Mathematical modeling of the shape of corneas before and one month and one year after prk for myopia

Purpose: To identify shape changes incurred by PRK. for myopia ami healing using a principled mathematical model fitted to data from multiple kcratoscopc images. Methods: For images of 42 corneas b-tbre PRK and one month and one year after PRK. Kcratron heights and distances v ithin 4.2 mm of the pupil center were fit by a pupil-centered, mathematical surface model which used Legendre polynomials, orders 0 - 6. 10 decompose cornea! sh; pe radially, and the Fourier scries, orders 0 l). 10 decompose shape circumferenlially. Differences between the group means of repeated measurements were statistically evaluated using the Adaptive Neyman Test with no assumptions of normality, wiich identified the number of Fourier orders which contributed to the minimum p-alue. Results: Along radiais, for Legendrcs 0. 1, 1. 5. and 6. maximally significanl differences were found between preoperative and both postoperative time periods and between the two postoperative time periods, using onh the Oth Fourier. Coefficients that increased from preoperative to one month decreased from one month to one year, and vice versa. Conclusions: Almost all shape changes were rotationally sy nmetric. The shape components that changed during and immediately after surger were the same components that regressed during the healing period from one month to one year. Color-coded maps of height and curvature illustrate the efficacy of modeling, the typical shape changes induced h\ PRK. and the clinical interpretation of shape decomposition.