Bootstrapping of Corneal Optical Coherence Tomography Data to Investigate Conic Fit Robustness

Fitting of parametric model surfaces to corneal tomographic measurement data is required in order to extract characteristic surface parameters. The purpose of this study was to develop a method for evaluating the uncertainties in characteristic surface parameters using bootstrap techniques.

We included 1684 measurements from a cataractous population performed with the tomographer Casia2. Both conoid and biconic surface models were fitted to the height data. The normalised fit error (height-reconstruction) was bootstrapped 100 times and added to the reconstructed height, extracting characteristic surface parameters (radii and asphericity for both cardinal meridians and axis of the flat meridian) for each bootstrap. The width of the 90% confidence interval of the 100 bootstraps was taken as uncertainty and quoted as a measure of the robustness of the surface fit.

As derived from bootstrapping, the mean uncertainty for the radii of curvature was 3 µm/7 µm for the conoid and 2.5 µm/3 µm for the biconic model for the corneal front/back surface, respectively. The corresponding uncertainties for the asphericity were 0.008/0.014 for the conoid and 0.001/0.001 for the biconic. The respective mean root mean squared fit error was systematically lower for the corneal front surface as compared to the back surface (1.4 µm/2.4 µm for the conoid and 1.4 µm/2.6 µm for the biconic).

Bootstrapping techniques can be applied to extract uncertainties of characteristic model parameters and yield an estimate for robustness as an alternative to evaluating repeat measurements. Further studies are required to investigate whether bootstrap uncertainties accurately reproduce those from repeat measurement analysis.