A Recurrent Neural Network for 
Generation of Ocular Saccades 
Lina L.E. Massone 
Department of Physiology 
Department of Electrical Engineering and Computer Science. 
Northwestern University 
303 E. Chicago Avenue, Chicago, I1 60611 
Abstract 
This paper presents a neural network able to control saccadic 
movements. The input to the network is a specification of a 
stimulation site on the collicular motor map. The output is the time 
course of the eye position in the orbit (horizontal and vertical angles). 
The units in the network exhibit a one-to-one correspondance with 
neurons in the intermediate layer of the superior colliculus (collicular 
motor map), in the brainstem and with oculomotor neurons. 
Simulations carried out with this network demonstrate its ability to 
reproduce in a straightforward fashion many experimental observations. 
1. INTRODUCTION 
It is known that the superior colliculus (SC) plays an important role in the control of eye 
movements (Schiller et al. 1980). Electrophysiological studies (Cynader and Berman 
1972, Robinson 1972) showed that the intermediate layer of SC is topographically 
organized into a motor map. The location of active neurons in this area was found to be 
related to the oculomotor error (i.e. how far the eyes are from the target) and their firing 
rate to saccade velocity (Roher et al. 1987, Berthoz et al. 1987). Neurons in the rostral 
area of the motor map, the so-called fixation neurons, tend to become active when the 
eyes are on target (Munoz and Wurtz 1992) and they can provide a gating mechanism to 
1014 
A Recurrent Neural Network for Generation of Ocular Saccades 1015 
arrest the movement (Guitton 1992). SC sends signals to the brainstem whose circuitry 
translates them into commands to the oculomotor neurons that innervate the eye muscles 
(Robinson 1981). 
This paper presents a recurrent neural network that performs a spatio-temporal 
transformation from a stimulation site on the collicular motor map and an eye movement. 
The units in the network correspond to neurons in the intermediate layer of the colliculus, 
neurons in the brainstem and to oculomotor neurons. 
Medial 
(up) 
! I Lateral I \ 
(down) 
Figure 1: An array of units that represents the collicular motor map. The dark square 
represents the fixation area. The units in the array project to four units that represent burst 
cells devoted to process rightward, leftward, upward and downward saccarles. 
The network was built entirely on anatomical and physiological observations. 
Specifically, the following assumptions were used: (1) The activity on the collicular 
motor map shifts towards the fixation area during movement (Munoz et al. 1991, Droulez 
and Berthoz 1991). (2) The output of the superior colliculus is a vectorial velocity signal 
1016 Massone 
that is the sum of the contributions from each active collicular neuron. (3) Such signal is 
decomposed into horizontal velocity and vertical velocity by a topographic and graded 
connectivity pattern from SC to the burst cells in the brainstem. (4) The computation 
performed from the burst-cells level down to the actual eye movement is carried out 
according to the push-pull arrangement proposed by Robinson (1981). (5) The activity on 
the collicular motor map is shifted by signals that represent the eye velocity. Efferent 
copies of the horizontal and vertical eye velocities are fed back onto the collicular map in 
order to implement the activity shift. 
(a) (b) 
(c) (d) 
Figure 2: The topographic and graded pattern of connectivity from the collicular array to 
the four burst cells. Black means no connection, brighter colors represent larger weight 
values. (a) To the right cell. (b) To the left cell. (c) To the up cell. (d) To the down cell. 
Simulations conducted with such a system (Massone submitted) demonstrated the 
network's ability to reproduce a number of experimental observations. Namely the 
network can: (1) Spontaneously produce oblique saccarles whose curvature varies with the 
ratio between the horizontal and vertical components of the motor error.(2) Automatically 
hold the eye position in the orbit at the end of a saccade by exploiting the internal 
dynamic of the network. (3) Continuously produce efferent copies of the movements 
A Recurrent Neural Network for Generation of Ocular Saccades 1017 
without the need for reset signals. (4) Account for the outcome of the lidocaine 
experiment (Lee et al. 1988) without assuming a population averaging mechanism. 
Section 2 describes the network architecture. A more detailed description of the network, 
it mechanisms and physiological ground as well as a number of simulation results can be 
found in Massone (submitted). 
2. THE NETWORK 
The network input layer is a bidimensional array of linear units that represent neurons in 
the collicular motor map. The array is topographically arranged as shown in Figure 1. 
Activity along the caudal axis produces horizontal saccades in a contralateral fashion, 
activity along the medio-lateral axis produces vertical saccares, activity in the rest of the 
array produces oblique saccares. The dark square in the center (rostral area) represents the 
fixation area. The units in this array project to four logistic units that represent two pairs 
of burst cells, one pair devoted to control horizontal movements, one pair devoted to 
control vertical movements. The pattern of connectivity between the collicular array and 
the units that represent the burst cells is qualitatively shown in Figure 2. The value of the 
weights of such connections increases exponentially when one moves from the center 
towards the periphery of the array. The fixation area projects to four other units that 
represent the so-called omnipause neurons. These units send a gating signal to the burst- 
cells units and are responsible for arresting the movement when the eyes are on target. i.e. 
when the activity in the input army reaches the center. Each pair of burst-cells units 
project to the network shown in Figure 3. This network is a computational version of the 
push-pull arrangement proposed by Robinson (1981). The bottom part of the network 
represents the oculomotor plant, the top part represents the brainstem circuitry and the 
oculomotor neurons. The weights in the bottom part of the network were derived by 
splitting into two equations the differential equation proposed by Robinson (1981) to 
describe the behavior of the oculomotor plant under a combined motomeuron input R. 
d01 
R1 =k01 +r clt 
d02 
R2 =k02 +r (It 
R 1 and R2 are the firing rates of the agonist and antagonist motorneurons, 01 and 02 are 
the components of the eye position due to motions in opposite directions (e.g. left and 
right), k is the eye stiffness and r is the eye viscosity. 
The weights in the top part of the network were analytically computed from the weights 
in the bottom part of the network by imposing the following constraints: (1) The 
difference between 01 and 02 must produce the correct 0. (2) The output of the neural 
integrators must be an efferent copy of the eye movement. (3) The output of the 
motorneurons must hold the eye at the current orbital position when the burst-cells units 
are shut off by the gating action of the omnipause cells. Efferent copies of the horizontal 
and vertical eye velocities were computed by differentiating the output of the neural 
1018 Massone 
from fixation neurons 
from fixation neurons 
from collicular array 
-t/r 
At/r At/r 
+1 +1 
k 
1 -kAt/r( 
t/r 
At/r LR2 
+1 
1 -kt/r 
-1 
01 02 
EYE 
!-- ................. I 
Figure 3: The recurrent network used to control eye movements in one direction, e.g. 
horizontal. An identical network is required to control vertical movements. OPN: 
omnipause neurons. BC1, BC2: burst cells. Nil, NI2: neural integrators. MN1, MN2: 
motor neurons. The architecture is based on Robinson's push-pull arrangement. k=4.0, 
r=-0.95, ix=0.5, At=l msec. 
A Recurrent Neural Network for Generation of Ocular Saccades 1019 
integrators. These signals were recurrenfly fed back onto the input array and made the 
activity in the array shift towards the fixation area. This architecture assumes that the 
output of the collicular array represents saccade velocity. The network is started by 
selecting one unit in the input array, i.e. a "stimulation" site. When the unit is selected, a 
square area centered at that unit becomes active with a gaussian activity profile (Ottes et 
al. 1986, Munoz and Guitton 1991). At the time the input units are activated the eye 
starts moving and, as a consequence of the velocity feedback the activity on the input 
army starts shifting. The movement is arrested when the fixation area becomes activated. 
The activity of all units in the network represents neurons firing rates and is expressed in 
spikes/second. 
Figure 4 shows the response of the network when the collicular array is stimulated at two 
sites sequentially. Each site causes an oblique saccade with unequal components. 
Stimulation number 1 brings the eye up and to the right, stimulation number 2 brings 
the eye back to the initial position. Fixation is maintained for a while inbetween 
stimulations and at the end of the two movements. The resulting trajectories in the 
movement plane (vertical angle versus horizontal angle) demonstrate the ability of the 
network to (i) maintain the eye position in the orbit when the burst cells activation is set 
to zero by the gating action of the omnipause neurons, (ii) produce curved trajectories 
with opposite curvatures when the eye moves back and forth between the same two 
angular positions. None of the units in the network is ever reset between saccades; 
because of the push-pull arrangement, when the activity of one neural integrator increases, 
the activity of the antagonist integrator decreases. This mechanism ensures that their 
activity does not grow indefinetely. 
3. CONCLUSIONS 
In this paper I presented an anatomically and physiologically inspired network able to 
control saccadic movements and to reproduce the outcome of some experimental 
observations. The results of simulations carried out with this network can be found in 
Massone (submitted). This work is currently being extended to (i) modeling the activity 
shift phenomenon as the relaxation of a dynamical system to its equilibrium 
configuration rather than as a feedback-driven mechanism, (ii) studying the role of the 
collicular output signals in the calibration and accuracy of arm movements (Massone 
1992). 
Acknowledgements 
This work was supported by the National Science Foundation, grant BCS-9113455 to the 
author. 
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