Patient-specific computational modeling of keratoconus progression and differential responses to collagen cross-linking

Abstract

Purpose: To model keratoconus (KC) progression and investigate the differential responses of central and eccentric cones to standard and alternative collagen cross-linking (CXL) patterns.

Methods: Three-dimensional finite element models (FEMs) were generated with clinical tomography and IOP measurements. Graded reductions in regional corneal hyperelastic properties and thickness were imposed separately in the less affected eye of a KC patient. Topographic results, including maximum curvature and first-surface, higher-order aberrations (HOAs), were compared to those of the more affected contralateral eye. In two eyes with central and eccentric cones, a standard broad-beam CXL protocol was simulated with 200- and 300-μm treatment depths and compared to spatially graded broad-beam and cone-centered CXL simulations.

Results: In a model of KC progression, maximum curvature and HOA increased as regional corneal hyperelastic properties were decreased. A topographic cone could be generated without a reduction in corneal thickness. Simulation of standard 9-mm-diameter CXL produced decreases in corneal curvature comparable to clinical reports and affected cone location. A 100-μm increase in CXL depth enhanced flattening by 24% to 34% and decreased HOA by 22% to 31%. Topographic effects were greatest with cone-centered CXL simulations.

Conclusions: Progressive hyperelastic weakening of a cornea with subclinical KC produced topographic features of manifest KC. The clinical phenomenon of topographic flattening after CXL was replicated. The magnitude and higher-order optics of this response depended on IOP and the spatial distribution of stiffening relative to the cone location. Smaller diameter simulated treatments centered on the cone provided greater reductions in curvature and HOA than a standard broad-beam CXL pattern.

Figures

Figure 1.

(A, B) Whole-eye FEM model showing the cornea and sclera. (C) A schematic representation of the model showing the weaker KC zone and the CXL zone in a standard 9-mm-diameter simulated treatment.

Figure 2.

Clinical tangential curvature maps of the anterior corneal surface of (A) the less affected right eye and (B) the more affected left eye of a patient with asymmetric KC before simulation of progression in the right eye. Tangential curvature maps of the anterior corneal surface of (C) a central cone (region of maximum curvature) in a second patient and (D) a more eccentric cone in a third patient before simulation of the CXL effects.

Figure 3.

Experimentally measured UV intensity normalized with its peak value at the center versus the unit diameter measured from a prototype UV-A source. This profile was used in simulations of variable-intensity broad-beam and cone-localized, variable-intensity treatment patterns.

Figure 4.

FEM-generated tangential curvature maps of the anterior corneal surface of the less affected eye of an asymmetric KC patient after elastic modulus reductions of (A) 10%, (B) 30%, and (C) 45%. (D–F) Associated tangential curvature difference maps for each elastic modulus decrement.

Figure 5.

Kmax as a function of the decrease in hyperelastic modulus in a simulation of KC progression in an eye with subclinical KC.

Figure 6.

Tangential curvature maps of a cornea with a central cone after simulated CXL to a maximum depth of 200 μm in (A) a standard broad-beam stiffening protocol, (B) a variable-intensity broad-beam protocol, and (C) a cone-localized, variable-intensity protocol. (D–F) The corresponding tangential curvature difference maps.

Figure 7.

Tangential curvature maps of a cornea with a central cone after simulated CXL to a maximum depth of 300 μm in (A) a standard broad-beam stiffening protocol, (B) a variable-intensity broad-beam protocol, and (C) a cone-localized, variable-intensity protocol. (D–F) The corresponding tangential curvature difference maps.

Figure 8.

Tangential curvature maps of a cornea with a more eccentric cone after simulated CXL to a maximum depth of 200 μm in (A) a standard broad-beam stiffening protocol, (B) a variable-intensity broad-beam protocol, and (C) a cone-localized, variable-intensity protocol. (D–F) The corresponding tangential curvature difference maps.

Figure 9.

Tangential curvature maps of a cornea with an eccentric cone after simulated CXL to a maximum depth of 300 μm in (A) a standard broad-beam stiffening protocol, (B) a variable-intensity broad-beam protocol, and (C) a cone-localized, variable-intensity protocol. (D–F) The corresponding tangential curvature difference maps.