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Perisaccadic Mislocalization of Visual Targets by Head-Free Gaze Shifts: Visual or Motor?

Department of Biophysics, Faculty of Science, Donders Centre for Neuroscience, Radboud University Nijmegen, Nijmegen, The Netherlands

Submitted 14 February 2008; accepted in final form 20 April 2008

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Such perisaccadic mislocalization is maximal in the direction of the saccade and varies systematically with the target-saccade onset delay. We have recently shown that under head-fixed conditions perisaccadic errors do not follow the quantitative predictions of current visuomotor models that explain these mislocalizations in terms of spatial updating. These models all assume sluggish eye-movement feedback and therefore predict that errors should vary systematically with the amplitude and kinematics of the intervening saccade. Instead, we reported that errors depend only weakly on the saccade amplitude. An alternative explanation for the data is that around the saccade the perceived target location undergoes a uniform transient shift in the saccade direction, but that the oculomotor feedback is, on average, accurate. This "visual shift" hypothesis predicts that errors will also remain insensitive to kinematic variability within much larger head-free gaze shifts. Here we test this prediction by presenting a brief visual probe near the onset of gaze saccades between 40 and 70° amplitude. According to models with inaccurate gaze-motor feedback, the expected perisaccadic errors for such gaze shifts should be as large as 30° and depend heavily on the kinematics of the gaze shift. In contrast, we found that the actual peak errors were similar to those reported for much smaller saccadic eye movements, i.e., on average about 10°, and that neither gaze-shift amplitude nor kinematics plays a systematic role. Our data further corroborate the visual origin of perisaccadic mislocalization under open-loop conditions and strengthen the idea that efferent feedback signals in the gaze-control system are fast and accurate.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Orienting the eyes toward a briefly flashed visual target in darkness requires the use of not only retinal but also extraretinal signals because any intervening change of gaze direction prior to the orienting response has to be accounted for. Thus programming a saccadic eye movement needs to incorporate the changes in eye position since the target flash. The present study investigates the occurrence of systematic localization errors of head-free gaze shifts that were elicited by a double-step target flash in darkness, in which the second flash was timed around the first gaze-shift onset. We will first briefly review similar experiments, so far carried out under head-fixed conditions.

Spatial updating

Hallett and Lightstone (1976) showed that the human saccadic system accurately localizes a visual target, flashed before or during an intervening saccadic eye movement in darkness. To account for this behavior, the system is thought to use an extraretinal signal about intervening eye movements to transform the retinal target coordinates into an oculocentric reference frame (Goldberg and Bruce 1990; Jürgens et al. 1981; Scudder 1988; Scudder et al. 2002). Sparks and Mays (1983) demonstrated that accurate open-loop reorienting occurs even when the intervening saccade is experimentally induced by microstimulation of the monkey midbrain superior colliculus (SC), which suggests that the extraretinal signal originates at or downstream from the stimulation site. Subsequent single-unit recordings showed that the saccade-related burst in the population of SC cells carried the oculocentric, updated coordinates of the target (Sparks and Porter 1983) and therefore indicated that the spatial remapping of targets occurred upstream from the recorded cells. Indeed, later experiments have shown that the visual activity of cells in posterior parietal cortex (Duhamel et al. 1992), frontal eye fields (FEFs; Umeno and Goldberg 1997), and SC (Walker et al. 1995) signal the updated target coordinates, even before the onset of a planned saccade (predictive remapping). In an elegant series of electrophysiological experiments Sommer and Wurtz (2002, 2006) showed that FEF cells receive an efference copy of the eye movement from saccade-related SC cells (Sommer and Wurtz 2002, 2006). A neural correlate of spatial updating in the human parietal cortex was recently demonstrated in a functional magnetic resonance imaging study by Medendorp et al. (2003).

Perisaccadic errors

However, a large number of studies have reported systematic localization errors of visual stimuli presented around the occurrence of an intervening saccade, both in darkness under open-loop conditions and in visual-perceptual studies in the light. This was first shown in a study by Matin and Pearce (1965), in which subjects had to report the location of a target flashed in otherwise darkness near the onset of a saccade. Their results indicated that the flash was mislocalized in the direction of the saccade and that the size of the error depended on the timing of the flash relative to saccade onset (the target delay). Dassonville and colleagues showed that similar mislocalizations also occurred for the second saccade in a double-step trial, hinting at the possibility that the perceived direction of the flash and the actual saccade target may share common processing mechanisms. The size of the error varied systematically with the target delay and could be as large as 70% of the first-saccade amplitude (Dassonville et al. 1992, 1995; Schlag and Schlag-Rey 2002). This phenomenon has become known as perisaccadic mislocalization.

The programming of saccades also interferes with the perception of allocentric visual cues. Cai et al. (1997) showed that relative retinal locations of visual dots are perceived to shift with the saccade when a briefly presented probe dot is flashed near the saccade onset, suggesting that the oculomotor system also influences visual processing. Sogo and Osaka (2002) further demonstrated that when two targets are briefly flashed around a saccade, they are both mislocalized. However, the amount of their mislocalization depends not only on the target delay, but also on the interflash interval of the targets, suggesting that the mechanisms causing perisaccadic mislocalization also affect allocentric visual relationships.

Perisaccadic mislocalization of visual stimuli is not confined to open-loop conditions in darkness, but also occurs in the light. There is now clear evidence that in addition to mislocalization in the saccade direction, the perception of visual space becomes transiently compressed toward the saccade endpoint (Ross et al. 1997). Lappe et al. (2000) and Awater and Lappe (2006) argued that this apparent compression results from postsaccadic visual analysis by the perceptual system, in which the presaccadic visual relations are stored in memory and compared with the visual situation immediately after the saccade. Their results thus suggested that visual-spatial perception and saccade programming, like in the open-loop double-step paradigm, may invoke different mechanisms (Bridgeman et al. 1994; Deubel et al. 1998).

The question arises as to why the visuomotor system performs so poorly around the saccadic event: Couldn't it do any better? According to Niemeier et al. (2003, 2007) the visuomotor system may operate in a statistically optimal way. They argued that, due to internal noise or to poor stimulus conditions, the brain has to deal with different and varying uncertainties of the sensory and motor events. They proposed that the visuomotor system builds a statistical model of the sensory environment and of its own motor state, such that it can account for these uncertainties through optimal inference. Simulations showed that, as a consequence, the system will produce the type of error patterns observed for saccadic suppression of target displacement (Niemeier et al. 2003, 2007). A similar line of reasoning was forwarded by Binda et al. (2007), who demonstrated that perisaccadic visual compression nearly disappears when visual stimuli were paired with auditory targets. Apparently, the default dominance of vision over audition in localization tasks may reverse around saccades, when vision becomes less reliable. They used a Bayesian framework to explain their results.

Visuomotor updating models

Under open-loop conditions, postsaccadic allocentric visual cues are absent, and a spatially accurate representation of a visual target in eye-centered coordinates after an intervening eye movement is determined by

(1)

where T_R is the initial retinal error of the target (i.e., prior to the gaze shift at the time of target presentation and S₁ is the intervening saccadic eye displacement since the target offset. Clearly, a localization error in a double-step experiment would occur when either of these two signals is not veridical. Several models have been proposed to explain perisaccadic mislocalization in the double step.

The oculomotor feedback model assumes that the internal representation of the eye movement in Eq. 1 is a sluggish, low-pass filtered version of the actual oculomotor command, but that the visual signal is accurate (Dassonville et al. 1992, 1995; Honda 1990, 1991; Schlag and Schlag-Rey 2002). The perceived direction of the visual flash is therefore given by

(2)

where S₁^P is the internally perceived, sluggish extraretinal eye movement that followed since the target disappeared. As a consequence, an error arises in the direction of the saccade that is given by the difference between the perceived and actual eye movement (Fig. 1A). Due to the dynamics of these signals, the predicted perisaccadic errors resemble those that were indeed observed experimentally.

View larger version (17K): [in this window] [in a new window]   FIG. 1. Different models explaining perisaccadic localization errors for gaze shifts. A: in visuomotor updating models, errors arise as a result of a damped representation of the actual gaze shift, G1 (dashed lines, G1P; Tlead: lead time of the internal signal). These models predict a systematic relation between the localization errors and the primary saccade kinematics, here illustrated for a small and fast (black) vs. a large and slow (red) gaze shift. E2,||: error in the direction of the first gaze shift. B: according to the visual shift hypothesis, the retinal representation of the flashed target, T2, transiently shifts by β(t0) deg in the direction of the primary gaze shift (blue) to T2, reaching the largest shift of about 10° near gaze-shift onset. The resulting error patterns are invariant to changes in the primary gaze-shift properties.

(3)

where t₀ and t₁ represent the visual persistence intervals and is the delay. He showed that the predicted localization error patterns were equivalent to those of the oculomotor model and that this model was also able to account for the visual interactions observed in double flashes (Pola 2007; Sogo and Osaka 2002). Thus perisaccadic localization errors could have a visual, rather than an oculomotor, origin.

Finally, Ross et al. (1997) explained their more complex mislocalization results in the light by errors in both the visual and oculomotor representations. In their formulation, the internal target updating, required by Eq. 1, was performed on the basis of

(4)

in which C(M, S) is a dynamic, nonlinear retinal compression factor (value between 0 and 1) that depends on the target probe's instantaneous retinal eccentricity, M = T_R – S₁ (the dynamic motor error), as well as on the difference between the perceived and actual saccade, S = S₁^P – S₁ (Ross et al. 1997; see Van Wetter and Van Opstal, unpublished data, and supplemental material for technical details).¹ Clearly, when compressed visual-spatial information is combined with a sluggish eye-movement signal, the perceived oculocentric location of the target will also be misjudged.

Similarities and differences

It is important to note that a common feature of the three different visuomotor schemes of Eqs. 2–4 is the use of a damped or blurred representation of the internal eye-movement signal, S₁^P. We have recently pointed out that, as a consequence, and despite their conceptual differences, these models all predict that the resulting localization errors depend in a systematic way on the properties of the intervening saccade, in particular on its amplitude and on its kinematics (see Ostendorf et al. 2007; Van Wetter and Van Opstal, unpublished data). Moreover, our simulations with these models over a large range of model parameters showed that they all predict equivalent error patterns (Pola 2004; Van Wetter and Van Opstal, unpublished data). Figure 1A illustrates this point for the oculomotor model, by showing the expected error patterns for a small and fast (black line), versus a slow and large saccade (red line).

Yet, the results from our double-step experiments indicated that the localization errors were unrelated to the variability in the intervening saccades, which suggested that the errors had a purely visual, rather than an oculomotor, origin. We therefore proposed that around the saccade the visual representation of the target undergoes a transient shift in the direction of the saccade, but that the extraretinal feedback signal is, on average, accurate. The shift depends only mildly on the planned saccade amplitude. According to this simple idea localization errors saturate for saccades exceeding 10 to 15°, and the saccade kinematics do not play a significant role (Fig. 1B).

Head-free gaze shifts

Perisaccadic mislocalization has typically been studied under head-fixed conditions. A recent exception is Vliegen et al. (2004, 2005) who elicited double-step eye–head gaze shifts to visual–visual and visual–auditory double-steps presented around and during the first gaze shift. They observed that the localization errors were smaller than expected from Dassonville's oculomotor model, but were unable to provide a conclusive explanation because stimulus intensities and durations in their experiments differed considerably from those of Dassonville et al. (1992, 1995).

The present study is designed to test the predictions of the four different models mentioned earlier for large and highly variable head-free gaze shifts. Under head-free orienting, the target representation should be invariant to eye- and head movements, and hence accurate updating of the oculocentric target coordinates now requires that

(5)

in which S₁, G₁, and H₁ are the intervening eye-, gaze-, and head-displacement signals since target offset, respectively.

In principle, one could extend the visuomotor updating models described earlier in two different ways, depending on whether the perisaccadic errors were to result from a process that updates the gaze coordinates (G₁) or whether the errors are entirely due to a misrepresentation of the rapid eye-movement (S₁) signal. The former possibility assigns the errors to erroneous feedback of a gaze-displacement signal, which is currently supposed to have a collicular origin (e.g., Freedman et al. 1996; Galiana and Guitton 1992; Goossens and Van Opstal 1997; Guitton 1992; Munoz et al. 1991). In the latter case, localization errors would result from sluggish feedback of eye movement signals, which are considered to arise in the brain stem burst generator (e.g., Scudder et al. 2002; Van Gisbergen et al. 1981). The associated head movement is then assumed to be accurate.

Note that the predictions of visuomotor updating will differ for these two scenarios, given that gaze- and eye-displacement signals are typically dissociated under head-free conditions (Goossens and Van Opstal 1997; Ron et al. 1993).

For the visual shift model, however, the predictions are the same, irrespective of the underlying motor programs. In particular, this simple model also predicts that localization errors should be similar to the patterns reported for much smaller head-fixed saccades (i.e., saturating at about 10° around the gaze-shift onset).

Here we test these predictions for large head-free gaze shifts (amplitudes between 40 and 70°) made to double-step visual flashes in otherwise complete darkness. In this paradigm the gaze-control system has to rely entirely on the retinal target coordinates and on eye- and gaze-feedback signals because no further visual cues are presented. Our data show that the errors are unrelated to the kinematics of the first gaze shift and that, in line with the prediction of the visual-shift model, error patterns are similar to those generated under head-fixed conditions for much smaller saccades.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Subjects

Six subjects (five male, one female, ages 20–49 yr) participated in the experiments. Subject jo is one of the authors; subjects il and bd were inexperienced in gaze-control studies, but were involved in the design and analysis of the experiments. The other three subjects (tg, rw, and pb) were naive regarding the purpose of this study. All subjects had normal uncorrected binocular vision, except for jo who is amblyopic in his right, recorded eye. Informed consent was obtained. Experiments adhered to the principles of the Declaration of Helsinki and the U.S. federal regulations for the Protection of Human Subjects.

Apparatus

Experiments were conducted in a completely dark room (W x L x H = 2.5 x 3.5 x 2.5 m³), in which two pairs of 2.5 x 2.5-m² coils were attached to the left/right walls and floor/ceiling to generate the horizontal (30 kHz) and vertical (40 kHz) magnetic fields needed for the scleral search coil technique (Robinson 1963). The subject was seated in a chair with the head in the center of the magnetic fields. Vision was binocular and the head was free to move in all directions. To provide the subject feedback about his/her posture during the experiment, a metal bar, fixed to the floor of the experimental room, softly rested against the lower part of the neck, without impeding the subject's head movements.

Visual stimuli were provided by green-light-emitting diodes (LEDs; = 568 nm; Knightbright Electronics, L59EGW/CA; diameter 2.5 mm, corresponding to 0.2° viewing angle). The LEDs were powered with current pulses (frequency 150 Hz) and set to a relatively low intensity of 0.8 cd/m² (calibrated with a Minolta LS-100 luminance meter).

To measure eye movements, the subject wore a search coil (Skalar Instruments, Delft, The Netherlands; Collewijn et al. 1975) on the right eye. Head rotations were measured with a custom-made small coil that was attached to a lightweight (150 g) helmet. During calibration of the eye- and head coils, a 40-cm-long thin aluminum rod protruded from the helmet, to position a red LED in front of the subject's recorded eye. This red LED defined a head-fixed visual stimulus that provided the subject accurate visual feedback about head orientation. After the calibration run (see following text), this rod was removed.

Horizontal and vertical components of eye movements were extracted from the eye-coil signal by lock-in amplifiers (model 128A, Princeton Applied Research) that were tuned to the respective field frequencies. Horizontal and vertical head-movement signals were measured with PAR 120 lock-in amplifiers. Signals were low-pass filtered with a fourth-order low-pass antialiasing filter (cutoff at 150 Hz) and amplified with custom-made amplifiers. Signals (four channels) were subsequently digitized at a sample frequency of 500 Hz/channel (DAS-16, Metrabyte) and stored on hard disk for further off-line analysis. Stimulus generation and data acquisition were controlled by a PC 486 that was equipped with a timer board (DT2817, National Instruments) and an I2C board to control the LEDs.

LEDs (n = 85) were mounted on a thin-wire hemisphere with a radius of 0.85 m. The LEDs were mounted at seven different polar coordinate eccentricities, R, and 12 directions, , with respect to the straight-ahead central LED ([R, ] = [0, 0] deg) at R [2, 5, 9, 14, 20, 27, 35] deg, and [0, 30, 60,....., 330] deg, where = 0 is rightward, and = 90° is upward with respect to the central LED.

Paradigms

CALIBRATION PARADIGM.  Each experimental session started with a calibration run to obtain steady fixations of the eye-in-space (gaze), head-in-space, and eye-in-head at all selected LED positions. Each trial started with fixation of the central LED for 600–800 ms. The subject had to align the red head-fixed LED with the central fixation spot. In this way, eye and head pointed roughly in the same direction. When this LED was extinguished, a peripheral LED, selected in pseudorandom order from one of 33 locations [target eccentricities at 0° (five times), at 9° (in the four cardinal directions), or at 20 or 35° (in all 12 directions)], was illuminated for 2.0 s. The subject was required to make an accurate gaze saccade to the new LED and to maintain fixation as long as it was illuminated. When this LED extinguished, the red head-fixed LED on the aluminum rod was illuminated for 500 ms. The subject had to make a saccade toward this second LED, while keeping the head stationary at its newly acquired orientation. In this way, the head-in-space orientation could be calibrated. From the five central LED trials, the eye-in-head offset position E₀, with respect to the helmet LED, could be determined (for more details, see e.g. Goossens and Van Opstal 1997). During calibration, the visual stimuli had an intensity of about 1.0 cd/m². After calibration, the rod was removed from the helmet to allow the subject to make natural eye–head gaze shifts without any restrictions or visual feedback about head movements.

DOUBLE-STEP PARADIGMS.  In the double-step paradigm the initial fixation position was located at [R₀, ₀] = [27, 180] deg, and presented for 600–1,000 ms. The subject had to foveate this fixation spot (note: eye and head were not necessarily aligned in this experiment because subjects did not receive feedback about their head orientation). When the fixation spot extinguished, the first visual target (0.8 cd/m²) would appear after a 100-ms gap of darkness for a duration of 20 ms at either [27, 30] or [27, 330] deg, with respect to straight ahead, i.e., at a retinal location of [R₁, ₁] = [52, ±15] deg from the initial fixation point. The subject had to make a natural gaze shift to this stimulus as fast as possible.

In 92% of the trials, a second brief visual target (0.8 cd/m²) would be presented for 15 ms. The onset of this stimulus was pseudorandomly selected from T [100, 120, ..., 240] ms after the offset of the first stimulus, to ensure an approximately homogeneous distribution of stimulus delays relative to the first gaze shift onset (which typically had a latency of about 200 ms; see Table 1). This second stimulus could be presented at either one of 10 different locations, pseudorandomly selected from [R₂, ₂] = [20, 60], [20, 120], [27, 60], [27, 90], or [27, 120] deg, with respect to straight ahead in the upper visual hemifield, and the other five locations mirrored about the horizontal meridian in the lower visual hemifield, thus creating a variety of retinal target locations. In these trials the subject was required to refixate the perceived location of the second visual stimulus as fast and as accurately as possible. The remaining 8% of trials served as catch trials, in which only the first target was presented. One experimental run consisted of 108 trials: 100 double steps and 8 catch trials. A typical recording session contained two to three experimental double-step runs. Subjects participated in three to five recording sessions, taken on different days.

CALIBRATION AND SACCADE SELECTION.  Data from the eye coil were calibrated off-line by mapping the end fixations of the 33 gaze-fixation points from the calibration paradigm onto their known locations. The optimal parameters that map the digitized voltages onto known degrees of eye rotation were found by training two feedforward neural networks for the horizontal and vertical components of the eye position signals, respectively (e.g., Goossens and Van Opstal 1997; Vliegen et al. 2005). To calibrate the data, the neural networks were applied to the raw data samples.

From the five central fixation trials in the calibration experiments, we determined the orientation of the eye, E₀, when it fixated the red LED on the rod, with respect to the central fixation spot. To calibrate the head-in-space orientation, we used the eye-coil calibration signals when the eye was fixating the head-fixed red LED, as "targets" for the head. Subsequently, the head-in-space orientation was obtained by subtracting the offset, E₀, from the calibrated head-coil signals. Finally, the eye-in-head orientation was found by subtracting the calibrated head-in-space orientation from the calibrated gaze orientation: E_H = G – H (see Goossens and Van Opstal 1997).

Gaze saccades were detected in the calibrated data on the basis of acceleration and velocity criteria for their on- and offsets that could be separately set, and adjusted, by the experimenter. First gaze-saccade responses with an onset latency of <80 or >500 ms and with an amplitude less than half the required gaze vector were excluded from the analysis. Second-saccade responses with a latency (relative to T₂) exceeding 600 ms, amplitude less than half the motor error vector, and a directional error exceeding 45° were also excluded. Double-step trials in which the first saccade was not followed by a valid second response were not considered in the analysis. After passing the selection criteria subjects yielded between 460 and 660 successful double-step responses.

Because the eye-in-head saccade often terminated well before the gaze-saccade offset (for an example, see Fig. 4), we defined the offset of the eye-in-head saccade as the moment of maximum eye displacement during the gaze shift.

View larger version (10K): [in this window] [in a new window]   FIG. 4. An example of spatial and temporal gaze, head and eye trajectories in the flashed gaze-double-step paradigm (subject bd). A: F, fixation spot; V1 and V2, target locations. The gaze localization error, measured in the direction of the first gaze shift, G2,||, is indicated (black-dotted lines). Eye-in-space (gaze) and head-in-space trajectories are similar. The eye-in-head trajectory (black line) is therefore dissimilar from the gaze- and head trajectories. For clarity, only the first eye-in-head saccade is shown. In the data analysis, the first gaze-in-space and eye-in-head trajectories are used to predict the gaze localization error, G2,|| (see METHODS). B: the movements are executed under open-loop conditions because both stimuli (V1 and V2) are extinguished before the first-gaze onset (thick black lines in top). Note that the eye-in-head movement duration (bottom) is shorter than the first gaze shift (measured by the on- (green) and offset (red) lines). After eye-movement offset, the eye-in-space is carried toward the goal by the head. In turn, the gaze duration is shorter than the head movement. Thus the eye stays on target through the operation of the vestibuloocular reflex (VOR).

(6)

where ₁ is the unit vector along the first gaze shift and · denotes the inner product. We also computed the component of the localization error vector along the first eye-in-head saccade vector, ₁. In that case

(7)

Because the gaze vector and the eye-in-head saccade may differ substantially (in size and direction), the errors predicted by the visuomotor updating models may also differ (Fig. 2B).

View larger version (16K): [in this window] [in a new window]   FIG. 2. A: double-step paradigm (inset) and associated gaze shifts, G1 and G2, toward flashed targets T1 and T2, respectively. Target T2 is flashed at delay t0 before the first gaze-shift onset. The primary gaze displacement consists of a head movement, H1, and an eye-in-head saccade, S1. The localization error of G2 is E2, which can be projected along the gaze shift (E2,||,G), or along the eye-in-head saccade (E2,||,S). For clarity, the systematic undershoot has been omitted. B: according to the visuomotor updating models (Fig. 1A), predicted error patterns for the gaze shift (red) and the associated eye-in-head saccade (blue) are different because of their different amplitudes and kinematics.

_G,2

₂

Because the target configurations in our experiments were such that the amplitude of the first gaze shift and the size of the motor error vector for the second target could be correlated, we incorporated both potential factors in our multiple regression analysis (see following text, Eq. 9, and Van Wetter and Van Opstal, unpublished data).

RUNNING AVERAGES.  To visualize the average trend of the errors as function of the target onset delay, a running average was computed by convolving the errors, ranked according to delay t₀, with a Gaussian filter (SD 5 data points; total window width 20 points).

RESIDUAL ERRORS.  Error data obtained from the double-step series were pooled to determine a grand running average, E_2,||(t₀), as a function of the flash delay t₀. To obtain the so-called residual errors, we removed the mean systematic trend in the data (see RESULTS, e.g., Fig. 9B) by subtracting this grand running average from the measured errors (separately for first gaze- and eye-in-head saccades)

(8)

View larger version (24K): [in this window] [in a new window]   FIG. 9. A: localization errors for subject jo (raw data), together with the running average through the data (red line). same format as Fig. 8A. B: running averages for all 6 subjects, together with their grand average (taken over pooled gaze shifts; black line). C: data from the 4 subjects in our previous eye-movement study, together with the grand average of pooled saccades (black line). Note that the magnitude and time course of the head-free gaze- and head-restrained eye-movement errors are remarkably similar.

(9)

in which (X – µ_X)/_X is the normalized (dimensionless) variable (z-score) and parameters [a(t₀), b(t₀), c(t₀)] are the dynamic (dimensionless) partial correlation coefficients obtained at delay t₀.

ILLUSTRATION OF THE ANALYSIS PROCEDURE.  Figure 3, A–C shows how the analysis of Eqs. 6–9 is applied on model saccades (see Van Wetter and Van Opstal, unpublished data, and supplemental data for details). In this example we simulated a large set of gaze saccades that were subjected to the visual persistence mechanism of Pola (2004, 2007; Eqs. 3 and 13). In this simulation, horizontal gaze shifts with amplitudes between 40 and 70° were generated by a simplified version of Robinson's feedback model, in which the asymptote of the nonlinear burst generator was varied to yield both fast (peak at 750°/s) and slow (peak at 350°/s) saccades (amplitudes and peak velocities were randomly selected). Target-flash locations were selected at random from [–14, 0, +14] deg and presented at a random delay between –220 and +220 ms around the saccade onset. In these simulations, it was further assumed that the second gaze shift would always undershoot the target by 10%, which imposed a systematic localization error, proportional to the motor error, across the entire delay interval. We applied the visual persistence model (Eq. 3) of Pola (2004, 2007) to predict the additional perisaccadic localization error as a function of target delay. To that end, the visual probe (a 5-ms pulse) was delayed (by _V ms, here 20 ms) and low-lass filtered (order n_V, and time constant T_V, here 15 ms; see Eq. 10) to produce the retinal persistence signal T_R(t). The internal representation of the gaze shift was identical to the actual gaze shift, but delayed by _G ms (here 30 ms). In these example simulations, we used two different visual filters, to generate different patterns of predicted gaze-localization errors. For the red symbols (and red line, which represents the running average through the 500 data points) the filter was of order n_V = 4 (parameters similar as in Pola 2004; see legend Fig. 3A), whereas for the blue symbols, n_V = 2. Figure 3A shows the predicted error patterns for the two implementations. The point of this panel is that the predicted patterns strongly depend on the precise parameter values (e.g., the mean peak error dropped from 22 to 10°). We then determined the residual errors for these two data sets, by subtracting from each data point the running average at that delay (Eq. 8). The result is shown in Fig. 3B. The two data sets now scatter around the zero line (both running averages are on the zero line), but an increase in error variability before and during the saccade can also be observed. Presumably, this is caused by the variability in the saccade parameters. To assess the influence of the gaze shift kinematics, we then subjected these data to the regression analysis of Eq. 9. Figure 3B illustrates the numerical results for the red data set selected in three different time windows, centered around t_on = [–150, –40, +70] ms. Finally, Fig. 3C shows the behavior of the regression parameters for both data sets across the entire delay interval (the three moments of Fig. 3B are also indicated). The main point here is that, despite some quantitative differences between the two model implementations, the qualitative dynamic behaviors of the parameters are remarkably similar: for amplitude, the dependence is monophasic, whereas the velocity dependence follows a clear biphasic pattern. As a consistency check, the reconstructed influence of the motor error was negative and nearly constant across the entire delay interval (due to the fixed 10% undershooting strategy). In Van Wetter and Van Opstal (unpublished data) we demonstrated that these curves are a hallmark for all models that assume an inaccurate, sluggish perceived eye-movement signal (Eqs. 2–4; see also Eqs. 10 and 11), irrespective of the exact properties of the underlying saccades and of the visuomotor feedback mechanisms.

View larger version (25K): [in this window] [in a new window]   FIG. 3. A: simulated gaze errors for 2 realizations (red and blue symbols and running averages, respectively; see legend) of the visual persistence model of Eq. 3. Gaze amplitudes (40–70°), gaze-shift kinematics (350–750°/s), second flash location, and flash timing were all selected at random, thus generating 500 responses for each model. B: residual errors for the 2 models after subtracting the running averages from each data point. Multiple regression was performed on these residues, for which 3 analysis windows (at –150, –40, and +70 ms) are highlighted with the resulting fit parameters. C: parameter dynamics for the 2 models across the entire delay interval. Note similarity of the curves, despite the large differences in absolute error predictions (see A).

View larger version (18K): [in this window] [in a new window]   FIG. 5. Dissociation of eye- and head movement contributions to head-free gaze shifts for a typical head mover (jo) (A) and eye mover (pb) (B). For the head mover, the amplitude of the eye-in-head saccade and the gaze-in-space saccade do not correlate well, and the eye movement is much smaller than the total gaze shift. For the eye mover, the eye- and gaze amplitudes have a positive correlation; the head-movement contribution to the gaze shift is typically smaller than that for the head movers.

Predicted localization errors of gaze shifts and eye saccades.

VISUOMOTOR UPDATING MODELS.  The same data analysis as in Fig. 3 was run on perisaccadic gaze errors that were predicted by the different models (see INTRODUCTION). In our previous study we ran various versions of the visuomotor updating models on our data and showed that the actual parameter values for the retinal stimulus filter, the eye-movement filter, or the combination of both, were not critical for the regression results. Indeed, a given error pattern could be obtained with all versions of these models, albeit each with its own parameter settings (Pola 2004; Van Wetter and Van Opstal, unpublished data).

Although the predicted amplitude of the localization errors depends strongly on the model parameters (e.g., Figs. 3A and 10A), the results of the normalized multiple linear regression analysis on the residual errors (Eq. 9) do not (Fig. 3C). Thus the dynamic parameter behaviors were very similar for the different visuomotor models, as well as for considerable variations in the parameters of each of these models (see Fig. 5 in Van Wetter and Van Opstal, unpublished data; and also Figs. 3 and 9 in this study).

View larger version (27K): [in this window] [in a new window]   FIG. 10. Sensitivity analysis of the visuomotor model predictions. A: the predicted error patterns (here illustrated for 12 different parameter sets of the gaze-motor feedback model, Eqs. 7–9) depend strongly on the model parameters (lead time and filter characteristics indicated on right). The prediction for the default model (solid black curve, identified by DEF) deviates strongly from the measured data (red curve, DATA, running average through data points). Note that some model parameters lead to a better approximation of the data. B: residual errors (Eq. 8) were computed by removing the average trend in the data (red) and in the different model predictions (black/gray lines) from the data points. All curves now nearly superimpose on the zero line. The multiple regression analysis of Eq. 9 was then performed on these data sets (n = 13). C: the predicted dynamic influence of gaze amplitude [a(t0), blue], mean gaze velocity [b(t0), red], and gaze motor error [c(t0), green] is not very sensitive to the different model parameters. Bold colored curves: default model parameters; thin curves: the 11 other parameter sets shown in A. Black curves: regression results on the measured data of subject bd, shown in B. The data do not follow any of the model predictions.

To that end, we filtered each measured gaze- and eye-in-head movement trajectory toward the first target, G₁(t) and S₁(t), respectively, with a low-pass filter. The default parameters of this filter were taken from our earlier eye movement experiments (Van Wetter and Van Opstal, unpublished data). The impulse response of this filter is given by

(10)

where T_s = 20 ms, the filter's time constant, and n_s = 5, the order of the filter. The perceived gaze-displacement or eye-movement trajectory is thus given by the convolution

(11)

The internal movement signal had a default lead of T_lead = 150 ms. The expected localization error for each trial is then determined by the difference between the internally perceived (Eq. 2) and the actual location (Eq. 1) of the target in oculocentric coordinates

(12)

In the gaze-motor feedback model, the retinal target location T_R in Eq. 5 is perceived correctly. Therefore the predicted perisaccadic error is given by the difference between perceived and actual gaze- or eye-displacement signals at the time of the flash (Figs. 1B and 2B)

(13)

The resulting pattern of simulated errors (applied to measured gaze- and eye-in-head saccades) was subjected to the same regression analysis as the measured errors (Eqs. 8 and 9; Figs. 9–11).

View larger version (36K): [in this window] [in a new window]   FIG. 11. Dynamic regression analysis (Eq. 9) for all 6 subjects. A and B: head movers (n = 4). C and D: eye movers (n = 2). Left column: results of regression on the measured data. Right column: results of regression on the data predicted on the basis of the first gaze saccade (B), or the first eye-in-head saccade (D), by taking the default parameters. The model predictions are very different from the measured values for all subjects, irrespective of their movement strategies.

(14)

We took E_max = 10 deg, = 0.2 deg^–1, and = 4.10^–4 ms^–2 (i.e., a temporal width of 35 ms), to get a reasonable approximation of the eye-movement data of Van Wetter and Van Opstal (unpublished; Fig. 1B).

STATISTICS.  Large gaze shifts toward dim and briefly illuminated targets are endowed with considerable inherent variability in their endpoints, even in the case of single visual targets (see, e.g., Figs. 4–6). Thus to assess whether the observed error patterns around the gaze-shift onset were due to a real effect of perisaccadic processing, we performed the following statistical analyses on the error data.

View larger version (15K): [in this window] [in a new window]   FIG. 6. First (A) and second (B) gaze shifts are goal directed. First gaze shifts end near the first target location (blue: responses for bottom target; red: responses for top target). Largest inaccuracies were found for largest negative delays, which may be caused by target averaging (Table 1). Second gaze-shift amplitudes correlate well with the component motor error, although a systematic overshoot is observed (most data points above the diagonal). This overshoot is partially explained by the delay-dependent gaze mislocalizations. Data from subject tg.

The KS test was also performed on the running averages through the data sets. In that case, the data could be ranked as a function of the target onset delay, out of which cumulative distributions were determined. The one-dimensional (1D) KS test then measures the distance between the two cumulative distributions and its associated P value.

As a third method, we determined the dynamics of the tu-statistic (Student's t-test on the means of two data sets, for which the variance need not be the same; Press et al. 1992) for the randomly generated noise and the measured error data. To that end, the data sets were binned in 50-ms-wide windows with 40-ms overlap (i.e., the window was shifted in 10-ms steps, from t₀ = –220 to +220 ms). For each time bin the significance of a difference in the means was determined, thus yielding 45 tu- and P values as a function of the target onset delay, tu(t₀) and P(t₀), respectively (see Fig. 7, B and C for results).

View larger version (26K): [in this window] [in a new window]   FIG. 7. Gaze-in-space and eye-in-head saccade parameters are broadly distributed. Subject bd.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

Two points are worth mentioning: first, the eye-in-head saccade (bottom) terminated well before the end of the first gaze shift. As a consequence, during the second portion of the gaze shift the eye-in-space was carried toward its goal by the head movement, which can also be observed in the spatial trajectories. Second, both gaze shifts terminated well before the head movements (center). Thus after gaze-shift offset, the vestibuloocular reflex (VOR) was fully operational.

In our analysis, we determined separate model predictions for the gaze localization errors as a function of the first gaze-in-space movement, G₁(t), or of the first eye-in-head saccade, S₁(t) (see INTRODUCTION and METHODS; Fig. 2). To verify that these two movements, and hence the model predictions, were indeed different, Fig. 5 shows their amplitudes plotted against each other. Figure 5A shows data from subject jo. Clearly, the amplitudes are very different and not positively correlated (we even obtained a negative correlation of r = –0.20). Typically, the eye-movement amplitudes were much smaller than the total gaze-shift amplitudes. Four subjects displayed qualitatively similar behavior, and were termed "head movers" because their gaze shifts were associated with relatively large head movements (cf. Fig. 4). Two of our subjects (pb and rw), however, followed a different movement strategy, in that their eye saccades were positively correlated with the gaze saccades. Figure 5B shows the data for subject pb (r = 0.77). Because the head movements during the gaze shift of these two subjects were typically smaller than those for the head movers (because they often started later or were slower), they were termed "eye movers" in this study.

Because the visual targets were dim (0.8 cd/m²), very brief, and presented at large retinal eccentricities, it is important to verify that subjects were indeed able to do the double-step task under these conditions. To that end, Fig. 6 shows the first- and second gaze responses of subject tg. In Fig. 6A it can be seen that the endpoints of the first gaze shifts landed near the (extinguished) target locations, although substantial errors also occurred. Part of these errors could be explained by target averaging, in that the largest localization errors of the first target were found when the delay t₀ of the second target was less than –100 ms, i.e., when both targets were presented well in advance of the first gaze onset and therefore hardly influenced by perisaccadic mechanisms. Indeed, in line with this observation the target delay and amplitude of the first gaze shift error vector were negatively correlated for all subjects (Table 1). Figure 6B shows that the horizontal component of the second gaze shift correlated well with the horizontal motor error (r = 0.85). Yet, a systematic overshoot may be observed, which may partially be attributed to the delay-dependent gaze mislocalizations (see following text).

To perform meaningful regressions on the influence of the amplitude and kinematics of the first gaze shift and the first eye-in-head saccade on the delay-dependent gaze localization errors, the respective variables should be widely distributed. Figure 7 shows the typical distributions that were obtained in these experiments (subject bd). The localization errors in the direction of the first gaze shift, E_2,||,G, have a positive mean (Fig. 7, top), which is to be expected if a systematic effect of target delay is present at all. The independent variables are all broadly distributed around a single peak that is close to the mean.

Perisaccadic mislocalization in head-free gaze shifts?

To assess whether head-free gaze shifts to visual flashes were also endowed with perisaccadic localization errors, we performed a statistical analysis on the error data according to the procedures described in METHODS. The results of these analyses are shown in Fig. 8 and in Table 2. Figure 8A shows the measured errors in the direction of the first gaze shift of subject tg (red symbols), together with the running average through the data (thick red line). The blue dots correspond to random noise that was generated with the same mean and SD as the measured errors outside the [–100, +60]-ms delay interval. The blue line shows that the running average through the random noise data meanders around 0°. We then computed the 2D- and 1D-KS statistics for these two independent data sets for the delay intervals of interest. The numerical results of this analysis are provided in Table 2. In five of six subjects the differences between the distributions in the perisaccadic interval [–100, +60] ms were highly significant. Only the data of subject il failed to reach significance. As a consistency check, the data distributions outside the perisaccadic interval were indeed statistically indistinguishable for all subjects. The 1D-KS statistic that was performed on the running averages was significant for all subjects.

View larger version (26K): [in this window] [in a new window]   FIG. 8. Statistical analysis on localization errors. A: gaze-localization errors in the direction of the first gaze shift (red data points, subject tg), together with running average (red solid line). Blue data points are random data, generated with the same mean and SD as the measured errors for which t0 < –100 ms or t0 > +60 ms. Blue line is the running average through the noise. B: behavior of the tu-statistic [gray (n.s.) and blue (significant) points] and P value (red points: P < 0.05) as function of delay. The statistics were computed in 50-ms-wide windows (see METHODS). Note that highly significant differences were found in the perisaccadic epoch. C: results of the tu-statistic for all 6 subjects.

Figure 9A shows the localization errors of the second gaze shifts of subject jo in the same format as in Fig. 8A. Despite the considerable scatter, for this subject a clear systematic trend can also be observed in these errors. For delays around the gaze-shift onset, between about –140 and +80 ms, errors are positive on average. The peak localization error occurs around the gaze-saccade onset, reaching a mean amplitude of about 10°. In Fig. 9B we show the running averages obtained for all six subjects (identified by different colors), together with the running average determined for the pooled data of all subjects (black line; n = 3,187 responses). Despite idiosyncratic differences, also apparent from the results of the statistical analysis in Fig. 8C, the overall trend in the data is consistent and appears to be qualitatively similar to the results obtained from head-fixed experiments. To illustrate this latter point, Fig. 9C includes the data from the four subjects who participated in our recent oculomotor study (adapted from Van Wetter and Van Opstal, unpublished data). Here, the eye-movement data have been pooled across all saccade amplitudes (ranging from 5 to 35°; individual subjects indicated by different colors; black line: pooled for all four subjects, n = 3,750 saccades).

To assess whether the measured error patterns can be understood from the assumption that efferent feedback of either the first gaze shift, or the first eye-in-head saccade, is inaccurate, we used the actually measured gaze- and eye saccades to predict the localization errors (see METHODS, and Figs. 1 and 2). Figure 10A shows the results for the data from subject bd in the same format as in Figs. 8A and 9A, together with the running average through the data (solid red line). The size of the predicted effects depends strongly on the particular model parameters. To illustrate this point, we ran the oculomotor feedback model with 12 different parameter sets. The results of these 12 simulations are indicated by the running averages, as black and gray solid lines. Results obtained with the visual persistence model (Eq. 3) and the visual compression model (Eq. 4) were similar (not shown here, but see supplemental data). Obviously, many parameter sets do not yield an adequate description of the actual data. This observation also holds for the predicted curve obtained with the default set of parameters taken from other studies (Dassonville et al. 1992, 1995; Pola 2004; indicated by DEF). Note that when T_lead is reduced from –150 to –120 and –90 ms, respectively, the amplitude of the predicted errors decreases substantially (light gray and dark gray curves, respectively). On the other hand, when either the order of the low-pass filter or the filter time constant is decreased, the predicted errors increase. There will exist a particular set of parameters—to be found for example by brute force or by a least-squares fit procedure—for which the measured localization errors could be described best.

However, the critical prediction of the different visuomotor schemes is that the variability in the errors should depend in a systematic way on the gaze-saccade (or eye-saccade) properties (Van Wetter and Van Opstal, unpublished data). To test this more sensitive prediction, the regression analysis of Eq. 9 should be performed on the data after removing the primary effect of the stimulus delay, on both the original data and on the predicted data sets. To that end, we applied Eq. 8 to determine the residual errors, by subtracting the running averages from the measured data and from each of the 12 different predicted data sets (Fig. 10B). We then performed the dynamic multiple linear regression analysis of Eq. 9 on the residual errors, as described in METHODS. In brief, the data were binned in 100-ms time windows that were shifted between t₀ = –200 and t₀ = 200 ms in 10-ms steps. The regression thus yields the dynamic influence of the primary gaze-saccade amplitude a(t₀), its mean gaze velocity b(t₀), and the second gaze-shift motor error c(t₀), as a function of the flash delay t₀.

The result of this regression on the data of subject bd is shown in Fig. 10C. Two points are worth noticing. First, although the regression curves differed in a quantitative sense for each particular parameter set, the overall patterns in the regression results were remarkably similar and appeared to be quite robust against large variations in the model parameters. This finding held for all three versions of the visuomotor updating schemes (not shown here; but see Van Wetter and Van Opstal, unpublished data, for specific examples). Second, the regression parameters found for the measured data (black curves) did not follow these model predictions in any way. The 1D-KS test performed between each of the three parameter curves from the experimental data and each of the corresponding 12 curves of the model simulations always indicated that these parameter curves were highly dissimilar (P < 1e-6). In conclusion, the data do not follow the predictions of the visuomotor updating models in any way.

Figure 11 shows the results for all six subjects. The left panels show the dynamic regression parameters for the measured residual errors (to be compared with the black curves in Fig. 10C), whereas the right panels show the results for the predicted errors (based on the oculomotor feedback model with default parameters; compare with the thick colored curves in Fig. 10C). On the basis of the results in Fig. 5 (and Table 1) we grouped our subjects as head movers (n = 4, Fig. 11, A and B) and eye movers (n = 2; Fig. 11, C and D), respectively. For the head movers we show the results of the analysis for the first gaze saccades (Fig. 11, A and B), whereas for the eye movers we provide the results for the eye saccades (Fig. 11, C and D). Thin lines provide the regression results [blue: a(t₀), amplitude; red: b(t₀), mean velocity; green: c(t₀), motor error of second gaze shift] as a function of flash delay t₀ for each individual subject, whereas the thick solid lines give the results, averaged across subjects. The pattern of results for the eye saccades (head movers) and gaze saccades (eye movers) was very similar (see supplemental data).

The predicted data show a clear and consistent modulation of the regression parameters as a function of stimulus delay for all subjects. The measured residual errors, however, did not follow any of these predicted patterns in our subjects, irrespective of their movement strategies (Fig. 11, A and C). Thus like for head-fixed saccades, the systematic localization errors around a head-free gaze shift cannot be explained by an erroneous, low-pass filtered version of the actual eye- and gaze saccades.

Figure 12 compares the measured error data with the predictions from the visual-shift model (Eq. 13). Figure 12A shows the raw error data for subject bd (gray circles), together with the running average through the data points (red line), and the model prediction (black line). Although we have not attempted to optimize the parameters of this simple model with a least-squares fit, it did a decent job in describing the average trend through the data, despite the large variability in the underlying gaze-shift amplitudes and kinematics (e.g., Fig. 6). Figure 12B shows the running averages for the six subjects, together with the grand running average (red), and the model prediction for the overall averages. In Fig. 12C we show the results of applying this model to the dynamic regression analysis on the residual errors (Eqs. 8 and 9). The model predicts nearly flat curves across the relevant delay interval, which is also observed in the actual data (compare with Fig. 10C, black curves).

View larger version (20K): [in this window] [in a new window]   FIG. 12. Prediction of perisaccadic errors (individual data points and running average, red line) for large head-free gaze shifts with the visual shift model of Eq. 10 (black line). Parameters were set to Emax = 10 deg, = 0.2 deg–1, and = 4.1e-4 ms–2. A: data from subject bd. B: running averages for each subject (thin lines, see legend), the average across all subjects (thick red line), and the prediction of the visual shift model (black). C: dynamic multiple regression on the visual-shift predictions shown in A. The results qualitatively agree with the experimental data of Fig. 11, A and C.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

Here we have studied the pattern of perisaccadic mislocalizations of visual targets flashed around large head-free gaze shifts. We showed that, like head-fixed saccades, head-free gaze shifts consistently mislocalize visual targets in the direction of the primary gaze shift, when the brief flash is presented near gaze-shift onset (Fig. 8). According to visuomotor updating models (Dassonville et al. 1992, 1995; Pola 2004, 2007; Ross et al. 1997), the errors should vary with the amplitude and kinematics of the primary gaze saccade (or eye saccade) as function of the second target delay (Van Wetter and Van Opstal, unpublished data; Figs. 1A, 10C, and 11, B and D). Instead, our data show that the gaze-shift properties have a negligible influence on perisaccadic gaze-localization errors (Figs. 10C and 11, A and C). According to the alternative visual-shift hypothesis, gaze errors should be similar, as observed for much smaller head-fixed saccades (Fig. 1B), and not depend on the movement kinematics. Our results support this simple idea, which yields a better description for the observed error patterns (Fig. 12). We conclude that our data provide further support for the hypothesis that perisaccadic localization errors under open-loop orienting conditions have a visuospatial, rather than a dynamic motor, origin.

Related studies

Our experiments set out to test the hypothesis that a sluggish representation of extraretinal gaze position would underlie perisaccadic mislocalization. This idea was forwarded by Dassonville et al. (1992, 1995) and Schlag and Schlag-Rey (2002) for head-fixed saccadic eye movements and provided an adequate model to predict the error data. Recently, Pola (2004) argued that visual mechanisms could explain the error patterns equally well. In his model, the brief target flash is not transmitted as such through the visual system, but produces prolonged activity in the visual pathways. Thus even when the oculomotor feedback itself would be accurate, the internal estimate of eye position at the time of the flash becomes inaccurate, in that it would be determined by a temporal weighted ("blurred") average. This mechanism causes the perceived estimate of eye position to be similar to the sluggish, low-pass filtered signal of Dassonville's model (Dassonville et al. 1992, 1995; Honda 1990, 1991; Pola 2004; Eq. 8). As a consequence, both models predict equivalent localization errors.

In the model proposed by Ross et al. (1997), localization errors arise from errors in both the visual and oculomotor representations. In their model the saccade distorts (compresses) visual space by a compression factor that depends on the target's retinal eccentricity and on the difference between internal and actual eye positions. This leads to an erroneous estimate of the actual retinal error T_E, provided the internal eye position estimate is also inaccurate. If the extraretinal signal would be veridical, visual compression vanishes. Thus to explain the observed localization errors, the extraretinal signal was modeled as a slow dynamic representation of final and initial eye-position estimates (for details see Ross et al. 1997).

We have demonstrated that all three proposals produce equivalent error patterns, irrespective of the details of the underlying mechanisms. Even the dynamics of the regression parameters (Eq. 6, Figs. 10 and 11) were insensitive to the specific differences in model implementations (e.g., Figs. 3 and 10; Van Wetter and Van Opstal, unpublished data). Consequently, the predictions of models relying on inaccurate motor feedback are unequivocal: the variability in the perisaccadic localization errors should systematically vary as a function of target delay and, moreover, depend on the primary gaze-shift amplitude and kinematics.

The only study so far that acknowledged the influence of saccade kinematics on perisaccadic mislocalization is by Ostendorf et al. (2007). They demonstrated that intersubject variability in saccade kinematics correlated with the amount of visual compression. However, they reported no effect of the saccade amplitude on compression. Moreover, as in our previous eye-movement study (Van Wetter and Van Opstal, unpublished data), they did not find an effect of the first-saccade properties on the forward perisaccadic errors. Although these latter results corroborate our own findings, several points are worth noticing. First, the variability in the saccade amplitudes in their study was relatively small, given that the first target was fixed at 10° eccentricity. Second, when performing an overall regression analysis on the influence of saccade amplitude and velocity (i.e., pooling data across the entire delay range, rather than performing a windowed analysis), the expected effect of amplitude and kinematics may in fact be quite small (Van Opstal and Van Wetter, unpublished data). Thus given the substantial random noise in response error distributions, a small effect of amplitude or velocity may easily get unnoticed. Indeed, in the present data set the correlation of this overall multiple regression model was also low (r 0.3; not shown), indicating that most of the variability in the data was due to random noise within the gaze control system. Third, the effects of saccade variability described in the present study concern the dynamic variability within individual subjects, rather than across subjects.

Perisaccadic mislocalization around head-free gaze shifts has not been studied in detail so far. Only two recent studies (Vliegen et al. 2004, 2005) have addressed this issue, albeit indirectly. In their double-step sound-localization study Vliegen et al. (2004) showed that the audiomotor system generated accurate gaze shifts toward brief noise bursts presented before and during a large intervening eye–head gaze shift. In that situation, the auditory system has to incorporate dynamically changing auditory localization cues (due to the ongoing head movement), as well as gaze- and head movements following the presentation of the sound. The results indicated that localization of the noise burst in the dynamic double-step was indistinguishable from single-target sound localization without the intervening gaze shift. This suggested that the motor feedback signals, needed to update the coordinates of the auditory target into a body-centered reference frame, were accurate. These results are therefore in line with our hypothesis that systematic perisaccadic localization errors are due to a visual, rather than to a motor feedback, mechanism.

Furthermore, the subsequent study of Vliegen et al. (2005) on localization of a visual target flash in double-step gaze-shifts indicated that the errors were, on average, much smaller than expected from sluggish motor feedback. In that study, however, the target flash was substantially longer (50 ms) than that used in the experiments of Dassonville and colleagues (2 ms). Although the sluggish motor-feedback hypothesis has no specific role for the sensory properties of the stimulus (neither its modality, nor its saliency), the alternative proposal of Pola (2004; see earlier text), as well as our visual-shift model, could be accommodated to produce smaller localization errors when the visual target duration or intensity increases. We recently showed that, indeed, longer stimulus durations had a negative effect on perisaccadic localization errors (Van Wetter and Van Opstal, unpublished data). Binda et al. (2007) recently provided further support for the visual origin of perisaccadic errors. They demonstrated that localization errors of a visual target diminished in the presence of an auditory stimulus, possibly because the dominance of vision over acoustic input was reversed in the perisaccadic interval. Indeed, such a strategy would be beneficial because auditory stimuli are not systematically mislocalized around saccades (Binda et al. 2007; Vliegen et al. 2004).

Note that the visual stimuli in our experiments were presented under open-loop conditions, were very brief (15 ms), dim (0.8 cd/m²), small (0.2°), and presented at large retinal eccentricities (52° for the first target flash and between 27 and 36° for the second flash). These factors all contribute to an increased (but not systematic) variability in the responses when compared with longer-duration and brighter stimuli (e.g., Vliegen et al. 2005). Nevertheless, subjects made goal-directed responses to both targets (Fig. 5) and the systematic pattern of perisaccadic localization errors stood out in all subjects (Figs. 8 and 9). In addition, our study on head-fixed saccades yielded comparable error patterns for much smaller saccades (Fig. 9; Van Wetter and Van Opstal, unpublished data) and the errors were also comparable to those observed in other studies (Dassonville et al. 1992, 1995). By increasing the saliency of the targets one could, of course, reduce the random response noise (as in Vliegen et al. 2005). However, as argued earlier, such a manipulation would have had a detrimental effect on the size of the perisaccadic localization errors.

The only response parameter that contributed significantly to the observed errors in Van Wetter and Van Opstal (unpublished data) was the motor error vector for the second saccade, M₂. Since head-fixed eye movements have a well-known tendency to undershoot visual targets by about 10%, this parameter yielded an expected negative partial correlation coefficient, which did not vary with the flash delay. In the present study, the contribution of motor error was substantially smaller than that observed for head-fixed saccades (Figs. 10 and 11). Apparently, the tendency to undershoot visual targets is weaker when the head is free to move.

Double-flash interaction?

Although two visual flashes in rapid succession served to elicit gaze shifts, our paradigm differs in several ways from the double-flash experiment of Sogo and Osaka (2002). In their study the flashes were both presented around the onset of the first saccade, which was elicited by a different, third, target. The target eccentricities used in their study were between 4 and 12° (as opposed to >30° in this study), the intervening saccade was 8° (here between 40 and 60°) and pointing was measured using a postsaccadic ruler, instead of gaze shifts. When the brief (2-ms) flashes were both presented around the saccade onset, they were both mislocalized, but their mislocalization was not simply understood from the effects to each target flash in isolation. Sogo and Osaka (2002) reported that the two targets appeared to interact, creating a different mislocalization pattern for the second target flash and hence a perceived change in the allocentric relations between the flashes. The interaction was significant when the flashes occurred within 120 ms and nearly disappeared when the interflash interval (IFI) exceeded 200 ms. This interaction could be understood from the visual persistence model of Pola (2007), whenever the two visual activities would overlap in time. Note, however, that Pola's visual persistence model also creates a sluggish extraretinal signal through Eq. 3 and therefore predicts a strong dependence of the localization errors on the first saccade amplitude and kinematics similar to that of the other visuomotor updating models described in the INTRODUCTION (see Fig. 3).

In our experiments, the first target flash served to elicit the gaze shift and was thus presented well before the gaze shift onset (on average about 200 ms, which is well outside the perisaccadic interaction interval; see Table 1). Yet, the IFIs in our experiments were roughly between 100 and 240 ms, which includes the interaction interval reported by Sogo and Osaka (2002). Note, however, that at the shortest IFIs (100 ms) the perisaccadic localization errors of the second gaze shift were not systematic because they fell at the edge of the perisaccadic error range (between –100- and +100-ms onset delays; Figs. 8–10). The peak localization errors occurred at, or slightly after, the gaze-shift onset, corresponding to typical IFIs of 200 ms. One of our subjects (pb) had shorter first-saccade response latencies, but the peak amplitude of his perisaccadic errors did not deviate significantly from the other subjects. Thus in our experiments, the interactions due to IFI were expected to be small around the gaze-shift onset. We have assessed the potential role of the IFI by incorporating this parameter in our normalized multiple linear regression analysis by extending Eq. 9 with d(t₀)·IFI as an additional regressor. In five subjects, the dynamic contribution of IFI to the residual localization errors was insignificant across the entire delay interval of [–250, +250] ms. Only subject pb, yielded a small positive contribution for d(t₀) for long negative delays (where the IFI was shortest) that declined to zero near the gaze-shift onset (data shown in supplemental data). In line with this analysis, the first target in our experiments was localized consistently (apart from the typical undershoot; see Fig. 6).

Nonetheless, we did observe a small effect on the first-saccade errors that depended on the IFI (see the consistent negative correlations in Table 1). Since this effect was maximal at the shortest IFIs, for which the perisaccadic errors of the second gaze shifts were minimal (rather than increased), we suggest that it could be due to a different mechanism. When two visual targets are presented in close spatial and temporal proximity, the saccade is often directed toward the center of gravity of the two locations (e.g., Ottes et al. 1985). Thus the longer the stimulus lead (negative delays), the shorter the IFI, and the more likely that the first saccade could be affected by such spatial averaging. As a result, the goal of the first target would be shifted in the direction of the second target flash, whereby the first-saccade error increases. It is possible that target averaging may also have been a factor in the Sogo and Osaka (2002) study, but to assess such an effect saccades toward the first target flash should also have been measured.

Statistical models

Recently, Niemeier et al. (2003, 2007) proposed a different explanation for perisaccadic localization errors, which is based on statistical optimal inference. This concept holds that errors are an unavoidable consequence of the fact that the visuomotor system has to deal with dynamically changing uncertainties in both visuomotor and oculomotor processing. Especially around a saccade, these uncertainties (internal noise) might grow. Rather than assuming errors in the mapping process of Eq. 1, the principle of optimal inference holds that the system optimizes its behavior against conflicting constraints and internal noise. Niemeier et al. (2003) showed that saccadic suppression of displacement (SSD) could be well explained by this principle.

Interestingly, the threshold for SSD increases with the saccade amplitude, an effect that is also successfully predicted by the optimal inference model (Niemeier et al. 2003). It may thus be expected that optimal inference would predict an amplitude and velocity dependence of perisaccadic errors in the double-step task similar to that of the other visuomotor models described by Eqs. 2–4 (see Figs. 3C, 10C, and 11, B and D). Indeed, the endpoint variability of saccades is known to increase nearly linearly with saccade amplitude, an effect that has been related to a decreasing retinal resolution at large visual eccentricities (Van Opstal and Van Gisbergen 1989). However, our data on head-free gaze shifts (Fig. 10, A and C) and also on head-fixed saccades (Van Wetter and Van Opstal, unpublished data) indicate that, beyond about 10–15°, the gaze shift amplitude and kinematics do not influence the size of the perisaccadic errors. Thus to explain our results in terms of optimal inference, other statistical uncertainties should somehow compensate this amplitude-dependent effect. A further complication for applying the optimal inference model is the complex and variable coordination of the eye- and head-motor systems in head-free gaze shifts. Further study of the optimal inference hypothesis is therefore needed to analyze both its consequences and its predictions for these more complex and dynamic conditions.

Interestingly, Binda et al. (2007) have provided evidence that statistical optimization principles could underlie perisaccadic visual compression, which is observed in perceptual localization experiments in the light (Ross et al. 1997). When the visual target is combined with an auditory stimulus, the effect of visual compression nearly disappears. Binda et al. (2007) explained this by a Bayesian model of auditory–visual integration that weights the different and continuously varying reliabilities of visual and auditory inputs. According to their hypothesis, the auditory input increases its weight around saccades because auditory stimuli are not influenced by perisaccadic errors (Binda et al. 2007; Vliegen et al. 2004).

Other optimization principles to understand oculomotor behavior have also been proposed. For example, the tendency for saccades to undershoot the target (Fig. 6A) could be understood from optimizing the speed–accuracy trade-off, in combination with the kinematic constraint that saccade durations increase with saccade amplitude and that the endpoint scatter increases with amplitude (Harris 1995). It has recently been argued that the nonlinear main sequence of saccades could be understood from principles that aim to minimize movement duration, given the internal noise in the system (Harris and Wolpert 2006; Tanaka et al. 2006). We have recently provided evidence that the midbrain superior colliculus could thus be regarded as an optimal saccade controller by specifying a vectorial gaze-velocity command that obeys the main sequence (Van Opstal and Goossens 2008).

Model specifics

In the present study, most simulations with the visuomotor models were restricted to the sluggish oculomotor feedback proposal of Dassonville et al. (1992, 1995; Eqs. 10–12) using default parameters (i.e., a lead time of 150 ms and a fifth-order low-pass filter with a time constant of 20 ms; see also Pola 2004). This model described the oculomotor error data for midrange saccadic eye movements (10–15° amplitude) quite well (Van Wetter and Van Opstal, unpublished data). A series of simulations with different implementations of the visuomotor models showed that varying the model parameters strongly affects the size of the predicted errors (see Figs. 3A and 10A; compare with Fig. 3 of Van Wetter and Van Opstal, unpublished data), but that it has only a small effect on the results of dynamic regression on the error residues (Eqs. 8 and 9; Figs. 3C and 9B). Therefore although the predicted errors of the default implementation of the visuomotor feedback model deviate greatly from the actually measured data (Fig. 10A, curve DEF), the results shown in Figs. 3C, 10C, and 11, B and D should be considered canonical for the predictions of all visuomotor models that use sluggish gaze-motor feedback.

The predicted patterns in the regression parameters of the visuomotor feedback schemes for head-free gaze shifts (Figs. 10 and 11) differ from those reported for head-fixed saccades (Van Wetter and Van Opstal, unpublished data). In that study, the expected influence of the first-saccade amplitude on the residual errors followed a single-peaked positive-only relation with a lead starting well before saccade onset, whereas mean eye velocity displayed biphasic (positive/negative) behavior. In contrast, for head-free gaze shifts the expected dynamics of the regression parameters depended on the adopted movement synergies. Head movers displayed a single-peaked relation for both gaze- and eye velocity, whereas the influence of gaze- and eye-saccade amplitude started well after gaze-shift onset (Fig. 11B). The results for the eye movers were qualitatively more similar to the head-fixed predictions, albeit that in this case the influence of eye-saccade amplitude was also delayed (Fig. 11D).

Our conclusion that our heuristic visual-shift hypothesis provides a better description of the data than that of the different visuomotor updating models is not based on its better performance in describing the actual errors (Fig. 12, A and B), but on the crucial difference between the more sensitive dynamic analyses of Figs. 3C, 10C, 11, B and D (sluggish motor feedback), and Fig. 12C (visual shift). The visual-shift hypothesis yields a dynamic behavior of the regression parameters that is qualitatively comparable to that of the actual data (Fig. 11, A and C).

Gaze versus eye-in-head

Because the different visuomotor feedback models were developed to explain the data obtained under head-fixed conditions, there are different ways to extend them to head-free gaze shifts. If errors are due to the internal eye-movement signal only (i.e., the head-movement estimate is, on average, correct), the oculomotor feedback signal is supposed to originate from the brain stem (e.g., from the saccadic burst generator; Scudder 1988; Scudder et al. 2002; Van Gisbergen et al. 1981). In subjects denoted as "head movers," the eye-in-head saccade was typically much smaller than the overall gaze-shift amplitude (Fig. 5A) because the head covered a substantial part of the gaze trajectory. As a result, the size of the predicted errors for the eye-in-head saccades was of the same order of magnitude as that of the actually measured errors (data not shown). However, the variation in either the eye-saccade amplitude or the kinematics was not related to the dynamic error patterns (Fig. 11).

A more parsimonious extension of the visuomotor updating models would be to attribute the observed localization errors to a gaze-feedback signal. A serious candidate for providing efferent feedback has been identified as the midbrain superior colliculus (SC) (Sommer and Wurtz 2002, 2006). The SC has a well-established role in the generation of saccadic eye–head gaze shifts (e.g., in cat: Munoz et al. 1991; in monkey: Freedman et al. 1996), indicating that the signal emitted by the SC is a gaze-displacement command, rather than an oculomotor command.

Recently, Goossens and Van Opstal (2006) proposed that the spatiotemporal distribution of SC activity faithfully encodes the planned trajectory and kinematics of the saccade. Their recordings suggested that the collicular signal contains an accurate dynamic representation of saccades with a lead time of about 20 ms (Van Opstal and Goossens 2008). Although their analysis has so far been restricted to saccadic eye movements only, the approach predicts that SC cells encode the planned gaze trajectory when the head is free to move. If true, the SC signal would represent a veridical gaze-motor command that could be combined at upstream levels with visual inputs to transform the coordinates of the target into a stable and accurate oculocentric reference frame. Note, however, that the signal represented by the SC can, under certain conditions, be dissociated from the actual eye movement. For example, Frens and Van Opstal (1997) showed that SC responses are unaffected by short-term adaptation of the saccade vector, indicating that the movement fields of SC cells change during adaptation. Thus the signal responsible for adaptation is thought to affect saccade motor signals downstream from the SC. Interestingly, Awater et al. (2005) demonstrated that the visual compression effect (Ross et al. 1997) incorporates the actual, adapted, saccade vector, rather than the intended, unadapted, saccade vector. If one assumes that this result would also hold for open-loop orienting in darkness, it would further support the notion that spatial updating relies on accurate motor feedback, rather than on some derived, sluggish or even erroneous version of the oculomotor command. Since the SC does not provide the actual motor command under all conditions, the feedback signal for spatial updating could require integration from several sources that include not only the SC, but also the motor signals that originate downstream from the site of adaptation. The distributed nature of the feedback could explain why disruption of the SC corollary feedback path induces only a partial deficit of spatial updating in the double-step paradigm (Sommer and Wurtz 2002).

Visual-shift hypothesis

Our visual-shift explanation of the data assumes that the remapping process of Eqs. 1 and 5 uses a kinematically correct representation of the eye- and gaze-displacement vectors. Thus to cause the observed perisaccadic errors, the only remaining possibility is a dynamic shift of the perceived retinal location around the saccade with a time course that is dictated by the measurements. In that sense, the model seems to be a post hoc heuristic explanation of the data, which, however, calls for new and different mechanisms than low-pass filtering of the gaze-displacement command. Note that although the hypothesis entails a spatial–visual origin of the effect, the shift itself is contingent on the planning process of saccades and thus some form of a dynamically varying signal (in combination with information of the upcoming saccade) into the visual system is needed to cause this shift. We propose that this saccade-related signal differs from the actual gaze-displacement feedback signal. The latter is supposed to be kinematically accurate, whereas the former reflects neither the saccade kinematics nor the saccade amplitude, in that it saturates at about 10°. For example, it is conceivable that there might be an extraretinal process with an anticipatory component representing the size and direction of the upcoming response, but that has little or nothing to do with the actual kinematics of the saccade. It is also conceivable that the dynamics of the retinal shift could reflect the type of perisaccadic processing that would emerge from optimal inference (e.g., Niemeier et al. 2003, 2007), or Bayesian reasoning. Thus the shift may be related to the amount of visual positional uncertainty in the presaccadic epoch. The observation that errors decrease with increasing probe duration (Van Wetter and Van Opstal, unpublished data) or stimulus luminance (Georg et al. 2008) might follow from such a statistical framework, since the visual signal becomes more reliable when its saliency increases. In addition, the absence of mislocalization errors to auditory stimuli (Binda et al. 2007; Vliegen et al. 2004) strengthens the idea that the gaze-motor signals are, on average, accurate, but that the perisaccadic errors are caused by visual processes.

Neural correlates

Since the visual-shift hypothesis outperforms the different visuomotor feedback schemes, the question arises at which stage these errors might be introduced. It is well established that motor signals influence visual receptive fields within several cortical and subcortical visuomotor areas. For example, visual receptive fields in posterior parietal cortex have been described as multiplicative gain fields, by which cells modulate their visuospatial tuning with static changes in eye position (Andersen et al. 1985). Similar eye-position modulations have been reported for saccade-related cells in the midbrain superior colliculus (Van Opstal et al. 1995), in primary visual cortex (Weyand and Malpeli 1993), and on the tuning curves of auditory cells in the monkey inferior colliculus (Groh et al. 2001; Zwiers et al. 2004). Such gain fields could mediate the transformation of retinal coordinates into a head-centered reference frame (Van Opstal and Hepp 1995; Zipser and Andersen 1988), or vice versa, from a head-centered acoustic reference frame into an oculocentric reference frame (Zwiers et al. 2004).

Later experiments have shown that parietal cells are also modulated by changes in head orientation, so that these cells could represent the visual target location in body-centered (in monkey: Brotchie et al. 1995; in human: Brotchie et al. 2003) or even in absolute world coordinates (Snyder et al. 1998).

Nonetheless, it is unclear whether a gain field mechanism could underlie perisaccadic mislocalization, visual compression, or both, because the responses of these cells have so far been studied under static changes in eye and head position only.

An alternative mechanism that has been proposed to underlie visuomotor spatial updating is predictive remapping in which visual receptive fields shift prior to saccade initiation in a direction that compensates for the retinal displacement of the target by the saccade. Predictive remapping occurs within several cortical and subcortical saccade-related regions, such as posterior parietal cortex (Duhamel et al. 1992), frontal eye fields (Umeno et al. 1997), and SC (Walker et al. 1995). Predictive shifts in receptive fields have also been observed in regions involved in visual object processing and visual attention, such as area V4 (Tolias et al. 2001). In predictive remapping, receptive fields shift in a direction opposing the saccade (Eq. 1). Thus perisaccadic errors in the direction of the gaze shift could emerge when feedback about the upcoming gaze displacement would fall short of the actual gaze shift, or when the retinal representation of the target would transiently shift. Recent evidence suggests that the dynamics of visual-receptive field shifts might be linked to perisaccadic localization errors because parietal neurons respond to stimuli presented in both the original and the future receptive field during the perisaccadic interval, thereby effectively increasing the receptive field size in the saccade direction (Kusunoki and Goldberg 2002). Whether this effect can be quantitatively connected to the measured mislocalization patterns is still unclear.

It would therefore be interesting to test whether this expansion disappears for target flashes of longer durations, or may even reverse sign, as observed in monkeys for 100-ms flashes (Jeffries et al. 2007), and whether the receptive field shifts are nearly invariant to large variations in saccade amplitudes and kinematics.

	GRANTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
This work was supported by Netherlands Organization for Scientific Research Earth and Life Sciences Grants 812.07.005 to S. van Wetter and 805.05.003/VICI to A. J. van Opstal and S. van Wetter, and by a grant from Radboud University Nijmegen to A. J. van Opstal.

	ACKNOWLEDGMENTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
We thank B. van Dijk and I. Leunissen for participating in the data collection and analysis; H. Kleijnen and S. Martens for valuable technical assistance; the naive subjects who kindly participated numerous times in these experiments; and both anonymous reviewers for constructive criticisms that helped to greatly improve the manuscript.

	FOOTNOTES

 
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

¹ The online version of this article contains supplemental data.

Address for reprint requests and other correspondence: A. J. van Opstal, Radboud University Nijmegen, Donders Centre for Neuroscience, Department of Biophysics, Geert Grooteplein 21, 6525 EZ Nijmegen, The Netherlands (E-mail: j.vanopstal{at}science.ru.nl)

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