Corneal Surface Reconstruction Using Modal Mathematical Methods. A Comparative Study.

To evaluate the complete reconstruction of both anterior and posterior surfaces of the cornea in healthy patients using Gaussian Radial Basis Functions (RBF).

Study performed in the National Network of Cooperative Research in Ophthalmology (RETICS), Universidad Politécnica de Cartagena, Spain.

A retrospective observational case series study was carried out including healthy patients without any previous ocular surgery (14 eyes of 14 patients, age 23-61 years). Three RBF functions were used for surface reconstruction, the gaussian (GA), the inverse multiquadric (IMQ) and the inverse quadratic (IQ). The raw data used for the reconstruction of the corneal surfaces were obtained from the Sirius tomographer (CSO, Italy). The mean quadratic error was evaluated for each adjustment and for each radial function.

Regarding the anterior and posterior corneal surfaces, the inverse multiquadric function presented the best fit in average value (anterior: 6.52025e-25; posterior: 9.76734e-30) for them both, when compared to the Gaussian function (anterior: 1.27699e-15; posterior: 1.00152e-27) and the inverse quadric function (anterior: 8.78742e-21; posterior: 6.44973e-30). Regarding computational cost, it was same for all reconstructions.

Gaussian Radial Basis Functions are valid modal mathematical methods for the complete reconstruction of non-pathological corneas. From a mathematical modelling point of view, the three reconstruction functions could be considered valid, since the average adjustment is above the intrinsic error of measurement of the equipment itself. The complete reconstruction of corneal geometries (anterior vs posterior) is an important factor to consider when aiming to improve the characterization of the corneal structure from corneal topographies. Complete development of corneal surfaces may help to improve detection of incipient corneal pathologies that may occur in limbal and peripheral corneal regions.