Biomechanical Properties of the Ocular Globe Based on Ex Vivo Testing and Multiscale Numerical Modelling

摘要

The present study is the culmination of quantifying and qualitative experimental and numerical research representing biomechanical behaviour of the human eye. A new experimental technique for testing intact eye globes in a form that is representative of in vivo conditions is developed which is suitable for determining the material properties of the complete outer ocular tunic. A test rig has been developed to provide closed-loop control of either applied intraocular pressure or resulting apical displacement, measurement of displacements across the external surface of eye globe using high-resolution digital cameras and digital image correlation software, prevention of rigid-body motion and protection of ocular surface from environmental drying. The method has been demonstrated on one human and i one porcine eye globe, which were cyclically loaded. Finite element models based on specimen specific tomography, free from rotational symmetry, were used along with experimental pressure-displacement data in an inverse analysis process to derive the mechanical properties of tissue in different regions of the eye’s outer tunic. The test method enabled monitoring of mechanical response to intraocular pressure variation across the surface of the eye globe. For the two eyes tested, the method showed a gradual change in the sclera’s stiffness from a maximum at the limbus to a minimum at the posterior pole, while in the cornea the stiffness was highest at the centre and lowest in the peripheral zone. Further, for both the sclera and cornea, the load-displacement behaviour did not vary significantly between loading cycles. The first methodology capable of mechanically testing intact eye globes, with applied loads and boundary conditions that closely represent in vivo conditions has been introduced. The method enables determination of the regional variation in mechanical behaviour across the ocular surface. Two numerical models based in continuum mechanics theory have been developed which represent the 3D anisotropic behaviour of the corneal stroma. Experimental data has been gathered from a number of previous studies to provide the basis and calibration parameters for the numerical modelling. The resulting models introduce numerical representation of collagen fibril density and its related regional variation, interlamellar cohesion and age-related stiffening in anisotropic and viscoelastic models of the human cornea. Further, the models incorporate previous modelling developments including representation of lamellae anisotropy and stiffness of the underlying matrix. Wide angle X-ray scattering has provided measured data which quantifies relative fibril anisotropy in the 2D domain. Accurate numerical description of material response to deformation is essential to providing representative simulations of corneal behaviour. Representing experimentally obtained 2D anisotropy and regional density variation in the 3D domain is an essential component of this accuracy. The constitutive model was incorporated into finite element analyses. Combining with inverse analysis, the model was calibrated to an extensive experimental database of ex vivo corneal inflation tests and ex vivo corneal shear tests. This model represented stiffness of the underlying matrix which is 2−3 orders of magnitude lower than the mechanical response representing the collagen fibrils in the lamellae. The presented model, along with its age dependent material coefficients, allows finite element modelling for an individual patient with material stiffness approximated based on their age. This has great potential to be used in both daily clinical practice for the planning and optimisation of corrective procedures and in pre-clinical optimisation of diagnostic procedures. The second constitutive numerical model based on the continuum mechanics theory was developed which extended the representation of the model above to include both age-related viscoelastic stiffening behaviour of the human cornea. Experimental data gathered from a number of previous studies on 48 ex vivo human cornea (inflation and shear tests) enabled numerical model calibration. The present study suggests that stiffness parallel to the lamellae of the cornea approximately doubles from an increase in strain-rate of 0.5 − 5%/min. While the underlying stromal matrix provides a stiffness 2−3 orders of magnitude lower than the lamellae. The model has been simultaneously calibrated to within 5% error across three age groups ranging from 50 − 95, multiple strain-rates and multiple loading scenarios. Age and strain-rate dependent material coefficients allow finite element modelling for an individual patient with material stiffness approximated by their age under varying loading scenarios. This present study addresses a significant gap in numerical representation of the cornea and has great potential in both daily clinical practice particularly in highly viscoelastic dependent simulations such as non-contact tomometry. Related to this thesis, the author has either primarily or secondarily authored the following related journal articles which are included in this thesis in modified forms: Whitford C. & Elsheikh A., Corneal Biomechanics Testing Methods, May 2014, Chinese Journal of Optometry and Ophthalmology Visual Science; Whitford C., Joda A., Jones S., Bao F., Rama P. & Elsheikh A., Ex-vivo Test- ing of Intact Eye Globes Under Inflation Conditions to Determine Regional Variation of Mechanical Stiffness, July 2016, Eye and Vision. Elsheikh, A., Whitford, C., Hamarashid, R., Kassem, W., Joda, A., B¨uchler, P., Stress free configuration of the human eye. Febuary 2013, Medical Engineering & Physics. Yu J., Bao F., Feng Y., Whitford C., Ye T., Huang Y., Wang Q., Elsheikh A., Assessment of Corneal Biomechanical Behavior Under Posterior and Ante- rior Pressure. January 2013, Journal of Refractive Surgery. Whitford C., Studer H., Boote K., Meek K.M. & Elsheikh A., Biomechanical Model of the Human Cornea: Considering Shear Stiffness and Regional Variation of Collagen Anisotropy and Density, Feb 2015, Journal of the Mechanical Behavior of Biomedical Materials. Elsheikh A., McMonnies C.W., Whitford C. & Boneham G.C., In-vivo study of Corneal Responses to Increased Intraocular Pressure, 2015, Eye and Vision. An additional journal publication has been prepared from the content in this present study: Whitford C., Movchan N. & Elsheikh A., A Viscoelastic Hyperelastic Anisotropic Model of the Human Cornea. Further, two book chapters have been published which related to this thesis: Whitford C., Studer H., Boote C., Meek K. & Elsheikh A., Modelo Biomecnico de la Crnea Humana Considerando la Variacin Regional de la Anisotropa, la Densidad y la Cohesin Interlaminar de las Fibrillas de Colgeno, in Biomec- nica y Arquitectura Corneal, May 2014. Geraghty B., Whitford C., Boote C., Akhtar R,. & Elsheikh A., Age-Related Variation in the Biomechanical and Structural Properties of the Corneo- Scleral Tunic, in Mechanical Properties of Ageing Soft Tissues, January 2015. In addition, a number of conference proceedings have been published.