The steady-state accommodative response can be affected by many factors, such as pupil size,1 stimulus contrast,2 spatial frequency,3 and luminance.4 Studies have reported that accommodative responses induced by negative lenses, positive lenses, or moving targets in real space were different.5–9 For example, Gwiazda et al5 reported that the slopes of the accommodative stimulus response curves (ASRCs) of myopic and emmetropic subjects were steeper when the accommodative stimulus was moved in space than when it was induced by negative lenses. Yeo et al7 found that the amount of accommodative lag was least when the target was moved in space, followed by the positive lens method, and then the negative lens method. However, Abbott et al6 replicated Gwiazda et al’s study5 and found that the accommodative responses elicited by positive lenses were more accurate than the accommodative responses to a target presented in real space, while the accommodative responses induced by negative lens were least accurate. All these studies suggested that the negative lens method could induce more accommodative response error. However, the difference in the accommodative response between using positive lenses and moving targets in real space was inconsistent. These results suggested that the proximal factor might play different roles in these methods. Because using the Badal stimulator10 can eliminate the proximal cue of the accommodative stimulus, it may help in understanding the discrepancy in previous studies comparing the difference in accommodative responses between methods using negative lens, positive lens, and the Badal stimulator.
The sequence of accommodative stimuli may also affect the steady-state accommodative response. Accommodative stimuli presented in ascending (far-to-near) or descending (near-to-far) sequence can cause accommodation or dis-accommodation, respectively. Studies of dynamic accommodative responses showed that accommodation and dis-accommodation had different dynamic characteristics, indicating that the neural control system of accommodation functions differently with increases or decreases of the refractive power of the crystalline lens.11,12 However, whether the ASRC measured in the steady-state condition is different between accommodation and dis-accommodation has not been thoroughly studied.
After steady-state accommodative responses are measured, it is critical to select a method for assessing the response error in a specific stimulus range. In previous studies, the slope of ASRC was used to compare the accommodative performance between different refractive error groups.5–7 However, there are two other parameters related to the regression line of the ASRC: the intercept on the y-axis and the Pearson correlation coefficient. The slope can be an indicator of the relationship between the stimulus and the response, but it is insufficient to quantify the accuracy of the accommodative response. This may be one of reasons for the inconsistent results in previous studies of comparing the ASRCs.5,6,13–16 Chauhan and Charman17 suggested an index named the accommodative error index (AEI) which combines the three parameters of the linear regression analysis, i.e., the slope, the intercept, and the correlation coefficient, to summarize the accuracy of the accommodative response over a given stimulus interval. They claim that this index is applicable to the linear region of an ASRC and unfit to assess the nonlinear parts of the curve. Therefore, in this study we suggest a new index called the “accommodative error area” (AEA) which is able to apply to either linear or nonlinear part of the response curve to quantify the accuracy of the ASRC.
In this study, we measured accommodative responses in 10 emmetropes under six stimulus conditions, i.e., the accommodative stimulus was induced using three methods: negative lenses, positive lenses, and a Badal stimulator; and the stimulus was presented using two sequences: decreasing and increasing sequences. Three indexes (AEI, AEA, and slope) were used to evaluate the ASRCs obtained from the six stimulus conditions. The aim of the study was to investigate the effects of the method and the sequence of accommodative stimuli to the ASRCs and to find an effective and comprehensive index to evaluate ASRCs.
Ten emmetropic optometry students (three males and seven females) in Nova Southeastern University participated in this experiment. The subject’s ages were from 22 to 30 years old (25 ± 2.4 years, mean ± SD). Standard subjective refraction and full examination of binocular vision were performed before the experiment. The inclusion criteria were that the refractive error in spherical equivalent (SE) was within ± 0.50 D of emmetropia, with astigmatism of no more than −0.50 D. Anisometropia of more than 1.00 D differences in SE between the two eyes was excluded. The average SE of the 12 subjects was 0.09 ± 0.19 D (mean ± SD). They all had visual acuity of 20/20 or better and were free from binocular dysfunction defined according to the criteria of Scheiman and Wick.18 Informed consent was obtained from each subject after the nature and possible consequences of the study were explained. The research followed the tenets of the Declaration of Helsinki and was approved by Nova Southeastern University’s Committee for the Protection of Human Subjects.
The ASRCs of 10 emmetropes were measured when the accommodative stimulus was induced using three methods: negative lenses, positive lenses, and a Badal stimulator; and the stimuli were presented using two sequences: decreasing and increasing sequences.
In all conditions, the accommodative response was measured with a Canon R-1 optometer (with a resolution of 0.125 D and a temporal resolution of 5 Hz) from the subject’s right eye while the left eye was occluded. The fixation target was a Maltese cross which subtended a constant angle of 1.6 degrees in diameter at each demand, with the mean luminance of 18 cd/m2. In the negative lens condition and the Badal stimulator condition, the fixation target was presented on a notebook computer screen, while in the positive lens condition the target was made from a black paper attached to a light box. The subject was instructed to keep the target as clear as possible during the measurements. Between each test, 5-second rest was given to avoid the effect of tonic accommodation.
(a) The negative lens method: the target was placed at 4 m in front of the subject’s right eye, while the accommodative stimulus was changed using negative lenses from 0 to −4.75 D (ascending sequence) and from −4.75 to 0 D (descending sequence) in 0.25-D steps. Each negative lens was placed in a trial frame mounted on the Canon R-1 optometer and tilted approximately 15 degrees to eliminate reflections of infrared light from the lens surfaces. In these conditions, the accommodative stimulus was calculated based on equation:
Here, F represents the power of the negative lens, 0.25 is the accommodative demand in diopters when the target is placed at 4 m from the eye, and 0.014 (m) is the distance from the lens to the corneal apex of the subject’s eye.
(b) The positive lens method: the target was placed at 20 cm in front of the subject’s eye. The subject viewed the target through positive lenses changed in 0.25-D steps from 0 to +4.75 D (descending sequence) and from +4.75 to 0 D (ascending sequence). Each lens was placed in the trial frame mounted on the Canon R-1 optometer and tilted approximately 15 degrees to eliminate reflections of infrared light from the lens surfaces. In these conditions, the accommodative stimulus was calculated based on the following equation:
Here, F represents the power of positive lens, 5 is the accommodative demand in diopter when the target is placed at 20 cm from the eye, and 0.014 (m) is the distance from the lens to the corneal apex of the subject’s eye.
(c) The Badal stimulator method: a Badal stimulator19 was mounted on the Canon R-1 optometer, behind the beam splitter and coaxial with the measurement optics of the optometer and the fixation target20 (Fig. 1). The target was placed at 4 m in front of the subject’s eye. Using the Badal stimulator with 0.25-D steps from +0.25 to +4.75 D in the ascending sequence or from +4.75 to +0.25 D in the descending sequence changed the accommodative stimulus.
ASRCs were measured in a random order of using the three methods, and in each method, the ascending sequence was prior to the descending sequence. The measured data were converted into SE value and then were used to calculate the accommodative responses. For each data point, the accommodative response was the average of 10 measures. In addition, in the two lens methods the accommodative response was converted to the AR at the entrance plane of the eye with the following equation:
Here, F represents the dioptric power of the trial lens, SE represents the spherical equivalent calculated from each Canon R-1 optometer’s reading because the reading represents a spectacle correction, and 0.014 (m) is the vertex distance.
The average accommodative responses for each stimulus condition were fitted with a 3-degree polynomial equation as a function of the accommodative stimulus. The accommodative error area (AEA in the unit of D2) was defined as the area between the response curve and the 1:1 line in the stimulus/response plot (Fig. 2). In this study, AEA was calculated from the following equation:
Here, AR is the accommodative response and AS is the accommodative stimulus. The stimulus interval is set between 0 and 5 D.
For a comparison, the accommodative error index (AEI) suggested by Chauhan and Charman17 was also used to describe the accommodative responses under each stimulus condition. The AEI combines the information of the slope, the intercept, and the correlation coefficient of the regression line of an ASRC. The AEI is calculated using the formula (5) when the regression line does not intersect the ideal line and the stimulus interval is set between 0 and 5 D. If the two lines intersect each other, then formula (6) was used. The shaded area in Fig. 3 represents the discrepancy between the regression line (y = 0.200 + 0.711x) of ASRC and the 1:1 line, which is defined as E (numerator of the formula 5 and 6) by Chauhan and Charman.17
In above formula, s is the slope of the regression line of a subject’s accommodative responses, y is the y-intercept of the regression line, r is the correlation coefficient, and x 1 and x 2 are the lowest and highest accommodative stimulus levels, respectively. In the calculation of this study, we let x 1 = 0, x 2 = 5, for each condition. However, we did the regression in AS interval from 1 to 4 D to avoid the non-linearity of the ASRC. The slope, y-intercept, and r value used in each AEI calculation are from this regression result.
In the three AS methods, the AS were slightly different, i.e., 0.25–4.67 D in the negative lens method, 0–4.87 D in the positive lens method, and 0–5 D in the Badal stimulator method. But in the calculations of the AEA, the AEI (AS interval was set between 0 and 5 D for these two indexes), and the slope (AS interval was set between 1 and 4 D), this slight difference can hardly affect the results.
Two-factor repeated measures analysis of variance (ANOVA) was used to compare the difference in ASRC between the two sequences (ascending and descending sequences of AS) and the three stimulus methods (positive lens, negative lens, and the Badal stimulator). In each ANOVA, the AEI, AEA, or slope of ASRC (which is the slope of the regression line of the AS on the AR) was used as the dependent variable. The stimulus method and the sequence were the two independent variables. When a significant difference was found by ANOVA, Fisher least significant difference (LSD) post hoc analysis was applied to test the difference between the three stimulus methods and the two sequences.
Data of AEI, AEA, and the slope of the ASRC of six accommodative stimulus conditions are presented in Table 1. As to the effect of the AS sequences to the ASRC, Fisher LSD multiple comparisons showed that the AEI and AEA values of Badal stimulator method in the ascending condition were significantly larger than that in the descending condition, but they were not significantly different in the negative lens or the positive lens methods (Figs. 4A, B; Table 2. The slope of ASRC in the ascending order was shallower than that of the descending order in all three AS methods, but the differences were not significant in Fisher LSD multiple comparisons (Fig. 4C; Table 2).
Two-factor repeated measures ANOVA showed that the effect of stimulus method on ASRCs was significant when AEI or AEA was used to evaluate the ASRCs (Table 3), indicating that the AS method affected the accommodative response error. The AEI and AEA were greatest for the Badal stimulator method and least for the positive lenses method (Figs. 4A, B). Fisher LSD multiple comparisons in AEI, AEA showed that the AEI or AEA values obtained with the positive lenses method were significantly different from those values obtained with the negative lenses method or the Badal stimulator method (all p < 0.05). There was no significant difference found between the values obtained with the latter two methods (p = 0.257 for AEI, p = 0.231 for AEA). The results indicate that the accommodative responses elicited with positive lenses were more accurate than the accommodative responses elicited with negative lenses or the Badal stimulator. However, when we used the slope of ASRC for comparing the difference between the stimulus methods, the result was not significant (Table 3).
The interaction between stimulus sequence and the stimulus method was found to have a significant effect to the ASRC when AEI and AEA were used (Table 3), indicating that the effect of the AS sequence depended on the AS method. However, as to the slope of ASRC, the interaction between stimulus sequence and the stimulus method was not significant (Table 3).
The relationships between AEI and AEA, between the slope of ASRC and AEA, and between the slope of ASRC and AEI were plotted in Figs. 5A, B, and C, respectively. We found that AEI was highly correlated with AEA (r = 0.977, p < 0.001), while the correlation between the slope and AEA and between the slope and AEI was relatively low (r = −0.311, p = 0.016, and r = −0.390, p = 0.002, respectively).
In this study, we compared the difference in the AEA, AEI, and the slope of ASRC between six accommodative stimulus conditions. We found that positive lenses used to change the AS might reduce the error in accommodative response compared to the use of negative lenses or a Badal stimulator. In addition, the accommodative responses caused by ascending and descending sequences in the Badal stimulator method were significantly different, which suggested that accommodation was different from dis-accommodation.
The Ways to Assess the Steady-State Accommodative Response
In the prior studies, slope of the regression line was often used to characterize the steady-state accommodative response.5–7,21,22 However, the results of some studies were inconsistent when the slope was used alone to assess the difference in accommodative response between refractive groups, especially between myopes and emmetropes. A possible explanation is that the slope of ASRC is not adequate to assess of the accuracy of the accommodative response. It is only one of the three parameters of a regression line of ASRC. The other two parameters, the intercept of ASRC on the y-axis and the Pearson correlation coefficient, are also related to the accuracy of ASRC. Therefore, comparisons based on the slope alone may be insufficient.17
According to the control theory model of steady-state accommodation of Jiang,23 the slope is dependent on the linear operators, the accommodative sensory gain, and accommodative controller gain,24,25 while accommodative error (accommodative stimulus − accommodative response) is affected by the slope, the dead space,24,25 and the tonic accommodation24,25 (ABIAS). The indexes of the AEI and the AEA, which represent the accommodative error of the ASRC, would be more comprehensive and effective in assessing the steady-state accommodation than the slope of ASRC.
The results of our study support the conclusion that the indexes of the AEI and the AEA are more effective in assessing the accommodative response. In our study, when AEI or AEA was used in evaluation of the ASRC results, the ASRCs measured with positive lens method was significantly different from that measured with the negative lens method. This result agrees with other studies suggesting that proximity cues (which could be greater in the positive lens method than that in the negative lens method)6,26,27 increase the accuracy of the accommodative response. When the slope of ASRC was used for evaluation, the difference of the ASRC measured with positive and negative lenses was not significant. This result supported that AEI and AEA were better than the slope of ASRC in comparison of the ASRCs.
In this study, we used AEI and AEA to evaluate the error of ASRC. Although we did not find a difference between using AEI and AEA in the ASRC evaluation, these indexes are slightly different in describing the error of accommodative response. The AEA value directly represents the area between the ASRC and the 1:1 line, i.e., the accommodative error of the overall curve, while in the calculation of AEI, the slope and y-intercept of the regression data of the ASRC, as well as the correlation coefficient value of the regression, must be obtained. The effect of the nonlinearity of the ASRC on AEI is revealed indirectly through the correlation coefficient value in the equation (5 or 6). Thus, if the interval of AS is from 0 to 6 D or even larger, the nonlinearity of the ASRC in both ends could appear, which affects the estimation of the AEI. However, the accuracy of the AEA is not affected by the nonlinearity of the ASRC; therefore, it is an effective and comprehensive index to evaluate ASRC in different stimulus conditions.
The Effect of the AS Methods on ASRC
Prior studies found inconsistent results in comparison of the slope of ASRC when positive and negative lenses were used.5–7 In our study, we found that the accuracy of the ASRC in the negative lens method was less than that in the positive lens method, but was not different from that in the Badal stimulator method when the AEA was used for the evaluation.
The Effect of the AS Sequence on ASRC
The results of this study indicated that the AEA values in the descending sequence measurements were lower than that in the ascending sequence measurements in the Badal stimulator method, but not in the negative lens or the positive lens method. In the Badal stimulator method, the size and brightness of the retinal image remain unchanged as the accommodative stimulus changes. Therefore, the proximity cues of the target distance and the magnification effect of the lenses (in the negative and positive lens conditions) can be excluded in this condition.10 The significant difference between the ascending and the descending sequence in the Badal stimulator method may truly reflect the difference between accommodation and dis-accommodation. Although we aimed to avoid the interferences of other factors, the use of different lenses in the negative or positive lens method may cause a change in the retinal image size.28 For example, in the negative lens method, the diopter of negative lens was lower in low AS level (i.e., when AS = 1.00 D, negative lens added = −0.75 D) than that at a high level (i.e., in our study, when AS = 4.00 D, negative lens added = −3.75 D). Thus, a larger retinal image was found at a lower AS level in the negative lens method. A similar situation happened with the positive lens method. According to the visual perception,29 the object is perceived closer when the retinal image is larger. Therefore, perceptual factor of the target distance, namely the proximal effect, was introduced in these two methods. This may weaken or suppress the difference between accommodation and dis-accommodation.
The result of the Badal stimulator method suggests that dis-accommodative responses are more accurate than accommodative responses in the steady state. The difference between the descending and ascending sequences in this method may be due to the depth of focus. The step change of the AS in this study was 0.25 D, which is at the level of the depth of focus of the eye.16,30 Wang and Ciuffreda31 stated that “the eye accommodates the minimum amount to place the target within its depth-of-focus/field to see the object clearly.” In the descending condition, the accommodative response started from a high demand, which might lead the next response to change less. As a result, the accommodative response would be relatively high. On the other hand, in the ascending condition the accommodative response started at a low demand, which might cause a less response in next step. As a result, the accommodative response would be relatively low. In addition, the stimulus of this study was changed systematically, which means the subjects were affected by an anticipation effect.32 A randomized paradigm might be a better choice to minimize this effect.
The results of this study showed that the accuracy of accommodative response was different between the increasing and the decreasing sequences, and the sequences and the methods in changing the accommodative stimulus were dependent on each other. Therefore, the AS sequence should be considered in the ASRC measurement, and a randomized paradigm33 should be recommended to avoid such kind of effect.
In summary, the current results show that the accommodative response in the steady state is affected by the AS methods (positive lens, negative lens, or Badal lens) and the sequence of AS presentation. In addition, the AEA is suggested to be used in the evaluation of the accuracy of ASRC in future studies.
School of Optometry & Ophthalmology
Wenzhou Medical College
270 Xueyuan Road
Wenzhou, Zhejiang 325027
People’s Republic of China
Received February 1, 2013; accepted July 3, 2013.
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