Charles Whitford

Evaluation of the relationship of corneal biomechanical metrics with physical intraocular pressure and central corneal thickness in ex vivo rabbit eye globes

The relationship of corneal biomechanical metrics provided by the Ocular Response Analyzer (ORA) and Corvis ST (CVS) with physical intraocular pressure (IOPp) and central corneal thickness (CCT) was evaluated. Thirty fresh enucleated eyes of 30 rabbits were used in ex vivo whole globe inflation experiments. IOPp was measured with a pressure transducer and increased from 7.5 to 37.5 mmHg in steps of 7.5 mmHg while biomechanical data was acquired using the ORA and CVS. At least 3 examinations were performed at each pressure level, where CCT and twelve biomechanical metrics were recorded and analyzed as a function of IOPp. The biomechanical metrics included corneal hysteresis (CH) and corneal resistance factor (CRF), obtained by the ORA. They also included the applanation times (A1T, A2T), lengths (A1L, A2L) and velocities (A1V, A2V), in addition to the highest concavity time (HCT), peak distance (PD), radius (HR) and deformation amplitude (DA), obtained by the CVS. The variation of CCT and the twelve biomechanical metrics for the 30 rabbit eyes tested across the 5 pressure stages considered (inter-pressure differences) were statistically significant (P = 0.00). IOPp was highly to moderately correlated with most biomechanical metrics, especially CRF, A1T, A1V, A2V, PD and DA, while the relationships with CH, A2T, A1L and HCT were poor. IOP has important influences on most corneal biomechanical metrics provided by CVS and ORA. Two biomechanical metrics A1V and HR were influenced by CCT after correcting for the effect of IOP in most pressure stages, while the correlation with others were weak. Comparisons of research groups based on ORA and CVS with different IOPs and CCTs may lead to possible misinterpretations if both or one of which are not considered in the analysis.

Biomechanical model of the human cornea: considering shear stiffness and regional variation of collagen anisotropy and density

A numerical model based on continuum mechanics theory has been developed which represents 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 model introduces numerical representation of collagen fibril density and its related regional variation, interlamellar cohesion and age-related stiffening in an anisotropic model of the human cornea. Further, the model incorporates 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 analysis. 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 represents stiffness of the underlying matrix which is 2-3 orders of magnitude 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.

Stress free configuration of the human eye

Numerical simulations of eye globes often rely on topographies that have been measured in vivo using devices such as the Pentacam or OCT. The topographies, which represent the form of the already stressed eye under the existing intraocular pressure, introduce approximations in the analysis. The accuracy of the simulations could be improved if either the stress state of the eye under the effect of intraocular pressure is determined, or the stress-free form of the eye estimated prior to conducting the analysis. This study reviews earlier attempts to address this problem and assesses the performance of an iterative technique proposed by Pandolfi and Holzapfel [1], which is both simple to implement and promises high accuracy in estimating the eyes stress-free form. A parametric study has been conducted and demonstrated reliance of the error level on the level of flexibility of the eye model, especially in the cornea region. However, in all cases considered 3-4 analysis iterations were sufficient to produce a stress-free form with average errors in node location <10(-6)mm and a maximal error <10(-4)mm. This error level, which is similar to what has been achieved with other methods and orders of magnitude lower than the accuracy of current clinical topography systems, justifies the use of the technique as a pre-processing step in ocular numerical simulations.

Ex vivo testing of intact eye globes under inflation conditions to determine regional variation of mechanical stiffness

BackgroundThe eye globe exhibits significant regional variation of mechanical behaviour. The aim of this present study is to develop a new experimental technique for testing intact eye globes in a form that is representative of in vivo conditions, and therefore suitable for determining the material properties of the complete outer ocular tunic.MethodsA test rig has been developed to provide closed-loop control of either applied intra-ocular pressure or resulting apical displacement; measurement of displacements across the external surface of the eye globe using high-resolution digital cameras and digital image correlation software; prevention of rigid-body motion and protection of the ocular surface from environmental drying. The method has been demonstrated on one human and 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.ResultsThe 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.ConclusionsThe first methodology capable of mechanically testing intact eye globes, with applied loads and boundary conditions that closely represent in vivo conditions is introduced. The method enables determination of the regional variation in mechanical behaviour across the ocular surface.

Assessment of Corneal Biomechanical Behavior Under Posterior and Anterior Pressure

PURPOSE To determine the biomechanical response of the rabbit cornea to inflation under posterior and anterior pressure. METHODS Twelve Japanese white rabbits were included in the study. A randomly selected eye from each animal was subjected to posterior pressure in an inflation test rig, and the other eye was subjected to anterior pressure after manually reversing its curvature. Specimens were loaded by cycles of pressure up to 40 mmHg, and the experimentally obtained pressure-deformation data were used to derive the stress-strain behavior of each eye using an inverse modeling procedure. RESULTS The differences between the two groups in corneal thickness, diameter, and intraocular pressure (IOP) were not statistically significant (P=.935, .879 and .368, respectively). Corneas tested under posterior pressure displayed significantly higher stiffness (as measured by the tangent modulus) than those inflated by anterior pressure (P<.001). CONCLUSIONS Cornea is a nonlinear viscoelastic tissue that presents different mechanical properties when tested under posterior and anterior pressure. The determination of the behavior under both forms of pressure could contribute to the construction of accurate finite element simulations of corneal behavior and the correction of tonometric IOP measurements. The difference in mechanical behavior between anteriorly and posteriorly loaded corneas in the study, although significant, could have been partly affected by the changes in microstructure possibly caused by changing corneal form to enable anterior loading.

A viscoelastic anisotropic hyperelastic constitutive model of the human cornea

A constitutive model based on the continuum mechanics theory has been developed which represents interlamellar cohesion, regional variation of collagen fibril density, 3D anisotropy and both age-related viscoelastic and hyperelastic 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 calibration of the constitutive model by numerical analysis. Wide-angle X-ray scattering and electron microscopy provided measured data which quantify microstructural arrangements associated with stiffness. The present study measures stiffness parallel to the lamellae of the cornea which approximately doubles with an increase in strain rate from 0.5 to 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 3% error across three age groups ranging from 50 to 95 years and three strain rates across the two loading scenarios. Age and strain-rate-dependent material coefficients allow numerical simulation under varying loading scenarios for an individual patient with material stiffness approximated by their age. This present study addresses a significant gap in numerical representation of the cornea and has great potential in daily clinical practice for the planning and optimisation of corrective procedures and in preclinical optimisation of diagnostic procedures.

The hierarchical response of human corneal collagen to load

Graphical abstract

Age-Related Variation in the Biomechanical and Structural Properties of the Corneo-Scleral Tunic

With increasing age, the mechanical performance of the cornea and sclera is impaired due to structural changes in the major structural proteins, namely collagens , proteoglycans and elastin. In addition, the level of hydration in the ocular tunic decreases over time. These structural changes profoundly impact on the biomechanical properties of the corneo-scleral tunic. This chapter focuses on the structural and biomechanical changes that occur in the corneo-scleral tunic with age. The techniques that are utilized in order to determine the mechanical properties of both the cornea and sclera are discussed, and a comprehensive review of studies which have characterized age-related changes in ocular biomechanics are presented. The cornea is found to increase in stiffness with age and all the characteristics of viscoelastic behavior (creep , stress-relaxation and hysteresis) decrease with age. Similarly, the stiffness of the sclera increases markedly with age although the reported magnitude of stiffening varies significantly from one study to another. This may be related to variations amongst the different techniques that have been utilized. Increased stiffening in the cornea and the sclera with age is strongly associated with the increase in collagen crosslinking that occurs as part of the natural aging process.