1Neurology Department, Zürich University Hospital, CH-8091 Zürich; 2Institute of Theoretical Physics, Eidgenössisch-Technische Hochschule, CH-8093 Zürich, Switzerland; and 3Department of Ophthalmology, Sapporo Medical University, 060-8543 Sapporo, Japan
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ABSTRACT |
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Scherberger, Hansjörg, Jan-Harry Cabungcal, Klaus Hepp, Yasuo Suzuki, Dominik Straumann, and Volker Henn. Ocular Counterroll Modulates the Preferred Direction of Saccade-Related Pontine Burst Neurons in the Monkey. J. Neurophysiol. 86: 935-949, 2001. Saccade-related burst neurons in the paramedian pontine reticular formation (PPRF) of the head-restrained monkey provide a phasic velocity signal to extraocular motoneurons for the generation of rapid eye movements. In the superior colliculus (SC), which directly projects to the PPRF, the motor command for conjugate saccades with the head restrained in a roll position is represented in a reference frame in between oculocentric and space-fixed coordinates with a clear bias toward gravity. Here we studied the preferred direction of premotor burst neurons in the PPRF during static head roll to characterize their frame of reference with respect to head and eye position. In 59 neurons (short-lead, burst-tonic, and long-lead burst neurons), we found that the preferred direction of eye displacement of these neurons changed, relative to head-fixed landmarks, in the horizontal-vertical plane during static head roll. For the short-lead burst neurons and the burst-tonic group, the change was about one-fourth of the amount of ocular counterroll (OCR) and significantly different from a head-centered representation. In the long-lead burst neurons, the rotation of the preferred direction showed a larger trend of about one-half of OCR. During microelectrical stimulation of the PPRF (9 sites in 2 monkeys), the elicited eye movements rotated with about one-half the amount of OCR. In a simple pulley model of the oculomotor plant, the noncraniocentric reference frame of the PPRF output neurons could be reproduced for recently measured pulley positions, if the pulleys were assumed to rotate as a function of OCR with a gain of 0.5. We conclude that the saccadic displacement signal is transformed from a representation in the SC with a clear bias to gravity to a representation in the PPRF that is closely craniocentric, but rotates with OCR, consistent with current concepts of the oculomotor plant.
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INTRODUCTION |
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Premotor saccadic burst
neurons provide a velocity signal for the extra-ocular motoneurons to
generate rapid eye movements in the head-restrained monkey
(Büttner-Ennever and Henn 1976; Fuchs and
Luschei 1970
; Henn and Cohen 1976
). In the brain
stem, burst neurons of the paramedian pontine reticular formation
(PPRF) code for horizontal components of eye movements (Cohen et
al. 1968
; Hepp and Henn 1983
; Keller
1974
; Luschei and Fuchs 1972
; Robinson
1970
), while neural coding of vertical and torsional eye
movement components has been demonstrated in the rostral interstitial nucleus of the medial longitudinal fasciculus (riMLF)
(Büttner et al. 1977
; Büttner-Ennever
and Büttner 1978
; King and Fuchs 1979
;
Vilis et al. 1989
). For saccade generation, the PPRF
receives a major direct input from the superior colliculus (SC), where saccade-related burst neurons represent eye displacements in a two-dimensional motor map (Mays and Sparks 1980
;
Raybourn and Keller 1977
; Robinson 1972
;
Van Opstal et al. 1991
; for a review see Sparks
1999
).
Recently, it was shown that the preferred direction of saccade-related
burst neurons in the SC is modulated by head roll with respect to
gravity (Frens et al. 1998). The preferred direction, defined individually for each neuron as the unique saccade direction associated with the most vigorous burst activity, stayed in the horizontal-vertical plane and rotated within that plane by an angle
that exceeded the amount of ocular counterroll (OCR). It was concluded
that SC burst neurons code the saccade vector in an intermediate
reference frame that, although closely oculocentric, has a clear bias
to gravity. In this study, we posed the same question for the saccadic
premotor burst neurons in the PPRF: we asked whether the preferred
direction of the three different types of presaccadic burst neurons,
i.e., short-lead burst neurons (SBN), burst-tonic neurons (BTN), and
long-lead burst neurons (LBN), (see, e.g., Hepp and Henn
1983
), vary under head roll, and if so, in what reference frame
they operate.
The exact mathematical relation between the horizontal-vertical
direction of gaze and the amount of ocular torsion with the head
stationary was first given by J. B. Listing (Helmholtz
1867; Ruete 1855
). Any eye position, if
described by a single rotation from primary position, lies in a plane
that is perpendicular to the direction of gaze in primary position.
This plane is called Listing's plane, and the corresponding
coordinates of eye positions having their origin in primary position we
will name Listing's coordinates. This law, Listing's law, holds true
not only for eye positions during static fixations, but also, to a good
approximation, during smooth pursuit and saccadic eye movements
(Ferman et al. 1987
; Haslwanter et al.
1991
; Straumann et al. 1996
; Tweed and Vilis 1990
). When the head is statically rolled, the amount of eye torsion varies due to OCR. OCR is a static vestibuloocular reflex
elicited by otolith input with a gain of about 0.1-0.2, good
stability, and no habituation (Haslwanter et al. 1992
;
Suzuki et al. 1997
). In Listing's coordinates, observed
three-dimensional eye positions are particularly simple to describe:
eye torsion is constant for each static head roll position (see, e.g.,
Hepp et al. 1997
).
The actual axis around which the eye rotates during a saccade is not
identical with the axis of the eye displacement (which is confined in
Listing's plane), but is tilted, for geometrical reasons, out of
Listing's plane by half the amount of the eye position's eccentricity
according to the so-called "half-angle rule" (Tweed and
Vilis 1990). This difference between the eye position
displacement (displacement vector, d-vector) and the actual eye
rotation (rotation vector, r-vector) touches the heart of the coding
problem. The question arose, whether the premotor burst neurons encode
the actual three-dimensional eye rotation, as predicted by a
mathematically correct extension of the earlier one-dimensional
Robinson (1975)
model (Tweed and Vilis
1987
), or whether a commutative signal is encoded instead, like
the eye position displacement (Crawford 1994
;
Schnabolk and Raphan 1994
), which would render the eye
velocity-to-position integration, for instance, particularly simple. As
an important consequence, an eye displacement (d-vector) coding scheme
of the premotor burst neurons would imply that Listing's law is
implemented downstream, e.g., at the level of the motoneurons or the
oculomotor plant, while an eye rotation (r-vector) scheme would require
Listing's law to be implemented upstream to the burst neurons.
In our lab, a recent study has found that the neural saccade activity
in reticular burst neurons correlates better with the three-dimensional
eye displacement (d-vector) than with the (also 3-dimensional) eye
rotation (r-vector) coding scheme (Hepp et al. 1999). In
this paper, we will consider both coding schemes as possible
alternatives for the formulation of our hypotheses and the discussion
of our results. For consistent description of our experimental results,
however, we will express saccadic eye movements in terms of eye
displacement (d-vector) only, and with respect to a head-centered
reference frame (Fig. 1A).
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For each coding scheme assumption, two anatomically different frames of reference can be considered (Fig. 1B). Let us first assume that the premotor burst neurons encode in an eye displacement scheme:
I. If the displacement coding is in a craniocentric reference frame, the preferred direction of eye displacement (d-vector) remains invariant under head roll. Figure 1B, I, illustrates this case for a hypothetical neuron with a leftward preferred direction. For all head roll positions, the d-vector (white upward arrow) points upward with respect to the head.
II. If the preferred direction of eye displacement stays invariant relative to the eye orientation (and therefore to a target on the retina), the frame of reference for eye displacement is oculocentric and deviates from the head-fixed reference frame by the amount of OCR (see Fig. 1B, II). The illustrated preferred direction of the hypothetical neuron (upward white d-vector) is not invariant with respect to the head, but follows OCR (as indicated by the dotted coordinate frame).
We introduce a rotation coefficient c to quantify the amount of rotation of the preferred direction (in eye displacement) with respect to OCR. Then, c = 0 indicates the craniocentric (I), and c = 1 the oculocentric reference frame hypothesis (II).
The actual eye rotation (r-) vector deviates from the eye displacement
(d-) vector by half the amount of OCR because of the nonzero torsion of
eye positions during OCR (half-angle rule) (Tweed and Vilis
1990). Consequently, a craniocentric coding scheme of eye
displacement does not coincide with a craniocentric scheme of eye
rotation or of gaze shift (Haustein 1989
), and vice
versa. For example, if the eye rotation (r-) vector is assumed to be head-fixed (Fig. 1B, III), the corresponding displacement
(d-) vector rotates with OCR with a gain of
0.5. Therefore the
rotation vector coding assumption leads to two different hypotheses.
III. If the coding of the rotation vector is in a craniocentric reference frame, the preferred direction of eye rotation (or of gaze shift) remains invariant under head roll. This is illustrated in Fig. 1B, III, where the r-vector (black arrow) indicates the leftward preferred direction of a hypothetical cell. The r-vector remains upright with respect to the head for all roll positions. The d-vector (white arrow), in contrast, is not head-fixed.
IV. Finally, if the preferred direction of eye rotation (or of gaze shift) stays invariant relative to the eye orientation, the coding is in an oculocentric frame of reference. The r-vector (black arrow) of a hypothetical premotor burst neuron deviates from the head-fixed system by the amount of OCR (Fig. 1B, IV).
Since a gaze shift is always perpendicular to the horizontal-vertical
component of the eye rotation vector, hypotheses III and IV are
equivalent to the assumption of a cranicentric or oculocentric representation of gaze. And since the d-vector deviates from the r-vector by half OCR, the rotation coefficient c (defined
for eye displacement) is 0.5 for the craniocentric (III) and +0.5 for
the oculocentric (IV) rotation vector assumption (Fig. 1B, III and IV).
In general, rotation vectors (r-vectors) describing saccadic eye movements have a nonzero torsional component that depends on the horizontal-vertical eye position at saccade onset (following the half-angle rule). This torsional component of the rotation vector will be ignored for the purpose of this study, since we are only concerned with changes of the r-vector projection in the horizontal-vertical plane.
In four rhesus monkeys, we recorded extracellular single-unit activity
and stimulated electrically in the PPRF, while the static head roll
position of the animals was varied using a three-dimensional turntable.
We found that all three considered PPRF burst neuron classes (SBN, BTN,
and LBN) had a preferred direction of eye displacement that was closely
craniocentric, but changed significantly with OCR with about one-fourth
to one-half of the amount of OCR. To explain this deviation of the PPRF
neurons from a simple craniocentric representation, we simulated the
effect of OCR on the muscle pulling direction in a simplified
three-dimensional geometric model of the oculomotor plant. Part of this
study has been presented in abstract form (Scherberger et al.
1998a,b
).
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METHODS |
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Subjects
Four rhesus monkeys (Macacca mulatta: Cr, De,
Sa, and Ta) were prepared for extracellular single-unit
recording and microstimulation. Surgical procedures were applied as
described elsewhere in more detail (Suzuki et al. 1999).
In short, anesthesia was initiated with Ketamine and pentobarbital
sodium. Animals were intubated and breathed a mixture of
O2 and N2O, and
supplemented with Halothane when required. Head bolts were chronically
implanted for stable head fixation. A custom-made dual search coil was
chronically implanted on one eye (Hess 1990
). Finally, a
recording chamber was placed on the surface of a trephine hole in the
skull that was stereotaxically located on top of the PPRF region.
During the course of the experiment, the monkeys were head-restrained,
such that in an upright position the horizontal stereotaxic plane of
the head was pitched nose-down 15° with respect to the earth-horizontal plane. This placed the response plane of the horizontal semicircular canals orthogonal to the gravity vector (Böhmer et al. 1985).
Procedures and animal care were in accordance with the guidelines set
by the Veterinary Office of the Canton of Zurich and the Guide
for the Care and Use of Laboratory Animals (National Academy of Sciences 1996).
Setup
Awake monkeys were seated in a three-dimensional turntable that
could be moved in various roll positions by computer control (Henn et al. 1992). The seat was arranged such that the
center of the interaural line of the monkey's head was located at the intersection of the three chair rotation axes.
We recorded three-dimensional eye position with the dual search-coil
technique, consisting of a large directional coil and a smaller,
secondary coil for the measurement of eye torsion rigidly attached
together and sealed (Hess 1990). A coil frame (31 cm diam) with two alternating magnetic fields in spatial and phase quadrature (Skalar Instruments, Delft, The Netherlands) was centered on
the monkey's interpupillary line. The monkeys were trained to fixate
targets (Wurtz 1969
), which were used for the
calibration of the eye position signal at the beginning of each
experimental session (Hess et al. 1992
).
For single-unit recording and electrical microstimulation in the PPRF,
we used varnished tungsten microelectrodes, custom-made or commercial
(FHC), with an impedance of 1.5-2 M at 1 kHz. We recorded from
saccade-related burst neurons, i.e., neurons presenting a short,
transient burst prior to and during saccadic eye movements. Neurons
were classified off-line as described below. To detect single-unit
spikes, the amplified and band-filtered signals (0.5-10 kHz) were sent
through a threshold discriminator, whose operation was constantly
monitored on an oscilloscope. Detected spikes were electronically
converted into an analog staircase signal, such that each spike was
represented by a single step. This analog signal as well as the eye and
the turntable position signals were then recorded at a sample rate of
833 Hz.
For electrical stimulation, 0.2-ms negative rectangular pulses at 500 Hz were repeated every 2 s in trains of 70 ms duration. Stimulation currents were well above threshold (20-100 µA) and typically in the order of 50 µA. At each site, stimulation intensity was kept constant for the entire testing in all roll positions.
Experimental protocol
Single-unit recording and electrical microstimulation in the PPRF was performed while monkeys made spontaneous eye movements in the light. The animals were motivated to perform saccades throughout the oculomotor range by presenting natural visual and auditory stimuli in the visual field, e.g., fruits, or movements of the experimenter. During each experiment, the animal was rotated from the upright to left-ear-down (LED) and right-ear-down (RED) static roll positions, typically up to 60° (40-90°) to either side.
Anatomical localization
The following oculomotor landmarks were electrophysiologically localized: SC was found below the fourth ventricle by identifying ocular motor burst units with activity for contralateral saccades and its typical topographic map. The trochlear nucleus was identified about 5 mm ventral to the SC where neurons showed eye-position-dependent tonic activity maximal for downward and intorsional eye positions. The abducens nucleus was localized about 10-12 mm ventral to the SC where neurons had burst-and-tonic activity with the preferred direction ipsilateral horizontal. The PPRF was localized rostral and dorsal to the abducens nucleus with a rostral extension of about 3 mm. SBN, BTN, and LBN were found intermingled in the PPRF.
After termination of the experiments, the monkeys were given an overdose of pentobarbital and perfused (paraformaldehyde 4%). One to 3 wk prior to perfusion, a chemical lesion (kainic acid) was set in the brain stem of three of the animals (Cr, Sa, and Ta) as part of a lesion experiment. Histological anatomy of the brain stem (Nissl and Golgi staining) identified lesion sites and recording tracks and was in agreement with the in vivo coordinates of the anatomical structures in all cases.
Data analysis
OCULAR COUNTERROLL.
When the head is stationary in space, three-dimensional eye positions
during fixation and saccades are confined to a Listing's plane (LP)
that is defined by a constant amount of eye torsion. Static head roll
shifts this plane along the torsional axis of the coordinate system
normal to LP (Haslwanter et al. 1992). OCR was
quantified by the amount of this torsional shift (Fig.
2). The angle between this eye torsional
axis and the head roll axis was small (<15°), hence head roll
stimulation was approximately orthogonal to LP.
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SACCADE CHARACTERISTICS. On- and offsets of saccadic eye movements were automatically marked in the calibrated eye position signal on the basis of a velocity and acceleration criterion (software Megadet, Paul Hofman, Nijmegen, The Netherlands). All markings were visually confirmed and corrected if necessary (e.g., to eliminate blinks). For saccades evoked by microstimulation, care was taken to discard movements elicited closely before, during, or after spontaneous saccades.
For each saccade we defined the horizontal and vertical eye displacement (d-vector) as the difference between the eye position off- and onset, dH := HoffNEURON ACTIVITY.
Among the burst units in the PPRF, we distinguished short-lead burst
neurons (SBN), burst-tonic neurons (BTN), and long-lead burst neurons
(LBN) according to their firing pattern (Hepp and Henn
1983). All neurons showed a high-frequency burst activity prior
to and during a saccade in the cell's preferred direction (mean firing
rate for a 20° saccade typically about 400 Hz, always exceeding 200 Hz). In addition, BTN showed a tonic discharge rate during fixation
periods that was eye-position dependent. We classified the three
neuronal groups according to the time lead of the neuronal burst before
saccade onset and the tonic firing rate during fixation. For this
purpose, we examined the peri-saccadic spike density histogram (aligned
to movement onset) of saccades not deviating more than 45° from the
neuron's preferred direction (see PREFERRED DIRECTION
below), and defined the beginning of the neuronal burst as the
time when the cell's firing rate first exceeded one-third of its
maximal burst activity, t1/3.
Following Hepp and Henn (1983)
, burst onset time was
then compared with the saccade onset time, ton. A unit was considered as a LBN if
the beginning of the burst led the saccade onset by more than 12 ms
(ton
t1/3 > 12 ms). Otherwise the unit was
considered to be either a SBN or BTN.
preferred direction.
For all selected saccades in a given static head roll position, we
related the number of discharged spikes in a burst, n, to
the horizontal and vertical saccade displacement component, dH and
dV, with a piecewise linear model and,
independently, also with a quadratic model (see RESULTS).
In both cases the cell's preferred direction for each head roll
position was determined from the parameters of the least-square
optimized fit (Matlab procedure: leastsq). The overall fit quality was
expressed by the coefficient of determination,
r2 = 1 [
(n
)2/
n2], with n the measured
and
the predicted number of spikes (Sachs 1984
). The statistical reliability of this measure was tested using the bootstrap procedure (Efron and Tibshirani
1993
), which generated a probability distribution and an
estimate of the variance of r2 by
re-sampling the data 100 times. The preferred direction at a given head
roll position was only further analyzed, if the underlying quadratic or
piecewise linear fit was statistically reliable
(r2 > 0.64 with P < 10
3).
Rotation coefficient.
For neurons with reliable fits in at least three different static head
positions, a rotation coefficient c was calculated as the
ratio of the change of the preferred direction to OCR over all
considered head positions (see RESULTS). The significance of this rotation coefficient was tested by bootstrap: re-sampling the
data 100 times gave the probability distribution of the rotation coefficient c, which was considered significantly different
from 0, if the mean of the distribution exceeded twice its standard deviation. The best-fit value of the whole sample was then taken as the
final estimate of c. At the population level, the rotation coefficients in the three neural groups were checked against difference from 0 or 1 using t-tests.
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RESULTS |
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Effect of static head roll
As expected, static head roll produced OCR, which we measured as the shift of Listing's plane along the torsional axis (Fig. 2). For any given head roll position, the eye torsion was approximately constant during saccades as well as during fixation periods. The standard deviation of the residual error of the linear fit was typically <1°. The ocular motor range was somewhat larger in the horizontal than the vertical component and exceeded 50 × 40°. This range was sufficiently large for a good estimate of LP and provided a variety of different saccade start- and endpoint locations.
Single-unit recordings
In four monkeys (Cr, De, Sa, and Ta), we
recorded a total number of 82 saccade-related burst neurons while the
static head roll was varied. In 59 of those neurons, the preferred
direction could be determined with high significance
(r2 > 0.64 with P < 103) in at least 3 head roll positions (LED, upright, and RED; range at least 60°) in
both a piecewise linear (PL-) and a quadratic (Q-) model fit (see
PIECEWISE LINEAR MODEL and QUADRATIC MODEL below). Only these neurons were further considered. According to our classification scheme, they split up in 31 SBN, 17 BTN, and 11 LBN (Table 1).
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The preferred direction of these units was mainly ipsilateral horizontal (left- or rightward), but occasionally also vertical (3 units: up; 1 unit: down) or oblique (1 unit: 35° right-up). Head roll typically caused a change of the preferred direction in the direction of OCR. Figure 3 illustrates the change of the preferred direction, in head coordinates, in two PPRF neurons with the head 60° LED, upright, and 60° RED. Circles represent individual saccades with their position on the panel indicating the horizontal and vertical saccade displacement and their diameter proportional to the number of spikes of the burst. For a quantitative description of the preferred direction (arrows), we related the number of spikes during the saccadic burst, n, with the saccade displacement vector, (dH, dV), using both a piecewise linear and a quadratic model.
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PIECEWISE LINEAR MODEL.
In the piecewise linear (PL-) model, the number of spikes,
n, was linearly related to the eye displacement vector,
(dH,
dV) and constrained by a lower limit,
n0, to prevent negative spike number
predictions
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QUADRATIC MODEL.
Since these significant deviations of the preferred direction from a
craniocentric reference frame were small, we analyzed the data also
with a second, independent method. In the quadratic (Q-) model, we
assumed a quadratic relationship between the component of the
horizontal and vertical saccade displacement and the number of spikes
of the sacadic burst
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ROTATION (R-) VECTOR ANALYSIS.
We also checked the PL-model with respect to the saccade rotation (r-)
vector. Here, the number of spikes during a saccadic burst,
n, was correlated to the horizontal and vertical component of the eye rotation vector, (rH,
rV)
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Microstimulation
In addition to single-unit recordings, we electrically stimulated the PPRF in two monkeys (De and Sa) at a total of 12 sites from which we had previously recorded. Immediately before stimulation, the presence of either single-unit signals or, as a minimum, saccade-related background activity was established. Electrical stimulation elicited ipsilateral horizontal eye movements in 9 of 12 sites (7 leftward, 2 rightward; see Table 2). The stimulation direction of the three other sites was oblique (40° right-up and twice 32° left-down from horizontal). Stimulation sites with oblique saccades were excluded from further analysis, since they most likely involved the stimulation of additional oculomotor structures, e.g., bypassing axons, and not just PPRF burst neurons, whose preferred direction are predominantly horizontal.
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To quantify the effects of stimulation, we determined the stimulation
direction, stim, as the mean displacement
direction of all elicited eye movements and defined, similar to the
analysis of the neural recordings, a rotation coefficient
cstim: =
stim/
OCR as the regression slope of the
stimulation direction with OCR (Table 2, last column). The changes of
the stimulation direction with head roll,
cstim, had a mean of 0.62 and a
standard deviation of 0.58 over the 9 sites (Fig. 7). The mean was
significantly different from the craniocentric (t-test,
P < 0.05), but not from the oculocentric hypothesis in the
eye displacement coding scheme (P = 0.09).
Individually, 8 sites had a significantly positive and one site a
significantly negative rotation coefficient.
The neural recording as well as the stimulation data provided evidence for co-variation of the preferred eye movement direction with OCR. This was true under the saccade displacement and even more so under the rotation coding assumption (Fig. 7). To better understand this deviation from a craniocentric representation in the premotor burst neurons, we simulated the effect of OCR on the pulling direction of horizontal extraocular eye muscles in a geometrical model of the oculomotor plant.
Oculomotor plant model
The pulling direction of extraocular eye muscles is restricted by
connective tissue fibers (so-called pulleys) in the orbit (Demer
et al. 1995, 2000
; Miller and Robins
1987
). The effect of muscle pulleys on the muscle pulling
directions (or "muscle moments") depends on their orbital position
and in particular on their relative location along the muscle path. OCR
modifies the effective pulling direction since it changes the effective muscle path from the pulley to the muscle insertion on the globe. To
demonstrate this effect, we simulated the pulling direction of
individual horizontal eye muscles [medial rectus (MR) and lateral rectus (LR) muscle] in a simplified pulley model of the oculomotor plant with the eye straight-ahead. We studied both the assumption of
1) orbit-fixed pulleys and 2) of pulleys that
rotate, to some extent, with OCR along the torsional axis.
Three-dimensional locations of the eye muscle origin and insertion
points were taken from anatomical measurements in the monkey (see
Suzuki et al. 1999). Pulley positions were assumed along the muscle path with the eye straight-ahead and parameterized by
relative muscle length (0: pulley position at the origin; 1: pulley at
insertion). The effective pulling direction of the muscle and its
projection on the horizontal-vertical plane,
m, was then computed from the
three-dimensional pulley and insertion position for any given OCR (see
APPENDIX for further specifications).
ORBIT-FIXED PULLEYS.
Under the assumption of an orbit-fixed pulley (1), the
muscle moment changed with OCR, since OCR rotated the muscle insertion position in the orbit. The ratio
cm :=
m/
OCR (m = MR, LR), which we call the rotation coefficient of the muscle, was therefore not
zero in general. With no pulley (or with the pulley at the origin), the
simulation showed a change of the muscle pulling direction close to the
amount of OCR (cm
1; Fig.
9A). If the pulley was located
further distal, i.e., closer to the muscle insertion, the rotation
coefficient decreased: cm < 1.
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CO-ROTATING PULLEYS.
The assumption of pulleys fixed in the orbit is not strictly valid.
Demer et al. (2000) have demonstrated that extraocular eye muscle pulleys change their orbital position in the
anterior-posterior direction as a function of the horizontal and
vertical eye position, and hence are not completely fixed in the orbit.
A torsional change in orbital pulley position during OCR has not been
demonstrated, but cannot be excluded on the basis of orbital gross
anatomy. The pulleys are embedded in a ring of connective tissue
fibers, and the fascia of the vertical rectus muscles are in contact
with the muscle fascia of the oblique eye muscles that control OCR. We
therefore evaluated our plant model in addition under the assumption that the pulleys co-rotate with OCR.
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DISCUSSION |
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We asked the question in which reference frame presaccadic PPRF burst neurons use to encode rapid eye movements. For each of two coding scheme assumptions currently in discussion (the eye displacement vector scheme, where a saccade is encoded by the displacement of eye position, and the eye rotation vector scheme, where the actual eye rotation is encoded), we considered two possible anatomical frames of reference; a "craniocentric frame of reference," where the neuronal activity remains invariant under head roll (I and III), and an "oculocentric frame of reference," where the activity stays invariant to the eye orientation (II and IV; Fig. 1).
The torsional eye position, or OCR, remained constant for a given
static head roll position (Fig. 2) as reported in previous studies
(Haslwanter et al. 1992; Suzuki et al.
1997
). Consequently, eye positions during spontaneous eye
movements in the light were confined, in good approximation, to a
two-dimensional horizontal-vertical plane, (the shifted) Listing's
plane, for any static head position.
From single-unit recordings and electrical stimulation experiments, we found that single neurons as well as populations of PPRF neurons reorient their preferred direction with respect to the head (Fig. 3). The change in the output cells (SBN) was about 25% of the amount of OCR (Fig. 7). Hence, the data were close to the craniocentric reference frame in the eye displacement scheme (I); however, there was a consistent shift in the direction of OCR. Since this deviation from the craniocentric hypothesis was rather small, the question of measurement precision became particularly important. Therefore we measured the preferred direction for each neuron in many different roll positions (3-13; see Table 1) and analyzed the data in two independent ways, using a piecewise linear and a quadratic model (Figs. 4-7). For each model, a different definition of the neuron's preferred direction was chosen, but the resulting change of preferred direction with OCR was essentially the same (Figs. 7 and 8).
During electrical stimulation, the mean rotation coefficient through all sites roughly matched the mean value of the LBN (Fig. 7). The stimulation effect was not closely correlated with the rotation coefficients of the neurons recorded in the neighborhood of the stimulation site. A reason for the difference between the stimulation data and the single-unit results might be that electrical stimulation activates LBN, SBN, and BTN simultaneously due to their intermingled distribution in the PPRF. In addition, electrical stimulation could easily activate other eye-movement-related structures, like bypassing axons, and hereby lead to effects difficult to interpret. This is more likely in the PPRF than in the SC. The particular high standard deviation of the stimulation direction at some stimulation sites (see Table 2) might be due to such co-stimulation (excluding these sites did not alter our results). Bearing these differences in mind, it is still noteworthy that the electrical stimulation results were, like the single-unit data and unlike the SC results, in-between the craniocentric and oculocentric representation for eye displacement (Fig. 7).
We focused our analysis on the dependence of the preferred direction of
PPRF neurons on eye torsion. The question, whether the preferred
direction of PPRF neurons depends on the horizontal and vertical eye
position is also of interest, as suggested by a recent model of
visuo-motor transformation (Crawford and Guitton 1997).
We were unable to detect a significant dependence of the (2-D)
preferred direction from the horizontal or vertical eye position,
neither for the eye displacement (d-) nor the eye rotation code
(r-vector). However, such subtle changes as predicted by these models
are difficult to detect for small- and medium-sized saccades.
The goodness-of-fit for the d- and the r-vector analysis was very
similar, as expected for this two-dimensional analysis, and the
rotation coefficient of the PPRF output cells (SBN) was right in
between the craniocentric eye displacement (I) and the oculocentric eye
rotation (IV) hypothesis (c = 0.25, Fig. 7). All of the
above did not provide additional evidence in favor of either the eye
displacement or the eye rotation coding scheme assumption. However, the
question of the appropriate coding scheme of saccades in premotor burst
neurons is of central importance for a more complete understanding of
the brain stem saccade generator and the visuo-motor signal
transformation process in general (Crawford and Guitton
1997; Quaia et al. 1999
; Tweed
1997
) and will be addressed in an upcoming three-dimensional
study of premotor saccadic burst neurons (Hepp et al.
1999
).
Klier and Crawford (1998) studied the question whether
eye torsion (OCR) leads to inaccurate saccades. They showed that the human oculomotor system compensates eye position effects under visual
feedback, but saccade traces toward visual targets during OCR were
initially misdirected and changed course toward the target only later
during the movement. In our data set of spontaneous eye movements in
the light (with saccade amplitudes not exceeding 20°), targets were
not presented explicitly, and hence the question of target accuracy
could not be addressed directly. However, saccade trajectories were
essentially straight, and we did not observe an increased number of
corrective saccades in the presence of OCR, which both could indicate a
decrease in saccade accuracy. On the other hand, their finding that the
torsional position compensation was not complete for saccades from OCR
positions does correspond rather well with our finding that the burst
neuron signals are not quite in head-fixed coordinates. One possible
explanation for both effects might be that the oculomotor system is not
optimally calibrated for saccades made in torsional eye positions.
Possible mechanisms
Presaccadic burst regions (PPRF and riMLF) receive input
directly and indirectly from cortical areas (frontal eye field, lateral intraparietal cortex) as well as from subcortical structures including SC (for a review see Hepp et al. 1989). In the SC, the
eye displacement command is encoded in an intermediate coordinate frame
that is neither cranio- nor oculocentric, but has a strong bias to
gravity (Fig. 7) (Frens et al. 1998
). The nature of this
coding scheme is not resolved. One possible explanation is that the
cortical visual input to the SC is also biased toward gravity, as
recently suggested (Sauvan 1998
; Sauvan and
Peterhans 1995
). Such an interpretation would predict a
corresponding shift in the tuning curves of cortical oculomotor areas,
like the lateral intraparietal area (LIP) and the frontal eye fields
(FEFs). In any case, the signal in the SC seems to represent neither
pure retinal nor oculomotor error, which might reflect its imminent
role in gaze control under head-free conditions (Sparks
1999
).
The saccadic signal transforms from the SC to the PPRF to an almost
craniocentric representation. For this transformation, a gravity or
torsional-eye-position input signal is required at the level of the
PPRF or upstream to it. It could originate, among other sources,
directly from the otoliths, indirectly from the cerebellum, or from the
brain stem neural integrator, which itself receives otolith input.
Evidence for the presence of a more direct otolith signal is the
finding that the preferred direction of PPRF burst neurons have
considerable torsional components during dynamic roll
stimulation, e.g., during sinusoidal body oscillations about a head
sagittal (naso-occipital) axis (Hepp et al. 1999). Both
the neural integrator of the brain stem and the cerebellum, however,
contain information on the current amount of eye torsion, which is
sufficient for the required coordinate transformation (Crawford
and Vilis 1999
; Quaia et al. 1999
).
The finding that the LBN rotate stronger with OCR than the SBN (even
though the difference is not statistically significant in our sample)
goes in line with the view that LBN play an intermediate role between
the SC and the SBN (Keller et al. 2000). Apart from the
SBN, which project monosynaptically to the motoneurons
(Büttner-Ennever and Henn 1976
), we recorded from
phasic BTN in the medial (or periMLF) PPRF, which are putative
floccular projection neurons and do not directly connect to the
motoneurons (Horn et al. 1999
). For this reason, we
analyzed SBN and BTN separately, but found their frame of reference to
be the same.
We also investigated the preferred direction of burst neurons in the
riMLF (see Hepp et al. 1999). Even though the
preferred direction of the riMLF burst neurons seemed to rotate with
OCR in the horizontal-vertical plane, this rotation was difficult to
interpret because of the large torsional components of the riMLF burst
neurons. Therefore, in this study, we focused on saccade-related burst
neurons in the PPRF, which contained less torsional activity.
Influence of the oculomotor plant
The significant deviation of the SBN from a craniocentric
reference frame could reflect properties of the oculomotor plant. To
test this hypothesis, we simulated the change of the muscle pulling
direction (in the horizontal-vertical plane) during OCR (Fig. 9). The
model revealed that the rotation coefficient of the SBN group could be
matched with the rotation coefficients of the horizontal eye muscles
for eye muscle pulley locations, consistent with anatomical
measurements (Demer et al. 2000) and theoretical studies
(Quaia and Optican 1998
; Raphan 1998
), if the additional assumption was made that the pulleys are not fixed in
the orbit but rotate with OCR to some degree (50% in our simulation). It is therefore possible that the small deviation from a craniocentric reference frame in the neural representation of the output layer of the
PPRF (SBN) corresponds to the change of the pulling direction of the
horizontal eye muscles with OCR.
Precise pulley locations and the amount of pulley stiffness are not
well established, in neither monkey nor man. For this reason, we kept
our model as simple as possible and restricted it to the straight-ahead
eye position. The assumption that the pulleys rotate with OCR in the
orbit is, to our knowledge, not yet experimentally supported. Such an
effect is certainly possible on the basis of the anatomy of the
connective tissue ring in the orbit and its close relationship to the
oblique eye muscles. Also, it has recently been shown (Demer et
al. 2000) that rectus muscle pulleys change their orbital
(anterior-posterior) position when the eye is moved in the horizontal
or vertical direction.
The pulley effects of the vertical muscles (superior and inferior rectus) are also important for oculomotor plant kinematics. Simulations for the vertical rectus muscles with our model revealed very similar results as for the MR. However, as we present no corresponding neural data here, they are not shown.
Since rectus muscle motoneurons actually drive the eye muscles, their
preferred directions are expected to closely reflect the effective
muscle moments (Suzuki et al. 1999). It is unclear, however, whether motoneurons also show a change of preferred direction under OCR similar to the burst neurons in the PPRF. Studying the preferred direction of extraocular motoneurons under OCR would be of
considerable interest, although it seems technically quite challenging
to record from motoneurons in different static roll positions for a
prolonged period of time. So far, it remains open whether output
neurons of the PPRF share the same reference frame as the motoneurons
and the oculomotor plant, or whether an additional coordinate
transformation is present at the level of the motoneurons.
We conclude that saccadic eye movement commands, which are encoded in a representation in the SC in between an oculocentric and head-fixed representation, are transformed to a representation in the PPRF that is closely craniocentric. The small but significant modulation of the preferred direction with OCR could reflect, either fully or in part, the modulation of the horizontal eye muscle pulling direction with OCR.
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APPENDIX |
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Specification of the geometric plant model
Suzuki et al. (1999, their Tables 1 and 2)
reported three-dimensional positions of the origins and insertions of
all six extraocular eye muscles of four monkey eyes, together with an
average of these measurements in an idealized right eye. Following
their method of anatomical description, we centered a stereotaxic
coordinate frame (x, y, z) in the middle of the globe of an
idealized right eye. Hereby, the x-axis was pointing forward
and the y-axis horizontally leftward in Reid's plane, while
the z-axis was normal to Reid's plane and pointing upward.
The previously reported coordinates were assigned to the matrix
variables origin and insertion in the following
Matlab code (see function get_phi below).
We assumed in our model that the eye globe is spherical and that the
eye muscles follow geodesic paths from the origin to a muscle pulley,
from there to a tangential point on the globe (if the pulley is not on
the globe), and from there along the surface of the globe to its
insertion point. A pulley was assumed to control the path of each
horizontal eye muscle, and its position set on the geodesic muscle path
with the eye straight ahead. The pulley position was quantified as the
relative path length along the muscle starting from the origin by a
parameter
[0, 1]. Hence,
= 0 located the pulley at
the origin,
= 0.5 along the muscle path halfway between origin
and insertion, and
= 1 at the insertion point. In our first
set of simulations (1), the pulleys were presumed to be
fixed in the orbit. In contrast, in the second set (2) the
pulleys were presumed to co-rotate with OCR along the x-axis
with a fixed gain k (0
k
1).
The effective muscle pulling direction for any given eye position
followed a geodesic path from the pulley (stable in the orbit for any
given amount of OCR) to the insertion point (fixed on the globe). The
direction of the three-dimensional muscle moment was described as the
unit-vector (ux,
uy, uz) that is normal
to the plane spanned by the muscle pulley, the muscle insertion, and
the center of the globe (and its vector orientation following the right
hand rule). Finally, the pulling direction in the horizontal-vertical plane was expressed as the angle m = arctan
(uz/uy) for
m = MR, LR.
The Matlab function get_phi computes
m for the eye looking straight ahead and in
various amounts of OCR. For each of the horizontal eye muscles
m (and a fixed pulley position
and gain k),
we defined a rotation coefficient cm
:=
m/
OCR as the regression of
m against OCR (varying ±10°). This was
implemented in the function rot_coef (see below). For the
pulleys fixed in the orbit (1), the gain was set to
k = 0, while we demonstrated the case of co-rotating
pulleys (2) with a gain of k = 0.5.
Matlab code
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ACKNOWLEDGMENTS |
---|
We thank B. Hess for helpful discussions and administrative support, P. Hofman for providing the saccade-detection program Megadet, and B. Disler, S. Elsässer, V. Furrer-Isoviita, and R. Stocker for excellent technical assistance. We also thank J. Büttner-Ennever and A. Horn for histological verification of the recording and stimulation sites, and two anonymous referees for excellent comments that greatly improved the manuscript.
This work was supported by the Swiss National Foundation, Esprit II (31-40484.94).
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FOOTNOTES |
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Present address and address for reprint requests: H. Scherberger, Div. of Biology, Mail Code 216-76, California Institute of Technology, Pasadena, CA 91125 (E-mail: hans{at}vis.caltech.edu).
Received 4 April 2000; accepted in final form 3 May 2001.
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REFERENCES |
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