Finite element analysis applied to cornea reshaping

The inclusion of the epithelium in numerical models of the human cornea

We present a patient-specific finite element model of the human cornea that accounts for the presence of the epithelium. The thin anterior layer that protects the cornea from the external actions has a scant relevance from the mechanical point of view, and it has been neglected in most numerical models of the cornea, which assign to the entire cornea the mechanical properties of the stroma. Yet, modern corneal topographers capture the geometry of the epithelium, which can be naturally included into a patient-specific solid model of the cornea, treated as a multi-layer solid. For numerical applications, the presence of a thin layer on the anterior cornea requires a finer discretization and the definition of two constitutive models (including the corresponding properties) for stroma and epithelium. In this study, we want to assess the relevance of the inclusion of the epithelium in the model of the cornea, by analyzing the effects in terms of uncertainties of the mechanical properties, stress distribution across the thickness, and numerical discretization. We conclude that if the epithelium is modeled as stroma, the material properties should be reduced by 10%. While this choice represents a sufficiently good approximation for the simulation of in vivo mechanical tests, it might result into an under-estimation of the postoperative stress in the simulation of refractive surgery.

Modeling the biomechanics of laser corneal refractive surgery

We present a finite element model of the human cornea used to simulate corneal refractive surgery according to the three most diffused laser procedures, i. e., photo-refractive keratectomy (PRK), laser in-situ keratomileusis (LASIK) and small incision lenticule extraction (SMILE). The geometry used for the model is patient-specific in terms of anterior and posterior surfaces of the cornea and intrastromal surfaces originated by the planned intervention. The customization of the solid model prior to finite element discretization avoids the struggling difficulties associated with the geometrical modification induced by cutting, incision and thinning. Important features of the model include the identification of the stress-free geometry and an adaptive compliant limbus to account for the surrounding tissues. By the way of simplification, we adopt a Hooke material model extended to the finite kinematics, and consider only the preoperative and short-term postoperative conditions, disregarding the remodeling and material evolution aspects typical of biological tissues. Albeit simple and incomplete, the approach demonstrates that the post-operative biomechanical state of the cornea, after the creation of a flap or the removal of a small lenticule, is strongly modified with respect to the preoperative state and characterized by displacement irregularities and stress localizations.

Ocular Fluid Mechanics and Drug Delivery: A Review of Mathematical and Computational Models

The human eye is a complex biomechanical structure with a range of biomechanical processes involved in various physiological as well as pathological conditions. Fluid flow inside different domains of the eye is one of the most significant biomechanical processes that tend to perform a wide variety of functions and when combined with other biophysical processes play a crucial role in ocular drug delivery. However, it is quite difficult to comprehend the effect of these processes on drug transport and associated treatment experimentally because of ethical constraints and economic feasibility. Computational modeling on the other hand is an excellent means to understand the associated complexity between these aforementioned processes and drug delivery. A wide range of computational models specific to different types of fluids present in different domains of the eye as well as varying drug delivery modes has been established to understand the fluid flow behavior and drug transport phenomenon in an insilico manner. These computational models have been used as a non-invasive tool to aid ophthalmologists in identifying the challenges associated with a particular drug delivery mode while treating particular eye diseases and to advance the understanding of the biomechanical behavior of the eye. In this regard, the author attempts to summarize the existing computational and mathematical approaches proposed in the last two decades for understanding the fluid mechanics and drug transport associated with different domains of the eye, together with their application to modify the existing treatment processes.

Modeling of the increased intraocular pressure effect on changes in the stress state of the eyeball’s internal structures

The aim of the study was creating a model and evaluating the effect of elevated IOP in the anterior chamber during phacoemulsification on the changes in the stress state of various ocular structures. Materials and methods.A simplified axial symmetrical anatomical model of the eyeball was created using the finite element method. Using the Deform software package, the deformation problem was worked out by calculating the redistribution of the excess pressure in the anterior chamber during phacoemulsification, on the changes in the stress state of different ocular structures.Results. At processing of modeling results, data were obtained on redistribution of the excess pressure delivered to the anterior chamber towards its decrease in the posterior pole area. The pressure level amounted to 0.85 % of excess pressure applied. The findings are supported by few animal experiments. Conclusions.Proposed model of the increased IOP level effect on changes in the stressed state of various ocular structures demonstrates that the autoregulation mechanism maintaining ocular blood flow at a constant level includes a compensating mechanism for a steep IOP increase due to elastic properties of the vitreous body. This model allows calculating the redistribution of pressure in different parts of the eyeball, depending on the state of resilient-elastic properties of the vitreous, as well as on avitreal eyes, and in patients with silicone oil tamponade.

Theoretical Analysis of Wave-Front Aberrations Induced from Conventional Laser Refractive Surgery in a Biomechanical Finite Element Model

Purpose

To examine the biomechanical effects-induced wave-front aberrations after conventional laser refractive surgery.

Methods

A finite element model of the human eye was established to simulate conventional laser refractive surgery with corrected refraction from –1 to –15 diopters (D). The deformation of the anterior and posterior corneal surfaces was obtained under the intraocular pressure (IOP). Then, the surface displacement was converted to wave-front aberrations.

Results

Following conventional refractive surgery, significant deformation of the anterior and posterior corneal surfaces occurred because of the corneal biomechanical effects, resulting in increased residual wave-front aberrations. Deformation of the anterior surface resulted in a hyperopic shift, which was significantly increased with the increasing refractive correction. The residual high-order aberrations consisted of spherical aberration, vertical coma, and y-trefoil. Spherical aberration was significantly positively correlated to enhanced refraction correction. The effect of posterior corneal surface on induced wave-front aberration was less than the anterior corneal surface. The IOP slightly affects the postoperative defocus, coma, and spherical aberration. When treatment decentration occurred during the procedure, the hyperopic shift decreased as the eccentricity increased. Treatment decentration had a significant impact on the spherical aberration and the coma. In addition, the ocular tissue elasticity played a key role in hyperopic shift, whereas it had little effect on the other aberrations.

Conclusions

Among the many factors that affect high-order aberrations after conventional laser refractive surgery, the alterations in corneal morphology caused by biomechanical effects must be considered, as they can lead to an increase in postoperative residual wave-front aberrations.

Line-Field Optical Coherence Tomography as a tool for In vitro characterization of corneal biomechanics under physiological pressures

There has been a lot of interest in accurately characterising corneal biomechanical properties under intraocular pressure (IOP) to help better understand ocular pathologies that are associated with elevated IOP. This study investigates the novel use of Line-Field Optical Coherence Tomography (LF-OCT) as an elastographic tool for accurately measuring mechanical properties of porcine corneas based on volumetric deformation following varying IOPs. A custom-built LF-OCT was used to measure geometrical and corneal surface displacement changes in porcine corneas under a range of IOPs, from 0-60 mmHg. Corneal thickness, elastic properties and hysteresis were calculated as a function of pressure. In addition, the effects of hydration were explored. We found that the elastic modulus increased in a linear fashion with IOP. Corneal thickness was found to reduce with IOP, decreasing 14% from 0 to 60 mmHg. Prolonged hydration in phosphate buffered saline (PBS) was found to significantly increase the elastic modulus and corneal hysteresis. Our study demonstrates that LF-OCT can be used to accurately measure the elastic properties based on volumetric deformation following physiological pressures. Furthermore, we show that prolonged hydration in PBS has a significant effect on the measured corneal properties.

A 3D fluid-solid interaction model of the air puff test in the human cornea

We present a numerical model of a contactless test commonly used to assess the biomechanics of the human cornea. The test, consisting in a rapid air jet applied to the anterior surface of the cornea, is controversial. Although the numerous studies documented in the literature have not been able yet to clarify its relevance as a diagnostic tool, the test has the potential to be combined with inverse analysis procedures to characterize the parameters of numerical models of the cornea. With the final goal of employing the air puff test in advanced material identification algorithms, here we propose to model the cornea with standard finite elements and the fluids filling the anterior chamber of the eye with a meshfree discretization. The interaction between moving fluids and deforming cornea is accounted for by modifying the interface boundary conditions of both fluid and solid. The proposed model represents the first fully 3D example of an aqueous-cornea fluid-solid interaction analysis which uses a robust meshfree approach for the fluid. Although we restrict our scope to isotropic nonlinear materials, numerical results confirm the undeniable importance of including internal fluids in the simulation of the air puff test. Thus the proposed approach stands as a procedural paradigm for the identification of the mechanical parameters of the human cornea.

Anvil-profiled penetrating keratoplasty: load resistance evaluation

The aim of this study was to qualitatively evaluate the biomechanical load resistance of different surgical wound configurations (mushroom, zig-zag, anvil and conventional trephination) in penetrating keratoplasty (PK) by designing a 2D and a 3D finite-element biomechanical model of the cornea. A mathematical model of the human cornea was developed, and different geometric configurations for PK were designed. The internal pressure was raised until the wound misaligned; wound prolapse then occurred. Better wound resistance was found in all the laser trephined profiles tested in comparison with the conventional straight one. The anvil profile was more resistant to the increasing internal pressure than was the mushroom or the zig-zag pattern. Thanks to its greater mechanical load resistance, the anvil profile made possible the apposition of a restricted number of sutures and early suture removal. These advantages can contribute to a faster visual recovery in patients undergoing penetrating keratoplasty.

Depth-Dependent Out-of-Plane Young's Modulus of the Human Cornea

Purpose/Aim: Despite their importance in accurate mechanical modeling of the cornea, the depth-dependent material properties of the cornea have only been partially elucidated. In this work, we characterized the depth-dependent out-of-plane Young's modulus of the central and peripheral human cornea with high spatial resolution.

MATERIALS AND METHODS

Central and peripheral corneal buttons from human donors were subjected to unconfined axial compression followed by stress relaxation for 30 min. Sequences of fluorescent micrographs of full-thickness corneal buttons were acquired throughout the experiment to enable tracking of fluorescently labeled stromal keratocyte nuclei and measurements of depth-dependent infinitesimal strains. The nominal (gross) out-of-plane Young's modulus and drained Poisson's ratio for each whole specimen was computed from the equilibrium stress and overall tissue deformation. The depth-dependent (local) out-of-plane Young's modulus was computed from the equilibrium stress and local tissue strain based on an anisotropic model (transverse isotropy).

RESULTS

The out-of-plane Young's modulus of the cornea exhibited a strong dependence on in-plane location (peripheral versus central cornea), but not depth. The depth-dependent out-of-plane Young's modulus of central and peripheral specimens ranged between 72.4-102.4 kPa and 38.3-58.9 kPa. The nominal out-of-plane Young's modulus was 87 ± 41.51 kPa and 39.9 ± 15.28 kPa in the central and peripheral cornea, while the drained Poisson's ratio was 0.05 ± 0.02 and 0.07 ± 0.04.

CONCLUSIONS

The out-of-plane Young's modulus of the cornea is mostly independent of depth, but not in-plane location (i.e. central vs. peripheral). These results may help inform more accurate finite element computer models of the cornea.

TO STUDY THE EFFECTS OF INTRASTROMAL CORNEAL RING GEOMETRY AND SURGICAL CONDITIONS ON THE POSTSURGICAL OUTCOMES THROUGH FINITE ELEMENT ANALYSIS

Intrastromal corneal ring (ICR) is a transparent circular implant inserted in the cornea to provide structural support in an attempt to alleviate preexisting refractive errors. This is a surgical procedure whose success depends on control parameters such as, ICR geometry which includes ICR thickness and diameter, and surgical conditions which includes ICR implantation depth and diameter of corneal pocket. This research utilizes finite element (FE) analysis techniques to develop a high fidelity and computationally efficient three-dimensional axisymmetric cornea model to study the relative effects of ICR implant geometry and surgical conditions on the postsurgical shape of the cornea utilizing corneal apical displacement results. The FE analysis results indicate that ICR implantation reduces myopia, and the amount of myopic rectification is dependent on the control parameters which include ICR geometry and surgical conditions. The results show that an increase in ICR thickness leads to an increase in myopic rectification, whereas an increase in ICR radius leads to a decrease in myopic rectification. ICR implantation depth analysis results suggest that corneal depth of 40–75% provides steady myopic rectification. Corneal pocket diameter analysis revealed that smaller corneal pockets lead to increase in myopic rectification. Overall, the FE model results are in qualitative agreement with published clinical studies. Finally, the combined impact of the control parameters on myopic rectification was studied by conducting a sensitivity analysis and an equation relating myopic rectification with control parameters was developed utilizing simple linear regression analysis.

Corneal elasticity after oxygen enriched high intensity corneal cross linking assessed using atomic force microscopy

The purpose of this study was to assess anterior and mid corneal stromal elasticity after high intensity (HI) corneal cross linking (CXL), with and without oxygen (O₂) enrichment, and compare these results to conventional CXL. Experiments were performed on 25 pairs of human cadaver eyes, divided into four different groups. Group 1 included corneas that did not receive treatment and served as controls; Group 2 included corneas that received conventional CXL treatment (Dresden Protocol: corneal epithelial debridement, 30 min of riboflavin pretreatment followed by 30 min of exposure to 3 mW/cm² of ultraviolet light); Group 3 included corneas that received HI CXL treatment (corneal epithelial debridement, 30 min of riboflavin pretreatment followed by 3 min of exposure to 30mW/cm² of ultraviolet light); and Group 4 included corneas that received the same treatment as Group 3, except that they were enriched with oxygen (4 L per minute pure O₂ gas stream) during ultraviolet irradiation. In each group, corneas were subdivided to assess anterior stromal elasticity and mid stromal elasticity. Corneal stromal elasticity was quantified using Atomic Force Microscopy (AFM) through micro-indentation. Young's modulus for the anterior corneal stroma was 14.5 ± 6.0 kPa, 80.7 ± 44.6 kPa, 36.6 ± 10.5 kPa, and 30.6 ± 9.2 kPa, for groups 1, 2, 3 and 4 respectively. Young's modulus for the mid corneal stroma was 5.8 ± 2.0 kPa, 20.7 ± 4.3 kPa, 12.1 ± 4.9 kPa, and 11.7 ± 3.7 kPa, for groups 1, 2, 3 and 4, respectively. In the anterior stromal region, conventional CXL demonstrated a significantly different result from the control, whereas the two HI CXL protocols were not significantly different from the control. There were no statistical differences between the two HI CXL protocols, although only the HI CXL protocol with O₂ enrichment was significantly different from the conventional CXL group. In the mid stromal region, once again only conventional CXL demonstrated a significantly different result from the control. There were no statistical differences between the two HI CXL protocols, and both HI CXL protocols were significantly different from the conventional CXL group. Oxygen enriched HI CXL seems to offer similar changes in corneal elasticity when compared to HI CXL without the presence O₂. Conventional CXL increases corneal stiffness more than HI CXL both with and without O₂ enrichment.

[Intravitreal injection as a possible model for studying biomechanics of fibrous tunic]

The article summarized the results of Russian and foreign research concerning biomechnical principles of eye functioning as an integral physiological system. Quite a number of studies have been published on corneal and scleral mechanics, which is also part of the said system. These studies fall largely into three groups: in vivo studies (involving living organism), in vitro studies (within an artificial environment), and mathematical modeling. In vivo techniques are often rather complicated and, therefore, most studies are based on in vitro procedures. Due to the growing number of intravitreal injections, they can be regarded as a stress test for studying fibrous tunic biomechanics in vivo. The results of such studies would contribute to a better understanding of the pathogenesis of various eye diseases and thus, a better clinical practice.

Impact of Hydration Media on Ex Vivo Corneal Elasticity Measurements

OBJECTIVES

To determine the effect of hydration media on ex vivo corneal elasticity.

METHODS

Experiments were conducted on 40 porcine eyes retrieved from an abattoir (10 eyes each for phosphate-buffered saline (PBS), balanced salt solution, Optisol, 15% dextran). The epithelium was removed, and the cornea was excised with an intact scleral rim and placed in 20% dextran overnight to restore its physiological thickness. For each hydration media, corneas were evenly divided into two groups: one with an intact scleral rim and the other without. Corneas were mounted onto a custom chamber and immersed in a hydration medium for elasticity testing. Although in each medium, corneal elasticity measurements were performed for 2 hr: at 5-min intervals for the first 30 min and then 15-min intervals for the remaining 90 min. Elasticity testing was performed using nanoindentation with spherical indenters, and Young modulus was calculated using the Hertz model. Thickness measurements were taken before and after elasticity testing.

RESULTS

The percentage change in corneal thickness and elasticity was calculated for each hydration media group. Balanced salt solution, PBS, and Optisol showed an increase in thickness and Young moduli for corneas with and without an intact scleral rim. Fifteen percent dextran exhibited a dehydrating effect on corneal thickness and provided stable maintenance of corneal elasticity for both groups.

CONCLUSIONS

Hydration media affects the stability of corneal thickness and elasticity measurements over time. Fifteen percent dextran was most effective in maintaining corneal hydration and elasticity, followed by Optisol.

Noncontact Elastic Wave Imaging Optical Coherence Elastography for Evaluating Changes in Corneal Elasticity Due to Crosslinking

The mechanical properties of tissues can provide valuable information about tissue integrity and health and can assist in detecting and monitoring the progression of diseases such as keratoconus. Optical coherence elastography (OCE) is a rapidly emerging technique, which can assess localized mechanical contrast in tissues with micrometer spatial resolution. In this work we present a noncontact method of optical coherence elastography to evaluate the changes in the mechanical properties of the cornea after UV-induced collagen cross-linking. A focused air-pulse induced a low amplitude (μm scale) elastic wave, which then propagated radially and was imaged in three dimensions by a phase-stabilized swept source optical coherence tomography (PhS-SSOCT) system. The elastic wave velocity was translated to Young's modulus in agar phantoms of various concentrations. Additionally, the speed of the elastic wave significantly changed in porcine cornea before and after UV-induced corneal collagen cross-linking (CXL). Moreover, different layers of the cornea, such as the anterior stroma, posterior stroma, and inner region, could be discerned from the phase velocities of the elastic wave. Therefore, because of noncontact excitation and imaging, this method may be useful for in vivo detection of ocular diseases such as keratoconus and evaluation of therapeutic interventions such as CXL.

The influence of intraocular pressure and air jet pressure on corneal contactless tonometry tests

The air puff is a dynamic contactless tonometer test used in ophthalmology clinical practice to assess the biomechanical properties of the human cornea and the intraocular pressure due to the filling fluids of the eye. The test is controversial, since the dynamic response of the cornea is governed by the interaction of several factors which cannot be discerned within a single measurement. In this study we describe a numerical model of the air puff tests, and perform a parametric analysis on the major action parameters (jet pressure and intraocular pressure) to assess their relevance on the mechanical response of a patient-specific cornea. The particular cornea considered here has been treated with laser reprofiling to correct myopia, and the parametric study has been conducted on both the preoperative and postoperative geometries. The material properties of the cornea have been obtained by means of an identification procedure that compares the static biomechanical response of preoperative and postoperative corneas under the physiological IOP. The parametric study on the intraocular pressure suggests that the displacement of the cornea׳s apex can be a reliable indicator for tonometry, and the one on the air jet pressure predicts the outcomes of two or more distinct measurements on the same cornea, which can be used in inverse procedures to estimate the material properties of the tissue.

Biomechanical and optical behavior of human corneas before and after photorefractive keratectomy

PURPOSE

To evaluate numerically the biomechanical and optical behavior of human corneas and quantitatively estimate the changes in refractive power and stress caused by photorefractive keratectomy (PRK).

SETTING

Athineum Refractive Center, Athens, Greece, and Politecnico di Milano, Milan, Italy.

DESIGN

Retrospective comparative interventional cohort study.

METHODS

Corneal topographies of 10 human eyes were taken with a scanning-slit corneal topographer (Orbscan II) before and after PRK. Ten patient-specific finite element models were created to estimate the strain and stress fields in the cornea in preoperative and postoperative configurations. The biomechanical response in postoperative eyes was computed by directly modeling the postoperative geometry from the topographer and by reproducing the corneal ablation planned for the PRK with a numerical reprofiling procedure.

RESULTS

Postoperative corneas were more compliant than preoperative corneas. In the optical zone, corneal thinning decreased the mechanical stiffness, causing local resteepening and making the central refractive power more sensitive to variations in intraocular pressure (IOP). At physiologic IOP, the postoperative corneas had a mean 7% forward increase in apical displacement and a mean 20% increase in the stress components at the center of the anterior surface over the preoperative condition.

CONCLUSION

Patient-specific numerical models of the cornea can provide quantitative information on the changes in refractive power and in the stress field caused by refractive surgery.

FINANCIAL DISCLOSURES

No author has a financial or proprietary interest in any material or method mentioned.

Air puff induced corneal vibrations: theoretical simulations and clinical observations

PURPOSE

To investigate air puff induced corneal vibrations and their relationship to the intraocular pressure (IOP), viscoelasticity, mass, and elasticity of the cornea based on theoretical simulations and preliminary clinical observations.

METHODS

To simulate the corneal movement during air puff deformation, a kinematic viscoelastic corneal model was developed involving the factors of corneal mass, damping coefficient, elasticity, and IOP. Different parameter values were taken to investigate how factors would affect the corneal movements. Two clinical ocular instruments, CorVis ST (Oculus Optikgeräte GmbH, Wetzlar, Germany) and the Ocular Response Analyzer (ORA; Reichert, Inc., Buffalo, NY), were employed to observe the corneal dynamical behaviors.

RESULTS

Numerical results showed that during the air puff deformation, there would be vibrations along with the corneal deformation, and the damping viscoelastic response of the cornea had the potential to reduce the vibration amplitude. With consistent IOP, the overall vibration amplitude and inward motion depths were smaller with a stiffer cornea.

CONCLUSIONS

A kinematic viscoelastic model of the cornea is presented to illustrate how the vibrations are associated with factors such as corneal mass, viscoelasticity, and IOP. Also, the predicted corneal vibrations during air puff deformation were confirmed by clinical observation.

Anterior and posterior corneal stroma elasticity after corneal collagen crosslinking treatment

The purpose of this project was to assess anterior and posterior corneal stromal elasticity after corneal collagen cross linking (CXL) treatment in human cadaver eyes using Atomic Force Microscopy (AFM) through indentation. Twenty four human cadaver eyes (12 pairs) were included in this study and divided into 2 groups (6 pairs per group). In both groups, the left eye (OS) served as a control (no riboflavin or CXL treatment was performed) and the right eye (OD) underwent CXL treatment (30 min of riboflavin pretreatment followed by 30 min of exposure to 3 mW/cm(2) of ultraviolet light). In group 1, the anterior stroma was exposed by manual delamination of approximately 50 μm of the corneal stroma including Bowman's membrane. In group 2, the posterior stroma was exposed by delamination of the anterior 50% of the corneal stroma including Bowman's membrane. Delamination was performed after crosslinking treatment in the case of the treated eyes. In all eyes, the stromal elasticity was quantified using AFM through indentation. Young's modulus of elasticity for the anterior cornea (group 1) was 245.9 ± 209.1 kPa (range: 82.3-530.8 kPa) for the untreated control eyes, and 467.8 ± 373.2 kPa (range: 157.4-1126 kPa) for the CXL treated eyes. Young's modulus for the posterior cornea (group 2) was 100.2 ± 61.9 kPa (range: 28.1-162.6 kPa) for the untreated control eyes and 66.0 ± 31.8 kPa (range: 31.3-101.7 kPa) for the CXL treated eyes. Young's modulus of the anterior stroma significantly increased after CXL treatment (p = 0.024), whereas the posterior stroma did not demonstrate a significant difference in Young's modulus after CXL treatment (p = 0.170). The anterior stroma was stiffer than the posterior stroma for both the control and CXL treatment groups (p = 0.077 and p = 0.023, respectively). Our findings demonstrate that stiffness of the anterior corneal stroma after CXL treatment seems to increase significantly, while the posterior stroma does not seem to be affected by CXL.

Anterior and posterior corneal stroma elasticity assessed using nanoindentation

Corneal biomechanics is an essential parameter for developing diagnostic and treatment methods of corneal-related diseases. It is widely accepted that corneal mechanical strength stems from the stroma's collagenous composition. However, more comprehensive insight into the mechanical properties within the stroma is needed to improve current corneal diagnostic and treatment techniques. The purpose of this study was to perform elasticity characterization of anterior and posterior stromal regions of human corneas using atomic force microscopy (AFM). Nine pairs of human whole globes were placed in 20% Dextran solution, cornea side down, to restore the corneal thickness to physiological levels (400-600 μm). The epithelium and Bowman's membrane were removed from all eyes. Anterior stromal AFM elasticity testing was then performed on left (OS) eyes. Additional stroma was removed from right (OD) eyes to allow posterior stromal measurements at a depth of 50% of the original thickness. All experiments were performed with corneas submerged in 15% Dextran to maintain corneal hydration. The results of the study showed that the Young's modulus of elasticity of the anterior stroma (average: 281 ± 214 kPa; range: 59-764 kPa) was significantly higher than that of the posterior stroma (average: 89.5 ± 46.1 kPa; range: 29-179 kPa) (p = 0.014). In addition, a linear relationship was found between the posterior stromal elasticity and anterior stromal elasticity (p = 0.0428). On average, the elasticity of the posterior stroma is 39.3% of the anterior stroma. In summary, there appears to be an elasticity gradient within the corneal stroma, which should be considered in the design and development of corneal diagnostic and treatment methods to enhance efficacy.

Experimental study on the mechanical strain of corneal collagen

Currently, investigations of biomechanical properties of the fibrous tunic are becoming even more topical, especially for diagnosis of corneal ectatic disease, as well as correct interpretation of intraocular pressure (IOP) parameters, particularly in patients with prior surgery on cornea. The study principle is based on the ability of substances to change optical anisotropy depending on mechanical strain applied to them. An experimental set-up was constructed which allows assessment of polarization degree of light which is emitted during luminescence of strained collagen. The study was performed on 18 corneoscleral discs of chinchilla rabbit eyes at 15 and 50mm Hg pressure, among them in 6 cases before and after making radial incisions, and in 6 cases before and after conducting the mechanical cornea abrasions that were asymmetrical by depth until reaching the local zone of iatrogenic keratectasia. Corneal collagen mechanical strain mappings were formed on 3 experimental models (intact cornea, cornea post radial keratotomy and keratectasia) under intra-chamber pressure of 15 and 50mm Hg. Corneal collagen mechanical strain is evenly allocated in the intact cornea. After radial keratotomy the main mechanical loading was concentrated over the middle part of corneal periphery, particularly in the bottom of keratotomic incisions. The increased intra-chamber pressure made the strain rise in those models. Upon cornea abrasion the main straining is distributed within the thinning zone, and the increase of intra-chamber pressure only increases the load over residual stroma. A new principle of corneal biomechanical properties investigation based on assessment of degree of light polarization emitted during luminescence of strained collagen, has been proposed and experimentally tested.

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.

MR elastography of the ex vivo bovine globe

PURPOSE

To evaluate the feasibility of using MR elastography (MRE) to assess the mechanical properties of the eye.

MATERIALS AND METHODS

The elastic properties of the corneoscleral shell of an intact, enucleated bovine globe specimen were estimated using MRE and finite element modeling (FEM), assuming linear, isotropic behavior. The two-dimensional (2D), axisymetric model geometry was derived from a segmented 2D MR image, and estimations of the Young's modulus in both the cornea and sclera were made at various intraocular pressures using an iterative flexural wave speed matching algorithm.

RESULTS

Estimated values of the Young's moduli of the cornea and sclera varied from 40 to 185 kPa and 1 to 7 MPa, respectively, over an intraocular pressure range of 0.85 to 9.05 mmHg (1.2 to 12.3 cmH(2)O). They also varied exponentially as functions of both wave speed and intraocular dP/dV, an empirical measure of "ocular rigidity."

CONCLUSION

These results show that it is possible to estimate the intrinsic elastic properties of the corneoscleral shell in an ex vivo bovine globe, suggesting that MRE may provide a useful means to assess the mechanical properties of the eye and its anatomy. Further development of the technique and modeling process will enhance its potential, and further investigations are needed to determine its clinical potential.

Finite element modeling of corneal biomechanical behavior

PURPOSE

To optimize the construction details of corneal numerical models while maintaining efficiency and reliability of predictions.

METHODS

Nonlinear finite element analysis of corneal models was carried out to assess the importance of considering the cornea's hyperelastic, hysteretic and anisotropic behavior, multi-layer construction, weak inter-lamellar adhesion, non-uniform thickness, elliptical topography, and connection to the sclera. The effect of each of these parameters was determined by removing it from the numerical models and assessing the effect on the results. This exercise was carried out under two load cases--a uniform posterior pressure subjecting the cornea to predominantly membrane tension stresses, and a concentrated anterior pressure as applied by the Ocular Response Analyzer (Reichert Ophthalmic Instruments), which creates mainly bending stresses.

RESULTS

Corneal models subjected to mainly bending stresses were particularly sensitive to simplifications in modeling corneal nonuniform thickness, weak interlamellar adhesion, and multi-layer construction. On the other hand, models under mainly membrane tension were more sensitive to simplifications in elliptical profile and connection to the sclera. Considering hyper-elasticity was important in both cases. Hysteresis was also important, but only in applications involving load reversal.

CONCLUSIONS

Although simplifications may be necessary to reduce the cost of numerical model construction and analysis, the selection of which simplifications to adopt should be done with care. They should only be considered when their effect on results is acceptably small, and their inclusion does not make the model significantly different from real-life conditions.

Optically inspired biomechanical model of the human eyeball

Currently available biomechanical models of the human eyeball focus mainly on the geometries and material properties of its components while little attention has been given to its optics--the eye's primary function. We postulate that in the evolution process, the mechanical structure of the eyeball has been influenced by its optical functions. We develop a numerical finite element analysis-based model in which the eyeball geometry and its material properties are linked to the optical functions of the eye. This is achieved by controlling in the model all essential optical functions while still choosing material properties from a range of clinically available data. In particular, it is assumed that in a certain range of intraocular pressures, the eye is able to maintain focus. This so-called property of optical self-adjustments provides a more constrained set of numerical solutions in which the number of free model parameters significantly decreases, leading to models that are more robust. Further, we investigate two specific cases of a model that satisfies optical self-adjustment: (1) a full model in which the cornea is flexibly attached to sclera at the limbus, and (2) a fixed cornea model in which the cornea is not allowed to move at the limbus. We conclude that for a biomechanical model of the eyeball to mimic the optical function of a real eye, it is crucial that the cornea is allowed to move at the limbal junction, that the materials used for the cornea and sclera are strongly nonlinear, and that their moduli of elasticity remain in a very close relationship.