Biomechanics of the keratoconic cornea: Theory, segmentation, pressure distribution, and coupled FE-optimization algorithm

Abstract

Understanding of the corneal biomechanical properties is of high interest due to its potential application in the early diagnosis of keratoconus (KC). KC by itself is a non-inflammatory eye disorder causes corneal structural and/or compositional anomalies. The biomechanically weakened cornea is no longer able to preserve the normal shape of the cornea against the intraocular pressure (IOP) and gradually starts to bulge outward, invoking a conical shape and subsequent distorted vision. The most popular way to measure the in vivo corneal biomechanical properties is the CorVis-ST, which enables to analyze the dynamic response of the cornea under a temporary air puff pressure. However, the complications, such as the lack of knowledge on the accurate air-puff pressure distribution on the cornea's surface as a function of the distance from the apex of the cornea as well as the time, hinder us to have a reliable estimation of the cornea's mechanical parameters. This study aims to establish patient-specific geometries of the healthy and KC corneas and calculate the pressure distribution on the cornea's surface as a function of both the distance from the apex of the cornea and time, and thereafter, the viscoelastic mechanical properties of both the healthy and KC corneas using a coupled finite element (FE)-optimization algorithm. To do that, the dynamic deformation response of six healthy and six KC corneas were measured via CorVis-ST. The videos of the in vivo deformation of the corneas under the applied air puff pressure were segmented using our segmentation algorithm to determine the anterior and posterior curvatures of the corneas during the dynamic movement of the cornea. The FE model of the corneas were established using the segmented data and subjected to a negative (pre-stress), positive IOP, and air puff pressure while the floating boundary conditions were applied to the two ends of the corneas' FE models. The simulation results were imported into a loop of FE-optimization algorithm and analyzed until the deformation amplitude at the apex of the cornea reaches to its minimum difference compared to the clinical data by CorVis-ST. The results revealed that the pressure distributions found in the literature as a function of the distance from the apex of the cornea and time unable to provide satisfactory results. Therefore, the pressure distributions both as a function of the distance and time were optimized using our coupled FE-optimization algorithm and employed to estimate the viscoelastic properties of the healthy and KC corneas. The mean percentage error (MPE) of 8.45% and 10.79% were found for the healthy and KC corneas compared to the clinical data of CorVis-ST, respectively. The results also revealed a significantly higher short-time shear modulus for the KC (62.33 MPa) compared to the healthy (37.45 MPa) corneas while the long-time shear modulus of both the healthy and KC corneas were almost the same (4.01 vs. 3.91 MPa). The proposed algorithm is a noninvasive technique capable of accurately estimating the viscoelastic mechanical properties of the cornea, which can contribute to understand the mechanism of KC development and improve diagnosis and intervention in KC.

Keywords: Air puff; CorVis-ST; Cornea; Inverse finite element; Keratoconus; Optimization.