Mathematical investigation of posterior corneal surface elevation topography in regression following LASIK for myopia

Abstract

Abstract: : Purpose: Several explanations for regression following corneal laser surgery for myopia have been advanced, but changes in the posterior surface have not been extensively investigated. Here 3 mathematical models describing the association between regression and posterior surface topographical changes are evaluated. Methods: The database of patients attending the St. Paul's Eye Unit Excimer Laser Service was scrutinised to identify patients who regressed following LASIK for myopia. Regression was defined as change in mean spherical equivalent (MSE) subjective refraction from week 1 to 12 months post–operatively of at least 1D. All patients received a complete pre and post–operative examination including refraction and Orbscan elevation topography. Fifty four eyes were identified. Pre–operative MSE was –8.5D (range –3 to –18). Mean regression was 1.56D (range 1 to 3.25). A group of eyes that regressed less than 0.5D was used as a control group. Raw posterior elevation data was exported to a MatLab programming environment. Three graphical models were fitted by least–square methods: i. simple 3–term aconic; ii. 5–term general ellipsotoric (with rotation but orthogonal principal axes); iii. 5–level Zernike polynomial. These models were considered in isolation and in the optimal combination identified using principal component analysis (PCA) followed by a 3–layer adaptative artificial neural network (AANN) Results: The general ellisotoric and Zernike models performed equally well (∼75% accuracy) in discriminating regression and normal groups. The 3–term aconic had only an accuracy of 50%. However, only the Zernike model achived a significant correlation (r2∼0.6, p<0.05) with degree of regression in the group that regressed. The optimal combination (PCA & AANN) of the three models did not show significantly improved discrimination (5–term general ellipsoid and Zernike) or correlation (Zernike) above those achived with the individual models alone. Conclusions:A 5–level Zernike description of Orbscan posterior elevation topography can be used to identify and classify regression after LASIK for myopia.

Keywords: refractive surgery: LASIK • topography • myopia