[Fourier analysis as a mathematical model for evaluating and presenting postoperative corneal topography data after non-mechanical perforating keratoplasty]

Abstract

Background: Videokeratography has given the possibility to obtain information in curvature from a much larger region of the cornea than that covered by keratometry. Fourier analysis as a mathematical model can be used to represent real physical attributes of the cornea and to divide corneal topography in its basic components: the zero-frequency component as the mean ring power, the one-cycle component as a representation of decentration and the two-cycle component as a representation of regular corneal toricity. The purpose of this study was the reconstruction of the corneal refraction after penetrating keratoplasty with a small number of characteristic parameters and the evaluation of the time course of the fourier coefficients as indices for a regular astigmatic cornea in the postkeratoplasty period including suture removal.

Patients and methods: Fourty patients (group 1: 20 primary dystrophies, group 2: 20 keratoconus) underwent nonmechanical trephination (excimer laser MEL60, Aesculap-Meditec, Heroldsberg, Germany) in penetrating keratoplasty. All procedures (7.5 mm in dystrophies, 8.0 mm in keratoconus, 8 orientation teeth, double-running 10-0 nylon suture) were performed by one surgeon. At a postoperative gate of 6 weeks, 6 months, before partial suture removal and after complete suture removal, corneal topography (TMS1, Tomey, Tennenlohe, Germany), keratometry, visual acuity and subjective refraction were assessed. Radial approximation with a 5th order polynomial fit of the refractive data on 25 non-centric rings of the TMS, within 256 hemimeridians was performed to get data at equally spaced concentric rings. Fast Fourier transformation of the data sets in the mid periphery (1.4-1.8 mm apical distance) was done to get DC-, one-cycle and two-cycle component. Fourier coefficients were correlated with keratometric readings, subjective refractive values and visual acuity.

Results: Spherical equivalent was fairly constant in the postoperative interval before suture removal. After suture removal, a corneal flattening of about 3 diopters occurred. The one-cycle component before suture removal tended to be higher in group 1 compared to group 2 before suture removal. This difference was statistically significant (p = 0.01) after suture removal. Comparing keratometry, calculated meridians by the Tomey software, two-cycle component of the fourier decomposition and subjective refraction, the best correlation (p = 0.02) was observed between two-cycle-component and the refractive cylinder in amplitude and axis after suture removal. Best corrected visual acuity was inversely correlated with the amount of energy of higher harmonics compared to the whole energy before (p = 0.04) and after (p = 0.01) suture removal.

Conclusions: Fourier transformation renders reconstruction of corneal topography data with a marked data reduction and a small error. From fourier coefficients conclusions may be drawn concerning potential best-corrected visual acuity and amplitude/axis of subjective cylinder, even in corneas with severe local irregularities.