsacross the retina which ensure the best resolution just in asmall central region called fovea outside this region visualresolution decreases sharply To overcome this perceptivelimit the human brain has developed fast and accurate eyemovements (saccades) for pointing the fovea at interestingobjects in space [1] In other words each saccade landingpoint represents the locus in space where the fovea gets themost detailed information outside this point elements of ascene may be localized but are less accurately distinguishedDue to this physiological constraint the amount of infor-mation that can be processed at once by visual system islimited therefore spatial attention is used to select relevantlocations of the visual field for enhanced processing [2] thatmay occur overtly when associated with an eye movement

toward the selected location or covertly without an eyemovementWhile overt attention is strictly related to saccademotor programming and focuses on the saccade goal covertattention is more linked to the perceptual characteristics ofthe peripheral vision and is under the influence of stimulusfeatures (bottom up attraction) and cognitive enhancement(top down conduction) It has been found that visual searchof complex scenes is influenced by both top-down factors [3]including previous knowledge expectations current cogni-tive status and expected goals and bottom-up factors thatreflect sensory features of the stimulus such as orientationluminance shape and brightness In particular bottom updriving of gaze toward the most salient stimuli occurs firstthen as visual exploration goes along there is an incrementof cognitive processes influencing visual search in a topdown modality By combining the top down and bottom upinformation during search our brain gets a clear view of theconspicuous items (both in terms of cognitive relevance and

Hindawi Publishing CorporationBioMed Research InternationalVolume 2014 Article ID 162423 13 pageshttpdxdoiorg1011552014162423

2 BioMed Research International

LGNSC

MC

Thalamus

Midbrain

Pons

CBLM

VA

FEFPFC

V1

Ventral stream

(what)

Dorsal stream(where)

V2V3V4

PUL

LIP

IT

Retinal projections (90to LGN 10 to SC)

MTMST

(a)

LGNSC

MTMST

MC

Thalamus

Midbrain

Pons

VL

INSpino-

cerebellumPN

CBLM

Cerebrocerebellarloop

VA

FEFPFC

(b)

Figure 1 Short reference of vision pathway (a) Selective attention pathway the LGN the striate and extrastriate cortex (V1 V4inferotemporal cortex and MT) SC pulvinar LIP FEF and PFC are known to be involved in attentional processes (b) Cerebrocerebellarcommunication loop the neuronal circuitry of the cerebellum is thought to encode internal models that reproduce the dynamic properties ofbody partsThese models control the movement allowing the brain to precisely control the movement without the need for sensory feedbackMC motor cortex IN interpositus nucleus PN pons VL ventrolateral nucleus SC superior colliculi LGN lateral geniculate nuclei Visualareas (VA) V1 V2 V3 V4 and MT (middle temporal) PFC prefrontal cortex FEF frontal eye fields LIP lateral intraparietal cortex

feature saliency) and their location becoming able to buildup an internal task specific representation of the scene [4ndash6] More specifically the relative conspicuity of each elementof the scene is reproduced into a saliency map which allowsto predict where the eyes will be attracted first during theexploration of a scene Although the saliency map simplyrefers to the bottom up characteristic of a scene a moretop-down influence of the visual search is represented in theprioritymap [7] Covert attention is particularly efficient dur-ing top-down visual search where it is used to collect globalinformation of the scene throughout a parallel processingof conspicuous elements and to increase the discriminationabilities of peripheral vision by enhancing spatial resolutionat the attended target location [8] and by fading irrelevantlocations From a neuro hysiological point of view objectrsquosfeatures and spatial localizations acquired during visualexploration through the retina [9] are principally sent tovisual cortex (V1) via lateral geniculate nucleus (LGN) ([10ndash12] for a review) However fast spatial information about thevisual scene is also sent to the superficial layer of the superiorcolliculi (SC) This subcortical structure integrating multi-sensory inputs with eye and head motor plan is importantfor orienting attention in retinotopic coordinates towardsnewly appearing objects in the visual field [10 13] Moreupstreaming information about objectrsquos features and spatiallocalization is elaborated in the dorsal (occipitotemporalwhere) and ventral (occipitoparietal what) streams [14ndash17]in order to construct a priority map [7 10 18 19] (seeFigure 1(a))

Various formal models have been proposed Feature Inte-gration Theory [20] Guided Search [21] Premotor Theory[22] Theory of Visual Attention [23] and Winner Takes All[24] Feature Integration Theory proposes a two-stage visualattention process during first stage humans process several

primary visual features during second stage the objects areanalyzed with details Winner Takes All and Guided Searchare devoted to assign saliency to locations in the visual fieldRecently Reynolds and Heeger [18] proposed a review ofa normalized model of attention the model studied howstimulus features and cognitive attention should work toperform an efficient visual search

These models describe how humans could select someaspects of the scene but how the motor control systemmay optimize visual search by predicting the sensory con-sequences of an impending saccade Eye movements arecontrolled by the cerebrocerebellar communication loop anddescribed by feedforward or inverse control models [25ndash27](see Figure 1(b))

Recently some authors [28 29] have applied the theoryof optimal control (OCT) in the mechanisms that regulatemotor control humans seem to adapt their behavior tominimize some cost function such as noise in performing anaction [30] Najemnik and Geisler argued that humans couldchoose fixations that maximize information gained about thetargetrsquos location this strategy [31] allows humans to selectfeatures from the scene optimally such as an ldquoideal searcherrdquo

Our work aims to extend the OCT principle to themechanisms that regulate visual search We proposed amethod to study how the strategies of selective attentionmay be modulated by the motor control performance Sincethe cerebellum is the brain structure where some dynamicaspects of motor control are optimized to reduce errors wecompare our formal model with the ocular motor behavior ofwell characterized cerebellar patientswhohave specificmotorcontrol failure [32 33]

Therefore we developed amathematical stochasticmodelbased on the Monte Carlo method (MC) able to simu-late ongoing visual search in a cognitively demanding task

BioMed Research International 3

t

500ms

30000ms

Fixation

CE

AB

D

5

2

4

3

1

Saccade

ion

E

AAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBB

5555555

22222222222222222222222222 3333333333

Figure 2 Example of a display shown in the task and a small portionof gaze data (red line) Subjects after a fixation point of 500ms wereasked to follow an alphanumeric sequence (1-119860-2-119861-3-119862-4-119863-5-119864)with their gaze The numbers and letters appeared in a pseudoran-dom distribution (letters on top and numbers on the bottom) on a1024 times 768 px and 51 times 31 cm black screen for 30000ms The redline shows some fixations and saccades made by a healthy subjectSaccades are rapid eye jumps from one region to another regionDuring fixations (time duration asymp 100ms sdot sdot sdot 800ms) humansacquire information from objects

(Figure 2) Some common energy functions were evaluatedand we compared model results with a control group ofhealthy subjects (CTRL) and two groups of patients withdegenerative cerebellar ataxia Indeed the cerebellum isimplicated inmaintaining the saccadic subsystem efficient forvision this ability is often disrupted in degenerative cerebellardiseases as demonstrated by saccade kinetic abnormalities

Therefore two groups of patients affected by spinocere-bellar ataxia type 2 (SCA2) and patients with late onsetcerebellar ataxia (LOCA) were enrolled in the study Theresults of subjects (CTRL SCA2 and LOCA) were comparedwith the modelrsquos outcome

2 Material and Methods

21 Patientrsquos Clinical Findings SCA2 is an autosomal domi-nantly inherited neurodegenerative disorder mainly charac-terized by cerebellar ataxia cerebellar atrophy at MRI andslow eye movements [34] LOCA is a group of patients withdegenerative genetically unrecognized pure cerebellar ataxiaassociated with atrophy limited to the cerebellum at MRIDemographic clinical and genetic data of a larger sampleincluding the patients recruited here have been reported byKlockgether Muzaimi et al and us [35ndash38]

22 ExperimentDesign Weused a highly cognitive demand-ing task namely the trail making test [39 TMT] in whichsubjects were asked to follow an alphanumeric sequence with

their gaze The trail making stimulus was a pop-up highcontrast image consisting of a sequence of numbers andletters (1-119860-2-119861-3-119862-4-119863-5-119864) arranged in an unpredictablemanner In our version of the trail making task (TMT)numberswere at the bottomand letters at the top of the image

The TMT version proposed was simplified to helpsubjects to perform the task efficiently and avoiding anyperformance requirement (In the current experiment weenrolled patients affected by cerebellar disease psychologicaltest proposed to patients could be biased by subjective self-underestimation fear of judgment or fatigue therefore weused a simplified easy version to avoid eliciting of frustration)The distribution of symbols in a predefined geometric orderallowed a more clear definition of the gaze shift duringsequencing since the distance from the center and betweenthe symbols required a real gaze shift avoiding the targetdetection by periphery [40 41]

During the task the subject was asked to fixate a centralred dot after 500ms the dot disappeared and the subjectcould explore the TMT (Figure 2) The TMT is particularlysuitable for studying selective attention as it does not requireany explicit feedback by subjects and the test performancecan be evaluated automatically and reproduced by a compu-tational model

221 Subjects Enrollment and Training Seven SCA2 patientsa mixed group of six patients with genetic cerebellar ataxia(LOCA) and 23 healthy subjects were enrolled in the studyAll were in the age range of 25ndash55 years

The patients included in the study were previously diag-nosed as reported by Federighi et al [37] Exclusion criteriafor control subjects included any history of neurological oreye problems toxic or drug abuse and current pharmacolog-ical treatment for neurological or eye diseases All subjectsgave their informed consent and the study was approved bythe Regional Ethics Committee

All subjects were trained by a psychologist before theexperiment showing a paper version of the TMT All subjectsperformed a first attempt of the experiment for 30 secondsafter a pause of five minutes the procedure started

222 TMT Procedure Subjects were seated at a viewingdistance of 78 cm from a 321015840 color monitor (51 cm times 31 cm= 332 deg times 216 degree of visual angle) Eye positionwas recorded using an ASL 6000 system which consistsof a remote-mounted camera sampling pupil location at240Hz Head movements were restricted using chin restand bite After the calibration phase subjects performeda simple validation phase eliciting four reflexive saccadesand measuring the error between the eye position and thetarget the calibration procedure was repeated until the errorwas less than 05 degree A red dot appeared at the screencenter for five seconds then a randomized version of TMT(different from the version used during the training step)appeared for 30 seconds Subjects could stop the experimentif they thought they had concluded All subjects performedthe experiment within the given time Different sessions ofthe experiment were performed for each patient on the same


A

E

C

5

FixationDTDN

Saccade

Nearest ROI

Next target (1middot middot middot 5 minus E)

Figure 3 Fixations distribution indicators For each fixation theeuclidean distance from the center of nearest ROI (DN) and theeuclidean distance in pixels from the center of target (DT) wereevaluated Dashed blue line represents the eye movement (saccade)

day as well as on different days When a patient asked tostop the experiment because heshe was tired the procedurewas restarted after a resting period All subjects were able toperform the task Seven patients reported fatigue

223 Patientrsquos Test Postassessment To verify the visual acuityand the ability to perform the test by patients we imple-mented a ldquoguided TMT searchrdquo a grayscale TMT versionwas proposed to patients (SCA2 LOCA) where letters andnumbers were highlighted by a red color step-by-step fol-lowing the alphanumeric sequence (1-119860-2-119861-3-119862-4-119863-5-119864)every 2 seconds We measured the sequencing ability andthe distribution of eye fixations Indeed some other studies[37 42ndash45] reported that cerebellar lesions injury may affectthe accuracy of saccades

23 Distribution of Eye Fixations Evaluation To analyzevisual search and model outcome we defined some indi-cators For each target (letter and number) we defined aregion of interest (ROI) (100 px times 100 px) ROI was definedas asymp 200 larger than the symbols of the test We evaluatedhow humans directed next exploration according to thedistribution of latest fixations (see Section 24) The fixationswere identified by the dispersion algorithm developed bySalvucci and Goldberg [46]

For each fixation we evaluated the Euclidean distancein pixels from the center of nearest ROI (DN) and theeuclidean distance in pixels from the center of target (DT)(see Figure 3)

24 Selection Mechanism Evaluation To evaluate ongoingvisual search Engel Ponsoda et al Findlay et al [5 47 48]and later us Veneri et al [41] developed a geometric method(Figure 4) the proposed procedure defined ldquoobserved direc-tionrdquo as the direction of the subjectrsquos gaze We evaluated the

119889 = (observed direction ⊖ direction reference) sdot 119908 (1)

119908 is a special weight avoiding artifact due to borders forexample the weight (119908) was set to 1 for letter in the centerand 16 = 85 for letter near the border The ⊖ operator is the

C

5

Fixation (tf)

Saccade (t)

Direction difference(DE)

Fixation (tfminus1)

(a)

5

E

C

Fixation

Saccade (t)

Direction difference(DX)


(b)

Figure 4 Projection of gaze the method evaluates the differencefrom the direction taken by subject (saccade dashed blue line) withrespect (DE DX) to a direction reference (a) Direction referencewas defined for DEas the vector to the previous fixations made in agiven time interval (on figure only one fixation is shown) and (b) theexpected target for DX

radial difference between the two directions and ranged from0 deg to 120587 deg

The selection mechanism was evaluated calculating thedirection of saccade at given time 119905 (Figure 4(a)) versus theprevious fixations made (DE) in a given time interval andthe direction of saccade versus the expected target (DX)(Figure 4(b))

Then setting the ldquodirection referencerdquo as the directionfrom the current fixation to the previous fixation at the giventime 119905

119891 the scalar direction difference DE was expressed as

DE = mean (119889) (2)

We defined also

DE (Δ119905) = mean (119889) forall fixations isin (119905119891minus Δ119905 119905

119891) (3)

Finally setting the ldquodirection referencerdquo as the directionfrom the current fixation to the expected direction (thedirection to target) at a given time 119905

119891 the scalar direction

difference DX was expressed as

DX =

mean ((direction observed ⊖ direction target expected)

sdot119908)

(4)

DX models the ability of humans to remember visitedROI and must be calculated


X

w

s

Fixationsdistribution

Relevant itemselection

Motor control

XY

Peripheral vision

MemoryΔt

Pp

Positionperturbation

Ppf

Pri

Figure 5 Stochastic model architecture the block ldquofixations distributionrdquo provided the probability of moving the gaze far from the latestfixations the block ldquorelevant item selectionrdquo provided the probability of directing the gaze to the correct target (next symbol) based on aninternal representation of the target ldquoperipheral visionrdquo directed the gaze to target when target is near 115 px asymp 4 degree with probability 119875

119901

Model perturbation was accomplished through the 119904 parameter

25 Calculation Figure 5 shows the model architecture Themodel was based on three subsystems the first block (ldquorel-evant item selectionrdquo of Figure 5) provided the probability ofdirecting the gaze to the correct target (next symbol) based onan internal representation of the target with probability 119875

119903119894

the second block ldquofixations distributionrdquo of Figure 5 providedthe probability ofmoving the gaze far from the latest fixationswith probability 119875

119901119891[41 49 50] Third block (ldquoperipheral

visionrdquo) directed the gaze to target when target was in aneighborhood of 115 px asymp 4 degree with probability 119875

119901and

modeled covert attention [19] Latest block perturbed (119904)fixations location in order to simulate model variability

After normalization the weighted union probabilitybetween two mutually exclusive events was calculated (5)

119875 next target = (1 minus 119908) sdot 119875119903119894(DX 1205902

119903119894) + 119908 sdot 119875

119901119891(DE 1205902

119901119891)

(5)

where 119908 isin (0 1)The model calculated the probability by (5) then it

selected the direction to move in accordance with the proba-bilityThe procedure was repeated for each symbol and exitedwhen the model performed the sequence correctly 119908 wasthe level of competition between the blocks ldquorelevant itemselectionrdquo and ldquofixations distributionrdquo

Probabilities are 119875119903119894

= N(DX 1205902119903119894) 119875119901119891

= N(DE 1205902119901119891)

and 119875119901= N(120583

119901 1) whereN(120583 120590) is the normal distribution

ofmean120583 and variance120590 DE andDXwere evaluated through(2) and (4)

Output of model was an array of fixations

(119909119891 119910119891) = Φ (119904 120583

119901 119908 1205902

119901119891 1205902

119903119894) (6)

where 1205902

119901119891was set to 2 according to variance of DE of

subjects 1205902119903119894was set to 34 according to variance of DX of

subjects 119904 and 120583119901and 119908 were free variables

26 Energy Function Optimization theory requires the def-inition of one (or more) energycost function to be mini-mized Therefore according to [45 51 52] we defined twofunction costs based on saccadesrsquo properties for each saccadewe evaluated the euclidean distance in pixels from the saccadestart point to the end of saccade (119860 sacc) skipping shortsaccade inside the same ROI A global function saccadeenergy was measured evaluating the path length through thefollowing formulas

119869sacc

= sum

forall119905isinsaccades

radic(119909 (119905) minus 119909 (119905 minus 120575119905))2+ (119910 (119905) minus 119910 (119905 minus 120575119905))

2

(7)

where 120575119905 = 4167ms is the sampling time Equation (7) is thesum of all saccadesrsquo length

Fixations represent the cognitive act to process the scenecardinality and duration are measures of task performance[19 53 54] Therefore the task execution energy was definedcounting the number of fixations inside the ROI to completethe task

119869fix = sum

forallfixations in ROI1 (8)

Equation (8) is the number of stepsmade to complete the task

27 Stochastic Model Application The basic idea was to applythe stochastic model defined in Section 25 to study sometarget function (energy 119869sacc 119869fix and 119860 sacc) as an optimalcontrol problem Optimization problems can mostly be seenas one of two kinds we need to find the extrema of a targetfunction cost over a given domain performance is highlydependent on the analytical properties of the target functionTherefore if the target function is too complex to allow an


Sequencingtest

(TMT)

Subjects gazedata

Mathematicalcalculation

DN

DX DE

Stochasticmodel

Jfix Jsacc andAsacc

Jfix Jsacc andAsacc

Model outcome for allvalid explorations

Understanding data

Monte Carlosimulation

Ppf Pri

120583p w and s

Figure 6 Analysis procedure Subjectsrsquo gaze data were evaluated through a mathematical procedure able to extract some basic indicators(DN DX and DE) and energy functions (119869sacc 119860 sacc and 119869fix) DX and DE were used to calculate variance (1205902

119901119891 1205902119903119894) to tune the model Then

using varying parameters 119904 120583119901 and119908 model reproduced all valid explorations Subjectsrsquo andmodelrsquos outcomes were compared to understand

the selection mechanism

analytical study or if the domain is too irregular the methodof choice is rather the stochastic approach [55 56] Sincevisual search is a complex systemunder the influence ofmanymechanisms it is not easy to predict the selectionmechanismthrough an implicit and deterministic model therefore wedeveloped a stochastic model based on the MC simulation(To understand Monte Carlo simulation the reader shouldconsider the following case a player wants to measure thesurface of his carpet in his room 3m times 3m the player mayrandomly launch a button 100 times and count the numberof times (119896) the button falls onto the carpet It is easy to verifythat the carpet surface is 119896 sdot (3m times 3m)100 In our workthe sought-after measure is the energy to execute the task(the carpet surface) and the sought after system is the setof parameters (the carpet geometry)) [57] Therefore themodel attempted all possible explorative strategies varyingparameters 119904 120583

119901 and 119908 For each 119899 = 1000 simulations we

varied parameters and we evaluated the function cost 119869sacc119860 sacc and 119869fix (Monte Carlo optimization)

From an intuitive point the model computed the solu-tions domain perturbing fixations distribution the outcomecould be compared with subjectsrsquo visual search (CTRLLOCA and SCA2) data see Figure 6

3 Results

31 Subjects The positive trend of DE(Δ119905) minus DE (Figure 7)for all groups suggested that saccadersquos direction tended tomove away from latest fixations In particular the trend ofgaze direction with respect to the distribution of fixationsmade increased in the last second (Δ119905 = 1 s) suggesting thatthe basic model operation (Section 25) was compatible withsubjectsrsquo exploration

To assess the differences of exploration strategy amonggroups we evaluated distance to nearest ROI (DN) andnumber of visited regions of interest (119869fix) ANOVA did notreport significant difference on 119869fix (119875 = 0126 119865(233) =2209) and it was confirmedby posthoc analysis (119901CTRL-SCA2 =06596 119901CTRL-LOCA = 00653 and 119901SCA2-LOCA = 00641)On the contrary ANOVA reported a significant difference

12345678916

165

17

175

18

185

CTRL

SCA2

SCA2LOCA

Δt (s)

DE

(deg

)

CTRLLOCA

Figure 7 Direction difference trend of subjects The methodcalculated the direction difference DE from previous fixations madeon the time intervals [0 sdot sdot sdot 9] [0 sdot sdot sdot 8] sdot sdot sdot [0 sdot sdot sdot 1] seconds (on the119909-axis only the upper intervalrsquos value is reported) The figure showsthe standard deviation of CTRL LOCA and SCA2 for Δ119905 = 1 4 6respectively The positive trend of the lines shows that saccadersquosdirection tended to move away from latest fixations

on DN (119875 = 0001 119865(233) = 952) and post-hoc Holm-Sidak confirmed the significant difference of DN CTRL-SCA2 (119901CTRL-SCA2 lt 0001 120572(33) = 00170) and betweenCTRL-LOCA (119901CTRL-LOCA = 00105 120572(33) = 00253) and nosignificant difference between patients (119901SCA2-LOCA = 04217120572(33) = 00500)

Our preliminary conclusion was that performance couldbe considered equivalent among groups but with differentstrategies (Table 1) Indeed patients (LOCA and SCA2)preferred sparser fixations instead of targeted saccades Thisstrategy was found by several authors [58ndash60] and has beenreferred fixation as ldquocenter-of-gravityrdquo fixations Center-of-gravity occurs when targets are surrounded by nontargets


Table 1 Mean value and standard deviation (in brackets) of tests

Indicators Acronym CTRL LOCA SCA2

Group dimension 119873 23 6 7

Age 27ndash50 40ndash55 42ndash55

Distance to nearest ROI (px) DN 239 (1435) 5731 (plusmn1368) 6554 (plusmn1849)

Number of fixations in ROI (visited ROI) 119869fix 2890 (plusmn1118) 375 (plusmn615) 292 (plusmn1116)

Number of fixations 39 681 493

Saccade amplitude (px) 119860 sacc 31736 (plusmn6964) 21222 (plusmn4610) 23332 (plusmn7305)

Within subject saccade amplitude variance 49634 (plusmn21329) 24040 (plusmn6200) 33138 (plusmn16031)

Percentage of saccade directed to targetwhen DT le 4 degree ()

119875119901

090 045 060

and the saccades instead of landing at the designated targetland in the midst of the whole configuration This effect wasfirstly attributed to an error of the filter selection [61] andthen was considered a necessary mechanism to execute moreefficient saccades [60 62] We concluded that patients coulddirect the gaze into the ROI but preferred sparse fixationsTo understand this effect we compared human results withmodel results

32 Model Simulation Using varying parameters 119904 120583119901 and

119908 the model (Figure 5) calculated the 119869fix 119869sacc and 119860 saccthe three surfaces (slightly smoothed for readability) shownin Figures 8 and 10 report the domain of all available explo-rations choosing the minimum value along the dimension ofthe parameter 119908

To assess the validity of the model we evaluated thenormalized root mean square error (NRMSD) of 119869fixNRMSD varied from 9 to 26 NRMSDCTRL = 0091NRMSDLOCA = 017 and NRMSDSCA2 = 026 We acceptedthis result as an acceptable error indeed only 11of subjectsreported a NRMSD gt 020 and in any case NRMSD lt 040

The model reported a local minimum 119869fix = 19 when119904 = 100 120583

119901= 100 and 119908 = 06 subjects however

performed a less efficient exploration (Table 1) To study thisresult in depth we calculated the 119869sacc parameter whichprovided an estimate of saccadic energy we have to note thatit is not possible to compare 119869sacc of subjects and model dueto noise on saccadersquos trajectory indeed in two recent papers[37 38] we found that motor control noise of SCA2 reporteda significant difference with CTRL and LOCA Figure 8(b)shows the overall solutions domain varying parameters 119904120583119901 and 119908 Overall minimum hyperplane was found at 119904 asymp

32 plusmn 82 which corresponded to DN asymp 60Comparison of model simulations with subjectsrsquo perfor-

mance was done by setting modelrsquos 120583119901equal to 119875

119901of subjects

(090 045 and 060) Figure 9 shows the model compared tosubjectsrsquo exploration the three groups of lines of Figure 9(a)showed themodel numbers of steps to complete the task (119869fix)for 120583119901

= 090 120583119901

= 045 and 120583119901

= 060 and varying 119904

and 119908 The 119904 parameter controlled the dispersion of fixationswith direct (nonlinear) influence on DN and119908 provided the

needful variability to adapt within group variability amongsubjects The three lines of Figure 9(b) show the saccadeenergy (119869fix) of the model and the corresponding value ofsubjects

To evaluate the influence of saccade control on visualsearch we analyzed saccade amplitude (119860 sacc) ANOVAreported a significant difference among groups (119875 = 00037119865(2 33) = 664) and post-hoc holm-sidak confirmedthe significant difference of 119860 sacc between CTRL-SCA2(119901CTRL-SCA2 lt 0001 120572(33) = 00170) and CTRL-LOCA(119901CTRL-LOCA lt 001 120572(33) = 00253) and no significantdifference between patients (119901SCA2-LOCA = 05769 120572(33) =

0050) Indeed we found that saccade amplitude of patients(SCA2 and LOCA) was less than 235 and 281 of healthysubjectsrsquo saccades (Table 1)

Comparing 119860 sacc of subjects and model model reportedsimilar value (Figure 10(a)) to subjects with an error rate ofasymp 7 analyzing the 119860 sacc trend varying fixationsrsquo dispersion(DN) it seems plausible that SCA2 and LOCA preferred anexploration which minimized saccade amplitude We triedto minimize the following empirical function cost bringingtogether the goal parameter 119860 sacc 119869sacc and 119869fix

ℎ (1205790 1205791 1205792)

= 1205790sdot

119860 saccmax (119860 sacc)

+ 1205791sdot

119869saccmax (119869sacc)

+ 1205792sdot

119869fixmax (119869fix)

(9)

We found that SCA2 and LOCA preferred to minimizesaccade amplitude (120579

0= 1) and saccade energy (120579

1asymp 13)

rather than steps to complete the task (1205792asymp 01) the opposite

was true for CTRL (120579012

= 1 0 529)

33 Patients Test Postassessment Results Since subjects withcerebellar injury have reported low precision on visual searchtasks we asked patients (SCA2 LOCA) to perform a ldquoguidedTMT searchrdquo where letters and numbers were highlighted inred step-by-step Patients were able to complete the sequencewith few fixations outside the ROI (DN = 301) Weconcluded that the low precision performance reported by


20

20

40

40

60

60 8080

100

100

Pp(

)

SCA2 LOCA

CTRL

150

s

100

50

0

J fix

(a)

2040

6080

100

2040

60

80100

Pp(

)

SCA2 LOCA

CTRL

s

3

25

2

15

1

05

0

times106

J sac

c(p

xmiddotm

s)

Minimum hyperplane

(b)

Figure 8 Results of the model varying parameters (a) The number of steps to complete the task by model and by subjects The surfacereports the domain of all available explorations of model that humans could perform Stressing covert attention humans could performthe best exploration (ldquocenter-of-gravityrdquo fixations) but similar performance could be gained directing the gaze to an intermediate region toacquire overall scene information this strategy was preferred by SCA2 and LOCA (b) Saccade energy spent by the model for all availableexplorations that humans could perform An overall minimum hyperplane was found at 119904 asymp 32 plusmn 82

239 5731 655415

20

25

30

35

40

45

5011 46 74

s

CTRLLOCA

SCA2

DN (px)

J fix

Data model Pp = 90

Data model Pp = 50

Data model Pp = 60

(a)

239 5731 6554

4

5

6

7

8

9

10

1111 46 74

s

SCA2

CTRL

LOCA

times105

J sac

c(p

xmiddotm

s)

Data model (5th order polynomial) Pp = 90 (CTRL)Data model (5th order polynomial) Pp = 50 (LOCA)Data model (5th order polynomial) Pp = 60 (SCA2)

DN (px)

Minimum hyperplane plusmn 120590

(b)

Figure 9 The graph reports the numbers of steps performed by model varying 119904 120583119901 and 119908 the 119904 parameter (upper axis) controlled the

dispersion of fixations with direct (nonlinear) influence on DN (bottom axis) 120583119901set 119875119901of subjects and119908 provided the needful variability to

adapt within group variability among subjects (a) The number of steps (119869fix) to complete the task of subjects and model (b) Saccade energy(119869sacc) to complete the task of subjects and model


300

250

200

150

20

4060

80

100

Pp ()

SCA2

LOCACTRL

10080

6040

20

s

Asa

cc(p

x)

(a)

239 5731 6554150

200

250

300

350

40011 46 74

s

CTRL

LOCA

SCA2

Asa

cc(p

x)

Data model (5th order polynomial) Pp = 90 (CTRL)

Data model (5th order polynomial) Pp = 50 (LOCA)

Data model (5th order polynomial) Pp = 60 (SCA2)

DN (px)

(b)

Figure 10 Mean saccade amplitude reported by model (a) Overallspace of saccade amplitude (119860 sacc) reported by model varyingparameters and (b) compared with subjectsrsquo performance Modelreported that patients (SCA2 and LOCA) preferred a visual searchexploration in order to reduce119860 sacc ANOVAconfirmed a significantdifference of 119860 sacc between CTRL and patients

several authors [37 42 45] was negligible compared to thesize of the ROI Similar findings were reported by van Beers

4 Discussion

Assuming an error rate asymp14 (NRMSD for 119869fix) of the modelboth patients and healthy subjects performed a subopti-mal exploration with different strategies trend reported inFigure 9(b) suggested that patients (SCA2 LOCA) preferred

sparser fixations at an intermediate position between thetargets (ldquocenter-of-gravityrdquo fixations) and optimally tuned tokeep saccade amplitude (119860 sacc) as low as possible and energysaccade (119869sacc) in a neighborhood of the minimum (subopti-mal exploration) on the contrary healthy subjects (CTRL)preferred saccades directed near targets (target selection)Performance (119869fix) of SCA2 patients was similar to healthysubjects (CTRL) LOCA patients completed the task withmore energy and steps but not with a significant differencefrom CTRL

These different strategies on visual search explorationbetween healthy subjects (CTRL) and cerebellar patients(LOCA and SCA2) suggested a direct or indirect influenceof the cerebellum on the visual selection processing

41 Theoretical Considerations about the Cerebellumrsquos RoleTraditional views of the cerebellum hold that this structureis engaged in the control of action with a specific role inthe motor skills [63] The properties of cerebellar efferentand afferent projections (see Figure 1(b) for a short ref-erence) suggest that the cerebellum is generally involvedin (ldquonot necessarilyrdquo [64]) integrating motor control andsensory information to coordinate movements The modelof neuronal circuitry of the cerebellum proposed by Ito [2732 65] makes it possible to consider more concrete ideasabout cerebellar processing cerebellum is thought to encodeinternal models that reproduce the dynamic properties ofbody partsThese models control the movement allowing thebrain to precisely predict the consequence of a movementwithout the need for sensory feedback [66ndash68] or to per-form a quick movement in the absence of visual feedback[27] Indeed cerebellum is able to reproduce a stereotypedfunction of the desired displacement of eyes and providesa reference signal during movement [69] To explain thismechanism two models have been proposed Kawato et al[26] proposed a forward model (cerebellum forward model)that simulates the dynamics (or kinematics) of the controlledobject including the lowermotor centers andmotor apparatus(Figure 1(b)) the motor cortex should be able to performa precise movement using an internal feedback from theforward model instead of the external feedback from thereal control object [65 67] As such motor learning canbe considered to be a process by which the forward modelis formed and reformed in the cerebellum through basedlearningWhen the cerebellar cortex operates in parallel withthe motor cortex as mentioned above it forms another typeof internal model that bears a transfer function which isreciprocally equal to the dynamics (or kinematics) of thecontrol object [25 26] The inverse model can then play therole of a feedforward controller that replaces themotor cortexserving as a feedback controller

As further proof of this theory it is well known that cere-bellar lesions [43 44] induce permanent deficits affectingdramatically the consistency [42 45] and the accuracy ofsaccades [37] While a wide range of evidence has emergedaccounting for a dominant role of cerebrocerebellar interac-tions in motor control and its movement-related functionsare the most solidly established that recent studies have


clearly suggested an influence of the cerebellum in cognitiveand behavioral functions [65 67 70 71] including fearand pleasure responses [72ndash74] Allen et al [75] through amagnetic resonance experiment found a direct activationduring visual attention of some cerebellar areas independentfrom those deputed to motor performance Paulin [64]developed a computational physical model estimating themovement status useful for trajectory tracking and trajectoryprediction Paulin concluded that the cerebellum is not amotor control device per se but a device for optimizingsensory information about movements Kellermann et al[76] identified a cerebelloparietal loop consisting of posteriorparietal cortex (visual area V5 cerebellum) that facilitatespredictions of dynamic perceptual events Other studies pro-vided findings about a direct implication of the cerebellumonlanguage verbal working memory [77ndash81] and timing [82]Gottwald et al reported significant defects of patients withfocal cerebellar lesions in the divided attention and workingmemory but not in selective attention task [83] In additionExner et al [84] Golla et al [85] and later Hokkanen et al[86] reported normal attentional shifting in patients affectedby cerebellar lesions

42 The Dominant Role of the Cerebellum A number offunctional hypotheses (sometimes contradictories [87]) havebeen advanced to account for how the cerebellum may con-tribute to cognition and a large amount of neuroanatomicalstudies showed cerebellar connectivity with almost all theassociative areas of the cerebral cortex involved in highercognitive functioning [73] nevertheless the hypothesis of thedominant role of the cerebellum on motor control remainsthe most probable to explain our findings and was confirmedby the proposed model Cerebellar patients have a well-known disturbance in controlling saccade endpoint errorThe two groups reported here however substantially showa different saccadic behavior due to the involvement ofdiverse anatomic structures The saccadic behavior mainlycharacterizing SCA2 is the low speed with quite preservedaccuracy indicating a failure of the brainstem saccade gen-erator more than cerebellum LOCA shows a well-preservedspeed but a complete loss of saccadic error control Thispathophysiological substrate however does not distinguishtheir visual exploration during sequencing indeed bothgroups of patients similarly performed a multi step visualsearch avoiding the direct foveation of the target Thismultistep spatial sampling strategy probably enables thesepatients to increase the discriminative potentialities of thecovert attention avoiding unnecessary large saccades movingthe eyes over wrong targets If this strategy is true saccadesnot only are associated with an overt shift of attention butalso increase the potentialities of covert attention duringactive search Moreover when the cerebellum has reducedcapacities the control of long saccade is difficult due topropagation of error [51] and [45] found that patientsaffected by SCA2 reduced saccade velocity in reflexive tasks(involuntary movement) Rufa and Federighi [88] foundthat SCA2 patients sometimes interrupted saccades Thenit is plausible that in voluntary movements (free visualsearch test) patients affected by cerebellar disease adapted

visual search exploration to minimize the saccade controleffort they preferred sparse fixations and short saccades butmaintained overall saccade energy around aminimum pointThe implemented model supported this hypothesis

5 Conclusions

In our work we implemented a stochastic model able toreplicate humans strategies during an ongoing sequencingtest the model results were compared to the performance ofa group of healthy subjects and two groups of patients havingwell-documented motor control disease

From the methodological point of view we introducedthe optimization method (OCT) to study the properties ofselective attention Todorov and later van Beers proposed theOCT as a valuable instrument to link eyehandmotor controland the central nervous system to minimize the consequenceof motor control noise Najemnik and Geisler implementeda Bayesian framework to validate that human visual search isa sophisticated mechanism that maximizes the informationcollected across fixations We ldquoconnectedrdquo these two theoriesto integrate the motor control and information-processingsystems on a single reproducible model Our conclusions aresimilar to the conclusion of Najemnik and Geisler humanstend to tune visual search in order to maximize informationcollected during the search but in clinical context patientstry to minimize the effort to control eye movements

Therefore our opinion is that humans tend to applyan optimal selection to minimize a function cost (effortenergy) and we provided evidence of this theory studyingthe motor control influence through a model based on MCoptimization method and comparing results with cerebellarpatients Proposed model however is affected by somerestrictions model is specific for the TMT test and it is noteasy to generalize to other psychological tests function costshave to be defined according to the disease studied In ourfuture work we aim to adapt the basic principle of OCT andMC on the real image processing model

Conflict of Interests

The authors certify that there is no conflict of interests withany financial organization regarding thematerial discussed inthe paper

Acknowledgments

Thanks are due to Professor Maria Teresa Dotti for thevaluable contribution The study in part was funded by ECFP7-PEOPLE-IRSES-MC-CERVISO 269263

References

[1] M I Posner and J Driver ldquoThe neurobiology of selectiveattentionrdquo Current Opinion in Neurobiology vol 2 no 2 pp165ndash169 1992

[2] J M Findlay and I D GilchristActive VisionThe Psychology ofLooking and Seeing Oxford University Press Oxford UK 2003


[3] M Siegel K P Kording and P Konig ldquoIntegrating top-down and bottom-up sensory processing by somato-dendriticinteractionsrdquo Journal of Computational Neuroscience vol 8 no2 pp 161ndash173 2000

[4] B G Breitmeyer W Kropfl and B Julesz ldquoThe existence androle of retinotopic and spatiotopic forms of visual persistencerdquoActa Psychologica vol 52 no 3 pp 175ndash196 1982

[5] J M Findlay V Brown and I D Gilchrist ldquoSaccade targetselection in visual search the effect of information from theprevious fixationrdquoVision Research vol 41 no 1 pp 87ndash95 2001

[6] A Haji-Abolhassani and J J Clark ldquoA computational model fortask inference in visual searchrdquo Journal of Vision vol 13 no 3p 29 2013

[7] J H Fecteau and D P Munoz ldquoSalience relevance and firinga priority map for target selectionrdquo Trends in Cognitive Sciencesvol 10 no 8 pp 382ndash390 2006

[8] M Carrasco and B McElree ldquoCovert attention acceleratesthe rate of visual information processingrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 98 no 9 pp 5363ndash5367 2001

[9] B Roska A Molnar and F S Werblin ldquoParallel processing inretinal ganglion cells how integration of space-time patterns ofexcitation and inhibition form the spiking outputrdquo Journal ofNeurophysiology vol 95 no 6 pp 3810ndash3822 2006

[10] R H Wurtz K McAlonan J Cavanaugh and R A BermanldquoThalamic pathways for active visionrdquo Trends in CognitiveSciences vol 15 no 4 pp 177ndash184 2011

[11] D A Leopold ldquoPrimary visual cortex awareness and blind-sightrdquo Annual Review of Neuroscience vol 35 p 91 2012

[12] Z Li ldquoA saliency map in primary visual cortexrdquo Trends inCognitive Sciences vol 6 no 1 pp 9ndash16 2002

[13] R J Krauzlis L P Lovejoy and A Zenon ldquoSuperior colliculusand visual spatial attentionrdquoAnnual Review ofNeuroscience vol36 pp 165ndash182 2013

[14] G E Schneider ldquoTwo visual systemsrdquo Science vol 163 no 3870pp 895ndash902 1969

[15] M Corbetta and G L Shulman ldquoControl of goal-directedand stimulus-driven attention in the brainrdquo Nature ReviewsNeuroscience vol 3 no 3 pp 201ndash215 2002

[16] C E Connor ldquoActive vision and visual activation in area v4rdquoNeuron vol 40 no 6 pp 1056ndash1058 2003

[17] R D McIntosh and T Schenk ldquoTwo visual streams for percep-tion and action current trendsrdquo Neuropsychologia vol 47 no6 pp 1391ndash1396 2009

[18] J H Reynolds and D J Heeger ldquoThe normalization model ofattentionrdquo Neuron vol 61 no 2 pp 168ndash185 2009

[19] M Carrasco ldquoVisual attention the past 25 yearsrdquo VisionResearch vol 51 no 13 pp 1484ndash1525 2011

[20] A M Treisman and G Gelade ldquoA feature-integration theory ofattentionrdquo Cognitive Psychology vol 12 no 1 pp 97ndash136 1980

[21] J M Wolfe ldquoGuided search 20-a revised model of visual-searchrdquo Psychonomic Bulletin amp Review vol 1 no 2 pp 202ndash238 1994

[22] G Rizzolatti L Riggio I Dascola and C Umilta ldquoReorientingattention across the horizontal and vertical meridians evidencein favor of a premotor theory of attentionrdquoNeuropsychologia Avol 25 no 1 pp 31ndash40 1987

[23] C Bundesen T Habekost and S Kyllingsbaeligk ldquoA neural theoryof visual attention bridging cognition and neurophysiologyrdquoPsychological Review vol 112 no 2 pp 291ndash328 2005

[24] L Itti and C Koch ldquoA saliency-based search mechanism forovert and covert shifts of visual attentionrdquo Vision Research vol40 no 10ndash12 pp 1489ndash1506 2000

[25] M Ito ldquoThe modifiable neuronal network of the cerebellumrdquoJapanese Journal of Physiology vol 34 no 5 pp 781ndash792 1984

[26] M Kawato K Furukawa and R Suzuki ldquoA hierarchicalneural-network model for control and learning of voluntarymovementrdquo Biological Cybernetics vol 57 no 3 pp 169ndash1851987

[27] M Ito ldquoBases and implications of learning in the cerebellum-adaptive control and internal model mechanismrdquo Progress inBrain Research vol 148 pp 95ndash109 2005

[28] E Todorov ldquoStochastic optimal control and estimationmethodsadapted to the noise characteristics of the sensorimotor systemrdquoNeural Computation vol 17 no 5 pp 1084ndash1108 2005

[29] R J van Beers ldquoSaccadic eye movements minimize the conse-quences ofmotor noiserdquoPLoSONE vol 3 no 4 pp 2000ndash20702008

[30] L C Osborne ldquoComputation and physiology of sensory-motorprocessing in eye movementsrdquo Current Opinion in Neurobiol-ogy vol 21 no 4 pp 623ndash628 2011

[31] J Najemnik and W S Geisler ldquoEye movement statistics inhumans are consistent with an optimal search strategyrdquo Journalof Vision vol 8 no 3 pp 1ndash14 2008

[32] R M Kelly and P L Strick ldquoCerebellar loops with motorcortex and prefrontal cortex of a nonhuman primaterdquo Journalof Neuroscience vol 23 no 23 pp 8432ndash8444 2003

[33] D S Zee and R J Leigh The Neurology of Eye Movements(BookDVD) Oxford University Press New York NY USA 4thedition 2006

[34] D A Restivo S Giuffrida G Rapisarda et al ldquoCentralmotor conduction to lower limb after transcranial magneticstimulation in spinocerebellar ataxia type 2 (SCA2)rdquo ClinicalNeurophysiology vol 111 no 4 pp 630ndash635 2000

[35] T Klockgether Handbook of Ataxia Disorders Mercel-DekkerNew York NY USA 2000

[36] M B Muzaimi J Thomas S Palmer-Smith et al ldquoPopulationbased study of late onset cerebellar ataxia in south east WalesrdquoJournal of Neurology Neurosurgery and Psychiatry vol 75 no8 pp 1129ndash1134 2004

[37] P Federighi G Cevenini M T Dotti et al ldquoDifferences insaccade dynamics between spinocerebellar ataxia 2 and late-onset cerebellar ataxiasrdquoBrain vol 134 part 3 pp 879ndash891 2011

[38] G Veneri P Federighi F Rosini A Federico and A RufaldquoSpike removal throughmultiscale wavelet and entropy analysisof ocular motor noise a case study in patients with cerebellardiseaserdquo Journal of Neuroscience Methods vol 196 no 2 pp318ndash326 2011

[39] C R Bowie and P D Harvey ldquoAdministration and interpreta-tion of the trail making testrdquo Nature Protocols vol 1 no 5 pp2277ndash2281 2006

[40] G Veneri E Pretegiani F Rosini P Federighi A Federicoand A Rufa ldquoEvaluating the human ongoing visual searchperformance by eye tracking application and sequencing testsrdquoComputer Methods and Programs in Biomedicine vol 107 no 3pp 468ndash477 2012

[41] G Veneri F Rosini P Federighi A Federico and A RufaldquoEvaluating gaze control on a multi-target sequencing task thedistribution of fixations is evidence of exploration optimisa-tionrdquoComputers in Biology andMedicine vol 42 no 2 pp 235ndash244 2012


[42] D S Zee L M Optican and J D Cook ldquoSlow saccades inspinocerebellar degenerationrdquoArchives of Neurology vol 33 no4 pp 243ndash251 1976

[43] L M Optican and D A Robinson ldquoCerebellar-dependentadaptive control of primate saccadic systemrdquo Journal of Neuro-physiology vol 44 no 6 pp 1058ndash1076 1980

[44] P Lefevre C Quaia and L M Optican ldquoDistributed modelof control of saccades by superior colliculus and cerebellumrdquoNeural Networks vol 11 no 7-8 pp 1175ndash1190 1998

[45] S Ramat R J Leigh D S Zee and L M Optican ldquoWhatclinical disorders tell us about the neural control of saccadic eyemovementsrdquo Brain vol 130 part 1 pp 10ndash35 2007

[46] D D Salvucci and J H Goldberg ldquoIdentifying fixations andsaccades in eye-tracking protocolsrdquo in Proceedings of the EyeTracking Research and Applications Symposium (ETRA rsquo00) pp71ndash78 ACM New York NY USA November 2000

[47] F L Engel ldquoVisual conspicuity visual search and fixationtendencies of the eyerdquo Vision Research vol 17 no 1 pp 95ndash1081977

[48] V Ponsoda D Scott and J M Findlay ldquoA probability vectorand transition matrix analysis of eye movements during visualsearchrdquo Acta Psychologica vol 88 no 2 pp 167ndash185 1995

[49] R M Klein ldquoInhibition of returnrdquo Trends in Cognitive Sciencesvol 4 no 4 pp 138ndash147 2000

[50] F Foti L Mandolesi D Cutuli et al ldquoCerebellar damageloosens the strategic use of the spatial structure of the searchspacerdquo Cerebellum vol 9 no 1 pp 29ndash41 2010


[52] H Matsumoto Y Terao T Furubayashi et al ldquoBasal gangliadysfunction reduces saccade amplitude during visual scanningin Parkinsonrsquos diseaserdquo Basal Ganglia vol 2 no 2 pp 73ndash782012

[53] A L Yarbus Eye Movements and Vision chapter 7 PlenumPress New York NY USA 1967

[54] C M Zingale and E Kowler ldquoPlanning sequences of saccadesrdquoVision Research vol 27 no 8 pp 1327ndash1341 1987

[55] C P Robert and G Casella Introducing Monte Carlo MethodsR Springer New York NY USA 2009

[56] B Kim and M A Basso ldquoA probabilistic strategy for under-standing action selectionrdquo Journal of Neuroscience vol 30 no6 pp 2340ndash2355 2010

[57] NMetropolis and S Ulam ldquoTheMonte Carlo methodrdquo Journalof the American Statistical Association vol 44 no 247 pp 335ndash341 1949

[58] J M Findlay ldquoGlobal visual processing for saccadic eye move-mentsrdquo Vision Research vol 22 no 8 pp 1033ndash1045 1982

[59] D Melcher and E Kowler ldquoShapes surfaces and saccadesrdquoVision Research vol 39 no 17 pp 2929ndash2946 1999

[60] E H Cohen B S Schnitzer T M Gersch M Singh and EKowler ldquoThe relationship between spatial pooling and attentionin saccadic and perceptual tasksrdquoVision Research vol 47 no 14pp 1907ndash1923 2007

[61] E Kowler ldquoEye movements the past 25 yearsrdquo Vision Researchvol 51 no 13 pp 1457ndash1483 2011

[62] J M Findlay and H I Blythe ldquoSaccade target selection dodistractors affect saccade accuracyrdquoVisionResearch vol 49 no10 pp 1267ndash1274 2009

[63] N Ramnani ldquoThe primate cortico-cerebellar system anatomyand functionrdquoNature Reviews Neuroscience vol 7 no 7 pp 511ndash522 2006

[64] M G Paulin ldquoEvolution of the cerebellum as a neuronalmachine for Bayesian state estimationrdquo Journal of NeuralEngineering vol 2 supplement 3 pp S219ndashS234 2005

[65] M Ito ldquoCerebellar circuitry as a neuronal machinerdquo Progress inNeurobiology vol 78 no 3ndash5 pp 272ndash303 2006

[66] J S Barlow The Cerebellum and Adaptive Control CambridgeUniversity Press Cambridge UK 2002

[67] M Ito ldquoControl of mental activities by internal models in thecerebellumrdquoNature Reviews Neuroscience vol 9 no 4 pp 304ndash313 2008

[68] S King A L Chen A Joshi A Serra and R J Leigh ldquoEffects ofcerebellar disease on sequences of rapid eyemovementsrdquoVisionResearch vol 51 no 9 pp 1064ndash1074 2011

[69] MMolinari V Filippini andMG Leggio ldquoNeuronal plasticityof interrelated cerebellar and cortical networksrdquo Neurosciencevol 111 no 4 pp 863ndash870 2002

[70] H C Leiner A L Leiner and R S Dow ldquoDoes the cerebellumcontribute to mental skillsrdquo Behavioral Neuroscience vol 100no 4 pp 443ndash454 1986

[71] J A Fiez ldquoCerebellar contributions to cognitionrdquo Neuron vol16 no 1 pp 12ndash15 1996

[72] A Tavano R Grasso C Gagliardi et al ldquoDisorders of cognitiveand affective development in cerebellar malformationsrdquo Brainvol 130 no 10 pp 2646ndash2660 2007

[73] H Baillieux H J D Smet P F Paquier P P De Deyn and PMarien ldquoCerebellar neurocognition insights into the bottomof the brainrdquo Clinical Neurology and Neurosurgery vol 110 no8 pp 763ndash773 2008

[74] C J Stoodley and JD Schmahmann ldquoEvidence for topographicorganization in the cerebellum of motor control versus cogni-tive and affective processingrdquo Cortex vol 46 no 7 pp 831ndash8442010

[75] G Allen R B Buxton E C Wong and E CourchesneldquoAttentional activation of the cerebellum independent of motorinvolvementrdquo Science vol 275 no 5308 pp 1940ndash1943 1997

[76] T Kellermann C Regenbogen M De Vos C Monang AFinkelmeyer and U Habel ldquoEffective connectivity of thehuman cerebellum during visual attentionrdquo The Journal ofNeuroscience vol 32 no 33 pp 11453ndash11460 2012

[77] H C Leiner A L Leiner and R S Dow ldquoThe human cerebro-cerebellar system its computing cognitive and language skillsrdquoBehavioural Brain Research vol 44 no 2 pp 113ndash128 1991

[78] H C Leiner A L Leiner and R S Dow ldquoCognitive andlanguage functions of the human cerebellumrdquo Trends in Neu-rosciences vol 16 no 11 pp 444ndash447 1993

[79] J E Desmond J D E Gabrieli A D Wagner B L Ginierand G H Glover ldquoLobular patterns of cerebellar activation inverbal working-memory and finger-tapping tasks as revealedby functional MRIrdquo Journal of Neuroscience vol 17 no 24 pp9675ndash9685 1997

[80] S M Ravizza C A McCormick J E Schlerf T Justus RB Ivry and J A Fiez ldquoCerebellar damage produces selectivedeficits in verbal working memoryrdquo Brain vol 129 no 2 pp306ndash320 2006

[81] L Passamonti F Novellino A Cerasa et al ldquoAltered cortical-cerebellar circuits during verbal working memory in essentialtremorrdquo Brain vol 134 no 8 pp 2274ndash2286 2011


[82] S Hong and L M Optican ldquoInteraction between Purkinjecells and inhibitory interneurons may create adjustable outputwaveforms to generate timed cerebellar outputrdquo PLoS ONE vol3 no 7 Article ID e2770 2008

[83] B Gottwald Z Mihajlovic B Wilde and H M MehdornldquoDoes the cerebellum contribute to specific aspects of atten-tionrdquo Neuropsychologia vol 41 no 11 pp 1452ndash1460 2003

[84] C Exner G Weniger and E Irle ldquoCerebellar lesions in thePICA but not SCA territory impair cognitionrdquo Neurology vol63 no 11 pp 2132ndash2135 2004

[85] H Golla P Thier and T Haarmeier ldquoDisturbed overt butnormal covert shifts of attention in adult cerebellar patientsrdquoBrain vol 128 no 7 pp 1525ndash1535 2005

[86] L S K Hokkanen V Kauranen R O Roine O Salonen andM Kotila ldquoSubtle cognitive deficits after cerebellar infarctsrdquoEuropean Journal of Neurology vol 13 no 2 pp 161ndash170 2006

[87] A Bischoff-Grethe R B Ivry and S T Grafton ldquoCerebellarinvolvement in response reassignment rather than attentionrdquoJournal of Neuroscience vol 22 no 2 pp 546ndash553 2002

[88] A Rufa and P Federighi ldquoFast versus slow different saccadicbehavior in cerebellar ataxiasrdquoAnnals of the New York Academyof Sciences vol 1233 no 1 pp 148ndash154 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of


Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology


Molecular Biology International

GenomicsInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


BioinformaticsAdvances in

Marine BiologyJournal of



Signal TransductionJournal of


BioMed Research International

Evolutionary BiologyInternational Journal of



Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Genetics Research International


Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational



Enzyme Research



Microbiology


LGNSC

MC

Thalamus

Midbrain

Pons

CBLM

VA

FEFPFC

V1

Ventral stream

(what)

Dorsal stream(where)

V2V3V4

PUL

LIP

IT

Retinal projections (90to LGN 10 to SC)

MTMST

(a)

LGNSC

MTMST

MC

Thalamus

Midbrain

Pons

VL

INSpino-

cerebellumPN

CBLM

Cerebrocerebellarloop

VA

FEFPFC

(b)

Figure 1 Short reference of vision pathway (a) Selective attention pathway the LGN the striate and extrastriate cortex (V1 V4inferotemporal cortex and MT) SC pulvinar LIP FEF and PFC are known to be involved in attentional processes (b) Cerebrocerebellarcommunication loop the neuronal circuitry of the cerebellum is thought to encode internal models that reproduce the dynamic properties ofbody partsThese models control the movement allowing the brain to precisely control the movement without the need for sensory feedbackMC motor cortex IN interpositus nucleus PN pons VL ventrolateral nucleus SC superior colliculi LGN lateral geniculate nuclei Visualareas (VA) V1 V2 V3 V4 and MT (middle temporal) PFC prefrontal cortex FEF frontal eye fields LIP lateral intraparietal cortex

feature saliency) and their location becoming able to buildup an internal task specific representation of the scene [4ndash6] More specifically the relative conspicuity of each elementof the scene is reproduced into a saliency map which allowsto predict where the eyes will be attracted first during theexploration of a scene Although the saliency map simplyrefers to the bottom up characteristic of a scene a moretop-down influence of the visual search is represented in theprioritymap [7] Covert attention is particularly efficient dur-ing top-down visual search where it is used to collect globalinformation of the scene throughout a parallel processingof conspicuous elements and to increase the discriminationabilities of peripheral vision by enhancing spatial resolutionat the attended target location [8] and by fading irrelevantlocations From a neuro hysiological point of view objectrsquosfeatures and spatial localizations acquired during visualexploration through the retina [9] are principally sent tovisual cortex (V1) via lateral geniculate nucleus (LGN) ([10ndash12] for a review) However fast spatial information about thevisual scene is also sent to the superficial layer of the superiorcolliculi (SC) This subcortical structure integrating multi-sensory inputs with eye and head motor plan is importantfor orienting attention in retinotopic coordinates towardsnewly appearing objects in the visual field [10 13] Moreupstreaming information about objectrsquos features and spatiallocalization is elaborated in the dorsal (occipitotemporalwhere) and ventral (occipitoparietal what) streams [14ndash17]in order to construct a priority map [7 10 18 19] (seeFigure 1(a))

Various formal models have been proposed Feature Inte-gration Theory [20] Guided Search [21] Premotor Theory[22] Theory of Visual Attention [23] and Winner Takes All[24] Feature Integration Theory proposes a two-stage visualattention process during first stage humans process several

primary visual features during second stage the objects areanalyzed with details Winner Takes All and Guided Searchare devoted to assign saliency to locations in the visual fieldRecently Reynolds and Heeger [18] proposed a review ofa normalized model of attention the model studied howstimulus features and cognitive attention should work toperform an efficient visual search

These models describe how humans could select someaspects of the scene but how the motor control systemmay optimize visual search by predicting the sensory con-sequences of an impending saccade Eye movements arecontrolled by the cerebrocerebellar communication loop anddescribed by feedforward or inverse control models [25ndash27](see Figure 1(b))

Recently some authors [28 29] have applied the theoryof optimal control (OCT) in the mechanisms that regulatemotor control humans seem to adapt their behavior tominimize some cost function such as noise in performing anaction [30] Najemnik and Geisler argued that humans couldchoose fixations that maximize information gained about thetargetrsquos location this strategy [31] allows humans to selectfeatures from the scene optimally such as an ldquoideal searcherrdquo

Our work aims to extend the OCT principle to themechanisms that regulate visual search We proposed amethod to study how the strategies of selective attentionmay be modulated by the motor control performance Sincethe cerebellum is the brain structure where some dynamicaspects of motor control are optimized to reduce errors wecompare our formal model with the ocular motor behavior ofwell characterized cerebellar patientswhohave specificmotorcontrol failure [32 33]

Therefore we developed amathematical stochasticmodelbased on the Monte Carlo method (MC) able to simu-late ongoing visual search in a cognitively demanding task


t

500ms

30000ms

Fixation

CE

AB

D

5

2

4

3

1

Saccade

ion

E


5555555

22222222222222222222222222 3333333333















A

E

C

5

FixationDTDN

Saccade

Nearest ROI










C

5

Fixation (tf)

Saccade (t)


Fixation (tfminus1)

(a)

5

E

C

Fixation

Saccade (t)



(b)






DE = mean (119889) (2)

We defined also


119891) (3)




DX =


sdot119908)

(4)



X

w

s



Motor control

XY

Peripheral vision

MemoryΔt

Pp


Ppf

Pri


119901



119903119894




119901and




119903119894) + 119908 sdot 119875

119901119891(DE 1205902

119901119891)

(5)




= N(DX 1205902119903119894) 119875119901119891

= N(DE 1205902119901119891)

and 119875119901= N(120583




(119909119891 119910119891) = Φ (119904 120583

119901 119908 1205902

119901119891 1205902

119903119894) (6)

where 1205902





119869sacc

= sum



2

(7)



119869fix = sum





Sequencingtest

(TMT)

Subjects gazedata


DN

DX DE

Stochasticmodel

Jfix Jsacc andAsacc

Jfix Jsacc andAsacc


Understanding data


Ppf Pri

120583p w and s









3 Results



12345678916

165

17

175

18

185

CTRL

SCA2

SCA2LOCA

Δt (s)

DE

(deg

)

CTRLLOCA















119875119901

090 045 060










119901of subjects


= 090 120583119901

= 045 and 120583119901







ℎ (1205790 1205791 1205792)

= 1205790sdot

119860 saccmax (119860 sacc)

+ 1205791sdot


+ 1205792sdot

119869fixmax (119869fix)

(9)



1asymp 13)



= 1 0 529)



20

20

40

40

60

60 8080

100

100

Pp(

)

SCA2 LOCA

CTRL

150

s

100

50

0

J fix

(a)

2040

6080

100

2040

60

80100

Pp(

)

SCA2 LOCA

CTRL

s

3

25

2

15

1

05

0

times106

J sac

c(p

xmiddotm

s)

Minimum hyperplane

(b)


239 5731 655415

20

25

30

35

40

45

5011 46 74

s

CTRLLOCA

SCA2

DN (px)

J fix

Data model Pp = 90

Data model Pp = 50

Data model Pp = 60

(a)

239 5731 6554

4

5

6

7

8

9

10

1111 46 74

s

SCA2

CTRL

LOCA

times105

J sac

c(p

xmiddotm

s)


DN (px)


(b)





300

250

200

150

20

4060

80

100

Pp ()

SCA2

LOCACTRL

10080

6040

20

s

Asa

cc(p

x)

(a)

239 5731 6554150

200

250

300

350

40011 46 74

s

CTRL

LOCA

SCA2

Asa

cc(p

x)




DN (px)

(b)



4 Discussion










5 Conclusions






Acknowledgments


References



































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


t

500ms

30000ms

Fixation

CE

AB

D

5

2

4

3

1

Saccade

ion

E


5555555

22222222222222222222222222 3333333333















A

E

C

5

FixationDTDN

Saccade

Nearest ROI










C

5

Fixation (tf)

Saccade (t)


Fixation (tfminus1)

(a)

5

E

C

Fixation

Saccade (t)



(b)






DE = mean (119889) (2)

We defined also


119891) (3)




DX =


sdot119908)

(4)



X

w

s



Motor control

XY

Peripheral vision

MemoryΔt

Pp


Ppf

Pri


119901



119903119894




119901and




119903119894) + 119908 sdot 119875

119901119891(DE 1205902

119901119891)

(5)




= N(DX 1205902119903119894) 119875119901119891

= N(DE 1205902119901119891)

and 119875119901= N(120583




(119909119891 119910119891) = Φ (119904 120583

119901 119908 1205902

119901119891 1205902

119903119894) (6)

where 1205902





119869sacc

= sum



2

(7)



119869fix = sum





Sequencingtest

(TMT)

Subjects gazedata


DN

DX DE

Stochasticmodel

Jfix Jsacc andAsacc

Jfix Jsacc andAsacc


Understanding data


Ppf Pri

120583p w and s









3 Results



12345678916

165

17

175

18

185

CTRL

SCA2

SCA2LOCA

Δt (s)

DE

(deg

)

CTRLLOCA















119875119901

090 045 060










119901of subjects


= 090 120583119901

= 045 and 120583119901







ℎ (1205790 1205791 1205792)

= 1205790sdot

119860 saccmax (119860 sacc)

+ 1205791sdot


+ 1205792sdot

119869fixmax (119869fix)

(9)



1asymp 13)



= 1 0 529)



20

20

40

40

60

60 8080

100

100

Pp(

)

SCA2 LOCA

CTRL

150

s

100

50

0

J fix

(a)

2040

6080

100

2040

60

80100

Pp(

)

SCA2 LOCA

CTRL

s

3

25

2

15

1

05

0

times106

J sac

c(p

xmiddotm

s)

Minimum hyperplane

(b)


239 5731 655415

20

25

30

35

40

45

5011 46 74

s

CTRLLOCA

SCA2

DN (px)

J fix

Data model Pp = 90

Data model Pp = 50

Data model Pp = 60

(a)

239 5731 6554

4

5

6

7

8

9

10

1111 46 74

s

SCA2

CTRL

LOCA

times105

J sac

c(p

xmiddotm

s)


DN (px)


(b)





300

250

200

150

20

4060

80

100

Pp ()

SCA2

LOCACTRL

10080

6040

20

s

Asa

cc(p

x)

(a)

239 5731 6554150

200

250

300

350

40011 46 74

s

CTRL

LOCA

SCA2

Asa

cc(p

x)




DN (px)

(b)



4 Discussion










5 Conclusions






Acknowledgments


References



































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


A

E

C

5

FixationDTDN

Saccade

Nearest ROI










C

5

Fixation (tf)

Saccade (t)


Fixation (tfminus1)

(a)

5

E

C

Fixation

Saccade (t)



(b)






DE = mean (119889) (2)

We defined also


119891) (3)




DX =


sdot119908)

(4)



X

w

s



Motor control

XY

Peripheral vision

MemoryΔt

Pp


Ppf

Pri


119901



119903119894




119901and




119903119894) + 119908 sdot 119875

119901119891(DE 1205902

119901119891)

(5)




= N(DX 1205902119903119894) 119875119901119891

= N(DE 1205902119901119891)

and 119875119901= N(120583




(119909119891 119910119891) = Φ (119904 120583

119901 119908 1205902

119901119891 1205902

119903119894) (6)

where 1205902





119869sacc

= sum



2

(7)



119869fix = sum





Sequencingtest

(TMT)

Subjects gazedata


DN

DX DE

Stochasticmodel

Jfix Jsacc andAsacc

Jfix Jsacc andAsacc


Understanding data


Ppf Pri

120583p w and s









3 Results



12345678916

165

17

175

18

185

CTRL

SCA2

SCA2LOCA

Δt (s)

DE

(deg

)

CTRLLOCA















119875119901

090 045 060










119901of subjects


= 090 120583119901

= 045 and 120583119901







ℎ (1205790 1205791 1205792)

= 1205790sdot

119860 saccmax (119860 sacc)

+ 1205791sdot


+ 1205792sdot

119869fixmax (119869fix)

(9)



1asymp 13)



= 1 0 529)



20

20

40

40

60

60 8080

100

100

Pp(

)

SCA2 LOCA

CTRL

150

s

100

50

0

J fix

(a)

2040

6080

100

2040

60

80100

Pp(

)

SCA2 LOCA

CTRL

s

3

25

2

15

1

05

0

times106

J sac

c(p

xmiddotm

s)

Minimum hyperplane

(b)


239 5731 655415

20

25

30

35

40

45

5011 46 74

s

CTRLLOCA

SCA2

DN (px)

J fix

Data model Pp = 90

Data model Pp = 50

Data model Pp = 60

(a)

239 5731 6554

4

5

6

7

8

9

10

1111 46 74

s

SCA2

CTRL

LOCA

times105

J sac

c(p

xmiddotm

s)


DN (px)


(b)





300

250

200

150

20

4060

80

100

Pp ()

SCA2

LOCACTRL

10080

6040

20

s

Asa

cc(p

x)

(a)

239 5731 6554150

200

250

300

350

40011 46 74

s

CTRL

LOCA

SCA2

Asa

cc(p

x)




DN (px)

(b)



4 Discussion










5 Conclusions






Acknowledgments


References



































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


X

w

s



Motor control

XY

Peripheral vision

MemoryΔt

Pp


Ppf

Pri


119901



119903119894




119901and




119903119894) + 119908 sdot 119875

119901119891(DE 1205902

119901119891)

(5)




= N(DX 1205902119903119894) 119875119901119891

= N(DE 1205902119901119891)

and 119875119901= N(120583




(119909119891 119910119891) = Φ (119904 120583

119901 119908 1205902

119901119891 1205902

119903119894) (6)

where 1205902





119869sacc

= sum



2

(7)



119869fix = sum





Sequencingtest

(TMT)

Subjects gazedata


DN

DX DE

Stochasticmodel

Jfix Jsacc andAsacc

Jfix Jsacc andAsacc


Understanding data


Ppf Pri

120583p w and s









3 Results



12345678916

165

17

175

18

185

CTRL

SCA2

SCA2LOCA

Δt (s)

DE

(deg

)

CTRLLOCA















119875119901

090 045 060










119901of subjects


= 090 120583119901

= 045 and 120583119901







ℎ (1205790 1205791 1205792)

= 1205790sdot

119860 saccmax (119860 sacc)

+ 1205791sdot


+ 1205792sdot

119869fixmax (119869fix)

(9)



1asymp 13)



= 1 0 529)



20

20

40

40

60

60 8080

100

100

Pp(

)

SCA2 LOCA

CTRL

150

s

100

50

0

J fix

(a)

2040

6080

100

2040

60

80100

Pp(

)

SCA2 LOCA

CTRL

s

3

25

2

15

1

05

0

times106

J sac

c(p

xmiddotm

s)

Minimum hyperplane

(b)


239 5731 655415

20

25

30

35

40

45

5011 46 74

s

CTRLLOCA

SCA2

DN (px)

J fix

Data model Pp = 90

Data model Pp = 50

Data model Pp = 60

(a)

239 5731 6554

4

5

6

7

8

9

10

1111 46 74

s

SCA2

CTRL

LOCA

times105

J sac

c(p

xmiddotm

s)


DN (px)


(b)





300

250

200

150

20

4060

80

100

Pp ()

SCA2

LOCACTRL

10080

6040

20

s

Asa

cc(p

x)

(a)

239 5731 6554150

200

250

300

350

40011 46 74

s

CTRL

LOCA

SCA2

Asa

cc(p

x)




DN (px)

(b)



4 Discussion










5 Conclusions






Acknowledgments


References



































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


Sequencingtest

(TMT)

Subjects gazedata


DN

DX DE

Stochasticmodel

Jfix Jsacc andAsacc

Jfix Jsacc andAsacc


Understanding data


Ppf Pri

120583p w and s









3 Results



12345678916

165

17

175

18

185

CTRL

SCA2

SCA2LOCA

Δt (s)

DE

(deg

)

CTRLLOCA















119875119901

090 045 060










119901of subjects


= 090 120583119901

= 045 and 120583119901







ℎ (1205790 1205791 1205792)

= 1205790sdot

119860 saccmax (119860 sacc)

+ 1205791sdot


+ 1205792sdot

119869fixmax (119869fix)

(9)



1asymp 13)



= 1 0 529)



20

20

40

40

60

60 8080

100

100

Pp(

)

SCA2 LOCA

CTRL

150

s

100

50

0

J fix

(a)

2040

6080

100

2040

60

80100

Pp(

)

SCA2 LOCA

CTRL

s

3

25

2

15

1

05

0

times106

J sac

c(p

xmiddotm

s)

Minimum hyperplane

(b)


239 5731 655415

20

25

30

35

40

45

5011 46 74

s

CTRLLOCA

SCA2

DN (px)

J fix

Data model Pp = 90

Data model Pp = 50

Data model Pp = 60

(a)

239 5731 6554

4

5

6

7

8

9

10

1111 46 74

s

SCA2

CTRL

LOCA

times105

J sac

c(p

xmiddotm

s)


DN (px)


(b)





300

250

200

150

20

4060

80

100

Pp ()

SCA2

LOCACTRL

10080

6040

20

s

Asa

cc(p

x)

(a)

239 5731 6554150

200

250

300

350

40011 46 74

s

CTRL

LOCA

SCA2

Asa

cc(p

x)




DN (px)

(b)



4 Discussion










5 Conclusions






Acknowledgments


References



































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology












119875119901

090 045 060










119901of subjects


= 090 120583119901

= 045 and 120583119901







ℎ (1205790 1205791 1205792)

= 1205790sdot

119860 saccmax (119860 sacc)

+ 1205791sdot


+ 1205792sdot

119869fixmax (119869fix)

(9)



1asymp 13)



= 1 0 529)



20

20

40

40

60

60 8080

100

100

Pp(

)

SCA2 LOCA

CTRL

150

s

100

50

0

J fix

(a)

2040

6080

100

2040

60

80100

Pp(

)

SCA2 LOCA

CTRL

s

3

25

2

15

1

05

0

times106

J sac

c(p

xmiddotm

s)

Minimum hyperplane

(b)


239 5731 655415

20

25

30

35

40

45

5011 46 74

s

CTRLLOCA

SCA2

DN (px)

J fix

Data model Pp = 90

Data model Pp = 50

Data model Pp = 60

(a)

239 5731 6554

4

5

6

7

8

9

10

1111 46 74

s

SCA2

CTRL

LOCA

times105

J sac

c(p

xmiddotm

s)


DN (px)


(b)





300

250

200

150

20

4060

80

100

Pp ()

SCA2

LOCACTRL

10080

6040

20

s

Asa

cc(p

x)

(a)

239 5731 6554150

200

250

300

350

40011 46 74

s

CTRL

LOCA

SCA2

Asa

cc(p

x)




DN (px)

(b)



4 Discussion










5 Conclusions






Acknowledgments


References



































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


20

20

40

40

60

60 8080

100

100

Pp(

)

SCA2 LOCA

CTRL

150

s

100

50

0

J fix

(a)

2040

6080

100

2040

60

80100

Pp(

)

SCA2 LOCA

CTRL

s

3

25

2

15

1

05

0

times106

J sac

c(p

xmiddotm

s)

Minimum hyperplane

(b)


239 5731 655415

20

25

30

35

40

45

5011 46 74

s

CTRLLOCA

SCA2

DN (px)

J fix

Data model Pp = 90

Data model Pp = 50

Data model Pp = 60

(a)

239 5731 6554

4

5

6

7

8

9

10

1111 46 74

s

SCA2

CTRL

LOCA

times105

J sac

c(p

xmiddotm

s)


DN (px)


(b)





300

250

200

150

20

4060

80

100

Pp ()

SCA2

LOCACTRL

10080

6040

20

s

Asa

cc(p

x)

(a)

239 5731 6554150

200

250

300

350

40011 46 74

s

CTRL

LOCA

SCA2

Asa

cc(p

x)




DN (px)

(b)



4 Discussion










5 Conclusions






Acknowledgments


References



































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


300

250

200

150

20

4060

80

100

Pp ()

SCA2

LOCACTRL

10080

6040

20

s

Asa

cc(p

x)

(a)

239 5731 6554150

200

250

300

350

40011 46 74

s

CTRL

LOCA

SCA2

Asa

cc(p

x)




DN (px)

(b)



4 Discussion










5 Conclusions






Acknowledgments


References



































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology





5 Conclusions






Acknowledgments


References



































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

































































































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

























































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology
















Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology








Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

Documents

Research Article Evaluating the Influence of Motor Control ...downloads.hindawi.com/journals/bmri/2014/162423.pdf · motor programming and focuses on the saccade goal, covert attention