Experience in the application of mathematical modeling for predicting the outcome of treatment of progressive keratoconus

Abstract Original article Experience in the application of mathematical modeling for predicting the outcome of treatment of progressive keratoconus E.G. Solodkova, S.B. Izmailova, B.E. Malyugin, I.N. Zakharov, V.P. Fokin, S.V. Balalin, E.V. Lobanov, V.A. Sivolobov, V.H. Le S. Fyodorov Eye Microsurgery Federal State Institution, Volgograd branch, Volgograd, Russian Federation S. Fyodorov Eye Microsurgery Federal State Institution, Moscow, Russian Federation Volgograd State Technical University, Volgograd, Russian Federation Purpose. To analyze the results of applying mathematical modeling to plan, predict and control the effects of ultraviolet corneal crosslinking (UVCXL), to develop a customized method of local crosslinking and to evaluate its safety and effectiveness in comparison with a standard UVCXL method. Material and methods. COMSOL Multiphysics® was used for modeling of corneal biomechanics in eyes with keratoconus under external diagnostic exposure. 3D-images of stress and strain distribution in reliance to finite elements calculation were obtained. Their correlation with topographic and tomographic maps from Pentacam AXL and Corvis ST allowed defining localization and dimensions of the weakened cornea and elaborating a modified technique of UVCXL with its subsequent application in treatment of 30 persons (30 eyes) with 1st and 2nd stage keratoconus (by Amsler – Krumeich classification). Effectiveness and safety of the proposed approach were evaluated in comparison with a reference group (20 patients, 20 eyes with keratoconus of the 1st and 2nd degree, standard UVCXL). Results. This study represents application of corneal «digital double» for selection of optimal treatment option. Improvement of UCVA and BCVA was observed in all the patients within 6–12 months follow-up (p<0,01). Decrease of maximum keratometric value Kmax along with increase of biomechanical resistance with a reliable improvement of corneal rigidity SP-A1 were achieved in all the cases within 6–12 months follow-up (p<0,01). A credible amelioration of UCVA, BCVA and SP-A1 along with a decrease of an average Kmax were registered one month postoperatively after the standard UVCXL. Effectiveness of the proposed UVCXL technique was confirmed by incurrence of demarcation line in site of UVCXL application at the depth of 242,37±46,27 µm. Conclusion. The proposed personalized topographically and tomographically reliable method of UVCXL provides an evident stabilizing action due to improvement of corneal biomechanical resistance. Key words: corneal biomechanical properties, keratoconus, ultraviolet crosslinking of corneal collagen