Error in the estimation of ablation centration using pachymetric difference maps.

In the article “Topographic Analysis of the Centration of the Treatment Zone After SMILE for Myopia and Comparison to FS-LASIK: Subjective Versus Objective Alignment” by Lazaridis et al.,1 a corneal thickness difference map was used to determine centration. The authors concluded that “the corneal thickness differential map in Scheimpflug-based systems is a useful tool to display the treatment zone and to estimate the centration after refractive surgery.” However, unlike curvature or elevation, corneal thickness is calculated normal to the anterior surface for most tomographic systems, including the Pentacam (Oculus Optikgeräte, Wetzlar, Germany), and then reflected to a two-dimensional display. This leads to two main problems. The anterior surface has been substantially altered and thus the normal-to-the-surface calculation and the direction in which corneal thickness is calculated are not comparable between preoperative and postoperative displays. Also, when potential misalignment exists between the preoperative and postoperative corneas relative to the reference axis (due to a change in the line of sight or other cause), the difference display can be adversely affected. This is illustrated in Figure 1A with a patient who underwent LASIK. The calculated point of maximum corneal thickness difference is far decentered from the thinnest points in both the preoperative and postoperative maps. A mathematical simulation was performed to investigate misalignment when calculating a corneal thickness difference map.2 The preoperative cornea was modeled as two aspheric ellipsoids, one representing the anterior surface with central radius of curvature (Ro = 7.8 mm, eccentricity = 0.5) and one representing the posterior surface (Ro = 6.4 mm, eccentricity = 0.45). Central corneal thickness was set to 500 μm. A 6-mm ablation zone was simulated with the Munnerlyn approach and central ablation depth of 50 μm, leading to a postoperative Ro value of 8.55 mm. Figure 1B shows the simulated corneal thickness difference map for a translation of 0.4 mm and a rotation of 5° of the specified postoperative cornea relative to the preoperative cornea. Note that the apparent point of maximum ablation depth is decentered, despite the simulation of perfectly centered treatment. Also note the pattern of tilt in the difference map, similar to the corneal thickness difference map in Figure 1A. A corneal thickness difference map is not an appropriate method to determine treatment centration. Although the case in Figure 1A is extreme because the locations of thinnest spots preoperatively and postoperatively are clearly displaced, it nevertheless illustrates the fundamental problem in using a corneal thickness difference map to determine treatment centration. In fact, this may explain the outliers Lazaridis et al. noted in their discussion. It is far more likely that artifact in the way the corneal thickness difference map is calculated would be the source for the outliers, rather than extreme decentration during the treatment itself. The many different ways in which corneal thickness can be interpreted are highlighted in a recent editorial3 due to the multiple possible algorithms that exist for defining the distance between two surfaces. This problem is not apparent in either the curvature or elevation difference maps because the direction of the subtraction is parallel to the reference axis rather than normal to the surface.