Impact of pupil and defocus ring intersection area on retinal defocus

With the rising prevalence of myopia, especially among the young, orthokeratology (Ortho‐K) stands out as a promising approach, not only to reduce myopia but also to control the progression of axial length (AL). This study examined how the intersection area between the pupil and defocus ring influenced retinal defocus and axial growth after Ortho‐K.


BACKGROUND
The prevalence of myopia has increased significantly, particularly among younger individuals. 1Projections indicate that by 2050, around 5 billion people worldwide (approximately 50% of the global population) will be myopic, with approximately 10% having high myopia. 2East Asian countries exhibit a higher prevalence of adult myopia than other regions. 3As the axial length (AL) increases, it may lead to abnormal morphological changes in the eyeball, resulting in complications such as myopic macular degeneration, glaucoma and retinal detachment, possibly leading to visual impairment or blindness. 4urrently, optical devices and pharmaceutical interventions are the most commonly used approaches for myopia control.Extensive research, encompassing both animal and clinical studies, consistently demonstrates that the primary methods for managing myopia focus on optical strategies that specifically target peripheral refraction.][7] Orthokeratology (Ortho-K) refers to the use of a rigid gas permeable contact lens that temporarily reduces the power of the central area of the cornea, resulting in flattening within a specific range. 8,9This reversible reduction has positioned Ortho-K as a highly effective approach for managing myopia progression. 10The lens achieves corneal flattening by means of back central optic zone diameters (BOZD), which create an optical treatment zone (OTZ) on the cornea. 11This process establishes a gap between the reverse curve of the lens and the front corneal surface, which is occupied by tears.As a consequence, a pressure gradient is generated, wherein positive pressure is exerted at the corneal centre and negative pressure is experienced in the surrounding areas.Accordingly, epithelial cells migrate from the central cornea towards the peripheral steepening zone, commonly known as the defocus ring.
Clinical studies have revealed that the effectiveness of myopia control in individuals wearing Ortho-K lenses is influenced by various factors, including the pupil diameter, as well as the size of the defocus ring and the OTZ.Specifically, subjects with larger pupils who wear Ortho-K lenses with a smaller effective OTZ experience increased myopic defocus in the peripheral retina.This heightened peripheral defocusing effect can delay axial growth and contribute to improved myopia control. 12,13In an examination of the impact of wearing Ortho-K lenses eccentrically, it was determined that the relationship between the position of the pupil and defocus ring affects the magnitude of myopic defocus formed at the peripheral retina. 14,15 comparative study was undertaken to evaluate manual and software-based measurement systems for quantifying the OTZ and defocus ring.The results indicated differences between the two measurement methods, although these fell within clinically acceptable limits. 16However, there is currently no definitive method to measure the position of the pupil and defocus ring, nor is there substantial evidence regarding any correlation between their positions and the magnitude of peripheral retinal defocus.In the present study, retinal defocus was expressed as the refraction difference value (RDV), which represents the average difference between the refractive error in specific regions (from 0 to 53°, 0 to 10°, 10 to 20°, 30 to 40° and 40 to 53°) compared with the refractive error at the fovea.The RDV was measured using multispectral refractive topography (MRT, Thondar, Inc., thond ar.cn).This technique provides good repeatability in measuring peripheral refractive error across different zones.Lu et al. 17 noted that due to its ability to measure a large area of the peripheral retina, MRT is a preferred choice for examining the effect of optical treatments on peripheral refraction.Furthermore, Liao et al. 18 described a high level of agreement between measurements of central refraction obtained using autorefractometry, subjective refraction by experienced optometrists and MRT.
In recent years, numerous studies have investigated the effectiveness of Ortho-K lenses for managing myopia.
These lenses achieve their effect by altering the shape of the cornea, particularly in the central area.6][17] However, currently there is no definitive method to measure the position of the pupil and defocus rings, and there is a lack of sufficient evidence regarding the correlation between their position and the magnitude of peripheral retinal defocus.Therefore, the main objective of this study was to examine the relationship between the cross-sectional area between the pupil and defocus rings and changes in RDV after wearing Ortho-K lenses for 3 or 6 months.By adjusting the parameters of the Ortho-K lenses, taking into account the pupil size and the state of the RDV, it is possible to enhance the management of myopia.Moreover, clinical guidance can aid in the personalised fitting of Ortho-K lenses, ensuring optimal outcomes for individual patients.

Study design
This study, approved by the Ethics Committee of The Ineye Hospital of Chengdu University of Traditional Chinese Medicine (2021yh-008) and conducted in accordance with the principles outlined in the Declaration of Helsinki, aimed to explore the impact of the intersection area between the pupil and defocus ring on RDV variation following the use of Ortho-K lenses.RDV was expressed as the average difference between refractive errors within specific angular ranges (from 0 to 53°, 0 to 10°, 10 to 20°, 30 to 40° and 40 to 53°) and the refractive error at the fovea.Specifically, the range from 0 to 53° encompasses all the subranges, with each 10-degree subrange (e.g., 0-10°, 10-20°, etc.) being a part of this overall range.By calculating RDV within each subrange, we could assess the average difference between refractive errors within these specific angular ranges and the

Key points
• Further investigation into retinal peripheral defocus can provide insights into axial elongation and myopia development.• The efficacy of orthokeratology in controlling myopia progression is influenced, to some extent, by the intersection area of the pupil and the defocus ring.• Future customised orthokeratology is expected to integrate corneal topography and retinal defocus measurements, aiming to provide more precise therapeutic effects.
refractive error at the fovea.This design aimed to provide a comprehensive evaluation of retinal defocus, enabling a better understanding of the impact of peripheral retinal defocus.

Subjects
Subjects were selected based on the criteria specified in Table 1.Extensive training was provided to both the subjects and their guardians regarding the correct use and maintenance of the lenses.The researchers consistently recorded and documented the subjects' adherence to wearing the lenses, which was closely monitored during each follow-up visit.It is important to note that all subjects and their guardians signed informed consent forms, demonstrating their understanding and agreement to participate in the study.

Contact lens fitting
Participants were provided with Paragon CRT™ 100 (vedeng.com/ zhuce zheng/ jk/ 164785.html) reverse geometry gas-permeable contact lenses manufactured using paflufocon D. These lenses had an oxygen permeability (Dk) of 100 (ISO) 10 −11 (cm 2 /s)/(mLO 2 /mL × mm Hg), a specific gravity value of 1.10 and a refractive index of 1.442.The lens fitting process followed the guidelines outlined by the manufacturer, taking into consideration the subjects' manifest refraction, fluorescein patterns observed during slit-lamp examination and corneal topography.A lens was then ordered based on these findings, with an overrefraction targeted between +0.50 and +1.00 D.

Follow-up visits
Subjects were scheduled for follow-up visits 3 and 6 months after initiating ortho-k treatment.If the initial contact lenses were uncomfortable or there were any other discomfort or vision issues, it was suggested that they schedule additional follow-up visits.During each visit, the subjects underwent various assessments, including measurements of visual acuity, slit-lamp examination, optical biomeasurement, corneal topograph and MRT (Figure 1).The AL (mm) and RDV (dioptres, D) were measured at baseline, as well as at the 3-and 6-month visits.
To ensure consistent results and minimise the impact of diurnal variation, participants were instructed to wear the contact lenses continuously for a minimum of 8 h every night.All measurements were conducted between 09:00 and 11:00 h, and participants were required to remove the lenses at least 2 h before the examinations.

Measurement of intersection area between pupil and defocus ring
All participants underwent measurements using the E300 Medmont (Medmont International Inc., medmo nt.com.au) topographer.The measurements were performed at least three times to obtain accurate and reliable data.The best-focused and properly aligned image was selected for analysis.In order to monitor the changes in the OTZ and defocus ring, tangential subtractive maps were generated by subtracting the post-treatment map from the baseline map.The size of the pupil was obtained from the topographic data collected under ambient photopic room lighting.Under photopic conditions, the objective infrared-based topographer automatically adjusted based on the intrinsic light levels to ensure the accuracy of the measurements. 19In the present study, the pupil centre and diameter were denoted as (x0, y0) and 'd', respectively.As illustrated in Figure 2a, 16 coordinate points were identified within the cornea's steep region.These points, located in both the middle and periphery, showed a curvature change of '0.00 D' at specific angles, including 30°, 60°, 120°, 150°, 210°, 240°, 300° and 330°.The region enclosed by these eight points, which demonstrated no dioptric shift on the tangential subtractive topography maps, was termed the OTZ.Conversely, the defocus ring's

Inclusion criteria
Exclusion criteria definition relied on the reverse curvature formed by these 16 points.The best-fitting regions of the pupil and defocus ring were calculated using Matlab (mathw orks.com) software.The fitted image was then imported into ImageJ (National Institutes of Health, imagej.net)and the intersection area (mm) between the pupil and defocus ring (as shown in Figure 2b) analysed.

Statistical analyses
Data analysis focused solely on measurements obtained from the right eye of each participant.All statistical analyses were performed using IBM SPSS version 26.0 (ibm.com).The distribution of each parameter was assessed using the Kolmogorov-Smirnov test.Normally distributed data were presented as mean (SD).Two-way repeated measures ANOVA compared multiple time points between the groups.Pairwise comparisons within groups were adjusted with the Bonferroni correction.Independent sample t-tests compared different time points between groups.Pearson correlation analysis evaluated variable correlation.For non-normally distributed data, median and inter-quartile range were used as descriptors.Generalised estimating equations were employed for comparisons of multiple time points and within-group time point comparisons.Spearman correlation coefficients assessed associations.A significance level of p < 0.05 was considered statistically significant.

R ESULTS The measurement results of the intersection area between the pupil and the defocus ring
According to the inclusion and exclusion criteria, a random sample of 100 participants who completed the 3-and 6month follow-up visits on time was selected (only the right eye was analysed).The red ring and yellow circle represent the defocus ring and the pupil, respectively.'Area' indicates the intersection area between the pupil and the defocus ring.
After 3 and 6 months of wearing the lenses, intersection areas were measured using a specialised optical measuring technique that combined high-resolution corneal topography with advanced imaging software.The results showed intersection areas of 4.58 mm 2 (0.31) and 4.51 mm 2 (0.30) after 3 and 6 months, respectively.No significant difference was observed between these two time points (t = 0.16, p = 0.88).Using the median value of the intersection area recorded after 3 months of lens wear, participants were categorised into two Group A, with an intersection area of <4.58 mm 2 (50 eyes), and Group B, with an intersection area of ≥4.58 mm 2 (50 eyes).

Comparison of the baseline characteristics between the two groups
To assess the impact of Ortho-K treatment, participants were randomly divided into the two groups described above.This grouping strategy aimed to ensure the statistical power of the data and the validity of the experiment.Prior to commencing the study, we ensured that there were no significant differences between the two groups in key baseline parameters such as age, refractive error, AL, pupil diameter, keratometry values and flatter keratometry finding (Kf) (all p > 0.05).This design guaranteed that our research findings predominantly reflected the effectiveness of the Ortho-K treatment, rather than being attributable to variations in baseline characteristics.Please refer to Table 2 for details.

Comparisons of AL growth between the two groups
Table 3 presents the AL growth for both groups over time.Through multivariate analysis accounting for the interaction between the groups and different wearing times, significant differences were observed in the AL growth between the two groups when wearing Ortho-K lenses (F group/time/interaction = 113.54,107.44, 66.94, p group/time/interaction < 0.01).Specifically, at the 3-and 6-month marks, Group A showed a markedly higher AL growth than Group B (both p-values <0.01).

Comparison of RDV variation between two groups
Significant differences in RDV changes were observed between the two groups at varying distances from the fovea, as presented in Table 4. Specifically, distances of 30-40° and 40-53° showed marked differences between the groups.However, no significant differences were found in the RDV changes in the 0-10° region.
Compared with pre-lens wear, both groups showed a significant decrease in RDV changes at 10-20°, 20-30°, 30-40° and 40-53° after wearing lenses for 3 and 6 months (all p < 0.01).After 3 months of lens wear, the RDV changes at 30-40° and 40-53° were significantly lower in Group B than Group A (p = 0.02 and < 0.01, respectively).After 6 months of lens wear, the RDV changes at 40-53° were significantly lower in Group B than Group A (p = 0.04), as shown in Table 5.

Correlation between the intersection area and both AL and RDV variation
The average increase in AL after 3 and 6 months of lens wear was 0.03 (−0.03, 0.14) mm and 0.16 ± 0.19 mm, respectively.Additionally, the intersection area showed a significant negative correlation with AL elongation at both 3 months (r s = −0.84,p < 0.01) and 6 months (r s = −0.94,p < 0.01), as detailed in Table 6.

DISCUSSION
The increasing prevalence of myopia poses a significant global public health challenge due to uncorrected refractive error and an elevated risk of visual impairment resulting from myopia-related ocular complications.Ortho-K lenses have emerged as an effective solution for myopia reduction and have been purported to slow down the progression of AL elongation, particularly in children.Cho et al. 20 were the first to demonstrate that children wearing Ortho-K lenses experienced only half the increase in AL compared with children using single-vision lenses (SVL S ) after 2 years of lens wear.Numerous studies have provided compelling evidence showcasing the ability of Ortho-K to reduce axial elongation by 43-63% in primary school-aged children. 5,9,19,21rtho-K lenses, through the induced relative corneal refractive power change, effectively control AL growth by producing peripheral myopic retinal defocus.This is known as the 'peripheral defocusing hypothesis,' which has been acknowledged by multiple researchers. 22,23Additionally, a previous study suggested that in an Ortho-K lens wearing group, nasal peripheral axial growth was accelerated, Note: Generalised estimating equation.Groups A and B were differentiated based on the size of the intersection area after 3 months of lens wear, being <4.58 mm 2 and ≥4.58 mm 2 , respectively.a Significant difference compared to pre-lens wear (p < 0.01).
b Significant difference between Group B and Group A (p < 0.05).

T A B L E 6
Correlation between the intersection area and both axial length (AL) and the refraction difference value (RDV).the relative peripheral refraction on the nasal side exhibited less hyperopic defocus and the overall eye shape became more symmetric and less prolate after 12 months. 24dditionally, Ni et al. 25 examined the refractive state of the retina in myopia patients using MRT.Following 1 year of treatment, the RDV for the 15-53° region in the Ortho-K group was significantly lower than that observed in the SVL group.Li et al. 26 utilised MRT to measure the RDV in children wearing both Ortho-K and SVLs.Their findings revealed that the RDV in the 15-30°, 30-45° and 15-45° regions was significantly smaller (indicating relative peripheral myopic defocus) for the Ortho-K wearers than the control group (all p < 0.05).Furthermore, among participants wearing Ortho-K lenses, the RDV for the 0-53°, 0-15°, 0-30°, 0-45°, 15-30° and 15-45° regions in the slow AL growth group were significantly smaller than for the fast AL growth group (all p < 0.05).the findings of the present study indicate that Group B, characterised by a larger intersection area between the pupil and defocus ring, exhibited significantly lower rates of axial growth and changes in RDV within the 30-40° and 40-53° ranges after 3 months of lens wear, compared with Group A (all p < 0.05).Likewise, after 6 months of lens wear, Group B exhibited significantly lower axial growth and RDV changes within the 40-53° range, compared with Group A (all p < 0.05).Based on current evidence, it was hypothesised that a larger intersection area between the pupil and defocus ring facilitated the increased entry of defocused light into the eye, resulting in greater optical impact on the peripheral retina and a higher degree of myopic defocus.This, in turn, led to more effective control of AL.

After 3 months
Research on the relationship between the pupil diameter and the effect of Ortho-K lenses on myopia control has gained considerable attention.Jian et al. 27 observed a significant negative correlation (r = −0.49,p < 0.01) between baseline pupil diameter and axial growth over 1 year.In addition, Chen et al. 28 assessed the relationship between axial growth at 24 months and baseline pupil area in both Ortho-K and SVL groups.They found a significant correlation (r 2 = 0.41, p < 0.001) between pupil size and axial growth in the Ortho-K group, indicating that larger pupil diameters enhanced the effect of Ortho-K lenses in slowing AL growth.The pupil and defocus ring are crucial factors in determining the effective defocusing of light entering the eye.The present study further verified the impact of the relationship between the pupil and defocus ring on the variation in RDV.The pupil and defocus ring were fitted using Matlab, while the intersection area between them was calculated using ImageJ software.Lin et al. 29 demonstrated the accuracy and repeatability of using ImageJ to measure the central corneal intersection area, as well as anterior and posterior corneal arc lengths.Furthermore, significant associations were identified between the intersection area of pupil and defocus ring, AL elongation and RDV variation.A larger intersection area between the pupil and defocus ring was associated with a greater myopia-defocusing effect in the peripheral retina (specifically within the 30-53° region), resulting in a smaller increase in AL over the respective time periods.
Previous research has established a connection between the size of the BOZD in Ortho-K lens design and its impact on myopia control.Guo et al. 30 demonstrated that participants wearing lenses with a 5.0 mm BOZD experienced a significantly reduced annual increase in AL compared with those wearing lenses with a 6.0 mm BOZD (0.04 ± 0.15 mm vs. 0.17 ± 0.13 mm) after 1 year of lens wear.Furthermore, Pauné et al. 31 observed that lenses with a smaller BOZD resulted in a smaller defocus ring diameter.Moreover, for individuals where a horizontal sector of the defocus ring fell inside the pupil, AL increased less than for those individuals where the defocus ring matched or fell outside the pupil (0.04 ± 0.10, 0.10 ± 0.11 and 0.17 ± 0.12 mm, respectively).This finding suggests a 76% reduction in axial growth or an absolute reduction of 0.13 mm per year.Li et al. 32 demonstrated that axial elongation was slower in a group wearing 5.0 mm BOZD lenses compared with a 6.0 mm BOZD, with a difference of 0.15 mm.The 5.0 mm BOZD lens group exhibited a reduction in the OTZ and a decrease in the 3/4× value (i.e., the peak level of the corneal refractive power profile relative to the apex distance) when compared with the group using 6.0 mm BOZD lenses.Additionally, after 1 year of treatment, the relative sum of the corneal refractive power within the pupillary area was higher in the 5.0 mm BOZD lens group, consistent with the findings of Zhang et al. 33 In the present study, a consistent 6.0 mm BOZD value was specifically chosen after Ortho-K lens wear.The results revealed individual differences in the effective OTZ formed on the cornea after lens wear, even with the same BOZD.Through the calculations of the intersection area between the pupil and defocus ring, the present investigation provided further explanation that a decrease in the effective OTZ led to an increase in the steep area of the mid-peripheral cornea in Ortho-K lens wearers.A wider and steeper mid-peripheral defocus ring with a larger area of intersection with the pupil will induce more peripheral myopic retinal defocus, resulting in improved myopia control.These findings are important when optimising the BOZD design.Indeed, differences in the size of the intersection between the pupil and defocus ring can be influenced by additional factors such as eccentricity and the biomechanical properties of the cornea.Lin et al. 34 found that individuals with larger OTZ decentration had increased relative power in the central 2 mm of the cornea compared with less decentration.Additionally, Chen et al. 14 recorded the distribution of refractive powers within the central 4 mm pupillary area, and suggested that the corneal positive-power area (positive D value) had a beneficial impact when confirming AL changes.This area may be related to lens decentration, as it increases the asymmetry of the cornea, resulting in a larger area of intersection between the pupil and defocus ring.Regarding the biomechanical properties of the cornea, Lam et al. 35 observed a significant correlation between baseline corneal stiffness and spherical reduction after 6 months of Ortho-K lens wear (r = 0.38, p = 0.02).In addition, González et al. 36 found that high corneal hysteresis, which indicates increased corneal stiffness, imparts a strong ability to resist lens pressure and leads to poor shaping of the cornea.Thus, it is postulated that the irregular variation in the intersection area between the pupil and defocus ring resulting from Ortho-K lens wear could potentially be associated with corneal biomechanics.Additional investigations are required to establish the definitive link between these two factors.
A strength of the current study lies in its calculation of the intersection area between the pupil and defocus ring, thus maximising the defocused light reaching the retina.Additionally, the study directly measured the actual amount of retinal defocus using an MRT instrument.However, it is important to note that the investigation used only a single lens design and had a relatively short duration.To gain a more comprehensive understanding, further studies should be conducted using alternative lens designs, to explore whether similar findings are noted regarding the intersection area between the pupil and defocus ring.Longer term research is necessary to determine whether the impact of the intersection area between the pupil and defocus ring on RDV variation and elongation rate persists for an extended period of time.Longitudinal studies will provide valuable insight into the long-term effectiveness and stability of this relationship.
The results suggest that the size of the intersection area between the pupil and the defocus ring is a significant factor influencing peripheral retinal defocus after Ortho-K lens wear.However, further investigation is required to explore other factors that may affect the change in peripheral retinal defocus, such as variations in choroidal thickness and corneal curvature.Expanding the sample size and extending the observation period in future studies may yield more comprehensive insights into these factors and their impact on myopia control with Ortho-K.In clinical practice, proper centring of the lens and adjustment of lens parameters are crucial to increase the intersection area between the pupil and defocus ring, maximising peripheral defocus and improving the effectiveness of Ortho-K lenses for myopia control.Considering changes in higher order aberrations is important to strike a balance between visual quality and myopia control.These aspects should be the main focus of future research in this field.

CONCLUSION
The present study extensively investigated the impact of the pupil and the crossing area of defocused rings on retinal defocus.This finding holds significance for clinical practice.First and foremost, retinal defocus is crucial for visual quality, as it affects patients' visual experience and daily activities.Through an investigation of the pupil and the crossing area of defocused rings, we gain a better understanding of their interaction with retinal defocus, thus providing more accurate diagnostic and treatment strategies.Furthermore, this study offers a novel perspective for evaluating and addressing complex issues related to ophthalmic diseases.Understanding the influence of the pupil and the crossing area of defocused rings can assist healthcare professionals in making more informed decisions concerning surgery, contact lens design or other treatment modalities, thereby ensuring optimal treatment outcomes for patients.

AC K N O W L E D G E M E N T S
This work was supported by Eye School of Chengdu University of Traditional Medicine, Ophthalmology Beijing Ming Vision and Ineye Hospital of Chengdu University of Traditional Medicine.The authors would like to express sincere appreciation to Zhou Yuehua and Zhang Jing for their invaluable guidance and encouragement throughout the research process.

CO N F L I C T O F I N T E R E S T S TAT E M E N T
The authors declare that they have no conflicts of interest.

F I G U R E 1
The average difference between the relative refractive error of each region (i.e., from the retinal centre to 53°, 0-10°, 10-20°, 30-40° and 40-53°) and the refractive error at the fovea.Positive and negative values indicate hyperopic and myopic defocus, respectively, while the value at the fovea was taken as 0.00 D. RDV, refraction difference value.F I G U R E 2 (a) The black dots indicate the corneal refractive power change of '0.00 D' (30°, 60°, 120°, 150°, 210°, 240°, 300° and 330°; N = 16).(b) Comparison of baseline characteristics between the two groups.
T A B L E 2 a Significant difference between Group B and Group A (p < 0.01).
Two-way, repeated measures analysis of variance F group/time/interaction and p group/time/interaction values across the different retinal regions.Comparison of the refraction difference value (RDV) between the two groups.
T A B L E 4