January 2017
Volume 58, Issue 1
Open Access
Eye Movements, Strabismus, Amblyopia and Neuro-ophthalmology  |   January 2017
Effects of Pure Vergence Training on Initiation and Binocular Coordination of Saccades
Author Affiliations & Notes
  • Aurélien Morize
    IRIS Team, Physiopathology of vision and binocular control, FR3636 (Fédération de Recherche en Neurosciences), University Paris Descartes, Centre National de la Recherche Scientifique (CNRS), Paris, France
  • Dominique Brémond-Gignac
    Ophthalmology, Assistance Publique des Hôpitaux de Paris (APHP) Necker, Paris, France
  • François Daniel
    IRIS Team, Physiopathology of vision and binocular control, FR3636 (Fédération de Recherche en Neurosciences), University Paris Descartes, Centre National de la Recherche Scientifique (CNRS), Paris, France
  • Zoï Kapoula
    IRIS Team, Physiopathology of vision and binocular control, FR3636 (Fédération de Recherche en Neurosciences), University Paris Descartes, Centre National de la Recherche Scientifique (CNRS), Paris, France
  • Correspondence: Zoï Kapoula, IRIS Team, University Paris Descartes, 45 rue des Saints Pères, 75006 Paris, France; zoi.kapoula@gmail.com
  • Aurélien Morize, IRIS Team, University Paris Descartes, 45 rue des Saints Pères, 75006 Paris, France; aurelien.morize@gmail.com
Investigative Ophthalmology & Visual Science January 2017, Vol.58, 329-342. doi:10.1167/iovs.16-19837
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      Aurélien Morize, Dominique Brémond-Gignac, François Daniel, Zoï Kapoula; Effects of Pure Vergence Training on Initiation and Binocular Coordination of Saccades. Invest. Ophthalmol. Vis. Sci. 2017;58(1):329-342. doi: 10.1167/iovs.16-19837.

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Abstract

Purpose: We hypothesized that saccade eye movement properties, particularly latency and binocular coordination, depend on vergence quality.

Methods: We studied 11 students clinically diagnosed for vergence disorders versus 8 healthy controls. Rehabilitation of vergence disorders was done with a novel research-based method, using vergence in midsagittal plane. Vergence and saccades were recorded in separate blocks, before and after five weekly rehabilitation sessions.

Results: Healthy controls showed higher accuracy and velocity of convergence and divergence relative to the vergence disorders group; then rehabilitation led to significant decrease of latency and increase of gain and peak velocity of vergence. Before rehabilitation of the vergence disorders, saccade parameters did not differ significantly from healthy controls, except the binocular coordination that was significantly deteriorated. Following vergence rehabilitation, saccade properties improved: The latency decreased significantly, the gain increased particularly at far, and the binocular coordination improved significantly. Latency and accuracy improved in a durable way, with values even better than the range of accuracy measured in healthy controls; binocular coordination of saccades, although improved, did not normalize. In healthy controls, binocular coordination was optimal at 40 cm (working distance), and the vergence disorders group showed improvement at 40 cm. Results confirm the hypothesis, which is further corroborated by the correlation between vergence and saccade latency.

Conclusions: Results are in line with the hypothesis of permanent interaction between saccades and vergence, even when the task requires only saccades. Relevance of such interaction is emphasized by improvements of binocular saccades through the novel research-based method of vergence rehabilitation.

Saccades are the fast stereotyped eye movements we make to move the two eyes together toward an object of interest, which requires foveal alignment; vergence eye movements are slower and allow adjustment of the angle of optic axes to the depth of such object, leading to single binocular vision. Saccades and vergence share the same cortical parietal–frontal substrates. However, at the brain stem level, horizontal saccades and vergence generators are distinct, albeit interactive. Locations of burst neurons in primates were identified close to the abducens nucleus, namely, in the paramedian pontine reticular formation for the saccades14 and dorsolateral to the oculomotor nucleus for the vergence, specifically in the mesencephalic reticular formation (MRF1,57): The supraoculomotor area and adjacent reticular formation contain premotor neurons related to vergence.8,9 Recently it was observed that the supraoculomotor area receives axonal projections from the central MRF.10 In natural life, most of the time vergence and saccades are activated together and they interact nonlinearly as vergence is accelerated by the saccade. Also, in real life we often make saccades at near with increased convergence angle when reading or working with a screen, or at far when exploring the natural visual environment. In this study, we are interested in horizontal saccades made at targets located on isovergence arcs, placed at near, intermediate, and far depths. 
Prior studies have shown an effect of depth on various parameters of saccades such as latency, which is the period of time between the target onset and the onset of the saccade. Yang et al.11 have shown that latency is shorter for saccades at near distance in adults. For horizontal saccades, this distance-in-depth effect is present at any age.12,13 For vertical saccades, Yang et al. did not report depth effect in line with an earlier study by Honda and Findlay.14 Such depth specificity for horizontal saccades suggests a possible link with the vergence system, meaning an interaction between horizontal saccades and the horizontal vergence, even when targets are presented at the same depth. 
Another parameter depending on the depth is the binocular coordination of saccades. Its quality is evaluated by the disconjugacy, that is, the difference of the saccade amplitude between the two eyes (left eye − right eye). Such depth specificity was observed for horizontal saccades but not so much for vertical saccades.15,16 Horizontal binocular coordination is not perfect: A difference between the adducting and the abducting eye is known to exist, and such difference is smaller for saccades at far than at near distance.17 This again has been attributed to the interaction with the vergence system. Binocular coordination is poor in children (i.e., showing high disconjugacy) but improves with age, thanks to visual experience and learning. A developmental study on children has shown that disconjugacy reduces with age more slowly for saccades at near distance than for the far distance: Disconjugacy reduces to adult level at the age of 7 to 8 years for saccades at far, while for saccades at near, it is at the age of 11 to 12 years when disconjugacy drops to the adult levels.18 Kapoula et al.19 proposed that binocular coordination of saccades improves in children via a neuroplastic mechanism based on the interaction between saccades and vergence: With visual experience, children learn to couple together with the saccade command a fast vergence command that reduces the above-mentioned adduction–abduction asymmetry between the two eyes. It should be noted that improvement of binocular coordination is essential for activities such as reading. Here we hypothesize that this interaction and learning process is continuously present throughout life. 
Given this theoretical framework, the present study had three objectives: (1) to reinvestigate this distance-in-depth effect for horizontal saccades in a population of young students, who were screened for their binocular function and their vergence capabilities; (2) to compare the healthy population with a group of age-matched students clinically diagnosed for vergence disorders; (3) to test the improvement of binocular coordination of saccades after vergence rehabilitation in students with vergence disorders. Because of the hypothetical involvement of vergence in the binocular coordination of the saccades, we expected poor binocular coordination in students with vergence disorders and improvement after vergence rehabilitation. 
Materials and Methods
Subjects
Nineteen students (mean age 23.1 ± 2.0) were screened with orthoptic and ophthalmologic evaluation as well as with the Convergence Insufficiency Symptom Survey (CISS). Considering normative values of clinical tests for vergence,20,21 stereoacuity,22,23 and CISS,24 8 of the subjects were considered healthy controls, while the 11 other subjects were diagnosed as presenting vergence disorders (i.e., high symptomatology score and presence of at least two abnormal values in orthoptic tests). Results are shown in Supplementary Table S1A, including heterophoria, which was measured with a Maddox rod test25: The latent misalignment of the eyes, when an eye is covered by the Maddox rod, was measured using a prisms bar. 
The investigation adhered to the tenets of the Declaration of Helsinki and was approved by the local human experimentation committee, the Comité de Protection des Personnes (CPP) Ile de France VI (No: 07035), Necker Hospital in Paris, France. Informed written consent was systematic. 
Visual Stimulus
Subjects sat in front of a visuoacoustic display, developed by one of the authors and named REMOBI (patent US 8851669), placed at the eye level (see Fig. 1). The REMOBI device was used in this study both for vergence and for saccade tests; it is a trapezoid surface upon which are displayed 56 light-emitting diodes (LEDs) at four isovergence arcs and along the median plane.26 The ingenuity of the REMOBI device also involves the visuoacoustic relationship.27 Each LED (nominal wavelength 626 nm, intensity 180 mCd, and diameter 3 mm) is paired with a buzzer (nominal frequency approximately 2048 Hz, sound level ≥ 70 dB, and diameter 12 mm): Just before a LED lights, a brief (100 ms) acoustic signal is emitted from the location adjacent to that of the LED. 
Figure 1
 
Temporal (A, B) and spatial (CE) arrangement of the REMOBI visual display. The targets were randomly interleaved in order to test saccades (C) or vergence (D) eye movements in different blocks using the temporal paradigm as shown in (A). During a rehabilitation block (E), subjects with vergence disorders performed only vergence eye movements along the midsagittal plane, using the vergence double-step paradigm; the corresponding temporal arrangement is shown in (B).
Figure 1
 
Temporal (A, B) and spatial (CE) arrangement of the REMOBI visual display. The targets were randomly interleaved in order to test saccades (C) or vergence (D) eye movements in different blocks using the temporal paradigm as shown in (A). During a rehabilitation block (E), subjects with vergence disorders performed only vergence eye movements along the midsagittal plane, using the vergence double-step paradigm; the corresponding temporal arrangement is shown in (B).
Vergence Test
Each trial begins with lighting an initial LED along the median plane (Fixation F, see Fig. 1A); after a variable fixation period of 1200 to 1800 ms, a target LED is lit for 2000 ms, at location T or T′, calling for divergence or convergence, respectively (see spatial arrangement in Fig. 1D). For the temporal arrangement, we used the overlap paradigm: the initial fixation LED was switched off 200 ms after the target LED. Between trials, a blank period of 300 to 700 ms was applied. This vergence test contains 20 convergence and 20 divergence trials randomly interleaved. 
Vergence Rehabilitation
Subjects with vergence disorders completed five training sessions dedicated to vergence rehabilitation. Each session lasted 35 minutes, and periodicity was once a week. All these sessions occurred in a mesopic environment, immediately after the vergence test described above. For vergence rehabilitation we used the vergence double-step rehabilitation protocol described in another study.27 
Briefly, the trial started with lighting the fixation LED for a random period of 1000 to 1600 ms (see Fig. 1B for the temporal arrangement, Fig. 1E for the spatial arrangement during a convergence rehabilitation session). Then the target LED appeared at position T1 or T′1 (respectively located at 100 and 26 cm from the eyes); 200 ms later the fixation LED switched off, and the target LED was displaced to a closer position, T2 or T′2 (respectively located at 95 and 23 cm), for 1300 ms. Thus, the target LED moved to its final position before the eye movement finished. In other blocks, the initial fixation LED was at near and the target LEDs were presented at far, calling for divergence movement. During the training session, subjects performed five blocks of divergence and six blocks of convergence. We held constant the order of these blocks, and trials within each block were randomly interleaved. 
Saccades to Isovergent Targets Performed at Three Depths
Each trial started with the initial fixation LED (F, see Fig. 1A) presented at the center of the arc; after a random period of 1200 to 1800, a peripheral target LED lit for 2000 ms, which was located at an eccentricity of 20° (e.g., see Fig. 1C). As in the vergence test, fixation and target LEDs lit with an overlap of 200 ms. A block of saccades contained 20 trials of leftward saccades and 20 trials of rightward saccades randomly interleaved. Three blocks were applied successively to targets located at an isovergence arc at 150, 40, and 20 cm. Between blocks a 1-minute pause was applied. 
Tests After Vergence Rehabilitation
To evaluate oculomotor changes induced by vergence rehabilitation, the vergence test was repeated at the beginning of the last session of rehabilitation; the saccade test was repeated twice, a week and a month after the end of the five vergence rehabilitation sessions. The experimental design, that is, the sequence of tests run for each group, is summarized in Figure 2
Figure 2
 
The overall experimental design was similar for healthy and vergence disorders groups: Clinical examination were performed separately to the oculomotor tests. Then subjects diagnosed for vergence disorders performed five weekly rehabilitation sessions and were tested again for saccades and vergence, especially for saccades, which were tested a week and a month after the end of vergence rehabilitation.
Figure 2
 
The overall experimental design was similar for healthy and vergence disorders groups: Clinical examination were performed separately to the oculomotor tests. Then subjects diagnosed for vergence disorders performed five weekly rehabilitation sessions and were tested again for saccades and vergence, especially for saccades, which were tested a week and a month after the end of vergence rehabilitation.
Eye Movement Recording
Eye movements were recorded binocularly with a video-oculography EyeSeeCam device (University of Munich Hospital, Clinical Neuroscience, Munich, Germany, see http://eyeseecam.com/). The sampling rate of the EyeSeeCam system was 222 Hz and the optimal spatial resolution was approximately 0.01°. The head was not stabilized, yet small and slow head rotations if they occurred during the experiment are unlikely to significantly affect measurements of latency and amplitude of saccades and vergence. 
Calibration
The standard EyeSeeCam five-point calibration was applied at every session using fixations to five laser dots: one located straight ahead and four on the horizontal and vertical meridians at 8.5° of eccentricity (left, right, up, and down). These five laser targets were simultaneously presented by a head-mounted laser, projecting through a diffraction grating at a viewing distance of 1.5 m. During 10 seconds, subjects fixated successively each dot at their own pace: center, right, down, left, and up. 
A further calibration task was performed before each block of trials using the REMOBI device to elicit 16 interleaved leftward and rightward saccades to LEDs located at 10° and 20° from the midsagittal plane, at a distance of 1.5 m from subjects' eyes. Given that no subject showed strabismus, binocular calibration was reliable. Note also that all but one of the subjects had a stereoacuity of 80 arc seconds (i.e., 0.02°) or better, which is possible only when binocular eye alignment is normal, confirming the absence of strabismus or microstrabismus. 
Data Analysis
Calibration factors were extracted from the calibration task; from individual calibrated eye position signal we derived the vergence signal, that is, the difference position between eyes (i.e., left eye − right eye). The conjugate signal was calculated as being the average of the horizontal signals of both eyes (i.e., left eye / 2 + right eye / 2). The velocity of each signal was computed with a symmetrical two-point differentiator combined with low-pass filtering through a Gaussian FIR filter (cutoff frequency 33 Hz). The time points of onset and offset vergence movements were defined by the velocity threshold of 5°/s (see Figs. 3D, 3E); the beginning and the end of saccade movements were defined as the time point when the eye velocity respectively exceeded 20°/s or dropped below 10% of peak velocity (I and P markers; see Figs. 3A, 3C). Automatic placement of markers by the software was carefully verified and completed by an investigator scrutinizing signals on the computer. These criteria used for marking vergence and saccades are standard and have been used in many other studies.11,2830 
Figure 3
 
Trajectories of a subject with vergence disorders (TC) illustrate the method of analysis, respectively, for the saccades (AC) and vergence (DE) tests. All trials are superimposed at t = 0, the instant of target appearance. The bold lines show an individual trial of saccade to the left (A) and a trial of divergence (D): Onset (I) and offset (P) of eye movements were defined according to velocity threshold (V), traces of velocity being illustrated at the bottom (C, E). Note that coordination of saccades was evaluated from the disconjugate amplitude between the onset and the offset of each saccade; we did not analyze the typical divergence–convergence pattern that occurred during the saccade itself.
Figure 3
 
Trajectories of a subject with vergence disorders (TC) illustrate the method of analysis, respectively, for the saccades (AC) and vergence (DE) tests. All trials are superimposed at t = 0, the instant of target appearance. The bold lines show an individual trial of saccade to the left (A) and a trial of divergence (D): Onset (I) and offset (P) of eye movements were defined according to velocity threshold (V), traces of velocity being illustrated at the bottom (C, E). Note that coordination of saccades was evaluated from the disconjugate amplitude between the onset and the offset of each saccade; we did not analyze the typical divergence–convergence pattern that occurred during the saccade itself.
To evaluate the quality of binocular coordination we measured the disconjugacy (see Fig. 3B), that is, the amplitude difference between the saccade of the right and the left eye (P − I); this criterion is standard also.17,18,3133 
Some eye movements were rejected from the analysis due to blinks or partial loss of signal, anticipation (latencies below 80 ms), temporal outliers (latencies above 800 ms), wrong direction or motionless trials (<<1°). For the vergence disorders group the total rejection rate was 10.1 ± 7.6% and 11.8 ± 11.1%, respectively, for vergence and for saccade tests; for the healthy control group these rates were, respectively, 9.3 ± 6.2% and 13.1 ± 6.9% except for subject EO (32.5 ± 17.7% and 35.0 ± 2.9%), who systematically blinked during eye movements. 
Statistical Analysis
All statistical tests were done on the mean individual values of each parameter (latency, gain, duration, peak velocity, and mean velocity), both for vergence and saccades of each group, and also on the absolute value of disconjugacy. For saccades, these tests were applied either to the mean of all saccades (i.e., taking all distances together) or for saccades to each distance. Significant threshold was defined as P < 0.05. 
As data homogeneity, at least for some parameters (e.g., latency), was violated in terms of normality of the distribution (Shapiro Wilks test) and/or variance of the samples (Fisher test), we used nonparametric statistical analysis with the Statistica software (Version 7.1; StatSoft, Tulsa, OK, USA). The Mann-Whitney U test was applied to compare data between the healthy group and the vergence disorders group. The Wilcoxon test was applied for follow-up comparisons of the vergence disorders group before and after vergence rehabilitation. Also, the Wilcoxon test was used to compare saccades at different distances for each group of subjects. For binocular coordination of saccades, which is a central point of the study, we performed two nonparametric analyses: first, Mann-Whitney or Wilcoxon test, then for a subgroup of the subjects a 2-way ANOVA with a ranking subset method34 that allows testing interaction. 
For multiple comparison tests, the Bonferroni correction was applied, and the corrected P values are shown in the text. For some cases, indicated in Results, this correction extended to Holm's method.35,36 
Finally, we ran a Pearson linear test of correlation on individual latencies (taking all distances together for saccades). 
Results
Clinical Results
Clinical characteristics illustrated in Supplementary Table S1 showed several significant differences between the two groups; the Mann-Whitney U test applied on positive fusional vergence (PFV) showed significantly lower values for the vergence disorders group than those for the healthy controls, both at near (P = 0.026) and at far (P = 0.012). Also the symptomatology score (CISS) was 27.6 ± 6.8 for the vergence disorders group, which was significantly higher than that for the healthy group (14.1 ± 6.4, P = 0.0008). 
In clinical follow-up assessment, 1 month after rehabilitation of vergence, far PFV and the CISS score were no longer significantly different from the values from the healthy subjects (Mann-Whitney U test, P = 0.37). Also the Wilcoxon test comparing the vergence disorders group itself before and after the rehabilitation showed two benefits: significant increase of PFV and significant reduction of the symptomatology (CISS score, respectively, P = 0.043 and P = 0.012). 
Next we present eye movement data for the vergence and saccade tests. 
Eye Movement Results
Vergence.
Results of Mann-Whitney U test are shown in Supplementary Table S2. Before rehabilitation of subjects with vergence disorders, the vergence gain, the peak velocity, and the mean velocity were significantly reduced compared to the healthy subjects, both for convergence (P ≤ 0.036) and for divergence (P ≤ 0.056 after correction for multiple testing using Holm's method). 
Vergence Rehabilitation Improved Vergence Properties.
Figure 4 shows convergence (upward inflection) and divergence traces from a subject with vergence disorders (TC) at the beginning of the first and of the last session of vergence rehabilitation. Several differences can be observed: decrease of latency, increase of amplitude, and decrease of intertrial variability; trajectories became smoother and more stereotyped. 
Figure 4
 
Trajectories of a subject with vergence disorders (TC) illustrate the results of the vergence test for the beginning of rehabilitation (A) compared to the last session of rehabilitation (B). All trials are superimposed similarly to Figure 3, and mean of trials toward the same target are illustrated with dotted lines, respectively, for convergence (upward traces) and divergence (downward); positions of the targets are indicated with horizontal dashed lines.
Figure 4
 
Trajectories of a subject with vergence disorders (TC) illustrate the results of the vergence test for the beginning of rehabilitation (A) compared to the last session of rehabilitation (B). All trials are superimposed similarly to Figure 3, and mean of trials toward the same target are illustrated with dotted lines, respectively, for convergence (upward traces) and divergence (downward); positions of the targets are indicated with horizontal dashed lines.
Quantitative results are shown also in Supplementary Table S2 (values after rehabilitation) and illustrated in Figure 5. Latencies were reduced from 205 ± 57 to 157 ± 22 ms for convergence and from 197 ± 33 to 171 ± 34 for divergence; the difference was significant for convergence (P = 0.036). The gain increased from 0.63 ± 16 to 0.92 ± 0.21 for convergence and from 0.54 ± 0.21 to 0.74 ± 0.12 for divergence; the increase was significant for convergence (P = 0.017) and approached significance for divergence (P = 0.069). Also, the peak velocity increased from 44 ± 24 to 67 ± 20°/s for convergence and from 25 ± 13 to 41 ± 41°/s for divergence; the increase was significant for divergence (P = 0.025). Concerning the ratio between amplitude of vergence and duration, that is, the mean velocity, its value increased from 18 ± 5 to 22 ± 5°/s for convergence and from 13 ± 4 to 15 ± 2°/s for divergence, but the increase failed to reach significance. 
Figure 5
 
Spatiotemporal parameters of vergence from the Table, namely latency (A), accuracy (B), and the mean velocity (C). Significant differences between the healthy and the vergence disorders groups are indicated by dots (•), and follow-up differences of the vergence disorders are indicated by asterisks (*). A perfect accuracy of 1.0 is illustrated with the dashed line.
Figure 5
 
Spatiotemporal parameters of vergence from the Table, namely latency (A), accuracy (B), and the mean velocity (C). Significant differences between the healthy and the vergence disorders groups are indicated by dots (•), and follow-up differences of the vergence disorders are indicated by asterisks (*). A perfect accuracy of 1.0 is illustrated with the dashed line.
Table
 
Parameters of Saccade
Table
 
Parameters of Saccade
In summary, the spatiotemporal parameters of vergence were all improved after vergence rehabilitation, namely latency, gain, and velocity. Next we will examine if and how such vergence improvement influences saccade properties. 
Saccades.
The main results are summarized in the Table
Latency.
Figure 6A shows the group mean saccade latency for each viewing distance for the healthy group versus the vergence disorders group. The horizontal dashed lines show the average group mean latency taking saccades for all distances together. The mean latency of saccades for the vergence disorders group was higher than that for the healthy group, but the difference did not reach significance. Yet, after the end of vergence rehabilitation, the mean latency of all saccades taken together decreased significantly (P = 0.045 a month after rehabilitation, considering correction for multiple testing using Holm's method); at specific distances, the Wilcoxon comparisons were significant at 20 cm (P = 0.036) and at 40 cm (P = 0.036 a month after rehabilitation, and P = 0.046 a week after rehabilitation, after Holm's correction). Significant differences before and after vergence rehabilitation are indicated with an asterisk in Figure 6
Figure 6
 
Spatiotemporal parameters of saccades from the Table are shown according to the distance. Dashed lines indicate means from all distances together; significant differences between healthy and vergence disorders are indicated by dots (•), and follow-up differences of the vergence disorders are indicated by asterisks (*); also, statistically significant distance effects are indicated by hash marks (#) for latency (A) and accuracy (B).
Figure 6
 
Spatiotemporal parameters of saccades from the Table are shown according to the distance. Dashed lines indicate means from all distances together; significant differences between healthy and vergence disorders are indicated by dots (•), and follow-up differences of the vergence disorders are indicated by asterisks (*); also, statistically significant distance effects are indicated by hash marks (#) for latency (A) and accuracy (B).
For distance specificity of saccades, significant differences are indicated with a hash mark in Figure 6. We call distance specificity an effect of distance on properties of saccades. For the healthy group, the latency was longer at 150 cm but not significantly (P = 0.069 comparing with 40 cm); for subjects with vergence disorders, again the latency was shorter for saccades at the more proximal distance, that is, 20 cm (P ≤ 0.05 after Holm's correction, for comparison of both saccades at 40 vs. 20 cm and saccades at 150 vs. 20 cm). Thus, after rehabilitation the statistical results showed the same distance specificity. 
In summary, before and after the vergence rehabilitation, saccade latency diminished significantly, at least at the nearest distances (20 and 40 cm); that is, latency increased with distance, particularly for subjects with vergence disorders. 
Gain.
Figure 6B shows the group means of gain of the saccades for each distance. Mean gain value of saccades from all distances taken together is shown for each group with dashed lines; the horizontal dotted line indicates a gain value of 1.0, that is, 100% accuracy of the saccades. The group mean gain of subjects with vergence disorders was not significantly different compared to the healthy group. Yet, a month after the end of the rehabilitation, the gain of the saccades executed at 150 cm was significantly higher for the rehabilitated subjects than for the healthy subjects: 0.98 ± 0.03 vs. 0.95 ± 0.03 (P = 0.037 after Holm's correction). No significant effects of rehabilitation were found using Wilcoxon test, even if a week after the end of rehabilitation the gain of saccades at 40 cm tended to be higher than before (P = 0.063). 
There was no significant specificity of distance for the healthy group. Concerning subjects with vergence disorders, saccades showed significantly higher gain when executed at distances beyond 20 cm (P = 0.044 after Holm's correction, for saccades at both 40 and 150 cm). After rehabilitation, similar distance specificity was observed: Saccades at 40 cm had higher gain than at 20 cm (P = 0.044 after Holm's correction, both a week and a month after the end of rehabilitation). 
In summary, after rehabilitation of vergence the gain of saccades at far reached higher accuracy than for the healthy controls, with a mean gain close to 1.0; the gain of saccades increased with distance for subjects with vergence disorders, and this was the case before and after rehabilitation. 
Velocity.
As both peak velocity and duration increase with the amplitude of saccades and as there are some differences on gain (see above), to consider the speed of the movement we analyzed the mean velocity, which is the ratio between amplitude and duration. Results are shown in Figure 6C. 
All statistical tests failed to reach significant difference of mean velocity, both when comparing the healthy versus the vergence disorders group (before and after rehabilitation: all P ≥ 0.08) and for comparison between distances within each group (all but one distance: P ≥ 0.24). At 40 cm only, the mean velocity of saccades measured a week after vergence rehabilitation tended to be higher than before (P = 0.052 after Holm's correction). 
In summary, saccade mean velocity was not different for the two groups, did not depend significantly on viewing distance, and did not change with vergence rehabilitation. 
Binocular Coordination of Saccades
As mentioned in Methods, the quality of binocular coordination was measured as the disconjugacy of saccades, that is, the difference in the amplitude of saccades (left eye − right eye, see Fig. 3B). Figure 7 shows representative disconjugacy traces during and after leftward and rightward saccades at each depth, from a healthy subject (EO) and from a subject with vergence disorders (TC) before and after vergence rehabilitation. Disconjugacy is clearly higher for subject TC, and some reduction is observed after vergence rehabilitation. 
Figure 7
 
All trajectories of conjugate displacement (namely, the eccentricity of saccades as abscissa) from a healthy subject (EO, AC, in blue) are plotted next to a subject with vergence disorders (TC), before (DF, in red) and a month after (GI, in green) rehabilitation; these traces show the time course of disconjugacy (as ordinate) during the saccades performed at each distance, namely, the separate blocks at 150 cm (A, D, G), 40 cm (B, E, H), and 20 cm (C, F, I). For healthy subjects the disconjugacy tended toward zero during the displacement from initial position to the lateral target, especially at 40 cm. Before rehabilitation the subjects with vergence disorders showed higher disconjugacy and variability than healthy controls; also for TC, note the exceptional twice-divergent disconjugacy of the double saccades to the right side at 20 cm. After rehabilitation the disconjugacy and variability decreased; also the exceptional stereotyped behavior of TC normalized for right-side saccades at 20 cm.
Figure 7
 
All trajectories of conjugate displacement (namely, the eccentricity of saccades as abscissa) from a healthy subject (EO, AC, in blue) are plotted next to a subject with vergence disorders (TC), before (DF, in red) and a month after (GI, in green) rehabilitation; these traces show the time course of disconjugacy (as ordinate) during the saccades performed at each distance, namely, the separate blocks at 150 cm (A, D, G), 40 cm (B, E, H), and 20 cm (C, F, I). For healthy subjects the disconjugacy tended toward zero during the displacement from initial position to the lateral target, especially at 40 cm. Before rehabilitation the subjects with vergence disorders showed higher disconjugacy and variability than healthy controls; also for TC, note the exceptional twice-divergent disconjugacy of the double saccades to the right side at 20 cm. After rehabilitation the disconjugacy and variability decreased; also the exceptional stereotyped behavior of TC normalized for right-side saccades at 20 cm.
The group results are illustrated in Figure 8. Mean disconjugacy of all saccades (taking three distances together) showed higher values for subjects with vergence disorders compared to healthy controls (P = 0.026); the difference was especially observed for saccades executed at 40 cm (P = 0.0051). Disconjugacy remained higher than that of healthy controls a week after the end of rehabilitation (P = 0.034 and P = 0.042 after Holm's corrections, respectively, for comparisons of the mean of all saccades and of saccades at 40 cm). A month later the mean disconjugacy of the saccades at 40 cm and the disconjugacy of all saccades were still higher than those of the healthy controls (P = 0.03 for the disconjugacy at 40 cm and P = 0.045 after Holm's correction for the disconjugacy of all saccades, that is, taking all distances together). But a month after the end of rehabilitation the mean disconjugacy of all saccades, that is taking together the mean disconjugacy from each distance, was significantly lower compared to the values of the same subjects before rehabilitation (P = 0.028 to the Wilcoxon test, after Holm's correction); saccades executed at the 40 cm distance had significantly lower disconjugacy than before rehabilitation (P < 0.05 after Holm's correction). 
Figure 8
 
Disconjugacy of saccades from the Table is illustrated similarly to Figure 6. This illustration shows the significantly lower disconjugacy of saccades from the healthy group when executed at 40 cm rather than farther (150 cm) or nearest (20 cm) distances (#). Before rehabilitation, subjects with vergence disorders did not show the same pattern but a significantly higher disconjugacy for all distances taken together (• symbol along the dashed lines) and for saccades at 40 cm (same symbol at the top). After rehabilitation these differences persisted, but a significant decrease occurred for all distances taken together and for saccades at 40 cm (*).
Figure 8
 
Disconjugacy of saccades from the Table is illustrated similarly to Figure 6. This illustration shows the significantly lower disconjugacy of saccades from the healthy group when executed at 40 cm rather than farther (150 cm) or nearest (20 cm) distances (#). Before rehabilitation, subjects with vergence disorders did not show the same pattern but a significantly higher disconjugacy for all distances taken together (• symbol along the dashed lines) and for saccades at 40 cm (same symbol at the top). After rehabilitation these differences persisted, but a significant decrease occurred for all distances taken together and for saccades at 40 cm (*).
Distance specificity was present for the healthy group: Disconjugacy of saccades executed at 40 cm was significantly lower than that of saccades at 20 or 150 cm (P = 0.05 after Holm's corrections). Subjects with vergence disorders showed no such distance specificity. A week after the end of rehabilitation, the disconjugacy of saccades at 150 cm was significantly different than that of saccades at 20 cm (P = 0.043 after Holm's correction); and a month after the end of rehabilitation, saccades at 20 cm showed the smallest disconjugacy. 
An additional nonparametric 2-way ANOVA on ranking data, with main factors being distance (three levels) and session number (three levels), was performed on five subjects with sufficient data for all these conditions, showing a significant interaction between the distance of saccades and the session: F(5,40) = 19,43, P = 0.006; this is in line with the results of the Wilcoxon analysis presented above, confirming that the rehabilitation effect varies with distance. 
In summary, subjects with vergence disorders showed in general higher disconjugacy of saccades than the healthy group. After vergence rehabilitation the disconjugacy decreased at the 40-cm distance, particularly a month after the end of rehabilitation. Similarly, the healthy group ever showed lower disconjugacy of saccades executed at 40 cm compared to saccades at 20 and 150 cm. 
Relations Between Saccades and Vergence
Comparison of Saccades and Vergence Initiation.
Latency of saccades was compared to the latency of vergence using the Wilcoxon test. For the healthy group, the latency of vergence was significantly shorter than the latency of saccades (P < 0.05 for both convergence and divergence). The latency of convergence was subtracted from that of saccades at each distance: The latency difference between convergence and saccades at each distance was, from near to far, 54 ± 71, 57 ± 38, and 75 ± 52 ms. Similarly, for the divergence latency subtracted from that of saccades, it was 45 ± 64, 48 ± 40, and 66 ± 49. For subjects with vergence disorders, no significant difference was reached before the rehabilitation. But after the vergence rehabilitation, the latency of convergence appeared significantly shorter than the latency of saccades at each distance (all P = 0.036 after Holm's correction); the latency difference between convergence and saccades at each distance was 53 ± 38, 61 ± 46, and 102 ± 28 ms; and between divergence and saccades, the latency difference was 38 ± 56, 45 ± 59, and 87 ± 37 ms (P = 0.036 after Holm's correction for saccades at 150 cm). 
Correlation of Latencies.
When considering latencies from healthy controls and latencies from the rehabilitated subjects, a positive correlation was observed between the latency of saccades (taking all distances together) and the latency of convergence (R2 = 0.45, P = 0.009, see Fig. 9). A similar positive correlation existed between latency of saccades and latency of divergence (R2 = 0.36, P = 0.03, not shown); thus, the longer the latency of vergence, the longer the latency of saccades. 
Figure 9
 
Correlation between the latency of convergence and the latency of saccades.
Figure 9
 
Correlation between the latency of convergence and the latency of saccades.
Discussion
The main results of the study were decrease of the latency and increase of the accuracy of vergence following rehabilitation, and secondly, decrease of saccade latency and some improvement of binocular coordination following the vergence rehabilitation. Moreover, there were distance-in-depth specificities, particularly for binocular coordination. These results will be discussed next. 
Benefits of Vergence Rehabilitation in Subjects With Vergence Disorders
The present study shows significant improvements of vergence properties after four sessions of vergence rehabilitation. We found significant improvement of the gain and peak velocity: The amplitude increased significantly for convergence and to a lesser extent for divergence. These results suggest functional improvement of the divergence and convergence systems, including their respective generators located at the MRFs.37 In humans, Takagi and Zee38 showed a similar increase in vergence amplitude for a healthy group through a similar double-step protocol. The present study extends these observations to a population of subjects with vergence disorders (see also Ref. 27). Next, we will discuss the major changes of saccade properties, as saccade substrate is the main focus of the study. 
Latency of Saccades: Role of Vergence and Depth
The latency of saccades reflects several processes that involve extended neural circuitry from the retina to visual cortex, parietal cortex, frontal lobe, superior colliculus, and then brain stem to extraocular muscles.1 
Hypothetical processes for saccade preparation include fixation release, localization of the target location, attention shift, computation of eye movement parameters, and decision to move (for a very exhaustive review, see Ref. 39). The present study shows that vergence rehabilitation leads to an optimization of the latency for both vergence and saccades. Stimulus properties could influence the measure of latency.12,40 Yet the latency differences for saccades and vergence lead us to suggest that high quality of vergence control influences the quality of saccade initiation, even though the saccades and vergence initiation mechanisms are similar but not identical. The common mechanism could be attributed to the omnipause neurons (OPN) located in the pontine reticular formation.5 
Shorter latency of saccades after vergence rehabilitation could be due to shorter time of computation for saccade metrics and/or faster fixation release, indicating a more efficient cortical preparation of the saccades. It should be noted that other studies of saccade adaptation using a double-step saccade task (e.g., Ref. 41) failed to show a latency decrease despite successful adaptation of the gain, duration, and velocities of saccades. In our study, even though the decrease of saccade latency was smaller than that of vergence, the reduction effect was durable and significant. We conclude that facilitation of vergence initiation after rehabilitation would spread to saccade initiation. 
Such arguments are corroborated by the correlation between the latency of saccades and the latency of vergence, indicating the existence of common cortical circuits controlling both types of eye movements. Further investigation of latency decrease after saccade versus vergence adaptation would be of interest. The interaction of saccades and vergence will be further discussed below. 
Latency of Saccades and Distance-in-Depth
Dependency of latency on depth was observed in adults and children11 as well as in older adults,12 that is, increase of latency with distance-in-depth. These authors suggested several factors explaining shorter latency for saccades at near: stimulus angular size, which increases at near; oculomotor fixation disengagement, which would be facilitated at near; and different cortical representation of the far and near space and/or fluctuation of attention. In the present study, the far–near difference of latency reached significance for subjects with vergence disorders only, but healthy young adults did not show a significant distance-in-depth effect. Relative to prior studies, this suggests that the strength of the distance effect on saccade latency depends on the population studied. In subjects with vergence disorders, such distance-in-depth would be explained with similar mechanisms compared to those in the other studies cited above for healthy subjects. Among subjects with vergence disorders, heterophoria was more frequent and there is some evidence that exophoria can induce shorter latency of saccades30; thus individual variability of heterophoria could explain the clear distance-in-depth effect on latency and differences between those with vergence disorders and the healthy group (see also Ref. 16). Yet new studies are needed with a larger number of subjects to establish the link between heterophoria and the decrease of latency with distance decrease for such populations. 
Relative Invariance of Accuracy and Speed of Saccades
The results did not show a significant effect of vergence rehabilitation on saccade accuracy and its velocity even though vergence velocity and gain increased. These observations are in line with existing physiological evidence for relatively distinct although interactive substrate of saccades and vergence generators at the brain stem level.1,5 There was, however, a single instance—saccades at far recorded a month after vergence rehabilitation—that showed significantly better accuracy, almost optimal, compared to that of the healthy group. Such optimization of the gain for saccades executed at a specific distance is presumably induced by an optimization of target localization hypothetically mediated by a better performance of the vergence system. In other words, accuracy of saccades could be related to vergence efficiency. After rehabilitation of vergence, accuracy of saccades can even reach supranormal quality compared to that in healthy subjects (see Fig. 6B). 
Abnormal Disconjugacy of Subjects With Vergence Disorders Decreased After Vergence Rehabilitation
Binocular coordination of saccades was poorer for subjects with vergence disorders than for healthy controls; that is, the disconjugacy of the saccades was higher for subjects with vergence disorders. But even if disconjugacy of saccades a month after vergence rehabilitation remained higher than for the healthy controls, its value decreased significantly, and such improvement occurred for saccades at all distances. Differences in the healthy compared to the vergence disorders group and intrasubject improvement in the vergence disorders group, on the other hand, are both observations that clearly show how the coordination of saccades is highly related to the quality of vergence control. Namely, these findings are in line with the hypothesis according to which control of disconjugacy during the saccades is related to the ability of programming, via a neuroplastic mechanism, an appropriate fast (intrasaccadic) vergence command, that helps to equalize the saccades of the two eyes. Indeed, most saccades in real three-dimensional (3D) space have unequal size; this is due to the interaction with the vergence system, which is naturally involved as the eyes move between objects located at both different depths and directions. When one is constrained to produce saccades within the same depth, as was the case in our study, the saccades of the adducting and abducting eye should become naturally equal; under these circumstances the vergence generator is called on to produce only the small intrasaccadic vergence that will be appropriate to compensate the naturally existing small asymmetries in the extraoculomotor muscles of the abducting and the adducting eye and their innervation.19,42 
If adduction–abduction asymmetry is not well corrected by an intrasaccadic vergence command, there will be residual disparity during the following fixation. Detection of such disparity could also be involved in the adaptative neuroplastic mechanism that aims to generate the appropriate intrasaccadic vergence for achieving the least possible disconjugacy. Note also that our vergence double-step paradigm involves steps of disparity and accommodation together during the rehabilitation process. Thus, disparity together with blur and accommodation comprises the essential stimuli of the neuroplastic changes reported here. Further evidence for the involvement of disparity-driven mechanisms in our data comes from the decrease of stereoacuity threshold observed in four of the subjects after vergence rehabilitation (see Supplementary Table S1), especially those (MB and DS) who had a higher stereoacuity threshold than normal before the rehabilitation and dropped into the normal range after rehabilitation. Stereoacuity tests such as the TNO are based on disparity detection. Perhaps improvements of stereoacuity might have occurred for other subjects, but the test used does not allow measurement of very fine changes. 
Distance Specificity and the Disconjugacy of Saccades
For the healthy subjects, distance specificity was significant only for the coordination of saccades: Their disconjugacy was smaller for saccades at 40 cm than for saccades at 20 or 150 cm. We propose the following interpretation: Students in this study had daily intense activity at the 40-cm distance, corresponding to the standard reading distance, especially in the optics college program, which involves high precision and manual tasks at 40 cm. Given that such distance is extensively used, everyday activity would boost the healthy group to develop high binocular coordination fine visual performance at this particular distance. Therefore, distance specificity of binocular coordination at 40 cm could be attributed to a long-term adaptation to such working distance. 
For subjects with vergence disorders, before rehabilitation the disconjugacy of saccades was significantly higher than that of the healthy controls for all distances, especially at 40 cm. In other words, vergence disorders spread to the coordination of saccades, and this phenomenon is in line with our main hypothesis.18 We postulate that there is continuous neuroplasticity activity to maintain saccade disconjugacy as small as possible; consequently, both groups of subjects would be particularly trained for the near working distance. To explain such difference before rehabilitation, we suggest that oculomotor neuroplasticity is somehow less efficient for the vergence disorders group. Limitations for the latter group could be due to inefficient detection of disparity and of blur signals needed by the cerebellum and brain stem circuits performing adjustment of the appropriate saccade vergence commands. 
After vergence rehabilitation, despite improvements, the disconjugacy of saccades remained significantly higher than for the healthy group. Such persistence is indicative of the complexity in the neurophysiological mechanism involved in the reduction of disconjugacy of saccades. Also, it is in line with studies in children15,18 showing that the maturation of binocular coordination is slow. It may be that a long-term adaptation similar to the one mentioned above in healthy subjects could occur slowly in vergence disorders even after vergence rehabilitation. Yet we did not gather sufficient evidence to sustain such an assertion, except that disconjugacy did not show significant improvement sooner than a month after rehabilitation, when it approached the level of the healthy controls. How could benefits spread to binocular coordination over the long term? Visual experience and systematic integration of disparity errors during natural life could be used by the continuous operating neuroplastic mechanism to adjust saccadic vergence motor commands. Further investigation with rehabilitation of combined saccade–vergence eye movements and its long-term consequences on the binocular coordination of saccades would be of interest. Note that following rehabilitation, saccade parameters tended to increase at 40 cm, namely, the mean velocity and to a lesser extent the gain. Transient disconjugacy of saccades was reported to increase with the amplitude of saccades.17,43 In our study, the mean disconjugacy of saccades decreased significantly at 40 cm even though saccade amplitude tended to increase. This observation suggests that reduction of disconjugacy of saccades relies on a nonlinear complex interaction with vergence. 
To summarize, spatiotemporal parameters of saccades such as latency and disconjugacy appear to be dependent on the efficiency of vergence, and to a lesser extent the gain also is dependent, suggesting a continuous interaction between saccades and vergence physiological generators even when they are stimulated separately. 
Distinctive substrates at the cortical level were observed through a fMRI study44,45 as well as at the brain stem level. Evidence of interaction between saccades and vergence has been reported previously in monkeys4648 and in humans using dichoptic conditions,49 but these studies needed to be sustained by testing this interaction further in a natural 3D environment, in order to objectivize the human cross-links between saccades and vergence more deeply than in the past.11,50,51 
In conclusion, the present study reports for the first time that benefits from rehabilitation of the vergence system spread to the saccade system, as the two are continuously interacting. In future studies it would be interesting to test the extent to which the neuroplasticity shown here in patients is higher than that in healthy subjects submitted to the same training protocol. 
Acknowledgments
The authors thank Thomas Eggert, Department of Neurology, Ludwig-Maximilians Universität, Germany, for improvement of software for vergence and saccade analyses; Fabienne Jonqua, orthoptist, for conducting orthoptic assessment. 
Disclosure: A. Morize, None; D. Brémond-Gignac, None; F. Daniel, None; Z. Kapoula, None 
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Figure 1
 
Temporal (A, B) and spatial (CE) arrangement of the REMOBI visual display. The targets were randomly interleaved in order to test saccades (C) or vergence (D) eye movements in different blocks using the temporal paradigm as shown in (A). During a rehabilitation block (E), subjects with vergence disorders performed only vergence eye movements along the midsagittal plane, using the vergence double-step paradigm; the corresponding temporal arrangement is shown in (B).
Figure 1
 
Temporal (A, B) and spatial (CE) arrangement of the REMOBI visual display. The targets were randomly interleaved in order to test saccades (C) or vergence (D) eye movements in different blocks using the temporal paradigm as shown in (A). During a rehabilitation block (E), subjects with vergence disorders performed only vergence eye movements along the midsagittal plane, using the vergence double-step paradigm; the corresponding temporal arrangement is shown in (B).
Figure 2
 
The overall experimental design was similar for healthy and vergence disorders groups: Clinical examination were performed separately to the oculomotor tests. Then subjects diagnosed for vergence disorders performed five weekly rehabilitation sessions and were tested again for saccades and vergence, especially for saccades, which were tested a week and a month after the end of vergence rehabilitation.
Figure 2
 
The overall experimental design was similar for healthy and vergence disorders groups: Clinical examination were performed separately to the oculomotor tests. Then subjects diagnosed for vergence disorders performed five weekly rehabilitation sessions and were tested again for saccades and vergence, especially for saccades, which were tested a week and a month after the end of vergence rehabilitation.
Figure 3
 
Trajectories of a subject with vergence disorders (TC) illustrate the method of analysis, respectively, for the saccades (AC) and vergence (DE) tests. All trials are superimposed at t = 0, the instant of target appearance. The bold lines show an individual trial of saccade to the left (A) and a trial of divergence (D): Onset (I) and offset (P) of eye movements were defined according to velocity threshold (V), traces of velocity being illustrated at the bottom (C, E). Note that coordination of saccades was evaluated from the disconjugate amplitude between the onset and the offset of each saccade; we did not analyze the typical divergence–convergence pattern that occurred during the saccade itself.
Figure 3
 
Trajectories of a subject with vergence disorders (TC) illustrate the method of analysis, respectively, for the saccades (AC) and vergence (DE) tests. All trials are superimposed at t = 0, the instant of target appearance. The bold lines show an individual trial of saccade to the left (A) and a trial of divergence (D): Onset (I) and offset (P) of eye movements were defined according to velocity threshold (V), traces of velocity being illustrated at the bottom (C, E). Note that coordination of saccades was evaluated from the disconjugate amplitude between the onset and the offset of each saccade; we did not analyze the typical divergence–convergence pattern that occurred during the saccade itself.
Figure 4
 
Trajectories of a subject with vergence disorders (TC) illustrate the results of the vergence test for the beginning of rehabilitation (A) compared to the last session of rehabilitation (B). All trials are superimposed similarly to Figure 3, and mean of trials toward the same target are illustrated with dotted lines, respectively, for convergence (upward traces) and divergence (downward); positions of the targets are indicated with horizontal dashed lines.
Figure 4
 
Trajectories of a subject with vergence disorders (TC) illustrate the results of the vergence test for the beginning of rehabilitation (A) compared to the last session of rehabilitation (B). All trials are superimposed similarly to Figure 3, and mean of trials toward the same target are illustrated with dotted lines, respectively, for convergence (upward traces) and divergence (downward); positions of the targets are indicated with horizontal dashed lines.
Figure 5
 
Spatiotemporal parameters of vergence from the Table, namely latency (A), accuracy (B), and the mean velocity (C). Significant differences between the healthy and the vergence disorders groups are indicated by dots (•), and follow-up differences of the vergence disorders are indicated by asterisks (*). A perfect accuracy of 1.0 is illustrated with the dashed line.
Figure 5
 
Spatiotemporal parameters of vergence from the Table, namely latency (A), accuracy (B), and the mean velocity (C). Significant differences between the healthy and the vergence disorders groups are indicated by dots (•), and follow-up differences of the vergence disorders are indicated by asterisks (*). A perfect accuracy of 1.0 is illustrated with the dashed line.
Figure 6
 
Spatiotemporal parameters of saccades from the Table are shown according to the distance. Dashed lines indicate means from all distances together; significant differences between healthy and vergence disorders are indicated by dots (•), and follow-up differences of the vergence disorders are indicated by asterisks (*); also, statistically significant distance effects are indicated by hash marks (#) for latency (A) and accuracy (B).
Figure 6
 
Spatiotemporal parameters of saccades from the Table are shown according to the distance. Dashed lines indicate means from all distances together; significant differences between healthy and vergence disorders are indicated by dots (•), and follow-up differences of the vergence disorders are indicated by asterisks (*); also, statistically significant distance effects are indicated by hash marks (#) for latency (A) and accuracy (B).
Figure 7
 
All trajectories of conjugate displacement (namely, the eccentricity of saccades as abscissa) from a healthy subject (EO, AC, in blue) are plotted next to a subject with vergence disorders (TC), before (DF, in red) and a month after (GI, in green) rehabilitation; these traces show the time course of disconjugacy (as ordinate) during the saccades performed at each distance, namely, the separate blocks at 150 cm (A, D, G), 40 cm (B, E, H), and 20 cm (C, F, I). For healthy subjects the disconjugacy tended toward zero during the displacement from initial position to the lateral target, especially at 40 cm. Before rehabilitation the subjects with vergence disorders showed higher disconjugacy and variability than healthy controls; also for TC, note the exceptional twice-divergent disconjugacy of the double saccades to the right side at 20 cm. After rehabilitation the disconjugacy and variability decreased; also the exceptional stereotyped behavior of TC normalized for right-side saccades at 20 cm.
Figure 7
 
All trajectories of conjugate displacement (namely, the eccentricity of saccades as abscissa) from a healthy subject (EO, AC, in blue) are plotted next to a subject with vergence disorders (TC), before (DF, in red) and a month after (GI, in green) rehabilitation; these traces show the time course of disconjugacy (as ordinate) during the saccades performed at each distance, namely, the separate blocks at 150 cm (A, D, G), 40 cm (B, E, H), and 20 cm (C, F, I). For healthy subjects the disconjugacy tended toward zero during the displacement from initial position to the lateral target, especially at 40 cm. Before rehabilitation the subjects with vergence disorders showed higher disconjugacy and variability than healthy controls; also for TC, note the exceptional twice-divergent disconjugacy of the double saccades to the right side at 20 cm. After rehabilitation the disconjugacy and variability decreased; also the exceptional stereotyped behavior of TC normalized for right-side saccades at 20 cm.
Figure 8
 
Disconjugacy of saccades from the Table is illustrated similarly to Figure 6. This illustration shows the significantly lower disconjugacy of saccades from the healthy group when executed at 40 cm rather than farther (150 cm) or nearest (20 cm) distances (#). Before rehabilitation, subjects with vergence disorders did not show the same pattern but a significantly higher disconjugacy for all distances taken together (• symbol along the dashed lines) and for saccades at 40 cm (same symbol at the top). After rehabilitation these differences persisted, but a significant decrease occurred for all distances taken together and for saccades at 40 cm (*).
Figure 8
 
Disconjugacy of saccades from the Table is illustrated similarly to Figure 6. This illustration shows the significantly lower disconjugacy of saccades from the healthy group when executed at 40 cm rather than farther (150 cm) or nearest (20 cm) distances (#). Before rehabilitation, subjects with vergence disorders did not show the same pattern but a significantly higher disconjugacy for all distances taken together (• symbol along the dashed lines) and for saccades at 40 cm (same symbol at the top). After rehabilitation these differences persisted, but a significant decrease occurred for all distances taken together and for saccades at 40 cm (*).
Figure 9
 
Correlation between the latency of convergence and the latency of saccades.
Figure 9
 
Correlation between the latency of convergence and the latency of saccades.
Table
 
Parameters of Saccade
Table
 
Parameters of Saccade
Supplement 1
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