Effect of numerical modelling assumptions on the simulated corneal response during Goldmann applanation tonometry

Abstract

It is widely known that Central Corneal Thickness (CCT) and Radius of Curvature (RoC) in uence the estimated IntraOcular Pressure (IOP) obtained from Goldmann Applanation Tonometry (GAT). However, not much is known about the in uence of corneal material properties, especially in a clinical setting. Several numerical studies have been conducted in an attempt to quantify the in uence of corneal material properties on the IOP. These studies agree that corneal material properties do in uence the estimated IOP, which contradict the initial premise on which GAT was designed, namely that material properties do not in uence the obtained GAT readings. Also, there is no consensus among these studies with respect to corneal material properties, thus a wide range of proposed properties exist. A possible explanation for this range of available corneal properties is the numerical modi elling assumptions used, which seem to be quite different. Different sets of experimental in ation test data were used to calibrate the constitutive models and different limbal boundary conditions were applied to simulate the experimental setup as well as in vivo conditions during GAT simulations. Therefore the purpose of this study is to determine whether these modelling assumptions in uence the obtained IOP and ultimately the overall conclusions. A Finite Element (FE) model of the human cornea is developed, implementing a constitutive model to represent the complex corneal structure and two limbal boundary conditions. This model is then calibrated using two different sets of experimental in ation test data. During calibration of the fibre reinforced elastic constitutive model it is found that independent of the assumptions made regarding the material coe cients, that the numerical in ation data compare well with the experimental data for all cases. Using this model a GAT simulation is conducted to estimate the IOP and the in uence of the modelling assumptions, cornea geometry and material properties are then investigated. The results indicate that the modelling assumptions, cornea geometry and material properties do infuence the estimated IOP. However, when assuming the cornea ground substance stiffness to be constant, it is found that the in uence on IOP due to material properties is not as significant. A correction equation is also proposed to account for the corneal geometric properties by calibrating the numerical model for a numerically normal cornea. This is done by utilising the various data sets which are obtained during the calibration of the constitutive model with the experimental inflation test data. It is concluded that using only inflation data to calibrate the constitutive model is not sufficient to uniquely describe the corneal material. This is evident as different material data sets are obtained, even though the experimental inflation data is matched well for a variety of considered cases. Each of these material data sets, in conjunction with geometric properties, yield different estimates for IOP during GAT simulations. This study therefore recommends the use of additional experimental data, such as strip extensometry, along with inflation test data to adequately calibrate a numerical model. It should also be noted that when modelling GAT care should be taken when considering the choice of limbal boundary condition, experimental data for calibration and assumptions made with regards to material coe cients, as these choices could potentially influence the outcomes and conclusions of a study.