Journal of Vestibular Research, Vol. 1, pp. 263-277, 1990/91 Printed in the USA. All rights reserved.

0957-4271/91 $3.00 + .00 Copyright © 1991 Pergamon Press pic

VISUAL-VESTIBULAR INTERACTION WITH TELESCOPIC SPECTACLES

J. L. Demer, * J. Goldberg, t F. I. Porter,t H. A. Jenkins,t and K. Schmidtt

*Jules Stein Eye Institute, University of California at Los Angeles; tCullen Eye Institute and Clayton Neurotology Laboratory, Baylor College of Medicine, Houston, Texas;

tUniversityof Houston College of Optometry, Houston, Texas Reprint address: J. L. Demer, Comprehensive Division Jules Stein Eye Institute, 100 Stein Plaza,

UCLA, Los Angeles, California 90024-7002, U.S.A.

D Abstract - Vestibularly and visually driven eye movements interact to compensate for head move­ments to maintain the necessary retinal image sta­bility for clear vision. The wearing of highly magnifying telescopic spectacles requires that such compensatory visual-vestibular interaction operate in a quantitative regime much more demanding than that normally encountered. We employed electro-oculography to investigate the effect of wearing of 2 x, 4 x, and 6 x binocular telescopic spectacles on visual-vestibular interactions during sinusoidal head rotation in 43 normal subjects. All telescopic spectacle powers produced a large, im­mediate increase in the gain (eye velocity Ihead ve­locity) of compensatory eye movements, called the visual-vestibulo-ocular reflex (VVOR). However, the amount of VVOR gain augmentation became limited as spectacle magnification and the ampli­tude of head velocity increased. Optokinetic re­sponses during wearing of telescopic spectacles exhibited a similar nonlinearity with respect to stimulus amplitude and spectacle magnification. Computer simulation was used to demonstrate that the nonlinear response of the VVOR with tele­scopic spectacles is a result of nonlinearities in vi­sually guided tracking movements. Immediate augmentation of VVOR gain by telescopic specta­cles declined significantly with increasing age in the subject pool studied. Presentation of unmagnified visual field peripheral to the telescopic spectacles reduced the immediate VVOR gain-enhancing ef­fect of central magnified vision. These results im­ply that the VVOR may not be adequate to maintain retinal image stability during head move­ments when strongly magnifying telescopic specta­cles are worn.

o Keywords - visual-vestibular interaction; vestibulo-ocular reflex; head motion; telescopic spectacles; plasticity.

Introduction

Most human activities produce head move­ments, intentional or inadvertent (1). Since motion of images on the retina would sub­stantially degrade visual acuity (2-5), two sen­sory inputs drive reflexes to produce eye movements to compensate for head move­ments and thus prevent retinal image motion (6). Head acceleration, transduced by the ves­tibular apparatus of the inner ear, produces compensatory eye movements called the ves­tibulo-ocular reflex (VOR). Visually perceived motion also produces tracking eye move­ments, described as pursuit for small tar­gets and optokinetic for motion of the entire visual surround. The interaction of vestibu­lar and visual compensatory reflexes, called visual-vestibula! interaction C\/VI), has been said to be nonlinear (7). Although the inter­action is not intrinsically nonlinear, the visual contribution may be a nonlinear function of retinal image motion, resulting in an overall system that is nonlinear in the input/output sense with respect to stimulus amplitude. Visual tracking also exhibits nonlinear inter­actions among frequency components of re­sponses to complex stimulus waveforms, and

RECEIVED 9 May 1990; ACCEPTED 26 November 1990.

263

264

a predictive contribution in the response to some repetitive stimuli (8).

The combined action of the VOR and VVI produces the visual-vestibulo-ocular reflex (VVOR). Best visual acuity during the wear­ing of telescopic spectacles demands that VVOR gain be equal to the magnification of the telescopes (5). However, the visual acuity achieved by normal subjects wearing tele­scopic spectacles has been found to be de­graded by head monon aboU[ tne vertiCal aXIS

(5). The degradation of this dynamic visual acuity depends upon both telescopic magnifi­cation and head velocity in a manner that suggests that VVOR gain is often insufficient to prevent retinal image motion. It has been demonstrated that the wearing of telescopic spectacles during head motion for a duration of as little as 15 minutes induces an adaptive increase in VOR gain (9). The increase in VOR gain that occurs during adaptation to telescopic spectacles is associated with a re­duction in the degradation by head motion of visual acuity with telescopes (5). Neverthe­less, such plastic adaptive changes in VOR gain are usually incomplete, at feast at some frequencies in the spectrum of natural head movement (10-12). The avoidance of retinal image motion during these head movements then requires that VVOR gain be optimized by VVI. While there is evidence that such VVI does occur with telescopic (11,13,14) and reversing (13) spectacles, this phenomenon has not been previously investigated over a range of head velocities or optical device powers.

While VVI with telescopic spectacles is cer­tainly of interest in the laboratory, it is also important for rehabilitation of the visually impaired. Telescopic spectacles are commonly prescribed as distance aids for patients having severe but incomplete visual impairments, the so-called low vision patients (15). These opti­cal devices are usually used intermittently for spotting objects of particular interest such as street signs (16), 'and because they are fre­quently worn so that unmagnified peripheral visual field inhibits plastic adaptation of VOR gain (9), VVI would be expected to play an important role in retinal image stabiliza­tion. Inadequate VVI would be expected to

J. L. Demer et al

result in significant retinal image slip during head movement, a factor known to signifi­cantly degrade visual acuity in normal (5), and low vision (17) subjects wearing tele­scopic spectacles.

The purpose of the present investigation was thus to characterize human VVI that oc­curs while wearing telescopic spectacles, with special attention to conditions relevant to ev­eryday use of these devices by visually im­paired persons. Several telescope powers were studied over a range of head velocities to ob­tain a description of VVI for widely ranging combinations of vestibular and visual input, sufficient to define parameters in a mathe­matical model of VVI. Such a model then concisely describes this VVI in a general sense, and allows quantitative prediction of VVI for arbitrary combinations of visual and vestibular input.

Subjects and Methods

This study was approved by the Institu­tional- Review Board for Human Research. All subjects gave written informed consent. A total of 46 normal volunteers was studied; three of these were unable to complete testing protocols due to symptoms of motion sick­ness and were excluded from further analysis. Several subgroups participated in various test­ing protocols, as described below, but it was not possible to have all subjects participate in all protocols due to the extensive nature of the testing and subject availability. Of the subjects completing test protocols, 18 were males and 25 were females. All subjects un­derwent an eye examination to verify that vi­sual acuity was correctable to normal (6/6). Bilateral function of the peripheral vestibular apparatus was verified with cool (30°C) and warm (42°C) water caloric irrigations of each external auditory canal. VOR data for these subjects has been reported elsewhere (9).

Binocular, focusable telescopic spectacles of 2x, 4x, and 6x powers were employed. The 2x telescopes were of Galilean configu­ration and had a total visual field diameter of 16.8°. The 4x telescopes were of astronomi­cal configuration (with image erecting prisms)

Visual-Vestibular Interaction with Telescopic Spectacles 265

and had a total visual field diameter of 10.3 ° (nominal 12.5°). The 6x telescopes were of astronomical configuration and had a total visual field diameter of 7.5° (nominal 10°). Emphasis was placed upon the 4 x telescopic spectacles for data collection. It was felt that a low vision aid of this power represents a good compromise among weight, field diam­eter, and magnification. Data were usually collected with the peripheral visual field out­side the telescope eyepieces occluded, unless otherwise noted. In a subgroup of subjects, data are also reported on experiments con­ducted without obstruction of this unmagni­fied visual field.

Subjects were seated in a chair mounted on a vertical axis servomotor, as described previ­ously (9). A digital computer controlled rota­tion of the chair and digitized its angular velocity as sensed by a tachometer. Subjects were rotated sinusoidally at various frequen­cies and velocity amplitudes. The rotatory chair could be surrounded by a full-field, verti­cally striped, optokinetic drum located 70 cm from the subject's eyes. This optokinetic drum was also driven by a servomotor. Horizontal and vertical eye position were recorded using DC coupled electro-oculography (EOG), with automated calculations of VOR, VVOR, and optokinetic gains as described previously (9).

VOR gain was measured in complete dark­ness for sinusoidal rotation at a frequency of 0.1 Hz. Most VOR gain measurements were made using a velocity amplitude of 600/s, which was near the maximum velocity at which the rotator could produce sinusoids without detectable distortion for large adults. This relatively high amplitude was chosen to maximize the signal to Heise' ::atic of the' sponse. As will be described below, VOR gain was essentially constant within a broad range of stimulus amplitudes, permitting VOR gain measured at the 600/s amplitude to be directly compared with VVOR gain measured at other amplitudes. Subjects were instructed to look straight ahead and to attempt to see anything that might be visible there. Nothing, of course, was visible in the total darkness.

VVOR gain was measured under condi­tions of normal laboratory lighting as sub­jects were instructed to look at objects in the

room. Since VVOR responses had consider­ably higher amplitudes than VOR responses, and since VVI with 4 x telescopic spectacles at a head rotational amplitude of 600/s frequently evoked motion discomfort, most VVOR test­ing was performed using a stimulus velocity amplitude of 300/s or less. Optokinetic gain was measured under normal room lighting as subjects were surrounded by the servo-driven optokinetic drum, with instructions to look at the stripes. The optokinetic drum was rotated sinusoidally at 0.1 Hz, with velocity ampli­tudes from 3.5° to 600/s. Alertness was main­tained for all testing using mental arithmetic and alphabetical listing tasks monitored via an intercom.

After initial measurements of gains, most subjects underwent a period of adaptation training during which they viewed a distant video monitor through telescopic spectacles for a period of 15 min while undergoing sinu­soidal rotation in normal room lighting at 0.2 Hz, amplitude 200/s. This period of com­bined visll~l-vestibular experience was de­signed to train ~ubjects to stabilize gaze against head moverrlent while wearing tele­scopic spectacles. It has been previously dem­onstrated that the adaptive increase in VOR gain induced by sinusoidal rotation at 0.2 Hz can be measured at any frequency of testing rotation from 0.025 to 0.8 Hz (9). For the

, present experiments, an adapting frequency of 0.2 Hz, amplitude 200/s was chosen for two reasons: 1) to reduce the angular position amplitude of the stimulus so that a video monitor could be viewed throughout rota­tion, enabling alertness of the subject to be maintained during an otherwise very boring

r'T""'T"ll' and 2) for comparability with a pre­vious study employing these conditions. Pilot studies had indicated that the prolonged wearing of telescopic spectacles during head rotation is considerably more fatiguing than without telescopes, and indicated the need to tailor experimental conditions to minimize this effect. The testing frequency of 0.1 Hz was chosen to minimize cycle-to-cycle vari­ability in the response, which we have found to be greater at 0.2 Hz. Gain measurements were repeated after adaptation.

Statistical comparisons between groups

266 J. L. Demer et al

were made using Student's t test. A 0.05 level 0 .!i CD

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The effect of telescopic spectacle magnifi- "0-co{g

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subject in Figure 1, which compares slow (/) c: ::::J Cl) ._ c: C. 0 ..... -

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28 ± 2 y) in darkness to 1.60 ± 0.05 (range U > ;:

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cles, magnified vision increased gain from 0 Q co ! II 0

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0.71, n = 4 subjects, mean age 30 ± 4 y) in 'oaS/Baa "- 0 ::::J.e:

darkness to 1.57 ± 0.46 (range 0.71 to 2.84, AJ!OOlaJ\ a 3 ~.~

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Figure 2C). There was no statistically signif­icant difference in VVOR gains among sub­ject groups wearing the telescopic spectacles of the three different powers (P > 0.25). Thus, above 2x, increasing telescopic specta­cle power did not produce further increases in mean VVOR gain for the group.

The apparent limitation in maximum VVOR gain prompted an investigation into the linearity of VOR and VVOR responses.

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Figure 2. VOR gain in darkness and VVOR gain in light using telescopic spectacles of several powers. Amplitude of head rotation used for VOR and VVOR testing was 60 0 /s and 30 0 /s, respectively. SEM = stan-dard error of the mean. (A) 2X telescopic spectacles, 8 subjects. (8) 4X telescopic spectacles, 31 subjects. (C) 6X telescopic spectacles, 4 subjects.

VOR gain was measured for sinusoidal rota­tions at 0.1 Hz at amplitudes ranging from 15°/s to 90 0/s in 6 subjects (mean age 28 ± 3 y, Figure 3). Mean gain measured at each frequency and across all subjects had a stan­dard deviation at the 15°/s amplitude of 0.18, much higher than the value of about 0.07 ob­served at all other amplitudes. This was be­cause at an amplitude of 15°/s, the responses were small relative to measurement noise.

268 J, L. Demer et al

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0 10 20 30 40 50 60 70 80 90

Amplitude of Head Velocity Oeg/Sec

Figure 3. VOR gain as a function of amplitude of sinusoidal head rotation at 0.1 Hz. Different symbols indi­cate gains of each of 6 subjects.

Multiple t-test comparisons showed no signif­icant differences among mean gains measured at any of the five amplitudes tested, confirm­ing that VOR gain was independent of ampli­tude in the range tested. Similar evidence for the linearity of the VOR for stimUlus ampli­tudes to 60 0/s is provided in the data of Fig­ure 4 for testing in darkness. The plots of VOR response amplitudes against head veloc­ity amplitude are essentially straight lines. This implies that VOR gains measured for amplitudes of head rotation of 30° or 60 0/s should be essentially the same.

Although the VOR was found to be linear, the VVOR response was found to be mark­edly nonlinear with respect to amplitude of head rotation. This nonlinearity is seen in Figure 4, which plots for three subjects (ages 21, 22, and 36 years) the amplitude of the slow phase eye velocity response against stim­ulus amplitude for VOR, unmagnified VVOR, and for VVOR with telescopic spectacles of various powers. Testing was rarely successful at stimulus amplitudes of 60° and 90 0/s using telescopic spectacles, because these conditions evoked excessive motion discomfort. The 4x and 6 x telescopic spectacles were associated with lower maximum amplitudes of eye veloc­ity than were the 2x telescopic spectacles. The nonlinearity in the VVOR is illustrated

for a subgroup of 26 subjects (having ages similar to the subgroups previously described) in Figure 5, which plots VVOR gain as a function of telescopic spectacle magnifica­tion. A 30°/ s amplitude of head rotation was employed. It may be seen from Figure 5 that the VVOR at this amplitude of head rotation satur'ates for telescopic spectacle powers of greater than 2 x .

It is evident from Figures 4 and 5 that for 4x telescopic spectacles, an amplitude of head rotation of 30 0/s requires the VVOR to operate in a nonlinear part of its range. For this reason, VVOR gain was reevaluated with 4x telescopic spectacles using a lower ampli­tude of 15°/s in 6 subjects who had also been tested at 30 0/s. The average age of the sub­jects was 26 ± 3 years (mean ± SEM, range 21 to 39). Mean VVOR gain at 0.1 Hz with 4x telescopic spectacles was 2.96 ± 0.17 (mean ± SEM, range 2.55 to 3.75) at an am­plitude of head rotation of 15°/s, significantly greater than the value of 1.90 ± 0.15 (range 1.55 to 2.55) at an amplitude of 300/s (P < 0.0005).

Three subjects (average age 31 years, range 21 to 39) were tested with 6x telescopic spec­tacles at stimulus amplitudes of both 15°/s and 30 0/s. Mean VVOR gain was 2.94 ± 0.82 (range 1.55 to 4.38) at an amplitude of head

Visual-Vestibular Interaction with Telescopic Spectacles 269

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Figure 4. Predicted and observed mean amplitude of VVOR eye velocity as a function of amplitude of 0.1 Hz sinusoidal head velocity for several visual conditions, and mean VOR eye velocity in darkness (3 subjects). VOR eye velocities are repeated in each panel. Predicted values were obtained from the mathematical model in Fig­ure 8. (A) 1 X viewing, without spectacles. (8) Viewing with 2X telescopic spectacles. (C) Viewing with 4X tele­scopic spectacles. (0) Viewing with 6X telescopic spectacles.

rotation of 15°/s, greater than the value of 1.75 ± 0.54 (range 1.19 to 2.84) at an ampli­tude of 30 0/s. The difference was not signif­icant, however (P > 0.1).

Visual Tracking Nonlinearity

Since the vestibular contribution to the VVOR had been found to be linear with re­spect to head velocity, it was suspected that the observed nonlinear VVOR response was

due to nonlinearity of the visual contribution. This was investigated by measuring, with un­magnified vision and with telescopic spec­tacles, sinusoidal optokinetic responses to stimulus velocity amplitudes ranging between 3.75 and 60 0/s in two of the three subjects whose data was illustrated in Figure 4. As may be seen in Figure 6, optokinetic re­sponses with telescopic spectacles were highly nonlinear, such that the velocity of the re­sponses decreased as stimulus amplitude in­creased, and such that at high stimulus

270

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Telescopic Spectacle Magnification

Figure 5. VVOR gain for multiple subjects plotted as a function of magnification of telescopic spectacles worn. The unmagnified condition is indicated as 1 X. Gain was tested during sinusoidal rotation at 0.1 Hz, amplitude 30 0 /s.

velocities the response with 4 X telescopic spectacles was less than that with 2 x tele­scopes. Measurements were also attempted using 6x telescopes, but subjects found this very fatiguing; measurements were quite in­consistent from cycle to cycle and were usu­ally small.

Effect of Adaptation

The effect of a IS-min period of viewing a distant video movie with telescopic spectacles during sinusoidal head rotation at 0.2 Hz, amplitude 200/s was studied in groups of sub­jects. The visual field peripheral to the tele­scopes was occluded. It was known that this was an adequate adapting stimulus to induce an increase in VOR gain in many subjects (9,12). VVOR gain was compared before and after adaptation, for each individual subject, as well as for groups of subjects undergoing similar testing. In some subjects, as discussed below, VVOR gain increased significantly af­ter adaptation, although in many subjects gain was either unchanged or decreased. In no group was the change in VVOR gain sta-

J. L. Derner et a\

tistically significant (P> 0.05) for any of the three telescope powers.

Effect of Peripheral Field

The effect of unmagnified peripheral field on initial VVOR gain was studied for 4x tel­escopic spectacles in a subgroup of 8 subjects. The mean age of this subgroup was 27 ± 2 years (mean ± SENI, range 21 to 39). VVOR

was measured for head rotation at 0.1 Hz, amplitude 30 0/s for 4x telescopic spectacles mounted in two different ways. In the first configuration, the peripheral visual field was masked to prevent any vision around the tele­scopes (occluded periphery), as during ex­periments described above. In the second configuration, the peripheral visual field was only minimally obstructed by the spectacle frames (nonoccluded periphery). With the oc­cluded periphery, mean initial VVOR gain was 1.93 ± 0.30 (mean ± SEM, n = 8), sig­nificantly greater than the value of 1.27 ± 0.30 obtained with the nonoccluded periphery (P < 0.0005).

Effect of Age

Thirty-four subjects ranging in age from 16 to 72 years were tested with 4 x telescopic spectacles using the 300/s amplitude. When VVOR gain was plotted against subject age (Figure 7), a linear relationship appeared rea­sonable, and a linear regression analysis was used to evaluate the effect of age on VOR and VVOR gain with this telescope power. The regression was of the form VVOR gain = 2.239 - 0.016 x age (years) and was signifi­cant at P < 0.001 (r = 0.677). There was no significant relationship between initial VOR gain and age.

Discussion

Similar to published values, the low fre­quency VOR gains measured in these normal subjects were significantly less than 1.0 (19). To achieve clear vision with telescopic specta­cles during head motion, VVOR gain must

Visual-Vestibular Interaction with Telescopic Spectacles 271

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Stimulus Velocity Amplitude (Degrees / Second)

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surpass 1.0 to approximate spectacle magni­fication. We have demonstrated that visual­vestibular interaction (VVI) does immediately increase VVOR gain with telescopic soectacles to a value greater than VOR gain; however, this increase is not proportional to spectacle power at higher stimulus amplitudes. At the highest amplitudes tested, increasing tele­scopic spectacle powers were actually asso­ciated with lower VVOR gains than lower telescope powers. A part of the explanation for the lack of increase in VVOR gain with increasing telescopic spectacle power may lie in the reduction in visual field associated with increasing telescope magnification. This re­duction in visual field is an almost unavoid-

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60

Figure 6. Observed and predicted optokinetic eye ve­locity as a function of stimulus velocity for several vi­sual conditions. Amplitude of slow phase eye velocity during sinusoi.dal head rotation at 0.1 Hz is plotted against amplitude of stimulus velocity. Mean data from two subjects in each panel. Predicted values were obtained from the mathematical model in Fig­ure 8. (A) 1 X viewing, without spectacles. (8) 2X tele­scopic spectacles. (C) 4X telescopic spectacles.

able consequence of telescope optics, and implies that telescopes of higher power will stimulate less retinal area than those of lower power. Plastic changes in VOR gain have been shown to be Inducible by head rotations correlated with motion of only a central 4.7° diameter (20) or even foveal (21) target. How­ever, we indicate below that visual field lim­itation is unlikely to be the major cause of the nonlinear behavior of the VVOR.

Nonlinearity of the vestibular input can be ruled out as the cause of the nonlinear VVOR response, since the VOR response itself is characterized by a gain independent of stim­ulus amplitude. There is, in contrast, a strik­ing nonlinearity of the optokinetic response

272

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J. L. Demer et al

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Age in Years

Figure 7. VVOR gain with telescopes as a function of age, Initial VVOR gain with 4X telescopic spectacles mea­sured during sinusoidal rotation at 0.1 Hz, amplitude 30 0 /s, is plotted against age for 34 subjects, The broken line indicates the best linear fit by least squares.

when telescopic spectacles of each power are worn. This is characterized by a mean maxi­mum optokinetic response amplitude of 30° to 40°/ s regardless of telescopic spectacle power.

The nonlinearity of the optokinetic re­sponse suggests that it is the cause of the non­linearity in VVI. Corroboration is provided by techniques of mathematical modeling and computer simulation, which have been exceed­ingly useful in interpreting hypotheses con­cerning the ocular motor system (22-25). The interaction of VOR and optokinetic tracking responses was analyzed quantitatively using a mathematical model, implemented on a PDP 11/73 digital computer using the ASP model­ing package, created by H. M. Goldstein and L. M. Optican. This model was chosen be­cause many of its components, including nec­essary dynamic elements, have been extensively tested in other contexts. The model imple­ments central velocity storage (26,27) using an elaboration of Robinson's positive-feedback, velocity-storage loop (28) and is illustrated in Figure 8. The model contains a visual process­ing delay and nonlinearity corresponding to the accessory optic tract (29,30) and visual re­sponse of the vestibular nucleus (31), as well as a visual smooth pursuit subsystem incorporat-

ing the acceleration and velocity nonlinearities described by others (32). The visual and vestib­ular inputs interact linearly (25,28,33,34). The incorporation of telescopic spectacles is a novel addition. Parameters establishing VOR gain were set equal to the observed mean VOR gain for all subjects. At the stimulus frequency used here, the velocity storage component makes a small contribution compared with the pursuit component of VVI. The dynamics of the model were not examined for stimulus fre­quencies other than 0.1 Hz, since such data were not obtained empirically, and the dy­namic behavior of the model should not be ex­trapolated to other frequencies. Details of the model are described in the Appendix.

The model of Figure 8 was used to test the hypothesis that the nonlinear properties of the VVOR with telescopic spectacles are results of nonlinearities is visually guided tracking movements. First, parameters and nonlinearities were empirically adjusted so that the model reproduced optokinetic re­sponses with and without telescopic spectacles for two subjects with robust responses in whom these were measured in detail (those whose data are illustrated in Figure 6). The following were subject to this adjustment: the visual sensory nonlinearity, the pursuit ve-

1'0 ---.J 0J

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Pursuit Acceleration Nonlinearity

ASATt-c=

ASAT

Sensory Nonlinearity

Spectacle Magnification

~I~ Y ! ~

Efference Copy

,.-----G ;J'-------.f'ZB

sTo + I

CVSE

L ~ rMl~ • t • H

Figure 8. Control systems model of VOR and VVI.

. p

• • .. E

Variable Gain

Element

Semicircular Canals

274

locity saturation nonlinearity, the pursuit ac­celeration saturation nonlinearity, and the parameter B. The first test of the model was the verification that its simulations could, with the chosen topology and constraints, re­produce the observed optokinetic responses. The results of these simulations are seen in Figure 6, which also plots observed responses. The essential characteristics of the data that are captured by the simulation are twofold: that the optokinetic response reaches a satu­rating maximum value, and that at stimulus velocities above 30°/ s, responses for compa­rable stimulus velocities actually decrease when telescopic spectacle power is increased from 2 x to 4 x. Maximum response velocities for individual subjects under similar testing conditions varied. While the predicted re­sponses tended to be modestly greater than the mean observed responses at some stimu­lus velocities, they were nonetheless within the range of interindividual variability in the ob­served data. It is also likely that visual nonlin­earities vary from subject to subject.

After the model parameters and nonlinear­ities were adjusted to fit the observed optoki­netic responses of the two subjects in Figure 6, the model was then further tested by compar­ing observed and simulated VVI for 2x, 4x, and 6x telescopic spectacles (Figure 4). The subjects were the two whose data are shown in Figure 6 and one additional subject who had a robust VVOR. Simulated responses were similar to observed responses over a broad range of stimulus amplitUdes and tele­scopic spectacle powers. This was true even for 6x telescopic spectacles, although the vi­sual processing nonlinearities were derived only from observations of optokinetic re­sponses during unmagnified vision, and with 2x and 4x telescopic spectacles. Note that at very high values, responses for all telescopes tend toward the predicted VOR response, since the visual contribution to the VVOR is predicted to be completely ineffectual at very high retinal slip velocities. It should be noted that the robust VVOR performance shown in Figure 4 was typified by higher gains than ob­served in a number of other subjects whose data are illustrated in Figure 2. Especially during wearing of 4x and 6x telescopic spec-

J. L. Demer et al

tacles, VVOR gain is sensitive to the visual processing nonlinearity, and individual vari­ations in the VVOR response with telescopic spectacles are readily explained by individual variations in visual processing nonlinearities.

The simulations thus indicate that linear interaction between the linear VOR and non­linear visual tracking reflexes can account quantitatively for observed VVI in subjects wearing telescopic spectacles. VVOR perfor­mance is both predicted and observed to be compensatory even for high telescopic magni­fications if the amplitude of head velocity is low, but the VVOR becomes less responsive at higher velocities, allowing retinal image slip to occur. This nonlinear, saturating be­havior of the visual subsystem is a character­istic of behavior and models of VVI without telescopic spectacles (7,22), but the present study extends this to the more physiologically stressful demands of telescopes that have not previously been studied.

When telescopic spectacles are employed as aids for patients having reduced vision due to ocular pathology, the telescopes are often mounted so that the unmagnified visual pe­riphery is unobstructed. This permits use of the perlpheral field for orientation with re­spect to large visual objects. Since magnifica­tion will be 1.0 in the periphery, and will be much greater in the magnified center, the VVOR cannot simultaneously cancel retinal image motion in all parts of the retina during head motion. A high VVOR gain, appropri­ate to central vision, would induce substantial retinal image motion in the periphery. While such a nonoccluded configuration is useful for orientation, failure to occlude the unmag­nified peripheral visual field impairs VVI for the magnified central field and substantially reduces VVOR gain. This would necessarily increase retinal image motion and might com­promise visual acuity with a telescope during head motion. This is the case despite the find­ing of Barnes that peripheral point source vi­sual targets are much less effective than central targets in mediating VOR suppression (35). In the case of telescopic spectacles, the relatively large area of unmagnified periphery carries a significant weighting in determining the ocular motor response.

Visual-Vestibular Interaction with Telescopic Spectacles 275

It has been previously demonstrated that wearing of telescopic spectacles during head motion for only 15 min induces an adaptive increase in VOR gain (9,12). In the present study, however, significant increases in VVOR gain for groups of subjects were not observed for any power of telescopic spectacles, despite use of an adapting stimulus adequate for in­ducing VOR gain plasticity. It is likely that the failure to observe a plastic increase in VVOR gain was due to saturation of the non­modifiable visual component of the response, and to the fact that the visual component com­prises most of the VVOR response when gains greatly exceed 1.0. The small contribution of the adaptive VOR gain increase was probably not detectable given the variability of gain measurements with telescopic spectacles.

Initial VVOR gains were no higher, on av­erage, for 4x and 6x telescopic spectacles than for 2 X telescopes, when tested at an am­plitude of head velocity of 30 0/s. Because tel­escopic spectacles of different powers were tested in different-sized groups of different subjects, it is possible that individual differ­ences could have contributed to the group mean values. However, subject age is not likely to have created a systematic bias, as the mean age in the subjects tested with 2 x tele­scopic spectacles (28 years) was quite similar to the mean age of subjects tested with 6x telescopic spectacles (30 years). For subjects tested with 4x telescopes, the mean age was greater (40 years) than in the other two groups; however, this group was large enough that the effect of age could be computed by linear regression. When the VVOR gain data from the groups tested with 4 x telescopic

spectacles is corrected to a mean age of 30 years using the regression equation described above, the resulting value is increased to 1.76. This higher value is nonetheless not statisti­cally significantly different (P > 0.05) from the mean VVOR gains observed with 2x and 6 x telescopic spectacles.

SUbject age was found to significantly in­fluence VVOR gain with telescopic spectacles. As shown in Figure 7, VV 0 R gain with a 4 x telescopic spectacle decreased by 50070, on av­erage, as subject age increased from the sec­ond to the ninth decade. Since VOR gain is not correlated with age in these subjects, this effect is probably related to an age-related degradation in maximum smooth pursuit (36-38) and optokinetic (39) tracking perfor­mance. Specific lesions of the vestibulocere­bellum are also known to impair VVI (40). Such findings imply that there are likely to be certain elderly patients who will have partic­ularly deficient VVI, and may, as a result, ex­perience marked disability from retinal image slip during ubjquitous head movement when telescopic spectacles are worn.

Acknowledgments- This research was supported by U.S. Public Health Service grants EY -06394, EY-02520, and NS-10940; grants from the Clayton Foundation for Research, the Karl Kirchgessner Foundation, the Permanent Charities Committee of the Entertainment Industries, and Research to Prevent Blindness. We thank Philip Szeto, Brad­ford Daniels, Margaret Kallsen, and Michael Wellman for computer programming. We thank Cyndy Cox and Sharon Congdon for assistance with laboratory testing.

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Appendix

Model

The model is described in Figure 8. La­place transform notation is used, and s is the

Laplace complex variable. Rightward eye ve­locities are positive by convention. Head ve­locity fl is sensed by the semicircular canals, which have high-pass dynamics and a time

Visual-Vestibular Interaction with Telescopic Spectacles 277

constant 'Fe set equal to 7 sec as estimated for the human inner ear (6). The estimate of head velocity according to the canals, He, is added to the estimate of head velocity of the veloc­ity storage mechanism Hy , to produce the best central estimate of head velocity flo. Es­timate Ho is multiplied by the variable gain element to produce velocity storage command V. The variable gain element is a nonlinearity having slopes GR and GL for eye velocity commands to the right and left, respectively. The velocity storage command signal V is added to the pursuit velocity command signal P to drive the oculomotor plant (assumed to have unity transfer function) to produce slow phase eye velocity E. Quick phases are not represented for the sake of simplicity. The ve­locity storage eye velocity command V is mul­tiplied by an efference copy element, and the resulting product enters the central velocity storage element (CVSE) consisting of a leaky integrator with time constant To, taken to be equal to Te (7 s). The slope of the efference copy element nonlinearity is KR or KL , for eye velocity commands to the right or left, re­spectively. The output of CVSE is the best central estimate of head velocity fly. The positive-feedback, velocity storage loop L contains the variable gain element, the effer­ence copy element, and the single central ve­locity storage element CVSE.

The variable Q represents the velocity of images on the retina; it is equal to head veloc­ity H times the magnification M of the tele­scopic spectacles worn, plus optokinetic velocity iJ times the magnification M of the telescopic spectacles. Retinal slip Q is subject to a sensory processing delay of about 100 illS

(6), as well as a nonlinearity having the veloc­ity tuning of neurons in the accessory optic tract (29,30) and vestibular nucleus (31). The nonlinearity has the form of a sinusoidal function about zero input, where its slope is 40/ 7r. It is noteworthy that the output of the sensory nonlinearity increases with increasing retinal slip input until about 200/s; it then re-

mains constant until the input reaches about 400/s before decreasing smoothly to zero at input values greater than about 1400/s. This nonlinearity is empirically determined for each subject. The output of the sensory nonlinearity is supplied to two motor sys­tems, entering (after multiplication by coef­ficient B = 1.5) the positive-feedback, velocity storage loop, L, as well as entering the pursuit pathway. The pursuit pathway incorporates saturating nonlinearities for both acceleration and velocity, as found by others (32,37). The detailed data of Lis­berger and coworkers related retinal slip ve­locity to eye acceleration (32), so the pursuit acceleration nonlinearity was modeled as a saturating exponential having a slip velocity input and an acceleration output. For these simulations, acceleration saturation ASAT

was set to 500 0/s 2, and the velocity satura­

tion VsAT was set to 900/s. For the acceler­ation nonlinearity, the slope at zero input was assumed to be about 3; for the velocity nonlinearity ,the slope at zero input was as­sumed to be unity. These values were de­termined empirically from optokinetic data obtained with unmagnified vision during wearing of 2x and 4x telescopic spectacles. In order to convert the output of the acceler­ation nonlinearity into a velocity signal (32), it was passed through a leaky integrator assumed to have a time constant Tp of 2 s.

While the interactions of all signals in the model are represented as summing junctions and are thus linear, the overall input-output behavior of the model can be nonlinear due to amplitude nonlinearities in the optokinetic and vestibular subsystems. The variable gain dement:; G L and are set to the high frequency VOR gain measured for slow phases to the left and right, respectively. The efference copy parameters KL and KR were set equal to 1.0. The vestibular portion is lin­ear in the special case where KL = KR and GL = OR (the symmetric case). In this study, symmetric V 0 R gains were assumed.