UVA/riboflavin corneal cross-linking (CXL) is a common used approach to treat progressive keratoconus. This study aims to investigate the alteration of corneal stiffness following CXL by mimicking the inflation of the eye under the in vivo loading conditions. Seven paired porcine eye globes were involved in the inflation test to examine the corneal behaviour. Cornea-only model was constructed using the finite element method, without considering the deformation contribution from sclera and limbus. Inverse analysis was conducted to calibrate the non-linear material behaviours in order to reproduce the inflation test. The corneal stress and strain values were then extracted from the finite element models and tangent modulus was calculated under stress level at 0.03 MPa. UVA/riboflavin cross-linked corneas displayed a significant increase in the material stiffness. At the IOP of 27.25 mmHg, the average displacements of corneal apex were 307 ± 65 μm and 437 ± 63 μm (p = 0.02) in CXL and PBS corneas, respectively. Comparisons performed on tangent modulus ratios at a stress of 0.03 MPa, the tangent modulus measured in the corneas treated with the CXL was 2.48 ± 0.69, with a 43±24% increase comparing to its PBS control. The data supported that corneal material properties can be well-described using this inflation methods following CXL. The inflation test is valuable for investigating the mechanical response of the intact human cornea within physiological IOP ranges, providing benchmarks against which the numerical developments can be translated to clinic.    

Fresh porcine eyes were obtained from a local abattoir (Morphets, Tan house farm, Widnes) and tested within 6-9 hours after death. Soft muscular tissue was removed with surgical scissors. The superior direction was marked and the eye globe was placed in a customized compartment for accurate needle insertion through the posterior pole. The internal eye components were removed through the posterior pole using a 14G needle. The needle was then lightly glued around the posterior pole and the intra-ocular cavity was washed with 5 to 6 ml PBS (Sigma, Dorset, United Kingdom). The outer surface of the globe was continually kept hydrated by applying PBS every 2-5 minutes. Random speckles were applied on the globe by lightly spraying a waterproof and fast drying black paint to facilitate deformation tracking in post-analysis. The prepared specimen was then placed into a custom-designed eye chamber filled with PBS, and transferred onto the inflation rig.

The inflation test rig provides full-field observation of ocular response to uniform intraocular pressure (IOP) changes. The physical test equipment is fully bespoke having been designed and built in-house. The equipment features closed loop control software written in LabVIEW (version 10.0.1, RRID:SCR_014325) to regulate IOP while collecting real-time data by triggering cameras to take pictures of the globe. The obtained images are used for measurement of deformation across the globe. The specimen was clamped in a horizontally placed eye chamber with high precision real-time laser (LK-2001, Keyence, UK) pointing towards the apical displacement. An array of six high resolution digital cameras (18.0 megapixels, 550D, Canon, Tokyo, Japan) surrounding the eye chamber and a pressure adjusting tank was placed vertically to inflate the eye while taking synchronous images. The camera setup allows an angle of 25° within each pair and an angle of 120° between each set.

A custom-built LabVIEW software was used to tightly control the pressure. The experiments started by 3 pre-conditioning cycles. The pre-conditioning cycles were to ensure the eye was sitting comfortably on the needle, and the tissue behavior was repeatable (15). An initial pressure of 2.5 mmHg was used to balance the external pressure applied by PBS in the pressure chamber, and was therefore considered a zero-pressure point for the inflation test. Specimens were loaded to a maximum internal load at a medium rate of 0.55 mmHg/s for each cycle. During each cycle the eye was allowed to relax for a period of 2 minutes which was obtained experimentally to allow tissue to fully recover to its relaxation state. The behavior of specimen in the final loading cycle was used for post-analysis.

After the experiment was completed, the eye was removed from the test rig and dissected into anterior and posterior parts. Eight meridian profiles of discrete thickness measurements were selected. The thickness at each desired point on each meridian line was determined using an in-house developed Thickness Measurement Device (TMD) (LTA-HS, Newport, Oxfordshire, UK) which was developed by the Biomechanical Engineering group to measure the thickness of biological tissue. A vertical measurement probe was located at a height of about 30 mm above the centre point of the support. The probe moved down with a controlled velocity until it reached the surface of the tissue. By precisely knowing the original distance between the initial position of probe and the surface of support, the measured value was recorded as the thickness of the tissue.

To decrease the geometrical complexity and understand the effect of CXL treatment on corneas where the application of interest is, we built up a corneal-only model by excluding the sclera part from a whole globe model. In this corneal model, the orphan mesh of geometry was constructed with Abaqus 6.13 (Dassault Systèmes Simulia Corp., Rhode Island, USA) using bespoke software. The 2592 elements with 8611 total nodes adopted the hybrid and quadratic type with triangular cross-section (C3D15H), which were arranged in 12 rings across the cornea surface and 3 layers through the thickness. Corneal apex was restrained against displacement in X- and Y-directions, whereas limbus was restrained in the X-, Y-, and Z-direction. The intraocular pressure was distributed on the posterior surface of the cornea. The apical displacement of the entire cornea was extracted by the displacement of corneal apex minus the average displacement of limbus in the anterior-posterior direction.

The image profiles obtained were analyzed using a 2D DIC method named Particle Image Velocimetry (PIV) to obtain deformations on the surface of the eye (Figure 3) (21, 22). PIV compares an un-deformed and deformed image pairs of specimen surface which was speckled to present the local displacements within the selected subsets. Three discrete locations including corneal apex and limbus were measured from each camera. As only cornea was considered in the study, the cornea deformation was calculated by subtracting the average displacement of limbus in the anterior-posterior direction from the displacement of corneal apex.

An in-house built software that uses Particle Swarm Optimization (PSO) as an optimization strategy was developed in Matlab (RRID:SCR_001622) to conduct the inverse analysis optimization due to its success in the engineering applications. PSO evaluates the fitness of the apical displacement between simulation and experiment and iterates over the different values of material parameters to decrease the error until the best fitness appears. The material constitutive model chosen to demonstrate the material behavior of ocular tissue during loading was Ogden model, utilized in a number of previous studies on soft tissues.

The Ogden material model order one relies on two parameters of μ (shear modulus) and α (strain hardening exponent) to define the non-linear material behavior. The use of first order material model (N=1) reduced the complexity of optimization and thus the computational cost as a result of less variables. The values of material parameters α and μ represented the output of the inverse modelling process that resulted in the highest fitness of simulation against inflation experiment. The design optimization process adjusts the value of μ and α within the constitutive model while setting a wide lower and upper boundary range (lower boundary = [0.005, 50]; upper boundary = [0.2, 200]). The error limit of RMS was set as 10%, which terminated the optimization once the error is lower than the limit. With these parameters, stress and strain could then be extracted from the numerical modelling results. The uniaxial-mode stress was calculated through obtained μ and α in Table 2, based on the previously described method and then tangent modulus was calculated numerically from the gradient of the resulting stress-strain curve.