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

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.

Automated summary

Fractal dimension and advances in imaging technologies have been increasingly applied to interpret biological phenomena, including in the field of ophthalmology for corneal diseases. This study investigated the fractal dimension of healthy corneas and compared it to corneas of patients with keratoconus before and after intracorneal implant surgery. The Katz fractal dimension showed better discriminating ability and revealed significant differences between healthy corneas and both pre- and post-implantation topographies. The study proposes a new method to describe the curvature feature of corneal topography.