Full-field deformation of bovine cornea under constrained inflation conditions

Corneal biomechanics and biomaterials

The ability to clearly observe one's environment in the visible spectrum provides a tremendous evolutionary advantage in most of the world's habitats. The complex optical processing system that has evolved in higher vertebrate animals gathers, focuses, detects, transduces, and interprets incoming visible light. The cornea resides at the front end of this imaging system, where it provides a clear optical aperture, substantial refractive power, and the structural stability required to protect the fragile intraocular components. Nature has resolved these simultaneous design requirements through an exceedingly clever manipulation of common extracellular-matrix structural materials (e.g., collagen and proteoglycans). In this review, we (a) examine the biophysical and optical roles of the cornea, (b) discuss increasingly popular approaches to altering its natural refractive properties with an emphasis on biomechanics, and (c) investigate the fast-rising science of corneal replacement via synthetic biomaterials. We close by considering relevant open problems that would benefit from the increased attention of bioengineers.

Depth-dependent transverse shear properties of the human corneal stroma

PURPOSE

To measure the transverse shear modulus of the human corneal stroma and its profile through the depth by mechanical testing, and to assess the validity of the hypothesis that the shear modulus will be greater in the anterior third due to increased interweaving of lamellae.

METHODS

Torsional rheometry was used to measure the transverse shear properties of 6 mm diameter buttons of matched human cadaver cornea pairs. One cornea from each pair was cut into thirds through the thickness with a femtosecond laser and each stromal third was tested individually. The remaining intact corneas were tested to measure full stroma shear modulus. The shear modulus from a 1% shear strain oscillatory test was measured at various levels of axial compression for all samples.

RESULTS

After controlling for axial compression, the transverse shear moduli of isolated anterior layers were significantly higher than central and posterior layers. Mean modulus values at 0% axial strain were 7.71 ± 6.34 kPa in the anterior, 1.99 ± 0.45 kPa in the center, 1.31 ± 1.01 kPa in the posterior, and 9.48 ± 2.92 kPa for full thickness samples. A mean equilibrium compressive modulus of 38.7 ± 8.6 kPa at 0% axial strain was calculated from axial compression measured during the shear tests.

CONCLUSIONS

Transverse shear moduli are two to three orders of magnitude lower than tensile moduli reported in the literature. The profile of shear moduli through the depth displayed a significant increase from posterior to anterior. This gradient supports the hypothesis and corresponds to the gradient of interwoven lamellae seen in imaging of stromal cross-sections.

A gimbal-mounted pressurization chamber for macroscopic and microscopic assessment of ocular tissues

The biomechanical model of glaucoma considers intraocular pressure-related stress and resultant strain on load bearing connective tissues of the optic nerve and surrounding peripapillary sclera as one major causative influence that effects cellular, vascular, and axonal components of the optic nerve. By this reasoning, the quantification of variations in the microstructural architecture and macromechanical response of scleral shells in glaucomatous compared to healthy populations provides an insight into any variations that exist between patient populations. While scleral shells have been tested mechanically in planar and pressure-inflation scenarios the link between the macroscopic biomechanical response and the underlying microstructure has not been determined to date. A potential roadblock to determining how the microstructure changes based on pressure is the ability to mount the spherical scleral shells in a method that does not induce unwanted stresses to the samples (for instance, in the flattening of the spherical specimens), and then capturing macroscopic and microscopic changes under pressure. Often what is done is a macroscopic test followed by sample fixation and then imaging to determine microstructural organization. We introduce a novel device and method, which allows spherical samples to be pressurized and macroscopic and microstructural behavior quantified on fully hydrated ocular specimens. The samples are pressurized and a series of markers on the surface of the sclera imaged from several different perspectives and reconstructed between pressure points to allow for mapping of nonhomogenous strain. Pictures are taken from different perspectives through the use of mounting the pressurization scheme in a gimbal that allows for positioning the sample in several different spherical coordinate system configurations. This ability to move the sclera in space about the center of the globe, coupled with an upright multiphoton microscope, allows for collecting collagen, and elastin signal in a rapid automated fashion so the entire globe can be imaged.

Computational simulation of altitude change-induced intraocular pressure alteration in patients with intravitreal gas bubbles

PURPOSE

To study the impact of altitude on the intraocular pressure (IOP) in an eye with an intravitreal gas bubble.

METHODS

A mathematical model was developed to simulate intravitreal gas bubble expansion caused by change in altitude. Mechanical deformation of the eye was simulated using a finite-element model. Intraocular pressure-driven changes in aqueous humor flow were also considered. Two cases were studied: 1) ascent from sea level to 3,000 ft followed by immediate return to sea level and 2) ascent to 3,000 ft followed by prolonged exposure to 3,000 ft. The effect of IOP-lowering medications was studied by changing the model parameters.

RESULTS

The IOP increase was directly related to the initial bubble size when ascent to 3,000 ft was simulated. When prolonged exposure to high altitude was modeled, loss of aqueous humor led to a less elevated value of IOP. In a typical simulated case, when the outflow facility was increased, the predicted IOP rise was reduced by 28%.

CONCLUSION

Theoretical modeling of an eye with an intravitreal gas bubble can help an ophthalmologist evaluate the impact of altitude-induced IOP changes. Our model suggests that IOP-lowering drugs could help manage altitude-induced IOP changes in the presence of intravitreal gas bubbles.

Scleral mechanics: comparing whole globe inflation and uniaxial testing

The purpose of this study was to assess fundamental differences between the mechanics of the posterior sclera in paired eyes using uniaxial and whole globe inflation testing, with an emphasis on the relationship between testing conditions and observed tissue behavior. Twenty porcine eyes, consisting of matched pairs from 10 pigs, were used in this study. Within pairs, one eye was tested with 10 cycles of globe pressurization to 150 mmHg (∼10× normal IOP) while biaxial strains were tracked via an optical system at the posterior sclera. An excised posterior strip from the second eye was subjected to traditional uniaxial testing in which mechanical hysteresis was recorded from 10 cycles to a peak stress of 0.13 MPa (roughly equivalent to the circumferential wall stress produced by an IOP of 150 mmHg under the thin-walled pressure vessel assumption). For approximately equivalent loads, peak strains were more than twice as high in uniaxial tests than in inflation tests. Different trends in the load-deformation plots were seen between the tests, including an extended "toe" region in the uniaxial test, a generally steeper curve in the inflation tests, and reduced variability in the inflation tests. The unique opportunity of being able to mechanically load a whole globe under near physiologic conditions alongside a standard uniaxially tested specimen reveals the effects of testing artifacts relevant to most uniaxially tested soft tissues. Whole globe inflation offers testing conditions that significantly alter load-deformation behavior relative to uniaxial testing; consequently, laboratory studies of interventions or conditions that alter scleral mechanics may greatly benefit from these findings.

Mechanical interferometry imaging for creep modeling of the cornea

PURPOSE

A novel nanoindentation technique was used to biomechanically characterize each of three main layers of the cornea by using Hertzian viscoelastic formulation of creep, the deformation resulting from sustained-force application.

METHODS

The nanoindentation method known as mechanical interferometry imaging (MII) with <1-nm displacement precision was used to observe indentation of bovine corneal epithelium, endothelium, and stroma by a spherical ferrous probe in a calibrated magnetic field. For each specimen, creep testing was performed using two different forces for 200 seconds. Measurements for single force were used to build a quantitative Hertzian model that was then used to predict creep behavior for another imposed force.

RESULTS

For all three layers, displacement measurements were highly repeatable and were well predicted by Hertzian models. Although short- and long-term stiffnesses of the endothelium were highest of the three layers at 339.2 and 20.2 kPa, respectively, both stromal stiffnesses were lowest at 100.4 and 3.6 kPa, respectively. Stiffnesses for the epithelium were intermediate at 264.6 and 12.2 kPa, respectively.

CONCLUSIONS

Precise, repeatable measurements of corneal creep behavior can be conveniently obtained using MII at mechanical scale as small as one cell thickness. When interpreted in analytical context of Hertzian viscoelasticity, MII technique proved to be a powerful tool for biomechanical characterization of time-dependent biomechanics of corneal regions.

Comparison of factors that influence the measurement of corneal hysteresis in vivo and in vitro

PURPOSE

The purpose of this study was to compare measurements of corneal hysteresis (CH) obtained in vivo, with similar measurements from excised human eyes and from excised human corneas mounted in an artificial anterior chamber.

METHODS

Corneal hysteresis was measured using an ocular response analyser (Reichert Ophthalmic Instruments) from three groups: 53 healthy normal corneas of fifty-three patients, six excised eyes and 17 excised corneas.

RESULTS

In vivo, it was found that CH was independent of gender, age and mean spherical equivalent, but has a significant inverse relationship with intraocular pressure (IOP(cc)) (r = 0.53; p < 0.0001). However, there was no correlation between CH and IOP(G) (r = 0.10; p = 461). The same inverse relationship with IOP(cc) was recorded in intact, excised eyes (r = 0.74; p < 0.0001), with no significant differences between the behaviour each individual eye. Excised corneas also showed an inverse relationship between CH and trans-corneal pressure (r = 0.72; p < 0.0001), but the measured values of CH were lower than those recorded in vivo and from intact globes. In both excised eyes and excised corneas, we found a significant correlation between CH and central corneal thickness [r = 0.86; p < 0.0001 and r = 0.611; p < 0.0005 (respectively)].

CONCLUSION

The in vitro results indicate that every normal human eye at physiological hydration shows an identical dependence of CH on IOP(cc) , the same dependence as is observed in vivo. This therefore would appear to be an intrinsic response of the tissue to a change in IOP. However, it is possible that the lower values of CH recorded from excised corneas reflect the influence of the artificial chamber replacing the eye globe, so in vivo values of CH may be influenced to some extent by the presence of the other components of the eye.

Deformation measurements and material property estimation of mouse carotid artery using a microstructure-based constitutive model

A series of pressurization and tensile loading experiments on mouse carotid arteries is performed with deformation measurements acquired during each experiment using three-dimensional digital image correlation. Using a combination of finite element analysis and a microstructure-based constitutive model to describe the response of biological tissue, the measured surface strains during pressurization, and the average axial strains during tensile loading, an inverse procedure is used to identify the optimal constitutive parameters for the mouse carotid artery. The results demonstrate that surface strain measurements can be combined with computational methods to identify material properties in a vascular tissue. Additional computational studies using the optimal material parameters for the mouse carotid artery are discussed with emphasis on the significance of the qualitative trends observed.

Patient-Specific Modeling of Corneal Refractive Surgery Outcomes and Inverse Estimation of Elastic Property Changes

The purpose of this study is to develop a 3D patient-specific finite element model (FEM) of the cornea and sclera to compare predicted and in vivo refractive outcomes and to estimate the corneal elastic property changes associated with each procedure. Both eyes of a patient who underwent laser-assisted in situ keratomileusis (LASIK) for myopic astigmatism were modeled. Pre- and postoperative Scheimpflug anterior and posterior corneal elevation maps were imported into a 3D corneo-scleral FEM with an unrestrained limbus. Preoperative corneal hyperelastic properties were chosen to account for meridional anisotropy. Inverse FEM was used to determine the undeformed corneal state that produced <0.1% error in anterior elevation between simulated and in vivo preoperative geometries. Case-specific 3D aspheric ablation profiles were simulated, and corneal topography and spherical aberration were compared at clinical intraocular pressure. The magnitude of elastic weakening of the residual corneal bed required to maximize the agreement with clinical axial power was calculated and compared with the changes in ocular response analyzer (ORA) measurements. The models produced curvature maps and spherical aberrations equivalent to in vivo measurements. For the preoperative property values used in this study, predicted elastic weakening with LASIK was as high as 55% for a radially uniform model of residual corneal weakening and 65% at the point of maximum ablation in a spatially varying model of weakening. Reductions in ORA variables were also observed. A patient-specific FEM of corneal refractive surgery is presented, which allows the estimation of surgically induced changes in corneal elastic properties. Significant elastic weakening after LASIK was required to replicate clinical topographic outcomes in this two-eye pilot study.

The in vitro inflation response of mouse sclera

The purpose of this research was to develop a reliable and repeatable inflation protocol to measure the scleral inflation response of mouse eyes to elevations in intraocular pressure (IOP), comparing the inflation response exhibited by the sclera of younger and older C57BL/6 mice. Whole, enucleated eyes from younger (2 month) and older (11 month) C57BL/6 mice were mounted by the cornea on a custom fixture and inflated according to a load-unload, ramp-hold pressurization regimen via a cannula connected to a saline-filled programmable syringe pump. First, the tissue was submitted to three load-unload cycles from 6 mmHg to 15 mmHg at a rate of 0.25 mmHg/s with ten minutes of recovery between cycles. Next the tissue was submitted to a series of ramp-hold tests to measure the creep behavior at different pressure levels. For each ramp-hold test, the tissue was loaded from 6 mmHg to the set pressure at a rate of 0.25 mmHg/s and held for 30 min, and then the specimens were unloaded to 6 mmHg for 10 min. This sequence was repeated for set pressures of: 10.5, 15, 22.5, 30, 37.5, and 45 mmHg. Scleral displacement was measured using digital image correlation (DIC), and fresh scleral thickness was measured optically for each specimen after testing. For comparison, scleral thickness was measured on untested fresh tissue and epoxy-fixed tissue from age-matched animals. Comparing the apex displacement of the different aged specimens, the sclera of older animals had a statistically significant stiffer response to pressurization than the sclera of younger animals. The stiffness of the pressure-displacement response of the apex measured in the small-strain (6-15 mmHg) and the large-strain (37.5-45 mmHg) regime, respectively, were 287 ± 100 mmHg/mm and 2381 ± 191 mmHg/mm for the older tissue and 193 ± 40 mmHg/mm and 1454 ± 93 mmHg/mm for the younger tissue (Student t-test, p<0.05). The scleral thickness varied regionally, being thickest in the peripapillary region and thinnest at the equator. Fresh scleral thickness did not differ significantly by age in this group of animals. This study presents a reliable inflation test protocol to measure the mechanical properties of mouse sclera. The inflation methodology was sensitive enough to measure scleral response to changes in IOP elevations between younger and older C57BL/6 mice. Further, the specimen-specific scleral displacement profile and thickness measurements will enable future development of specimen-specific finite element models to analyze the inflation data for material properties.

Characterization of age-related variation in corneal biomechanical properties

An experimental study has been conducted to determine the stress-strain behaviour of human corneal tissue and how the behaviour varies with age. Fifty-seven well-preserved ex vivo donor corneas aged between 30 and 99 years were subjected to cycles of posterior pressure up to 60 mm Hg while monitoring their behaviour. The corneas were mechanically clamped along their ring of scleral tissue and kept in physiological conditions of temperature and hydration. The tissue demonstrated hyper-elastic pressure-deformation and stress-strain behaviour that closely matched an exponential trend. Clear stiffening (increased resistance to deformation) with age was observed in all loading cycles, and the rate of stiffness growth was nonlinear with bias towards older specimens. With a strong statistical association between stiffness and age (p < 0.05), it was possible to develop generic stress-strain equations that were suitable for all ages between 30 and 99 years. These equations, which closely matched the experimental results, depicted corneal stiffening with age in a form suitable for implementation in numerical simulations of ocular biomechanical behaviour.

An inverse finite element method for determining the anisotropic properties of the cornea

An inverse finite element method was developed to determine the anisotropic properties of bovine cornea from an in vitro inflation experiment. The experiment used digital image correlation (DIC) to measure the three-dimensional surface geometry and displacement field of the cornea at multiple pressures. A finite element model of a bovine cornea was developed using the DIC measured surface geometry of the undeformed specimen. The model was applied to determine five parameters of an anisotropic hyperelastic model that minimized the error between the measured and computed surface displacement field and to investigate the sensitivity of the measured bovine inflation response to variations in the anisotropic properties of the cornea. The results of the parameter optimization revealed that the collagen structure of bovine cornea exhibited a high degree of anisotropy in the limbus region, which agreed with recent histological findings, and a transversely isotropic central region. The parameter study showed that the bovine corneal response to the inflation experiment was sensitive to the shear modulus of the matrix at pressures below the intraocular pressure, the properties of the collagen lamella at higher pressures, and the degree of anisotropy in the limbus region. It was not sensitive to a weak collagen anisotropy in the central region.

The use of X-ray scattering techniques to quantify the orientation and distribution of collagen in the corneal stroma

The bulk of the corneal stroma is comprised of a layered network of fibrillar collagen. Determining the architecture of this unique structure may help us to better understand the cornea's biomechanical and optical function. The analysis of diffraction patterns obtained when X-rays are passed through the regularly arranged collagen molecules and fibrils of the stromal matrix yields quantitative data on fibrillar organisation, including the orientation and distribution of collagen lamellae within the corneal plane. In recent years, by exploiting the radiation from powerful synchrotron sources, techniques have been developed to enable the mapping of collagen fibril, and therefore lamellar, directions across whole corneas. This article aims to summarise the use of X-ray diffraction to map the orientation and distribution of collagen in the corneal stroma. The implications of the knowledge gained so far are discussed in relation to the optical and biomechanical properties of the cornea, and their alteration due to disease and surgical intervention.

Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo

The mechanical properties of human soft tissue are crucial for impact biomechanics, rehabilitation engineering, and surgical simulation. Validation of these constitutive models using human data remains challenging and often requires the use of non-invasive imaging and inverse finite element (FE) analysis. Post-processing data from imaging methods such as tagged magnetic resonance imaging (MRI) can be challenging. Digital image correlation (DIC), however, is a relatively straightforward imaging method. DIC has been used in the past to study the planar and superficial properties of soft tissue and excised soft tissue layers. However, DIC has not been used to non-invasive study of the bulk properties of human soft tissue in vivo. Thus, the goal of this study was to assess the use of DIC in combination with FE modelling to determine the bulk material properties of human soft tissue. Indentation experiments were performed on a silicone gel soft tissue phantom. A two camera DIC setup was then used to record the 3D surface deformation. The experiment was then simulated using a FE model. The gel was modelled as Neo-Hookean hyperelastic, and the material parameters were determined by minimising the error between the experimental and FE data. The iterative FE analysis determined material parameters (micro=1.80kPa, K=2999kPa) that were in close agreement with parameters derived independently from regression to uniaxial compression tests (micro=1.71kPa, K=2857kPa). Furthermore the FE model was capable of reproducing the experimental indentor force as well as the surface deformation found (R(2)=0.81). It was therefore concluded that a two camera DIC configuration combined with FE modelling can be used to determine the bulk mechanical properties of materials that can be represented using hyperelastic Neo-Hookean constitutive laws.