Determination of corneal asphericity after myopia surgery with the excimerlaser: A mathematical model

PURPOSE. TO determine the theoretical change of corneal asphericity within the zone of laser ablation after a conventional myopia treatment, which con forms to Munnerlyn's paraxial formula and in which the initial corneal asph ericity is not taken into consideration. METHODS. The preoperative corneal shape in cross section was modeled as a c onic section of apical radius R-1 and shape factor p(2). A myopia treatment was simulated, and the equation of the postoperative corneal section withi n the optical zone was calculated by subtracting the ablation profile confo rming to a general equation published by Munnerlyn et al. The apical radius of curvature r(2) of the postoperative profile was calculated analytically . The postoperative corneal shape was fitted by a conic section, with an ap ical radius equal to r(2) and a shape factor p(2) equal to the value that i nduced the lowest sum of horizontal residuals and the lowest sum of squared residuals. These calculations were repeated for a range of different diopt ric treatments, initial shape factor values, and radii of curvature to dete rmine the change of corneal asphericity within the optical zone of treatmen t. RESULTS. Analytical calculation of r(2) showed it to be independent of the initial preoperative shape factor p(1). The determination of p(2) was unamb iguous, because the same value induced both the lowest sum of residuals and the lowest sum of the squared residuals. For corneas initially prolate (p( 1) < 1), prolateness increased (p(2) < p(2) < 1), whereas for oblate cornea s (p(1) > 1), oblateness increased (p(2) > p(2) > 1) within the treated zon e after myopia treatment. This trend increased with the increasing magnitud e of treatment and decreased with increasing initial apical radius of curva ture R-1. CONCLUSIONS. After conventional myopic excimer laser treatment conforming t o Munnerlyn's paraxial formula, the postoperative theoretical corneal asphe ricity can be accurately approximated by a best-fit conic section. For init ially prolate corneas, there is a discrepancy between the clinically report ed topographic trend to oblateness after excimer laser surgery for myopia a nd the results of these theoretical calculations.