## 2 Materials and Methods
### Topographical Assessment  
Corneal topography was performed at each visit (Medmont E300 USB, Precision Ophthalmic, Vancouver, BC, Canada). Due to the nature of the clinic, data acquisition was performed by different individuals over the course of the study, but they were trained to use the same methodology according to a standard written protocol. The patient was asked to look at the same target each time, and the images were checked for quality (>95 of the quality index) before interpretation. Centration was also validated, and maps decentered by more than 1 mm from the center of the pupil, vertically or horizontally, were discarded. A minimum of 4 validated maps were taken each time and a composite map was generated. In this study, tangential maps were selected, and all images were analyzed by the main author and double-checked by a second reader (2 nd author). Using these maps, the localized radius of each curvature point was calculated with respect to the tangents to those points. This was a representation of the true radius, taking into account the asphericity of the corneal surface. Tangential maps have been recommended for fitting and monitoring OK contact lenses, especially for analyzing the corneal periphery [24]. Participants with analyzable baseline and follow-up topographies were kept for analysis.  
The following data were recorded:  
Distance treatment zone diameter (DTZD) represents the area where the cornea is flattened, producing a negative (more concave) power on the comparative tangential power map. In this study, the treatment zone was measured in millimeters along the horizontal meridian (Figure 1).  
The mid-peripheral width (MPW) is the width of the area of increased curvature that produces a positive (more convex) power on the comparative tangential map, expressed in millimeters.  
Relative peripheral power (RPP) represents the difference between the peak of the power curve and the corrected myopia as shown on the differential map (Figure 1), expressed in diopters.  
The plus power ratio (PPR) represents the ratio (%) of the area of the proportion of the pupillary area covered by the positive power ring generated in the midperiphery. The pupil size was measured with an infra-red pupillometer (Neuroptics, Irvine, CA, USA) looking at distance under photopic conditions.  
Two main formulas are used to calculate the PPR according to the location of the end of the plus power ring created by orthokeratology. If the diameter of the treatment  
Figure 1: Differential tangential power map, in diopters, showing the impact of a customized OK lens on a cornea and graphical representation of mid-peripheral width (MPW, mm), distance treatment zone diameter (DTZD, mm), and relative peripheral power (RPP, D). Blue describes, in diopter, more negative power difference (corneal flattening) while hotter colors (red-orange) identify where convex power was increased (corneal steepening).  
zone area is greater than the pupil diameter or equivalent, the PPR is calculated using the following formula (Equation (1)):  
\[\text{PPR}=1-\left(\frac{r_{1}}{p}\right)^{2} \tag{1}\]  
\(r_{1}\) = radius of distance treatment zone diameter  
\(p\) = radius of pupil diameter  
If the diameter of the treatment zone area is smaller than the pupil diameter, the following formula is used (Equation (2)):  
\[\text{PPR}=\frac{r_{2}^{2}-r_{1}^{2}}{p^{2}} \tag{2}\]  
\(r_{1}\) = radius of distance treatment zone diameter  
\(r_{2}\) = radius of treatment zone diameter  
\(p\) = radius of pupil diameter  
Parameters described in the equations above are represented in Figure 2.