Analysis of Saccades and Peak Velocity to Symmetrical Convergence Stimuli: Binocularly Normal Controls Compared to Convergence Insufficiency Patients

Abstract

Purpose.: To assess the potential peak velocity asymmetry between the left-eye and right-eye movement responses stimulated by symmetrical vergence steps in those with normal binocular vision and those with convergence insufficiency (CI) before and after vergence training. This study also evaluated whether vergence training influenced convergence peak velocity and the prevalence of saccades within the first second of the response.

Methods.: The peak velocities of the left-eye, right-eye, and combined vergence response evoked from symmetrical 2°, 4°, and 6° convergence step stimuli were assessed in 10 controls and 7 CI subjects. Four of the CI subjects participated in vergence training. An asymmetry ratio was calculated as the peak velocity of the slower eye movement response divided by the peak velocity of the faster eye movement response.

Results.: Controls were significantly more symmetrical (left-eye peak velocity was approximately equal to right-eye peak velocity) compared to CI subjects (P < 0.001). After vergence training, the CI subjects' left-eye and right-eye movements became significantly more symmetrical, convergence peak velocity increased, and the prevalence of saccades within the first 1 second decreased (P < 0.01). Peak convergence velocity was significantly correlated to the prevalence of saccades observed within the first second of the response (r = 0.8; P < 0.05).

Conclusions.: Data suggest that vergence training improves the symmetry between the left-eye and right-eye movements, increases convergence peak velocity, and decreases the prevalence of saccades within the first second of the response, which facilitates binocular coordination in CI patients. Saccades may be a compensatory mechanism used by CI subjects when convergence peak velocity is reduced.

Introduction

During daily activities, the brain acquires visual information by utilizing a combination of version and vergence eye movements. The eyes typically shift in tandem for version responses (i.e., saccadic movements), whereas the eyes rotate in opposition for vergence responses via either inward (convergence) or outward (divergence) movement. Vergence is defined as the difference between the left-eye and right-eye movement responses. Version is the average of the left-eye and right-eye movement responses. Although unusual within natural viewing conditions, pure vergence stimuli can be easily created within the laboratory setting to study the neural control of vergence responses. 

Binocular coordination is a critical skill necessary for the activities of daily living, such as reading, which most individuals can perform with ease. However, those with the vergence dysfunction known as convergence insufficiency (CI) report visual stress and strain (asthenopia) when engaged in near work. CI is common within the general population (4.2%–7.7%). ^1–5 Symptoms for those with CI include blurred vision, double vision (diplopia), eye strain, loss of concentration, frequent loss of place causing a rereading of text, reading slowly, print moving on the page, difficulty remembering what was read, sleepiness, and headaches. ^6–10 These symptoms negatively impact daily activities such as school work ^11–13 and employment. ¹⁴ CI is described as a binocular coordination problem because the eyes have a strong tendency to drift outward (defined as exophoria) when engaged in reading or performing other close visual work. ¹⁵ In addition, several independent studies report that the peak convergence velocity from CI patients is reduced compared to that from age-matched controls. ^16–18 Randomized clinical trials support that repetitive vergence training reduces the visual symptoms of CI patients, ^6,15 where the reduction of symptoms is sustained at 1 year posttraining. ¹⁹ Although clinicians commonly prescribe vergence training, also known as vision therapy or orthoptic exercises, to reduce symptoms, the underlying neurophysiological basis for improvement in symptoms in CI patients is unknown. ^15,20  

One method to evaluate binocular coordination is through an assessment of the left-eye and right-eye convergence peak velocity. On average, the left-eye and right-eye convergence movement responses elicited from symmetrical convergence stimuli (along the midsagittal plane with no conjugate stimulus) have approximately the same peak velocity (are symmetrical) in binocularly normal controls. ^21,22 Some individual responses may show that the convergence peak velocity of one eye is up to twice the speed of the other convergence eye movement response. ²¹ Symmetrical vergence responses are also reported for binocularly normal primates. ²³ Conversely, primates with infantile esotropia (pathologic inward misalignment of the visual axes) exhibit asymmetric convergence responses in which one eye has a reduced peak velocity compared to the other. ²³ Studies of the differences between the left-eye and right-eye movements report that the degree of asymmetry between the left and right eyes is dependent on the severity of strabismus in humans and primates. ^23,24 Surprisingly, even though CI is described as a problem in binocular coordination, a systematic study of the differences between the left-eye and right-eye convergence movement responses in those with CI has not been conducted and was one of the primary aims of this study. 

The second aim of this study was to assess saccades within convergence responses elicited from symmetrical convergence stimuli. A pure symmetrical convergence stimulus should elicit a pure symmetrical convergence response. Yet, studies report that saccades are commonly observed within convergence responses to symmetrical convergence stimuli. ^25–28 Prior research supports that when a saccade is initiated within convergence, the peak velocity of convergence is enhanced through a nonlinear interaction compared to saccade-free convergence responses. ^29–31 These studies suggest an interaction between the convergence and saccade systems. 

Thus, this investigation had two aims: (1) assessment of the peak velocity in the left-eye and right-eye movement responses elicited from pure symmetrical convergence stimuli, comparing binocularly normal controls to CI subjects before and after vergence training; and (2) evaluation of a potential relationship between convergence peak velocity and the prevalence of saccades stimulated from symmetrical convergence stimuli within the first second of the vergence responses from CI subjects before and after vergence training. The study tested two hypotheses. The first hypothesis was that since CI is described as a binocular coordination dysfunction, CI subjects may demonstrate greater asymmetries of left- and right-eye convergence movements mediated from symmetrical convergence stimuli, compared to binocularly normal controls, before vergence training. Asymmetry is defined as one eye movement having, on average, reduced peak velocity compared to the other eye movement. Further, the asymmetry in CI before training may be reduced after vergence training and thus be more similar to values in binocular normal controls. CI subjects have reduced peak convergence velocity before vergence training, which increases after training. The second hypothesis tested was that when the peak velocity of convergence movements is reduced, saccades will be recruited (even though the stimuli do not stimulate conjugate movements) presumably as a means to increase convergence peak velocity. When the convergence peak velocity increases after vergence training, the prevalence of saccades will be reduced compared to the baseline sessions, presumably because the need for saccades to facilitate convergence movement will decline with improvement in convergence binocular coordination. 

Methods

Subject Attributes

Seventeen subjects participated in this study: 10 control subjects (5 male and 5 female) with normal binocular vision between 20 and 31 years of age and 7 subjects diagnosed with CI (3 male and 4 female) between 19 and 29 years of age. The 4 female CI subjects participated in 18 hours of vergence training. 

The controls had normal binocular vision. Normal binocular vision was defined as having a normal near point of convergence (<8 cm), assessed by measuring the distance a high-acuity target was perceived as diplopic along the subject's midline, ³² and a normal stereopsis (≤50 seconds of arc), assessed by the Randot Stereopsis Test (Bernell Corp., South Bend, IN). Most subjects were emmetropes. Control subjects CONS1 (−1.25 diopters [D]) and CONS9 (−2.25 D) were myopes, and CI subjects CIS3 (−1.0 D) and CIS5 (−2.5 D) were myopes. The myopic subjects wore their contact lenses to correct for their refractive error during the experimental sessions. The remaining control and CI subjects did not require refractive correction. 

The CI subjects were diagnosed with convergence insufficiency by an optometrist. CI was diagnosed when the patient's near point of convergence was greater than 8 cm and failed Sheard's criterion, which states that the fusional vergence reserve should be at least twice the magnitude of the near dissociated phoria (measured at 40 cm along midline). ³³ Stereopsis was assessed using the Randot Stereopsis Test (Bernell Corp.). Near positive fusional vergence (PFV) range was measured using base-out prisms with the Bernell horizontal prism bar. The prism bar contained 15 prisms: 1Δ, 2Δ through 20Δ in increments of 2Δ, and 20Δ through 45Δ in increments of 5Δ. The subject held a high-acuity target, which was placed 40 cm (measured with a ruler) away along midline. The subject was instructed to look at the high-acuity target and try to keep it clear and single. The operator held the prism bar over the right eye. A new prism was introduced approximately every 2 seconds, and the subject was asked to report when the target doubled. The dissociated near phoria was assessed subjectively using a Maddox rod with the Bernell Muscle Imbalance Measure (MIM) card. This card has a resolution of 1Δ and a range of 28Δ exophoria to 28Δ esophoria. The MIM card is calibrated for the right eye; hence, the phoria was measured with the left eye fixating on penlight shown through the card. The MIM card was placed a measured 40 cm away along the subject's midline. Details of these methods are available in a prior study. ¹⁶  

Symptoms were quantified using the Convergence Insufficiency Symptom Survey (CISS), which is a 15-question survey. ⁷ Each symptom is scored between zero and 4, where zero represents that the symptom never occurs and 4 represents that the symptom always occurs. The responses are summed; a score of 21 or higher has been validated to have a sensitivity of 98% and specificity of 87% in young adults. ³⁴  

This study was approved by the Institution Review Board (IRB) of the New Jersey Institute of Technology in accordance with the Declaration of Helsinki. All subjects signed written informed consent approved by the IRB committee. 

Eye Movement Measurement Experimental Design

Instrumentation Used During Eye Movement Experiment.

Eye movements were recorded using a Skalar Iris (model 6500; Skalar Medical, Delft, The Netherlands) infrared (λ = 950 nm) limbus tracking system. The manufacturer reports that the linear range of the system is ±25° where all responses are within the linear range of the device. Prior research confirms a high degree of linearity, within 3% between ±25° horizontally for this system. ³⁵ A 12-bit acquisition hardware card (National Instruments 6024 E series; National Instruments, Austin, TX) digitized the individual left-eye and right-eye movements with a sampling rate of 200 Hz. The visual stimuli utilized green light-emitting diodes (LEDs) (Stanley model MU07 part 5101; Stanley, London, OH) 2 mm wide by 25 mm in height with a wavelength of 555 nm. Subjects were situated in a head and chin rest assembly to reduce influence from the vestibular system. ³⁶ The subject initiated each experimental trial by pressing a button, which allowed the subject to blink between experimental trials. Potential subject fatigue was also reduced by allowing the subject to initiate the experimental trial. ³⁷  

Visual Stimuli.

Convergence responses from symmetrical stimuli were collected from both binocularly normal controls and CI subjects. For the binocularly normal controls, 4° convergence step stimuli starting at an initial vergence angle of 12° (29 cm along the subject's midline assuming an interpupillary distance of 6 cm) and 2° (172 cm) were investigated; these have been shown to evoke a range of peak velocities in convergence steps. ²⁸ Studying a range of peak velocities is important to assess whether the prevalence of saccades is significantly correlated to peak velocity. However, the CI subjects were unable to maintain fusion of the stimulus located initially at a vergence angle 12° with a 4° inward step ending at a vergence angle of 16° (21 cm). In order to study convergence responses with a range of convergence peak velocities, the visual stimuli for CI subjects included 2°, 4°, and 6° convergence steps with an initial vergence angle of 2° (172 cm), as well as 2° and 4° steps starting from an initial vergence angle of 4° (86 cm). Visual stimuli also included divergence 4° steps beginning from an initial vergence angle of 8° (43 cm). A schematic of the visual stimuli is shown in Figure 1. All steps were randomly intermixed. All stimuli were presented after a random delay of 0.5 to 2.0 seconds. Both the randomization of stimulus direction (convergence compared to divergence) and the time when the stimulus was presented ensured that the subject could not predict when the next stimulus would begin. Such a design is important because prediction has been reported to influence both the latency and peak velocity of vergence responses. ^38–41 Divergence eye movements were not analyzed within this study since significant differences between binocularly normal controls and CI subjects were not observed in a prior investigation. ¹⁶  

Figure 1

 

Schematic of symmetric convergence step stimuli used to study the symmetry between the left and right convergence eye movement responses and the prevalence of saccades evoked via symmetric convergence step stimuli.

Vergence Training Laboratory Protocol for Convergence Insufficiency Subjects

The CI subjects participated in a total of 18 hours of vergence training, 6 hours at home and 12 hours in the laboratory. The vergence laboratory and home training was described in detail in a previous publication. ¹⁶ Home training entailed two 10-minute sessions (morning and evening) 3 days per week for 6 weeks. Laboratory training was composed of 1-hour sessions, twice per week for 6 weeks. Within a single day, a subject participated in either the laboratory or the home training but not both. The laboratory and home training consisted of step and ramp stimuli similar to those used clinically. ^42,43  

Subjects mediated step responses for approximately 25 to 30 minutes per laboratory training session in which eye movements were recorded. The step stimuli used within the laboratory vergence training were symmetrical convergence 2°, 4°, and 6° steps, as well as 4° divergence steps shown along the subject's midline using LED targets; see Figure 1. Subjects were instructed to track stimuli starting at an initial vergence angle of 2° or 4° vergence demand for convergence steps, and 8° vergence demand for divergence steps. To allow a subject adequate time to fuse the new target, step stimuli were presented and eye movement responses were acquired for 4 seconds. 

The subject also mediated ramp responses for approximately 25 to 30 minutes per laboratory training session. Ramp stimuli used within the laboratory vergence training were 1°/s and 2°/s between the range of 2° to 8° vergence angular demand. For the 1°/s ramp, the visual stimulus was presented for 12 seconds; for the 2°/s ramp, the visual stimulus was presented for 6 seconds. The ramp stimuli were presented using a custom haploscope (developed by New Jersey Institute of Technology, Newark, NJ). Two computer screens were used to generate a symmetrical disparity vergence stimulus along the subject's midline. The stimulus was a green vertical line 2 cm in height and 2 mm in width with a black background. Two partially reflecting mirrors projected the two vertical lines from the computer screens into the subject's line of sight. 

Eye Movement Analyses

A custom MATLAB (Waltham, MA) program was used for all eye movement analyses. Left-eye and right-eye movement data were converted from voltage values to degrees using the individual calibration data. Calibrations for vergence step responses were composed of four sustained convergence angles (1°, 2°, 3°, and 4° inward rotation for each eye). For all individual left- and right-eye movement responses, inward convergent rotation is plotted as positive to facilitate direct comparison between the left- and right-eye movement responses. Specifically, the right-eye movement response was inverted. Vergence was calculated as the difference between the right-eye and the left-eye movement to yield a net vergence response. Convergence responses were plotted as positive. Blinks were easily identified based upon manual inspection of the left-eye and right-eye movement response. Responses with blinks at any point during the movement were omitted (up to 2.1% of the data depending upon the subject). Only convergence responses were analyzed, since convergence responses have been reported to have reduced peak velocities in CI subjects compared to binocularly normal controls. ¹⁶  

Peak velocity was a primary measure within this study. Velocity was computed by taking the derivative of the position response using a two-point central difference algorithm. ⁴⁴ Each individual left-eye and right-eye convergence movement response was manually inspected for the presence of a saccade; saccades were easily identified because saccade dynamics were an order of magnitude greater than vergence. A phase plot (vergence velocity as a function of vergence amplitude) for the left-eye and the right-eye movement was used to determine whether the saccades obscured the peak velocity of the vergence response to a symmetrical stimulus. Only when saccades obstructed the convergence peak velocity was the response omitted from the peak velocity analysis, which occurred in less than 10% of the responses depending on the subject. The peak velocity of the left-eye, right-eye, and combined vergence response was quantified as the maximum value within the transient portion of the vergence movement. 

An asymmetry ratio was computed per subject. First, the right-eye peak velocity assessed from the 2°, 4°, and 6° step responses was plotted as a function of the left-eye peak velocity for each individual response. Convergence responses, including those that had saccades present where the saccades did not obstruct the peak velocity, were analyzed to compute the left- and right-eye peak velocity. A linear regression analysis was performed, and the trend line was plotted and compared to the perfect symmetry line. The perfect symmetry line was the line where the left-eye peak velocity exactly equaled the right-eye peak velocity. If the linear regression was below the perfect symmetry line, then the right-eye response was on average slower than the left-eye response. In this case, the asymmetry ratio was computed as the right-eye peak velocity divided by the left-eye peak velocity. Conversely, if the linear regression was above the perfect symmetry line, then the left-eye response was on average slower than the right-eye response. Hence, the asymmetry ratio was computed as the left-eye peak velocity divided by the right-eye peak velocity. Using this method, the asymmetry ratio will be less than one regardless of whether the left or right eye is slower. Hence, this method determines whether a subject has one eye that is on average slower than the other, or whether a subject may be asymmetrical on occasion but have, on average, approximately the same peak velocity in the left-eye and right-eye movements. The method also allows a group analysis because it accounts for some subjects having slower left-eye movements while other subjects may have slower right-eye movements. If the analysis simply divided the left-eye peak velocity by the right-eye peak velocity, then within a group analysis, it might appear that on average the group was symmetrical when in actuality the asymmetry was dependent upon a preferred eye. 

Saccades have been commonly reported within the transient portion of convergence responses initiated from symmetrical convergence stimuli. ^25–27 The second analysis of this study investigated the prevalence of saccades within the first second of the convergence response. Saccades within the convergence responses elicited from symmetrical steps were detected by using a semiautomated custom software program written in MATLAB, with the operator inspecting each response. ^26,27 Within the conjugate position trace, any saccades that were greater than 0.15° in magnitude were identified by the software. The average number of saccades within the first second of the convergence response was quantified. Saccades in the 10 binocularly normal controls were published in a prior paper and are not repeated here. The prior study showed that the prevalence of saccades was dependent on peak velocity, where the responses with slower peak velocities contained more saccades than the responses with faster peak velocities. ²⁸  

Statistical Analyses

For the CI subjects, the asymmetry ratio was calculated from the 2°, 4°, and 6° symmetrical vergence step responses. For the binocularly normal controls, the asymmetry ratio was calculated using the 4° near (initial vergence angle of 12°) and 4° far (initial vergence angle of 2° responses. Potential statistical differences were evaluated between the 10 binocularly normal controls and the 7 CI subjects using an unpaired t-test to determine whether differences in the asymmetry ratio existed between populations. In addition, the asymmetry ratio, near point of convergence, PFV range, near phoria, and the CISS from the 4 CI subjects who participated in vergence training were compared to study potential differences between the baseline data and the data after vergence training using a paired t-test. Statistical significance was defined as P < 0.05. The prevalence of saccades and combined convergence peak velocity for the 4 CI subjects who participated in vergence training were evaluated using an ANOVA. The two main factors (combined convergence peak velocity and the number of saccades) were analyzed for statistical differences using a within-subject three-way ANOVA in which time of recording (before versus after vergence training), convergence stimulus step size (2°, 4°, and 6°), and subject were the independent variables. Post hoc Bonferroni all pairwise comparisons were calculated to determine whether significant differences were observed in the convergence peak velocity or the prevalence of saccades by comparing (1) the before to after vergence training measurements and (2) the step size (2°, 4°, and 6°) of the symmetrical stimuli. Statistical comparisons were calculated using NCSS2004 software (Number Cruncher Statistical System, Kaysville, UT). 

A linear regression analysis was calculated with MATLAB software. Linear regression assessed the correlation between the left-eye convergence peak velocities and the right-eye convergence peak velocities for the binocularly normal controls and the CI subjects before and after vergence training to determine the asymmetry ratio. In addition, a linear regression analysis assessed the correlation between the prevalence of saccades observed within the first 1 second of the convergence response and the convergence peak velocity before and after vergence training. 

Results

Static Parameters and Convergence Insufficiency Symptom Survey

Seven subjects had a diagnosis of CI, and four CI subjects participated in vergence training. Three CI subjects did not participate in vergence training due to time constraints, leading to an inability to complete the 18 hours of training. The Table summarizes the clinical parameters and symptoms quantified via the CISS. All CI subjects had a stereopsis of 40 seconds of arc or better. A paired t-test revealed a significant difference between the baseline (before vergence training) parameters and the parameters after vergence training for the following clinical measurements: the near point of convergence (NPC) break (t = 4.9; P = 0.04), base-out (BO) PFV range (t = 9.5; P = 0.01), near dissociated phoria (t = 11; P = 0.008), and CISS (t = 3.6; P = 0.05). All significant changes were improvements to each parameter studied. Although the recover point of convergence improved, the changes were not statistically significant (t = 2.3; P = 1.5). 

Table

 

CI Subject Attributes: NPC Break and Recovery, BO PFV Range, Near Dissociated Phoria (40 cm), and CISS; Average With One Standard Deviation of the Group Is Reported

Subject No.	Stereopsis, min arc	Before Vergence Training					After Vergence Training
		NPC Break, cm	NPC Recovery, cm	BO PFV, Δ	Near Phoria, Δ	CISS	NPC Break, cm	NPC Recovery, cm	BO PFV, Δ	Near Phoria, Δ	CISS
CIS1	40	14	25	18	10 exo	24	10	15	45	2 exo	11
CIS2	20	9	12	10	10 exo	21	6	10	35	2 exo	8
CIS3	40	12	25	10	10 exo	34	6	9	45	4 exo	6
CIS4	35	22	24	20	8 exo	28	12	14	40	6 exo	8
CIS5	30	19	21	12	12 exo	25	NA	NA	NA	NA	NA
CIS6	40	12	14	16	10 exo	27	NA	NA	NA	NA	NA
CIS7	25	17	20	14	14 exo	30	NA	NA	NA	NA	NA
Ave ± std	33 ± 8.1	15 + 4.5	20 ± 5.3	14 ± 3.9	11 ± 1.9 exo	27 ± 4.2	8.5 ± 3.0	12.5 ± 2.4	41.3 ± 4.8	3.5 ± 1.9	8 ± 2.1

 Ave ± std, average with one standard deviation; min arc, minutes of arc; exo, exophoria.

Asymmetry Ratio Analysis

An eye movement response from a binocularly normal control, from a CI subject (CIS3) before any vergence training, and from the same CI subject (CIS3) after vergence training is plotted in the left, middle, and right column, respectively, in Figure 2. Figure 2A plots the right-eye (black) and left-eye (gray) movement responses, with convergence, inward rotation, plotted as positive for both eyes to facilitate direct comparison (the right-eye convergence response is inverted). For the CI subject, CIS3 (Fig. 2A, middle plots), the left-eye convergence response is slower compared to the right eye, showing the asymmetry between the convergence responses in the position and velocity traces. After vergence training, the left-eye and right-eye convergence movements are more similar, with the peak velocity almost the same. Figure 2B plots the convergence trace (difference between the eye movements) in black and the conjugate trace (average of the eye movements) in gray. Since the stimulus is a symmetrical convergence step change presented on the subject's midline, there should be no stimulus to the conjugate system. Hence, the conjugate response should be approximately zero. All responses in Figure 2B are saccade-free from the stimulus onset to the first 1 second of the response. 

Figure 2

 

Eye movement responses from a binocularly normal control (left column), a subject with CI (CIS3) before vergence training (middle column), and the same CI subject after vergence training (right column). (A) Position (upper plots) and velocity (lower plots) traces of the right-eye (black line) and left-eye (gray line) responses. Note that convergence movements are both plotted as positive to facilitate comparison; hence conjugate movements are plotted in opposing directions. (B) Convergence or the difference between the left- and right-eye movements (black line) and the conjugate or the average of the left- and right-eye (gray line) position (upper plots) and velocity (lower plots) responses. Note that saccades are not present within the first second of the convergence response. However, the left-eye response is slower compared to the right-eye response before vergence training, and the left-eye and right-eye movements are more similar after vergence training.

All 10 binocularly normal controls' and 7 CI subjects' left-eye and right-eye peak velocity was analyzed. In the interest of comparison, 4 of the binocularly normal controls (Fig. 3A), 4 CI subjects before vergence training (Fig. 3B), and the same CI subjects after training (Fig. 3C) are shown, with the subject number listed in the figure. Figure 3 plots the right-eye peak velocity from 2° (open diamond), 4° with a far initial vergence angle (solid circles), 4° with a near initial vergence angle (x symbol), and 6° (gray triangles) step responses as a function of left-eye peak velocity before vergence training. The perfect symmetry line is plotted in dashed gray, and the linear regression is plotted in solid black. The linear regression analyses of the right-eye peak velocity as a function of the left-eye peak velocity data for the seven CI subjects showed a Pearson correlation coefficient average and standard deviation of r = 0.68 ± 0.17, P < 0.01 (range, r = 0.44–0.89), compared to the 10 binocularly normal controls; for these subjects the linear regression analysis showed an average with one standard deviation of r = 0.63 ± 0.09, P < 0.005 (range, r = 0.49–0.75). For the 4 CI subjects who participated in vergence training, their baseline measurements showed a linear regression of r = 0.68 ± 0.17, P < 0.01 (range, r = 0.44–0.85), compared to the same subjects' measurements after vergence training, which were r = 0.78 ± 0.12, P < 0.001 (range, r = 0.69–0.95). For the binocularly normal controls, the perfect symmetry line was very similar to the linear regression trend of the data. The CI subjects before training exhibited an asymmetry on average whereby one eye was slower than the other. The left-eye convergence movements for CIS1 and CIS4 were on average slower compared to the right-eye convergence movements. Conversely, the right-eye convergence movements for CIS2 and CIS3 were on average slower compared to the left-eye convergence movements. After training, although the same eye was still slower in CIS1 and CIS3, the differences between the eye movement peak velocities were reduced. 

Figure 3

 

Right-eye peak velocity as a function of left-eye peak velocity for four binocularly normal controls (BNC) (A), CI subjects before vergence training (B), and the same CI subjects after vergence training (C). Peak velocities mediated from 2° (open diamonds), 4° beginning at a near vergence angle (solid circles), 4° beginning at a far vergence angle (x symbol), and 6° (gray triangles) symmetrical vergence step stimuli are plotted. The perfect symmetry line is plotted as a dashed gray line and the linear regression fit is plotted as a solid black line.

A group-level analysis was conducted through calculation of the asymmetry ratio as described in the Methods section. Figure 4 plots the average with one standard deviation of the asymmetry ratio for the 10 binocularly normal controls (black), 7 CI subjects' baseline measurements (gray), and 4 CI subjects after training (white). The 10 normal binocular controls had an asymmetry ratio of 0.93 ± 0.06, which was significantly more symmetrical than that of the 7 CI subjects, whose average asymmetry ratio was 0.77 ± 0.09, assessed using an unpaired t-test (degrees of freedom [df] = 15; t = 5.4; P < 0.001). The 4 CI subjects who participated in vergence training had a baseline ratio of 0.76 ± 0.12, which became significantly more symmetrical after training, reaching an average of 0.93 ± 0.11 as assessed using a paired t-test (df = 2; t = 5.6; P < 0.03). 

Figure 4

 

Average asymmetry ratio plus one standard deviation of the group-level analysis of subjects who were binocularly normal controls (black bar), CI subjects measured at baseline (gray bar), and CI subjects after vergence training (white bar). The number of subjects (N) is denoted per bar.

A unique behavior observed from CIS1 is shown in Figure 5. This response is to a symmetrical 4° convergence step with an initial vergence angle of 2°. Figure 5A plots the right-eye (black line) and left-eye (gray) movement position (upper) and velocity (lower) responses. Interestingly, the right eye exhibits two high-velocity convergence movements while the left eye has only one high-velocity convergence movement. Figure 5B plots the convergence (black) and conjugate (gray) position (upper) and velocity (lower) responses. Saccades were not observed within the conjugate response during the first 1 second of the movement. These responses were rare and were observed in 4 of the 7 CI subjects during the baseline measurements. This type of response was also not observed within the binocularly normal controls. The double high velocity in one eye movement convergence response with a single high-velocity component in the other eye movement convergence response was observed during the end of the experimental session, which was conducted prior to the vergence training. However, these responses were not observed after vergence training. 

Figure 5

 

Unique and rare response observed in CIS2 from the baseline session toward the end of the experimental trial. (A) Right-eye (black) and left-eye (gray) position (upper plot) and velocity (lower plot) responses. (B) Vergence (black) and conjugate (gray) position (upper plot) and velocity (lower plot) responses. This type of behavior was not observed in the responses after vergence training.

Saccades Within the First 1 Second of Convergence

Figure 6 plots an eye movement response from CIS1 before vergence training (left column) and after vergence training (right column). Figure 6A plots the inward convergence rotation as positive for both the left- and right-eye movements. The right-eye convergence movement is inverted to facilitate direct comparison. The right-eye and left-eye position and velocity traces are shown as black and gray lines, respectively. Hence, saccades are plotted in opposing directions. Figure 6B plots the convergence (black line) and conjugate (gray line) position (upper plot) and velocity (lower plot) traces. A saccade (denoted by the gray dashed line) is clearly observed from its much faster velocity characteristics compared to convergence. A saccade is observed within the left-eye and right-eye responses as well as the conjugate response denoted by the gray dashed vertical lines. Within the first second of the response, the CI subject before vergence training had a slower convergence velocity, with two saccades within the first second compared to the response after vergence training. After vergence training, the peak convergence velocity increased and no saccades were observed within the first second of the response. 

Figure 6

 

Eye movement response from a symmetrical convergence 4° step target from CIS1 before vergence training (left column) and after vergence training (right column). (A) Plot of the right-eye (black line) and left-eye (gray line) position (upper plots) and velocity (lower plots) traces. Note that the inward convergence rotation of each eye movement is plotted as positive to facilitate comparisons between the eye movements. Hence, conjugate movements are plotted in opposing directions. (B) Plot of the vergence (black line) and conjugate (gray line) position (upper plots) and velocity (lower plots) traces. A saccade is denoted by the dashed vertical gray line and can be observed within the left-eye and right-eye movement responses and within the conjugate response.

As discussed in the Methods section, the number of responses per step stimuli (2°, 4°, and 6°) was not exactly the same due to the randomization procedure needed to reduce prediction. Hence, the prevalence of saccades was quantified as an average. This analysis sought to compare the responses recorded during the baseline to the responses recorded after vergence training to determine whether the prevalence of saccades within the first 1 second of the convergence responses was significantly correlated to convergence peak velocity. Hence, only the four CI subjects (CIS1–CIS4) who participated in vergence training were studied within this analysis. Responses that had a saccade obstruct the convergence peak velocity were omitted from this analysis. The group-level analysis is shown in Figure 7. Figure 7 summarizes the mean plus one standard deviation of the average number of saccades present within the first second of the convergence response (Fig. 7A) and the convergence peak velocity (Fig. 7B) for responses from 2°, 4°, and 6° symmetrical convergence step stimuli, before (gray bars) and after (black bars) vergence training. A significant difference was observed when the responses after vergence training were compared to the baseline responses for the following two measurements: combined convergence peak velocity [F(1,3) = 48; P < 0.01] and the average number of saccades observed within the first 1 second of the convergence response [F(1,3) = 280; P < 0.001]. A post hoc Bonferroni (all pairwise) multiple comparison test confirmed that the before measurements were significantly different from the after measurements for both combined convergence peak velocity and the average number of saccades within the first second of the response. The post hoc Bonferroni multiple comparison test also confirmed that peak velocity and the number of saccades within the first second of the response were significantly different between the responses stimulated from 2° and 6° steps. Figure 7C is the linear regression analysis of the average number of saccades as a function of the average convergence peak velocity. A significant correlation assessed using the Pearson correlation coefficient was observed (r = 0.83; P < 0.05). Figure 7 supports that as the convergence peak velocity increases, the prevalence of saccades decreases when the measurements after vergence training are compared to the measurements before vergence training. 

Figure 7

 

Group-level analysis of the number of saccades within the first 1 second of the response (A) and combined convergence peak velocity (B) for 2°, 4°, and 6° convergence step stimuli plotted as the mean (bar) plus one standard deviation (error bar) before (gray bars) and after (black bars) vergence training. (C) Linear regression analysis of the average number of saccades within the first second of the convergence response as a function of convergence peak velocity. Gray diamonds represent the baseline measurements before vergence training, and black squares are the measurements after vergence training.

Discussion

The first finding of this study was that CI subjects exhibited differences in the peak velocity between the left-eye and right-eye convergence movement responses. Convergence eye movement responses from one eye were consistently slower than the other eye movement convergence responses when presented with symmetrical convergence stimuli. For binocularly normal controls, the left-eye and right-eye movement convergence responses were, on average, similar. A second finding was that the combined convergence peak velocity increased and the number of saccades within the first second of the convergence response decreased after vergence training compared to the baseline measurements. Third, the peak velocity of convergence was significantly correlated to the number of saccades within the first second of the convergence response. The following sections compare the results of the current study to others within the literature. 

Asymmetry Between Left-Eye and Right-Eye Movement Responses

Considering the rules of Euclidean geometry, vergence responses are normally asymmetric at all gaze eccentricities. However, when symmetrical vergence stimuli are presented on the midsagittal plane with the head stabilized, the responses should theoretically elicit isovergence responses without saccades. In 10 binocularly normal controls, the asymmetry ratio was 0.93 ± 0.06 with a range of 0.83 to 1.0, indicating that the vergence responses of the two eyes were similar. For 4 subjects, the ratio was 0.98 or greater. The findings of this study confirm prior research on 4 binocularly normal controls showing that, on average, subjects with normal binocular vision have approximately equal left-eye and right-eye peak velocity convergence eye movements. ²¹  

The asymmetry ratio of peak vergence velocity was 0.77 ± 0.09 with a range of 0.66 to 0.83 prior to vergence training in the 4 CI subjects, supporting that the vergence responses of the two eyes were more asymmetric. Patients with strabismus respond to symmetric binocular disparity convergence step stimuli using asymmetrical vergence and disjunctive saccades. ⁴⁵ Primates reared to have strabismus also generate asymmetrical responses to symmetrical disparity steps. ²³ When these primates were binocularly decorrelated using prism goggles for 3 to 24 weeks, the use of prism goggles was sufficient to cause esotropia. ⁴⁶ Tychsen ⁴⁶ reported that disparity vergence was asymmetrical in response to symmetrical vergence stimuli in primates that were binocularly decorrelated for 3 weeks compared to control primates. The primates who were decorrelated had a lack of binocular connections but retained monocular connections within V1. This suggests that the lack of binocular connections within V1 was, in part, the cause of strabismus and the asymmetrical vergence eye movement behavior. ⁴⁶ However, an animal model does not exist for CI. 

The etiology of CI is unknown. Many clinicians define CI as a greater exophoria at near compared to far with a receded near point of convergence. ³³ It is suggested that CI patients are symptomatic because of the excessive convergence needed to compensate for high exophoria at near. ¹⁵ It is important to note that primary CI does not have significant exophoria at near and that patients may be esophoric or orthophoric, so not all CI will have a large exophoria. ³² Schor ^47–51 and Saladin ^52,53 hypothesized that CI patients have reduced convergent (base-out prism) adaptation in near compared to far space and that the imbalance in adaptation between the accommodative and convergence systems (via the AC/A ratio) may be a major cause of CI. AC/A is the ratio of the accommodative convergence AC (in prism diopters, Δ) to the stimulus to accommodation A (in diopters, D). In addition, the mechanism(s) by which vision therapy (via vergence training) remediates symptoms is unknown. ¹⁵ A randomized clinical trial on children reported that the reduction of symptoms from office-based vergence and accommodative therapy with home reinforcement was sustained at 1 year posttreatment in 89% of patients. ¹⁹ Such a long-term reduction in symptoms implies some form of anatomical and/or functional changes. 

A different study of humans investigated visually evoked cortical potentials (VECP) in controls and patients with binocular and oculomotor dysfunction with mild traumatic brain injury. ⁵⁴ The patients were divided into two groups—one group received optometric rehabilitation, which trains the vergence system, and the other group did not. Initially, 72% of the patient group who participated in vergence training had abnormalities of the P100 VECP, quantified as increased latencies of 15% or more, a decrease in amplitude of 50% or more, and/or differences of 15% or more between the left and right P100 VECP wave compared to age-matched controls. The abnormalities of the VECP within this group decreased to 38% after training. By comparison, 81% of the other patient group who did not participate in vergence training had VECP abnormalities as described above; and during a repeat measurement, 78% of this patient group still had VECP abnormalities. These data suggest that vergence training improved the electrical activity recorded from the primary visual cortex, V1, for those with binocular and oculomotor dysfunction. ⁵⁴ Alvarez and colleagues ¹⁶ reported changes in functional activity within the frontal, parietal, and cerebellar regions after vergence training compared to baseline measurements, supporting that maximum functional activity and spatial extent were increased after vergence training compared to baseline measurements. The changes were sustained 6 months to 1 year posttraining. ¹⁶ The results of the present study support that convergence responses mediated from symmetrical convergence steps from CI subjects exhibit an asymmetry (one convergence eye movement was slower than the other), and that this asymmetry was reduced after vergence training. Future studies may consider examining potential cortical asymmetries before and after vergence training to assess, first, whether hemispheric asymmetry is observed and within which neural substrates; and second, if asymmetry is observed, whether it is decreased after vergence training compared to baseline measurements. 

In addition to the potential neural mechanisms, differences within the extraocular muscles may potentially lead to an asymmetry between the left-eye and right-eye peak convergence velocities. Specifically, the arc of contact is defined as the arc between the tangential point and the center of the insertion of the muscle on the sclera. Depending on the axis of the orbit, differences in the arc of contact of the medial and lateral rectus muscles can be found. ⁵⁵ The medial rectus muscle is closer to the corneal limbus than the lateral rectus; the medial rectus has a longer length and cross section compared to the lateral rectus and therefore weighs more. ⁵⁵ Perhaps these physiological differences in the medial and lateral recti muscles between the left eye and right eye lead to nonlinearities in the kinematics of the muscles that may, in part, explain the asymmetry between the eye movements in CI subjects. Since the vergence training conducted within this study took place over 6 to 8 weeks, it is possible that the training altered the physiology of the extraocular muscles. Physiological and biochemical studies of the extraocular muscles conclude that the patterns of coexpression of myosin heavy chain (MyHC) result in a range of shortening velocities and contractile forces, which may have a role in the power output of the muscle. ⁵⁶ However, the relationship between myosin isoform and eye position/movement is currently unknown. McLoon and colleagues stress that the heterogeneity of the extraocular muscles needs further investigation to understand its impact on oculomotor control, specifically its ability to accurately and reliably generate a range of eye movement velocities. ⁵⁶ Thus, future research should consider studying the potential physiological and biochemical changes associated with the lateral and medial recti muscles before and after vergence training. 

Saccades May Be a Potential Compensatory Mechanism for Those With CI

One finding of this study was that the prevalence of saccades during the first 1 second of the eye movement response significantly decreased after vergence training. Interestingly, the prevalence of saccades was inversely correlated to the combined convergence peak velocity. Specifically, as the convergence peak velocity increased, the prevalence of saccades decreased. Numerous studies support an interaction between the saccadic and vergence systems, with results showing that saccades enhance the speed of convergence compared to saccade-free convergence responses. ^{29,31,57–60} Several independent studies also support that CI subjects have reduced peak velocities compared to binocularly normal controls. ^16–18 The slowed convergence dynamics lead to a longer period of diplopia, which is a common visual symptom for those with CI. ^34,61,62 Prior research on binocularly normal controls reported that the presence of saccades was significantly correlated to vergence peak velocity; the slower the vergence response, the greater the prevalence of saccades. ²⁸ Van Leeuwen and colleagues (1999) observed two types of responders to symmetrical convergence stimuli: vergence and saccadic responders. ¹⁸ Vergence responders maintained binocularity during the gaze shift, but the shift was slow (between 800 and 1000 ms). Saccadic responders were monocular during the gaze shift, but the shift was faster. The present results show that the CI subjects before training exhibited many saccades such that they could attain faster gaze shift. However, these subjects also reported visual symptoms. After vergence training, the visual symptoms were reduced. Convergence peak velocity increased even though the overall gaze shift was slower due to the reduction of saccades. 

Prior studies support that saccades increase the speed of vergence. ^25,29 Perhaps the saccadic system is recruited as a potential compensatory mechanism to facilitate the speed of convergence for a CI subject. The saccade brings the object of interest onto the fovea of the subject's preferred eye. This study supports that after vergence training, convergence peak velocity increases. Furthermore, this study supports that after vergence training, as the convergence peak velocity increases, the prevalence of saccades within the first second of the response decreases in a correlated manner. Hence, once convergence peak velocity increases, the need to generate a saccade is reduced, which may be one of the potential mechanisms leading to the sustained reduction in visual symptoms for CI subjects. Future studies should include measuring motor and sensory eye dominance to determine whether the direction of the saccade correlates to a subject's sensory or motor dominance. This information was not collected in the current study and is a study limitation. 

Saccade–Vergence Interaction

Even though the stimulus used in the current study was a symmetrical convergence step in which no conjugate stimulus was presented, these data support a significant negative correlation between the number of saccades and convergence peak velocity. Controversies exist in the literature concerning the interaction between saccade and vergence eye movements; some view convergence and saccadic movements as independent, thus supporting Hering's Law, ⁶³ while others support nonlinear interactions between the systems. ^64,65 Several models have been proposed to describe the enhancement of the vergence peak velocity response induced by saccade–vergence stimuli. These models are based upon (1) inhibition of the saccadic omnipause neurons (OPN), ^29,66 (2) both the saccadic pulse and omnipause neuron inhibition, ^67,68 and (3) a multiplicative interaction between a weighted saccadic burst signal and vergence motor error. ⁶⁹  

It is important to note that the visual stimuli within this present study were pure, symmetrical convergence step stimuli and hence involved no retinal stimulation to the saccadic system. Yet saccades were observed, especially within the slower convergence responses from the CI subjects before vergence training. Interestingly, as the peak velocity increased after vergence training, the prevalence of saccades within the first second of the response decreased. Peak convergence velocity and the prevalence of saccades were significantly correlated (r = 0.83; P < 0.03). These data support that an interaction may exist between the vergence and saccade subsystems. In a prior investigation studying a range of convergence peak velocities from binocularly normal controls, a significant correlation between convergence peak velocity and the prevalence of saccades was also observed (P < 0.03). ²⁸ Based upon the neurophysiology studies, one potential explanation is that the responses to symmetrical vergence stimuli evoke the near response (NR) cells ^70,71 ; and when the vergence velocity is below a designated threshold, a saccade may be initiated by the inhibition of OPNs, the excitation of saccade burst neurons (SBN), or both the excitation and inhibition of SBNs and OPNs, respectively. However, future studies are needed to test this hypothesis and to further understanding of the interaction between saccade and vergence eye movements before and after vergence training, examining evoked potentials from primates. 

The Neural Control of Binocular Coordination: Monocular Compared to Binocular Control

Different theories exist in the literature regarding the neural control of binocular movements. ^64,65,72,73 One view by Hering suggests that the two eyes are equally innervated by common command signals such that the two eyes can be considered a single organ. ⁶³ Conversely, Helmholtz argues that binocular coordination is a learned behavior and that the left and right eye are independently controlled. ⁷⁴ Behavioral studies of smooth pursuit and convergence responses to ramp stimuli support that neither are controlled monocularly and favor Hering's Law of equal innervation. ^50,75,76  

Although many studies support Hering's Law, recent research has reported evidence in favor of Helmholtz's theory. ^64,65,77 Zhou and King showed that premotor neurons in the paramedian pontine reticular formation, which were thought to encode for saccadic velocity commands, encoded monocular saccadic commands for the left and right eye. ^73,77 In addition, Van Horn and Cullen reported that SBNs carry monocular vergence-related information during disconjugate saccades, further suggesting evidence of monocular control. ⁷⁸ Figure 5 shows a unique and fascinating behavior from a CI subject before vergence training. This behavior was not observed in any of the binocularly normal controls. It was observed in four of the seven CI subjects and was present toward the end of the baseline experimental session (before vergence training) when a CI subject may have been less attentive or fatigued. Subject fatigue may potentially occur, resulting in drowsiness or a decrease in attention since the extraocular muscles are fatigue resistance. ⁷⁹ In addition, the asymmetry and long latencies of the CI response before vergence training shown in Figure 2 support a failure of Hering's Law. CI subjects commonly report diplopia, ²⁰ which may be a result of such long latencies to fuse the visual stimulus. Stark and colleagues reported more violations of Hering's Law for saccadic movements when subject fatigue was experienced. ⁸⁰ Within these results, the single high-velocity response in one convergence eye movement and the double high-velocity response in the other convergence eye movement suggest a breakdown in binocular coordination between the left-eye and right-eye movement convergence responses. Perhaps the transient portion of convergence is monocularly controlled in some of the CI subjects, with the transient component stimulated twice in one eye and only once in the other eye. Further study is needed to determine whether this behavior becomes more common when the experiment is of a longer duration, since this response was observed toward the end of the experiment. This behavior was not observed after vergence training in any of the CI subjects, supporting the Helmholtz theory that binocular coordination is learned through vergence training. 

However, for subjects with normal binocular vision, neither the literature ^64,78 nor the data presented in this study can evaluate whether the vergence commands required to drive movements in response to symmetrical disparity vergence stimuli (i.e., when the saccadic burst neurons are not bursting with action potentials) utilize monocular control. Future neurophysiology and behavioral studies are needed to investigate whether these two types of responses (saccade-facilitated convergence and pure symmetrical convergence movements in response to symmetrical disparity stimuli) are monocularly or binocularly controlled. 

Limitations and Future Direction

One limitation to this study is that the binocularly normal control data were collected first; these subjects could mediate 4° convergence steps, beginning at near (12°) and far (2°) initial vergence angles. However, when the CI subjects were recruited, the CIs were unable to generate many responses beginning at the closer 12° vergence angle; hence the CIs were given 2°, 4°, and 6° convergence step movements beginning from 2° or 4° vergence angles. Future experiments could have both binocularly normal controls and CI patients all respond to the same eye movement stimuli. 

Future research should include having binocularly normal controls also participate in vergence training to study whether vergence training improves the symmetry and combined peak convergence velocity. It is hypothesized that since controls are on average symmetrical (asymmetry ratio was approximately equal to one), the asymmetry ratio may not substantially change after vergence training for binocularly normal controls. However, the variance within the individual eye movement responses may decrease after vergence training. It is also hypothesized that binocularly normal controls will have some improvements in peak convergence velocity but that the increase in peak velocity will be less than that observed within CI patients. 

The multisite randomized clinical trial called the Convergence Insufficiency Treatment Trial (CITT) defined the clinically relevant true mean difference for CISS, NPC, and PFV as 10, 4 cm, and 10Δ with standard deviations of 12, 4.5, and 11.3, respectively. ⁷ The data from the present study had an estimated correlation of −0.3, 0.9, and −0.4 for CISS, NPC, and PFV, respectively. Assuming 80% power and an alpha of 0.05 yields a sample size of 25, 4, and 25, respectively. While this study had sufficient power to study the near point of convergence, a larger sample size is needed to study the CISS and PFV. Future studies are needed to determine whether the current trends generalize to a larger population; hence the sample size is also a limitation of the current study. 

In conclusion, this study reports that in CI subjects, one eye had a consistently slower convergence eye movement response when compared to the other convergence movement mediated via symmetrical convergence step stimuli. Conversely, the left-eye and right-eye movement responses for binocularly normal controls were on average similar. When the CI convergence eye movements after training were compared to initial baseline measurements, the convergence eye movements became more symmetrical; convergence peak velocity was enhanced; the prevalence of saccades within the first 1 second was reduced; near point of convergence receded; positive fusional vergence range increased; dissociated near phoria became less exophoric; and the subject's visual symptoms decreased as assessed using the CISS. 

Acknowledgments

The authors appreciate comments from John Semmlow, Clifton Schor, an editorial board member, and two anonymous reviewers, which strengthened this manuscript. 

Supported in part by National Science Foundation (NSF) Major Research Instrumentation (MRI) Chemical, Bioengineering, Environmental, and Transport (CBET) 1228254 (TLA). 

Disclosure: T.L. Alvarez, None; E.H. Kim, None