Ellipsoidal fitting of corneal topography data after arcuate keratotomies with compression sutures

Abstract

Background and objective: After paired arcuate keratotomies and compression sutures (AK) for treatment of high postkeratoplasty astigmatism, corneal topography tends to be irregular. The purpose of this study was to demonstrate a mathematical method for approximation of discrete corneal topography power data with an ellipsoid for better appreciation of the clinical outcome after AK.

Patients and methods: Thirty-one eyes of 28 consecutive patient who underwent AK for excessive postkeratoplasty astigmatism were studied. Regular keratometry, corneal topography (TMS-1), subjective refraction, and best-corrected visual acuity (VA) were assessed preoperatively and at 1 week and 1 year postoperatively. A simplex algorithm was applied for fitting an ellipsoidal surface to raw corneal topography power data. A set of parameters (meridional power, axis, and asphericity) were calculated. The cylinder of subjective refraction was correlated with the keratometric readings, the simulated keratometry (SimK) of the topography system, and the respective parameters of the model surface.

Results: Keratometric astigmatism and the cylinder of the model surface decreased from 8.1 +/- 3.2 and 7.9 +/- 2.9 D preoperatively to 4.5 +/- 2.1 and 5.3 +/- 2.0 D after 1 year, respectively. The asphericity in both meridional cross sections changed from a prolate ellipse preoperatively to an ablate ellipse at the early postoperative follow-up stage. Regarding the cylinder axis, there was a significant correlation of the model surface with the refractive cylinder at all examinations (P < .05), whereas there was no significant correlation of the SimK axis and the refractive cylinder axis.

Conclusion: The approximation of corneal topography power data with an ellipsoidal model surface renders reconstruction of clinically relevant corneal topography parameters, including corneal asphericity with a marked data compression. Even in markedly irregular corneal surfaces, such as after AK, the correlation of amount/axis of refractive cylinder with the model surface parameters is more accurate than it is with respective SimK values of corneal topography analysis.