A Fractal Approach to Nonlinear Topographical Features of Healthy and Keratoconus Corneas Pre- and Post-Operation of Intracorneal Implants

Abstract

Fractal dimension (FD) together with advances in imaging technologies has provided an increasing application of digital images to interpret biological phenomena. In ophthalmology, topography-based images are increasingly used in common practices of clinical settings. They provide detailed information about corneal surfaces. Few-micron alterations of the corneal geometry to the elevation and curvature cause a highly multifocal surface, change the corneal optical power up to several diopters, and therefore adversely affect the individual’s vision. Keratoconus (KCN) is a corneal disease characterized by a local alteration of the corneal anatomical and mechanical features. The formation of cone-shaped regions accompanied by thinning and weakening of the cornea are the major manifestations of KCN. The implantation of tiny arc-like polymeric sections, known as intracorneal implants, is considered to be effective in restoring the corneal curvature. This study investigated the FD nature of healthy corneas (n = 7) and compared it to the corresponding values before and after intracorneal implant surgery in KCN patients (n = 7). The generalized Hurst exponent, Higuchi, and Katz FDs were computed for topography-based parameters of corneal surfaces: front elevation (ELE-front), back elevation (ELE-back), and corneal curvature (CURV). The Katz FD showed better discriminating ability for the diseased group. It could reveal a significant difference between the healthy corneas and both pre- and post-implantation topographies (p < 0.001). Moreover, the Katz dimension varied between the topographic features of KCN patients before and after the treatment (p < 0.036). We propose to describe the curvature feature of corneal topography as a “strange attractor” with a self-similar (i.e., fractal) structure according to the Katz algorithm.