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J Neurophysiol 80: 680-695, 1998;
0022-3077/98 $5.00
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The Journal of Neurophysiology Vol. 80 No. 2 August 1998, pp. 680-695
Copyright ©1998 by the American Physiological Society

Three-Dimensional Organization of Otolith-Ocular Reflexes in Rhesus Monkeys. III. Responses to Translation

Dora E. Angelaki

Department of Surgery (Otolaryngology), University of Mississippi Medical Center, Jackson, Mississippi 39216-4505

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Angelaki, Dora E. Three-dimensional organization of otolith-ocular reflexes in rhesus monkeys. III. Responses to translation. J. Neurophysiol. 80: 680-695, 1998. The three-dimensional (3-D) properties of the translational vestibulo-ocular reflexes (translational VORs) during lateral and fore-aft oscillations in complete darkness were studied in rhesus monkeys at frequencies between 0.16 and 25 Hz. In addition, constant velocity off-vertical axis rotations extended the frequency range to 0.02 Hz. During lateral motion, horizontal responses were in phase with linear velocity in the frequency range of 2-10 Hz. At both lower and higher frequencies, phase lags were introduced. Torsional response phase changed more than 180° in the tested frequency range such that torsional eye movements, which could be regarded as compensatory to "an apparent roll tilt" at the lowest frequencies, became anticompensatory at all frequencies above ~1 Hz. These results suggest two functionally different frequency bandwidths for the translational VORs. In the low-frequency spectrum (<< 0.5 Hz), horizontal responses compensatory to translation are small and high-pass-filtered whereas torsional response sensitivity is relatively frequency independent. At higher frequencies however, both horizontal and torsional response sensitivity and phase exhibit a similar frequency dependence, suggesting a common role during head translation. During up-down motion, vertical responses were in phase with translational velocity at 3-5 Hz but phase leads progressively increased for lower frequencies (>90° at frequencies <0.2 Hz). No consistent dependence on static head orientation was observed for the vertical response components during up-down motion and the horizontal and torsional response components during lateral translation. The frequency response characteristics of the translational VORs were fitted by "periphery/brain stem" functions that related the linear acceleration input, transduced by primary otolith afferents, to the velocity signals providing the input to the velocity-to-position neural integrator and the oculomotor plant. The lowest-order, best-fit periphery/brain stem model that approximated the frequency dependence of the data consisted of a second order transfer function with two alternating poles (at 0.4 and 7.2 Hz) and zeros (at 0.035 and 3.4 Hz). In addition to clearly differentiator dynamics at low frequencies (less than ~0.5 Hz), there was no frequency bandwidth where the periphery/brain stem function could be approximated by an integrator, as previously suggested. In this scheme, the oculomotor plant dynamics are assumed to perform the necessary high-frequency integration as required by the reflex. The detailed frequency dependence of the data could only be precisely described by higher order functions with nonminimum phase characteristics that preclude simple filtering of afferent inputs and might be suggestive of distributed spatiotemporal processing of otolith signals in the translational VORs.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

A fundamental question in investigations of movement control is the neural computations and underlying sensorimotor transformations that convert primary sensory inputs into neural signals utilized in the regulation of motor behavior. Despite a wealth of information about semicircular canal-ocular reflexes that are activated during head rotation (rotational VORs), surprisingly little is known about the otolith-ocular reflexes. Nevertheless, translational components are often encountered in everyday life. Similar to head rotation, translational movements require the generation of temporally and spatially specific eye movements for accurate gaze stabilization (we will refer to the eye movements generated during translation as translational VORs). The task of the translational VORs is kinematically more complex. The compensatory response depends not only on the perturbing head translation, but also on the spatial location of the viewed image with respect to each eye (Paige 1989; Paige and Tomko 1991a,b; Schwarz and Miles 1991; Schwarz et al. 1989; Snyder and King 1992; Telford et al. 1997; Viirre et al. 1986). Furthermore, the central processing of otolith signals is complicated by the fact that the peripheral otolith system responds identically to both translational and gravitational accelerations. This dual role of the otolith system has complicated its properties and has impeded our understanding of its function.

Several studies of monkey or human eye movements generated during lateral translation were carried out during the past decades (Baloh et al. 1988; Bronstein and Gresty 1988; Buizza et al. 1980; Bush and Miles 1996; Gianna et al. 1997; Gresty et al. 1987; Israel and Berthoz 1989; Melvill Jones et al. 1980; Niven et al. 1966; Oas et al. 1992; Paige 1989; Paige and Tomko 1991a,b; Schwarz and Miles 1991; Shelhamer and Young 1991; Skipper and Barnes 1989; Telford et al. 1997; Tokita et al. 1981). Most of these studies using steady-state sinusoidal stimulation were limited to one or a few frequencies and not enough information was available to characterize the dynamic properties of the reflex. This lack of experimental data has also hindered modeling efforts and our understanding of the central processing mechanisms necessary to transform primary otolith afferent discharge into the translational VORs. Three main ideas have been put forward regarding the central transformation of otolith-ocular signals. First, the most widespread hypothesis is that otolith afferent signals (which are largely proportional to linear acceleration) are centrally integrated to derive linear velocity commands that can be directed to the neural integrator and the oculomotor plant. Second, because primary otolith afferents have significant discharge modulation during static tilts and because translational VORs are generally characterized by high-pass filter dynamics and zero DC sensitivity, it was proposed that a jerk signal, proportional to the rate of change of linear acceleration, is needed to filter out low-frequency signals (Angelaki and Hess 1996d; Angelaki et al. 1993; Hain 1986; Niven et al. 1966). Third, the extensive distribution of response dynamics and spatial tuning properties of primary otolith afferents has been proposed to form the basis for the dynamics of the reflex (Angelaki and Hess 1996d; Raphan et al. 1996). Simple linear summation of temporally and/or spatially distinct signals is mathematically equivalent to a spatiotemporal filter whose output can be shaped with the correct dynamic properties of the translational VORs (Angelaki 1993; Angelaki and Hess 1996d).

These three hypotheses regarding the neural computations in the translational VORs are not necessarily exclusive and contradicting. It is possible that the dynamics of the reflex depend strongly on frequency, such that "jerk-like" properties could be present at low frequencies and "velocity-like" properties at high frequencies. Moreover, spatiotemporal summation of afferent signals could be involved at least partly in shaping reflex dynamics. As mentioned above however, the translational VORs were studied only over a limited frequency range. Although the properties of the reflex depend strongly on the "point of regard" and binocular fixation parameters, the only way to study reflex dynamics in a broad frequency range would be in darkness. This is particularly important at low frequencies when large vergence angles cannot be maintained for prolonged tests in darkness and visual influences are important when translated in the light. Thus in this study, a wide range of steady-state sinusoidal stimuli was used to characterize the three dimensional (3-D) properties of the translational VORs of rhesus monkeys during lateral, fore-aft, and up-down translational motion in darkness. It has been usually assumed that translational VORs are also generated during constant velocity off-vertical axis rotations (Angelaki and Hess 1996a; Paige and Tomko 1991a). This assumption, however, was never tested experimentally. In the present experiments, we directly compare the horizontal and torsional eye movements elicited during constant velocity yaw rotation with those generated during lateral translation.

Finally, the present experiments also were motivated by a growing speculation regarding a differential low-pass/high-pass filtering of torsional versus horizontal eye movements during head translation (Paige and Tomko 1991a; Telford et al. 1997). According to this hypothesis, the otolith response ambiguity is resolved by the parsing of linear accelerations on the basis of frequency content (Mayne 1974; Vieville and Faugeras 1990). That is, tilt pathways (generating torsional eye movements) select for static and low-frequency accelerations, whereas translation pathways (eliciting horizontal eye movements) select for high-frequency inputs (Telford et al. 1997). In support of this hypothesis, torsional and horizontal responses during lateral translation were described to be governed by different frequency-dependent dynamics (Paige and Tomko 1991a; Telford et al. 1997). If the frequency-segregation hypothesis were to provide a solution to the tilt/translation ambiguity, the horizontal and torsional responses should be segregated in frequency when expressed in the same units. Unfortunately, the arguments used to support the frequency-segregation scheme were all based on comparisons of horizontal sensitivities (°/cm) with torsional "tilt gains" (°/° of tilt). In the present experiments we specifically examined the frequency dependence of the horizontal and torsional eye movements during lateral translation to provide support for or dispute of the frequency-segregation hypothesis.

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

Animal preparation

Five young rhesus monkeys (3-4 kg) were used in the present studies. Each animal was chronically implanted with a delrin ring imbedded in dental acrylic that was anchored to the skull by six stainless steel screws that were inverted and placed into T-slots cut into the skull. The ring was lightweight but provided a strong head restraint for vigorous stimulus motion and was used extensively for similar types of experimentation (e.g., Correia et al. 1992). In separate surgical procedures, a dual search coil designed for recording 3-D eye movements was implanted on each eye under the conjunctiva at ~3-5 mm from the limbus cornea and anterior to all eye muscle insertions (Hess 1990). The lead wires from the eye coil were passed out of the orbit, under the muscle and skin, to the top of the skull where they exited inside the delrin ring. A connector plug was soldered to the lead wires and secured to the head ring with dental acrylic. When the animals were in their cages, the implanted delrin ring was covered with a cap to protect the eye coil plugs. After control responses were collected, all six semicircular canals were inactivated in two animals by plugging the canal lumen (c.f., Angelaki and Hess 1996c; Angelaki et al. 1996). Canal-plugged animals showed no evidence of increased spontaneous nystagmus either acutely or chronically. Following the surgery, the animals were kept in complete darkness until the following morning when the animals were brought to the laboratory for vestibular testing ("acute" experimental protocol). After this acute VOR testing, the animals were returned to the regular, daily light-dark cycle. All surgical procedures were performed under sterile conditions in accordance with the NIH guidelines. The animals were anesthetized initially with an intramuscular injection of ketamine (10 mg/kg), followed by administration of an inhalative anesthesia that consisted of an O2/isoflurane mixture. Respiration, body temperature, and heart rate were monitored continuously during all surgical procedures. Each animal was given antibiotics and analgesics following the completion of each surgery.

Experimental setup during vestibular testing

During experimental testing, the monkeys were seated in a primate chair with their heads statically positioned such that the horizontal stereotaxic plane was tilted 18° nose down. This head position was used to place the lateral semicircular canals approximately parallel to the earth-horizontal plane, whereas at the same time keeping the vertical semicircular canals as vertically oriented as possible. The animal's body was secured with shoulder and lap belts, whereas the extremities were loosely tied to the chair. The primate chair was then secured inside the inner frame of a vestibular turntable consisting of a 3-D rotator on top of a linear sled (Acutronics). The two inner frames of the turntable were manufactured by nonmetalic composite materials to minimize interference with the magnetic fields. In addition, the whole rotator assembly was specially constructed to provide rigid coupling between the motion generator (in these experiments, the linear sled) and the animal. The linear sled (2-m length) was powered by a servo-controlled linear motor that could deliver steady-state sinusoidal stimulation in a large frequency range (0.16-25 Hz). Using the 3-D turntable, the animals were repositioned relative to the direction of translation such that translational VORs were recorded during lateral (i.e., along the interaural axis, with the animals either upright or supine), fore-aft (i.e., along the naso-occipital axis, with the animals upright), and up-down (i.e., along the vertical head- and body-axis, with the animals either supine or right ear down) motion. For the present experiments, eye movements were recorded in complete darkness. For this, the animal's chair was completely surrounded by a light-tight sphere (61-cm radius).

Eye movement recording and calibration

Binocular 3-D eye movements were recorded by using the magnetic search coil technique. The driver coils, which generated horizontal and vertical magnetic fields (100 and 66 kHz, respectively) were mounted on a fiberglass cubic frame of 16 in. side length (CNC Engineering). The heavy fiberglass coil frame was mounted on the inner gimbal of the rotator and was constructed specifically to avoid deformation or bending during the high-frequency motion.

The dual eye coil assembly that was implanted on each eye consisted of two serially interconnected miniature coils (Sokymat, Switzerland) that were attached at diagonal points along the circumference of a ~15 mm three-turn stainless steel coil (Cooner wire). The planes of the miniature coils and of the large three-turn coil were approximately perpendicular. After implantation, the axis of the large pericorneal coil was approximately aligned with the optic axis of the eye, thereby measuring the direction of the line of sight (direction coil). The axes of the miniature coils were approximately in the plane of the large pericorneal coil, thereby measuring the torsion of the eye about the line of sight (torsion coil). The exact orientation of the two coils relative to each other, as well as the orientation of the dual eye coil on the eye were precisely determined based on both preimplantation and daily calibration procedures, as described below (see Hess et al. 1992).

Before surgical implantation, each dual eye coil was calibrated using a 3-D calibration cube. Using rotations about all three axes, this calibration yielded the horizontal and vertical angular orientations of the two coil sensitivity vectors, as well as the angle between them. Because of the stable geometry of the dual coil assembly, these parameters were assumed to remain unchanged before and after implantation. On each experimental session and before the experimental protocols, pretrained animals performed a visual fixation task. The eye coil voltages, measured during visual fixation, along with the precalibrated values for the sensitivity vector of the torsion coil and the angle between the two coils were used to calculate the orientation of the dual coil on the eye, and were also used to offset voltages. As a consistency check, the direction coil sensitivity vector estimated from the preimplantation calibration, which was not used in the daily calibration calculations, was compared with the respective sensitivity computed on the basis of the fixation task. In all experiments, the difference between the two values was <10%. In addition, Listing's plane was generated daily using spontaneous eye movements in the light. Listing's plane had zero torsional displacement and its thickness was consistently <0.5°.

3-D eye positions were expressed as rotation vectors using straight ahead as the reference position. Angular eye velocity was computed from these rotation vectors (c.f., Angelaki and Hess 1996a). Both eye position and angular eye velocity vectors were expressed relative to a head-fixed right-handed coordinate system, as defined in the 18° nose-down position. Torsional, vertical, and horizontal eye position and velocity were the components of the eye position and eye velocity vectors along the naso-occipital, interaural, and vertical head axes, respectively. Positive directions were clockwise, as viewed from the animal (i.e., rotation of the upper pole of the eye toward the right ear), downward, and leftward for the torsional, vertical, and horizontal components, respectively.

Experimental protocols

The animals were sinusoidally oscillated in complete darkness either along their interaural axis (lateral motion), along their naso-occipital axis (fore-aft motion), or along their vertical axis (up-down motion). For lateral and fore-aft motions, the animals were maintained upright during the stimulation with frequencies ranging between 0.16 and 25 Hz. At the lowest frequencies (0.16 and 0.2 Hz), the stimulus amplitude was 0.1 g, whereas at the higher frequencies the amplitude was held constant at 0.4 g. For up-down motion, the animals were positioned either supine or with their right ear down and only oscillation frequencies up to 5 Hz were tested. Finally, while in supine position, the animals also were translated laterally at frequencies up to 5 Hz to examine the effects, if any, of static head position on eye movement responses. For each animal, a minimum of three different runs were analyzed at each frequency. To minimize fluctuations in vergence angle, translation started several seconds after the animals were placed in darkness. Under these conditions, vergence was maintained between 0.8 and 2 MA (corresponding to distances of ~50-120 cm), values too low to induce large vergence-dependent changes in VOR sensitivity (Telford et al. 1997).

In addition to the translational protocols, a series of constant velocity off-vertical axis yaw rotations (OVAR) at ± 8°/s, ±18°/s, ±36°/s, ±58°/s, ±110°/s, and ± 180°/s were also delivered with the axis of rotation tilted 23.6° off-vertical (imparting a 0.4 g stimulus in the animal's horizontal plane). These limited OVAR protocols were delivered to directly compare translational responses with those during constant velocity yaw OVAR (e.g., Angelaki and Hess 1996a).

For each recording session, the eight voltage signals of the left and right dual eye coil assemblies (or 4 right eye voltages and 4 head voltages; see following text), the three output signals of a 3-D linear accelerometer (mounted on fiberglass members that firmly attached the animal's head ring to the inner gimbal of the rotator), as well as linear velocity and position feedback signals from the linear sled were low-pass filtered (200 Hz, 6-pole Bessel), digitized at a rate of 833.33 Hz (Cambridge Electronics Design, model no. 1401), and stored on a microcomputer for off-line analysis. Based on the 16-bit acquisition system and the noise levels in filtered traces, the eye movement resolution was estimated to be >= 0.01°. Before the experimental sessions, the animals were given 1.0 mg d-amphetamine orally to maintain a constant level of alertness.

Possible problems

High-frequency oscillations with 0.4 g peak acceleration, as those used in the present studies, are associated with very small linear displacements (e.g., at 5 Hz, 0.4 cm; at 10 Hz, 0.1 cm; at 25 Hz, 0.02 cm). One potential problem associated with these high-frequency stimuli is the possibility of angular movement of the head relative to the magnetic field coils because of an imprecise coupling of the animal's head to the coil frame. To address this problem, several controls were implemented. First, both the animal's head and the field coils (heavy fiberglass coils specially constructed by CNC Engineering to avoid any flexing during motion) were securely fastened to the thick fiberglass inner gimbal of the 3-D turntable. Second, on selected high-frequency experiments, a "head coil" (a precalibrated dual coil identical to those implanted on each eye) was attached securely to the monkey's head through bolts and dental acrylic. The output of this dual head coil often was recorded simultaneously with the right eye coil output (only 2 eyes or 1 eye and head coil could be monitored simultaneously). Head signals were processed and were calibrated similar to the eye coil signals. As explained in more detail below, any detectable head movements were subsequently subtracted off-line from the eye coil signals. In general, horizontal head movement components were negligible at all frequencies. The largest head oscillations were observed at 18-20 Hz and were torsional and vertical for lateral and fore-aft motion, respectively. Because these head movements were similar across animals and experimental days, averages were computed and subtracted from eye signals (see following text).

One of the results of this study is the presence of torsional eye velocity components during lateral translation at all frequencies tested. The following measures were taken to ensure that these torsional eye movements were genuine. First, as explained earlier, any rotation of the head inside the coil frame was detected and subtracted from the eye signals. Second, a rate sensor was regularly mounted on the inner gimbal such that its sensitivity axis would be aligned either with the animal's pitch or roll axis. The peak velocity detected by the rate sensor during high-frequency translation was usually negligible (<0.5°/s). At frequencies >13 Hz (that were close to the resonant frequency of the superstructure) peak roll velocities of up to 1°/s were observed. With a roll VOR gain of ~0.7 (e.g., Angelaki and Hess 1996b), such roll motion of the head would elicit only a torsional eye velocity of <0.7°/s or 2°/s/g. This number is within the SD range of the torsional data (e.g., Figs. 3 and 4, top). Finally, in two animals the translational VORs were tested the day after all semicircular canals were inactivated. If roll VOR had contributed substantially to the normal torsional responses, one would expect to encounter reduced torsional responses in the plugged animals. This was not the case and torsional eye velocity was indistinguishable before and acutely after canal inactivation.


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  		FIG. 3. Response sensitivity and phase of (A) horizontal and (B) torsional slow phase velocity during lateral translation (solid symbols) and constant velocity OVAR (open symbols). Response sensitivity is expressed relative to linear acceleration (g = 9.81 m/s2) and response phase relative to linear velocity. Different symbols are used to display average data from each animal.


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  		FIG. 4. Response sensitivity and phase of the horizontal component of eye velocity during lateral translation (solid symbols) and constant velocity OVAR (open symbols) in an animal before (squares), acutely (diamonds), and at different intervals after canal inactivation. Response sensitivity is expressed relative to linear acceleration (g = 9.81 m/s2) and response phase relative to linear velocity. Different symbols are used to display average data acquired at different times.

Data analyses

All data analyses were performed on microcomputers off-line as follows. Calibrated 3-D eye positions were expressed either as Fick angles or as rotation vectors (Haustein 1989; Van Opstal 1993). The horizontal, vertical, and torsional components of the calibrated eye position vectors were smoothed and differentiated with a Savitzky-Golay quadratic polynomial filter that had a 15-point forward and backward window (Press et al. 1988; Savitzky and Golay 1964). This digital filter did not alter phase characteristics but did cause a frequency-dependent gain attenuation of response sensitivity that was negligible (<5%) below 6 Hz but was significant at higher frequencies. Thus the response sensitivity values were corrected using appropriate multiplication factors. The adequacy of the correction procedure was verified in selected experimental runs by comparing eye velocity computed as described earlier with that computed from the same set of data which were now processed by two cascade notch filters (60 and 120 Hz) instead of the polynomial filter. The results of the two processing methods were indistinguishable.

The angular eye velocity vector was computed from 3-D eye position, as described previously (c.f., Angelaki and Hess 1996a-c). The fast phases of nystagmus were removed using a semi-automated procedure based on time and amplitude windows set for the second derivative of the eye velocity vector amplitude. For translational protocols at frequencies <1 Hz, average response cycles were computed from steady-state response components (i.e., horizontal, vertical, and torsional) for each eye. For each of these average response cycles, gain and phase were determined by fitting a sine function (and a DC offset) to both response and stimulus (output of the 3-D linear accelerometer) using a nonlinear least squares algorithm based on the Levenberg-Marquardt method. Sensitivity was expressed as the ratio of response (eye velocity) peak amplitude to peak linear velocity or peak linear acceleration of the head (in g units where g = 981 cm/s2). Phase was expressed as the difference (in deg) between peak eye velocity and peak linear velocity (except Fig. 9 where it is expressed relative to linear acceleration). On the basis of sine definitions used, the phase of the compensatory horizontal (vertical) response during lateral (up-down) motion should be ~0°. Similarly, for torsional responses to be compensatory to "an apparent tilt" (c.f., Telford et al. 1997), torsional response phase during lateral motion should be ~180°. This is because lateral translation to the right, which is a positive stimulus in our experimental setup, would impart an inertial acceleration along the interaural axis that is identical to the linear acceleration during a right ear down roll tilt. The compensatory torsional eye movement during a right ear down roll tilt should be negative.


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  		FIG. 9. Model fits for the horizontal response during lateral translation. Average data from translation (0.16-25 Hz) and OVAR (0.02-0.5 Hz; OVAR sensitivities represent averages from the two plugged animals, normalized at 0.5 Hz to values during translation 2). Both response sensitivity (°/s/g) and phase are expressed relative to linear acceleration. Error bars represent SD. The regular and irregular afferent squirrel monkey data are shown as dotted lines (Fernandez and Goldberg 1976c; afferent sensitivities were normalized to the horizontal velocity sensitivity at 0.5 Hz). The transfer function fitted to the data were H(s) = Ho(s)·Hint(s)·He(s) where the neural integrator Hint(s) = s/1 + stau int and the oculomotor plant He(s) = (1 + stau e4)/(1 + stau e1)(1 + stau e2)(1 + stau e3) are set to the following parameters: tau int = 20 s, tau e1 = 0.28 s, tau e2 = 0.037 s, tau e3 = 0.003 s, and tau e4 = 0.14 s (Fuchs et al. 1988; Minor and Goldberg 1991). Parameters fitted; Ho(s) = -0.37(s + 0.22)(s + 13.5)(s - 26.1)(s - 198.4)/(s + 2.4)(s + 40)(s - 10.6)e-0.008s (thick solid lines) and Ho(s) = Hos(s)= -120(s + 0.23)(s + 21.7)/(s + 2.6)(s + 45.5)e-0.01s (thin solid line). The minuses in the equations reflect the addition of 180° to the translational VOR phase data (such that comparison with afferent data will be easier).

Analyses of the translation responses at frequencies >1 Hz were slightly different from those used for low-frequency sinusoidal data. Because it is known that response amplitude and direction of the translational VORs depend on the point of regard and binocular eye position (e.g., Paige and Tomko 1991b; Schwarz and Miles 1991), data between any two consecutive fast eye movements were averaged and fitted separately. Therefore for each experimental run, 2-8 sensitivity and phase values were obtained, each corresponding to a particular binocular 3-D eye position that was computed as the average of eye position of the corresponding data segment consisting of a variable number of complete cycles. Even though average vergence information was routinely available for each data set, no attempt was made to group responses as a function of vergence angle for the following reasons. 1) Because motion commenced several seconds after the lights were turned off, vergence angles were always <2 MA. For these small changes in vergence, there is little corresponding change in translational VOR sensitivity (Telford et al. 1997). 2) Because changes in VOR sensitivity were reported to precede vergence angle changes (Snyder et al. 1992), cycle-by-cycle analysis is problematic. As mentioned earlier, a small head movement was present at frequencies >6 Hz. Thus the eye movement data were corrected by first computing at each frequency an average sensitivity and phase for the torsional, vertical, and horizontal components of head velocity. These values subsequently were subtracted vectorially component-wise from the right and left eye signals.

For OVAR protocols, each component of desaccaded slow phase eye velocity was fitted by the equation Omega (t) = Omega v + Omega p cos (omega t + phi ), where Omega v is the steady-state response component, Omega p is the modulation amplitude, and phi  is the spatiotemporal phase angle. The sensitivity vector for each response component was computed as the average of response gains during the two directions of motion (in °/s/g). Similarly, temporal response phase was computed as the average of the spatiotemporal phases phi  for the two directions of motion (see Angelaki and Hess 1996a).

All statistical comparisons were based on analysis of variance with repeated measures.

Transfer function fits

The dynamic properties of the translational VOR were characterized by fitting transfer functions to both sensitivity and phase data. These procedures were performed in Matlab (Mathworks). Different iteration procedures (and several different initial conditions) were utilized for fitting, including the Newton-Gauss and Newton-Raphson algorithms, the Levenberg-Marquardt algorithm, and/or singular value decomposition. The data presented here were based on the Levenberg-Marquardt algorithm with singular value decomposition [unrestrained fit of Ho(s)] or the Newton-Raphson algorithm [restrained fit of Hos(s)]. The derived transfer function related the linear acceleration input to the oculomotor output, i.e., H(s) = Ho(s)· Hint(s)·He(s) where Hint(s) = s/1 + stau int is the velocity-to-position neural integrator and He(s) = (1 + stau e4)/(1 + stau e1)(1 + stau e2)(1 + stau e3) is the oculomotor plant with parameters set to: tau int = 20 s, tau e1 = 0.28 s, tau e2 = 0.037 s, tau e3 = 0.003 s, and tau e4 = 0.14 s (Fuchs et al. 1988; Minor and Goldberg 1991). That is, the derived periphery/brain stem transfer function Ho(s) provided the neural processing of both primary otolith afferents and central circuits. Because primary otolith afferent dynamics are unknown for frequencies >2 Hz and because afferent (primarily regular) dynamics are relatively flat in the frequency range tested, no attempt was made to specifically incorporate the previously estimated afferent transfer functions into the estimates of Ho(s).

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

General observations

Lateral translation elicited robust horizontal eye movements in complete darkness. Examples of binocular eye position and slow phase eye velocity are illustrated for two different frequencies, 0.5 and 5 Hz, in Fig. 1, A and B, respectively. In addition to the horizontal components of the response, torsional slow phase velocity was also usually modulated, particularly at high frequencies. Torsional slow phase velocity at frequencies <1 Hz was generally small and variable (e.g., Fig. 1A). No consistent vertical response was elicited during lateral translation and the eyes close to zero vertical elevation.


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  		FIG. 1. Binocular torsional, vertical, and horizontal components of eye position (Etor, Ever, and Ehor) and slow phase eye velocity (Omega tor, Omega ver, and Omega hor) during lateral translation at (A) 0.5 Hz, 0.4 g and (B) 5 Hz, 0.4 g in complete darkness. Dotted lines illustrate zero position (straight ahead gaze) and zero eye velocity. The stimulus (bottom trace) shows output of a linear accelerometer mounted on the animal's head. Sections of fast eye movements were removed from the slow phase eye velocity plots.

Responses from a different animal during constant velocity yaw rotation (yaw OVAR), lateral (IA), and fore-aft (NO) translation are illustrated in Fig. 2, A-C, respectively. During yaw rotation at 180°/s with the axis of rotation tilted 23.6° from the earth-vertical, the linear acceleration stimuli activating the otolith system can be decomposed into two sinusoidally varying 0.4 g components oscillating at 0.5 Hz in temporal quadrature along the interaural and naso-occipital axes, respectively. If the sinusoidal modulations during yaw OVAR are elicited in response to the shear accelerations along the interaural axis, the horizontal/torsional components would be identical to those elicited during lateral translation. Nevertheless, qualitative comparison of the responses during yaw OVAR and lateral translation suggests several differences. First, torsional eye position during yaw OVAR systematically modulated around zero with a relatively large peak-to-peak amplitude of ~10° (Fig. 2A). This periodic modulation that was phase locked to head position was produced through an interplay of fast and slow eye movements, as previously described (Angelaki and Hess 1996a; Hess and Angelaki 1997a,b). No such consistent modulation in mean torsional eye position was observed during lateral translation (Figs. 1A and 2B). Second, the large amplitude sinusoidal modulation in horizontal slow phase velocity elicited during lateral translation was much smaller during yaw OVAR (compare Omega hor in Fig. 2, A and B). In the following text, we will quantitatively compare the torsional and horizontal slow phase velocity responses elicited in the same animals during yaw OVAR and lateral motion. Quantitative comparisons of the mean torsional eye position modulations and the associated dynamic changes in primary eye position and Listing's coordinates are reported elsewhere (Hess and Angelaki 1997c).


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  		FIG. 2. Binocular torsional, vertical, and horizontal eye position (Etor, Ever, and Ehor) and monocular (right eye) slow phase velocity (Omega tor, Omega ver, and Omega hor) (A) during constant velocity off-vertical axis yaw rotation (OVAR) at 180°/s; (B) during lateral (IA) translation at 0.5 Hz, 0.4 g; and (C) during fore-aft (NO) translation at 0.5 Hz, 0.4 g. Dotted lines illustrate zero position (straight ahead gaze) and zero eye velocity. The stimulus (bottom trace) shows either (A) turntable potentiometer output or (B, C) head-mounted linear accelerometer output. Sections of fast eye movements were removed from the slow phase eye velocity plots.

In contrast to the robust, large-amplitude horizontal responses routinely observed during lateral translation, only a small horizontal slow phase velocity modulation was observed during low-frequency fore-aft motion in darkness. In addition, negligible torsional, as well as small and variable vertical components were observed during low-frequency fore-aft motion. As frequency increased, however, all components increased in amplitude in an eye position-dependent manner, as expected from the kinematic requirements for ideal gaze stabilization during fore-aft translation. In the following text, we will first examine the dynamic properties of the horizontal slow phase velocity responses during linear translation in complete darkness and subsequently investigate the eye and head position dependencies of these responses in three dimensions.

Frequency response during lateral and fore-aft motion

Average response sensitivity and phase of the horizontal response component during lateral translation are illustrated in Fig. 3A (solid symbols). Horizontal response sensitivity (when expressed relative to linear acceleration expressed in g units where g = 981 cm/s2) remained relatively constant for frequencies up to ~5 Hz and slightly decreased thereafter. In addition, horizontal eye velocity was in phase with linear velocity for frequencies between 2 and 10 Hz. At higher frequencies, relatively large phase lags were introduced. At frequencies lower than ~2 Hz, phase was variable, with some animals exhibiting phase leads and most animals exhibiting phase lags. Response sensitivity and phase obtained from fitting the horizontal slow phase velocity elicited in the same animals during yaw OVAR are superimposed (Fig. 3A, open symbols). Despite the large variability in the phase of the horizontal slow phase velocity modulation during OVAR, values were generally comparable to those during lateral motion for each animal. Horizontal response magnitude however, was lower during yaw OVAR compared with those during translation at a similar frequency. It is interesting that horizontal response sensitivity during OVAR increased after all six semicircular canals were inactivated (Fig. 4, compare open squares with other open symbols). Similar observations were also made in a second canal-plugged animal (see Angelaki and Hess 1996a,b). This was true despite the fact that horizontal eye movements during translational motion were unchanged after canal plugging (Fig. 4, solid symbols). For both intact and canal-plugged animals, horizontal response sensitivity declined as frequency decreased below ~0.5 Hz.

Average sensitivity and phase of the torsional response component for each animal during both lateral motion and yaw OVAR are plotted in Fig. 3B (solid and open symbols, respectively). Two main observations were made from the data. First, torsional response sensitivity and phase overlapped during yaw OVAR and lateral translation for all animals tested with both stimuli. Second, the dynamics of the torsional response component at frequencies above ~0.5 Hz were similar to those of the horizontal. Torsional slow phase sensitivity (when expressed relative to acceleration) was relatively independent of frequency, hovering between 3 and 10°/s/g for all frequencies up to 25 Hz. Torsional response phase was strongly frequency-dependent, shifting 180°-270° in the frequency range tested (0.02-25 Hz).

To compare more directly the similarity in the frequency dependencies of horizontal and torsional response sensitivities during lateral motion, average values (in °/s/g) are superimposed in Fig. 5, top. Furthermore, because the frequency dependence of response sensitivity depends on the units used, horizontal and torsional eye velocity sensitivities expressed relative to linear velocity (in °/s/cm/s, which is equivalent to °/cm) also are plotted (Fig. 5, middle). Expressed this way, both horizontal and torsional sensitivities increased with increasing frequency. Moreover, to compare with previous studies (Telford et al. 1997) (dotted lines in Fig. 5, bottom), torsional responses also are expressed relative to an apparent tilt gain computed as eye velocity divided by (2pi f) tan-1 (G) with G being the linear acceleration in units of g where g = 981 cm/s2 (Fig. 5, bottom). When expressed this way, horizontal response sensitivity behaved similarly (not shown).


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  		FIG. 5. Average (±SD) horizontal (open symbols) and torsional (solid symbols) response sensitivities during lateral translation plotted as eye velocity/linear acceleration (°/s/g, g = 9.81 m/s2), as eye velocity/linear velocity (°/s/cm/s, which is equivalent to °/cm), or as tilt gain (for the latter, only torsional data are shown). Dotted lines plot data from Telford et al. 1997.

During fore-aft motion, responses were small and variable (e.g., Fig. 2C) and strongly dependent on binocular eye position (see following text). On average, the horizontal response sensitivities during fore-aft motion in darkness were an order of magnitude lower than those during lateral motion but exhibited similar dynamics.

Dependence on binocular eye position

For frequencies >1 Hz, sensitivity and phase were computed from response segments that were devoid of fast eye movements. It was then possible to correlate translational VOR sensitivity with binocular eye position (see METHODS). The dependence of horizontal, vertical, and torsional response sensitivities on horizontal and vertical eye position are illustrated in Figs. 6 and 7 for fore-aft and lateral motion, respectively. For fore-aft motion, both the horizontal and vertical response components during fore-aft motion depended on eye position (Fig. 6). During backward translation, for example, a compensatory eye movement should be rightward and upward for a gaze direction to the left and down (according to our coordinate definitions, leftward and downward eye movements are positive). Because backward motion is defined here to be positive, the elicited horizontal and vertical eye movement should be negative for positive horizontal and vertical eye positions, respectively (and vice-versa). Both the horizontal and vertical eye velocity sensitivities were characterized by such an eye position dependency. Torsional eye velocity was variable and exhibited some dependence on vertical but not horizontal eye position.


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  		FIG. 6. Dependence on eye position during fore-aft motion. The horizontal, vertical, and torsional slow phase velocity components are plotted as a function of horizontal and/or vertical eye position. Linear regressions were fitted through data points (see Table 1 for regression parameters). Only data at 1-6 Hz are illustrated. Dotted lines represent zero eye position and velocity.


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  		FIG. 7. Dependence on eye position during lateral translation. Horizontal and torsional sensitivities are plotted as a function of horizontal and/or vertical eye position. Vertical response sensitivity is plotted as a function of the product of horizontal and vertical eye positions (see Footnote 1). Linear regressions were fitted through data points (see Table 1 for regression parameters). Only data at 1-6 Hz are illustrated. Dotted lines represent zero eye position and velocity.

For small eye eccentricities, ideal gaze stabilization would require a linear dependence of both horizontal and vertical response sensitivities on horizontal and vertical eye position, respectively. The linear regression equations separately fitted to the right and left eye data are included in Table 1. Because the ratio of response sensitivity over the respective eye position is equal to the inverse of viewing distance,1 we used the slopes of these lines to calculate a "default viewing distance" at which translational VORs would provide on average perfectly compensatory responses in complete darkness. This average distance at which rhesus monkeys tend to optimize their default translational VOR gain during fore-aft motion is ~1 m (see Table 1).

 
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  		TABLE 1. Translational VOR sensitivity vs. eye position: linear regression parameters

For lateral motion, horizontal responses were independent of horizontal eye position (Fig. 7). In this case, the inverse of viewing distance is equal to the zero-intersect of the linear regression line (see Table 1 and Footnote 1). Based on the zero-intersect of the horizontal response sensitivity, the average distance at which rhesus monkeys tend to optimize their default lateral VOR gain was also estimated to be 1 m (similar to the average vergence angle in darkness). The vertical VOR component during lateral translation should be proportional to the product of double the horizontal and vertical eye positions. When plotted as a function of this product, no such correlation was observed. Torsional eye velocity sensitivity depended on vertical but not horizontal eye position.

Up-down (vertical) motion

Four animals were also tested in a more limited frequency range (0.16-5 Hz) during translation along the longitudinal (vertical) body axis. Because the position of the linear sled could not be altered, the animals were appropriately repositioned relative to the direction of movement. The vertical translational VOR responses were therefore computed for two different static head positions: supine and right ear down. In both positions, the main eye movement generated was vertical (Fig. 8; supine, open symbols; right ear down, filled symbols). Even though vertical response sensitivity was similar to the horizontal response sensitivity during lateral motion, phase characteristics differed. Whereas horizontal velocity phase hovered around zero or lagged head linear velocity at low frequencies, vertical response phase was characterized by large phase leads at low frequencies, reaching values of 90-180° at 0.16 Hz.


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  		FIG. 8. Response sensitivity and phase (expressed relative to translational velocity) of vertical eye velocity elicited during vertical translation in complete darkness. Different symbols correspond to data from different animals that were oscillated in one of two different static orientations; right ear down (solid symbols) or supine (open symbols).

Dependence on static head position

The dependence of response sensitivity on static head position was investigated by positioning the animals in both upright and supine orientations during lateral translation and in both right-ear down and supine orientations during up-down motion. No statistically significant differences were observed in either the horizontal or the torsional response sensitivity for the two different static head orientations during lateral translation [F(1,1) = 3.6 and 6.0; P > 0.05]. During up-down motion, vertical response sensitivity was also independent of static head orientation [F(1,1) = 91.2; P > 0.05]. The small amplitude torsional eye movements that also were elicited during up-down motion exhibited a small dependence on static head orientation, being larger in ear down compared with supine orientation [F(1,1) = 229.1, P = 0.04]. Nevertheless, responses were small and variable with no evidence of any consistent disconjugacy between the two eyes.

Input-output system identification for the translational VORs

One of the goals of this study was to quantitatively characterize the translational VOR dynamics in a broad frequency range. For this, average horizontal response sensitivity and phase are replotted from Figs. 3 and 4 (Fig. 9, solid circles). To combine OVAR with linear motion data, average OVAR sensitivities after plugging were normalized to the translational VOR sensitivity values at 0.5 Hz.2 In addition, average sensitivity and phase of the regular and irregular squirrel monkey primary otolith afferents are illustrated as dotted lines (Fernandez and Goldberg 1976a-c; because of the difference in units used, afferent sensitivities were also normalized to coincide with translational VOR sensitivity values at 0.5 Hz). For an easier comparison between primary afferent and reflex dynamics, both translational VOR sensitivity and phase are expressed relative to linear acceleration, as are primary afferent data.

The minimum order input/output transfer function that would adequately describe the data were searched by specifying the order of the numerator and denominator of a periphery/brain stem function Ho(s), s = 2pi fj, that relates the linear acceleration stimulus to the velocity input to the neural integrator at each frequency (j2 = -1). Because primate otolith afferent transfer functions were only estimated for frequencies up to 2 Hz (Fernandez and Goldberg 1976c) and because regular afferent dynamics were nearly flat, the otolith afferent transfer function was not explicitly included in the fits. Thus the transfer function fitted to the data were H(s) = Ho(s)·Hint(s)·He(s), with Hint(s) and He(s) the transfer functions of the neural integrator and the oculomotor plant, respectively, fixed to values previous determined (Fuchs et al. 1988; Minor and Goldberg 1991) (see METHODS and Fig. 9). In other words, the presence of one integrator (corresponding to the velocity-to-position neural integrator; e.g., Skavenski and Robinson 1973) in the reflex pathway was assumed. It is only the remaining aspects of the reflex dynamics (which according to one hypothesis should also be described by another brain stem integration) that were investigated.

Up to eighth-order transfer functions were fitted to the data in one of the following ways. First, the location of the roots of the denominator and numerator polynomials were unconstrained such that either positive or negative poles/zeros were allowed. Second, the optimization algorithm was constrained to only stable poles (i.e., the real part of the denominator polynomial was always negative). Using the unconstrained method, a third order system provided the best, lowest order approximation to the data (Fig. 9, thick solid lines)
<IT>H</IT><SUB>o</SUB>(s) = <FR><NU>−0.37(<IT>s</IT> + 0.22)(<IT>s</IT> + 13.5)(<IT>s</IT> − 26.1)(<IT>s</IT> − 198.4)</NU><DE>(<IT>s</IT> + 2.4)(<IT>s</IT> + 40)(<IT>s</IT> − 10.6)</DE></FR>e<SUP>−0.008s</SUP>
The term e-0.008s represents the contribution of the reflex time delay (in this case, 8 ms) and is responsible for part of the high-frequency phase lags. When the constrained minimization algorithm was used, a second order transfer function approximated the data (Fig. 9, thin solid lines)
<IT>H</IT><SUB>os</SUB>(s) = <FR><NU>−120(<IT>s</IT> + 0.23)(<IT>s</IT> + 21.7)</NU><DE>(<IT>s</IT> + 2.6)(<IT>s</IT> + 45.5)</DE></FR>e<SUP>−0.01s</SUP>
Further increase in the order of the numerator and denominator did not improve the fit. There was no rational transfer function with stable poles that provided better fits to the data. This is, in fact, not surprising when comparing Ho(s) and Hos(s). Two of the poles and two of the zeros of Hos(s) were similar to the two stable poles and zeros of Ho(s). The unstable pole, s = 10.6 rad/s, of Ho(s) corresponds to a corner frequency of 10.6/2pi  = 1.7 Hz. It is in fact in the frequency range >1.7 Hz for sensitivity and ~1.7 Hz for phase that Hos(s) provided a poor description of the data. Low order, stable transfer functions could adequately describe the data only if restricted to low or high frequencies (<1 and >4 Hz, respectively).

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

There were three goals in the present study. First, to determine the translational VOR dynamics in a broad frequency range (0.02-25 Hz) such that a better understanding of the input/output characteristics of the reflex can be obtained. Second, to quantitatively compare the horizontal and torsional eye movements generated during lateral motion with those generated during constant velocity OVAR and to test a common assumption regarding their equivalency. Third, to test another commonly used assumption regarding a differential low- versus high-pass filtering of torsional and horizontal eye movements, respectively, during lateral translation. Each of these questions are specifically addressed below.

Off-vertical axis rotations versus translational motion

In a recent series of studies we have examined the 3-D properties of the primate otolith-ocular system from responses generated during off-vertical axis rotations (Angelaki and Hess 1996a,b; Hess and Angelaki 1997a,b). On the basis of these studies, we have shown that there exist two distinct otolith-ocular contributions to slow phase eye velocity during OVAR, i.e., responses phase-locked and compensatory to head angular velocity and separate responses to linear acceleration or head position relative to gravity. Otolith-ocular responses compensatory to angular head velocity are part of the inertial vestibular system and responsible for generating a steady-state compensatory nystagmus during constant velocity rotation and for improving the low-frequency VOR dynamics during off-vertical axis oscillations (Angelaki and Hess 1996b; Rude and Baker 1988; Tomko et al. 1988). Horizontal responses phase-locked to head position relative to gravity have been attributed to translational VORs (Angelaki and Hess 1996a; Paige and Tomko 1991a). One of the aims of this study is to directly investigate this question by comparing responses during lateral motion and constant velocity yaw OVAR in the same animals. Our data suggest that the horizontal modulation during OVAR seem indeed to reflect the low-frequency end of the translational VORs (Fig. 3). In animals with intact labyrinths, however, OVAR responses were consistently lower than those during lateral motion. The fact that response sensitivity increased after canal inactivation (Fig. 4) suggests that rotational signals from the semicircular canals (and velocity storage activation) suppress the sensitivity of the horizontal component of the translational VORs during OVAR. An enhanced eye velocity modulation during constant velocity OVAR also was reported previously (Angelaki and Hess 1996a,b; Correia and Money 1970). Other than the reduced horizontal sensitivity during OVAR, the frequency dependence and phase characteristics of the horizontal and torsional responses during lateral motion and OVAR were superimposable in the common frequency range of 0.16-0.5 Hz, suggesting that the torsional and horizontal slow phase eye velocity modulations during yaw OVAR reflects indeed activation of the translational VORs.

Despite an equivalency in terms of slow phase velocity, the pattern of eye position and fast phase orientation differs for lateral translation and OVAR (e.g., Fig. 2). On the basis of a 3-D analysis of eye position, it has been proposed that the vertical and torsional eye position modulations during OVAR reflect an underlying change in oculomotor coordinates and primary eye position (Angelaki and Hess 1996a; Hess and Angelaki 1997a,b). In essence, primary eye position in primates tends to remain fixed in space, similarly as gaze lines tend to be maintained earth-horizontal through compensatory otolith-driven counter-rolling and counter-pitching reflexes in lateral-eyed species (Hess and Angelaki 1997a,b). A similar analysis of 3-D eye position has yielded no or negligible modulation of primary eye position during lateral and fore-aft translations (Hess and Angelaki 1997c).

Frequency response characteristics of the translational VORs

A second goal of the present study was to quantify the dynamic characteristics of the translational VORs in a broad frequency range. The most conspicuous aspect of the reflex dynamics is a functional relationship between sensitivity and phase. Between ~0.5 and 10 Hz, horizontal eye velocity is in phase with velocity but sensitivity is relatively independent of frequency only when expressed relative to linear acceleration. Such a dynamic behavior is clearly not indicative of a simple, low-order filtering process.

Three different but not mutually exclusive ideas have been proposed to explain the frequency-dependence of the translational VORs. 1) The most widespread belief is that linear acceleration signals from primary otolith afferents must be integrated twice to yield eye position. A problem with this hypothesis is that double integration would entail large sensitivities at low frequencies and gain attenuation at high frequencies, resulting in a dynamic behavior that would be opposite from experimental observations. 2) It also was proposed that afferent signals must be high-pass filtered such that low-frequency acceleration input signals be reduced or eliminated (Angelaki and Hess 1996d; Hain 1986; Niven et al. 1966). This ideal has been motivated by the need to filter out low-frequency signals that are within the bandwidth of primary otolith afferent transmission. 3) Finally, a spatiotemporal summation has been proposed as an alternative to discrete high-pass filtering (Angelaki 1993; Angelaki and Hess 1996d). According to this proposal, a wide variety of response dynamics, including those characteristic of nontraditional filtering (i.e., positive poles and zeros) could be generated simply by summation of afferents differing in spatial and temporal properties. All three hypotheses assume a common integration of eye velocity commands into eye position. It is only the brain stem processing before the velocity-to-position neural integrator which has been debated.

Primary otolith afferents encode linear acceleration, albeit specific frequency dependencies can vary depending on discharge regularity (Fernandez and Goldberg 1976c; Goldberg et al. 1990). In contrast, eye velocity is in phase with head velocity for a wide frequency range. A comparison of reflex and otolith afferent dynamics suggests the following (Fig. 9). First, the increasing reflex sensitivity and phase at frequencies between 0.02 and 0.5 Hz compared with relatively flat afferent dynamics are in fact suggestive of a high-pass filter or jerk-like computation as previously suggested (Angelaki and Hess 1996d; Angelaki et al. 1993; Hain 1986; Niven et al. 1966). Second, the constant or decreasing reflex sensitivity (reacceleration) and the ~90° phase differences at frequencies between 0.5 and 25 Hz resemble velocity-like properties.

The presence of two different bandwidths for the translational VORs is also suggested by the transfer functions fitted to the data. The lowest corner frequency of the periphery/brain stem function, Ho(s) [or Hos(s)], is a zero at ~0.035 Hz, corresponding to a differentiation of linear acceleration with a time constant of 1/(2pi 0.035) = 4.5 s. Because data were not collected at frequencies <0.02 Hz, the differentiation time constant might be underestimated and the corner frequency might in fact be <0.035 Hz. This zero is only compensated by a pole at ~0.4 Hz, suggesting that brain stem pathways clearly differentiate the input linear acceleration for at least a decade of frequencies up to ~0.4 Hz. At higher frequencies, the transfer function is more complex. Nevertheless, the important characteristic of the fitted function is that the zero/pole alternation is such that in no frequency bandwidth can the properties of the reflex be described or even approximated by a brain stem integrator. Considering the stable transfer function Hos(s), for example, the zero/pole pair described above is accompanied by a second zero/pole pair (s + 21.7)/(s + 45.5), where the numerator's corner frequency (21.7/2pi  = 3.4 Hz) is again lower than that of the denominator (45.5/2pi  = 7.2 Hz). Thus both pole/zero pairs represent compensated differentiators rather than integrators as previously suggested (Raphan et al. 1996).

Telford et al. (1997) have modeled the horizontal response sensitivity in squirrel monkeys using the combination of a leaky integrator (corner frequency at 0.6 Hz) and a high-pass filter (corner frequency at 3.2 Hz). This relatively simple transfer function adequately described the dependence of response sensitivity at 0.5-4 Hz. The transfer function used by Telford et al. (1997) is in fact very similar to the mid-frequency subset of Hos(s), i.e., the smaller pole and the larger zero. Interestingly and similarly to our results, this simple transfer function did not describe adequately response phase (thin lines in Fig. 9, bottom; see also Fig. 12 of Telford et al. 1997). This is perhaps the most interesting observation of the present study. Both the results of Telford et al. (1997) and the present data suggest that the details of input/output characteristics of the translational VORs in the broad frequency range of 0.02-25 Hz cannot easily be described with a low order, rational transfer function with stable (i.e., negative) poles. In addition to stable poles at 0.4 and 7.2 Hz, inclusion of an unstable pole with a corner frequency of 1.7 Hz was necessary to accurately model the data (Fig. 9, compare thin and thick solid lines). It is possible but unlikely that local minima or inadequate models were responsible for this observation, because not only several iteration algorithms but also several different initial conditions and different transfer functions (up to eighth-order systems) were attempted (see METHODS). In addition to the positive poles, the lowest order transfer function that would accurately describe the data was also characterized by two positive numerator roots. The distributed spatiotemporal nature of the input signals and possible convergence of signals from the two sides of the striola (Uchino et al. 1997), as well as central spatiotemporal interactions (Angelaki 1993) might be responsible for these nonminimum phase properties.

The suggestion of high-pass filtered dynamics in the afferent/brain stem aspects of the reflex do not negate the need for a second integration in the translational VOR. A recent proposal by Green and Galiana (1998), whereby the low-pass characteristics of the eye plant not only remain uncompensated in the translational VOR but are rather constructively used by the reflex to shape its dynamic properties, presents a refreshing alternative to the long-debated second integrator process. By contrast to the angular VOR where plant dynamics must be compensated closely through parallel brain stem pathways (e.g., Minor and Goldberg 1991; Skavenski and Robinson 1973), Green and Galiana (1998) propose that otolith signals are slightly differently processed such that the eye plant dynamics constitute important contributions to the translational reflex properties. The transfer functions used here are also motivated by a similar concept; the dynamics of the eye plant were considered as an important contributor to the reflex performance, providing effectively for the missing integrator filtering at high frequencies.

Translational VOR latency

The reflex delay estimated by fitting the transfer functions to the steady-state sinusoidal responses during lateral translation were ~8-10 ms. We have measured similar latencies during near target fixation and transient head translation using steps of linear acceleration (Angelaki and McHenry 1997). Large latencies of the horizontal translational VOR (~34-60 ms) were reported previously using slower transient translation in humans (Bronstein and Gresty 1988; Gianna et al. 1997). A more recent study of vertical eye movements elicited during free fall reported response latencies of ~16-18 ms (Bush and Miles 1996).

Lateral, fore-aft, and up-down translational VORs

An interesting result of the present study was the observation that the horizontal responses generated during lateral and fore-aft motion were characterized by similar dynamic properties, despite a more than fivefold difference in their absolute sensitivities. In fact, based on the slopes and intersects of the linear regression lines relating horizontal and vertical eye velocity sensitivity of the reflex to horizontal and vertical eye fixation position, both translational VORs are characterized in complete darkness by response sensitivities that would provide ideal gaze stabilization for targets located approximately at a distance of 1 m (the average vergence state in darkness). The difference in absolute sensitivity of the horizontal responses during lateral and fore-aft motions is then because of the fact that a larger horizontal eye movement is required to fixate a target at the same distance during lateral compared with fore-aft motion (see Footnote 1).

Despite a similarity in horizontal response dynamics for lateral and fore-aft motions, the vertical translational VOR generated during up-down motion in supine or right ear down positions were characterized by different dynamics at low frequencies. Specifically, vertical slow phase velocity led linear velocity by as much as 90°-180° at 0.1-0.3 Hz. Different horizontal versus vertical translational VOR dynamics were also reported previously in rhesus monkeys during OVAR (Angelaki and Hess 1996a). Nevertheless, no such difference was observed in squirrel monkeys (Telford et al. 1997).

Torsional eye movements during lateral and up-down motion

A third goal of the present experiments was to investigate the nature of torsional responses during translation. Torsional eye movements during lateral translation were first observed in human subjects during low-frequency (<1 Hz) oscillations (Lichtenberg et al. 1982). More recently, similar responses were also reported in squirrel monkeys (Paige and Tomko 1991a; Telford et al. 1997). It is a common assumption that the interaural component of linear acceleration is the only important inertial cue inducing torsion (Bucher et al. 1992; Markham 1989; Woellner and Graybiel 1959). This assumption has been based on the observation that torsional eye movements are elicited during lateral translation in both upright and supine positions, as well as during off-vertical axis yaw rotations (Angelaki and Hess 1996a; Markham and Diamond 1985; Paige and Tomko 1991a; Telford et al. 1997). The idea that torsional eye movements are solely elicited in response to interaural linear accelerations has been recently challenged by showing that human torsional eye movements differ during lateral translation in upright versus supine positions (Merfeld et al. 1996). If torsional eye movements were tilt responses, their properties would depend on static head orientation relative to gravity. Specifically, if torsion represented the apparent tilt of the resultant gravitoinertial acceleration, torsional eye movements would be larger when tested in upright compared with supine position. On the basis of their results, Merfeld et al. (1996) concluded that two separate inertial cues elicit torsion; interaural linear accelerations and a roll tilt of the gravitoinertial acceleration.

The present results in rhesus monkeys support the hypothesis that torsional eye movements are elicited only in response to interaural linear acceleration and not in response to a roll tilt of the resultant gravitoinertial acceleration. This conclusion is based on the following two observations. First, similar to results in squirrel monkeys (Paige and Tomko 1991a; Telford et al. 1997), torsional slow phase eye velocity during lateral translation was indistinguishable in upright versus supine positions. Second, torsional slow phase eye velocity during lateral translation was indistinguishable with that during yaw OVAR. These results demonstrate that at least in primates the roll tilt of the gravitoinertial acceleration has no contribution to torsional eye movement generation during lateral translation.

Recent evidence suggests that vertical linear accelerations also elicit torsional eye movements (De Graaf et al. 1996; Merfeld et al. 1996). Torsional eye movements also were observed during up-down motion in the present study. These torsional responses were approximately one-half of those during lateral translation. Moreover, there was a small dependence of torsional sensitivity on static head orientation during up-down motion in supine and right ear down positions. Contrary to previous human studies (De Graaf et al. 1996; Merfeld et al. 1996), no consistent disconjugacy in torsional eye movements was observed during up-down motion in supine orientation. Nevertheless, the torsional eye movement components during up-down motion were small and highly variable in both primates and humans and their functional significance, if any, remains largely unknown.

Torsional vs. horizontal eye movements during lateral translation: Is there any evidence of differential low- vs. high-pass filtering?

A more important question regarding torsion arises during lateral motion. The sensitivity and dynamic properties of torsional eye movements during lateral translation are tightly related to a more general problem associated with inertial navigation and the ability of the vestibular system to distinguish between gravitational and translational components of linear acceleration. Inertial accelerations due to translation or gravity are physically identical. Thus any linear accelerometer will measure the same acceleration independently of whether it results from translation or the action of a gravitational field. Indeed, primary afferent neurons innervating otolith receptors in the vertebrate ear produce equivalent responses to both tilts relative to gravity and to translational movements (Anderson et al. 1978; Fernandez and Goldberg 1976a-c, Loe et al. 1973). One of the hypotheses proposed to resolve this ambiguity is based on a frequency-segregation of linear accelerations (Mayne 1974; Paige and Tomko 1991a; Telford et al. 1997). According to this hypothesis, high-frequency linear accelerations (>~0.5 Hz) are processed as translational movements (requiring the generation of horizontal eye movements) whereas low-frequency linear accelerations (<0.5 Hz) are centrally interpreted as roll tilts relative to gravity (requiring the generation of torsional eye movements).

If frequency segregation is mainly how the vestibular system discriminates between translational and tilting movements, the horizontal and torsional response components generated during lateral translation should be segregated in frequency, i.e., horizontal eye movements should be characterized by high-pass filter properties and torsional eye movements by low-pass filter properties. This frequency-parsing properties of the horizontal versus the torsional components of the response should be, however, present when each component's sensitivity is expressed in similar units.

When sensitivity was expressed similarly for the two components, there was no evidence for differential low- versus high-pass filtering for torsional and horizontal eye movements at frequencies higher than ~0.5 Hz. Instead, the dynamics of the torsional and horizontal eye velocity were similar during lateral translation (Fig. 5). With sensitivity expressed as eye velocity/linear acceleration, both response components changed little with frequency between 0.16 and 25 Hz. With sensitivity expressed as eye velocity/linear velocity, both response components increased with frequency. Finally, when sensitivity was expressed as eye velocity/tilt velocity (or equivalently, eye position/tilt position), responses decreased sharply with frequency. In fact, other than four-times larger horizontal versus torsional magnitudes, they both had similar frequency dependencies and, depending on definition, sensitivities were flat, increased or decreased with frequency.

Paige and Tomko (1991a) and Telford et al. (1997) have reported that there is a differential low- versus high-pass filtering of torsional and horizontal responses during lateral translation between 0.5 and 5 Hz. Their data are very similar to ours (e.g., Fig. 5, bottom; compare solid with dotted lines). The difference only lies in the fact that the authors based their conclusion on comparisons between horizontal sensitivity expressed in °/cm (or equivalently °/s/cm/s), and torsional sensitivity expressed in °/° of tilt (Telford et al. 1997). In fact, when expressed similarly (e.g., as eye velocity/linear velocity), both torsional and horizontal response sensitivity increased with increasing frequency (see Figs. 5 and 7 in Telford et al. 1997), similarly as in the present study (Fig. 5, middle). Previous reports of the low-pass filtering for torsional eye movements during lateral translation also were based on a similar definition of torsional sensitivity. Lichtenberg et al. (1982) and Merfeld et al. (1996), for example, reported low-pass filter properties when torsional sensitivity was expressed in °/° of tilt. It is true that if the function of the torsional eye movements elicited during lateral translation is to compensate for the apparent tilt, this contribution would decrease with frequency. It is inappropriate, however, to globally describe that torsional eye movements during lateral translation are characterized by low-pass filtered properties without a reference to the sensitivity measure used and the frequency bandwidth of the data.

Two different functional bandwidths for torsional eye movements?

Contrary to the similarity of torsional and horizontal response dynamics at frequencies higher than ~0.5 Hz, the two response components differed substantially at low frequencies. Whereas horizontal sensitivity (°/s/g) decreased sharply with decreasing frequency, torsional sensitivities exhibited only a minor, if any, decline (Fig. 3). In addition, whereas small phase lags developed with decreasing frequency for horizontal slow phase velocity, large phase leads were introduced for torsional responses at low frequencies. According to the sign conventions of this study, torsional eye velocity should lead head velocity by 180°, if the responses were compensatory to an apparent roll tilt of the head. In fact, the data show that this is the case only for frequencies <0.1-0.2 Hz (Fig. 4B, bottom). At higher frequencies, phase leads decrease and above ~1 Hz, torsional responses become anticompensatory to such an apparent head tilt.

In conclusion, the results of this study suggest that there seem to be two different functional bandwidths for the translational VORs. At frequencies above ~0.5 Hz, both horizontal and torsional eye movements are generated with similar dynamics, suggesting a common role during lateral translation. At frequencies <0.5 Hz, the two response components diverge. Horizontal responses are high-pass filtered such that translational VORs would have a negligible contribution to gaze stabilization during translation. Presumably, smooth-pursuit, ocular following and optokinetic mechanisms would completely take over the function of gaze stabilization during translation in the light. Torsional responses, on the other hand, exhibit relatively constant sensitivities (in °/s/g) at low frequencies. Large phase advances, however, change the functional role of these responses such that torsional eye movements could now become appropriate for compensation during an apparent roll tilt (albeit with a very small gain).

Do these results suggest that because of the inherent otolith response ambiguity, the brain "confuses" tilts and translation? Undoubtedly not. In the frequency range where the vestibular system has a major role in motor control and spatial orientation (>0.5 Hz), both horizontal and torsional eye movements are functionally related to the translation, and as long as the semicircular canals are intact and functional the brain correctly discriminates between tilts and translations (Newlands et al. 1997). During low-frequency (<0.2 Hz) movements in the light, the visual system dominates and provides the brain with the necessary information for correct motion discrimination. It is only during low-frequency (<0.2 Hz) motion in complete darkness, that the issue of tilt/translation ambiguity remains, albeit its functional significance is questionable.

    ACKNOWLEDGEMENTS

  The author is grateful to D. Dickman and Q. McHenry for valuable help in setting up the laboratory and to S. Newlands for performing the canal plugging operations, as well as S. Rand and J. Loya for technical assistance. Drs. Bernhard Hess, Shawn Newlands, and David Dickman provided helpful comments on the manuscript.

  This work was supported by grants from the National Eye Institute (EY-10851), the National Aeronautics and Space Administration (NAGW-4377), and the Air Force Office of Scientific Research (F-49620).

    FOOTNOTES

1   Based on simple geometrical considerations, where D is the fixation distance, theta  the horizontal angle, and phi  the vertical angle (theta , phi  < 20°), the sensitivity of an ideal VOR response (defined as eye velocity/linear velocity) can be calculated as
&cjs0358;<FR><NU>dθ/d<IT>t</IT></NU><DE>d<IT>Δy</IT>/d<IT>t</IT></DE></FR>&cjs0359; ≅ 1/<IT>D</IT>and &cjs0358;<FR><NU>dφ/d<IT>t</IT></NU><DE>d<IT>Δy</IT>/d<IT>t</IT></DE></FR>&cjs0359; ≅ −(θφ)/<IT>D</IT>for lateral motion
&cjs0358;<FR><NU>dθ/d<IT>t</IT></NU><DE>d<IT>Δx</IT>/d<IT>t</IT></DE></FR>&cjs0359; ≅ −θ/<IT>D</IT>and &cjs0358;<FR><NU>dφ/d<IT>t</IT></NU><DE>d<IT>Δx</IT>/d<IT>t</IT></DE></FR>&cjs0359; ≅ −φ/<IT>D</IT>for fore-aft motion

2   Because of the nonlinear interactions that suppress horizontal eye velocity modulation during OVAR in intact animals, only OVAR data from the two plugged animals were used in Fig. 9. Linear motion data were averages from all five intact animals. Because of this difference, OVAR sensitivity values were "parallel-shifted" such that OVAR and lateral motion data points coincided at 0.5 Hz. Phase values were not altered.

  Address for reprint requests: Dept. of Surgery (Otolaryngology), University of Mississippi Medical Center, 2500 North State St., Jackson, MS 39216-4505.

  Received 4 February 1998; accepted in final form 17 April 1998.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References
0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society



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