 |
INTRODUCTION |
The translational vestibuloocular reflex (tVOR)
stabilizes gaze in response to translational movements. This is a
complicated task because the peripheral otolith organs respond
identically to tilt and to linear translation, whereas the ocular
response to these stimuli differ; tilting of the head (sensing gravity) elicits torsional eye movements, whereas translations elicit horizontal eye movements. In addition, to accurately maintain images on the fovea,
the brain must consider the target distance and eccentricity of the
image with respect to each eye (Paige and Tomko 1991a
,b
; Telford et al. 1997
).
Perhaps the greatest obstacle to understanding the tVOR has been the
elucidation of the necessary central processing required to transfer
the otolith primary afferent signals into appropriate oculomotor
commands. Otolith primary afferents encode a signal that is in phase
with, and even leads, linear head acceleration, although these data are
only available for frequencies up to 2 Hz (Fernandez and
Goldberg 1976
; Goldberg et al. 1990
). In
contrast, the canal afferents, measured to frequencies up to 8 Hz,
encode head velocity (Fernandez and Goldberg
1971
).
The oculomotor plant is known to require signals in phase with velocity
and position (Robinson 1981
). Single-cell recordings from position-vestibular pause (PVP) cells and eye-head-velocity (EHV)
cells in the vestibular nucleus have shown that these cells carry
otolith signals in phase with linear velocity, indicating that the
acceleration signal coming from the peripheral organs has already been
processed (McConville et al. 1996
; McCrea et al.
1996
). Several models have been proposed that attempt to
produce a velocity and a position signal from the incoming acceleration signal while attempting to maintain consistency with observed high-pass
filtering behavior (Angelaki 1998
; Paige
and Tomko 1991b
; Telford et al. 1997
). The most
popular hypothesis is that of integrating the primary otolith afferent
signal and then sending the integrated signal to the neural integrator
and the oculomotor plant (Paige and Tomko 1991b
;
Telford et al. 1997
). Alternatively, it has been proposed that the acceleration signal be differentiated and then integrated (Angelaki et al. 1993
). However, we propose a
simpler model. Specifically, primary afferent signals are passed
through the neural integrator to yield the velocity signal. The
position signal is obtained directly from the primary afferents because a signal in phase with acceleration is just a signal in phase with
position but with the sign reversed. Therefore a second integrator is
not needed, suggesting that the brain stem dynamics of the tVOR reflex
are different from those of the angular vestibuloocular reflex (aVOR)
only because the respective inputs to the brain stem differ. There is
evidence that there exists monosynaptic primary afferent innervation of
the oculomotor nuclei of otolithic origin (Uchino et al.
1996
). We propose that this signal acts as the position input
in response to translational movement. A simple model is presented that
has as its input an acceleration signal. Then, given this model and the
selected parameters and after computing the difference between the
output of the model and the experimental data, we shall deduce the
exact input (high-frequency primary afferent behavior) necessary to
accurately reproduce the experimental data.
 |
METHODS |
The model shown in Fig.
1A was written using Matlab's
Control System (Mathworks) package. The neural integrator and the
oculomotor plant are expressed as (Fuchs et al. 1988
).
where
1 = 0.14 s,
2 = 0.28 s,
3 = 0.037 s,
4 = 0.003 s, and
int = 20 s.

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Fig. 1.
A: model presented in this paper. a(t), acceleration; NI,
neural integrator; EP, eye plant; K1
and K2 are as discussed in
METHODS. B: comparison of sensitivity
(deg/s/cm/s = deg/cm) and phase (C) values for the
output produced by the model (solid line) shown in A, with
K1 = 1.0 and
K2 = 100 for a pure acceleration
signal, and data from Angelaki (1998) (long dashed line)
and Telford (1997) (short dashed line up to 4 Hz). The
phase from the model leads by up to 20° at 2 Hz while the sensitivity
has a smaller slope and a greater intercept. Phase for this and all
subsequent plots is relative head acceleration.
|
|
The open loop transfer function of the model in Fig. 1A is
simply
|
(1)
|
where K1 provides the system
with position information,
K2Hint with
velocity information, e0.01s
represents a 10-ms delay, and a is the acceleration. The
output from Eq. 1 (Eye velocity) was compared with
Angelaki's data (Angelaki 1998
) and the values
K1 and
K2 optimized to minimize both phase and gain errors. Because the Angelaki data are available to frequencies beyond 15 Hz, we have chosen to model this data instead of the Telford
data, which is included for completeness. Nevertheless, our results
show that the phase of the model's output differs from the Telford
data by ~10° between 1 and 4 Hz (Fig. 3). For a pure acceleration
input, the appropriate values for K1
and K2 were deduced by minimizing the
least-squared difference between the experimentally obtained complex
number geip (where g
is the gain and p is the phase) and the one produced by the
model. Other minimization methods were also used without any
significant change to the values of K1
and K2. Then, the difference between
the output of the model using the derived
K1 and
K2 and the experimental data were
computed. This difference corresponds to the required filtering of the
acceleration signal to adequately simulate the experimental data. The
difference between the two outputs was fitted to an equation according
to the Goldberg et al. (1990)
classification of
afferents (see RESULTS).
 |
RESULTS |
Figure 1, B and C, depicts the output of the
model (solid line) for K1 = 1.0 and
K2 = 100 as compared with experimental
data [Angelaki 1998
(long dashed line up to 15 Hz) and
Telford et al. 1997
(short dashed line up to 4 Hz)] for
a pure acceleration input. There is a fairly good phase agreement
between the two plots with the largest phase difference occurring at 2 Hz where the output of the model lags the experimental results of
Angelaki by <20°. However, the value of the model's sensitivity
curve is greater than those found experimentally below 1 Hz. As the
frequency increases, the slope of the model's sensitivity curve is
smaller than the experimental one, and as the frequency increases
further, the sensitivity curve levels off.
From Fig. 1, it can be seen that to accurately simulate the
experimental data, the model still needs a slowly rising high pass
filter and an almost flat phase response, exhibiting a 20° phase lag
as the frequency increases. Up to 2 Hz, this is the behavior of
utricular regular afferent neurons recorded by Goldberg et al.
(1990)
. The two curves shown in Fig. 1 extending up to 15 Hz
(dashed line is Angelaki data, solid line is model output) were divided
into each other and the result labeled Haff.
Haff represents the required filtering of the
acceleration signal (primary afferent behavior) so that the output of
the model agrees with the Angelaki data. Haff was
then fitted according to Goldberg et al. (1990)
classification of primary afferents. Specifically, the overall transfer
function describing otolith primary afferent behavior is
where
Representative values of the parameters are
M1
3 s,
M2
0.10 s, KM1
0.15,
A
15 s,
KA
0.13,
V1
200 s, and
V2
1 s (Goldberg et al.
1990
). For Haff, all values were as above except for
V2 = 0.25, KV = 0.15, and
HV = [(1 + s
V1)(1
s
V2)]KV. This
results in a signal that has a phase response consistent with a very
regular primary afferent but with a gain described by a dimorphic
afferent (see Fig. 2). Indeed, this could
be the behavior of some afferents above 2 Hz, because for primary
afferents recorded by Goldberg et al. (1990)
the phase
began to lag acceleration as the frequency increased.

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Fig. 2.
Comparison of the sensitivity (A) and phase (B)
of experimental translational vestibuloocular reflex (tVOR) data
(- - -) and the model ( ) in Fig. 1 for a primary afferent input
with KV = 0.16 (dimorphic),
K1 = 3.5, and
K2 = 80. The sensitivity curve is
almost identical with that of Angelaki (1998) (long
dashed line extending to 15 Hz), and with a slight adjustment in gain,
can also be made to accurately reproduce Telford (1997)
data (short dashed line extending to 4 Hz). However, up to a 60°
phase lead is introduced. Also shown is a comparison of the sensitivity
(C) and phase (D) of experimental tVOR data
(- - -) and the model ( ) in Fig. 1 for a primary afferent input
with KV = 0.01 (highly regular),
K1 = 0.8, and
K2 = 1. In contrast with A
and B, the phase curve is almost identical with that of
Angelaki (1998) . However, the sensitivity is flat and
exhibits a high intercept.
|
|
Figure 2 depicts the output of the model in response to an input of a
regular primary afferent and a dimorphic primary afferent. The
dimorphic afferent (KV = 0.16; Fig. 2,
A and B) converges onto the experimentally
deduced sensitivities but with as much as a 50° phase lead at 1 Hz.
For the dimorphic afferents, least-square optimization resulted in
K1 = 3.5 and
K2 = 80. In contrast, the regular afferent (KV = 0.01, K1 = 0.8, and
K2 = 1) approximates the experimental
phase curve almost perfectly but with a large loss in sensitivity (Fig.
2, C and D). Figure
3 depicts the output of the model in
response to the input composed of the combined behavior derived from
the regular and dimorphic afferents shown in Fig. 2. Least-square
optimization resulted in values of K1 = 1.2, K2 = 150,
V2 = 0.25, and
KV = 0.15. The combined behavior of
the afferent is represented by Haff derived
above. The model's sensitivity curve (solid line) closely resembles
that of Angelaki (Angelaki 1998
), whereas the maximum
phase difference is a lag of 10° and occurs at ~1 Hz.

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Fig. 3.
Output of the model from an input composed of a combination of the
behavior of the primary afferents from Fig. 2. The model's sensitivity
curve ( ) is quite close to experimental values, whereas the phase
exhibits up to a 10° lag below 4 Hz.
K1 = 1.2 and
K2 = 150, KV = 0.16. V2 = 0.25, KV = 0.15, and
HV = [(1 + s V1)(1 s V2)]KV.
|
|
 |
DISCUSSION |
As shown in Fig. 1A, the tVOR pathway in our model is
identical to the Robinson model for the aVOR. However, because the
canal primary afferents encode angular head velocity and the utricular primary afferents encode linear head acceleration, the input to the
integrator from the two systems is different. The question is, how are
the utricular primary afferent signals processed to provide the eye
plant with the necessary velocity and position signals.
The model presented here is simple in that it takes advantage of known
pathways in the brain stem. For horizontal conjugate eye movements, the
nuclear prepositus hypoglossi (NPH) is an important site for neural
integration. There is a large projection of inputs from the lateral
vestibular nucleus (LVN) onto the NPH in the squirrel monkey
(Belknap and McCrea 1988
) and a corresponding large projection of utricular afferents onto the LVN (McCrea et al. 1987
). No second integration of the otolith signal
is required. The position signal is obtained directly from the primary
afferents with a modification in gain. Utricular afferents synapsing
directly onto oculomotor nuclei have been reported by Uchino et
al. (1996)
. Because an acceleration signal is in phase with
position, this makes the signal that the otolith primary afferents
carry adequate to code position.
In deriving Haff, it became clear that the behavior of
regular afferents is more suited to drive the system. Unfortunately, no
afferent data are available for frequencies >2 Hz. However, Haff gives an idea of the type of afferent behavior needed
to realize the model presented here. It is consistent with extrapolated regular afferent (bordering on dimorphic) behavior; a slow rising high-pass filter with a flat phase response increasing in lag as the
frequency increases. We are not suggesting the existence of a new class
of afferents. The behavior of primary afferents for frequencies >2 Hz
is not known. Therefore Haff may represent the response of
several primary afferents converging onto central neurons or even the
central processing of primary afferent signals. Either way, given
Haff, a signal that deviates slightly from observed low-frequency afferent signals, the model shows how existing pathways may be used to reproduce tVOR behavior.
The high-frequency phase lag exhibited by the response of the model is
partly due to the 10-ms delay that was used while fitting the afferent
transfer function. This short latency is consistent with Angelaki's
result (Angelaki 1998
).
The simplicity of the model presented here would also generate
horizontal eye movements during sustained head tilts. The model has as
its purpose only the reproduction of horizontal eye movements. Clearly
additional circuitry and processing is required to inhibit horizontal
eye movements during tilts. The mechanism involved in differentiating
between translations and tilts is currently not known and has not been
included in the current model. Several hypotheses have been proposed to
account for the tilt/translation duality. The most popular of these
hypothesis is frequency filtering (Telford et al. 1997
).
According to this hypothesis, torsional eye movements are produced by a
low-frequency pathway while horizontal eye movements by a
high-frequency pathway. Because primary afferent neurons synapse
directly onto the motoneurons (Uchino et al. 1996
), this
hypothesis fails to fully explain the observed behavior. Nevertheless,
this mechanism would simply require additional circuitry to
differentiate between the two stimuli. Once the brain has decided that
the stimulus is translational in nature, then the output of this
hypothesized tilt/translational filtering will just feed the model
presented here.
For angular rotations, an integrator lesion leads to an inability
to keep gaze steady (no position signal) (Cannon and Robinson 1987
). Perhaps the most striking consequence of our model is
that on integrator lesions, a partial loss of eye movements in response to translational motion will occur, although some eye movement may
still occur due to the monosynaptic primary afferent connection to the
plant. Another consequence of this model is that irregular primary
afferents have little or no effect on the behavior of the tVOR. Because
the behavior of primary afferent neurons for frequencies >2 Hz is not
known, this prediction is based solely on theory. Galvanic current
studies for the aVOR have shown that irregular afferents do not
contribute to the aVOR (Minor and Goldberg 1991
). Also,
regular and irregular inputs remain segregated at the level of the
vestibular nuclei (Goldberg et al. 1987
), although this
segregation is incomplete. However, this could result in parallel
pathways for the primary afferents that have distinct functions. We
have shown here that it is possible for the function of the regular
afferent to be to provide the integrator with input to obtain the
velocity command. The function of the irregular afferent remains a
question. The VOR is not the only reflex that these afferents drive.
Therefore the irregular afferents could be used for the vestibulcollic
reflex (Goldberg et al. 1987
) or even to adjust the gain
of the tVOR for vergence sensitivity.
Address for reprint requests: R. D. Tomlinson, Rm. 7310, Medical Science Building, 1 King's College Circle, Toronto, Ontario
M5S 1A8, Canada.
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