Proceedings - 19th International Conference - IEEE/EMBS Oct. 30 - Nov. 2,1997 Chicago, IL. USA

BLUNTNESS OF SACCADIC EYE MOVEMENT
DEPENDING ON VIGILANCE STATES- EXAMINATION BY MODEL SIMULATION Akmori Uenot”

Tsuyoshi Tateyamat

Moriichiro TakasettHaruyuki M i n a i t a n i t

t Institute of Biomedical Engineering, Faculty of Science and Technology, Keio University,

Hiyoshi 3-14-1, Kohoku-ku, Yokohama, Kanagawa 223, Japan
ttSchool of Medicine, Keio University, Shinanomachi 35, Shinjuku-ku, Tokyo 160, Japan*Email address : ueno@bmel.elec.keio.ac.jp
Abstract- In our previous research we revealed that eye
velocity become blunt during saccade as vigilance state
get lower. In this study we examined bluntness of saccade
velocity by simulating saccadic eye movements using amodel of saccade generation. Blunt saccade was achieved
by way of changing parameters of pulse generator in themodel. Adequate values of the model arameters to 4 typical experimental data were assumedgy fittin simulated
eye velocity to the experimental eye velocity. Eompansonof the values of the model parameter t o (Y power calculated from the EEG measured with saccade revealed ahigh correlation between characteristics of pulse generator and vigilance states. Since pulse generator exists inpontine reticular formation, which also belongs to controlling system of vigilance state, it was su ested fromthe results that decline in the activity of puge generator
in brain stem caused to the blunt saccade.

I. INTRODUCTION
It was reported in previous study that blunt saccade(saccadic eye movement) was observed when vigilance stateis low and that bluntness of saccade velocity related to thedegree of vigilance state[l][2].But the cause of bluntness
and its relation to the vigilance states is not still clear. In
this paper we examined possible factors influencing eye
velocity during saccade by modelling and simulating saccadic generation based on the concept that burst neurons
in the brain stem are driven by motor error.
11. METHODSI-- II 1

(a)

(b)

(C)

(d)

Fig. 1. A scheme of model of saccade generation based on theconcept that burst neurons are driven by motor error. 0 isorientation of the eye in the retina, 0’ is orientation of the eyein the head, OT is orientation of the target in the retina, and 0;
is orientation of the target in the head.

in Fig. 1. Basically the model can be categorized into 4
parts corresponding to (a) t o (d) in Fig. 1. The functionof part (a) is to translate the input based on retinal coodinate t o the data based on head coodinate and to generate
trigger of saccade. The part (b) is so-called pulse generator which codes saccadic velocity signal. Burst rateof the pulse generator relates t o the eye velocity and isapproximately determined according to the equations (1)and (2).

A . Description of the Model of Saccade Generation-For simulating blunt saccade we constructed a modelof saccade generation. In study of horizontal saccade, amodel proposed by Robinson in 1964[3] is commonly considered as a confidential basical model. But it doesn’t
have detailed expressions concerning to the pulse generator, which codes velocity signal of saccade to the motoneurons. In 1981 Van Gisbergen et a1 proposed a modelof saccade generation based on the concept that burst
neurons are driven by motor error[4]. Since Gisbergen’s
model has sufficient expressions about pulse generator,
we combined Robinson’s model and Gisbergen’s model toused for the simulation.
A scheme of the model used for simulation is illustrated

where BL and BR are burst cell firing rates in left andright burst cell, e , (motor error) is the difference between
instantaneous eye position and desired eye position in theorbit, and b,, bk and eo are invariable that characterize
the pulse generator. The part (c) consists of integrator
and direct part. The function of the integrator is t o makesignal associated with the torque against restoring torque,which is made by viscosity of tissues surrounding the eye.
Finally both direct and integrated signals are combined

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Proceedings - 19th International Conference - IEEE/EMBS Oct. 30 - Nov. 2, 1997 Chicago, IL. USALTABLE I

Pulse Generatorb,[deg/s] bk[deg] eo[deg]
1100

10.0

2.0- Simulation I3a 2.5
82Eye PlantTel[s] T~z[s]0.015

Experiment

ISTANDARDVALUES OF MODEL PARAMETERS USED FOR SIMULATION.

8 1.552 1bm = 640 deg/s
Te2= 0.018 s

E 0.50.004< oI-0.5 I

0100

100

and coded to eye plant. In the part (d) of eye plant,
including lateral and medial recti, pulse data are changed
into movement of eyeball (i.e. saccade). Standard valuesof model parameters we used are shown in the TABLE I.

300

200

400

500

600

700

1A

3 60
bm = 640deg/s
Te2= 0.0I8 s-20 L0B. Acquisition of Experimental Data

100200300

400500600

I
700

Time [ms]For application of the model to experimental data, weexecuted target tracking task to one subject and obtained
experimental data. In tracking task a preceding target
appears for 2s at Odeg from the center of the display, thenit jumps to one of a probable position of 2.5, 5.0 or 7.5deg
and disappear Is later. In the task this sequence wasrepeated for 3min andwas executed at 11, 13, 15 o’clock.
Eye movement and EEG from the scalp of Fz, Cz and Pz
were measured.

Fig. 2. Examples of eye position and eye velocity during saccade.Dotted line is experimental data. Solid line shows simulated data when b, is 64deg/s and Te2 is 0.018s.

50454035C. Simulation of the Model30

In the model in Fig. 1 there are 4 probable parameters
to effect bluntness of eye velocity during saccade, those axe
bm, bk, Te1 and Te2.Preliminary trial of changing these 4parameters revealed that b, and Te2are dominant to theoutput of the model. To achieve similar output to selected
4 typical experimental data in different vigilance state, wevaried these 2 parameters and evaluated the similarity to
the experimental data by calculating the summation ofabsolute error between simulated data and experimentaldata. Values of model parameters of bk, eo and Tel were
fixed to the standard values in TABLE I.
111. RESULTS
Fig. 2 illustrates examples of experimental data andsimulated data. The upper figure is time course of eye
position containing generation of saccade and the lower
figure is time course of eye velocity calculated by derivation of the eye position data above. As can be seen in
Fig. 2 simulated data (solid line) agreed with the experimental data (dotted line). Fig. 3 shows relation of velocity
error to b, and Tez.The values of b, and Te2written in
Fig. 2 was determined by this result at point of the smallest velocity error.
We applied the same analysis to the other 3 experimental data and investigated the relation of velocity error tob, and Te2.
From the results of velocity error it was foundthat Te2values stable and that it only varies from 0.015

2520151050Fig. 3. An example of relation among b,, Te2 and velocity error
between experimental data aFd simulated data. Density of theblack color correspind to the amount of velocity error. The more
dense, the smaller velocity error become.

to 0.020. Then we fixed the value of Te2at 0.018 anddetermined b, from the relation of velocity error to b,.
Fig. 4 shows relation between b, and spectral powerof cy wave band ( a power) extracted from the EEG data
which was measured with eye movement during target
tracking task. As can be seen in Fig. 4 a negative high correlation between b, and cy power was observed. Since theincrease of a power means decline in the vigilance states,
this correlation means that according to the decrease ofvigilance states b,, which can effect on the firing rates ofpulse generator also decays.

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Proceedings - 19th International Conference - IEEE/EMBS Oct. 30 - Nov. 2, 1997 Chicago, IL. USA
by burst neurons,” J . Neurophysiol., vol. 45, no. 3, pp.417-442,March, 1981.

700600-hg 500
ED4003001.21.4

1.6

1.8

2

2.2

2.4

a powerFig. 4. Relation between model parameter of bm and experimental
parameter of Q power which reflects vigilance states.

IV. DISCUSSION
Since 6, is associated with firing rate of pulse generator,
high correlation between (Y power and b, in Fig. 4 implies
that there are some factors (or a factor) which have somerelation with vigilance states and characterise the activityof pulse generator. In physiological study it is known that
pulse generator exist in pontine reticular formation, andalso known that temporal vigilance states is controlled byreticular controlling system. As the pontine reticular formation is contained to reticular controlling system, there
is a possibility that activities of pulse generator in thepontine reticular formation are inhibited while vigilancestate is low and that it reduced firing rates of burst cell,so that eye velocity become blunt during saccade.

V. CONCLUSION
By simulating blunt eye movement during saccade using
the model based on the concept that burst neurons aredriven by motor error, it was suggested that decline in
the vigilance states cause to the decline in the activityof pulse generator in brain stem and that this cause tothe reduce of firing rate in pulse generator, so that eye
velocity become blunt during saccade.
REFERENCES[l] A. Ueno, Y.Ota, M. Takase,H. Minamitani, “Relationship be-tween vigilance states and characteristics of saccadic eye movement,” in Pmc. 17th Ann. Int. Conf. IEEE Eng. Med. Bao.
SOC.,pp.572-573, 1995.
[2] A..Ueno, Y.Ota, M. Takase,H. Minamitani, “Parametric analysis of saccadic eye movement depending on vigilance states,”in Proc. 18th Ann. Int. Conf. IEEE Eng. Med. Bio. Soc.,
pp.319-320, 1996.
[3] D.A. Robinson, “The mechanics of human saccadic eye movement,” J. Physiol., ~01.174,pp.245-264, April, 1964.
[4) J. A. M. Van Gisbergen, D. A. Robinson and S. Gielen, “A
quantitative analysis of generation of saccadic eye movements

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