Saccade Dynamics before, during, and after Saccadic Adaptation in Humans

Abstract

purpose. When saccade amplitude is systematically inadequate relative to the desired target position, the saccadic system adaptively modifies the amplitude of subsequent saccades so as to recover precise targeting capabilities. The effect of saccadic adaptation on saccade metrics (amplitude, direction) is well documented, but the effect on dynamics (velocity, duration, acceleration, deceleration) remains to be fully elucidated.

methods. The dynamics of adapted saccades were compared with that of baseline saccades of similar amplitudes.

results. The peak deceleration and skewness (duration of the acceleration period/duration of the deceleration period) were modified by adaptation.

conclusions. The results point toward involvement of the cerebellum rather than the brain stem saccade generator in human saccadic adaptation.

Saccadic eye movements are very fast (up to ∼500°/sec) and visual afferent delays are too long for visual feedback to play a role in their trajectory. Saccades are therefore coded in an open-loop manner, and maintaining precise targeting throughout developmental and pathologic changes requires adaptive mechanisms that evaluate previous errors and update future behavior accordingly. Faced with systematic targeting errors as a result of extraocular muscle damage, the saccade system adjusts its amplitude and patients recover normal targeting capabilities within a few days. ¹ Short-term saccadic adaptation can also be investigated noninvasively in the laboratory by means of the double-step paradigm. ² In this paradigm, the saccade target is systematically displaced forward or backward during the saccade directed toward it, mimicking targeting errors, which leads to a progressive amplitude increase or decrease, respectively, to correct for the error. 

The adaptive modifications of saccade metrics (amplitude and direction) are well documented. ³ However, the effect of adaptation on saccade dynamics (duration, velocity, acceleration, and deceleration) has been controversial. The dynamic characteristics of saccades are not under voluntary control. They are relatively stereotyped and are usually described by the main-sequence relationships: a linear relationship between duration and amplitude on the one hand ⁴ and a logarithmic ⁵ or exponential ⁴ relationship between peak velocity and amplitude on the other. In patients without peripheral lesions of the oculomotor system (i.e., without ocular muscle damage or ocular nerve paresis), modifications of main-sequence dynamics are a sign of a modification of brain stem saccade generator function. ^{6 7} The ratio between the duration of the acceleration period (time from saccade onset to peak velocity) and that of the deceleration period (time from peak velocity to saccade offset) measures the skewness of the velocity and acceleration profiles and is usually close to 1 (i.e., symmetrical). The skewness ratio of larger saccades tends to be smaller than 1, yielding a velocity profile with a rightward skew. This results from the fact that while the deceleration period duration increases with amplitude, the acceleration period duration remains relatively constant. ⁴ Several neurophysiological studies have suggested that acceleration and deceleration are coded in the oculomotor cerebellum. ^{8 9} Indeed, an early burst in the caudal fastigial neurons correlates with the acceleration phase of contralateral saccades, and a late burst correlates with the deceleration phase of ipsilateral saccades. ⁸  

In examining the effect of adaptation on saccade dynamics, it is essential to compare normal (nonadapted) saccades of a given amplitude to saccades of that amplitude after adaptation. Indeed, as dynamics depend crucially on amplitude, any observed dynamic modification could result not from the adaptive process itself, but simply from the amplitude change. Straube and Deubel ¹⁰ examined duration, peak velocity, and acceleration-deceleration ratios before and after amplitude-decreasing adaptation. No significant modifications of average duration or peak velocity were observed, but there was a decrease of the peak acceleration-peak deceleration ratio. Frens and van Opstal ¹¹ observed that both peak velocity and duration decreased as expected with the adaptive decrease of saccade amplitude and noted that the main-sequence profiles were not altered. Absence of main-sequence modifications was also reported by Alahyane et al. ¹² In macaque monkeys, Straube et al. ¹³ reported idiosyncratic changes in the main-sequence profiles of four monkeys. In one monkey, there was a decrease in peak velocity and an increase in duration greater than expected, based only on the adaptive amplitude reduction. However, 50% to 100% of this decrease could be accounted for by fatigue, as eliciting many saccades without adaptation caused similar dynamic changes. Frens and van Opstal ¹⁴ also noted departures from the main-sequence profiles after adaptive amplitude decrease with slowed duration and peak velocity in their two monkeys. Caution must be exercised when monkey data are used to formulate hypotheses about human saccadic adaptation, because of differences in the characteristics of saccadic adaptation between the two species. For instance, the rate of adaptation is about 10 times faster in humans than in monkeys. ^{13 15} Furthermore, the specificity of saccadic adaptation also differs: an absence of transfer or partial transfer of reactive saccade adaptation to volitional saccades has been reported in humans, whereas robust transfer has been described in monkeys. ^{16 17}  

The goal of the present study was to examine saccade dynamics systematically before, during, and after saccadic adaptation in humans. We adaptively decreased a 10° rightward horizontal saccade and compared its dynamics to nonadapted saccades of comparable amplitudes. When comparing preadaptation and adaptation conditions, some researchers take all trials into account, including the early trials where amplitude and dynamics are likely to resemble the preadaptation characteristics, whereas others take only the final trials into account. Yet others perform a posttest in which saccades to the same target are elicited but the target is extinguished during the saccade. Because saccadic adaptation is progressive and reaches an asymptote in humans after approximately 50 to 100 trials, ¹⁵ we examined saccade dynamics in three distinct time periods: before adaptation (baseline), during the initial decrease of amplitude (during-adaptation), and during the maintenance of adaptation (posttest). 

Methods

Subjects

Four subjects (age range, 25–35; three women) participated in the experiment after giving informed consent. One was an author (subject [S]1) and the rest were naïve with respect to the goals of the experiment. The experimental methodology adhered to the ethical standards laid down in the Declaration of Helsinki (2004). 

Stimuli

Stimuli were 1° × 1° white crosses on a medium-gray background. The fixation cross was located left of screen center, equidistant from the top and bottom. Saccade targets could appear at 8°, 9°, 10°, or 12° to the right of the fixation point, depending on the stage of adaptation (Table 1and the following sections). 

Instruments and Eye Movement Recording

The experimental sessions took place in a dark room. The subjects were seated 57 cm away from the screen with the head kept stable with a submaxillar dental print and forehead rest. The stimuli were presented on a monitor (HM240DT; Iiyama, Nagano, Japan) monitor with a refresh rate of 170 Hz. Eye movements were monitored by a Bouis oculomotor system, ¹⁸ an infrared tracker with an absolute resolution of 0.1° of visual angle, and a linear output over 12°. Viewing was binocular, but only the movements of the right eye were monitored and calibrated. The signal from the oculometer was sampled every 2 ms. Saccade onset was detected with an in-house program (LabView 7.1; National Instruments, Austin, TX) based on velocity (>40°/sec), acceleration (>3000°/sec/sec), and minimal displacement (0.15°) thresholds. After saccade onset detection, offset was defined as the moment the velocity fell below 15°/sec. 

Procedure

Each session began with a full calibration procedure during which subjects had to saccade to five bars presented successively from left to right of the screen in steps of 3°. If the variability of each eye position at each bar did not exceed a threshold (0.4 volts, ∼0.1°), and if they were linear, the calibration was considered successful and the experiment started. Each experimental trial started with a calibration check. A bar appeared on the left of the screen, and subjects were required to fixate it. If the recorded value was different from that in full calibration by more that 0.1°, the calibration was repeated. Otherwise, the left calibration bar was extinguished, and the fixation cross appeared. After the fixation cross disappeared and the saccade target appeared (gap–0 paradigm), subjects were required to saccade toward it as quickly and accurately as possible. All saccades were rightward. Once subjects had made the saccade, they were able to blink freely for at least 2000 ms before pushing on a button to initiate the next trial. 

Each experimental session (200 trials) was composed of three successive stages: baseline, adaptation, and posttest. A session started with 60 baseline trials. We tested three target steps (8°, 9°, and 10°) from two fixation points (4° or 6° left of screen center) and five fixation durations (500–800 ms in steps of 75 ms), yielding 30 trial types. Each trial type was tested twice in the baseline stage. During saccade execution, the saccade target was extinguished to remove visual feedback. One hundred adaptation trials followed. Only the target step of 10° was presented, with the two different fixation positions and five fixation durations, yielding 10 trial types tested 10 times each. During saccade execution, the target stepped back to 8° and remained there for 2000 ms. In the posttest stage, two target eccentricities were tested (10° and 12°) from both fixation positions and with all five durations. Each of the 20 trial types was tested twice, for a total of 40 trials for the posttest. During saccade execution, the saccade target was extinguished. This was done so that adaptation was no longer being evoked by a visual error signal but rather maintained. The testing conditions are summarized in Table 1 . Each subject completed eight experimental sessions of approximately 30 minutes each, except S2 who completed five sessions. Sessions separated by more than 48 hours were preceded by 30 trials in which subjects had to make a saccade to a 10° target that remained on and did not step back. This procedure was used to complete the extinction of any residual adaptation from previous sessions. 

Data Analyses

We first examined saccade amplitude with a one-way analysis of variance including stage (baseline versus posttest) as a factor. We then determined the period at the beginning of the adaptation stage when amplitude was different from baseline but had not yet reached the stable level at the end of the adaptation stage. This time period was singled out for every subject and every session and was called “during adaptation.” We compared the dynamics of this stage to those observed before adaptation (baseline) and after adaptation (posttest). The during-adaptation stage was identified by the following linear interpolation procedure. For each data point, the slope of the linear relationship between saccade amplitude and trial number was calculated taking successively more and more data points into account. The minimal trial number (T _min) was fixed at trial 1, and the slope calculated for trials 1 to 6. The slope was then calculated for trials 1 to 7, then 1 to 8, and so forth, each time adding one more trial. No systematic amplitude changes were expected during baseline; therefore, we expected the slope to oscillate around 0. We expected the slope to depart from 0 at some point early in the adaptation stage when a systematic amplitude change occurred. Thus, the first data point where the slope differed from 0 was marked as the onset of the during-adaptation stage. The offset of the adaptation stage was calculated in a similar manner. The last trial of the adaptation condition was fixed (T _max, trial 160), and the slope calculated for the six preceding trials (trials 154–160), then for trials 153 to 160, and so forth. Again, no systematic amplitude changes were expected at the end of the adaptation stage, and we expected the slope to oscillate around 0. The first data point where the slope differed from 0 was marked as the offset of the during-adaptation stage (Fig. 1) . 

The average during-adaptation stage spanned trials 73 ± 7 to 114 ± 8. However, because adaptation was variable between and within subjects on different sessions, ³ each individual session was treated separately. Therefore, the exact number of trials included in the during-adaptation stage varied from individual to individual and from session to session. 

We grouped the data into three amplitude classes where we obtained data in all baseline, during-adaptation and posttest stages: 8° to 8.9° (average number of observations per subject: 110 ± 28 baseline, 161 ± 44, during-adaptation, 69 ± 23 posttest), 9° to 9.9° (average number of observations per subject: 93 ± 31, 59 ± 25, and 73 ± 14 for the three stages, respectively), and 10° to 10.9° (average number of observations per subject: 35 ± 20, 7 ± 5, and 65 ± 18). We examined duration, peak velocity, acceleration, deceleration, and skewness ratio (time between saccade onset and peak velocity/time from peak velocity to saccade offset). Analyses of variance were performed with amplitude (8°, 9°, and 10°) and stage (baseline, during-adaptation, and posttest) as factors. Probabilities are given in parentheses. 

Results

Latency and Amplitude

Average saccadic latency was 191 ± 37 and did not depend on amplitude or stage (P > 0.25). Such latency is typical of reactive saccades, as expected in the gap–0 paradigm used herein. In the baseline stage, saccades directed to the three target steps of 8°, 9°, and 10° showed typical undershooting behavior (Fig. 2A) . After 100 adaptation trials, the mean amplitude of saccades directed to 10° target steps decreased significantly from 9.6 ± 0.5° to 8.3 ± 0.1° (P < 0.009). Adaptation was progressive, as can be seen in the example individual time course in Figure 2B . The amount of adaptation (gain change: preadaptation amplitude − adapted amplitude/preadaptation amplitude) across all subjects and replications was 14% ± 4%. Within-subject (i.e., between-session) variability was 5%. 

Duration

Saccade duration increased with both amplitude (P < 0.005) and stage (P < 0.005) but the two factors did not interact (Fig. 3A) . Example main-sequence relationships between saccade duration and amplitude are given for each subject in Figure 4A . The increase in duration with adaptation was small and therefore cannot be seen on visual inspection of the main-sequence profiles. All three stages (baseline, during adaptation, and posttest) were well fit by a linear function (R ² > 0.15). 

Peak Velocity

Peak velocity (V _max) depended on amplitude (P < 0.0005): on average, a 1° increase in amplitude led to a peak velocity increase of approximately 20°/s. Indeed, the saccade amplitudes tested were smaller than the amplitude for which peak velocity tends to saturate ⁴ (≥30°). Average peak velocity did not depend on stage (P > 0.14; Fig. 3B ). The main-sequence relationship between saccade duration and amplitude was fit with a logarithmic function (R ² > 0.25). The three stages did not differ systematically from each other, as shown in the individual main-sequence examples (Fig. 4B) . 

Acceleration

Peak acceleration depended neither on amplitude nor on stage (P > 0.10; Fig. 5A ). The duration of the acceleration period (delay between saccade onset and peak velocity) did not vary with amplitude or stage (P > 0.12). 

Deceleration

Peak deceleration did not depend on amplitude (F < 1) but did depend on stage (P < 0.03). Peak deceleration decreased with adaptation for all amplitudes (Fig. 5B) . The duration of the deceleration period (delay between peak velocity and saccade offset) depended on both stage and amplitude (P < 0.02), with no interaction (F < 1). Indeed, the duration of the deceleration period increased with adaptation and amplitude (Fig. 5C) . 

Skewness

One way to define the skewness of the velocity profile is by the ratio between the duration of the acceleration period and that of the deceleration period. ¹⁹ Normal, nonadapted saccades have a skewness ratio of approximately 1, which decreases with amplitude, yielding skewed velocity profiles. ⁴ In the baseline stage, the skewness ratio was 0.86, 0.84, and 0.79 for 8°, 9°, and 10° saccades, respectively. The modest decrease was significant (P < 0.04). Amplitude and stage did not interact (F < 1) but skewness depended on stage (P < 0.01; Fig. 5D ). For all amplitudes, skewness was smaller in the posttest (0.77) than at baseline (0.83) or during adaptation (0.80). 

The skewness ratio can decrease either because the acceleration period duration is shortened or because the deceleration period duration is lengthened. As mentioned, the acceleration period duration did not depend on stage, but deceleration period duration increased during and after adaptation relative to baseline. The reason for the modified skewness ratio therefore appears to be a longer deceleration period. This can also be seen in Figure 6which shows several example acceleration profiles: the profiles of during-adaptation and posttest saccades are wider than those of baseline saccades, but only after the deceleration period. 

Fatigue

An increase in duration and/or a slowing of saccades can occur with fatigue. ^{13 20} We sought to verify that the effects we observed were the result of adaptation rather than the repetition of saccades. To do this, we ran a session identical with the experimental sessions described in the Methods section, with the important difference that no target step (such as that in the adaptation stage described above in the main experiment) ever occurred. All other characteristics of the procedure were identical with the procedure described earlier. Thus, the first 60 trials elicited saccades to targets with 8°, 9°, and 10° eccentricity from two fixation points (4° and 6° left of screen center), and the saccade target disappeared during saccade execution. The following 100 trials elicited saccades to 10° targets with no backward step, the saccade target remaining at the same position throughout the trial. The final 40 trials elicited saccades to targets at 10° and 12° eccentricity, with targets disappearing during the saccade. We separated the 200 trials into three periods: the first 60 trials, trials 71 to 115, and the last 40 trials. Trials 71 to 115 correspond to the average trials included in the during-adaptation stage for this subject. 

Figure 7shows the acceleration profiles of 9° or 10° saccades elicited during these three periods. No increase or slowing in the duration of the deceleration period was seen. 

Discussion

Saccadic adaptation modified the dynamic characteristics of saccades, especially deceleration. Indeed, the peak deceleration of adapted saccades was slower than that of nonadapted saccades of similar amplitude. Furthermore, the deceleration period was longer in adapted saccades, leading to an overall increase in saccade duration. Because the time to peak velocity (i.e., the duration of the acceleration phase) was not modified by adaptation, whereas the duration of the deceleration period was, a change in the skewness (delay between saccade onset and peak velocity/delay between peak velocity and saccade offset) of the saccade was also observed. 

First, we examined the baseline main-sequence relationships between duration, peak velocity, and amplitude for saccades directed to three different target locations. We then adapted a 10° saccade such that its amplitude decreased (to ∼8–9°) and compared to baseline saccades of 8° to 9°. We also measured the adaptation of 12° saccades obtained by transfer and compared them to baseline 10° saccades. For the trials during which amplitude was decreasing relative to baseline (during-adaptation stage), the main-sequence relationship between peak velocity and amplitude was not modified but remained comparable to baseline. Saccade duration increased for all amplitudes, due entirely to an increase in the duration of the deceleration period. In the posttest stage, the peak velocity-amplitude main-sequence relationship was comparable to baseline, and there was again an increase of duration due to an increase in deceleration period duration. 

These results are partially at odds with those described in macaque monkeys. Although the monkey data remains sparse and important individual differences have been reported, the most consistent finding was a departure from baseline main-sequence profiles due to an increase in duration and a decrease in peak velocity. ^{13 14} It is not known whether the increased duration was specifically due to an increased deceleration period duration. The absence of velocity main-sequence modifications in humans could be another example of an interspecies difference in saccadic adaptation, along with those mentioned in the introduction. 

The main-sequence relationships would depend on the function of the brain stem saccade generator, ^{6 7} and a modification of these relationships would indicate that the function of the brain stem saccade generator may be affected by adaptation, not just its inputs. ^{6 10} We found no evidence for a modification of the peak velocity-amplitude main-sequence during or after amplitude decreasing adaptation, confirming previous reports in humans. ^{6 10 11 12 21} The longer saccade duration after adaptation was not the result of overall slowing but was specifically due to slowing of the deceleration period duration, and the linear relationship between duration and amplitude was not modified. If saccadic adaptation influenced the inputs of the brain stem saccade generator, we would not expect a change of the main-sequence relationships. Findings in our behavioral investigations support those in physiological studies showing that adaptation modifies the function of brain areas upstream of the brain stem generator. ^{22 23 24 25}  

We found that saccadic adaptation led to a skewed acceleration profile. Independent of amplitude, the ratio between the duration of the acceleration period and that of the deceleration period decreased with adaptation: the baseline skewness ratio of a saccade was greater relative to saccades of similar amplitude during and after adaptation. This was the result of an increase in the deceleration period’s duration. The effect was small, but systematic across our subjects and was statistically significant. Furthermore, this effect was not observed in fatigued saccades. Straube and Deubel ¹⁰ also observed a modification of the skewness which they defined as the ratio between peak acceleration and peak deceleration (A/D ratio). However, the observed modification could have been expected based on amplitude alone and independent of any adaptation, and it is unknown whether the A/D ratio was modified for saccades having the same amplitude. Several studies have suggested that acceleration and deceleration would be controlled by the caudal fastigial nucleus (cFN) of the cerebellum. ^{8 9} Of interest, the discharge rate of cFN neurons is modified after behavioral adaptation. ^{26 27} Our behavioral results therefore point toward cerebellar involvement in the control of amplitude adaptation. As for any link between a behavioral modification and a brain area, the link between a modified skewness and cFN involvement in adaptation must remain hypothetical. Nevertheless, such a result can constrain the candidate sites for saccadic adaptation. Furthermore, this result is consistent with imaging studies showing cerebellar activation during adaptation ^{28 29} and neuropsychological investigations of cerebellar patients whose capacity to adapt is reduced or absent. ^{30 31}  

We measured saccade dynamics during the progressive reduction of saccadic amplitude, before the amplitude-trial number relationship reached an asymptote (during-adaptation stage). We hypothesized that the mechanisms reducing amplitude might be different from those maintaining the new sensory-motor correspondence. Indeed, distinct short- versus long-term adaptations have been identified on a behavioral level. Repeatedly exposing macaque monkeys to adaptation continued to decrease amplitude even after 19 days. ³² These long-term amplitude reductions were longer lasting than those caused by single-day adaptation sessions and did not interfere with short-term adaptation. Robinson et al. ³² proposed that two mechanisms would control amplitude, one that rapidly adapts amplitude and another that would maintain such changes over a longer time scale. Distinct neural mechanisms between early and stable stages have also been described. Complex spike activity in the cerebellar Purkinje cells is correlated with saccadic adaptation and depends on the early or stable stage, although the exact difference between the two stages is still unresolved. ^{33 34}  

In our posttest stage, we assumed that adaptation was no longer occurring because there was no longer a visual error to drive the adaptation and thus that we were measuring the characteristics of saccades in which the new sensory-motor correspondence was being maintained. However, long-term adaptation has been described as occurring over a much longer time frame. An interesting next step would thus be to compare the dynamics of saccades during short-term adaptation as described herein with saccade dynamics during such long-term adaptation. 

 Submitted for publication June 19, 2007; revised August 29 and October 3, 2007; accepted December 18, 2007.

 Disclosure: T. Collins, None; A. Semroud, None; E. Orriols, None; K. Doré-Mazars, None

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Table 1.

 

Trial Types in Each of the Three Successive Stages

	Baseline	Adaptation	Posttest
Fixation target position (deg)	−4/−6	−4/−6	−4/−6
Fixation target duration (ms)		500, 575, 650, 725, 800 (random)
Target position (deg)	4, 5, 6/2, 3, 4	6/4	6, 8/4, 6
Target eccentricity (deg)	8, 9, 10	10	10, 12
Total of trial types (n)	30	10	20
Repetitions of each trial (n)	2	10	2
Total trials (n)	60	100	40

 Target positions are given relative to screen center (0°).

Figure 1.

 

Linear interpolation. (A) Example linear interpolation for one subject (S4) in one session (no. 4). The slope of the linear function relating saccade amplitude to trial number is given by taking successively more and more trials into account, maintaining constant the first (○) or the last (•) trial. The first data point on each curve takes six trials into account. Arrows: the trial for which a change of slope occurred. (B) Corresponding time course. Each data point is one saccade.

Figure 2.

 

Saccade amplitude. (A) Amplitude distributions of saccades directed to targets at 8° (♦), 9° (▴), and 10° (▪) in the baseline stage, to targets at 10° (□) that stepped backward during the adaptation stage and to targets at 10° ( ) and 12° ( ) in the posttest stage, for each of the four subjects averaged across all individual sessions. (B) Time course of adaptation (amplitude as a function of trial number) in each of the four subjects, in one representation session. Target at 10° was turned off during the saccade in the baseline (•) and posttest (▪) stages and stepped backward at 8° during the saccade in the adaptation stage (×).

Figure 3.

 

Saccade duration (A) and peak velocity (B) as a function of saccade amplitude (8–8.9°, 9–9.9°, and 10–10.9°) and stage (baseline, during-adaptation, and posttest), for each of the four subjects averaged across all individual sessions. Error bars, +1 within-subject SD.

Figure 4.

 

Individual main-sequence profiles. (A) Duration as a function of saccadic amplitude. R ² of the linear function is given for the three successive stages. (B) Peak velocity as a function of saccade amplitude. R ² of the logarithmic relation is given for the three stages. Recall that saccades were made to 10° or 12° targets in the posttest stage. Each main sequence is from one representative session.

Figure 5.

 

Characteristics of acceleration and deceleration, for each of the four subjects, as a function of stage (baseline, during-adaptation, and posttest) and amplitude (8–8.9°, 9–9.9°, and 10–10.9°), averaged across all individual sessions. Error bars, +1 within-subject SD. (A) Peak acceleration; (B) peak deceleration; (C) duration of the deceleration period (delay between peak velocity and saccade offset). (D) Skewness (duration of the acceleration period/duration of the deceleration period).

Figure 6.

 

Acceleration profiles for adapted saccades. Example 9° saccades before, during, and after adaptation (thin and thick gray and thick black lines, respectively). Each curve represents one saccade, obtained from one subject in one session. Insets: example of 8° saccades from the same subject and session. Only the deceleration period is shown, because there was no difference between the three stages during the acceleration period, as for the 9° saccades. Data in parentheses: average actual amplitude of the 9°/8° saccades shown ± SD.

Figure 7.

 

Acceleration profiles for fatigued saccades. Example 9° (A) or 10° (B) saccades recorded during the “fatigue” session, for early, middle and final trials (thin, thick gray, and thick black lines, respectively). Each curve represents one saccade, obtained from subject 1 in one session. Actual saccade amplitude was 9.2 ± 0.1° and 10.1 ± 0.2°, respectively.