Department of Neurology, University of Zurich, CH-8091 Zurich, Switzerland
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ABSTRACT |
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Jaggi-Schwarz, Karin, Hubert Misslisch, and Bernhard J. M. Hess. Canal-Otolith Interactions After Off-Vertical Axis Rotations I. Spatial Reorientation of Horizontal Vestibuloocular Reflex. J. Neurophysiol. 83: 1522-1535, 2000. We examined the three-dimensional (3-D) spatial orientation of postrotatory eye velocity after horizontal off-vertical axis rotations by varying the final body orientation with respect to gravity. Three rhesus monkeys were oriented in one of two positions before the onset of rotation: pitched 24° nose-up or 90° nose-up (supine) relative to the earth-horizontal plane and rotated at ±60°/s around the body-longitudinal axis. After 10 turns, the animals were stopped in 1 of 12 final positions separated by 30°. An empirical analysis of the postrotatory responses showed that the resultant response plane remained space-invariant, i.e., accurately represented the actual head tilt plane at rotation stop. The alignment of the response vector with the spatial vertical was less complete. A complementary analysis, based on a 3-D model that implemented the spatial transformation and dynamic interaction of otolith and lateral semicircular canal signals, confirmed the empirical description of the spatial response. In addition, it allowed an estimation of the low-pass filter time constants in central otolith and semicircular canal pathways as well as the weighting ratio between direct and inertially transformed canal signals in the output. Our results support the hypothesis that the central vestibular system represents head velocity in gravity-centered coordinates by sensory integration of otolith and semicircular canal signals.
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INTRODUCTION |
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During off-vertical axis rotation the vestibular system detects head velocity and position from semicircular canal and otolith afferent signals. Whereas the semicircular canal afferents encode endolymph velocity relative to the skull (i.e., relative to a head-fixed reference) the otolith organs provide information about absolute head position relative to gravity (i.e., relative to a space-fixed reference). To determine head motion and orientation in space, there must be considerable central processing of these signals based on an internal representation of the outer physical space.
Earlier studies of the vestibuloocular reflex (VOR) during
off-vertical axis rotations have shown that a vertical eye velocity component was generated when a subject was stopped in ear-down position
after a constant velocity rotation about the yaw axis (cat:
Harris 1987; humans: Harris and Barnes
1987
; monkey: Raphan et al. 1992
). Thus it
appeared that postrotatory eye velocity did not decay along the former
rotation axis but rather tended to align with gravity. Although it has
become clear that this spatial reorientation of the VOR is mediated via
the velocity storage network in the brain stem, the underlying
computational mechanisms are still a matter of debate. In a recent
study on the spatial orientation of the optokinetic nystagmus (OKN) in primates, it has been shown that in the horizontal but not vertical system there is a similar alignment of the optokinetic afterresponse with gravity (Dai et al. 1991
; Raphan and Sturm
1991
). A reorientation of eye velocity toward gravity can also
be found during postrotatory VOR when applying quick changes in head
(and body) orientation relative to gravity (Angelaki and Hess
1994
; Merfeld et al. 1993
). In contrast to OKN
findings, this reorientation occurred independently of the head
rotation axis (before tilting the head) and the particular tilt plane
(Angelaki and Hess 1994
). Analyzing the spatial
characteristics of the yaw or pitch/roll VOR suggested a rotation or
projection of postrotatory eye velocity toward the spatial vertical
following the head tilt. It is not known whether the same mechanisms
underlie the reorientation of postrotatory VOR in static tilt
positions. Off-vertical axis rotation (OVAR) is the vestibular analogue
of visual surround rotation about a tilted stationary observer. Because during OVAR the observer is rotated relative to gravity, the
postrotatory response results from a complex interaction of otolith and
semicircular canal signals. In this paper, we determine the relative
contribution of the otolith and canal signals after yaw OVAR by
extending an empirical analysis of the VOR spatial characteristics with
a parametric analysis based on a three-dimensional (3-D) spatial
orientation model. In the companion papers, we shall present the
results of a corresponding analysis applied on data collected after
pitch and roll OVAR. Preliminary results have been published in
abstract form (Jaggi-Schwarz et al. 1999
).
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METHODS |
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Preparation of animals
Experiments were performed on three juvenile rhesus monkeys
(Macaca mulatta; monkeys JU, SU, and
RO). The animals were chronically prepared for 3-D eye
movement recordings. Using sterile surgical techniques, skull bolts for
head restraint and a dual search coil were implanted under intubation
anesthesia with O2-N2O
supplemented with halothane if required to maintain a constant level of
anesthesia (Hess 1990). Animals were trained to fixate
small target lights for fluid reward. All procedures were in accordance
with the National Institutes of Health Guide for the Care and Use of
Laboratory Animals, and the protocol was approved by the Veterinary
Office of the Canton of Zürich.
Measurement of 3-D eye position and calibration
3-D eye positions were measured with the magnetic search coil technique using an Eye Position Meter 3000 (Skalar, Delft, The Netherlands). A horizontal and vertical magnetic field (20 kHz; phase and space quadrature) was generated by coils mounted on a cubic frame of 0.3 m side length.
The output of the dual search coil corresponded to the horizontal and vertical angular orientation of two sensitivity vectors: one pointing roughly in the direction of the visual axis and the other about perpendicular to that. The four voltage output signals of the search coil, as well as the head position and velocity signals, were sampled at a rate of 833 Hz (Cambridge Electronics Device 1401 Plus) and stored on the hard disk of a PC for off-line analysis.
3-D eye position was calibrated as described in detail elsewhere
(Hess et al. 1992). Briefly, in an in vitro procedure,
the magnitude of the two coil sensitivity vectors as well as the angle between them was computed. In an in vivo procedure performed on each
experimental day, the monkeys repeatedly fixated three light-emitting diodes placed at straight ahead, 20° up and 20° down. The measured voltages were used in combination with the coil parameters determined in vitro to compute the orientation of the search coil on the eye and
offset voltages. Eye positions were expressed as rotation vectors
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(1) |
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(2) |
Experimental setup and protocol
The monkeys were seated in a primate chair and secured with shoulder and lap belts. The head was restrained in a 15° nose-down position such that the lateral semicircular canals were approximately earth-horizontal when the monkey was upright. The primate chair was placed inside a vestibular rotator with three motor-driven axes (Acutronic, Bubikon, Switzerland). The accuracy of the position control on each axis was <0.1°. The rotator was surrounded by a light-proof sphere of 0.8 m radius to guarantee complete darkness.
Animals were pitched 24° nose-up (JU and
SU; see Fig.
1A) or 90° nose-up
(supine; JU, SU, and RO; see Fig.
1B) and rotated around the tilted z-axis
with a constant velocity of ±60°/s (left- or rightward) for 10 cycles (initial acceleration 180°/s2). In the following
we refer to these two paradigms as "24° yaw OVAR" and "90°
yaw OVAR." Then they were stopped with decelerations of
180°/s2 to reach any of 12 predefined end positions in
space-fixed coordinates, equally spaced at 30° intervals: 30°,
60°, . . . , 360° (positive, i.e., leftward yaw OVAR) or 330°,
300°, . . . , 0° (negative, i.e., rightward yaw OVAR).
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For data analysis and for representation of results, we describe the
orientation of the gravity vector in a head-fixed coordinate system as
follows. The rightward rotation of the head by 240° (Fig.
1C) relative to space is equivalent to a rotation of the gravity vector in the opposite direction by +240° relative to the
head, corresponding to a final orientation of the gravity vector of
60° (Fig. 1D).
Data analysis
To compute the velocity vector dE/dt, the
three eye position components were digitally differentiated with a
quadratic polynomial filter using a 15-point forward and backward
window (Press et al. 1992; Savitzky and Golay
1964
). This filter has a cutoff frequency with respect to
smoothing of 29.3 Hz. Eye angular velocity (
) was
computed using Eq. 2. To compute slow phase eye velocity,
fast phases of vestibular nystagmus were removed based on time and
amplitude windows, set for the magnitude of the second derivative of
eye velocity (jerk).
In a first approach, the spatial orientation of postrotatory slow phase
eye velocity was evaluated in several steps. First, the orthogonal
response component orth, i.e., the
vectorial sum of the torsional and vertical eye velocity, was computed. The magnitude of this component reflected the deviation of postrotatory eye velocity from the principal response direction (i.e., from a
velocity vector parallel to the z-axis). Second, the sum of two exponentials was fitted (in the least-squares sense) to the time
course of each of the three components of eye velocity as well as to
the orthogonal component, starting at cessation of chair rotation (see
Figs. 3 and 4)
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(3) |
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In a second approach, we fitted the postrotatory responses with an
analytic function that was derived from an explicit model of the
inertial transformation of vestibular signals (Fig. 10). In this 3-D
spatial orientation model we assumed that the postrotatory response
following off-vertical axis rotation resulted from linear superposition
of three signals: 1) a direct input from the lateral semicircular canal (rll, combined
right-left lateral semicircular canal input), 2) an
otolith-dependent head velocity signal
(
oto), and 3) a spatially
transformed (inertial) head velocity signal (
inertial). Accordingly we fitted the
equation
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(4) |
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RESULTS |
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Rotating a monkey around its earth-horizontal longitudinal axis
("barbecue-spit rotation") elicits 3-D vestibuloocular reflexes consisting of a steady-state horizontal nystagmus and a head
position-dependent modulation of eye position and velocity
(Angelaki and Hess 1996a,b
; Hess and Dieringer
1991
). This response pattern perseveres as long as the stimulus
lasts. Figure 3 shows an example of perrotatory VOR responses during
the last two cycles of yaw rotation at
60°/s and the following
postrotatory responses after the stop of rotation. Superimposed on the
horizontal, vertical, and torsional eye velocity vectors (gray curves
on top, middle, and bottom panel) are the exponential functions fitted to each velocity component (solid lines;
see Eq. 3 in METHODS).
In this example, the monkey was stopped in a final body orientation of
240° in the space-fixed coordinate system (see Fig. 1C). This corresponded to a rotation of the gravity
vector through 240° from an initial position at 180° to a final
position at 60° in the head-fixed coordinate system,
as illustrated by the head caricature (see also Fig.
1D). The time indicated by the vertical dashed line in
Fig. 3 represents the midpoint of the deceleration period (with peak
deceleration of 180°/s2). The postrotatory response
consisted of a prominent negative horizontal (rightward) slow phase eye
velocity which decayed very slowly, whereas a positive vertical
velocity (downward) built up to reach a large peak value from which it
declined gradually; similarly a torsional positive eye velocity
(clockwise) built up, followed by a slow decay to zero. The observation
that horizontal eye velocity sometimes decayed to nonzero offset values
was found in all animals and for both OVAR conditions (rotations around 90 or 24° tilted axes). This behavior did not systematically depend on the direction of yaw rotation or the static end position.
If the postrotatory response died off along the original stimulation axis, then one would expect to observe only a horizontal eye velocity component. The relatively large vertical and the smaller torsional velocity components reflect a reorientation of the eye rotation axis toward alignment with gravity: initially, just after the stop of rotation, the eye rotation axis is closely aligned with the (former) rotation axis, i.e., parallel to the earth-horizontal body longitudinal axis. In head coordinates, this corresponds to an ocular rotation around the z-axis and a horizontal (rightward) eye velocity component. Over a time course of a few seconds after rotation stop, the eye's rotation axis reorients toward alignment with space-vertical. This corresponds to an ocular rotation around an axis in the yaw plane parallel to gravity, i.e., an axis with a large y-, a smaller x-component, and a vanishing z-component.
The effect of the reorientation mechanism on the spatial orientation of the VOR response can be better understood when plotting the projections of the different response components of eye angular velocity onto the respective (pitch, roll, and yaw) planes. Figure 4 shows the projections of the data starting from the midpoint of deceleration (gray curves), the exponential functions fitted to the data (solid lines), and the lines fitted to these exponential functions (dashed lines) beginning at the peak of the orthogonal response (arrows in Fig. 3). Arrowheads plotted along the exponential function give the direction of buildup and subsequent decay of the fitted postrotatory response. Figure 4A displays torsional velocity plotted versus horizontal velocity in the pitch plane. Stop of rotation after horizontal rightward OVAR elicited a postrotatory rightward horizontal eye velocity (i.e., negative horizontal velocity along the abscissa). While this horizontal velocity component decreased, a torsional component built up. After the torsional component reached its peak value, both horizontal or torsional velocities declined approximately along a straight line to small residual values or zero.
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A similar pattern can be seen when plotting the vertical component of
eye velocity against the horizontal component (in the roll plane, Fig.
4B): while horizontal velocity decreased, an increasing
vertical velocity component was generated, reaching a peak and then
declining to zero. The ratio between the (larger) vertical and
(smaller) torsional eye velocity buildup reflects the orientation of
the orthogonal response component in the yaw plane (Fig.
4C). This orientation can be determined by the angle between the line fitted to the declining part of the postrotatory response in the yaw plane and the positive x-axis (see
METHODS).
Finally, the orientation of eye velocity in the resultant plane
(Fig. 4D) was determined by computing the angle between the z-axis and the fitted line in the resultant
plane (see METHODS).
Spatial orientation of the orthogonal response component after rotation about a 90° tilted yaw axis
Postrotatory VOR responses showed precise reorientation toward
earth-vertical in two animals (JU and SU) and
were somewhat more variable in one animal (RO). This is
illustrated in Fig. 5, which shows the
tilt angle of the orthogonal eye velocity (see METHODS)
plotted versus the orientation of gravity in the yaw plane for all
final body orientations. On the right side, individual values for each
monkey are displayed for both rotation directions (solid line: +60°/s
leftward OVAR; dashed line:
60°/s rightward OVAR). The left
graph shows tilt angles averaged across all three subjects as well
as over positive and negative rotations, with vertical bars denoting
one standard deviation. Final body orientations of 90, 0,
90, and
±180° correspond to left ear-down, prone, right ear-down, and supine
positions.
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If the orthogonal component of the postrotatory VOR response would
perfectly align with gravity, then the tilt angle should be equal to
the tilt of the gravity vector relative to the head for each body
orientation. This is precisely the pattern seen in the data. For
example, when the gravity vector tilted 90° left ear-down, then the
tilt angle averaged to ~90°. The close correlation between the tilt
angle and the direction of the gravity vector was quantified by
computing the linear regression, for individual subjects (not shown)
and averaged data (dotted line, left graph). The
r2 value for the averaged data was
0.993.
Spatial orientation of the resultant response after rotation about a 90° tilted yaw axis
Figure 6 shows the tilt angles ()
of the eye velocity vector in the resultant plane as a function of the
orientation of gravity in the yaw plane. The individual
angles
plotted in Fig. 6A reveal that after positive yaw rotations
(filled symbols representing the 3 animals) the horizontal component of
the postrotatory eye velocity vector predominantly rotates away from
the direction of the gravity vector, i.e., toward the zenith (negative
values, see METHODS). When the animal is rotated in the
negative yaw direction, the postrotatory response rotates mainly toward
the direction of the gravity vector (positive values). This pattern was
consistently observed in one animal and predominantly in the other two
animals. If the horizontal component would rotate exactly into the
orthogonal plane, we would expect a tilt angle of ±90°.
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Figure 6B displays absolute tilt angles as a function of
final body orientation, averaged over all animals and both rotational directions (mean ± SD). The data cluster around an overall mean tilt angle of 68.6° (dotted line).
Spatial orientation of orthogonal and resultant eye velocity after rotation about a 24° tilted yaw axis
To examine whether the reorientation pattern seen after the
barbecue-spit yaw rotations also holds for less extreme cases, we
studied the orientation of postrotatory eye velocity in two monkeys
after yaw rotations about an axis that was tilted by only 24° from
earth-vertical (0.4 G). The orientation of the orthogonal and resultant
responses, quantified by the tilt angles and
, are depicted for
one animal (JU) in Fig. 7. As
can be seen in Fig. 7A, there is a very good correlation
between the orientation of declining postrotatory eye velocity in the
yaw plane and the orientation of the gravity vector with respect to the
head. The regression line ( · · · ) yielded a mean
R2 = 0.995 (positive direction:
R2 = 0.982; negative direction:
R2 = 0.992). Similar to the findings
for barbecue spit rotations, the principal component of eye velocity
after negative or positive yaw rotations turns in the direction of or
opposite to the direction of gravity (data not shown), yielding an
average absolute
(all final body positions, both directions) of
16.7° ( · · · , Fig. 7B), thus
undershooting the spatial vertical by ~29%.
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Identical analysis for the second animal (SU, not shown)
yielded correlation coefficients r2 of
0.898, 0.728, and 0.850 (positive/negative yaw rotation and averages)
and an average absolute of 29.6°, thus overshooting the spatial
vertical on average by ~25%.
Fitting orthogonal and resultant postrotatory yaw VOR responses using the spatial orientation model
The spatial orientation of postrotatory slow phase eye velocity was also determined by fitting the measured response with an analytic function derived from the 3-D spatial orientation model (see METHODS and APPENDIX for details). Examples of VOR responses fitted with this model (solid lines) are plotted on top of the data (gray curves) in Fig. 8. The diagrams show the same data as in Figs. 3 and 4, in the same views as in Fig. 4, A-C. Clearly, the model fits the data well and deviates only little from the exponential function fitting predictions (cf. Fig. 4): while horizontal velocity decreases, torsional and particularly vertical velocity increases until they reach some peak value and then decline to zero or some small residual value.
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Figure 9 summarizes the performance of the spatial orientation model for this animal and for all final head positions and compares the model predictions with the empirically determined results. The model predicts an accurate reorientation of orthogonal velocity toward earth-vertical (Fig. 9A) along with head orientation invariant reorientation of the resultant response by 73.1° (Fig. 9B).
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Tables 1 (data from 90° yaw OVAR) and 2 (data from 24° yaw OVAR)
compare the tilt angles predicted from fitting the same responses with
the analytic model predictions and empirically with the double
exponential functions. Clearly, the estimated tilt angles show a
closer correspondence between the two methods of analysis than the tilt
angle
(see Fig. 9, A and B; compare
m with
e and
m with
e in Tables 1
and 2). Estimation of the tilt angle
is more difficult because it
is a nonlinear function of both the magnitude of the horizontal and the
orthogonal afterresponse. Because the orthogonal component is the
vectorial sum of the torsional and vertical velocity components, it
could be biased by a downbeat velocity component that amounted to
~2.5-5°/s or less in our animals. In the model fits we accounted
for this vertical velocity bias whenever it could be clearly identified.
The 3-D spatial orientation model provides supplementary information on
the time constants of the low-pass filters in the semicircular canal
and otolith pathways of the inertial system (1
and
2 in Fig.
10). As a consequence of the model
structure, the time constant of the inertial network
(Tstor) was not related to the degree
of spatial alignment of the inertial response (for further details
about the model structure, see DISCUSSION). However, there
was a correlation between the length of the otolith and the inertial
filter time constants: the shorter the otolith filter time constant
(Toto), the shorter the inertial
filter time constant (Tstor).
Moreover, the two time constants tended to be equal in magnitude,
although this was not true when the otolith time constant exhibited
only little variation (see Table 1, negative rotation). Finally, the
time constants of both the otolith and the inertial filters tended to
be shorter for rotations about a 90° tilted axis (barbecue-spit) than
for rotation about a 24° tilted axis.
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DISCUSSION |
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This work studies the interaction of otolith and lateral semicircular canal signals in postrotatory VOR responses when varying final head position. We find a remarkably precise alignment of the head tilt plane and the plane in which postrotatory eye velocity reorients toward the spatial vertical. The ratio between the tilt of the eye velocity vector and head tilt is more variable. Whereas most of the lateral canal signal is used to cancel the otolith-driven bias velocity, only a relatively small fraction of the canal signal that underwent transformation from a head-centered into a gravity-centered reference frame contributes to the total response. In the following paragraphs we discuss these results in the light of a parametric dynamic model of vestibular processing.
Comparison with previous studies
A number of recent investigations have shown that the vestibular
system codes head velocity in the VOR in space- (gravity-) centered
rather than in head-centered coordinates (Angelaki and Hess
1994; Dai et al. 1991
; Gizzi et al.
1994
; Merfeld et al. 1993
; Raphan and
Sturm 1991
). The difference in coding most clearly emerges when
the originally coinciding reference frames dissociate. When rotational
motion cues from the semicircular canals fade away during prolonged
rotation, the otolith organs continue to signal position and, except
for pure earth-vertical axis rotations, velocity of the head-in-space
motion (Angelaki and Hess 1996a
,b
; Darlot and
Denise 1988
; Denise et al. 1988
; Guedry
1965
; Harris 1987
; Haslwanter and Hess
1993
; Hess and Dieringer 1990
; Raphan et
al. 1981
; Young and Henn 1975
). Postrotatory VOR
after off-vertical axis rotations results from a complex interaction of
otolith and semicircular canal signals, each of which functions in
different reference frames. It is not a priori clear which reference
will prevail in the combined afterresponse. Our findings agree with previous studies that have demonstrated that the rotation axis of the
afterresponse following a prolonged constant-velocity rotation shifts
toward alignment with gravity when the subjects are stopped in ear-down
positions (cat: Harris 1987
; humans: Harris and
Barnes 1987
; monkey: Raphan et al. 1992
). The
present study differs from these investigations, however, by applying a
3-D analysis of postrotatory VOR responses to reveal the underlying
computations involved in 3-D spatial reorientation.
Empirical description of spatial reorientation of postrotatory yaw VOR
In our study we applied two methodological approaches to estimate the spatial orientation of postrotatory eye velocity after a constant-velocity rotation. In a first, more descriptive approach, we fitted the sum of two exponentials separately to the horizontal, vertical, and torsional response components as well as to the algebraically determined component orthogonal to the principal (i.e., horizontal) response component. This orthogonal component, i.e., the vectorial sum of the torsional and vertical response component, was by definition located in the yaw plane. Together with the principal response component, it defined the resultant plane, in which postrotatory eye velocity rotated toward the spatial vertical. In all our animals the orientation of this plane was close to parallel to the actual tilt plane, independent of the amount of tilt (Figs. 5 and 7A). This finding proves two important points: 1) rotation of postrotatory eye velocity occurs about a single space-fixed axis, and 2) this axis is always orthogonal to the tilt plane. The internal coding of this plane presumably depends on lateral canal signals that code the axis of head rotation and utricular otolith signals that detect the direction of the projected gravity vector in the utricular plane. The combination of both signals unequivocally determines the orientation of the tilt plane.
The observation of an orthogonal response component that varies with
the projection of gravity into the yaw (utricular) plane indicates that
the postrotatory velocity vector always rotates toward the spatial
vertical. This rotation could be downward, i.e., such that the response
vector and gravity end up as parallel vectors (i.e., pointing in the
same direction), a pattern usually found after stop of a negative head
rotation (solid symbols with negative values in Fig.
6A). Alternatively, the response could also rotate upward,
i.e., such that the response vector and gravity end up as antiparallel
vectors (i.e., pointing in opposite directions), a pattern generally
seen after stop of a positive head rotation (see open symbols with
positive
values in Fig. 6A). Whereas the spatial
reorientation of the postrotatory responses in one animal always
followed this rule, i.e., rotation toward (anti-)parallel alignment
with gravity after stop of a negative (positive) head rotation,
responses in the other two animals occasionally broke this rule. In
either case, rotations were always toward the spatial vertical, and
absolute tilt angles deviated on average by ~20-30% from the head
tilt angle (Figs. 6 and 7B). Whereas most of the orientation
responses at 90° tilt were undershooting the spatial vertical,
overshooting responses could also be observed. At 24° tilt one animal
showed consistently undershooting responses (Fig. 7B),
whereas the other animal exhibited both under- and overshooting responses. It remains an open question whether there exists a consistent trend for over- and undershooting responses as a function of
the tilt following OVAR as has been reported for the spatial reorientation of optokinetic afterresponses (Dai et al.
1991
; Raphan and Cohen 1988
).
The results obtained from this first descriptive approach were compared
with the predictions obtained by fitting the data with a model that
implemented a spatial transformation of the lateral semicircular canal
input downstream to a low-pass filter. This low-pass filtered VOR
pathway has traditionally been called velocity storage integrator to
suggest a supplementary function in gaze stabilization at the
low-frequency end of head movements (Raphan et al. 1977,
1979
). Recent evidence, however, has proven that this
network is part of an inertial vestibular system that encodes head
motion in space (Angelaki and Hess 1994
,
1995
; Raphan and Cohen 1988
). In the
following paragraph we describe this second analytic approach and its
significance in disclosing the mechanisms of spatial orientation.
Underlying canal-otolith interactions: 3-D-spatial orientation model for yaw VOR
To reveal the interaction between semicircular canal and otoliths,
we describe postrotatory VOR after horizontal head rotations with a 3-D
linear dynamic system, in which the spatial transformation is described
by an otolith-dependent rotation (Fig. 10). In this spatial orientation
model, the postrotatory response (VOR) results from superposition of three different velocity signals: 1) a direct semicircular signal
(
rll) due to activation of the lateral
semicircular canals, 2) a velocity signal
(
oto) that has been generated by an
otolith-dependent head velocity detection network
(
g and
2), and
3) a head-in-space velocity signal
(
inertial) from the inertial
transformation network (
1 and
Rg).
The vectorial time signals in the gray panels in Fig. 10 highlight the
intermediate steps in lateral semicircular canal signal processing
based on the interactions with the static and/or dynamic otolith
signals that detect head orientation relative to gravity. In the
particular example illustrated (see Fig.
11A) the lateral semicircular canal signals undergo a spatial tranformation such that
the vectorial output signals of the network are almost perfectly aligned with the spatial vertical. The animal was stopped from rotating
about its longitudinal axis in the earth-horizontal plane when it was
close to right ear-down (head = 90°,
head = 240°). As shown in the gray panel
next to "
inertial " in Fig. 10, the
spatial transformation network Rg
rotates the low-pass filtered head velocity signal in this example such
that its z-(horizontal) component decreases, whereas a
relatively large y-(vertical) and a smaller
x-(torsional) component emerges.
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How does the inertial transformation network
Rg efficiently measure instantaneous
head orientation relative to gravity? To see this, it is helpful to
notice that any change in head orientation relative to gravity can be
understood as a rotation about an earth-horizontal axis. Therefore the
transformation Rg can be described by
only two parameters: a first parameter, the angular orientation of the
tilt axis ( +
/2), is defined by the line of intersection of the
head yaw plane with the earth-horizontal plane (Fig. 2, dashed line).
The orientation of this line could be coded by utricular signals
because it is always perpendicular to the projection of gravity onto
the yaw plane. Because of the fixed geometric relation between the
utricles and the head yaw plane, the transformation from utricular
sensory to yaw plane coordinates could be hardwired. The second
parameter, the head tilt angle
, is more difficult to estimate by
the vestibular system, presumably requiring both utricular and saccular
information. On the other hand, least-squares estimation of this
parameter in the framework of our proposed model (Fig. 10) depends on
the relative strength and dynamics of the lateral semicircular
(
rll) and the otolith
(
oto) signals, both of which contribute
to the spatial characteristics of VOR velocity
(
VOR). Whereas the relatively small
scatter found in the estimated
-angle of final head orientation may
be due to the precise spatial tuning of both the canal- and the
otolith-born head velocity signals, the larger variability in the
dynamics of these signals may underlie the larger scatter in the
estimated
-values.
The head velocity detection network g
estimates absolute head angular velocity relative to space based on the
characteristic spatiotemporal pattern of otolith activity due to the
rotating gravity vector (Angelaki 1992a
,b
; Hain
1986
; Hess 1992
; Schnabolk and Raphan
1992
). This otolith-born velocity signal (output from
g) is low-pass filtered to enhance or
sustain VOR eye velocity at low-frequency and constant-velocity head
rotations where the canal-born velocity signals are deficient in
magnitude or fading away (Angelaki and Hess 1996b
). At
stop of rotation, the postrotatory VOR
(
VOR) results from convergence of a
low-pass filtered output signal from the head velocity detection network
g, a directly transmitted and an
inertially transformed lateral semicircular canal signal.
An important feature of the model structure is the functional
segregation of the spatial orientation and dynamic elements. Whereas
the spatial orientation (angles and
) shows no correlation with
the filter time constants (compare
m* and
m* with Tstor* in Tables
1 and 2), the dynamics of the postrotatory responses basically reflect
the interplay of the low-pass frequency canal and otolith-dependent
head velocity signals. If the head velocity signals at stop of rotation
should efficiently cancel each other (see
rll and
oto in Fig. 10), the amplitude and time
constants need to be appropriately adjusted. Even though the animals
were not reinforced to optimize a certain response behavior, yaw eye
velocity was often strongly reduced in amplitude at stop of rotation.
An example of this cancellation of the horizontal afterresponse that
results from a close match of the amplitude and time constants of the
otolith and semicircular canal signals is illustrated in Fig.
11A. If amplitudes and time constants are less well matched,
an overshooting horizontal postrotatory response results (see example
in Fig. 11B). Note that in this case the late residual
horizontal eye velocity consists almost exclusively of the inertial
response component.
Our model approach differs from that used by Raphan and Sturm
(1991) by the explicit assumption that low-pass filters and spatial transformation networks are functionally segregated elements. This formal difference between the two models becomes important when
the head tilts dynamically. In this case our equations yield an
additional additive dynamic element in the form of the time derivative
of the spatial transformation element
Rg (see Angelaki and Hess 1995
).
Because the same model also predicts the spatial characteristics of
dynamic tilt responses (Angelaki and Hess 1994
, 1995
), it appears that the underlying mechanisms of the
spatial reorientation of postrotatory yaw VOR are identical for both
static as well as dynamic head tilts. Whether the same is true for the roll and pitch VORs is still a matter of debate (Angelaki and Hess 1994
; Dai et al. 1991
; Hess and
Angelaki 1995
; Raphan and Sturm 1991
). From a
more practical point of view, our explicit formulation of the spatial
transformation network allows to derive an analytic solution of the
inertial equations as a function of the input signals, filter time
constants, convergence ratios, and spatial orientation parameters. This
analytic solution allows the extraction of important information about
physiologically relevant parameters.
Conclusions
VOR responses following yaw OVAR show a remarkable precision in
alignment with the spatial vertical, in particular with respect to the
estimated orientation of gravity in the yaw plane (angle ). A
parametric analysis of the afterresponses based on a 3-D spatial
orientation model revealed that inertial vestibular signals represent
only a relatively small fraction of the total postrotatory response. We
propose that these inertial signals are unimportant for gaze
stabilization but, instead, reflect a mechanism that realigns the
internal coordinates of the vestibulomotor system with gravity after
abrupt changes in body motion. Clearly, such a mechanism may be
advantageous for visuomotor coordination and posture control during
self-motion.
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APPENDIX |
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Inertial transformation of lateral semicircular canal signals
It has been shown earlier that the horizontal VOR exhibits
different spatial characteristics as compared with the torsional and
vertical VOR (Angelaki and Hess 1994,
1995
). These characteristics are best modeled by a
rotation operator downstream to a leaky integrator as shown in Fig. 10.
The integration of the right and left lateral semicircular canal
signals that operate in push-pull (
rll)
is described by a first-order linear differential equation
(
1 in Fig. 10)
![]() |
(A1) |
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(A2) |
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(A3a) |
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(A3b) |
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(A4) |
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(A5) |
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(A6) |
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(A7) |
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(A8) |
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ACKNOWLEDGMENTS |
---|
We thank B. Disler for excellent technical assistance.
This work was supported by Swiss National Science Foundation Grant 31-47 287.96.
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FOOTNOTES |
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Address for reprint requests: B.J.M. Hess, Dept. of Neurology, University of Zurich, Frauenklinikstr. 26, CH-8091 Zurich, Switzerland.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 23 August 1999; accepted in final form 15 November 1999.
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REFERENCES |
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