Corneal topography analysis has institutional review board IRB approval at the study sites where the research was conducted. All research adhered to the tenets of the Declaration of Helsinki. Corneal topography data were collected and measured with the corneal topography modeling system (TMS-1 instrument, software ver. 1.61; Tomey, Inc., Waltham, MA) and concurrent high-contrast, best spectacle-corrected visual acuity (BSCVA) measurements for each patient were obtained from clinical records. The ring detection and reconstruction algorithms used in the software are identical with the ones currently in use in the TMS-2N and TMS-3 (Tomey, Inc.) systems currently available. We did not use topography maps with poor or questionable mire images for analysis, nor did we use maps that had missing data within the zone of analysis. The data set consisted of 32 keratoconus (KC) cases and 27 postoperative penetrating keratoplasty (PKP) cases obtained from the LSU Eye Center clinic, and 29 postconductive keratoplasty (CK; Refractec, Inc., Irvine, CA) cases obtained from the Southern Vision Institute in New Orleans, courtesy of Marguerite McDonald (88 total cases). The purpose of using these three categories was to provide a wide range of visual acuities from −0.2 to 1.3 logarithm of the minimum angle of resolution (LogMAR) units (20/12.5–20/400).
Image analysis software for computer tomography (CTView 4.07; Sarver and Associates, Merritt Island, FL) was used for retrospective analysis of the corneal topography for two parameters: the corneal wavefront error and the corneal elevation surface fit error, based on a Zernike polynomial fitting procedure. With CTView analysis, a zone of the corneal surface is used to define the “pupil” across which the wave aberration is determined. The number of orders of Zernike terms desired to fit the surface is user selectable, and the user also has control over the inclusion and extraction of specific aberrations during the analysis by using an individual Zernike term-masking option. The wavefront error is presented both in terms of the signed coefficient values and as RMS values.
To determine the positive and negative values of the Zernike terms, a reference surface sphere is needed. This reference sphere is determined from the average surface curvature of the corneal topography. In the present study, a 4-mm diameter zone was used to establish the reference wavefront, as well as to analyze the wavefront error and surface elevation fit error. A 4-mm pupil was chosen, because it corresponds closely to the average adult pupil diameter during photopic viewing conditions and under the typical clinical conditions in which visual acuity is assessed. The analysis was performed with a 4th-order Zernike polynomial expansion and then repeated using a 10th-order expansion. For the wavefront error, the 0th-order piston term and the 1st-order tip and tilt terms were removed, using the CTView Zernike term-masking option, leaving only 2nd-order and higher terms to define the aberrations that generate blur. The wavefront error and elevation fit error obtained from CTView analysis of each map were recorded as the sum of the RMS error and expressed in micrometers.
The BSCVA of each case was plotted as a function of the wavefront error and the elevation fit error for each of the two expansion series. BSCVA was obtained under ordinary photopic viewing conditions, which would have resulted in a pupil diameter of approximately 4 mm on average. Because pupil size can fluctuate slightly during the course of acuity testing, assigning a constant pupil diameter to the BSCVA measure is not meaningful, but using an average diameter is acceptable. Linear regression analysis was performed to determine the strength (R 2) of each correlation from the Pearson product moment correlation coefficient (R). If it had been possible to determine the patient’s precise pupil diameter for the BSCVA measurement, the correlations we obtained would have been more significant, but the correlation coefficient would not necessarily have changed. A t-test on regressions was performed to assess whether the correlations were significant among the different test conditions.