Model interpretation of visual-vestibular interaction in patients with labyrinthine and cerebellar pathologies

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Biol. Cybern. 47, 203-211(1983) Biological 
Cybernetics 
�9 Springer-Verlag 1983 
Model Interpretation of Visual-Vestibular Interaction 
in Patients with Labyrinthine and Cerebellar Pathologies* 
A. Buizza and R. Schmid 
Dipartimento di Informatica e Sistemistica, Universit/t di Pavia, Pavia, Italy 
Abstract. Oculomotor responses to combined optoki- 
netic and vestibular stimulations in labyrinthine and 
cerebellar defective patients are discussed in terms of 
parametric changes in a model describing the in- 
teraction between the vestibulo-ocular reflex (VOR) 
and the optokinetic reflex (OKR). By making a few 
reasonable hypotheses about model parameter va- 
riations in relation to the type of pathology, the 
experimental results obtained by several authors can 
correctly be predicted and explained by the model. The 
model can therefore be used to define a set of parame- 
ters giving an estimate of the state of the system 
subserving VOR-OKR interaction in the examined 
patients. The model is also shown to be a powerful tool 
to assess the validity and the diagnostic significance of 
the procedures used to test VOR-OKR interaction. 
Introduction 
In every day life a clear vision of the external world can 
be maintained through an appropriate interaction 
between the vestibulo-ocular (VOR) and the optoki- 
netic (OKR) reflex. VOR is activated by stimulation of 
the semicircular canals and operates as an open loop 
system. OKR is excited by the slip of the image of the 
external world on the retina and behaves as a closed 
loop system. Thus, OKR will contribute to visual 
stabilization for as much as it is needed to complement 
vestibular compensation. Since VOR operates as a 
high-pass filter (Melvilt Jones and Milsum, 1971) and 
OKR as a low-pass filter, at low frequencies visual 
stabilization is mainly supported by OKR. At higher 
frequencies OKR contribution still remains significant, 
* Work supported by CNR, Rome, Italy. Some results reported in 
this paper have been previously presented at the Eighth 
Extraordinary Meeting of the B~trgny Society, Basle, June 22th-25th, 
1982 
at least in man whose VOR has a gain of only 0.4-0.6 
(Meiry, 1971). 
Besides dynamic limitations, the range of complete 
visual stabilization is normally bounded by OKR 
saturation. When the retinal slip velocity remaining 
after vestibular compensation makes OKR to saturate, 
eyes will no longer be locked to the motion of the 
visual surround relative to the head (Koenig et al., 
1978). In cerebellar and in vestibular patients OKR 
may saturate at abnormally low levels of stimulation, 
and the interpretation of the oculomotor responses in 
these conditions can be highly intriguing. Obviously, 
linear models of visual-vestibular interaction cannot 
offer any helpful suggestion. Only models giving a 
precise description of OKR non-linearities have some 
chance of providing a correct interpretation of the 
experimental data obtained in these pathological 
situations. 
The aim of this paper is to show how the non-linear 
model proposed by the authors in previous papers 
(Schmid et al., 1980; Buizza and Schmid, 1982) can be 
used to interpret oculomotor responses evoked by 
vestibular and optokinetic stimuli in patients suffering 
from peripheral vestibular disorders or from cerebellar 
pathologies. Model interpretation of the experimental 
data is also shown to be a way to obtain the same 
amount of clinical information by a reduced number of 
tests. 
Model of VOR-OKR Interaction 
A model of VOR-OKR interaction in oculomotor 
control is shown in Fig. 1. This model has been 
extensively discussed in a previous paper (Buizza and 
Schmid, 1982). Only its main characteristics are here 
reviewed. 
VOR is represented in the lower part of the block 
diagram in Fig. 1 as an open loop system receiving 
head angular velocity (On) as input signal. The dy- 
204 
~H BEH 
HEAD XE 
ANGULAR eOSITION 
VELOCITY V S B R A I N S T E M NI IN HEAD 
Fig. l. Model of visual-vestibular interaction in oculomotor control 
(from Buizza and Schmid, 1982). PTH 1 : slow (indirect) optokinetic 
pathway; PTH2: fast (direct) optokinetic pathway; FI: flocculus; 
NI: central neural integrator; NL 1: non-linear gain characteristic 
of PTH 1 ; NL 2: non-linear gain characteristic of PTH 2; R s: retinal 
slip velocity (always equal to zero in darkness); VN: vestibular 
nuclei; VS: vestibular system 
RETINA 
PTH 1 PTH 2 
-I1§ sty I1 , 
VS BRA I NSTEM N [ 
Fig. 2. Simplified model of visual-vestibular interaction in ocul- 
omotor control (redrawn from Schmid et al., 1980). Same notations 
as in Fig. 1 
namics of the vestibular system (VS) is described by a 
high-pass filter with a time constant T v. The output of 
VS, which is proportional to 0~ in the frequency range 
between 0.2 and 2Hz (Melvill Jones and Milsum, 1971), 
is integrated in the brainstem in order to provide the 
oculomotor nuclei with a neural command propor- 
tional to head position (Robinson, 1975). The dy- 
namics of the oculomotor apparatus has been 
neglected. 
OKR is represented in the upper part of Fig. 1 as a 
closed loop system. Visual surround velocity (Ov) is 
compared to eye velocity (0 E = OEn + 0~) at the level of 
retinal receptors. The error signal (retinal slip velocity 
Rs=O v-O~) is processed by two distinct pathways 
(PTH 1 and PTH 2) with non-linear gain characteris- 
tics (NL 1 and NL 2). PTH 1 reaches the brainstem at 
the level of the vestibular nuclei (VN). Its dynamics can 
be described by a first order low-pass filter with a time 
constant T 1 of the same order of magnitude as Tv., 
PTH 2 passes through the flocculus (F1) and reaches 
the brainstem downstream VN. Its dynamics can be 
neglected. Two non-visual projections to F1 have been 
introduced according to the experimental results ob- 
tained by Lisberger and Fuchs (1978a and b) and by 
Miles et al. (1980) in the monkey. PTH 1 and PTH 2 are 
sometimes referred to as the '"subcortical" and the 
"cortical" optokinetic pathway, respectively (Ter 
Braak, 1936; Dichgans, 1977). They correspond to the 
indirect and to the direct, or smooth pursuit, pathways 
in the models proposed by Raphan et al. (1977), by 
Robinson (1977) and by Barnes et al. (1978). 
In order to validate the model of Fig. 1 and to 
estimate all its parameters, not only oculomotor re- 
sponses but also single unit discharge patterns in VN 
and in F1 should be considered. An almost complete 
set of such experimental data was available for monkey 
(Waespe and Henn, 1979 and 1981 ; Waespe et al., 1980 
and 1981) and for cat (Keller and Precht, 1979), and the 
model in Fig. 1 was completely identified for these two 
species of animals (Buizza and Schmid, 1982). In man 
only input-output data can be collected and there is no 
possibility of identifying all the model parameters 
separately. In principle, some information about the 
inner organization of visual-vestibular interaction in 
man can be obtained by comparing the oculomotor 
responses of normal subjects with those of patients 
suffering from lesions in the central nervous system. In 
practice, the site, the extent, and the gravity of such 
lesions are always ill-defined. Thus it should realisti- 
cally be concluded that in man a model as detailed as 
that in Fig. 1 will never be completely identified. It is 
therefore worth trying to reduce that model to one 
identifiable from only input-output data. 
A reduced model keeping the distinction between 
the two parallel OKR pathways has been proposed by 
Schmid et al. (1980) (Fig. 2). Since these two pathways 
present completely different dynamic characteristics, a 
separate identification of them from input-output data 
is possible, even if it cannot be established how the 
gain of each input-output pathway in the model in 
Fig. 2 is sharedamong its peripheral and central parts. 
Consequently, the shape of the two OKR non-linear 
characteristics can only be estimated but a proportio- 
nality factor. Assuming an arbitrary value of 1 for K 1, 
K z, and K• experimental data from normal subjects 
can be used to evaluate the average value of K v and to 
define average normal non-linear characteristics. Then, 
intra- and inter-subject variability, and the influence of 
experimental conditions (e.g. "look" or "stare" con- 
205 
60 
40 
~= 20 
0 
, " - . NLI+NL2 
/ NL 1 
f 
i i i I = I r r I 
20 40 60 80 100 
RETINAL SLIP VELOCITY (DEG/SE(2) 
Fig. 3. Diagrams defining the non-linear gain characteristics NL 1 
and NL 2 
EXPERIMENTAL DATA (ZEE ET AL,, 1976) 
NORMALS +- S ,D, A = LABYRINTHINE 
DEFECTIVE t 
- - MODEL PREDICTION 
a0 
30 
.(l , l , , , , , ~ 9"0 30 60 
0PTOKINETIC STIMULUS VELOCITY (DEG/SEC) 
Fig. 4. OKN slow phase velocity versus stimulus velocity for 
normals and for labyrinthine defective patients. Experimental data 
from Zee et al. (1976) are compared with model prediction 
ditions in optokinetic tests) can be accounted for by 
small adjustements of the values of Kt, K 2, K I, and 
K v. Variations of the same parameters can also si- 
mulate the effects of drug administration or character- 
ize the presence of pathological situations. 
By giving the model parameters the following 
values : 
KF=0.4-- 0.6 T 1 =6s 
Tv= 10--20s K2=1 
K 1 = 1 K~= 1 
and by using the non-linear characteristics reported in 
Fig. 3, the model in Fig. 2 was succesfully used to fit 
the oculomotor responses of normal subjecfs for a 
number of different conditions of visual-vestibular 
interaction (Schmid et al., 1980; Buizza et al., 1981). An 
attempt can now be made to interpret pathological 
responses in terms of parametric changes in the same 
model. 
Model Interpretation of Pathological Situations 
Two classes of pathologies, vestibular and cerebellar, 
will be discussed. 
1 Vestibular Pathologies 
Optokinetic responses of patients with deafness and 
loss of vestibular function from childhood meningitis 
have been examined by Zee et al. (1976). Patients were 
submitted to constant velocity (5 to 90 ~ optokinetic 
stimuli in "look" condition. At lower velocities, optoki- 
netic nystagmus (OKN) was normal. Significant de- 
fects in the ability to produce appropriate OKN slow 
phase velocity begun to appear at drum velocity of 
60~ (Fig. 4). Optokinetic afternystagmus (OKAN) 
was always strongly reduced or totally absent. 
These results can be interpreted in both a qualita- 
tive and a quantitative way by making reference to the 
model in Fig. 2. Since OKAN is due to the discharge of 
the low-pass filter (storage mechanism) in PTH 1, the 
absence of OKAN in these patients would indicate an 
interruption of PTH 1, probably at the level of VN. As 
for OKN, if the optokinetic stimulus is weak enough to 
be supported by PTH 2 without saturation, no signifi- 
cant changes should be expected in steady state re- 
sponses, in spite of the absence of PTH 1 contribution. 
Continuous lines in Fig. 4 show model predictions 
obtained by giving K 1 = 1, K2= 1, and KI= 1.2 for 
normal subjects; K I=0 ~TH 1 interrupted), K2=l 
~TH2 intact), and KI= 1.2 for patients t. The non- 
linear characteristics of Fig. 3 were used for both 
normals and patients. 
Optokinetic-vestibular interaction in patients with 
vestibular pathologies was examined by Yee et al. 
(1978). Patients were suffering from either unilateral 
(5 VIII nerve transections and 10 vestibulopathies of 
unknown etiology) or bilateral (6 ototoxic drug vesti- 
bulopathies, 1 congenital vestibulopathy, and 4 vesti- 
bulopathies of unknown etiology) horizontal semi- 
circular canal paralysis. Ten normal subjects were 
considered for control. Four experimental conditions 
were adopted: sinusoidal rotation in the dark at 
0.05 Hz with peak velocity of 30 and 60 ~ ; optokinetic 
stimulation at constant (30 ~ and sinusoidal (0.05 Hz 
with peak velocity of 30 and 60 ~ velocity; sinusoidal 
oscillation (0.05 Hz with peak velocities of 30 and 
60 ~ in the light with stationary optokinetic drum; 
sinusoidal oscillation (0.05 Hz with peak velocities of 
7.5, 15, and 30 ~ in the light with the drum rotating at 
constant velocity (30~ with respect to the subject 
(superimposition test). 
In the first three experimental conditions, the re- 
sponses were quantified by computing the ratio be- 
1 An average value of K x greater than 1 was considered to 
account for "look" instead of "stare" conditions 
206 
Table l. Comparison between the experimental results obtained by Yee et al. (1978) for VOR and OKR gains in patients with peripheral 
vestibular disfunctions and model predictions obtained by giving the model parameters Kv, Kt, and K 2 the values reported in the last three 
columns. N: normals; UP: unilateral patients; BP: bilateral patients; v30, v60: sinusoidai body rotation in darkness with peak velocities of 
30 and 60'7s, respectively; oc: constant velocity optokinetic stimulation; o30, o60: sinusoidal optokinetic stimulation with peak velocity of 
30 and 60"/s, respectively; i30, i60: natural combination (interaction) of vestibular and optokinetic sinusoidal stimulations with peak veloci- 
ties of 30 and 60'/s, respectively; si: superimposition test. Simulations were performed assuming 7 v = 15 s0 7 i = 6 s, K l = 1 
v30 v60 oc 030 060 I30 ~ 60 si K v K1 K2 
N EXP 0.42 0.57 0.81 0.75 0.71 0.92 0.88 0.12 
MOD 0.49 0.49 0.81 0.74 0.67 0.88 0.86 0.14 0.50 1.0 1.0 
U P EXP 0.49 0.44 0.79 0.84 0.64 0.85 0.83 0.14 
MOD 0.44 0.44 0.76 0.73 0.65 0.86 0.84 0.14 0.45 0.5 1.0 
BP EXP 0.07 0.07 0.70 0.68 0.63 0.75 0.77 0.03 
MOD 0.07 0.07 0.71 0.71 0.63 0.73 0.65 0.02 0,07 0.0 1.0 
tween slow phase eye velocity and stimulus velocity 
(gain). In the last experimental condition the vestibular 
stimulation produced a sinusoidal modulation of the 
response evoked by the optokinetic stimulus. The 
amplitude of modulation was computed and the slope 
of the regression line fitting the data was assumed to 
represent the "gain of the vestibular-optokinetic 
interaction". 
The results obtained by Yee et al. (1978) are 
summarized in the rows of Table 1 labeled by "exp". 
As a first attempt to interpret these results in terms of 
parametric changes in the model of Fig. 2, the simplify- 
ing assumption was made that only the gain K 1 of 
PTH 1 and the gain K v of VS were modified by the 
pathology. PTH1 contribution to oculomotor re- 
sponses was assumed to be completely abolished in 
bilateral (BP) patients (K 1 = 0) and reduced by 50 % in 
unilateral (UP) patients (K 1 =0.5). As for VOR param- 
eters, since only one frequency was considered for 
sinusoidal oscillations in darkness, it can not be estab- 
lished whether pathologies influenced both the gain 
K v and the time constant T v or only one of these 
parameters. On the other hand this distinction is 
unessential for the interpretation of the responses 
recorded in conditions of visual-vestibular interaction. 
For the sake of simplicity the time constant T v was 
kept unchanged with respect to normals and the gain 
K v was determined from the observed ratios between 
slow phase eye velocity and stimulus velocity during 
oscillation in the dark. 
The results of computer simulation are reported in 
the rows of Table 1 labeled by "mod". A general 
agreement with the experimental results can be noted. 
Thus an attempt can be made to use the model for a 
functional interpretation of these results. The small 
decrease of OKR gain in patients during constant 
velocity optokinetic stimulation confirms the previous 
findings by Zee et al. (1976) and it has been already 
justified. What could seem rather surprising is that the 
same gain decreasealso appears in normals when 
sinusoidal optokinetic stimulations are adopted. As a 
matter of fact, PTH 1 behaves as a low-pass filter with 
a cut-off frequency which decreases as the gains of the 
two optokinetic pathways decrease, and, thus, as re- 
tinal slip velocity increases. It can be computed from 
the model that PTH 1 cut-off frequency at the retinal 
slip velocity produced by a stimulus of 30 ~ is of 
about 0.04 Hz. Thus during oscillation at 0.05 Hz the 
dynamics of the storage mechanism reduces PTH 1 
gain by about 6dB. This corresponds to a 50% gain 
reduction with respect to a condition of constant 
velocity stimulation. A peak velocity of 60 ~ will 
produce a further saturation of the two optokinetic 
pathways. Consequently a lower cut-off frequency and 
a weaker PTH 1 contribution should be expected. 
The increase of the response gain in normals and in 
UP patients during sinusoidal oscillation in the light 
with respect to the values observed during optokinetic 
stimulation is due to the fact that in the former 
condition VOR and OKR are working sinergistically. 
The compensatory eye movement produced by VOR 
reduces the contribution required to OKR and makes 
it working in zones of its non-linear characteristics 
with higher gains. In BP patients the vestibular contri- 
bution to visual stabilization is strongly reduced and 
smaller gain improvements can be expected. 
It can be noted from Table 1 that superimposition 
tests represent the only condition of visual-vestibular 
interaction producing a significant difference between 
the responses of normal and UP patients and those of 
BP patients. In this rather complicated situation the 
drum is rotating at constant velocity with respect to 
the subject and OKR is engaged to rotate the eyes at 
the same velocity in order to obtain a retinal stabili- 
zation of the visual surround. OKR is disturbed in this 
task by subject's oscillation which injects a sinusoidal 
input into the vestibular nuclei. This additional input 
provokes a modulation of the constant eye velocity 
207 
Table 2. Comparison between the experimental results obtained by Baloh et al. (1979) for VOR and OKR gains in cerebellar patients, and 
model predictions obtained by giving the model parameters Kv, K1, K2 the values reported in the last three columns. OKN: gain of OKR; 
VOR: gain of VOR; VVOR: gain measured in natural conditions of VOR-OKR interaction. Simulations were performed by assuming 
7v= 15 s, 71 =6 s, Kt= 1 
Subj. OKN VOR VVOR Kv KI K2 
no. 
EXP MOD EXP MOD EXP MOD 
1 Friedreich ataxia 0.65 0.65 0.32 0.32 0.67 0.69 0.33 1.00 0.35 
2 Cerebellar degen. 0.66 0.66 0.61 0.61 0.67 0.83 0.62 1.00 0.37 
3 Cerebellar degen. 0.58 0.57 0.71 0.71 0.90 0.84 0.73 1.00 0.19 
4 Spinocereb. degen. 0.20 0.20 0.19 0.19 0.29 0.24 0.19 0.46 0.00 
5 Spinocereb. degen. 0.66 0.66 0.53 0.53 0.69 0.79 0.54 1.00 0.37 
6 Olivopontocer. deg. 0.49 0.49 0.52 0.52 0.58 0.68 0.53 1.00 0.08 
7 Olivopontocer. deg. 0.49 0.49 0.48 0.48 0.64 0.65 0.49 t.00 0.08 
8 Cerebellar degen. 0.31 0.31 1.02 1.02 0.96 0.93 1.04 0.73 0.00 
9 Freidreich ataxia 0.49 0.49 0.37 0.37 0.63 0.56 0.38 1.00 0.08 
10 Cerebellar degen. 0.41 0.41 0.68 0.68 0.75 0.75 0.69 1.00 0.00 
mean 0.49 0.49 0.54 0.54 0.68 0.70 0.55 0.92 0.15 
produced by the optokinetic stimulation and compro- 
mises visual stabilization. Due to the closed loop 
structure of OKR, the amplitude of modulation will 
depend on the actual gains of the forward pathways of 
OKR and, therefore, on (a) the velocity of the optoki- 
netic stimulus which determines the average working 
points on NL 1 and NL 2, and (b) the amplitude of the 
vestibular input to VN, which determines the ampli- 
tude of the oscillation of the working points on the 
non-linear characteristics. The higher the forward 
gains, the smaller eye velocity modulation is. It should 
therefore be expected that (a) for the same vestibular 
stimulation, visual stabilization is the more effective 
the smaller the optokinetic stimulus velocity is, and (b) 
for the same optokinetic stimulation, the smaller the 
vestibular input is. Normal subjects and UP patients 
present comparable values of K v (0.5 and 0.45, re- 
spectively) and comparable OKR responses. Then the 
same amplitude of modulation of nystagmus slow 
phase velocity should be expected in superimposition 
tests. On the contrary, BP patients present extremely 
tow values of K v (K/~=0.07) and normal values of 
OKR gain. Then no appreciable modulation should be 
expected. Experimental results and model predictions 
confirm this analysis. 
2 Cerebellar Pathologies 
Optokinetic-vestibular interaction in 10 patients with 
different varieties of cerebellar atrophy was examined 
by Baloh et al. (1979). The clinical diagnosis and the 
experimental values of the response gains in the dif- 
ferent experimental conditions considered by these 
authors are reported in Table 2 for each subject. The 
common finding in all patients was a reduced response 
in the optokinetic test performed at the constant 
velocity of 30~ (average gain =0.49___0.15 with re- 
spect to a normal value of 0.8 _+ 0.09). VOR gain tested 
by sinusoidal rotation (peak velocity of 30~ at 
0.05 Hz) in the dark was significantly increased in three 
patients with pure cerebellar degeneration (patients 3, 
8, and 10), significantly reduced in three patients who 
also presented signs of a vestibular nerve degeneration 
(patients 1, 4, and 9), and normal in the remaining 
patients. Optokinetic-vestibular interaction was tested 
by rotating the subjects sinusoidally (peak velocity of 
30 ~ at 0.05 Hz) in the light with the drum stationary. 
The response was normal in the three patients with 
pure cerebellar degeneration. In the remaining patients 
the gain was significantly reduced (0.60_+0.14 with 
respect to a normal value of 0.90_+ 0.09). 
In terms of model, the general decrease of the 
optokinetic response in cerebellar patients can be 
viewed as the effect of a reduction of the gain K 2 of 
PTH 2 which actually passes through the flocculus. It 
could be proved via simulation that a decrease of K 2 
from 1 (normal subjects) to 0.08 with K 1 = 1 (intact 
PTH 1) produces a gain decrease of the steady state 
optokinetic response at 30 ~ from 0.8 (average experi- 
mental value for normals) to 0.49 (average experimen- 
tal value observed in this group of patients). The 
question arises whether the gain K 1 of PTH 1 also 
underwent to significant changes. A compromission of 
PTH 1 is unlikely in patients with pure cerebellar 
lesions, but a decrease of K1 can be expected in 
patients with signs of vestibular nerve degeneration 
(patients 1, 4, and 9). As far as only steady state 
optokinetic responses are considered, a variation of K 1 
cannot be proved unless the decrease of the response is 
so dramatic that it cannot be justified only by the 
interruption of PTH 2. This is the case of one of the 
208 
0,8 
0,6 
z 
0,4 
0,2 
-130 
-140 
I 
m 
-150 
v 
-160! 
r 
= -170 
m_ 
-180 i 
••AKv=I, 
Tv=15 SEc 
~ Y-,v=O.7, Tv=lO SEC Kv=0.55, Tv=15 SEC 
! I I 
0,0125 0,025 0,05 0,1 
FREQUENCY ( Hz ) 
~ NORMALS • S,D, 
A FATIENTS 
x 
(FROM BALOH ET AL,, 1981) 
MODEL PREDICTIONS 
Tv=lO $EC 
Tv=15 SEC 
Fig. 5. Frequency response of the vestibulo-ocular reflex in normals 
and in three patients suffering from lesions of the vestibulocerebel- 
lum. Experimental data from Baloh et al. (1981) are compared with 
model prediction 
spinocerebellar patients (patient 4) who presented an 
OKR gain of only 0.2 with a VOR gain of only 0.19. 
Once the model parameters K~, K 2, and K v had 
been adjusted according to the previous discussion and 
in such a way as to predict patient's individual re- 
sponses to pure vestibular and pure optokinetic stimu- 
lations,the values of response gain measured in the 
visual-vestibular interaction tests could be predicted 
for each patient with good accuracy (Table 2). 
A separate group of 7 patients with similar cerebel- 
lar pathologies was submitted by Jenkins et al. (1977) 
to superimposition tests. Also in this case the responses 
observed in interaction conditions could be correctly 
predicted by the model after estimation of K1, K 2, and 
K v from pure vestibular and pure optokinetic re- 
sponses (Buizza et al., 1981). 
Further information about VOR and OKR 
changes in cerebellar patients was provided by Baloh 
et al. (1981) in a second study on 5 patients with well 
defined lesions of the vestibulocerebellum (Chiari mal- 
formations and caudal midline cerebellar atrophy). 
Patients were submitted to step optokinetic stimu- 
lations of 30~ Each of them exhibited a gradual 
build-up of OKN slow phase velocity and a normal 
OKAN. The absence of the fast build-up component of 
OKN indicates a severe compromission of the fast 
optokinetic pathway (PTH 2). On the other hand, the 
presence of a slow build-up and the normality of 
OKAN suggest that the slow optokinetic pathway 
(PTH 1) was preserved almost intact. These results 
confirm our previous assumption that in the presence 
of pure cerebellar lesions the gain K 1 of PTH 1 does 
not significantly change and, consequently, that the 
reduction of OKR gain previously observed by Baloh 
et al. (1979) is mainly due to a decrease of the gain K 2 
of PTH 2. 
The frequency response of VOR was examined by 
Baloh et al. (1981) using sinusoidal stimulations at four 
different frequencies between 0.0125 and 0.1 Hz, with a 
peak chair velocity of 60 ~ With respect to normals, 
cerebellar patients exhibited an increased gain and a 
normal phase lead (Fig. 5). The increase of VOR gain 
after cerebellar lesions is probably due to a release of 
the inhibition exerted by the vestibulocerebellum on 
the vestibular nuclei (Robinson, 1976). The mechanism 
of such a VOR gain control was not described in the 
models of Figs. 1 and 2. Its effect can be simulated by 
appropriately adjusting the gain K v. The experimental 
results reported in Fig. 5 Could be correctly fitted by 
the model after changing K v from 0.55 (normal value) 
to 0.7 for one patient and to t for the remaining two 
patients submitted to this test. 
The same sinusoidal stimulations were also applied 
in the light to compare optokinetic-vestibular in- 
teraction in normals and in cerebellar patients (Baloh 
et al., 1981). Experimental values of gain and phase are 
reported in Fig. 6. 
The question is still whether this new set of data 
adds further information to that acquired by separate 
vestibular and optokinetic tests. Since the superimpo- 
sition principle cannot be applied due to OKR non- 
linearities, an answer cannot be given straight away 
but it can be obtained via model computer simulation. 
The theoretical results reported in Fig. 6 by continuous 
lines were obtained by giving K v and T v the values 
estimated from the VOR frequency responses in Fig. 5, 
and by setting K~ =K2= 1 for normals, and K~ =1 
(PTH1 intact) and K2=0 (PTH2 interrupted) for 
patients, as suggested by the optokinetic responses. 
The general agreement between experimental and 
theoretical data confirms also in this case the possi- 
bility of predicting the results of visual-vestibular 
interaction tests after an appropriate separate testing 
of VOR and OKR. 
Conc lus ion 
A model of optokinetic-vestibular interaction pre- 
viously validated for normal humans (Schmid et al., 
1980) has been used to interpret oculomotor responses 
of vestibular and cerebellar patients submitted to pure 
or combined vestibular and optokinetic stimulations. 
A good agreement between experimental data and 
A 
1, 9 ? ? 
0,8 
z 0 .6 
O,4 
0,2 ' ' ' 
-140 
m 
v 
-160 
c.) 
.,:z: 
-180 
0,0125 0,025 0,05 
B 
�9 ~ ~ Kv=l , Tv=15 sEc 
A ~.-- , - - -" ' - - - ' - - Kv=O'7 " Tv=lO SEC 
k 
Kv=l �9 Tv=15 SEC 
~.- , , , , Kv=0.7. Tv=10 SEC 
0,1 0.0125 0,025 0,05 0.1 
FREQUENCY (Hz) 
209 
Fig. 6A and B. Gain and phase shift (slow phase 
velocity re. stimulus velocity) of nystagmus slow 
phase velocity recorded during sinusoidal rotation 
in an earth stationary visual surround (peak 
velocity of 60 ~ Experimental data from Baloh et 
al. (1981) are compared with model predictions 
(continuous lines). A normals; B same patients as 
in Fig. 5 
model predictions could be obtained after an appropri- 
ate adjustement of those model parameters which were 
the most likely related to the examined pathology. For 
the classes of pathology here considered, the most sen- 
sitive parameters were found to be the gain K v of the 
vestibular system, the gain K 1 of the optokinetic path- 
way passing through the vestibular nuclei and the gain 
K 2 of the optokinetic pathway passing through the 
flocculus. Small changes of the model time constants 
within the range of normality were needed only for fine 
adjustement of model predictions to patient's individu- 
al responses. Unilateral vestibular patients were char- 
acterized by values of K v and K 2 within the range of 
normality and by a value of K1 reduced by about 50 % 
with respect to normal. Bilateral vestibular patients 
were characterized by values of K v and K 1 almost 
reduced to zero, and by a normal value of K 2. Due to 
the variety of cerebellar pathologies considered for this 
study, a less systematic picture of model parameter 
variations could be observed. A distinction can be 
made between lesions restricted to the cerebellum and 
lesions involving other neural structures. Pure cerebel- 
lar patients were characterized by an increased value of 
Kv, a normal value of K~, and a strongly reduced value 
of K 2. Patients with diffused cerebellar lesions were 
characterized by values of K v and K~ either normal or 
reduced, and by a strongly reduced value of K 2. K v 
and K 1 were reduced only in those patients who also 
presented signs of vestibular nerve degeneration. 
The analysis made in this paper also showed that 
all responses recorded in interaction conditions both in 
normals and in patients could accurately be predicted 
once model parameters were estimated from the results 
of pure vestibular and pure optokinetic tests. Then two 
conclusions can reasonably be drawn. First, the simul- 
taneous stimulation of OKR does not change the 
characteristics of VO R, and viceversa. Second, after an 
appropriate battery of pure vestibular and pure opto- 
kinetic tests and a model interpretation of the experi- 
mental results, visual-vestibular interaction tests do 
not provide further clinical information. 
These conclusions do not exclude some practical 
reason for performing interaction tests in the clinical 
routine. First of all, models and computer facilities are 
not always available. If the analysis is restricted to eye 
inspection or to hand processing of the chart-records, 
the presence of abnormalities could be more easily 
detected in the responses to combined than to separate 
VOR and OKR stimulations. Second, VOR character- 
istics seem to be more stable in interaction conditions 
than during rotation in darkness. 
Appendix 
The aim of this appendix is to illustrate a simple 
procedure for the estimation of the parameters of the 
model of Fig. 2 from pure vestibular and pure optoki- 
netic responses. To this purpose information on both 
static and dynamic characteristics of VOR and OKR 
should be made available. Such an information can be 
easily obtained from tests in which step-wise stimuli 
are used, i.e. from post-rotational rotatory tests and 
from step optokinetic tests. 
1 Estimation of K v and T V from post-rotational vesti- 
bular responses 
The typical time courseof nystagmus SPV in a post- 
rotational response is schematically shown in Fig. A-1. 
The value of K V can be computed as the ratio between 
210 
Vp 
,37 Vp 
, - ~ T IME 
Fig. A-1. Estimate of VOR parameters from the diagram of nys- 
tagmus slow phase velocity in post-rotational responses 
I-- 
v~ 
v s f 
R s 
AV 
~ light of f 
vA 
T IME - -~ 
Fig. A-2. Estimate of OKR parameters from the diagram of OKN 
and OKAN slow phase velocity in optokinefic step responses 
the peak value of SPV (Vp) and the amplitude of chair 
velocity step. The time constant T V can be estimated by 
drawing the tangent to the SPV diagram from its peak 
as shown in the same figure. Alternatively, T V can be 
estimated as the duration of the interval between the 
peak of SPV and the instant at which SPV is equal to 
37 % of Vp. 
In the acute stage of unilateral vestibulopathies, 
different values of K v and T v should be expected in 
relation to the direction of rotation. Both CW and 
CCW post-rotatory tests should therefore be perfor- 
med. In the chronic stage, a good simmetry is normally 
restored, although both CW and CCW responses can 
still be altered with respect to normality. In this case 
the state of the vestibular system can be adequately 
defined by only one value of K v and one value of T w 
This was the case of the patients considered in this 
paper. 
2 Estimation of K t, K 2, and T I from optokinetic step 
responses 
Due to the presence of non-linearities in OKR, several 
tests with different stimulus velocities (e.g. 20, 40, 60, 
and 100~ should be performed. 
The typical time course of nystagmus SPV in 
optokinetic step responses is shown in Fig. A-2. Let V D 
be the adopted drum velocity, V s the steady state value 
of SPV, A Vthe step change in SPV following light off, 
and V A the initial value of afternystagmus SPV. The 
retinal slip velocity at steady state (Rs) can be com- 
puted as R s = V D- V s. By considering the responses to 
different stimulus velocities, the diagrams of V a and A V 
versus R s can be constructed. These diagrams repre- 
sent the gain characteristics NL 1 and NL 2 for the 
examined patient. They should be compared with the 
corresponding average characteristics for normals 
shown in Fig. 3. Usually, in the absence of lesions in 
the peripheral visual system, the shapes of NL 1 and 
NL 2 are preserved. Thus, the difference between nor- 
mal and pathological gain characteristics can be de- 
fined by two proportionality factors, which actually 
correspond to the gains K s and K 2 of the model in 
Fig. 2 for the examined patient. An estimate of these 
two parameters can be obtained by computing the 
average values of the ratios VA(patient)/VA(normal ) and 
A V(patient)/A V(normal) for the retinal slip velocities 
resulting from each test. 
The time constant T~ o fPTH 1 can be estimated by 
averaging the durations of the interval denoted as T A in 
Fig. A-2. 
The procedures so far described can provide only a 
rough estimation of model parameters. Nevertheless, 
acceptable results were obtained whenever these pro- 
cedures were applied for the interpretation of the 
normal and pathological responses considered in this 
paper. A better precision can be reached by more 
sophisticated best-fitting procedures which, on the 
other hand, require the use of computers (Stefanelli et 
al., 1978). 
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Received:January 17, 1983 
Dr. A. Buizza 
Dipartimento di Informatica e Sistemistica 
Universit/t di Pavia 
Strada Nuova 106/c 
1-27100 Pavia 
Italy