All patients were retrospectively enrolled from the clinical case files of myopic children who were fitted with Ortho-K lenses [corneal refractive therapy (CRT) and vision shaping treatment (VST) lens design] from January 2018 to December 2019 in the Optometry Centre of Peking University People's Hospital. A total of 133 patients who met the recruitment criteria were recruited for the study. To eliminate correlative effects between the two eyes, only data from the right eyes were collected in this study.

The inclusion criteria were as follows: (1) no history of using atropine eye drops, (2) a best-corrected visual acuity (BCVA) value of no less than 20/20 for either eye, (3) a cycloplegic spherical power of no less than − 0.75 diopters (D) and astigmatism no greater than 3.00 D, and (4) no prescription modification during Ortho-K lens wear follow-up. Patients with any other ocular diseases or poor topographic measurement quality were excluded from the study. The final parameters of the ordered lenses were confirmed by both fluorescein staining at lens delivery and an ideal “bull’s eye” corneal topography pattern after lens treatment. No severe corneal complications were observed. The purpose and details of the study were explained to all the subjects and their parents or guardians, and signed informed consent was obtained. This study followed the tenets of the Declaration of Helsinki and was approved by the Medical Ethics Committee of Peking University People’s Hospital.

The data collected in this study included age at the initial visit, sex, baseline spherical and cylindrical refraction, initial mean keratometry (K) readings, corneal eccentricity (E value), horizontal visible iris diameter (HVID), anterior chamber depth (ACD), lens design (VST or CRT), treatment zone decentration, pupil diameter and 12-month AL change (AL at the 12-month follow-up minus baseline AL). Corneal parameters were obtained using a Sirius corneal topography system (CSO, Italy), and the pupil diameter was measured using the Sirius device with the examination room lights off (room illuminance 2 lx). The.csv files of the corneal sagittal height data (at baseline and one-month after Ortho-K treatment) were exported from the Sirius system. An IOLMaster (Carl Zeiss, Ltd., Germany) was used to measure the AL of all subjects, and the results for data analysis were obtained by averaging six repeated measurements in which intrasession differences were no greater than 0.02 mm. Cycloplegic refraction was measured 35 min after three instillations of 1% cyclopentolate administered at five-minute intervals, and spherical and astigmatic refraction readings were obtained using an autorefractor. The spherical equivalent (SE) was calculated as the spherical power plus 1/2 cylindrical power.

Clinically, the tangential power difference map after Ortho-K treatment was a bowl-like shape in three-dimensional space, which can be generated by minus tangential power map after Ortho-K treatment from the initial visit (Fig. 1). The raw data of these two maps were exported from the Sirius corneal topography system as two 31 × 256 matrices. On this difference map, the data within the maximal positive defocus border was extracted, and the matrix of tangential power difference (D) was calculated using:

Reconstruction of tangential power difference map after Ortho-K treatment. a Two-dimensional original tangential power difference map; b Real tangential power difference map in three-dimensional space; c Reproduction of tangential power difference map by Zernike fitting

\(_(\rho ,\theta ) = _(\rho ,\theta )-_(\rho ,\theta )\), where \(\rho \epsilon [\mathrm], \theta \epsilon [\mathrm\pi ]\)

where ρ is the power of the radial defocus ring coordinate, and the border is defined as the maximal positive defocus point on the tangential difference map; θ is the azimuthal angle; T is the matrix of tangential corneal power; and \(_(\rho ,\theta )\), \(_(\rho ,\theta )\) and \(_(\rho ,\theta )\) are the matrices of the tangential power difference map and the tangential power maps before and after Ortho-K treatment, respectively. A Zernike fitting was then performed to calculate the Zernike defocus coefficient (\(_^\), D), which can be expressed as [22]:

$$_^ = \frac_^_^_(\rho ,\theta )\sqrt(2^-1)\rho d\rho d\theta$$

Then, the weighted Zernike defocus coefficient of the treatment zone (Cweighted defocus, D/mm2) can be defined as:

To calculate the treatment zone area (π·r2), 256 points on the treatment zone border, which were defined as the points of transition from negative to positive values, were automatically extracted from this tangential difference map by a customized MATLAB program. The least squares method was then used to estimate the best fitting “ring” for these points. The treatment zone area can be calculated as π·r2 (r: radius of the best fitted ring), and the decentration of the treatment zone can also be deduced from this ring.

SPSS software (version 19.0, SPSS Inc. Chicago, IL, USA) was used for statistical analysis. The Shapiro-Wilk test was used to examine the normality of the data. Means and standard deviations or counts and percentages are reported as appropriate. The clinical characteristics were compared between groups A and B using independent t-test, a Mann-Whitney U test, a χ2 test, or Fisher's exact test as appropriate.

Univariate and multivariate binary logistic regression were used to analyze the correlations of AL elongation (> 0 defined as yes; ≤ 0 defined as no) with age, sex, Cweighted defocus (large Cweighted defocus was defined as an index ≥ 0.35 D/mm2 based on the median of the calculated data), treatment zone decentration, lens design and pupil diameter. The confounding factors were defined as clinical variables with P values less than 0.05 in the comparison analysis. A two-tailed P value less than 0.05 was considered as statistically significant.

The Pearson correlation coefficient was used to evaluate the simple correlations between 12-month AL elongation and the Cweighted defocus of the treatment zone. The association was further examined using linear regression analyses. Variables, including the baseline age, sex, SE, horizontal decentration, vertical decentration, pupil diameter, mean K, HVID, E value, and Cweighted defocus, were first examined using univariate linear regression analysis. Variables that showed statistically significant associations (P < 0.05) with the 12-month AL change in univariate analyses were included in the multivariate regression model. These variables included baseline pupil diameter, age, SE, horizontal decentration and Cweighted defocus of the treatment zone.