Finite Element Modelling of Corneal Paired Arcuate Relaxing Incisions for the Treatment of Astigmatism

Background: Corneal astigmatism is a refractive error caused by distortion of the normal shape of the cornea. Most corneal astigmatism is regular and can be corrected using a sphero-cylindrical lens. When the refractive error of regular astigmatism is too high, arcuate relaxing incisions can be made. Currently most incisions are done by hand but can also be made using femtosecond laser.

The aim of this study is to develop a method to calculate the optimal geometrical parameters of relaxing corneal incisions in specific patients.

Methods: Data obtained from a Pentacam corneal topography of a healthy patient, was used to create a similar patient-based model. Abaqus FEM software was used to analyze the changes caused by paired arcuate relaxing incisions preformed at different parameters. A Python-based code was written to calculate the radii of curvature, for the purpose of evaluating the changes in refractive power caused by the incisions.

Results: Paired arcuate incisions done on the steepest corneal meridian caused its flattening. This effect was increased when the incisions were deeper (300 vs. 400 microns) and closer to the central cornea (3 vs 4 mm away from the center). Performing longer incisions, resulted in increased effect but only up to 60 degrees of arc length. Conversely, when tested on the human-based cornea model, 70 degrees incision had a larger effect than 60 degrees incisions.

Conclusion: Unexpected differences found between the effect of incisions in the theoretical model and the human-based model, demonstrate the complexity of anterior segment bio-mechanics. Further development of this tool can allow us to study the effect of incisions with different geometries on regular and irregular astigmatism.