Calibrating corneal material model parameters using only inflation data: An ill‐posed problem

Abstract

SUMMARYGoldmann applanation tonometry (GAT) is a method used to estimate the intraocular pressure by measuring the indentation resistance of the cornea. A popular approach to investigate the sensitivity of GAT results to material and geometry variations is to perform numerical modelling using the finite element method, for which a calibrated material model is required. These material models are typically calibrated using experimental inflation data by solving an inverse problem. In the inverse problem, the underlying material constitutive behaviour is inferred from the measured macroscopic response (chamber pressure versus apical displacement). In this study, a biomechanically motivated elastic fibre-reinforced corneal material model is chosen. The inverse problem of calibrating the corneal material model parameters using only experimental inflation data is demonstrated to be ill-posed, with small variations in the experimental data leading to large differences in the calibrated model parameters. This can result in different groups of researchers, calibrating their material model with the same inflation test data, drawing vastly different conclusions about the effect of material parameters on GAT results. It is further demonstrated that multiple loading scenarios, such as inflation as well as bending, would be required to reliably calibrate such a corneal material model.

A predictive tool for determining patient-specific mechanical properties of human corneal tissue

“…Therefore, it appears that the mechanical behavior of the matrix will play a significant role in reproducing the corneal response during a tonometry test. Furthermore, some authors have suggested that only one in vivo technique may not be sufficiently accurate for properly characterizing the material properties, such as Kok et al [19,4]. However, at present, it is the only clinical device that permits a non-invasive analysis of the human cornea, as biaxial or inflation tests can only be performed ex vivo.…”

“…The range for the material parameters was determined by considering the experimental results from an inflation test reported in the literature [24,38] and the physiological response of the cornea to an air-puff device (i.e., displacement of the cornea using a CorVis device). First, the inflation tests were used to initially screen the model parameters, to constrain the search space of the optimization and in an attempt to avoid an ill-posed solution [19]. Second, the range of each material parameter was then determined such that the in silico inflation curve was within the experimental window.…”

Individualized Characterization of the Distribution of Collagen Fibril Dispersion Using Optical Aberrations of the Cornea for Biomechanical Models

“…To focus on the characterization of the distribution of fibril dispersion κ(ρ, θ), we did not vary other biomechanical parameters and used average values from previous literature. 4 , 31 , 37 The same simplified axially symmetric corneal geometry (0.572-mm central thickness, 0.779-mm peripheral thickness, and 7.97-mm radius of curvature of anterior surface) was used for the three models. 31 The preferential orientations of the collagen fibrils were also assumed to be known and modeled based on previous studies.…”

“… 4 Material parameter k 1 and k 2 were set to average values of 91.55 kPa and 785.68, respectively. 37 …”

“…Average values of 91.55 kPa and 785.68 37 were assumed for material parameters k 1 and k 2 . There are no published data regarding the collagen fibril orientation in rhesus monkey corneas, but because rhesus monkeys and human are closely related species the preferential orientations of the collagen fibrils in the monkey cornea model were assumed to be the same as the human cornea model in previous numerical simulations.…”