How the topographies are simulated

Corneal topographies have been simulated using R and RStudio software.^1,2

Firstly, the sagittal height for the principal meridians has been determined based on the shape of an ellipse,^3,4 and from these, the intermediate meridians have been calculated by applying a square sinusoidal function.^4,5 These calculations were performed for a 4 mm radius, in steps of 0.1 mm, over the entire 360º of the cornea, in steps of 5º. The result of the principal meridians is represented in the sagittal profile graph (lower figure).

The curvature was determined by calculating the actual radius formed between each point and the consecutive anterior and posterior points, and then determining the length between the point and the extension of its radius to the corneal axis. Therefore, axial curvature (also called sagittal) is represented. The result of all meridians is shown in the curvature map (upper left figure); while the principal meridians are represented in the curvature profile graph (central left figure).

The elevation was determined by calculating the best fit sphere that fits each cornea using the R package 'conicfit',⁶ and then determining the difference in sagittal heights between the simulated cornea and the best fit sphere at each point. The result of all meridians is represented in the elevation map (upper right figure); while the principal meridians are represented in the elevation profile graph (central right figure).

The graphs were created using the R package 'ggplot2'.⁷