742 DeWeerth and Mead 
An 
Analog 
in the 
VLSI Model of Adaptation 
Vestibulo-Ocular Reflex 
Stephen P. DeWeerth and Carver A. Mead 
California Institute of Technology 
Pasadena, CA 91125 
ABSTRACT 
The vestibulo-ocular reflex (VOR) is the primary mechanism that 
controls the compensatory eye movements that stabilize retinal im- 
ages during rapid head motion. The primary pathways of this sys- 
tem are feed-forward, with inputs from the semicircular canals and 
outputs to the oculomotor system. Since visual feedback is not 
used directly in the VOR computation, the system must exploit 
motor learning to perform correctly. Lisberger(1988) has proposed 
a model for adapting the VOR gain using image-slip information 
from the retina. We have designed and tested analog very large- 
scale integrated (VLSI) circuitry that implements a simplified ver- 
sion of Lisberger's adaptive VOR model. 
I INTRODUCTION 
A characteristic comlnonly found in biological systems is their ability to adapt their 
function based on their inputs. The combination of the need for precision and 
the variability inherent in the environment necessitates such learning in organisms. 
Sensorimotor systems present obvious examples of behaviors that require learning 
to function correctly. Simple actions such as walking, jumping, or throwing a ball 
are not performed correctly the first time they are attempted; rather, they require 
motor learning throughout many iterations of the action. 
When creating artificial systems that must execute tasks accurately in uncontrolled 
environments, designers can exploit adaptive techniques to improve system perfor- 
mance. With this in mind, it is possible for the system designer to take inspiration 
from systems already present in biology. In particular, sensorimotor systems, due to 
An Analog VLSI Model of Adaptation in the Vestibulo-Ocular Reflex 743 
their direct interfaces with the environment, can gather an immediate indication of 
the correctness of an action, and hence can learn without supervision. The salient 
characteristics of the environment are extracted by the adapting system and do not 
need to be specified in a user-defined training set. 
2 THE VESTIBULO-OCULAR REFLEX 
The vestibulo-ocular reflex (VOR) is an example of a sensorimotor system that 
requires adaptation to function correctly. The desired response of this system is 
a gain of -1.0 from head movements to eye movements (relative to the head), so 
that, as the head moves, the eyes remain fixed relative to the surroundings. Due 
to the feed-forward nature of the primary VOR pathways, some form of adaptation 
must be present to calibrate the gain of the response in infants and to maintain this 
calibration during growth, disease, and aging (Robinson, 1976). 
Lisberger (1988) demonstrated variable gain of the VOR by fitting magnifying spec- 
tacles onto a monkey. The monkey moved about freely, allowing the VOR to learn 
the new relationship between head and eye movements. The monkey was then 
placed on a turntable, and its eye velocity was measured while head motion was 
generated. The eye-velocity response to head motion for three different lens mag- 
nifications is shown in Figure 1. 
G = -1.57 
eye veloci 1.05 
0.32 
30 deg/sec 
150 msec 
Figure 1: VOR data from Lisberger (1988). A monkey was fitted with magnifying 
spectacles and allowed to learn the gain needed for an accurate VOR. The monkey's 
head was then moved at a controlled velocity, and the eye velocity was measured. 
Three experiments were performed with spectacle magnifications of 0.25, 1.0, and 
2.0. The corresponding eye velocities showed VOR gains G of -0.32, -1.05, and 
-1.57. 
Lisberger has proposed a simple model for this adaptation that uses retinal-slip 
information from the visual system, along with the head-motion information from 
the vestibular system, to adapt the gain of the forward pathways in the VOR. 
744 DeWeerth and Mead 
Figure 2 is a schematic diagram of the pathways subserving the VOR. There are 
two parallel VOR pathways from the vestibular system to the motor neurons that 
control eye movements (Snyder, 1988). One pathway consists of vestibular inputs, 
VOR interneurons, and motor neurons. This pathway has been shown to exhibit an 
unmodified gain of approximately -0.3. The second pathway consists of vestibular 
inputs, floccular target neurons (FTN), and motor neurons. This pathway is the 
site of the proposed gain adaptation. 
Vestibular 
Inputs  
Flocculus 
( 
FTN 
)PC 
() VOR interneuron 
eye movement I 
feedback I 
: 
 Motor neuron 
retinal 
slip 
Figure 2: A schematic diagram of the VOR (Lisberger, 1988). Two pathways 
exist connecting the vestibular neurons to the motor neurons driving the eye mus- 
cles. The unmodified pathway connects via the VOR interneurons. The modified 
]athway (the proposed site of gain adaptation) connects via the fioccular target 
neurons (FTN). Outputs from the Purkinje cells (PC) in the fiocculus mediate gain 
adaptation at the FTNs. 
Lisberger's hypothesis is that feedback from the visual system through the fiocculus 
is used to facilitate the adaptation of the gain of the FTNs. Image slip on the 
retina indicates that the total VOR gain is not adjusted correctly. The relationship 
between the head motion and the image slip on the retina determines the direction 
in which the gain must be changed. For example, if the head is turning to the right 
and the retinal image slip is to the right, the eyes are turning too slowly and the 
gain should be increased. The direction of the gain change can be considered to be 
the sign of the product of head motion and retinal image slip. 
3 THE ANALOG VLSI IMPLEMENTATION 
We implemented a simplified version of Lisberger's VOR model using primarily 
subthreshold analog very large-scale integrated (VLSI) circuitry (Mead, 1989). We 
interpreted the Lisberger data to suggest that the gain of the modified pathway 
An Analog VLSI Model of Adaptation in the Vestibulo-Ocular Reflex 745 
varies from zero to some fixed upper limit. This assumption gives a minimum VOR 
gain equal to the gain of the unmodified pathway, and a maximum VOR gain equal 
to the sum of the unmodified pathway gain and the maximum modified pathway 
gain. We designed circuitry for the unmodified pathway to give an overshoot re- 
sponse to a step function similar to that seen in Figure 1. 
neuron circuits 
Vb qlib 
Figure 3: An analog VLSI sensorimotor framework. Each input circuit consists 
of a bias transistor and a differential pair. The voltage Vb sets a fixed current 
i b through the bias transistor. This current is partitioned into currents i and i2 
according to the differential voltage V1 - V, and these currents are summed onto a 
pair of global wires. The global currents are used as inputs to two neuron circuits 
that convert the currents into pulse trains P1 and P2. 
The VOR model was designed within the sensorimotor framework shown in Figure 3 
(DeWeerth, 1987). The framework consists of a number of input circuits and two 
output circuits. Each input circuit consists of a bias transistor and a differential pair. 
The gain of the circuit is set by a fixed current through the bias transistor. This 
current is partitioned according to the differential input voltage into two currents 
that pass through the differential-pair transistors. The equations for these currents 
are 
1 1 
il = ib i -- ib 
1 + e v -v 1 + e v -v 
The two currents are summed onto a pair of global wires. Each of these global 
currents is input to a neuron circuit (Mead, 1989) that converts the current linearly 
into the duty cycle of a pulse train. The pulse trains can be used to drive a pair 
of antagonistic actuators that can bidirectionally control the motion of a physical 
plant. We implement a system (such as the VOR) within this framework by aug- 
menting the differential pairs with circuitry that computes the function needed for 
the particular application. 
746 DeWeerth and Mead 
Figure 4: The VLSI implementation of the unmodified pathway. The left differen- 
tial pair is used to convert proportionally the differential voltage representing head 
velocity (Vhead -- Vef) into output currents. The right differential pair is used in con- 
junction with a first-order section to give output currents related to the derivative 
of the head velocity. The gains of the two differential pairs are set by the voltages 
Vp and VD. 
The unmodified pathway is implemented in the framework using two differential 
pairs (Figure 4). One of these circuits proportionally converts the head motion into 
output currents. This circuit generates a step in eye velocity when presented with 
a step in head velocity. The other differential pair is combined with a first-order 
section to generate output currents related to the derivative of the head motion. 
This circuit generates a broad impulse in eye velocity when presented with a step 
in head velocity. By setting the gains of the proportional and derivative circuits 
correctly, we can make the overall response of this pathway similar to that of the 
unmodified pathway seen when Lisberger's monkey was presented with a step in 
head velocity. 
We implement the modified pathway within the framework using a single differential- 
pair circuit that generates output currents proportional to the head velocity (Fig- 
ure 5). The system adapts the gain of this pathway by integrating an error signal 
with respect to tine. The error signal is a current, which the circuitry computes 
by multiplying the retinal image slip and the head velocity. This error current is 
integrated onto a capacitor, and the voltage on the capacitor is then converted to 
a current that sets the gain of the modified pathway. 
4 EXPERIMENTAL METHOD AND RESULTS 
To test our VOR circuitry, we designed a simple electrical model of the head and 
eye (Figure 6). The head motion is represented by a voltage that is supplied by a 
function generator. The oculomotor plant (the eye and corresponding muscles) is 
modeled by an RC circuit that integrates output pulses from the VOR circuitry into 
a voltage that represents eye velocity in head coordinates. We model the magnifying 
An Analog VLSI Model of Adaptation in the Vestibulo-Ocular Reflex 747 
slip 
f 
I 
' rhead 
Figure 5: The VLSI implementation of the modified pathway. A differential pair 
is used to convert proportionally the differential voltage representing head velocity 
(Vhead -- Vref) into output currents. Adaptive circuitry capacitively integrates the 
product of head velocity and retinal image slip as a voltage V. This voltage is 
converted to a current ig that sets the gain of the differential pair. The voltage VA 
sets the maximum gain of this pathway. 
reye 
R1 
R 
C 
Vref -- 
R2 
rhead: : -- 
Figure 6: A simple model of the oculomotor plant. An RC circuit (bottom) 
integrates pulse trains P1 and P2 into a voltage Vye that encodes eye velocity. The 
magnifying spectacles are modeled by an operational amplifier circuit (top), which 
has a magnification m = B2/R1. The retinal image slip is encoded by the difference 
between the output voltage of this circuit and the voltage Vhead that encodes the 
head velocity. 
748 DeWeerth and Mead 
spectacles using an operational amplifier circuit that multiplies the eye velocity by 
a gain before the velocity is used to compute the slip information. We compute the 
image slip by subtracting the head velocity from the magnified eye velocity. 
k" .G = --1.45 
.G = --0.92 
G = -0.32 
eye velocity 
1.0 Volt 
head velocity 
4.0 msec 
Figure 7: Experimental data from the VOR circuitry. The system was allowed to 
adapt to spectacle magnifications of 0.25, 1.0, and 2.0. After adaptation, the eye 
velocities showed corresponding VOR gains of -0.32, -0.92, and -1.45. 
We performed an experiment to generate data to compare to the data measured by 
Lisberger (Figure 1). A head-velocity step was supplied by a function generator and 
was used as input to the VOR circuitry. The VOR outputs were then converted to an 
eye velocity by the model of the oculomotor plant. The proportional, derivative, and 
maximum adaptive gains were set to give a system response similar to that observed 
in the monkey. The system was allowed to adapt over a number of presentations 
of the input for each spectacle magnification. The resulting eye velocity data are 
displayed in Figure 7. 
5 CONCLUSIONS AND FUTURE WORK 
In this paper, we have presented an analog VLSI implementation of a model of a 
biological sensorimotor system. The system performs unsupervised learning using 
signals generated as the system interacts with its environment. This model can 
be compared to traditional adaptive control schemes (]tstrSn, 1987) for perform- 
ing similar tasks. In the future, we hope to extend the model presented here to 
incorporate more of the information known about the VOR. 
We are currently designing and testing chips that use ultraviolet storage techniques 
for gain adaptation. These chips will allow us to achieve adaptive time constants of 
the same order as those found in biological systems (minutes to hours). 
We are also combining our chips with a mechanical model of the head and eyes to 
give more accurate environmental feedback. We can acquire true image-slip data 
using a vision chip (Tanner, 1986) that computes global field motion. 
An Analog VLSI Model of Adaptation in the Vestibulo-Ocular Reflex 749 
Acknowledgments 
We thank Steven Lisberger for his suggestions for improving our implementation of 
the VOR model. We would also like to thank Massimo Sivilotti, Michelle Mahowald, 
Michael Emerling, Nanette Boden, Richard Lyon, and Tobias Delbriick for their help 
during the writing of this paper. 
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