INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

There is general agreement that the control of rapid eye movements relies on a common circuit involving burst neurons that is called into action both for goal-directed saccades to a selected target and during quick phases generated by the vestibuloocular reflex (VOR). Studies on VOR quick phases have typically side-stepped the issue how they might interact with goal-directed saccades. However, preliminary findings by Kitama et al. (1992) in the cat may have interesting implications for this question. These authors reported saccade-vestibular interactions in electrically induced collicular saccades (E-saccades) involving an anticompensatory vestibular signal. Since, if confirmed, such results would seem to provide an interesting window on the neglected topic of saccade-quick phase interaction, we have performed similar experiments in the passively rotated monkey. Our major motivation to pursue the basic observation of Kitama and co-workers is that it argues against the notion of gaze constancy that has become a key feature of most current gaze-control models. To provide a more detailed account of the relevant issues, the subsequent sections will briefly review the literature on the neural control of fast eye movements and on current ideas concerning saccade-vestibular interaction.

Neural control of rapid eye movements

It is well-established that signals for the generation of goal-directed saccades and quick phases of nystagmus finally converge on a common brain stem circuit, involving excitatory burst cells (EBNs) and omnidirectional pause neurons (Fig. 1), known as the pulse generator (for reviews see Hepp et al. 1989; Keller 1991; Moschovakis et al. 1996; Scudder et al. 2002). EBNs specialized for horizontal and for vertical/torsional rapid eye movements have been identified in the pontine reticular formation and the rostral midbrain, respectively. They burst both during goal-directed saccades and quick phases into their ON-direction.

View larger version (19K): [in this window] [in a new window]   Fig. 1. Control signals underlying the generation of goal-directed rapid eye movements and vestibular quick phases. The scheme illustrates the final common pathway for goal-directed saccades and vestibular quick phases. To generate a saccade to a visual target (top), the superior colliculus (2nd row) sends a displacement signal to the burst cells (EBNs) downstream. When the bursters are enabled by the gate, embodied by the omnipause neurons (P), they send an eye-velocity signal to the motoneurons (MN). To generate quick phases during head rotation, the head velocity signal from the semicircular canals (far right) is sent by primary afferents (A) to the vestibular nucleus (VN). After further processing of this signal, burster driving neurons (BDNs) activate the EBNs. An alternative and more hypothetical pathway for generating quick phases, through the colliculus is also indicated (?). In parallel, the position-vestibular-pause cells (PVP) carry a compensatory vestibuloocular reflex (VOR) signal, that is suppressed during large gaze shifts. For simplicity, all neurons contributing to rightward rapid eye movements have been depicted in the right half of the scheme. Internal feedback signals have been omitted.

Omnipause neurons show a steady discharge during fixation and slow phases of nystagmus, but cease firing during both types of rapid eye movements in any direction. By disinhibiting burst neurons in this fashion, the omnipause neurons gate the pulse generator and control the timing of rapid eye movements (Gandhi and Keller 1999; Keller 1974).

In principle, this picture of how the pulse-generator circuit works can explain the stereotyped and intermittent nature of rapid eye movements (Robinson 1975; Van Gisbergen et al. 1981; Zee et al. 1976). The wider question of how and when this system is called into action has been pursued mainly in studies concentrating on more central saccadic control mechanisms (for reviews, see Guitton 1991; Sparks and Hartwich-Young 1989; Wurtz 1996). This work has provided clear evidence that the pathways for saccades to visual, auditory, and tactile targets have already converged at the level of the superior colliculus (SC), which plays an important role in the sensory-motor transformation for the control of saccadic eye movements (Groh and Sparks 1996; Jay and Sparks 1987; Sparks 1986). Burst cells in the deeper layers of the SC exhibit a vigorous burst, tightly linked to saccade onset. In contrast to the temporal coding of saccade components in EBNs, collicular neurons are organized into a two-dimensional topographic map, representing the contralateral hemifield, that specifies the relation between the locus of activity in the map and the saccade vector (Robinson 1972) (see also Fig. 1). Collicular saccade-related burst cells have limited movement fields (Schiller and Stryker 1972; Wurtz and Goldberg 1972).

The generation of quick phases by vestibular signals has received much less attention. Experiments in the cat (Kitama et al. 1995; Ohki et al. 1988; see Markham 1996 for review) have suggested an important role for burster driving neurons (BDNs) in activating the pulse generator during these rapid eye movements (see Fig. 1). The possible role of the SC in the control of quick phases has received only very scant attention, but there is some evidence that quick phases also have a neural representation in the colliculus map. For example, Schiller and Stryker (1972) found that collicular burst cells that become active during goal-directed saccades, may also show movement-related activity during quick phases. Furthermore, Wurtz and Goldberg (1972) described cells in the SC that were active both before horizontal visually guided saccades and before quick phases of caloric nystagmus of equal amplitude. A systematic movement-field study, however, has never been undertaken so that virtually nothing is known on how the spatial distribution of this activity relates to the layout of the collicular map. Reversible-inactivation experiments in the monkey by Hepp et al. (1993) showed that the SC plays an essential role in the generation of voluntary and goal-directed saccades: after inactivation, hardly any saccades were made. Quick phases, on the other hand, could still be generated, although their peak velocities were clearly reduced.

Earlier studies on saccade-vestibular interactions

These results on the afferent signals to the pulse generator for saccades and quick phases, pictorially summarized in Fig. 1, were mostly obtained in dedicated studies concentrating on either system that left open how they operate in conjunction. For example, the fact that gaze shifts often involve a combined eye-head movement immediately raises questions on how collicular targeting signals and oculomotor signals of vestibular origin are combined. The prevailing view is that the SC, long seen as an area for the control of eye saccades, is actually a control center for combined eye-head gaze shifts (Freedman et al. 1996; Freedman and Sparks 1997; Roucoux et al. 1980). If the brain decides that the head should contribute to a voluntary gaze shift, will this simply lead to the addition of the vestibularly driven eye movements that normally accompany head movements when there is no explicit target? Investigations concerning this question have mostly concentrated on the slow-phase signal of the VOR and have provided mixed evidence for slow-phase suppression during large gaze shifts (Guitton and Volle 1987; Laurutis and Robinson 1986; Pélisson et al. 1988; Tabak et al. 1996; Tomlinson and Bahra 1986). Position-vestibular-pause (PVP) cells, which are thought to carry a VOR slow-phase signal, are inhibited during voluntary gaze shifts (Roy and Cullen 1998), possibly by inhibition mediated by the pulse generator (see Fig. 1). On this basis, it has been suggested that the PVPs may play a role in VOR suppression.

If gaze shifts can affect the generation of VOR slow phases, how about the quick-phase mechanism? While it is not hard to see a rationale for suppressing slow-phase signals, which would counteract the gaze shift, predicting the fate of the anticompensatory quick phases is not trivial from a theoretical point of view. In any case, since different neurons are involved, slow-phase suppression does not automatically imply quick-phase suppression. Experimental and theoretical studies considering the issue of whether quick-phase signals may contribute to goal-directed rapid eye movements when the head is moving have been rare (but see, e.g., Barnes 1981; Barnes and Prosser 1981; Guitton and Volle 1987). Against this general background, the present study was undertaken with the objective to clarify how collicular saccadic commands and vestibularly related signals are combined when both systems are activated. We asked how E-saccade properties would be affected by yaw rotation in either direction, at various velocities. One potential scenario is that gaze-shift constancy is maintained by modifying the E-saccade to compensate for the ongoing head movement so as to keep the sum of eye and head movement constant (see Fig. 2). Alternatively, as suggested by earlier findings of Kitama et al. (1992) in the cat, vestibular stimulation may add an anticompensatory component to the E-saccade (see Fig. 2). Such loss of spatial constancy in anticompensatory E-saccades was seen in many experiments. The anticompensatory effect may come about when electrical SC stimulation opens the pause-cell gate, thereby allowing the expression of an anticompensatory movement from the quick-phase system.

View larger version (14K): [in this window] [in a new window]   Fig. 2. Schematic illustration of possible effects of yaw rotation on E-saccades. To preserve gaze constancy during rotation, the saccade vector induced by superior colliculus (SC) stimulation in the stationary animal (E) must compensate for the head displacement occurring during the saccade (H) such that the resulting E-vector equals E-H (gray vector labeled "compensatory"). According to the alternative scenario explained in the text, rotation may cause a manifest violation of gaze constancy by adding an anticompensatory signal to the E-saccade (gray vector labeled "anticompensatory").

This result raised the important further question of whether this putative quick-phase contribution was generated at 1) the vectorial coding stage embodied by the SC motor map or 2) at downstream oculomotor centers carrying component-related signals. Since vector averaging (Robinson 1972) would be expected if quick phases have a collicular origin, the data were analyzed to check for this possibility. The results show no sign of averaging but rather reflect changes in the component aligned with the direction of rotation and therefore seem compatible with the second hypothesis.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Animal preparation and neurophysiological procedures

The experiments were performed in two adult male rhesus monkeys (Macaca mulatta), weighing 6-7 kg, that had been trained to accurately fixate visual targets. The animals will be denoted as BR and GI. All surgical and experimental procedures were reviewed and approved by the university committee for the use of experimental animals. Surgery was carried out in the local central animal facility, which was responsible for housing, feeding, and veterinary care.

SURGERY. To prepare the animals for chronical neurophysiological experiments, two separate sterile surgical procedures were performed under inhalant anesthesia with N₂O/O₂ and ethrane, in combination with infusion of pentobarbital sodium. Blood pressure, heart rate, oxygen saturation, and body temperature were continuously monitored during surgery. The animal was artificially ventilated, and end-tidal CO₂ was maintained around 4%. A venous canule was inserted in a hind leg to allow a steady infusion of pentobarbital and saline. In the first surgical session, a thin gold-plated copper ring (diameter about 17 mm) was implanted underneath the conjunctiva of the right eye, following a method similar to Judge et al. (1980). The ring, which became firmly attached to the eye by connective tissue, served to record two-dimensional eye movements (see below for details). In the second operation, a solid cap was tightly fitted to the skull. This was done by placing 14 tapered titanium bone screws (length 7.5 mm, diameter 2.7 mm) in drilled and tapped holes in the skull and embedding them in sterile orthopedic bone cement (Palacos). Four stainless steel bolts were fixed in the cement cap to allow rigid fixation of the head during experiments. A stainless steel recording chamber (11 mm ID) was stereotaxically implanted over a trephine hole, centered on the midline above the intersection of the midsagittal plane and the interaural line, such that both colliculi could be reached by microelectrode penetrations.

RECORDING OF NEURONAL ACTIVITY. The localization of the SC was based on a number of neurophysiological criteria (Melis and Van Gisbergen 1996). Extracellular activity in the SC was recorded using glass-coated tungsten microelectrodes (impedance 0.3-1.2 M). The electrode was placed inside a stainless steel guide tube to prevent damage to the tip during penetration of the dura and was moved downward by a hydraulic stepping motor (Trent Wells), mounted on the chamber. After amplification (BAK Electronics, Model A-1) and filtering (bandpass 100 Hz to 10 kHz), the electrode signal was monitored on an oscilloscope and fed into a level detector such that individual action potentials could be detected with a time resolution of 10 µs.

Experimental procedures and setup

All experiments were conducted in a completely dark room. While seated in a primate chair, the head-restrained monkey was rotated about either a vertical or horizontal axis through the cyclopean eye using a motor-driven vestibular stimulator. Chair position was measured using a digital position encoder with an angular resolution of 0.04° (sample rate: 500 Hz). Visual targets were presented using an array of red light-emitting diodes (LEDs). The array was attached to the vestibular stimulator, with the center LED on the monkey's naso-occipital axis at 0.39 m from the cyclopean eye, so that it moved with the monkey during rotations. LEDs were positioned on the intersections of seven circles at 5, 10, ... , 35° and 12 meridians every 30°. To calibrate the eye-ring signals, sessions started with a run in which the monkey made refixations from the central fixation LED to each of all 84 peripheral targets and maintained fixation as long as it was visible.

EYE POSITION RECORDING. Two-dimensional eye position relative to the head was recorded using the double-magnetic induction technique (Bour et al. 1984). Two oscillating perpendicular magnetic fields (horizontal: 48 kHz, vertical: 60 kHz) induced an eye-position-dependent electrical current in the implanted eye ring, which, in turn, induced secondary currents in a sensitive pickup coil that was mounted directly in front of that eye. A nulling coil, placed some distance away from the recording eye on a rigid manipulator, electronically canceled the primary eye-position-independent signal component induced by the magnetic fields. After amplification and demodulation by lock-in amplifiers (PAR 128A), the raw horizontal and vertical eye position signals were low-pass filtered (3 dB at 200 Hz, 4th-order Bessel filter) and sampled with 12-bit resolution at 500 Hz per channel (CED 1401plus). This technique provides a high-resolution eye-position recording (~0.2° in all directions) with only small nonlinearities that can be easily accounted for using a relatively simple calibration procedure (see Data analysis).

Paradigms combining collicular microstimulation and vestibular stimulation

VESTIBULAR STIMULATION. The experiments were designed to investigate how E-saccades were affected by vestibular stimulation compared with control data collected in absence of vestibular stimulation. In all sessions, vestibular stimulation was applied by rotation about the vertical axis, using a 0.15-Hz sinusoidal profile with a maximal velocity of 66°/s and an amplitude of 70°. In each run, the monkey was rotated continuously for 80 s. In six sessions, the monkey subsequently was also rotated about a horizontal axis (0.2 Hz, 57°/s, 45°). In these combined yaw-pitch sessions, we used the same velocity profile also for yaw rotation.

ELECTRICAL STIMULATION. E-saccades were elicited by electrical stimulation of sites in the deeper layers of the caudal SC with a train of constant-current biphasic pulses (BAK Electronics, Model BPG-1). The train always had a pulse frequency of 500 Hz with each pulse lasting 0.2 ms. We reliably elicited various amplitude saccades at 26 different collicular sites (n_BR = 20, n_GI = 6). At each site, threshold was determined by gradually increasing the current strength. Stimulation threshold was defined as the current intensity where at least 90% of all stimulations led to a saccadic response while the monkey was scanning the experimental room. Experiments were then conducted with a current up to 2.5 times threshold. With respect to train duration, two different stimulation paradigms were in use. In the long paradigm (n_BR = 21, n_GI = 5), we used train durations between 34 and 66 ms, ensuring that the site-specific maximum amplitude E-saccade (Stanford et al. 1996) was elicited. At some sites (n_BR = 7, n_GI = 4), we also applied a short 20-ms pulse train (short paradigm). Since the two paradigms typically yielded different E-saccades, we will describe the results as coming from different experiments. As a result, the total number of experiments (37) exceeds the number of sites.

Data analysis

CALIBRATION OF EYE POSITION. Horizontal and vertical eye-coil signals were calibrated off-line using fixation data obtained in the eye-coil calibration run at the beginning of each experimental session. Two neural networks, one for each position component, were trained to fit the raw fixation data to the target locations, using a back-propagation algorithm based on the gradient-descent method of Levenberg-Marquardt (Matlab, the Mathworks). This algorithm was used to correct for the inherent nonlinearity of the double-magnetic induction technique. Each network consisted of two input units, representing the raw horizontal and vertical signal, three hidden units and one output unit, representing either the desired calibrated horizontal or vertical position signal (Melis and Van Gisbergen 1996). Raw eye-coil signals were subsequently calibrated by applying the resulting feed-forward networks. Calibration errors, i.e., the remaining error between actual target position and corrected signal, were typically less than 0.5°, on average. In all figures rightward and upward eye and chair position will be denoted as positive.

SACCADE DETECTION AND SELECTION. Saccade detection was performed on the calibrated eye position signals on the basis of separate velocity and acceleration/deceleration criteria for saccade onset and offset, respectively. All detection markings were checked by the experimenter and adjusted if necessary.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

To investigate the effect of vestibular stimulation, E-saccades were elicited by electrical microstimulation in the SC during passive head rotation and during rest. We will first provide data on the rapid and slow eye movements during vestibular stimulation and present an overview of the range of E-saccade vectors tested in the yaw-rotation experiments. Subsequently we describe the effect of vestibular stimulation on the metric and kinematic properties of E-saccades.

Characteristics of nystagmic eye movements and range of tested E-saccade vectors

Figure 3A shows eye position traces during yaw rotation. At the time marked by the arrow, the electrical pulse train started and after a short latency an E-saccade was made to the left and down. Since the E-saccade was elicited during ongoing sinusoidal rotation, it occurred against a background of nystagmus eye movements. The compensatory slow phase moved the eye in a direction opposite to the head rotation (average gain: 0.79 ± 0.08), while the anticompensatory quick phases prevented the eyes from getting stuck at the border of the oculomotor range. As noted before, the quick phases did not just reset the eye to the straight-ahead position, but typically ended at a more eccentric position, displaced into the direction of rotation (see, e.g., Chun and Robinson 1978). This so-called shift of the beating field is further illustrated in Fig. 3B, which shows quick phase end positions relative to the head as a function of head-velocity phase, revealing a clear relation between the end points of quick phases and instantaneous head velocity (gray line).

View larger version (41K): [in this window] [in a new window]   Fig. 3. Properties of quick phases and E-saccade vectors. A: horizontal (H) and vertical (V) eye-position traces of nystagmus and an E-saccade elicited during a half cycle of vestibular stimulation (chair). B: the horizontal offset position of a large number of quick phases (n = 2,000) as a function of head rotation phase to illustrate the shift of the beating field. Since the monkey's attention was attracted by flashing the central light-emitting diode (LED) every 4 s (see METHODS), all eye movements made until 750 ms after this flash were discarded in order to isolate pure vestibular quick phases. Quick phases did not reset the eye to the straight ahead position, but moved the eye to a more eccentric position. Note that there is a clear relation with instantaneous head velocity (gray line), with a small phase lead (6.7°). Quick phase end position was roughly linear with chair velocity (slope 0.47 s). The distribution of quick-phase displacement vectors is presented in C, coded by gray levels. Quick-phase vectors (n > 29,000) ended up in 2 similar distributions, associated with leftward and rightward rotation. Note that the mean leftward and rightward quick-phase vectors (+) showed a clear downward vertical component of almost 5°, probably to compensate for upward eye position drift (see A). This downward bias was also observed in monkey GI (3.4°, data not shown). The open circles represent the E-saccade vector end points that were elicited in monkey BR by microstimulation in the right SC.

As shown by the gray-shaded density plot in Fig. 3C, the metric properties of quick phases in the absence of electrical stimulation showed wide scatter. The mean quick-phase vector (+) had a horizontal component of 23.0°. The downward component of the mean quick-phase vector may reflect compensation for the clear upward eye position drift in the dark (see trace V in A), as proposed by Fuchs et al. (1996). The upward drift (velocity ~5°/s) was present in both monkeys. For comparison, the open circles in Fig. 3C represent all mean E-saccade vectors that were obtained in the control experiments performed in monkey BR (stimulation in right SC). As can be seen, their amplitudes varied between 3.2 and 27.6°, and their directions covered the range from 113 to 243°.

Dependence of E-saccade metrics on head velocity

Qualitative observations by Kitama et al. (1992) in the cat suggest that vestibular stimulation may change E-saccade metrics. We checked to what extent this is also true in the monkey and pursued the suggestion from this earlier work that yaw rotation affects primarily the horizontal component. Our results show convincing metric changes in most experiments but also revealed that not all effects were alike.

Figure 4 shows results from an experiment where rotation introduced an obvious change in end point distribution. E-saccades in the stationary control condition, represented by gray squares, were directed to the left and down. Filled circles indicate E-saccades elicited when the monkey was rotated to the right at chair velocities exceeding 20°/s; open circles denote saccades elicited during leftward yaw rotation in the same velocity range. Note that during rotation, saccade vectors scattered more widely than the controls. It is clear that saccades elicited during rightward rotation generally had smaller horizontal components than those elicited during leftward rotation, i.e., into the half field of the E-saccade vector. In addition, in this experiment, the vertical component also showed an effect of yaw rotation. So, effectively, yaw rotation into the half field of the E-saccade tended to make it bigger while opposite rotation made it smaller than in the control condition. However, as further analysis will show, just looking at end points may be deceiving since effects of head velocity are superimposed on effects of initial eye position. A statistical analysis was performed to isolate these two effects. First, vestibular stimulation gave rise to nystagmic eye movements that caused some variability in E-saccade starting positions, despite measures to limit this effect (see METHODS). Since it is known that E-saccade vectors may depend on initial eye position (Freedman et al. 1996; Klier et al. 2001; Segraves and Goldberg 1992), it was essential to quantify the impact of this phenomenon on E-saccade metrics. Second, we ascertained to what extent the variability in E-saccade metrics could be related to the direction and magnitude of head velocity. Both factors were investigated separately for horizontal and vertical components.

View larger version (19K): [in this window] [in a new window]   Fig. 4. Example of the effect of yaw rotation on E-saccade metrics. E-saccades elicited during rest () and during leftward () and rightward rotation () are shown (the 1st 15 saccades recorded in each condition). Note that yaw rotation systematically changed the E-saccade vector. In general, E-saccades elicited during rightward rotation were smaller than the control saccades. E-saccades evoked when the monkey was rotated to the left, into the half field of the E-saccade, were larger. Data from monkey BR. Stimulation duration: 20 ms.

To quantify how horizontal (E_H) and vertical components (E_V) of E-saccades in a given experiment were related to initial eye position at saccade onset and to head velocity, we performed a multiple-linear regression

(1)

where E_Hini and E_Vini represent initial horizontal and vertical eye position and _yaw represents horizontal head velocity. Figure 5 shows the linear regression results for the horizontal (left-hand panels) and vertical (right-hand panels) component of all E-saccades elicited during the same experiment as shown in Fig. 4. For both components there was a reasonable correlation between data and model fit (goodness-of-fit values 0.69 and 0.49, A and B). Model fits were generally better for the horizontal component (mean R² for horizontal 0.47 ± 0.25; vertical 0.30 ± 0.21, based on all data from the 2 monkeys).

View larger version (26K): [in this window] [in a new window]   Fig. 5. Combined effect of initial eye position and head velocity on E-saccade metrics. A multiple linear-regression analysis was performed to quantify the relation between E-saccade component size, initial eye position and head velocity (see Eq. 1). Together, E-saccade onset position and head velocity can explain a considerable proportion of the variations in both horizontal (A) and vertical (B) component, as can be seen from the goodness-of-fit values (0.69 and 0.49, respectively). A graphic impression of the underlying relationships can be derived from so-called partial regression plots that show how changes in initial eye position (C and D) or head velocity (E and F) account for variations in component size, here shown relative to the mean component size. The slopes of the regression lines equal the coefficients found in the multiple regression. Note that an eccentric onset position at E-saccade onset had a clear effect. The effect of head velocity was stronger on the horizontal than on the vertical component. Note that both relationships are linear. Since initial eye position and head velocity have an effect of equal magnitude on E-saccade metrics, end-position plots like Fig. 4, where both effects are expressed superimposed, are of no use to get an impression of the specific effect of head rotation. Arrows in E and F indicate how the slope of the 2 relationships determines M-vector components. Same experiment as in Fig. 4.

As can be seen from the coefficient values (a_H = 0.45 ± 0.04 and a_V = 0.55 ± 0.06), significant at the P < 0.001 level (t-test), the experiment in Fig. 5 had a clear E-saccade onset-position effect in both components. To visualize this effect of initial eye position in isolation, the partial-regression plots in Fig. 5, C and D, show how variations in E-saccade onset position correlate to changes in component size. The slopes of the regression lines reflect coefficients a_H and a_V, respectively. The effects of initial eye position in this experiment were far from negligible, as the range of approximately 10° in associated component variations indicates. Note that both components showed a similar onset position dependence, with comparable slopes and goodness-of-fit values. The position effect was significant (t-test, P < 0.05) in the majority of experiments, both for the horizontal (26/37) and the vertical component (33/37).

However, initial eye position accounted only partly for the observed E-saccade scatter. As shown by the partial-regression plots in Fig. 5, E and F, there was an additional clear relationship between head velocity and saccade component size. Note that changes in component size increased linearly with head velocity, and that leftward and rightward rotation altered the metrics of the E-saccade in opposite directions. The effect, however, was more pronounced in the horizontal component as expressed by the difference between coefficients m_H = 0.095 ± 0.006 s and m_V = 0.025 ± 0.005 s.

If the two factors in the multiple regression equation (initial eye position and head velocity) are strongly correlated, caution is warranted to avoid erroneous conclusions. Collinearity becomes a possible point of concern for correlations beyond r = 0.80 (Glantz and Slinker 1990). We found that the actual correlations between the two factors remained below this value without a single exception (horizontal: r = 0.40 ± 0.16; vertical r = 0.22 ± 0.15). As an additional check, we compared goodness-of-fit values (R²) for Eq. 1 and a reduced version lacking the head velocity term. The results showed that the head velocity term significantly improved the R² values of the model in 31 of 37 experiments for the horizontal component. This number was considerably smaller for the vertical component (20/37). The partial R² for head velocity ranged from 0.00 to 0.91 (mean: 0.37 ± 0.28) for the horizontal component. In the vertical component we found a range from 0.00 to 0.37 (mean: 0.09 ± 0.11). An additional indication that the analysis yielded consistent results is the similarity of the initial eye position dependence in rest and during rotation (correlation coefficient r = 0.90, slope 0.88 ± 0.06). The bias (coefficients b_H and b_V) was also similar during rest and during yaw rotation (correlation coefficient r = 0.99, slope 0.98 ± 0.01).

We focused the regression analysis on head velocity, but could the relation with head velocity actually represent a hidden relation with head position? Since in a sinewave each head position has two head velocities associated with it, it is unlikely that variations in head position would produce a tight relation with velocity. Indeed, only two experiments that showed a significant relation with head velocity displayed a stronger relation with head position when we did the regression with head position rather than head velocity. Only one experiment without a significant head velocity relation yielded a significant effect of head position. Since head position and head acceleration are perfectly negatively correlated in a sinusoidal profile, this result also argues against a hidden relation with head acceleration in the overwhelming majority of experiments.

In summary, the multiple-regression analysis is an adequate approach to separate and quantify two distinct sources of variability in E-saccades with consistent results. Most sites show a robust relation between the size of the horizontal component and head velocity.

Characteristics of the metric rotation-effect

In what follows, we found it convenient to visualize the isolated metric effect of head rotation as a vector, termed M-vector. The M-vector was defined as the change in the E-vector in response to a 50°/s rotation into the half field of the E-saccade. As illustrated in Fig. 5, its components were computed by taking m_H × 50°/s for the horizontal (Fig. 5E) and m_V × 50°/s for the vertical component (Fig. 5F). Note that each experiment yields one M-vector. So, the experiment in Fig. 5 yielded an M-vector with a horizontal component of 4.75° (0.095 s × 50°/s) and a vertical component of 1.25° (0.025 s × 50°/s) that was directed to the left and downward. Since the M-vector was directed into the left half field, just as the E-vector (see Fig. 4), the head-velocity effect was anticompensatory. If the system were to keep the rapid gaze shift constant in the presence of head rotation (see Fig. 2), the M-vector should have been directed away from the E-saccade (rightward in this case). The M-vector was also slightly downward, but less than suggested by the raw data in Fig. 4, which still contain the initial eye position effect. Our further analysis will first concentrate on the question to what extent these M-vectors had the appropriate characteristics (sign and amplitude) to maintain E-saccade gaze constancy during head rotation.

In Fig. 6 we show all E-saccade vectors (left-hand column) and the corresponding M-vectors (right-hand column), both for monkey BR (top row) and for monkey GI (bottom row). Since the monkeys were stimulated in different colliculi, their E-saccades were directed into opposite hemifields. M-vectors occupied a much narrower direction range than the E-saccades, mostly close to the horizontal axis.

View larger version (24K): [in this window] [in a new window]   Fig. 6. Overview of E-saccade vectors and M-vectors obtained in the 2 monkeys. Data from all yaw rotation experiments in monkey BR (top panels) and monkey GI (bottom panels). A variety of E-saccades was elicited, with amplitudes up to ~25°, and a wide range of directions (A and C). This is in clear contrast to the M-vectors, that all lie close to the horizontal axis (B and D), showing that yaw rotation mainly modulated the horizontal component. Note that M-vectors can have amplitudes up to 8.3°, indicating that the vestibular modulation effect was often substantial. Notice also that M-vectors can be directed opposite to the corresponding E-vector. Pooled for both monkeys, the majority of the experiments (BR: 26 of 28; GI: 5 of 9) showed a significant modulation of the horizontal component, whereas a smaller number (BR: 14; GI: 6) exhibited a significant effect on the vertical component (P < 0.05).

VIOLATIONS OF GAZE CONSTANCY. Recall that adjusting the E-saccade for the head rotation, in order to keep the gaze shift constant, requires a horizontal M-vector that is directed away from the E-saccade. Such oppositely directed M-vectors were found in 14 of 37 experiments (t-test, P < 0.05), but these vectors were always relatively small. By contrast, in 17 experiments we saw typically very robust anticompensatory effects (t-test, P < 0.05). In the remaining experiments (6/37), the M-vector was not significant.

View larger version (18K): [in this window] [in a new window]   Fig. 7. Lack of spatial constancy during E-saccades. The size of the horizontal M-vector component is shown as a function of E-saccade duration in A. The solid line is a prediction of the horizontal M-vector component if a 50°/s head movement occurring during the E-saccade were completely compensated: e.g., for a 40-ms duration saccade, the horizontal M-vector component would be 0.040 s × 50°/s = 2.0°. The points would scatter around the horizontal dashed line if there were no effect of head-rotation at all. Note that full compensation was rare. Using the same format, B shows all horizontal K-vector components from both monkeys. The solid line, corresponding to Kh = 50°/s, denotes the expected result if horizontal peak velocity in the E-saccade head slowed down during the passive head movement so that gaze peak velocity would remain constant. Actually, virtually all experiments yielded the opposite effect (velocity enhancement). Data points near the dashed line (Kh = 0°/s), showing no kinematic effect, are rare. Note that, unlike in A, there is no clear relation with E-saccade duration.

DIRECTIONAL SCATTER. A plausible explanation of the trend toward anticompensatory effects is that the electrical stimulation may have enabled both the saccadic and the quick-phase system. If so, the question arises whether the putative quick-phase system contribution had a collicular or a more peripheral origin (see INTRODUCTION). With this issue in mind, we analyzed the directional variability in M-vectors (Fig. 6) from the perspective of two hypotheses, each with different predictions.

View larger version (9K): [in this window] [in a new window]   Fig. 8. Schematic illustration of 2 vestibular-saccade interaction hypotheses. The 2 hypotheses predict different effects of yaw rotation on the E-saccade vector. The white vector marked Es denotes the E-saccade vector during rest, in the absence of vestibular stimulation. The gray vector Ev is the prediction of the E-saccade during a 50°/s leftward rotation that yields leftward quick-phase vector Q. The rotation-alignment idea (left) proposes that only the E-component aligned with the direction of rotation is modulated. So, in the case of yaw rotation, only a horizontal vestibular contribution is added, while the vertical component remains unaffected. The vector-averaging hypothesis (right) assumes that E-saccades during rotation reflect a compromise between the E-saccades during rest and the ongoing quick phases, based on weighted averaging. The M-vector for each hypothesis (M = Ev  Es) is also shown.

View larger version (12K): [in this window] [in a new window]   Fig. 9. Illustration of M-vector predictions. A: the E-saccade vectors from 3 experiments in monkey BR. The end point of the average quick-phase vector during head velocities between 45 and 55°/s is marked by a plus sign (+). The effect of vestibular stimulation on E-saccade metrics is expressed in the M-vector (see text for details). The M-vectors obtained in the 3 experiments (B) all point to the left, indicating that rotation into the hemifield of the corresponding E-saccades increased their amplitudes, mainly by modulating the horizontal component. Predictions of the vector-averaging hypothesis are shown in C. Note that predictions from the averaging hypothesis do not match the observed M-vectors at all (see text for more details).

View larger version (27K): [in this window] [in a new window]   Fig. 10. Summary of yaw-rotation effect on E-saccade metrics. A: all E-saccade vectors, pooled from both monkeys. Saccades were elicited in a wide variety of directions, with different amplitudes. The corresponding M-vectors are shown in B. Note that in contrast to the directions of the E-vectors, most M-vectors were close to the horizontal axis, indicating that mainly the horizontal component was modulated by yaw rotation. As explained in the text, we tested 2 vestibular-saccade interaction hypotheses. The M-vector distribution according to the averaging idea is shown in C. The predicted M-vector population shows a clear discrepancy with the actual M-vectors (B). To evaluate both schemes quantitatively, D shows the actual vertical M-vector component against the predicted value. If the hypothesis was valid, points would scatter round the unity-slope line (labeled "averaging"). Note, however, that the points actually scatter near the horizontal line, representing no vertical metric changes, as predicted by the rotation-alignment model (labeled "align"). Open circles denote experiments in monkey BR; filled circles represent data from monkey GI.

Specific kinematic changes in E-vectors induced by yaw rotation

This section will provide evidence to show that, in addition to the metric effect described earlier, vestibular stimulation often also had clear consequences for the kinematic properties of metrically matched E-saccades. Figure 11 shows the relation between component size and component peak velocity for an experiment yielding left-down E-saccades (E_H = 21.9°, E_V = 8.1°). Open circles represent E-saccades during leftward rotation; filled circles denote E-saccades when the monkey was rotated to the right, both at chair velocities exceeding 50°/s. There was a distinct effect of vestibular stimulation on the kinematic properties of the horizontal component as indicated by the vertical offset in the two clusters. E-saccades with comparable horizontal components exhibited an approximately 100°/s higher horizontal peak velocity during leftward rotations (i.e., into the half field of the E-vector). The vertical component showed hardly any change in peak velocity during leftward rotations (Fig. 11B).

View larger version (14K): [in this window] [in a new window]   Fig. 11. Illustration of vestibular-stimulation effect on E-saccade kinematics. Component peak velocity is shown as a function of component size for E-saccades elicited during leftward () and rightward () rotation at rotation velocities exceeding 50°/s. E-saccades with equal horizontal components (A) showed an increased peak velocity during leftward rotation (into the half field of the saccade). The kinematic effect in the vertical component (B) was much less apparent. Data from monkey BR. Stimulation duration: 66 ms.

Relying on a multiple-regression analysis, the dependence of horizontal and vertical peak velocity in the E-saccade, _Hmax and _Vmax, on component size (E_H and E_V) and horizontal head velocity (_yaw) was quantified with

(2)

For both the horizontal and the vertical component, the regression fits provided a good overall description of the peak-velocity data with goodness-of-fit values of 0.77 for horizontal and 0.80 for vertical (Fig. 12, A and B). Although it is known that the amplitude peak-velocity relation saturates at large amplitudes, we found that good fits could be obtained using the linear approximation of Eq. 2, due to the limited amplitude range in a given experiment (mean R² for horizontal 0.69 ± 0.17; vertical 0.76 ± 0.10). In the experiment of Fig. 12, there was a significant relation between peak velocity and component size as described by coefficients a_H = 20.5 ± 1.4/s and a_V = 24.2 ± 1.1/s (see partial-regression plots in Fig. 12, C and D). Similar highly significant relations were seen for both components in all experiments (horizontal mean partial R²: 0.58 ± 0.17; vertical: 0.74 ± 0.10). The important result from the multiple-regression analysis is that yaw rotation affected horizontal peak velocity of components of equal size in a linear fashion (Fig. 12E). Note that yaw rotation gave rise to a positive or negative change in peak velocity (up to 10%), depending on the direction of rotation and head velocity. The vertical component, on the other hand, showed only a minor kinematic effect (Fig. 12F).

View larger version (26K): [in this window] [in a new window]   Fig. 12. Statistical separation of component size and head velocity effects on E-saccade kinematics. A multiple linear-regression analysis was performed to quantify the relation between component peak velocity, saccade component size, and head velocity (see Eq. 2). This model provides a good overall description of the data for both horizontal and vertical components (goodness-of-fit values 0.77 and 0.80, respectively). As presumed on the basis of the saccadic main-sequence relation, there was a clear correlation between component size and component peak velocity (C and D). As indicated by the different slopes in E and F, the effect of yaw rotation on component peak velocity was more pronounced in the horizontal than the vertical component. Arrows in E and F indicate how the slope of the 2 relationships determines K-vector components. Same experiment as Fig. 11.

Correlations between the terms of the multiple regression were modest (horizontal: r = 0.49 ± 0.25, with 4 experiments exceeding r = 0.80; vertical r = 0.22 ± 0.15), indicating that collinearity was generally not a point of concern. The head velocity term contributed a significant increase in R² values for the horizontal component in 30 of 37 experiments, and in 19 experiments for the vertical component. Partial R² values for the head velocity term ranged from 0.00 to 0.75 (mean: 0.27 ± 0.21) for the horizontal component and from 0.00 to 0.28 (mean: 0.08 ± 0.09) for the vertical component.

Figure 13 provides an overview of the effects of vestibular stimulation on E-saccade kinematics in the two monkeys. Using a similar approach as in the metric analysis (see section "Characteristics of the metric rotation-effect"), the change in peak velocity due to a 50°/s rotation into the half field of the saccade, based on the coefficients k_H and k_V as illustrated in Fig. 12, E and F, was taken as a measure of the kinematic effect (denoted as K-vector). Figure 13, A and C, displays the peak-velocity vectors of the E-saccades whose directions show a close resemblance to the E-vectors in Fig. 6, indicating that E-saccades followed a roughly straight path. The corresponding K-vectors (Fig. 13, B and D) scatter about the horizontal axis, with on average a slight downward component. Kinematic changes were more pronounced in the horizontal component, the horizontal range was approximately three times the vertical range. The typical kinematic effect, seen in almost all (34/37) experiments, was that horizontal peak velocity increased for rotation into the half field containing the -vector (see also Fig. 12).

View larger version (25K): [in this window] [in a new window]   Fig. 13. Overview of E-saccade peak-velocity vectors and corresponding K-vectors for both monkeys. Data from all yaw rotation experiments in monkey BR (top panels) and monkey GI (bottom panels). The directions of E-saccade peak-velocity vectors () closely resemble those of the E-saccade (see Fig. 6, A and B). In both monkeys, the K-vectors scattered about the horizontal axis (B and D). As indicated by the size of the largest K-vectors, yaw rotation at 50°/s could change peak velocity by as much as 70°/s. Most experiments (BR: 24 of 28; GI: 7 of 9) showed a significant change in horizontal peak velocity, whereas a smaller number (BR: 16; GI: 3) exhibited a significant effect on the vertical component (P < 0.05).

To allow comparison with the metric data in Fig. 7A, we show the horizontal components of K-vectors from both monkeys as a function of E-saccade duration in Fig. 7B. The solid line denotes the horizontal K-vector component expected in case of addition of a perfect VOR signal, slowing the E-saccade. Instead, the majority of experiments yielded negative horizontal K-components, reflecting increased peak velocities caused by an anticompensatory effect of rotation. K-vectors clearly fail to show the inverse relation with saccade duration seen in M-vectors (Fig. 7A). As a further sign that the metric effect and the kinematic effect are independent, at least to some extent, there were 23 experiments where M-vector and K-vector were directed in opposite hemifields. In other words, irrespective of whether rotation into the half field of the E-saccade made it larger or smaller, the resulting saccade almost invariably showed velocity enhancement.

As Fig. 14, A and B, shows, K-vectors clustered more tightly about the horizontal axis than the -vectors. Nevertheless, since the vertical K-components are not negligible, the question arises how the data should be interpreted. We compared two hypotheses. 1) K-vectors are aligned with the direction of rotation and 2) K-vectors represent a change in vectorial peak velocity. As in the metric analysis, we found that the rotation-alignment hypothesis provided the best description of the data (Fig. 14C). The vertical K-vector components predicted on the basis of the vectorial hypothesis (line marked "vector") fail to match the observed data, which are close to the rotation-alignment prediction (marked "align"). An analysis of residual errors (listed in Table 1, right-hand side) further substantiated that the rotation-alignment hypothesis was clearly better, in both monkeys.

View larger version (14K): [in this window] [in a new window]   Fig. 14. Effect of yaw rotation on E-saccade kinematics. A: the pooled E-saccade peak-velocity vectors (). The corresponding K-vectors are shown in B (see also Fig. 13). The rotation-alignment hypothesis provides the best description for the data. This is illustrated by the relation between the predicted vertical K-vector component and the actual K-vector component (C). Since the vector-averaging hypothesis specifically concerns a metric effect, it was excluded from the kinematic analysis. Open circles denote experiments in monkey BR; filled circles represent data from monkey GI.

Yaw versus pitch rotation

The yaw-rotation data presented above, strongly suggest that changes in metrics and kinematics of E-saccades predominate in the horizontal component, aligned with rotation direction. To test whether the rotation-alignment hypothesis has a more general validity, we performed separate horizontal and vertical rotation experiments in six different sites and determined M- and K-vectors for each rotation direction. According to the rotation-alignment hypothesis, M- and K-vectors should be aligned with the horizontal axis during yaw rotation, and be aligned with the vertical axis during pitch rotation.

The top panels of Fig. 15 display the results of the metric analysis. E-saccades had various directions into the left hemifield (A), but most yielded horizontally directed M-vectors during yaw rotation (B). During pitch rotation, E-saccades elicited at the same site showed mainly changes in the vertical component (C). Even more convincing support for the alignment hypothesis was provided by the kinematic analysis (bottom panels). Note that during yaw rotation all K-vectors pointed to the left, in the same half field as the peak-velocity vectors. By contrast, pitch rotation changed the picture entirely (F). The fact that peak-velocity vectors showed both positive and negative vertical components (D) explains why there were both upward and downward K-vectors during pitch rotation. A summary of a quantitative comparison is listed in Table 2.

View larger version (25K): [in this window] [in a new window]   Fig. 15. Comparison of the effects of yaw and pitch rotation on E-saccade metrics and kinematics. E-saccades were elicited at the same stimulation sites (n = 6) during yaw and pitch rotation. To further test the rotation-alignment model, we analyzed E-saccade metrics (summarized in the top panels) and kinematics (summarized in the bottom panels). As predicted on the basis of the rotation-alignment model, the M-vectors during yaw and pitch rotation are clearly different. Whereas horizontal rotation results mostly in modulation of the horizontal component, vertical rotation acts mainly on the vertical component. This rotation dependency is also observed in E-saccade kinematics. Only the E-saccade peak-velocity component that is aligned with rotation direction is modulated. The yaw-rotation data from these combined sessions was included in the metric and kinematic analysis of yaw-rotation effects, presented before. Data from monkey BR.