Can we model keratoconus’ growth?

Abstract

Purpose : Keratoconus is a bilateral disease, characterized by steepening and thinning of corneal tissue, which alters its mechanical properties. Etiology and development of this pathology are still not clear, even if its histopathology has been described in literature. We developed a finite-element strain-driven keratoconus growth model, based on non-linear elastoplastic formulation, to establish the growth process, and we conducted a material sensitivity analysis, to see how the matrix, the collagen fibers and their orientation could affect the growth.

Methods : An average corneal model was built, an intraocular pressure of 15 mmHg was applied to the posterior corneal surface and the corneal base was fixed. A strain-driven law was defined as φ = λ_e - λ_crit, where λ_crit is the maximum principal strain at model’s pressurization and λ_e is the strain when the degradation and growth of the corneal tissue start. When φ>0, in-plane growth starts following the law: F_g^t = F_g^t-1 + K⁺((F_{g max} - F_g^t)/(F_{g max} - 1))^γ *φ*dtime, where F_g is the growth component of the deformation gradient F=F_eF_g, composed also by an elastic (F_e) contribution, F_{g max} is the growth limit, K⁺ and γ are two constants for growth’s velocity and dtime is the time increment. To understand how each component of the corneal material model (Fig. 1) contributes to the growth, we set the material degradation of one component of the cornea i.e., matrix, fibers and fibers’ orientation, at time, by applying a F_{g max} ranging from 1.02 to 1.20.

Results : Fig. 1 shows the influence of the components on keratoconus’ growth. The degradation of the matrix causes an isotropic growth and, even for the low limit cases (1.02-1.04), a severe keratoconus develops (stages 3-4 according to Belin ABCD classification – Table 1). Both the degradation of fibers and the loss of fibers’ orientation cause an anisotropic growth, that appears to be more gradual, obtaining keratoconus’ stages from 1 to 4.

Conclusions : We developed a growth model able to reproduce different keratoconic shapes, depending on the severity of the case and on the degraded components, and we analyzed the influence of each material component on the growth. The interaction among different components will be studied on the same model, as different phenomena occur when keratoconus arises.

This abstract was presented at the 2024 ARVO Annual Meeting, held in Seattle, WA, May 5-9, 2024.

 

F_g in the corneal section of the models.

 

Sagittal Curvatures of the anterior and posterior surfaces (Km AS and Km PS), pachymetry and Belin ABCD classification of the cases.