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The Journal of Neuroscience, June 1, 2001, 21(11):3968-3985
Differential Sensorimotor Processing of Vestibulo-Ocular Signals
during Rotation and Translation
Dora E.
Angelaki,
Andrea M.
Green, and
J. David
Dickman
Department of Anatomy and Neurobiology, Washington University
School of Medicine, St. Louis, Missouri 63110, and Department of
Research, Central Institute for the Deaf, St. Louis, Missouri 63110
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ABSTRACT |
Rotational and translational vestibulo-ocular reflexes (RVOR and
TrVOR) function to maintain stable binocular fixation during head
movements. Despite similar functional roles, differences in behavioral,
neuroanatomical, and sensory afferent properties suggest that the
sensorimotor processing may be partially distinct for the RVOR and
TrVOR. To investigate the currently poorly understood neural correlates
for the TrVOR, the activities of eye movement-sensitive neurons in the
rostral vestibular nuclei were examined during pure translation and
rotation under both stable gaze and suppression conditions. Two main
conclusions were made. First, the 0.5 Hz firing rates of cells that
carry both sensory head movement and motor-like signals during rotation
were more strongly related to the oculomotor output than to the
vestibular sensory signal during translation. Second, neurons the
firing rates of which increased for ipsilaterally versus
contralaterally directed eye movements (eye-ipsi and eye-contra cells,
respectively) exhibited distinct dynamic properties during TrVOR
suppression. Eye-ipsi neurons demonstrated relatively flat dynamics
that was similar to that of the majority of vestibular-only neurons. In
contrast, eye-contra cells were characterized by low-pass filter
dynamics relative to linear acceleration and lower sensitivities than
eye-ipsi cells. In fact, the main secondary eye-contra neuron in the
disynaptic RVOR pathways (position-vestibular-pause cell) that exhibits
a robust modulation during RVOR suppression did not modulate during TrVOR suppression. To explain these results, a simple model is proposed
that is consistent with the known neuroanatomy and postulates differential projections of sensory canal and otolith signals onto
eye-contra and eye-ipsi cells, respectively, within a shared premotor
circuitry that generates the VORs.
Key words:
eye movement; binocular; vestibular; vestibulo-ocular; modeling; otolith organs; sensorimotor
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INTRODUCTION |
The vestibulo-ocular reflexes (VORs)
play an essential role as part of an integrated gaze control system to
ensure stable perception of the environment during movement. Despite
similar functional goals, however, several lines of evidence suggest
that the translational VOR (TrVOR) is likely to be organized
differently from the rotational VOR (RVOR). First, the dynamic
processing must be different in the two reflexes because over the
frequency range of natural head movements, primary otolith afferents
encode linear acceleration whereas semicircular canal afferents
carry signals most closely related to angular velocity (Fernández
and Goldberg, 1971 , 1976a-c). Second, the frequency range of effective operation is different for the two reflexes. Although the RVOR elicits
compensatory eye movements down to ~0.05 Hz, the TrVOR only exhibits
a robust response above ~0.5 Hz (Paige and Tomko, 1991a; Telford et
al., 1997; Angelaki, 1998). Finally, there is increasing evidence that
the synaptic organization of the otolith-ocular and canal-ocular
pathways is different. Whereas the shortest latency RVOR pathways are
mediated dominantly by excitatory projections to the contralateral
abducens, the shortest latency TrVOR pathways are instead excitatory to
the ipsilateral abducens (Schwindt et al., 1973; Uchino et al., 1994,
1996, 1997; Imagawa et al., 1995). These differences at both sensory
and motor levels, as well as the existence of unique neuroanatomical
connections, suggest that the sensorimotor processing of canal and
otolith signals in the RVOR and TrVOR is at least partially distinct.
In the case of the RVOR, it has been well established that the most
direct vestibulo-ocular connections are disynaptic, involving second-order neurons in the rostral vestibular nuclei (Richter and
Precht, 1968; Baker et al., 1969; Precht et al., 1969; Schwindt et al.,
1973; McCrea et al., 1987; Scudder and Fuchs, 1992). The majority of
these premotor neurons carry a combination of signals that are
correlated with both vestibular canal inputs (i.e., "sensory" signals) and eye movement-related activity (i.e., "motor-like" signals). The neural elements in the TrVOR are only now beginning to be
identified. To date, data regarding the neural processing of
otolith-ocular signals on eye movement-sensitive neurons have been
obtained mainly during eccentric rotations when the semicircular canals
and otolith organs are simultaneously activated (McConville et al.,
1996; Snyder and King, 1996; Chen-Huang and McCrea, 1999). Assumptions
regarding the linear superposition of canal and otolith signals were
thus required in these studies to parse out the RVOR- versus
TrVOR-related contributions on individual cells.
The present study represents a first attempt to investigate directly
the neural elements that participate in the dynamic transformations of
the TrVOR during pure translational movements. The study focuses on the
identification and quantitative comparison of translational and
rotational responses of eye movement-sensitive neurons in the
vestibular nuclei, a subset of which represents the main premotor cells
in the RVOR. During 0.5 Hz rotation, most premotor cells carry both
sensory head movement and oculomotor-like signals. We demonstrate that,
in contrast, during 0.5 Hz translation, cell responses were more
closely related to the oculomotor output than to the vestibular sensory
signal. Furthermore, distinct differences were observed in the
sensitivity and dynamics of eye movement-sensitive neurons that code
for ipsilaterally directed versus contralaterally directed eye
movements (i.e., eye-ipsi vs eye-contra cells). On the basis of these
results and the unique neuroanatomy of the otolith-ocular system, we
propose that otolith signals join the premotor circuitry by selectively
projecting onto eye-ipsi cells (as opposed to the semicircular canals
that make direct projections onto eye-contra cells). Therefore,
although the same subsets of neurons may participate in both reflexes,
the pattern of sensory signal flow may be different for the
translational and rotational components of the VORs.
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MATERIALS AND METHODS |
Surgical procedures and animal preparation. Data
reported here were collected from three juvenile rhesus monkeys that
were prepared for chronic recording of binocular eye movements and single-unit activity. In a first surgery, animals were chronically implanted with a delrin head-restrainment ring that was anchored by
stainless steel screws, placed as inverted T-bolts under the skull and
then secured to the ring. In addition, a delrin platform (3 × 3 cm; 5 mm height) was stereotaxically secured to the skull and fitted
inside the head ring. The platform had staggered rows of holes (spaced
0.8 mm apart) that extended from the midline to 10 mm bilaterally. In
separate surgeries, all animals were also implanted with dual eye coils
on both eyes (cf. Angelaki, 1998; Angelaki et al., 2000a,b). In two of
the animals, labyrinthine stimulating electrodes were implanted
bilaterally (cf. Angelaki et al., 2000b). All surgical procedures were
performed under sterile conditions in accordance with institutional and
National Institutes of Health guidelines.
Eye movement recordings. Eye movements were measured with a
two-field magnetic search coil system (16 inch cube; 66 and 100 kHz;
CNC Engineering) that was attached to the inner gimbal of the
turntable. Binocular eye movements were recorded in three dimensions.
Eye coils were calibrated both before implantation as well as daily
during experiments, as explained in detail elsewhere (Angelaki, 1998;
Angelaki et al., 2000a,b; McHenry and Angelaki, 2000).
Experimental conditions. During experiments, the monkeys
were seated in a primate chair that was secured inside the inner frame
of a vestibular turntable consisting of a three-dimensional rotator on
top of a 2 m linear sled (Acutronics, Inc.). Rotational stimulus
profiles were delivered using two independently controlled rotational
drives. The translational stimulus profiles were generated using the
linear sled that moved in an earth-horizontal plane. Both stimulus
presentation and data acquisition were controlled with custom-written
scripts within the Spike2 software environment using the Cambridge
Electronics Device (CED, model 1401) data acquisition system. The
behavioral performance of the animal was monitored via interactions
with a second "slave" computer that provided a continuous on-line
TTL pulse as long as both ocular positions were maintained
within 1° of ideal target fixation. This "eye-in-window" signal
was monitored by the CED for on-line juice reward delivery and was
saved for off-line analyses. Behavioral windows for each eye were
calculated on-line on the basis of the geometrical relationships that
should govern appropriate target fixation or ideal target stabilization
for a given motion of the target and/or head movement (Angelaki
et al., 2000a; McHenry and Angelaki, 2000). Juice rewards were
typically given at a frequency of ~1-2 per second as long as the
gaze directions of both eyes were within the specified behavioral windows.
Animals were trained to fixate a small target light that was
backprojected using a laser and x-y mirror
galvanometer system (General Scanning) on a near screen that moved with
the animal (mean vergence angle of ~6.4°). For head-stationary
horizontal and vertical fixations and pursuit, the galvanometer was
controlled directly by using Spike2 scripts and the CED system. Because
the target-laser assembly was fixed to the inner gimbal of the rotator and sled superstructure, a constant galvanometer signal (i.e., no
target movement) provided a head-fixed target for the RVOR and TrVOR
suppression paradigms. Earth-fixed targets during rotation and lateral
translation were presented using an appropriately scaled position
feedback signal from the motion delivery system to drive the
galvanometers on-line during motion. Because of the underlying
geometry, stabilization of a near earth-fixed target during translation
elicits a slightly triangular eye velocity (see Figs. 1-3).
[For an earth-fixed target during a sinusoidal translational movement
trajectory, appropriate ocular angular deviations are nonsinusoidal
under near viewing conditions. This is in contrast to the case of near
target pursuit in which the angle of the laser target was changed
sinusoidally. Thus, ocular deviations should also be approximately
sinusoidal (given similar ocular-to-screen and galvanometer-to-screen
distances).]
Extracellular recordings from vestibular nuclei neurons were obtained
with epoxy-coated, etched tungsten microelectrodes (MicroProbe; 2-4
M impedance) that were inserted into the brain through a 26 gauge
stainless steel guide tube (outside diameter of 457 µm). Electrodes
were inserted into guide tubes and then advanced through a predrilled
hole in the recording platform and manipulated vertically with a
remote-control mechanical microdrive. Neural activity was amplified,
filtered (300 Hz to 6 kHz), and passed both to an audio amplifier and
to a BAK Instruments dual time-amplitude window discriminator
the output of which was displayed on an oscilloscope.
For each recorded cell, acceptance pulses from the BAK window
discriminator were used to trigger the event channel of the CED data
acquisition system that stored the time of the spike at a 10 µsec
resolution. In addition, the eight voltage signals from the two eye
coil assemblies [four for each dual eye coil (see Angelaki, 1998)],
the eye-in-window signal from the slave computer to confirm
appropriate behavioral performance, the three output signals of a
three-dimensional linear accelerometer (mounted on Fiberglas members
that firmly attached the head ring of the animal to the inner gimbal of
the rotator), and the velocity and position feedback signals from the
rotator were antialias filtered (200 Hz; six-pole Bessel) and digitized
by the CED at a rate of 833.33 Hz (16-bit resolution). All acquired
data were stored on a personal computer for off-line analysis.
Vestibular nuclei neuron recordings. During the first
experiments in each animal, the abducens nuclei were identified on the basis of the characteristic burst-tonic activity of the neurons (Fuchs
and Luschei, 1970; Fuchs et al., 1988). Subsequent penetrations were
concentrated in a relatively small area in the rostral part of the
vestibular nucleus extending 3 mm posterior and 4 mm lateral from the
center of the abducens nuclei. These areas, consisting mainly of the
rostral medial vestibular nuclei (with a few penetrations extending
into the caudal aspects of the superior vestibular nucleus), have been
shown to contain eye movement-sensitive cells, many of which project
directly to the abducens and oculomotor nuclei (McCrea et al., 1987;
Scudder and Fuchs, 1992; Cullen and McCrea, 1993). In the animals that
were implanted with bilateral labyrinthine stimulating electrodes,
localization of the vestibular nuclei was also guided by vestibular
field potentials evoked with electrical stimulation of the ipsilateral
vestibular nerve (0.1 msec monophasic pulses; 50-400 µA).
After a vestibular nuclei neuron was isolated, a specific set of
protocols was used to characterize the responsiveness of each cell.
Neural responses were first recorded during both horizontal and
vertical smooth pursuit (0.5 Hz; ±10°), as well as during visually
guided saccades to different fixation points (±20°). Neural activity
was subsequently recorded during 0.5 Hz (±10°) sinusoidal rotation
in yaw and pitch with the animal upright during fixation of head-fixed
and earth-fixed central targets. The axis of yaw rotations was always
earth-vertical and passed through the midsagittal plane of the monkey,
intersecting the line connecting the two auditory meati. The axis of
pitch rotations was earth-horizontal and closely aligned with the
interaural line. During smooth pursuit, stable gaze (i.e., earth-fixed
target stabilization), and suppression (i.e., head-fixed target
stabilization) paradigms, trained animals followed the target with
smooth eye movements, whereas catch-up saccades or fast phases were
usually <1°. As a result, cell responses to saccadic eye movements
are not clearly evident in the neural traces (see Figs. 1-4).
On the basis of their neural responses during these preliminary
protocols, cells were classified into one of four groups (Scudder and
Fuchs, 1992). (1) Position-vestibular-pause (PVP) and
position-vestibular (PV) neurons were characterized by sensitivities to
angular head velocity and to eye velocity in opposite directions such
that these signals superimposed during stabilization of an earth-fixed target. PV and PVP cells included units the activities of which modulated either in-phase with ipsilateral head velocity during yaw
RVOR suppression and contralaterally directed eye velocity during
horizontal smooth pursuit (type I PV/PVP) or in-phase with contralateral head velocity during RVOR suppression and ipsilaterally directed eye velocity during smooth pursuit (type II PV/PVP). The
majority of these neurons paused during saccades (PVP cells), although
a number of such cells did not exhibit a clear pause (PV cells).
Because the firing properties of the cells during saccades were
independent of their responses during the slow eye movement protocols
tested, PV neurons have been grouped together with PVP neurons in this
analysis. (2) Eye-head (E-H) neurons exhibited a sensitivity to head
velocity during RVOR suppression and to eye velocity during smooth
pursuit in the same direction, such that the two signals opposed each
other during rotation while stabilizing an earth-fixed target. This
group included cells with ipsilaterally directed eye and head velocity
sensitivities (Ei-Hi) as well as cells with contralaterally directed
eye and head velocity sensitivities (Ec-Hc). The majority of these
neurons exhibited bursts during saccades in at least one direction. (3)
Burst-tonic (BT) neurons did not demonstrate modulations in firing
activity during either yaw or pitch RVOR suppression but exhibited
significant responses during either horizontal or vertical fixations
and smooth pursuit eye movements. (4) Vestibular-only (VO) neurons
included all cells that did not exhibit any slow eye movement
sensitivity but modulated during either rotational or translational
head movements. The present analysis focuses specifically on the
translational responses of those neuron types the firing rates of which
exhibited some form of correlation with the slow component of the eye
movement (i.e., PV/PVP, BT, and E-H cells), because it is a subset of
these cell groups that has been shown to be the premotor neurons in the
RVOR pathways (McCrea et al., 1987; Scudder and Fuchs, 1992).
All PV/PVP and E-H cells the properties of which were extensively
studied during translation were also tested during RVOR suppression
with the animal pitched 30° nose-up and nose-down to verify that
their major rotational input was from the horizontal semicircular
canals. For example, the PV/PVP and E-H cells that exhibited responses
of the same polarity (i.e., type I or type II) during RVOR suppression
with the animal in upright, 30° nose-up and 30° nose-down
orientations were classified as horizontal neurons. Such cells
typically were also confirmed to exhibit no response modulation during
pitch RVOR suppression. Cells that responded during pitch RVOR
suppression and/or reversed response polarity (i.e., from type I to
type II or vice versa) for yaw RVOR suppression in nose-up versus
nose-down orientations were classified as vertical cells. All
horizontal E-H and PV/PVP neurons also exhibited larger response
modulations during horizontal pursuit and fixations as compared with
vertical pursuit and fixations. For BT cells, the distinction between
horizontal and vertical was based exclusively on their eye movement sensitivities.
Head translation protocols. This study primarily focused on
the characterization of the steady-state sinusoidal responses of
PV/PVP, BT, and E-H neurons at 0.5 Hz where both pursuit and VOR
suppression performance are excellent. After a cell was satisfactorily characterized on the basis of its responses for various combinations of
visual and head rotational stimuli, the following paradigms were used
to characterize its response to translational movements.
(1) All neurons were tested during lateral and fore-aft translation at
0.5 Hz (±0.2 g) while the animal viewed a near
head-fixed central target (TrVOR suppression). If neural isolation was
maintained, the spatiotemporal properties of the cell were also tested
during TrVOR suppression at different frequencies and for different
translation directions (0.16 Hz, 0.1 g; 0.3-2 Hz, 0.2 g). This was done by reorienting the animal relative to the
linear track to achieve translations in different directions (i.e.,
translation directions in between the interaural and naso-occipital
axes). The animal was repositioned in steps of 30°, through a maximum
angle of 180°, as long as cell isolation was maintained.
(2) In approximately one-third of the neural population, responses were
also examined during lateral translation while the animal fixated an
earth-fixed near, central target (0.5 Hz at ±0.05 g; ±4.8
cm) eliciting an eye movement of approximately ±10°. This
translational stimulus was chosen specifically to ensure that the
ocular deviations required to maintain target fixation were of the same
peak amplitude and vergence angle as those elicited during the
horizontal smooth pursuit paradigm (0.5 Hz; ±10°; 6.4° mean
vergence angle; performed as part of the "classification" protocol).
The rationale behind the latter experimental protocol was to enable a
direct comparison of central neuron responses during rotation or
translation with those during pursuit in an assumption-free manner. In
particular, head movement stimuli were chosen such that they would
elicit eye movements of amplitude, frequency, and mean vergence angle
similar to those during pursuit. In previous studies, estimates of the
degree to which different signals contribute to the response of a cell
have typically been made by parsing out cell-firing rates according to
their eye position, eye velocity, and head movement sensitivities.
However, these sensitivity values were often isolated during different
experimental paradigms without keeping stimulus frequency and viewing
distance constant. Our experimental protocol was specifically chosen to
avoid making assumptions about the independence of eye movement-related
activity on viewing distance and frequency. Furthermore, this approach allowed us to avoid the particular problems associated with parsing out
signal components on eye-head cells, which often exhibit highly nonlinear sensitivities to ocular deviations (Scudder and Fuchs, 1992;
Lisberger et al., 1994; Chen-Huang and McCrea, 1999).
The use of sinusoidal stimulation at 0.5 Hz to study stable gaze
responses during translation deserves further comment because of the
fact that this is a low-frequency stimulus for the TrVOR, which is
robust in the absence of visual feedback only at relatively high
frequencies (>0.5 Hz) (Paige and Tomko, 1991a; Telford et al., 1997).
In other words, the observed eye movements during 0.5 Hz TrVOR stable
gaze are presumably primarily visually evoked (i.e., pursuit
responses). It is for this reason that the 0.5 Hz stimulus frequency is
in fact optimal for the goals of the present study. Specifically,
although the TrVOR in darkness at 0.5 Hz is small, both primary otolith
afferent and central otolith-only neurons do indeed exhibit robust
responses to translation at this frequency (Angelaki and Dickman,
2000). Hence, an investigation of cell responses at 0.5 Hz under both
stable gaze and suppression conditions was expected to provide a clear
means of addressing the degree to which neural activities reflect motor
versus sensory vestibular information.
Data analyses. All data analyses were performed off-line
using Matlab (Mathworks, Inc.). Eye positions were calibrated and expressed as three-dimensional rotation vectors, as described in detail
elsewhere (Angelaki, 1998; Angelaki et al., 2000a). During many of the
recordings in one of the animals, the torsion coil of the left eye was
broken. In these cases, only right eye movements were included in the
illustrations (e.g., see Figs. 1-2), although behavioral control
(i.e., verification of appropriate performance and reward) was based on
binocular eye position. Saccades were detected and marked using a
semiautomated algorithm that detects saccades by thresholding the
second derivative of the eye velocity vector. For the neural activity,
unit clock values were converted to an instantaneous firing rate that
was computed as the inverse of interspike interval and assigned to the
middle of the interval. For each experimental run, neural data were
first desaccaded using a window that extended from 50 msec before to 100-200 msec after each saccade (Scudder and Fuchs, 1992). Fixation data and multiple linear regression analyses were used to estimate the
eye position sensitivity of the neuron.
Firing rates from 3 to 20 cycles were then folded into a single cycle
(no averaging was performed). Only portions of data in which the
positions of both eyes were within ±1° of the target were included
in the folding and further analyses. The peak amplitude and phase of
eye and head velocity as well as neural firing rates during
translation, rotation, and pursuit were then determined by fitting a
sine function (first and second harmonics and a DC offset) to the
overlaid data using a nonlinear least-squares algorithm based on the
Levenberg-Marquardt method. Portions of the cycle in which neurons were
silent were excluded from the least-squares optimization. Whenever
neural response gains were estimated, units were
spikes · sec 1 per
degree · sec1 for
rotation and pursuit and
spikes · sec1 · gravity1
(with g = 9.81 m/sec2) for
translation (the latter was chosen for a direct comparison of the TrVOR
suppression responses of eye movement-sensitive cells with those
reported previously for otolith afferent and vestibular-only neurons).
Phase was expressed as the difference (in degrees) between peak neural
activity and peak head (for rotation and translation) or eye (for
pursuit) velocity.
A cell was considered to exhibit a significant response to TrVOR
suppression, RVOR suppression, or smooth pursuit if the following criteria were met: (1) Harmonic distortion was <35% during rotation, translation, and/or pursuit in at least one stimulus direction. (2)
Response gain was greater than a minimum of 0.10 spikes · sec1 per degree · sec1
for head rotation and pursuit and >20
spikes · sec1 · g1
for translation along the directions of minimum harmonic distortion. For the cells that fulfilled these two criteria, a clear modulation in
firing rate was also heard through the audio amplifier.
The spatial tuning characteristics of the cells that exhibited a
significant modulation during TrVOR suppression were evaluated by
fitting a two-dimensional spatiotemporal model to the gain and phase
data as a function of stimulus direction (for details, see Angelaki,
1991; Angelaki and Dickman, 2000). This model is an extension of the
one-dimensional, cosine-tuning equations that are often used to
describe the spatial tuning of vestibular signals. The two-dimensional
spatiotemporal technique differs from the traditional one-dimensional
cosine approach in that it considers the dependence of both gain and
phase on spatial orientation and provides the ability to describe
neural responses in cases in which the response of the cell in the
minimum sensitivity direction is nonzero (the one-dimensional approach
assumes a zero response in the direction of minimum sensitivity). The
ratio of the response gain of the cell in the minimum sensitivity
direction over that in the maximum sensitivity direction is referred to
as the tuning ratio and provides a measure of the spatial specificity
of the cell. The majority of VO neurons in the rostral vestibular
nuclei of primates have been shown recently to exhibit two-dimensional spatiotemporal coding properties and to have tuning ratios >0.1 (Angelaki and Dickman, 2000).
Bode plots were constructed to compare the response dynamics among the
different cell groups during TrVOR suppression over a frequency range
of 0.16-2 Hz. Only portions of each trial in which the animal
maintained fixation within 1° of the target (based on the
eye-in-window signal) and for which peak eye velocity was <2°/sec
were included in the analysis. For a convenient visual inspection of
differences in dynamics among different groups of neurons and to
preserve the appropriate frequency response shape despite averaging
over multiple neurons with different sensitivities, gains at all
frequencies were normalized to the sensitivity of the cell at 0.5 Hz
(see Fig. 7). That is, before averaging, all cell gains were scaled to
unity at 0.5 Hz, whereas at other frequencies, cell gains were larger
or smaller than unity depending on whether sensitivities were larger or
smaller than those at 0.5 Hz. Statistical comparisons were based on ANOVA.
Histology. At the completion of all recording experiments,
the animals were deeply anesthetized (Pentobarbital sodium) and perfused transcardially with a 2% paraformaldehyde and 2%
glutaraldehyde solution. The brain was removed, sectioned (80 µm),
and counterstained (alternate sections with cresyl violet and Weil). An
approximate recording location map was reconstructed for each animal,
using the penetration records and identified location of the abducens nucleus as guides. The exact recording sites could not be verified on
the basis of histological examination.
Model simulations. A model (see Fig. 10 for illustration)
was explored as a means of interpreting both our current data and the
differences in the short-latency neuroanatomy of the canal-ocular versus otolith-ocular pathways. The model represents an extension of
that proposed by Green and Galiana (1998) to incorporate an additional
eye-ipsi cell type. The basis for the model and its key characteristics
are described in detail in Results. Model predictions were investigated
analytically by deriving Laplace transform descriptions of ocular and
central responses (see Appendix). By use of these analytical
descriptions, Bode plots describing response gains and phases were
constructed using Matlab (Mathworks, Inc.; version 5.2). In addition,
the model was implemented with the Matlab dynamic simulation
environment Simulink (version 2.2). Model simulations were performed
using a Runge-Kutta integration routine with time steps of 0.01 sec.
Simulated responses were cross-checked with analytical predictions to
ensure consistency.
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RESULTS |
Experimental data
General comparison of responses to head rotation
versus translation
Of 224 neurons that were characterized in the rostral vestibular
nuclei of three animals, 130 exhibited eye movement-related activity
and were isolated long enough to complete the classification protocol.
On the basis of neural firing rates during visual fixation, smooth
pursuit, and yaw or pitch rotations while an animal fixated a
head-fixed target, neurons were classified into three groups (see
Materials and Methods for a more detailed description). These included
PV/PVP, BT, and E-H cells (Keller and Kamath, 1975; Tomlinson and Robinson, 1984; Scudder and Fuchs, 1992; Cullen and McCrea, 1993;
Lisberger et al., 1994). Typical example responses from each group of
eye-contra cells (i.e., type I PV/PVP, BT, and Ec-Hc neurons) have been
illustrated (see Figs. 1-3). Two example responses from eye-ipsi cells
(i.e., type II PV/PVP and Ei-Hi neurons) are also illustrated (see Fig.
4).
Type I PV/PVP neurons increased their firing rates with contralaterally
directed eye velocity during horizontal pursuit and with ipsilaterally
directed head velocity during RVOR suppression (Fig.
1). During yaw rotation while an animal
fixated a near earth-fixed target, these two signals superimposed. When
the animal was translated laterally while stabilizing an earth-fixed
target, all type I PV/PVP neurons exhibited a robust response
modulation and increased their firing rates during ipsilateral
translation. Hence, their responses to translation during earth-fixed
target viewing were consistent with those during head rotation (i.e.,
the cells demonstrated activities appropriate to drive contralaterally
directed eye movements). A clear distinction could be made between type
I PV/PVP cell responses to head rotation and translation when their
activities were compared during head-fixed target viewing. Whereas type
I PV/PVPs demonstrated a robust modulation in the absence of eye
movements during head rotation, these cells exhibited no response
during TrVOR suppression (Fig. 1, Table
1). Type II PV/PVPs (i.e., neurons with
ipsilateral eye movement and contralateral head velocity
sensitivities), however, behaved differently from type I PV/PVP cells.
Specifically, most type II PV/PVP neurons exhibited clear response
modulations during both head rotation and translation under head-fixed
target stabilization conditions (see Fig. 4A, Table
1).
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Figure 1.
Responses of a horizontal type I
position-vestibular-pause (PVP) neuron during smooth
pursuit, yaw rotation, and lateral translation. During head movement,
subjects stabilized either a head-fixed (RVOR or TrVOR suppression) or
an earth-fixed (0.5 Hz, ±10° ocular deviations) target. The pause of
the cell is only evident for one of the largest saccades during RVOR
suppression (fast changes in eye position are usually  1° during
all experimental paradigms). From top to
bottom, right eye position (E),
right eye velocity ( ), stimulus (head velocity,
 ang for rotation and
head acceleration,  lin
for translation), and instantaneous firing rate (IFR) of
the neuron are shown. RVOR, Rotational vestibulo-ocular
reflex; sp, spikes; TrVOR, translational
VOR.
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Neurons that were classified as BT behaved comparably during head
translations and rotations, apparently coding always for eye
movement-related signals, regardless of the source of sensory input.
For example, the cell illustrated in Figure
2 was excited during contralaterally
directed eye movements but did not respond during RVOR suppression.
Similarly, none of the BT neurons encountered exhibited a consistent
response modulation during lateral TrVOR suppression. As typical for
all contralateral BT cells, the neuron exhibited an increase in firing
rate during both ipsilaterally directed head rotations and translations
while an earth-fixed target was stabilized.
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Figure 2.
Responses of a horizontal burst-tonic
(BT) cell with contralateral eye movement
sensitivity during horizontal smooth pursuit, head rotation, and
translation. During head movement, subjects stabilized either a
head-fixed (RVOR or TrVOR suppression) or an earth-fixed (0.5 Hz,
±10°) target. See Figure 1 legend for other abbreviations.
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Eye-head neurons exhibited all the salient features that have been
described previously in primates, including eye and head velocity
sensitivities in the same direction, nonlinear firing rate/eye position
curves, and inconsistent behavior during saccadic eye movements
(Scudder and Fuchs, 1992; Lisberger et al., 1994; Chen-Huang and
McCrea, 1999). Ec-Hc cells increased their firing rates with
contralaterally directed eye velocity during horizontal pursuit and
contralaterally directed head velocity during yaw RVOR suppression
(Fig. 3). Ipsilateral E-H cells were
excited for ipsilaterally directed eye and head deviations (Fig.
4B). In general,
response sensitivity and phase during rotation while an earth-fixed
target was stabilized was variable. Some neurons exhibited a similar
phase relationship to the head velocity stimulus for both head-fixed
and earth-fixed target stabilization conditions during rotation (e.g.,
the cell in Fig. 3, which increased its firing rate with contralateral
head velocity). However, other E-H cells exhibited a phase reversal
during RVOR suppression relative to their direction of modulation under
earth-fixed target viewing conditions.
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Figure 3.
Responses of a horizontal eye-head cell with
contralateral eye movement sensitivity (Ec-Hc) during
horizontal smooth pursuit, head rotation, and translation. During head
movement, subjects stabilized either a head-fixed (RVOR or TrVOR
suppression) or an earth-fixed (0.5 Hz, ±10°) target. See Figure 1
legend for other abbreviations.
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Figure 4.
Responses of two neurons with ipsilateral eye
movement sensitivity. A, A type II PV/PVP.
B, An eye-head (Ei-Hi) cell. Cell responses during
horizontal smooth pursuit, RVOR suppression, and TrVOR suppression (0.5 Hz) are shown. See Figure 1 legend for abbreviations.
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In contrast to type I PV/PVP cells that exhibited negligible responses
during translation while a head-fixed target was stabilized, approximately one-half of the recorded E-H cells exhibited a clear (although often small) modulation in their firing rates when the animal
suppressed his eye movements (Figs. 3, 4B; TrVOR
suppression; see Table 1). Notably, E-H cells did not always hold the
same relationship to head/eye movement during rotations and
translations. Specifically, neurons sensitive to contralateral rotation
under head-fixed target stabilization conditions could be excited
during ipsilateral translation (and vice versa). Moreover, despite the inconsistent behavior of E-H cells during head rotation under stable
gaze conditions (whereby response phase was not always consistent with
the eye movement preference of the cell during head-stationary
pursuit), their responses to translation during earth-fixed target
viewing were always appropriate to drive contralaterally (for Ec-Hc
cells) or ipsilaterally (for Ei-Hi cells) directed eye movements. With
the exception of one vertical eye-head cell, none of the cells that
were classified as having predominately vertical eye and head movement
sensitivities during pursuit and rotation modulated their firing rates
during TrVOR suppression.
In summary, all eye movement-related cell types examined demonstrated
activities during translation (but not necessarily rotation) while an
animal viewed an earth-fixed target that were appropriately directed
for their respective eye movement preference. Notably, however, during
TrVOR suppression only a subpopulation of type II PV/PVP and E-H cells
demonstrated a significant modulation, suggesting that distinct cell
types may receive more direct sensory otolith signals. Thus, responses
under both suppression and stable gaze conditions were examined in more
detail to test the hypothesis that there are differences among eye-ipsi
and eye-contra PV/PVP and E-H neurons in terms of their locations
within the pathways underlying the transformation of sensory
information into oculomotor signals in the TrVOR.
Responses during TrVOR suppression
As outlined in the previous section, only a few cells (nine type
II PV/PVP, seven Ec-Hc, six Ei-Hi, and one vertical E-H; see Table 1)
exhibited a clear and consistent response modulation during 0.5 and/or
2 Hz TrVOR suppression. The mean (±SD) sensitivity relative to
translational acceleration for all TrVOR suppression-sensitive cells at
0.5 Hz was 85 ± 82 spikes · sec1 · g1
(n = 18; range of 21-266
spikes · sec1 · g1).
These suppression responses were similar in amplitude to those of VO
central cells and primary otolith afferents tested under identical
experimental conditions (Angelaki and Dickman, 2000). For Ei-Hi cells,
no correlation was observed between cell sensitivities to head movement
during TrVOR suppression and RVOR suppression (R2 = 0.04). For Ec-Hc and type
II PV/PVP neurons, a weak correlation existed
(R2 = 0.54 and 0.60, respectively).
Figure 5A illustrates the cell
responses during lateral TrVOR suppression at 0.5 Hz, in which response
phase has been described by a polar angle and response sensitivity has
been described by the amplitude in the radial direction. In general,
response phase during lateral TrVOR suppression varied widely among
neurons, with the majority of cells exhibiting responses that either
led or lagged contralaterally directed head velocity (Fig.
5A). Furthermore, the ipsilateral/contralateral preference
of neurons was not always identical during RVOR and TrVOR suppression.
For example, most Ei-Hi cells that responded with ipsilaterally
directed sensitivities to head rotation during RVOR suppression
increased their activities for contralaterally directed head velocity
during TrVOR suppression. In fact, there was a general trend for all
groups of cells that responded during TrVOR suppression to be excited
during contralaterally directed head movement (Fig. 5A).
Hence, the E-H cell classification during head rotation (i.e., in terms
of the sensitivity of the cell to eye velocity during pursuit and to
head velocity during suppression) does not in general extend to their
responses during lateral translation.
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Figure 5.
Response sensitivity and phase during lateral
TrVOR suppression are plotted in polar coordinates for the horizontal
type II PV/PVP, Ec-Hc, and Ei-Hi cells and one vertical E-H cell that
exhibited clear response modulations during stabilization of a
head-fixed target. A, Individual neuron responses at 0.5 Hz (±0.2 g) are shown. B, Average
responses for the type II PV/PVP, Ec-Hc, and Ei-Hi neurons are
compared for 0.5 and 2 Hz translational stimuli (solid
and open symbols, respectively). Sensitivity has been
expressed in
spikes · second1 · gravity1
(g = 9.81 m/sec2). Phase
has been expressed relative to contralaterally directed head velocity.
Vert, Vertical. See previous figure legends for other
abbreviations.
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The average sensitivity and phase for each group of cells during
lateral TrVOR suppression at 0.5 and 2 Hz are compared in Figure
5B (solid and open symbols,
respectively). Eye-contra neurons (i.e., Ec-Hc) differed from eye-ipsi
neurons (i.e., Ei-Hi and type II PV/PVP) in several respects. First,
there were significant differences both in terms of sensitivity and
phase between eye-contra and eye-ipsi cell responses
[F(1,33) = 6.05 (gain), = 6.41 (phase); p < 0.05]. Specifically, eye-contra cells
exhibited lower sensitivities and smaller leads relative to linear
velocity than did eye-ipsi cells. Second, there was a significant
decrease in the sensitivity of eye-contra (but not in the sensitivity
of eye-ipsi) cells between 0.5 and 2 Hz
[F(1,10) = 6.1; p < 0.05]. The only difference between type II PV/PVP and Ei-Hi neurons
was a tendency for the former to have larger phase leads relative to
contralaterally directed head velocity
[F(1,21) = 4.4; p = 0.05].
A subpopulation of the cells that responded during TrVOR suppression
was also tested during linear motion along different directions in the
horizontal plane (usually six positions spaced every 30°, including
lateral and fore-aft motion) to investigate their spatial-tuning
properties. For all heading directions, the animal fixated a central
head-fixed target and suppressed the generation of compensatory eye
movement. The direction of maximum sensitivity, as well as the gain and
phase of the neuron along the maximum sensitivity direction, was then
computed by fitting a two-dimensional spatiotemporal model to the
sensitivity and phase of each cell as a function of heading direction
(see Materials and Methods) (for details, see also Angelaki et al.,
1992; Angelaki and Dickman, 2000). Approximately one-half of the cells
that responded during TrVOR suppression exhibited two-dimensional
spatial-tuning properties and ratios of minimum over maximum
sensitivity that were >0.1 (Angelaki, 1991; Angelaki et al., 1992;
Angelaki and Dickman, 2000).
The distribution of maximum sensitivity vectors of those neurons that
were tested for multiple translational directions has been plotted in
Figure 6. As expected on the basis of the
phase of the responses during lateral motion (Fig. 5), the majority of
vectors were directed contralaterally [i.e., similar to the majority
of primary otolith afferents and central vestibular-only neurons
(Angelaki and Dickman, 2000)]. This appeared to be true for all types
of responsive cells, independently of whether they exhibited
ipsilaterally or contralaterally directed eye movement sensitivities or
whether they were excited for ipsilaterally or contralaterally directed
rotation during RVOR suppression.
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Figure 6.
Distribution of maximum sensitivity vector
orientations during translations in the horizontal plane for the
horizontal type II PV/PVP, Ec-Hc, and Ei-Hi cells and one vertical E-H
cell that exhibited clear response modulations during TrVOR suppression
at 0.5 Hz. Vector sensitivity is expressed in
spikes · second1 · gravity1
(g = 9.81 m/sec2).
sup, Suppression. See previous figure legends for other
abbreviations.
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The average response phase of the neurons along their maximum
sensitivity direction hovered between velocity and acceleration throughout the frequency range that animals suppressed their TrVOR (0.16-2 Hz; Fig. 7). All ipsilateral eye
movement cells (i.e., type II PV/PVP and Ei-Hi; Fig. 7,
squares and inverted triangles) exhibited
response dynamics that resembled those of "high-pass" or "flat"
otolith-only VO cells [Fig. 7, dashed lines are means of
the two VO groups; replotted from Angelaki and Dickman (2000)]. Accordingly, average response sensitivity (expressed in
spikes · second1 · gravity1)
increased slightly with frequency. The response phase tended to either
remain flat or demonstrate an increased lead relative to head velocity
as a function of frequency.
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Figure 7.
Response dynamics of eye-ipsi and eye-contra cells
during TrVOR suppression. The mean (±SD) response sensitivity
(top) and phase (bottom) for translation
in the maximum sensitivity direction are plotted as a function of
frequency for five type II PV/PVP, two Ec-Hc, and four Ei-Hi cells.
Dashed lines are used to illustrate the mean sensitivity
and phase from two groups of otolith-only (i.e., not eye
movement-sensitive) neurons that exhibited high-pass and flat dynamics
and were recorded rostrally in the vestibular nuclei, in the vicinity
of the eye movement cells of the present study (Angelaki and Dickman,
2000). Phases of 0° (linear velocity) and 90° (linear acceleration)
are indicated with dotted horizontal lines.
Sensitivities are expressed in
spikes · second1 · gravity1
(g = 9.81 m/sec2) and
normalized to a gain of unity at 0.5 Hz before the calculation of each
average. Phase values were expressed relative to translational head
velocity in the interval of -90 to +90°, independently of whether
the firing rate of a given cell increased for ipsilaterally or
contralaterally directed head movements. VO OTO,
Vestibular-only otolith neurons. See previous figure legends for other
abbreviations.
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In contrast to the dynamic properties of the eye-ipsi neurons (i.e.,
type II PV/PVP and Ei-Hi cells), the few Ec-Hc cells that exhibited
clear responses during TrVOR suppression and were tested at several
frequencies and for different movement directions were characterized by
low-pass filter dynamics. Specifically, response sensitivity declined,
and phase leads relative to head velocity decreased with frequency
(Fig. 7, triangles). Decreases in gain and phase lead with
frequency between 0.5 and 2 Hz were also observed for all responsive
Ec-Hc neurons, as illustrated previously in Figure 5B.
Responses to translation during earth-fixed
target stabilization
To address further the degree to which cell responses reflect
sensory otolith modulation versus information that has primarily been
transformed previously into motor-like signals, we directly compared
TrVOR and RVOR responses under earth-fixed target stabilization conditions with those during pursuit of similar ocular amplitude and
vergence angle. Thus, peak response amplitude and phase during 0.5 Hz
lateral translation while animals fixated an earth-fixed target have
been plotted as a function of cell peak modulation amplitude and phase
during 0.5 Hz horizontal pursuit in Figure 8A. Similarly, peak
response modulation and phase during head rotation are plotted as a
function of peak horizontal pursuit modulation and phase in Figure
8B. To facilitate comparison of the neural responses
associated with each stimulus, the parameters of the respective stimuli
were chosen such that the evoked eye movements were similar during
lateral translation, yaw rotation, and horizontal pursuit (i.e., the
same frequency, same vergence angle, and similar peak eye position and
velocity; see Materials and Methods). This analysis facilitates a
direct comparison of the rotational and translational responses of each
cell with those during an equivalent eye movement in the absence of
head motion, without assumptions about the signal content and linearity
of cell activities.
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Figure 8.
Functional distinction between sensory and motor
signals during lateral translation (A) and yaw
rotation (B). This is illustrated by plotting the
peak firing rate (top) and phase (bottom)
during movement while an animal fixated a central earth-fixed target
versus the corresponding peak firing rate and phase during horizontal
smooth pursuit with the animal stationary. The stimuli during
translation and rotation were adjusted such that the elicited eye
movements were close to identical to those during smooth pursuit (0.5 Hz, ±10°). Different symbols are used for different
classes of cells (BT, type I PV/PVP, type II PV/PVP, Ec-Hc, and Ei-Hi).
Open symbols in A
correspond to the few (3) cells that were tested for both stable gaze
and suppression conditions and exhibited small but consistent responses
during TrVOR suppression (22-68
spikes · sec1 · g1).
Dotted lines with unity slope indicate
equal responses during head movement and pursuit. Solid
lines are linear regressions (A, top, slope = 0.89, R2 = 0.94; A,
bottom, slope = 0.98, R2 = 0.77; B,
top, slope = 0.55, R2 = 0.28; B,
bottom, slope = 1.61, R2 = 0.30). See previous figure
legends for abbreviations.
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Under these conditions, neurons with motor-like responses would be
expected to respond identically to head-stationary pursuit and lateral
translation while an earth-fixed target was stabilized. As seen in
Figure 8A, this indeed seems to be the case for cell responses during head translation that fall along the unity-slope dotted line when plotted as a function of their respective
activities during pursuit. This observation holds true even for the few
cells that exhibited a consistent response modulation during TrVOR
suppression (Fig. 8A, open symbols) and
can be explained by the fact that, in general, cell modulations during
0.5 Hz TrVOR suppression were significantly smaller than were their
activities under stable gaze conditions [85 ± 82 spikes · sec1 · g1
(n = 18) vs 616 ± 677 spikes · sec1 · g1
(n = 9); range 211-2366
spikes · sec1 · g1).
It is interesting, however, to contrast this motor-like behavior during
translation with the case of head rotation, in which the majority of
PV/PVP and eye-head neuron responses demonstrated clear evidence of a
sensory canal signal under earth-fixed target stabilization conditions.
When peak rotational responses are plotted versus those during pursuit,
the data points do not fall along the unity-slope dotted
line (Fig. 8B, top). For example,
data points for PV/PVP cells fall above the unity-slope dotted
line, reflecting the fact that their responses during rotation
under stable gaze conditions were larger than were those during an
identical target pursuit. Thus, their responses clearly reflect a
contribution of sensory signals from the canals during head rotation.
The eye-head cell data typically fall below the unity line slope (i.e.,
smaller amplitude responses during stable gaze than during pursuit)
(Fig. 8B, top). In contrast, during
translation the activities of all eye movement-sensitive cells appear
to dominantly reflect the underlying oculomotor behavior.
In Figure 8 neural response phases during head rotation and translation
are also plotted against those observed during head-stationary target
tracking. To facilitate comparison, all neural phases during horizontal
pursuit were expressed relative to eye velocity in the interval between
 90 and +90°, independently of the oculomotor preference of the cell
(i.e., whether it exhibited an ipsilaterally or contralaterally
directed eye movement sensitivity). Phase during head movement was
expressed in the range of 90 to +90°, only if the modulation of a
cell relative to eye velocity during the head movement was consistent
(i.e., in the same direction) with that during head-stationary pursuit.
Otherwise, if a cell demonstrated oppositely directed phases during
target tracking and head movement while an earth-fixed target was
stabilized (which was often the case for E-H cells; Fig.
8B, bottom), its phase was expressed in
the range of 90-270° (i.e., phase was shifted by 180°).
Despite a wide distribution of pursuit phases (Scudder and Fuchs, 1992;
see also Lisberger et al., 1994), translational response phases closely
match those during pursuit (Fig. 8A,
bottom). Thus, all neurons with ipsilaterally directed eye
movement sensitivity were excited during contralateral translation,
whereas all neurons with contralaterally directed eye movement
sensitivity were excited during ipsilateral translation. As described
above, this was not in general the case during rotation, particularly
for those E-H cells that did not reverse phase during RVOR-stable gaze
as compared with RVOR-suppression conditions (Fig.
8B, bottom, plotted in the upper
cluster). Thus, a direct comparison of cell responses during 0.5 Hz translation and pursuit supports the conclusion that cell activities
during head translation are dominated by oculomotor-like (or
pursuit-related) signals in contrast to the case of head rotation in
which the influence of both motor-related and sensory vestibular
signals are readily evident in cell responses.
Model structure and simulations
Several hypotheses have been put forward in the past years to
account for the differences in the dynamic processing of sensory signals in the TrVOR as compared with the RVOR (Paige and Tomko, 1991b;
Raphan et al., 1996; Telford et al., 1997; Green and Galiana, 1998,
1999; Musallam and Tomlinson, 1999). The goal of this section is
two-fold: first, to justify the structure of the model supported here
(see Fig. 10) in the context of previous modeling efforts of the VORs;
and second, to simulate model cell responses and examine whether the
observed differences in the sensitivity and dynamics of eye-ipsi and
eye-contra neurons could be predicted by the model structure.
Feedforward and feedback realizations for the RVOR
To illustrate the conceptual process for the model, let us first
consider a classical feedforward realization for the RVOR network (see
also Skavenski and Robinson, 1973; Robinson, 1981) that involves a
parallel set of pathways from the semicircular canals [C(s)] to
extraocular motoneurons (Fig.
9A). The function of these
parallel pathways, consisting of an indirect pathway via a nearly
perfect neural integrator (with time constant > 20 sec;
illustrated for simplicity as 1/s, where s is the
Laplace operator representing complex frequency) and a direct sensory projection via the vestibular nucleus, is twofold. The first function is to provide a neural integration of sensory signals in the RVOR so
that velocity signals originating from the semicircular canals are
transformed into eye position commands. Second, the combined effect of
the direct and integrator pathways results in a high-frequency lead
that cancels the lag associated with the low-pass filter properties of
the eye plant P(s). For this cancellation to be effective, the relative weights for the contribution of each pathway are determined by the dynamic characteristics of the eye plant. For
example, if P(s) = 1/(1 + Tps)
[Tp  0.25 sec (Robinson, 1981)] and
if the gain of the integrator pathway is assumed to be 1, the direct
pathway must have a gain equal to Tp
(Tp = 0.25 sec in Fig. 9A).
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Figure 9.
Feedfoward and feedback models of the RVOR
(A, B) (Skavenski and Robinson, 1973; Robinson, 1981;
Galiana and Outerbridge, 1984) and the RVOR and TrVOR (C,
D) [modified following Green and Galiana (1998); Musallam and
Tomlinson (1999)]. The neural filter
F(s) represents an internal model
of the eye plant [i.e., F(s) = P(s)] that is presumed to exist
in the nucleus prepositus hypoglossi (PH).
Parameter Tp in A and
C is chosen to provide neural compensation for the
low-pass filter dynamics of the eye plant (Robinson, 1981), whereas
parameters a and b in B
and D are set to provide an appropriate RVOR gain and
integrator time constant (Galiana and Outerbridge, 1984).
C(s), Semicircular canals;
E, eye position; E*, efference copy or
internal estimate of E; EM, eye
movement-sensitive vestibular neurons;
ang, angular head velocity;
lin, linear head
acceleration; MN, extraocular motoneurons;
O(s), otolith organs;
VO, vestibular-only neurons. See previous figure legends
for other abbreviations.
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An alternative feedback realization of the RVOR was proposed by Galiana
and Outerbridge (1984) (outlined in Fig. 9B). The basic
structure of the model incorporates a lumped premotor eye movement-sensitive cell type (EM) interconnected in a positive feedback
loop with a neural filter, F(s), that represents
an internal model of the eye plant [F(s) = P(s)]. The output of F(s)
provides an internal estimate (efference copy) of eye position,
E*, that can represent eye position-sensitive neurons in the
nucleus prepositus hypoglossi (PH). The input/output properties of this
realization are equivalent to the feedforward parallel pathway model of
Robinson (1981) (Fig. 9A). However, the feedback realization
is more realistic in terms of the highly interconnected nature of the
premotor circuitry (cf. McCrea et al., 1981, 1987). Furthermore, the
neural integration relies on distributed positive feedback loops around
a neural filter with a relatively small time constant (i.e., equal to
the dominant eye plant time constant of ~0.25 sec), as opposed to a
localized integrator with a large time constant. In fact, lesion studies have demonstrated that the neural integrative properties of the
premotor network involve several brain areas including the vestibular
nuclei, the PH, and the cerebellum (Robinson, 1974; Cannon and
Robinson, 1987; Cheron and Godaux, 1987; Kaneko, 1997).
Hypotheses for the dynamic processing in the TrVOR pathways
Because primary otolith afferents encode linear head acceleration
(as compared with the angular head velocity signals provided by the
semicircular canals), the processing described above for semicircular
canal signals in the RVOR is not appropriate for the processing of
otolith signals in the TrVOR. The most widespread hypothesis for the
dynamic processing of otolith signals has been based on a proposal by
Paige and colleagues that the additional required low-pass filtering of
otolith signals in the TrVOR is performed by a preliminary neural
processing stage including either an integrator or a low-pass filter
cascaded with a high-pass filter (Paige and Tomko, 1991b; Telford et
al., 1997). The prefiltered otolith signals are then combined with the
angular head velocity signals from the semicircular canals and are
commonly processed via the parallel pathways proposed by Skavenski and
Robinson (1973), as outlined above.
An alternative strategy to the "prefiltering" hypothesis has been
proposed that we will refer to here as the "eye plant" hypothesis (Green and Galiana, 1998, 1999; Musallam and Tomlinson, 1999). Briefly, the eye plant hypothesis proposes that no additional neural
filtering of otolith signals is required if, in contrast to the case of
the RVOR, the dynamic characteristics of the eye plant remain
uncompensated. The eye plant itself then provides the second required
low-pass filtering of otolith signals in the TrVOR (Green and Galiana,
1998). In a Robinson-style feedforward model, the eye plant hypothesis
can be realized as illustrated in Figure 9C, where the same
parallel pathway circuitry is used to process both otolith,
O(s), and semicircular canal,
C(s), signals. The difference in otolith-ocular
versus canal-ocular processing lies in the ratio of the relative
projection strengths from each sensor onto the direct and integrator
pathways, respectively. This ratio must be equal to the dominant eye
plant time constant Tp (~0.25 sec) in
the case of canal projections to provide compensation for the dominant
eye plant pole. However the ratio must be very small in the case of
otolith projections [for example, a ratio of 1/100 was used in the
simulations of Musallam and Tomlinson (1999); Fig. 9C] so
that the resulting lead term in the TrVOR will have a very short time
constant, too small to provide a temporal compensation for the dynamics
of the eye plant at frequencies below ~16 Hz.
The implementation of the eye plant hypothesis in a positive feedback
model of the VOR is illustrated in Figure 9D [according to
Green and Galiana (1998)]. Specifically, otolith and canal signals
were proposed to join the premotor circuitry at unique sites such that
the premotor eye movement-sensitive vestibular neurons EM involved in
the disynaptic RVOR pathways receive direct projections from the
semicircular canals but only indirect otolith signal inputs via the
neural filter F(s) in the PH. Because there are
no direct vestibular afferent projections to the PH (Baker and Berthoz,
1975; Hikosaka et al., 1978) in the original formulation of Green and
Galiana (1998), otolith signals were conveyed to the PH through a VO
interneuron. With the exception that no disynaptic (i.e., no direct)
otolith-ocular projection was incorporated in the original formulation
of the model of Green and Galiana (1998), the dynamic processing
performed by the neural network in Figure 9D is equivalent
to that in Figure 9C.
Both the eye plant (Green and Galiana, 1998) and the prefiltering
hypotheses (Paige and Tomko, 1991b; Telford et al., 1997) can
qualitatively predict TrVOR dynamics [although an exact match between
experimental data and model predictions is problematic because TrVOR
dynamics exhibits nonminimum phase behavior when evaluated in an
extended frequency range (Angelaki, 1998)]. This is so because the
proposed realizations of these alternative hypotheses are practically
identical in terms of the overall input-output characterization of the
system. For example, in the model of Telford et al. (1997), the
low-pass filtering stage is equivalent to a first-order approximation
of the dynamic characteristics of the eye plant (i.e., a low-pass
filter with a time constant of 0.25 sec). In addition, the proposed
high-pass filtering stage in the Telford et al. (1997) model produces
an effect similar to that of a weak direct pathway at high frequencies
(e.g., in Fig. 9C). What remains unaddressed in the model of
Telford et al. (1997) is why such a central low-pass filtering of
otolith signals is necessary, because the effects of this prefiltering
will be cancelled downstream by the eye plant compensation network,
only to be reintroduced again by the actual eye plant.
We believe that the eye plant hypothesis is more realistic for the
following reasons. First, the introduction of an additional neural
prefiltering stage is redundant and thus less efficient. Second, if
such a central filtering existed, one would not expect eye-ipsi and
eye-contra cells to exhibit distinct dynamic characteristics during
translation. Third, the eye plant hypothesis is more compatible with
the differential short-latency neural connections of the otolith-ocular
compared with the semicircular canal-ocular systems (see Discussion).
For these reasons, in the schematic diagram illustrated in Figure
10A we have extended
the feedback realization of the eye plant hypothesis model proposed by
Green and Galiana (1998) by explicitly representing an additional group
of neurons with ipsilaterally directed eye movement sensitivity.
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Figure 10.
Proposed model of the VORs. A,
Schematic of the feedback realization of the eye plant hypothesis (Fig.
9D) (Green and Galiana, 1998) that has been extended
here to include both lumped eye-ipsi
(EMI)- and eye-contra
(EMC)-sensitive cell types. The
dotted line indicates an assumed weak projection from
EMI cells to the ipsilateral abducens to account for the
disynaptic utriculo-ocular pathways (Uchino et al., 1994, 1996). The
dashed line indicates an inhibitory projection from PH
neurons [i.e., at the output of
F(s)] to the contralateral
abducens (McCrea and Baker, 1985; Langer et al., 1986; Escudero and
Delgado-Garcia, 1988) that may account for the inhibitory polysynaptic
utriculoabducens pathway (Uchino et al., 1997). B,
Actual model structure based on the schematic in A that
was used to examine the predicted responses of the EMC and
EMI cell types under different visual-vestibular
interaction conditions. Dashed pathways associated with
visuomotor areas (VM) are activated by the
presence of a visual target and represent a simplified lumped pursuit
system (Green and Galiana, 1998, 1999; Green, 2000). Negative
signs denote projections that on the basis of anatomy are
presumed to be either inhibitory to the ipsilateral side of the brain
or excitatory to the contralateral side of the brain. Similarly,
positive projections (i.e., no negative sign) are
assumed to be either excitatory to the ipsilateral side or inhibitory
to the contralateral side of the brain. Because the projections in the
positive feedback loop interconnecting the EMC and
EMI cells are illustrated as negative (inhibitory), both
cell types should be assumed to be located on the same side of the
brain in interpreting model simulations. Vestibular stimulation is
provided by the angular head velocity
ang, sensed by the
semicircular canals, C(s) = Tcs/(Tcs + 1), and linear head acceleration
lin, sensed by the otolith
organs, O(s) = 1/(Tos + 1). The negative
sign at the output of O(s)
indicates that afferents associated with the medial portions of the
utricular maculae (excited for contralaterally directed translation)
are assumed to provide the TrVOR drive.
Tconj describes the conjugate target
position in a head-fixed reference frame. The neural filter,
F(s) = Kf/(Tfs + 1), represents an internal model of the eye plant,
P(s) = Kp/(Tps + 1), when Tf = Tp. The output of the model,
E, represents conjugate eye position. Model parameters
are as follows: a = 0.19, b = 0.75, d1 = 0.21, d2 = 1.1, e = 0.03, Kp = 1, Kf = 2.81, Kv = 9.51, p = 1, q = 0.27, r1 = 0.1, r2 = 0.1, Tf = 0.25, Tp = 0.25, Tc = 5, and
To = 0.0159. Note that to simulate
appropriate responses for a vergence angle of 6.4°, the primary
otolith projection weight q was adjusted to produce a TrVOR gain of 1.2 cm/° at 4 Hz (equivalent to a TrVOR gain of 0.32 cm · degree1 · MA1).
MA, Meter-angles, defined as the reciprocal of viewing distance in
meters. See previous figure legends for other abbreviations.
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In Figure 10A (as in Fig. 9D), otolith
signals are conveyed only indirectly to eye-contra neurons
(EMC; representing a lumped cell type
corresponding to type I PV/PVP and Ec-Hc neurons) that represent the
main secondary interneurons in the three-neuron-arc RVOR pathway. We
suggest that otolith signals join the premotor pathways through
eye-ipsi cells (EMI) that represent a lumped population corresponding to type II PV/PVP and Ei-Hi neurons. These
cells are assumed to make weak excitatory projections to the
ipsilateral abducens (Fig. 10A, dotted
line). However, the dominant output of cell population
EMI is to the neural filter F(s) in the PH. Although not illustrated in
Figure 10, a VO otolith projection to the PH is also possible (Fig.
9D). In the simulations presented below and as will be
further elaborated on in the Discussion, we argue that the model of
Figure 10A can both account for our experimental
observations and provide a rationale for the observed differences in
the short-latency neuroanatomical connectivity of otolith-ocular and
canal-ocular pathways.
Model predictions
The predictions of the model illustrated in Figure
10A are briefly investigated here to illustrate that
the proposed model can replicate the main characteristics of eye-ipsi
and eye-contra cells. The model that was actually simulated is
illustrated in Figure 10B and represents a more
detailed version of that in Figure 10A. Specifically,
to incorporate motor projections from the PH (Fig.
10A, dashed line) (McCrea and
Baker, 1985; Langer et al., 1986; Escudero and Delgado-Garcia, 1988;
Spencer et al., 1989; Escudero et al., 1992; McFarland and Fuchs,
1992), a collateral PH output projection to the
EMI cell type was included in the model of Figure
10B to maintain the appropriate dynamic processing of
canal signals in the RVOR. In addition, projections to and from
visuomotor areas have been included (for details, see Green and
Galiana, 1998, 1999; Green, 2000). These loops are activated by the
presence of visual feedback and provide a simple representation of the
pursuit system sufficient to explore model predictions under different
visual-vestibular stimulus conditions (Fig. 10B, dashed pathways).
Frequency response predictions of the model during TrVOR suppression
are illustrated in Figure 11. The model
EMI cell exhibits gains and phases with respect
to head acceleration that are relatively flat and thus sensory-like,
whereas the EMC cell population exhibits a
low-pass-filtered response relative to linear acceleration (Fig. 11,
dashed vs solid lines, respectively). Thus, in
agreement with our experimental observations (Fig. 7), the model
predicts that EMC and EMI
cells will exhibit differential dynamic properties during TrVOR
suppression. Analytical descriptions of the model EMI and EMC cell responses
under both head-fixed target stabilization and dark conditions are
provided in the Appendix and demonstrate that the model of Figure 10
also predicts different dynamic properties for the two cell populations
during translation in darkness. This latter prediction remains to be
confirmed experimentally.
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Figure 11.
Predicted frequency response plots for the
EMC and the EMI cell types
(solid and dashed lines, respectively) in
the model of Figure 10B during TrVOR suppression.
Cell response gains are expressed relative to translational head
acceleration. The response phase of the EMI cell is
expressed relative to contralaterally directed head velocity, whereas
the EMC cell response phase is expressed relative to
ipsilaterally directed head velocity. See previous figure legends for
abbreviations.
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Simulated responses of the model EMC and
EMI cell types during smooth pursuit are compared
with those for earth-fixed target stabilization during rotation and
translation in Figure 12. To duplicate
our experimental protocols, stimuli for these simulations were adjusted
to generate a similar oculomotor response (±10° sinusoidal ocular
deviations). In agreement with Figure 8, model EMC cell responses are predicted to be similar
during translation and head-stationary pursuit. During head rotation,
however, the model EMC cell exhibits larger
modulations with phases that are more closely aligned with head/eye
velocity. Hence, although EMC cells are predicted
to exhibit motor-like responses during head translation, they clearly
reflect the contribution of a sensory canal signal during head
rotation, as observed experimentally (Fig. 8, circles,
triangles). EMI cells in the model, on
the other hand, exhibit comparable gains and phases under all
conditions. Notably this was also true for many of the recorded Ei-Hi
cells (Fig. 8, inverted triangles).
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Figure 12.
Simulated EMC and EMI
cell responses in the model of Figure 10B for 0.5 Hz pursuit (A), earth-fixed target stabilization
during head translation (B), and earth-fixed
target stabilization during head rotation (C).
Target or head movement stimuli were adjusted in all cases to elicit
ocular deviations of ±10° for a vergence angle of 6.4° (as in our
experimental conditions). Assuming the convention that leftward ocular
deviations are positive, the model EMC and EMI
cell populations are both presumed to be located in the left vestibular
nucleus. Hence, EMC cells are excited for contralaterally
directed eye movements, whereas EMI cells are excited for
ipsilaterally directed ocular deviations. See previous figure legends
for abbreviations.
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In summary, despite its limited structure (i.e., lumped cell types and
unilateral representation), the predictions of the model in Figure 10
appear to be at least qualitatively consistent with our general
experimental observations under both head-fixed and earth-fixed target
stabilization conditions. Hence, we believe that our current
investigation provides support for the recent proposal that the dynamic
processing of sensory signals in the RVOR and TrVOR is achieved by
virtue of unique projection sites for canal and otolith signals onto a
shared premotor network (Green and Galiana, 1998).
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DISCUSSION |
The responses of eye movement-sensitive cell types in the rostral
vestibular nuclei that represent important premotor neurons in the RVOR
were examined during head translation with the goal of elucidating the
role that these cells play in the TrVOR. The results are in agreement
with previous eccentric rotation studies (McConville et al., 1996;
Chen-Huang and McCrea, 1999) but present new observations that have
important implications for the organization of the TrVOR. Specifically,
several distinctions in the activities of individual cell types were
identified when their rotational and translational responses were
directly compared for different visual-vestibular stimulus conditions.
First, all eye movement-sensitive vestibular neurons demonstrated
modulations during translation that were closely associated with motor
responses. This is in contrast to the case of head rotation in which
both motor-related and sensory signals are clearly evident in the
majority of eye movement-sensitive cell activities. Second, during
TrVOR suppression, type I PV/PVP and BT neurons could be distinguished
from type II PV/PVP cells and a subpopulation of E-H cells in that only the latter cell types demonstrated significant modulations in activity.
Notably, the type I PVP cell, traditionally considered the main
interneuron in the shortest latency RVOR pathways, displayed no clear
evidence of a sensory otolith signal modulation during translation.
Third, among the cells that responded during TrVOR suppression, Ec-Hc
neurons displayed dynamic characteristics distinct from those sensitive
to ipsilaterally directed eye movements (i.e., Ei-Hi and type II PV/PVP
cells). Specifically, Ec-Hc neuron responses during TrVOR suppression
were lower in sensitivity and reflected a low-pass filtering of the
sensory acceleration signal. In contrast, type II PV/PVP and Ei-Hi
cells exhibited responses with relatively flat gain characteristics and
phases between linear acceleration and velocity.
In the following sections we will attempt to interpret these results in
terms of both the current understanding of the neuroanatomy associated
with otolith-ocular versus canal-ocular pathways and the different
dynamic processing requirements for the TrVOR as compared with the RVOR.
Relationship between specific cell groups and
utriculoabducens connectivity
The classical three-neuron-arc pathways for the horizontal RVOR
involve secondary neurons in the vestibular nuclei that receive direct
primary afferent inputs from the semicircular canals and make
excitatory projections to contralateral abducens motoneurons (Richter
and Precht, 1968; Baker et al., 1969; Precht et al., 1969; Schwindt et
al., 1973). In contrast, the shortest latency excitatory
utriculoabducens pathway is a weak ipsilateral projection, whereas the
contralateral projections are at least trisynaptic and inhibitory
(Schwindt et al., 1973; Uchino et al., 1994, 1996, 1997; Imagawa et
al., 1995). Because it is known that the large majority of type I PVP
neurons make direct excitatory connections to the contralateral
abducens (McCrea et al., 1987; Scudder and Fuchs, 1992), one must
conclude that primary otolith afferents do not make monosynaptic
projections to type I PVP neurons (Fig. 13). In support of this conclusion,
none of the type I PV/PVP cells in the present study responded during
TrVOR suppression, nor did they display differences in their responses
during head-stationary pursuit versus head translation while an
earth-fixed target was viewed. Similarly, a sensory otolith signal was
not obvious in the response properties of BT neurons.
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Figure 13.
Postulated relationship between specific cell
groups and disynaptic utriculoabducens connectivity. The
vertical dashed line represents the midline. The
dashed line from Ec-Hc cells to the ipsilateral AB
represents an inhibitory projection. The question marks
illustrate postulated but undocumented weak excitatory projections from
the type II PV/PVP and Ei-Hi neurons to the ipsilateral abducens
nucleus. Polysynaptic connectivities are not included.
AB, Abducens nucleus. See previous figure legends for
other abbreviations.
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In contrast to the exclusively motor-like signals apparent in type I
PV/PVP and BT activities during translation, many type II PV/PVP and
E-H neurons may receive more direct sensory otolith inputs (Fig. 13).
Three results support this conclusion. First, a subset of type II
PV/PVP and E-H cells modulated during TrVOR suppression in the absence
of eye movements. Second, the responses of all type II PV/PVP and Ei-Hi
cells during TrVOR suppression were similar in terms of both amplitude
and phase to those described previously for the majority of central
vestibular-only otolith neurons (Angelaki and Dickman, 2000),
suggesting that they most likely represent sensory otolith signals.
Finally, the existence of direct otolith inputs onto these cells is
consistent with the ipsilateral utriculoabducens pathway (Uchino et
al., 1994). In particular, on the basis of their eye movement
sensitivities, type II PV/PVP and Ei-Hi cells would drive appropriately
directed eye movements if they were excitatory to the ipsilateral
abducens nucleus (Fig. 13, question marks) (McCrea et al.,
1987). Although such ipsilateral motor projections from these cell
types have not been confirmed, we suggest that at least a subset of
type II PV/PVP and/or Ei-Hi cells could represent the secondary
interneurons in the weak ipsilateral disynaptic utriculoabducens pathway.
There are reasons to propose that Ec-Hc cells occupy a distinct
location in the premotor pathways associated with sensorimotor transformations in the TrVOR, as compared with cells that code for
ipsilaterally directed eye movements (i.e., Ei-Hi and type II PV/PVP
cells). First, the response sensitivities of Ec-Hc cells during TrVOR
suppression were smaller than were those of eye-ipsi cells. Second,
eye-contra and eye-ipsi cells exhibited different dynamic properties
during translation. Specifically, the Ec-Hc neurons that modulated
during TrVOR suppression exhibited sensitivities relative to linear
acceleration that decreased with frequency, suggesting a low-pass
filtering of otolith signals. In contrast, eye-ipsi neuron dynamics was
relatively flat over the frequency range of 0.16-2 Hz and was similar
to that of the majority of rostrally located VO neurons (Angelaki and
Dickman, 2000). These observations and the fact that Ec-Hc cells make
inhibitory connections to the ipsilateral abducens nucleus (Scudder and
Fuchs, 1992), whereas to date only disynaptic excitatory utricular
projections to the ipsilateral abducens have been identified, suggest
that Ec-Hc cells probably receive otolith signals only indirectly
(i.e., not monosynaptically; Fig. 13).
Differences in neuroanatomical topology and processing between
TrVOR and RVOR
These conclusions have been summarized in a simple model for the
generation of the VORs (Fig. 10A). The basic
structure of the model is based on a recent proposal by Green and
Galiana (1998) that illustrated that appropriate RVOR and TrVOR
responses may be generated if canal and otolith signals project
differentially onto a shared premotor network. The structures in Figure
10 represent one realization of the hypothesis that the low-pass filter
dynamics of the eye plant rather than central filtering provides the
additional high-frequency temporal integration that is required in the
TrVOR as compared with the RVOR pathways (Green and Galiana, 1998,
1999; Musallam and Tomlinson, 1999). In the proposed model structure, otolith signals are conveyed directly to EMI
cells but only indirectly to EMC cells via the
neural filter F(s) that is shared with the RVOR
pathway. As a result, otolith information appears differentially processed relative to the sensory signal on each cell type (see simulations in Fig. 11), in agreement with our experimental
observations during TrVOR suppression (Fig. 7). Model cell predictions
are also consistent with the experimental observation that during 0.5 Hz translation while an earth-fixed target was stabilized, all eye
movement-sensitive cell types exhibited responses that were comparable
with those during head-stationary pursuit. Although our current study
focused entirely on cell responses during translation under
visual-vestibular interaction conditions, a key model prediction is
that EMC and EMI cells will
also demonstrate differential dynamic properties in the dark. Hence, an
investigation of eye movement-sensitive cell activities in the absence
of visual feedback will be important in confirming the viability of the
proposed structure.
Of particular relevance is the fact that the model of Figure 10 is not
only compatible with, but also provides a functional explanation for,
the known differences in the neuroanatomy of otolith-ocular versus
canal-ocular pathways. Specifically, the projections from PH neurons
[output of F(s)] to the contralateral abducens
in the model can account for the polysynaptic contralateral inhibitory
utriculoabducens projections (Uchino et al., 1994, 1996). The model
also remains consistent with the disynaptic ipsilateral utriculoabducens connectivity, if EMI cells make
weak excitatory projections to the ipsilateral abducens (Fig.
10A, dotted line). The dominant projection
of cell EMI is, however, proposed to be to the PH
so that otolith signals are conveyed to motor neurons mainly indirectly
via neural filter F(s) that is shared with the semicircular canal pathway.
It is important to point out that although the shortest latency
utriculo-ocular pathway is ipsilateral and does not involve the type I
PVP neurons, this does not by any means imply that the type I PVPs do
not contribute to the TrVOR (see also Chen-Huang and McCrea, 1999).
Type I PVPs and the neurons in the PH represent the main oculomotor
projections to the abducens nuclei, as compared with the much weaker
disynaptic ipsilateral utriculoabducens connections. Thus, in contrast
to the case of the RVOR in which the disynaptic three-neuron-arc
pathway is a heavy projection, the bulk of the signals to move the eyes
during translation seem to use polysynaptic (minimum trisynaptic)
pathways. Such pathways could still elicit eye movements at short
latency, ~8-12 msec, as has been shown for the TrVOR (Angelaki and
McHenry, 1999).
It should be added that, although the model of Figure 10 does not
incorporate an involvement of the cerebellar flocculus/ventral paraflocculus (FL/VPF), some of the postulated eye-ipsi and eye-contra neurons might be flocculus target neurons (FTNs) (Lisberger and Pavelko, 1988; Lisberger et al., 1994; Zhang et al., 1995). In fact, a
FL/VPF projection might account for the response reversal of many E-H
cells during translation under stable gaze and suppression conditions.
Because the main conclusions of the present study are independent of
these projections and because we did not identify our neurons as FTNs,
we have not explicitly incorporated the role of the FL/VPF in Figure
10. The model of Figure 10 also does not address other aspects of the
TrVOR properties, such as the dependence on viewing distance and gaze
direction as well as the role of the bilateral labyrinths and different
otolith afferent contributions (Schwarz et al., 1989; Paige and Tomko,
1991a,b; Schwarz and Miles, 1991; Telford et al., 1997; Angelaki et
al., 2000b,c; McHenry and Angelaki, 2000; Angelaki and Hess, 2001). A
more detailed investigation of these topics requires further studies.
In summary, our current results demonstrate that the eye-contraversive
cell types involved in the shortest latency RVOR pathways either
exhibit negligible responses during TrVOR suppression (i.e., type I
PV/PVP and approximately one-third of Ec-Hc cells) or responses that
reflect low-pass-filtered linear acceleration (i.e., the majority of
Ec-Hc cells), suggesting that these cell types receive mainly indirect
sensory otolith signals. In contrast, eye-ipsiversive cell types (the
majority of type II PV/PVP and approximately one-half of Ei-Hi cells)
exhibited on average a more robust modulation during TrVOR suppression,
with dynamics that would be consistent with otolith sensory signals.
Thus, our results provide evidence of a differential processing of
sensory information on EMC versus EMI cell types. Our current neurophysiological
observations as well as previous neuroanatomical data are consistent
with a model for the RVOR and TrVOR pathways that postulates
differential projections of canal and otolith signals onto
EMC and EMI cells,
respectively. Furthermore, although recent studies have focused on the
responses of premotor EMC cells involved in the
disynaptic RVOR pathways, here we suggest a prominent role for
EMI cells in the TrVOR. The role of these cells
is nevertheless less important in terms of their direct oculomotor
projections than in terms of their function as a conduit for otolith
signals in polysynaptic TrVOR pathways, required to ensure that canal
and otolith signals project onto a shared network at unique sites so
that sensory vestibular signals with distinct dynamic properties may be
differentially processed by a common premotor network.
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FOOTNOTES |
Received Nov. 16, 2000; revised Feb. 12, 2001; accepted March 7, 2001.
This work was supported by grants from the National Institutes of
Health (EY12814, EY10851, and DC04260) and the McDonnell Foundation
for higher brain function. We thank Quinn McHenry and Asim Haque
for valuable technical assistance, as well as Mimi Galiana and Steve
Highstein for reading previous versions of this manuscript.
Correspondence should be addressed to Dr. Dora Angelaki, Department of
Anatomy and Neurobiology, Box 8108, Washington University School of
Medicine, 660 South Euclid Avenue, St. Louis, MO 63110. E-mail:
angelaki{at}thalamus.wustl.edu.
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APPENDIX |
We have summarized here analytical descriptions of the responses
of the lumped EMC and the
EMI cell types in the model of Figure
10B under both dark and TrVOR suppression conditions.
To illustrate the model predictions, Laplace domain descriptions of the
responses of each cell type were derived from the model in Figure
10B by treating the schematic as a signal flow graph in which each model parameter represents the gain associated with a
given pathway, circles (e.g., EMC and
EMI cells) represent simple summing junctions and
boxes [e.g., F(s) and
P(s)] represent dynamic elements or
filters. A summing junction is assumed at the input of each
box such that all inputs to the filter are summed before the
filtering process is applied. Because the goal of the modeling investigation was not to replicate detailed dynamic characteristics of
behavioral and cell responses but rather to illustrate that the general
predictions of the model structure are qualitatively consistent with
our experimental observations, the following simplified representations
of the sensors and eye plant were chosen. (1) A first-order low-pass
model was used to represent the eye plant dynamics: that is,
P(s) = Kp/(Tps + 1), where Tp = 0.25 sec (Robinson, 1981). Similarly, the neural filter F(s)
represents an internal model of the eye plant such that
F(s) = Kf/(Tfs + 1), where Tp = Tf = T (Galiana and
Outerbridge, 1984). (2) Canal afferent dynamics relative to head
velocity is approximated by a first-order high-pass filter:
C(s) = Tcs/(Tcs + 1) (Fernández and Goldberg, 1971). (3) Otolith afferent
dynamics relative to head acceleration was modeled as a first-order
system with a pole at 10 Hz: O(s) = 1/(Tos + 1) (Fernández and
Goldberg, 1976c).
Model predictions regarding the sensitivity and phase of the RVOR and
TrVOR, as well as those of the EMC and PH cell
types [output of F(s)] during rotation and
translation, have been reported previously (Green and Galiana, 1998,
1999; Green, 2000). Here we focus on Laplace domain descriptions of
EMI and EMC cell responses to canal and otolith stimulation both in darkness and under VOR suppression conditions. Because the rotational responses of eye movement-sensitive neurons in a feedback realization of the RVOR have
been described previously (Galiana and Outerbridge, 1984; Green, 2000),
discussion of the analytical expressions for the model
EMC and EMI cells will
focus on the component of their activities related to otolith
stimulation during head translation.
Dark conditions
Under dark conditions the following set of equations may be
written to describe the model system:
Solution of the above system equations yields the following
expressions describing EMC and
EMI cell responses to canal and otolith
stimulation:
where dark system gain terms GxxD
and time constants TxxD are expressed
in terms of model parameters as:
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Under dark conditions, the system is characterized by a pole associated
with the time constant TD. Model
parameters (see Fig. 10 legend) were adjusted to set
TD to a large value of ~20 sec such that
the system provides an integration of vestibular signals at frequencies
above ~0.01 Hz (i.e., this pole represents the central neural
integrator). During head translation, the response of the
EMC cell reflects this pole, and hence otolith
signals on this cell type appear to have been integrated relative to
linear acceleration (Green and Galiana, 1998, 1999). The expression for the EMI cell, in addition to being characterized
by a pole associated with the neural integrator time constant
TD, also includes a zero (lead term)
associated with the time constant
ToVID = T = 0.25 sec
[notice that the expression for
EMC(s) is not characterized by such a
zero]. As a result, although the EMI cell is
expected to modulate in-phase with linear head velocity at low
frequencies, at frequencies above ~0.6 Hz the zero cancels the
effects of the pole. During high-frequency translation in the dark,
EMI cells are therefore predicted to exhibit
responses that code more closely for linear head acceleration, whereas
EMC cells are predicted at these same high
frequencies to exhibit responses closely associated with linear head velocity.
Head-fixed target-viewing conditions
Under visual feedback conditions, the dashed pathways
in the schematic of Figure 10B are active, and the
model system is now described by the equations:
Under head-fixed target-viewing conditions, there is no movement
of the target relative to the head (i.e., the target and head move in
tandem). Therefore, assuming a centrally located target such that
Tconj = 0, the terms associated with
Tconj drop out of the equations. The
equations are further simplified by imposing the condition
d1 = d2a [i.e., the strength of PH
output projections to P(s) and
F(s) are equal] that is required in the model to
ensure that RVOR dynamics is appropriate and that the output of
F(s) provides an accurate internal estimate of
eye position E* during head rotation and smooth pursuit.
After incorporation of these simplifications, the following expressions
may be written to describe EMC and
EMI cell responses under head-fixed
target-viewing conditions:
where gains GxxL and time
constants TxxL under light conditions
are expressed in terms of model parameters as:
Time constants ToVCL1 and
ToVCL2 and gain
GoVCL are obtained from the
expressions:
where a', b', and c' are written
in terms of model parameters as:
The above equations illustrate that similar, but slightly more
complex, equations also predict a differential processing of otolith
signals on EMC and EMI
cells during TrVOR suppression. Under visual feedback conditions, cell
responses are characterized by the system time constant
TL that has a small value of 0.12 sec,
reflecting the model pursuit bandwidth of ~1.3 Hz (Lisberger et al.,
1987; Barnes, 1993). EMI cell responses are again
characterized by a lead term associated with a time constant under
light conditions of ToVIL = 0.089 sec
(zero at ~1.8 Hz). Because this zero and the light system pole are
closely matched in frequency, the effect of one cancels that of the
other so that the EMI cell modulates with
sensory-like dynamics at all frequencies (see Fig. 11, dashed lines). In contrast, the response of the EMC
cell is characterized by two zeros associated with time constants
ToVCL1 = 0.078 sec and
ToVCL2 = 0.0085 sec (a negative or
left-hand plane zero at ~2 Hz and a positive or right-hand plane zero
at ~19 Hz) as well as an additional pole with time constant
T = Tf = Tp = 0.25 sec (~0.6 Hz). As a result,
because the system pole at 1.3 Hz and the zero at 2 Hz are relatively
closely matched, the effect of one primarily cancels that of the other.
However, the additional pole associated with the time constant
T = 0.25 sec that appears selectively in the expression
for EMC(s) gives rise to a falloff in
gain and an accompanying phase lag relative to linear acceleration; thus, at frequencies above ~0.6 Hz the response of the
EMC cell appears low-pass filtered relative to
the sensory otolith signal (Fig, 11, solid lines). The
positive (right-hand plane) zero only has an effect at very high
frequencies, beyond the range considered in the present study.
The above equations therefore clearly illustrate that under both dark
and TrVOR suppression conditions, EMC and
EMI cells are predicted to exhibit different
dynamic characteristics relative to the linear head acceleration signal
lin.
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TOP
ABSTRACT
INTRODUCTION
