The Effect of Lens Design on Corneal Power Distribution in Orthokeratology

FU1

Orthokeratology is a technique that uses reverse geometry gas-permeable contact lenses to reshape the cornea and temporarily correct refractive errors.1,2 Orthokeratology lenses consist of a flatter central optic zone, surrounded by a much steeper zone called the reverse curve. Adjacent and external to the reverse curve is a series of curves or tangents to align with the cornea called alignment curve or landing zone. These designs can induce central corneal flattening and midperipheral corneal steepening.3–5 Parallel to the change in corneal shape is a shift in the retinal image plane, namely, retinal defocus.6–9 These changes appear shortly after wearing the lenses overnight and stabilize after 7 to 10 days.10,11

It has been proposed that changes in peripheral retinal defocus induced by orthokeratology may be one of the mechanisms for the retardation of myopia progression.12 Based on this assumption, various orthokeratology lenses of different optic zone designs result in different treatment zone shape and diameter and may have different efficacy in myopia control.13 One of the previous studies investigated the influence of pupil size on myopia control efficacy in orthokeratology. The authors found that axial elongation was slower in children subjects who had larger-than-average pupil diameter. They hypothesized that a larger pupil size may allow more peripheral defocus to fall within the pupil margin and therefore provide greater myopia control efficacy.14 Consistent with this hypothesis is that, in animal studies, larger peripheral zones in optical lenses can result in greater compensation in a bidirectional manner, showing a dose-dependent treatment effect.15–18

In recent years, attempts have been made to change conventional orthokeratology designs to increase myopia control efficacy. Some earlier modified designs revealed a minor effect on peripheral defocus.19 More recent lens designs have shown promise in effectively decreasing the treatment zone size and bringing the midperipheral defocus ring closer to the pupil.20,21 However, most of the studies are limited to the analysis of the treatment zone size and the maximum change in corneal power after orthokeratology. Few studies have used mathematical method to quantify the spatial corneal power distribution after orthokeratology.22 The purpose of this study was to evaluate the overall spatial corneal power distribution after orthokeratology using mathematical methods. This will enhance our understanding of the effects of orthokeratology lens design on corneal profile, the results of which may be useful in developing future orthokeratology lens designs.

METHODS Ethical Approval

The study protocol was approved by the Ethical Committee of the Eye and ENT Hospital of Fudan University, Shanghai, China, and complied with the tenets of the Declaration of Helsinki. Each subject and their parents signed an informed consent form, after risks and benefits of the treatment were explained.

Subjects

A total of 63 subjects (126 eyes) were recruited from November 2020 to December 2020 for this prospective study. These subjects aged 8 to 45 years were enrolled for a 12-month study that was designed to evaluate the safety and efficacy of two orthokeratology lens designs. We selected and analyzed data from 1 day, 1 week, 2 weeks, and 1 month after commencement of orthokeratology treatment for this study. Inclusion criteria comprised subjects with refractive error between −1.00 and −4.00 D, astigmatism less than 1.50 D, corneal refractive power along the flat meridian between 40.00 and 46.00 D, and monocular corrected distance visual acuity no worse than 20/20. Exclusion criteria included subjects with eye disorders or systemic disease, intraocular pressure higher than 21 mmHg or lower than 10 mmHg, a history of contact lens wear in the past 30 days, and atropine treatment for myopia control. Before treatment, a complete optometric and ophthalmological examination was performed.

Contact Lenses

Two orthokeratology lens designs were used in this study, the Euclid (Euclid Systems Corporation, Herndon, VA) and double reservoir lens (DRL; Precilens, Creteil, France). The detailed information about each lens design was provided by the manufacturer and listed in Table 1.

TABLE 1 - Comparison of the two lenses studied Euclid Double reservoir lens Design Base curve, reverse curve, alignment curve 1, alignment curve 2, and peripheral curve Base curve, reverse curve 1, reverse curve 2, alignment curve and peripheral curve Back optic zone diameter (mm) 6.2 5.0–6.6 Power (D) +1.50 to −5.00 +3.50 to −7.00 Central thickness (mm) 0.20–0.32 0.20 DK 87(ISO)10−11(cm2/seg)/(mL × mmHg) 100(ISO)10−11(cm2/seg)/(mL × mmHg) Material Boston Equalens II Boston XO

DK = oxygen permeability.


Lens Fitting

Euclid and DRL orthokeratology lenses vary in their back surface geometry, and therefore, the enrolled subjects were subdivided into four groups. Seventy eyes of 35 subjects were fitted with Euclid lenses of 6.2-mm back optic zone diameter and further divided into two groups according to the subject's age: 52 eyes of 26 subjects to the younger group (<14 years) and 18 eyes of 9 subjects to the elder group (≥14 years). Twenty-six eyes of 13 subjects (<14 years) were fitted with DRL lenses of 5.0-mm back optic zone diameter, and 30 eyes of 15 subjects (≥14 years) were fitted with DRL lenses of 6.0-mm back optic zone diameter. Uncorrected distance visual acuity, corrected distance visual acuity, manifest refraction, slit-lamp examination, and corneal topography were checked at baseline and 1 day, 1 weeks, 2 weeks, and 1 month after the commencement of lens wear. All the measurements were taken in the morning after the lens removal for around 2 hours.

Orthokeratology lens fitting was evaluated by slit-lamp biomicroscopy and fluorescein pattern evaluation after adaptation to the lens. The lenses do have an overcorrection at the back surface to allow for daytime regression. To compensate for this resultant hyperopia with the lens in the eye, the front surface of the lens usually has a plus power between +0.50 and +1.25 D, yielding plano during overrefraction. Then, lenses were ordered upon the base curve of the trial lens used, the manifest refraction, the keratometry readings, and overrefraction. All the lenses used in this study were of spherical design. No toric lens designs were used. On receipt of the lenses, we would check the lens label, which included the overall diameter, back optic zone diameter, width and curvature of the base curve, reserve curve, alignment curve, and peripheral curve, respectively, and check whether they are consistent with the medical records before dispensing. All subjects were instructed to insert, remove, and care for their contact lenses. They were instructed to wear the lenses overnight during sleep, with a recommended minimum of 8 hours.

Corneal Topography

Subjects were instructed to stare into the fixation target within the topographer (Medmont E300, Nunawading, Australia) during the whole measurement process. Topography maps on the same subject at each visit were captured by the same examiner (ZC). In case their eyes had insufficient exposure, the examiner would gently retract the eyelid without touching the eyeball. During the measurement, we generally took at least four images and selected the maps with largest palpebral exposure and clearest image of Placido rings. The minimum alignment score in the Medmont software for each image selected was 95.

The axial maps from the topographer were used for calculation of corneal refractive power. One advantage of this topographer is to get a quick overview of the corneal power and its change after corneal reshaping. Data from the central cornea are more accurate on the axial map because the averaging algorithms in the software assume the cornea to be a spherical surface. Because the central data were of greatest importance in this research, the raw data derived from the axial maps were deemed accurate.

Corneal Refractive Power Data Processing

The assessment of the change in corneal refractive power was made by comparing the baseline and the follow-up (1 day, 1 week, 2 weeks, and 1 month) axial power maps using a differential map. The change in corneal refractive power normalized to the apical corneal refractive power was defined as relative corneal refractive power change. Because Asian eyes have narrow palpebral fissures, corneal refractive power data from the vertical meridian were usually interfered by eyelids and eyelashes and therefore not reliable. To eliminate these confounding factors, refractive power along the horizontal meridian (averaged on 0 and 180° to cancel out nasal and temporal asymmetry) was selected to represent the overall relative corneal refractive power change. In this study, we evaluated the relative corneal refractive power change with a diameter of 6.2 mm along the horizontal meridian.

The raw topographical data of each subject were then exported to MATLAB (Version 7.9; Math Works, Natick, MA). Corneal refractive power change across different visits was combined and fitted with a polynomial function using the form y = Ax + Bx2 + Cx3 + Dx4 +…+ Nxn (where x is the distance from corneal apex and y is corneal refractive power change). After the best-fit polynomial function has been generated, the maximum corneal refractive power change and the corresponding distance from corneal apex (Xmax) were output by the software. The Y values corresponding to 1/4 Xmax, 1/2 Xmax, and 3/4 Xmax were defined as 1/4 Ymax, 1/2 Ymax, and 3/4 Ymax, respectively, and calculated (Fig. 1).

F1FIGURE 1:

Description of the curve fitted with a polynomial function. Blue line, raw data; red line, the curve after polynomial function fitting.

To illustrate the spatial distribution of corneal refractive power change in a straightforward way, the relationship between corneal refractive power change and its corresponding corneal radial distance was assessed using a monomial function fitting with the form y = xn (where x is the radial distance from corneal apex, n is the power exponent, and y is corneal refractive power change). A lower power exponent represents a higher asphericity of the treatment zone.

Statistical Analysis

To test the correlation between the two eyes, we used intraclass correlation efficient, and the results showed that the intraclass correlation efficient was 0.07, indicating that the two eyes of the same subject are relatively independent and can be treated as two individual eyes. Therefore, data from both eyes of subjects were included for analysis. All statistical analyses were performed using SPSS version 23 (IBM Corp., Armonk, NY). Normality of data was assessed using the Shapiro-Wilk test and met in all cases. The baseline variables including age, spherical equivalent refractive, and corneal refractive power change of each follow-up visit of the 65 subjects who completed the study were compared using one-way analysis of variance (ANOVA). Comparison of sex was conducted using the χ2 test. The overall corneal refractive power change and spherical equivalent refractive were also compared using repeated-measures ANOVA, with time being the intragroup factor and treatment modality being the intergroup factor. Tukey multiple comparison tests were used for pairwise comparisons. P < .05 was considered statistically significant.

RESULTS Subjects and Baseline Biometrics

All the subjects completed the study without dropouts. No severe adverse events (e.g., microbial keratitis) were reported in either group. Baseline biometrics and comparison among groups are shown in Table 2. There were no statistically significant differences among groups as regard to sex, spherical equivalent refraction, and corneal refractive power along the flat and steep meridian values (all P > .05). Age was significantly different among groups (P < .001). The age of the <14-year group in DRL is not different from the age of the <14-year group in Euclid (P = .98) and likewise for the age of the ≥14-year groups (P = .27).

TABLE 2 - Biometric data of subjects at baseline Lens design (BOZD) Sex
(male/female) Age (y) SER (D) Kf (D) Ks (D) DRL (<14 y)
(5.0 mm) 9/4 10.4 ± 1.6
(8–13) −2.53 ± 1.01 42.38 ± 1.21 43.56 ± 1.23 DRL (≥14 y)
(6.0 mm) 5/10 26.0 ± 8.7
(14–40) −2.45 ± 0.98 42.72 ± 0.90 43.56 ± 0.84 Euclid (<14 y)
(6.2 mm) 15/11 9.7 ± 1.9
(8–13) −2.81 ± 0.71 42.03 ± 1.25 43.30 ± 1.34 Euclid (≥14 y)
(6.2 mm) 4/5 26.6 ± 7.5
(15–40) −3.02 ± 0.88 42.13 ± 1.04 42.72 ± 1.03 P .24 <.001 .10 .09 .08

BOZD = back optical zone diameter; DRL = double reservoir lens; Kf = corneal refractive power along the flat meridian; Ks = corneal refractive power along the steep meridian; SER = spherical equivalent refractive.


Changes in Refraction over Time

The remaining refractive error after corneal reshaping over time was illustrated in Fig. 2. The higher refractive reduction was seen after the first night of lens wear for all groups, with a significant difference among the four groups (one-way ANOVA, F = 7.59, P = .001). The 5.0-mm back optical zone diameter group reached higher refractive reduction compared with the other three groups (all P < .01). After 1 week of lens wear, no significant differences were found among the four groups (all P > .05).

F2FIGURE 2:

Change in manifest spherical equivalent refraction over time in the four groups. Error bars represent standard deviation, **P < .01; ****P < .0001.

Relative Corneal Refractive Power Change Distribution

Relative corneal refractive power change for each lens design at different follow-up visits is displayed in Fig. 3. Central corneal flattening was seen at all follow-up visits after orthokeratology lens wear (P < .001). Away from the center (corneal radial distances <0.6 mm), the cornea steepened in an aspheric way toward the midperiphery (range from 0.6 to 1.95 mm of corneal radial distances) and peaked at approximately 2 to 3 mm off the apex, being different among the four groups. Overall, the 5.0-mm back optical zone diameter design produced greater midperipheral steepening than the 6.0-mm back optical zone diameter and 6.2-mm back optical zone diameter design (repeated-measures ANOVA, F = 60.28, P < .001). Tukey multiple comparison tests revealed a significant difference between the 5.0-mm back optical zone diameter (<14 years) and 6.0-mm back optical zone diameter (≥14 years) group (P < .001), and between the 5.0-mm back optical zone diameter (<14 years) and 6.2-mm back optical zone diameter (<14 years) group (P < .001). No difference was found between the two age groups (<14 vs. ≥14 years) using the 6.2-mm back optical zone diameter design (P = .98). Table 3 shows the relative corneal refractive power change at different corneal radial distances. The 5.0-mm back optical zone diameter design produced a significantly greater relative corneal refractive power change than the other designs over the range from 0.75 to 1.95 mm of corneal radial distances (P < .05).

F3FIGURE 3:

Distribution of corneal refractive power change as a function of corneal radial distance at different follow-up visits. (A) One day, (B) 1 week, (C) 2 weeks, (D) 1 month. Standard deviation was removed for better profile comprehension.

TABLE 3 - Change in relative corneal refractive power (mean ± SD; from baseline) in each group (data from the topography maps) Distance from corneal apex (mm) DRL 5.0 mm DRL 6.0 mm Euclid 6.2 mm (<14 y) Euclid 6.2 mm (≥14 y) P 0.30 0.09 ± 0.68 −0.18 ± 0.82 0.01 ± 0.69 −0.02 ± 0.94 .09 0.45 −0.05 ± 0.66 −0.12 ± 0.83 0.03 ± 0.75 0.20 ± 1.03 .06 0.60 0.17 ± 0.66 −0.11 ± 0.88 0.09 ± 0.70 0.17 ± 0.86 .04 0.75 0.31 ± 0.62 −0.05 ± 0.89 0.15 ± 0.69 0.14 ± 1.06 .02 0.90 0.46 ± 0.70 −0.00 ± 0.94 0.24 ± 0.71 0.20 ± 1.03 .002 1.05 0.68 ± 0.75 0.10 ± 0.95 0.36 ± 0.76 0.29 ± 1.14 <.001 1.20 0.81 ± 0.84 0.21 ± 1.07 0.51 ± 0.83 0.45 ± 1.11 <.001 1.35 1.23 ± 0.73 0.36 ± 1.18 0.63 ± 0.88 0.65 ± 1.22 <.001 1.50 1.43 ± 0.82 0.57 ± 1.28 0.83 ± 0.96 0.84 ± 1.23 <.001 1.65 1.61 ± 0.97 0.79 ± 1.41 1.03 ± 1.05 1.05 ± 1.26 <.001 1.80 1.85 ± 1.10 1.05 ± 1.56 1.26 ± 1.11 1.31 ± 1.29 <.001 1.95 1.94 ± 1.26 1.32 ± 1.66 1.47 ± 1.16 1.58 ± 1.26 .005 2.10 2.08 ± 1.37 1.55 ± 1.71 1.68 ± 1.18 1.79 ± 1.35 .06 2.25 2.18 ± 1.46 1.72 ± 1.68 1.86 ± 1.18 2.04 ± 1.35 .11 2.40 2.16 ± 1.40 1.85 ± 1.62 2.00 ± 1.21 2.17 ± 1.37 .33 2.55 2.10 ± 1.35 1.96 ± 1.61 2.13 ± 1.23 2.31 ± 1.43 .45 2.70 2.05 ± 1.27 2.00 ± 1.63 2.20 ± 1.26 2.37 ± 1.48 .31 2.85 1.95 ± 1.23 2.01 ± 1.64 2.24 ± 1.26 2.39 ± 1.50 .12 3.00 1.96 ± 1.07 1.94 ± 1.56 2.24 ± 1.24 2.40 ± 1.51 .06 3.15 1.94 ± 1.06 2.00 ± 1.36 2.24 ± 1.22 2.23 ± 1.38 .17 3.30 1.91 ± 1.06 1.84 ± 1.48 2.16 ± 1.17 2.29 ± 1.44 .05 3.45 1.87 ± 1.04 2.00 ± 1.35 2.14 ± 1.15 2.23 ± 1.43 .22 3.60 1.86 ± 1.09 1.88 ± 1.36 2.10 ± 1.13 2.23 ± 1.46 .14

DRL = double reservoir lens; SD = standard deviation.


Relative Corneal Refractive Power Change Calculation by Polynomials

After the polynomials were acquired through calculation, relative corneal refractive power change and their corresponding corneal radial distances can be drawn from the subsequent function. Overall, there was no significant difference in maximum relative corneal refractive power change (Ymax) among the four groups (repeated-measures ANOVA, F = 0.86, P = .46; Fig. 4A). However, when the maximum relative corneal refractive power change was reached, the distance from the corneal apex (Xmax) was different among the four groups (repeated-measures ANOVA, F = 7.78, P < .001), with the 5.0-mm back optical zone diameter design being significantly shorter than the other designs (Fig. 4B). A further comparison of 1/4 Ymax, 1/2 Ymax, and 3/4 Ymax among the four groups is demonstrated in Fig. 4. At 1/2 Xmax, relative corneal refractive power change (1/2 Ymax) of the 5.0-mm back optical zone diameter design was significantly higher than that of the other three groups (all P < .05; Figs. 4C to E).

F4FIGURE 4:

Relative corneal refractive power change induced by different lens designs (mean ± standard deviation) as a function of corneal radial distance, with X and Y values drawn from polynomial functions. *P < .05; **P < .01; ***P < .001; ****P < .0001.

Relative Corneal Refractive Power Change Calculated by Monomial

The power exponent of the monomial of the 5.0-mm back optical zone diameter design was lower than that of the other three groups, and the difference was statistically significant (repeated-measures ANOVA, F = 4.81, P = .003; Fig. 5), indicating that the 5.0-mm back optical zone diameter design tended to yield a steeper slope of corneal power change from the center to the midperiphery (more aspheric).

F5FIGURE 5:

Power exponent of monomial fittings for relative corneal refractive power change induced by different lens designs (mean ± standard deviation). *P < .05; **P < .01.

DISCUSSION

In the current study, we found a significant impact of different orthokeratology lens designs on the spatial distribution of relative corneal refractive power change after corneal reshaping, especially in the midperipheral zone close to the corneal apex.

Previous studies have used methods to calculate corneal refractive power change in orthokeratology by collecting data at certain points along two corneal meridians23 or by adding the corneal refractive power within a certain area to generate cumulative corneal refractive power change.24 These methods are less effective in interpreting the detailed profile of corneal refractive power change (e.g., spherical vs. aspheric) within the treatment zone, thereby confounding the elements that are responsible for the individual variation in myopia control effect after orthokeratology treatment. A recent study has used Fourier transformation to decompose the relative corneal refractive power change distribution after orthokeratology treatment and found that a larger modulation of maximal relative corneal refractive power change was associated with a slower axial elongation at 1 year.22 Although the modeling of relative corneal refractive power change in that study was more comprehensive compared with the previous ones,23,24 the mathematical method applied was difficult to admire. Furthermore, that study used only one lens design and therefore could not answer the question as to whether the size of orthokeratology lens back optical zone diameter had any impact on relative corneal refractive power change distribution.22

The method of using polynomial function in modeling relative corneal refractive power change in the current study has yielded reasonably good fitting of curves. It reserved as much topographical data as possible as compared with the previous methods.23,24 Based on previous research, treatment zone was defined as the area enclosed by points of zero dioptric changes on the axial subtractive topography maps.25 By analyzing the detailed data, we found that lenses with a smaller back optical zone diameter (5.0 mm) tended to induce a smaller (≈2.0 mm) and more aspheric treatment zone than those of the other two lens designs (2.5 to 3.0 mm), meaning that the cornea steepened faster toward the midperiphery and reached maximum in relative corneal refractive power change at a smaller corneal radial distance in the 5.0-mm back optical zone diameter group (Fig. 3).

In the current study, we also found a different reshaping speed among groups. A previous study with a sample of eight eyes revealed that the corneal biomechanical properties might affect the reshaping speed of orthokeratology treatment, with less corneal resistance showing faster effect and faster recovery.26 Although it remains unclear whether children and adults have different corneal biomechanical properties, the current study did not suggest age to play a significant role in corneal reshaping speed based on the fact that a significant difference in remaining spherical equivalent refractive at day 1 was only found between the 5.0-mm back optical zone diameter (<14 years) and other three back optical zone diameter groups, but not between different age groups. These results altogether indicated that the size of back optical zone diameter, rather than the other factors, played a dominant role in corneal reshaping speed.

A recent study compared axial elongation in juveniles wearing orthokeratology lens designs with different back optical zone diameters.27 The authors found that the lenses with smaller back optical zone diameter had a greater myopia control effect on axial elongation as compared with lenses with larger back optical zone diameter. Despite its retrospective design in nature, this was the first study directly investigating the relationship between orthokeratology lens design (especially back optical zone diameter) and myopia control efficacy in children and juveniles, which opened a possibility of optimizing orthokeratology lens designs for better myopia control efficacy. Recently, Guo et al.25 also reported that children wearing orthokeratology lenses with smaller (5.0 mm) back optical zone diameter had significantly slower annual axial elongation (0.04 ± 0.15 mm) as compared with those wearing larger (6.0 mm) back optical zone diameter (0.17 ± 0.13 mm), resulting in a retardation effect of 0.13 mm.

However, the exact mechanism underlying the effect of orthokeratology treatment on myopia control is unknown. The seemingly straightforward causal relationship between induced peripheral myopic defocus and myopia control can be complicated by mutual factors, including increased higher-order aberrations after orthokeratology lens wear.28 Two studies even found that a higher third-order higher-order aberration, most likely induced by a decentered treatment zone, was beneficial for myopia control.29,30 A smaller treatment zone after orthokeratology should have yielded a higher spherical aberration, as in the case of 5.0-mm back optical zone diameter. However, we did not measure higher-order aberration in the current study, which should be considered in future studies.

The strength of this study was to compare relative corneal refractive power change among well-matched groups including two identical lens designs except for the back optical zone diameter (DRL 5.0 mm vs. DRL 6.0 mm). The first limitation of this study was that the analysis of relative corneal refractive power change was done along the horizontal meridian only, and all the lenses used were of spherical design. Corneas of significant astigmatism to be corrected by toric lens designs might have different relative corneal refractive power change profiles after lens wear. The second limitation was that the question remains unclear as whether a smaller aspheric treatment zone after orthokeratology would be more effective in myopia control. We originally designed a 1-year study to explore this relationship, and the current result reported herein served as a pilot study for the whole project.

To conclude, the current study provided a methodology to better understand the detailed corneal profile following different orthokeratology lens designs. An orthokeratology lens design with smaller back optical zone diameter might yield a faster myopic reduction and a smaller aspheric treatment zone. These results offered a possibility of optimizing orthokeratology lens designs for better myopia control efficacy.

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