A forward incremental prestressing method with application to inverse parameter estimations and eye-specific simulations of posterior scleral shells

Abstract

Numerical simulations or inverse numerical analyses of individual eyes or eye segments are often based on an eye-specific geometry obtained from in vivo medical images such as computed tomography (CT) scans or from in vitro 3D digitiser scans. These eye-specific geometries are usually measured while the eye is subjected to internal pressure. Due to the nonlinear stiffening of the collagen fibril network in the eye, numerical incorporation of the pre-existing stress/strain state may be essential for realistic eye-specific computational simulations. Existing prestressing methods either compute accurate predictions of the prestressed state or guarantee a unique solution. In this contribution, a forward incremental prestressing method is presented which unifies the advantages of the existing approaches by providing accurate and unique predictions of the pre-existing stress/strain state at the true measured geometry. The impact of prestressing is investigated on (i) the inverse constitutive parameter identification of a synthetic sclera inflation test and (ii) an eye-specific simulation that estimates the realistic mechanical response of a pre-loaded posterior monkey scleral shell. Evaluation of the pre-existing stress/strain state in the inverse analysis had a significant impact on the reproducibility of the constitutive parameters but may be estimated based on an approximative approach. The eye-specific simulation of one monkey eye shows that prestressing is required for accurate displacement and stress/strain predictions. The numerical results revealed an increasing error in displacement, strain and stress predictions with increasing pre-existing pressure load when the pre-stress/strain state is disregarded. Disregarding the prestress may lead to a significant underestimation of the strain/stress environment in the sclera and overestimation in the lamina cribrosa.

Keywords::

• prestressing
• sclera
• eye-specific models
• inverse problems
• inflation experiments

Acknowledgements

The authors would like to thank Michael D. Roberts, Vicente Grau, Johnathan Grimm and Juan Reynaud for their involvement in creating the eye-specific model and to Claude F. Burgoyne for use of histologic data on which the monkey eye model was based.

Notes

Supported in part by U.S. Public Health service Grants R01-EY18926 (JCD), R01-EY19333 (JCD) and R01-EY011610 from the National Eye Institute, National Institutes of Health, Bethesda, Maryland; and the Legacy Good Samaritan Foundation, Portland, OR.