Cornea modelling

Biomechanical properties of porcine cornea; planar biaxial tests versus uniaxial tensile tests

The cornea is a transparent tissue whose mechanical properties are important for its optical and physiological functions. The mechanical properties of cornea depend on the composition and microstructure of its extracellular matrix, which is composed of collagen fibrils with preferential orientations. The present research was done in order to characterize corneal mechanical response using the biaxial mechanical testing method and to compare biaxial measurements with those found from uniaxial tensile tests. For this purpose, thirty square-shaped specimens excised from the center of porcine cornea were mounted into an ElectroForce TestBench device such that their superior/inferior (SI) and nasal/temporal (NT) meridians were aligned with motor axes. Furthermore, ten corneal strips dissected from the NT direction (n = 5) and SI direction (n = 5) were mounted into an RSA-G2 Solid Analyzer testing machine. The biaxial experiments were performed at stretch ratios of 1:1, 1:0.5, 0.5:1, 1:0.01, and 0.01:1 and displacement rates of 2 mm/min (n = 20) and 10 mm/min (n = 10). The uniaxial experiments were done using the displacement rate of 2 mm/min. The planar square-shaped samples tested under equibiaxial loading showed similar mechanical response in NT and SI directions. Furthermore, uniaxial experiments revealed no significant difference in tensile response of corneal strips excised from NT and SI directions. However, equibiaxial testing tensile stresses were significantly larger than those found from uniaxial tensile measurements. The mechanical behavior of cornea in biaxial tests was dependent on the applied stretch ratio. The differences and similarities between uniaxial and biaxial experimental measurements were discussed and it was concluded that the planar biaxial testing method characterized the mechanical response of cornea by mimicking its in vivo loading state more closely than uniaxial experiments.

A combined experimental-computational approach for retinal characterization

Subretinal injection of gene products is the only treatment option for inherited retinal diseases. However, this procedure induces localized high multiaxial deformations, potentially causing irreversible tissue damage due to retinal overstretching and tearing. Comprehensive characterization of retinal mechanical behavior is essential for performing safe injections. Although uniaxial tensile test has been used in the literature, it has many limitations for retinal characterization. To date, retinal mechanical properties are poorly understood due to the lack of standardized testing protocol. This study aimed to introduce a combined experimental-computational approach using small punch testing and finite element simulations to investigate retina elastic behavior under biaxial deformations. To develop a suitable testing protocol for retinal samples, we evaluated the impact of environmental conditions on retinal elasticity by performing uniaxial tensile tests on porcine retinal strips in air, in a saline bath, and at different temperatures. The results showed that conditions did not significantly affect the elastic modulus. We then developed an easy and reproducible small punch test protocol, allowing to measure for the first time the load-displacement response of the retina under biaxial deformations. Computational simulations enabled the analysis of retinal deformations and the identification of its elastic modulus (5.5 kPa). The outcomes of this study highlight the great potential of the combined approach as a viable alternative to uniaxial tensile test to advance the understanding of retinal biomechanics. This is essential not only for minimizing sight-threatening surgical complications during injections, but also for building predictive in silico models, and developing biomimetic scaffolds.

Biomechanics of soft biological tissues and organs, mechanobiology, homeostasis and modelling

The human body consists of many different soft biological tissues that exhibit diverse microstructures and functions and experience diverse loading conditions. Yet, under many conditions, the mechanical behaviour of these tissues can be described well with similar nonlinearly elastic or inelastic constitutive relations, both in health and some diseases. Such constitutive relations are essential for performing nonlinear stress analyses, which in turn are critical for understanding physiology, pathophysiology and even clinical interventions, including surgery. Indeed, most cells within load-bearing soft tissues are highly sensitive to their local mechanical environment, which can typically be quantified using methods of continuum mechanics only after the constitutive relations are determined from appropriate data, often multi-axial. In this review, we discuss some of the many experimental findings of the structure and the mechanical response, as well as constitutive formulations for 10 representative soft tissues or organs, and present basic concepts of mechanobiology to support continuum biomechanical studies. We conclude by encouraging similar research along these lines, but also the need for models that can describe and predict evolving tissue properties under many conditions, ranging from normal development to disease progression and wound healing. An important foundation for biomechanics and mechanobiology now exists and methods for collecting detailed multi-scale data continue to progress. There is, thus, considerable opportunity for continued advancement of mechanobiology and biomechanics.

Biomechanical behavior of deep anterior lamellar keratoplasty: a finite element analysis

Deep Anterior Lamellar Keratoplasty (DALK) is a surgical procedure used to restore sight and manage corneal diseases by replacing cloudy corneal tissue with allogeneic normal corneal tissue or artificial corneal material. However, the limited availability and mechanical defects of artificial corneal materials pose challenges in DALK. To predicting postoperative mechanical behavior of Deep Anterior Lamellar Keratoplasty (DALK), a three-dimensional finite element model of the postoperative DALK cornea with suture holes was developed. The postoperative corneal displacement and von Mises (VM) stress changes were also simulated under varying depths of cut (DOC: 0.16-0.26 μm), intraocular pressure (IOP: 12, 15, 18 mmHg), and central corneal thickness (CCT: 420-620 μm). The model indicated that higher IOP and CCT were associated with improved postoperative corneal stability. The postoperative corneal displacement increased from the edge to the center, while the maximum VM stress value occurs at the corneal suture hole. Corneal displacement and VM stress decrease with increasing CCT and decreasing IOP. DOC has a slight effect on corneal displacement and VM stress, with an overall positive relationship. The model has potential application in the preoperative assessment of risk in keratoplasty.

Influence of Contact Lens Parameters on Cornea: Biomechanical Analysis

This study presents a finite element analysis to model ocular biomechanics and the interactions between the human eye and contact lenses in the closed-eye condition. The closed-eye state, where the eyelids are fully shut, presents challenges for experimental measurements due to the invasive nature of accessing and analysing the contact lens and corneal interface, making simulation tools valuable for accurate characterisation. The primary objective of this study was to examine how CLs fold and twist and their impact on the cornea when the eye is closed. The secondary aim of this study was to assess how crucial contact lens parameters (Young's modulus, base curve, and diameter) influence corneal stress distribution and the overall fit of the lens on the eye. The findings show that increasing Young's modulus significantly reduces corneal stress and promotes uniform stress distribution, making it the most influential factor for wearer comfort and safety. While base curve and diameter variations primarily affect contact area, their impact on stress distribution is minimal. This research provides insights for improving contact lens design and enhancing safety for contact lens wearers.

Contact lens fitting and changes in the tear film dynamics: mathematical and computational models review

PURPOSE

This review explores mathematical models, blinking characterization, and non-invasive techniques to enhance understanding and refine clinical interventions for ocular conditions, particularly for contact lens wear.

METHODS

The review evaluates mathematical models in tear film dynamics and their limitations, discusses contact lens wear models, and highlights computational mechanical models. It also explores computational techniques, customization of models based on individual blinking dynamics, and non-invasive diagnostic tools like high-speed cameras and advanced imaging technologies.

RESULTS

Mathematical models provide insights into tear film dynamics but face challenges due to simplifications. Contact lens wear models reveal complex ocular physiology and design aspects, aiding in lens development. Computational mechanical models explore eye biomechanics, often integrating tear film dynamics into a Multiphysics framework. While different computational techniques have their advantages and disadvantages, non-invasive tools like OCT and thermal imaging play a crucial role in customizing these Multiphysics models, particularly for contact lens wearers.

CONCLUSION

Recent advancements in mathematical modeling and non-invasive tools have revolutionized ocular health research, enabling personalized approaches. The review underscores the importance of interdisciplinary exploration in the Multiphysics approach involving tear film dynamics and biomechanics for contact lens wearers, promoting advancements in eye care and broader ocular health research.

Blast injury: Impact to the cornea

Visual disorders are common even after mild traumatic brain injury (mTBI) or blast exposure. The cost of blast-induced vision loss in civilians, military personnel, and veterans is significant. The visual consequences of blasts associated with TBI are elusive. Active military personnel and veterans report various ocular pathologies including corneal disorders post-combat blasts. The wars and conflicts in Afghanistan, Iraq, Syria, and Ukraine have significantly increased the number of corneal and other ocular disorders among military personnel and veterans. Binocular vision, visual fields, and other visual functions could be impaired following blast-mediated TBI. Blast-associated injuries can cause visual disturbances, binocular system problems, and visual loss. About 25% of veterans exposed to blasts report corneal injury. Blast exposure induces corneal edema, corneal opacity, increased corneal thickness, damage of corneal epithelium, corneal abrasions, and stromal and endothelial abnormality including altered endothelial density, immune cell infiltration, corneal neovascularization, Descemet membrane rupture, and increased pain mediators in animal models and the blast-exposed military personnel including veterans. Immune response exacerbates blast-induced ocular injury. TBI is associated with dry eyes and pain in veterans. Subjects exposed to blasts that cause TBI should undergo immediate clinical visual and ocular examinations. Delayed visual care may lead to progressive vision loss, lengthening/impairing rehabilitation and ultimately may lead to permanent vision problems and blindness. Open-field blast exposure could induce corneal injuries and immune responses in the cornea. Further studies are warranted to understand corneal pathology after blast exposure. A review of current advancements in blast-induced corneal injury will help elucidate novel targets for potential therapeutic options. This review discusses the impact of blast exposure-associated corneal disorders.

In Vivo Optical Coherence Elastography Unveils Spatial Variation of Human Corneal Stiffness

OBJECTIVE

The mechanical properties of corneal tissues play a crucial role in determining corneal shape and have significant implications in vision care. This study aimed to address the challenge of obtaining accurate in vivo data for the human cornea.

METHODS

We have developed a high-frequency optical coherence elastography (OCE) technique using shear-like antisymmetric (A0)-mode Lamb waves at frequencies above 10 kHz.

RESULTS

By incorporating an anisotropic, nonlinear constitutive model and utilizing the acoustoelastic theory, we gained quantitative insights into the influence of corneal tension on wave speeds and elastic moduli. Our study revealed significant spatial variations in the shear modulus of the corneal stroma on healthy subjects for the first time. Over an age span from 21 to 34 (N = 6), the central corneas exhibited a mean shear modulus of 87 kPa, while the corneal periphery showed a significant decrease to 44 kPa. The central cornea's shear modulus decreases with age with a slope of -19 +/- 8 kPa per decade, whereas the periphery showed non-significant age dependence. The limbus demonstrated an increased shear modulus exceeding 100 kPa. We obtained wave displacement profiles that are consistent with highly anisotropic corneal tissues.

CONCLUSION

Our approach enabled precise measurement of corneal tissue elastic moduli in situ with high precision (<7%) and high spatial resolution (<1 mm). Our results revealed significant stiffness variation from the central to peripheral corneas.

SIGNIFICANCE

The high-frequency OCE technique holds promise for biomechanical evaluation in clinical settings, providing valuable information for refractive surgeries, degenerative disorder diagnoses, and intraocular pressure assessments.

Establishing Standardization Guidelines For Finite-Element Optomechanical Simulations of Refractive Laser Surgeries: An Application to Photorefractive Keratectomy

Purpose

Computational models can help clinicians plan surgeries by accounting for factors such as mechanical imbalances or testing different surgical techniques beforehand. Different levels of modeling complexity are found in the literature, and it is still not clear what aspects should be included to obtain accurate results in finite-element (FE) corneal models. This work presents a methodology to narrow down minimal requirements of modeling features to report clinical data for a refractive intervention such as PRK.

Methods

A pipeline to create FE models of a refractive surgery is presented: It tests different geometries, boundary conditions, loading, and mesh size on the optomechanical simulation output. The mechanical model for the corneal tissue accounts for the collagen fiber distribution in human corneas. Both mechanical and optical outcome are analyzed for the different models. Finally, the methodology is applied to five patient-specific models to ensure accuracy.

Results

To simulate the postsurgical corneal optomechanics, our results suggest that the most precise outcome is obtained with patient-specific models with a 100 µm mesh size, sliding boundary condition at the limbus, and intraocular pressure enforced as a distributed load.

Conclusions

A methodology for laser surgery simulation has been developed that is able to reproduce the optical target of the laser intervention while also analyzing the mechanical outcome.

Translational Relevance

The lack of standardization in modeling refractive interventions leads to different simulation strategies, making difficult to compare them against other publications. This work establishes the standardization guidelines to be followed when performing optomechanical simulations of refractive interventions.

Simultaneous tensile and shear measurement of the human cornea in vivo using S0- and A0-wave optical coherence elastography

Understanding corneal stiffness is valuable for improving refractive surgery, detecting corneal abnormalities, and assessing intraocular pressure. However, accurately measuring the elastic properties, specifically the tensile and shear moduli that govern mechanical deformation, has been challenging. To tackle this issue, we have developed guided-wave optical coherence elastography that can simultaneously excite and analyze symmetric (S0) and anti-symmetric (A0) elastic waves in the cornea at around 10 kHz frequencies, enabling us to extract tensile and shear properties from measured wave dispersion curves. We verified the technique using elastomer phantoms and ex vivo porcine corneas and investigated the dependence on intraocular pressure using acoustoelastic theory that incorporates corneal tension and a nonlinear constitutive tissue model. In a pilot study involving six healthy human subjects aged 31 to 62, we measured shear moduli (Gzx) of 94±20 kPa (mean±standard deviation) and tensile moduli (Exx) of 4.0±1.1 MPa at central corneas. Our preliminary analysis of age-dependence revealed contrasting trends: -8.3±4.5 kPa/decade for shear and 0.30±0.21 MPa/decade for tensile modulus. This OCE technique has the potential to become a highly useful clinical tool for the quantitative biomechanical assessment of the cornea. STATEMENT OF SIGNIFICANCE: This article reports an innovative elastography technique using two guided elastic waves, demonstrating the measurement of both tensile and shear moduli in human cornea in vivo with unprecedented precision. This technique paves the way for comprehensive investigations into corneal mechanics and holds clinical significance in various aspects of corneal health and disease management.

Study of the Influence of Boundary Conditions on Corneal Deformation Based on the Finite Element Method of a Corneal Biomechanics Model

Implementing in silico corneal biomechanical models for surgery applications can be boosted by developing patient-specific finite element models adapted to clinical requirements and optimized to reduce computational times. This research proposes a novel corneal multizone-based finite element model with octants and circumferential zones of clinical interest for material definition. The proposed model was applied to four patient-specific physiological geometries of keratoconus-affected corneas. Free-stress geometries were calculated by two iterative methods, the displacements and prestress methods, and the influence of two boundary conditions: embedded and pivoting. The results showed that the displacements, stress and strain fields differed for the stress-free geometry but were similar and strongly depended on the boundary conditions for the estimated physiological geometry when considering both iterative methods. The comparison between the embedded and pivoting boundary conditions showed bigger differences in the posterior limbus zone, which remained closer in the central zone. The computational calculation times for the stress-free geometries were evaluated. The results revealed that the computational time was prolonged with disease severity, and the displacements method was faster in all the analyzed cases. Computational times can be reduced with multicore parallel calculation, which offers the possibility of applying patient-specific finite element models in clinical applications.

A mechanical model of ocular bulb vibrations and implications for acoustic tonometry

In this study, we propose a comprehensive mechanical model of ocular bulb vibrations and discuss its implications for acoustic tonometry. The model describes the eye wall as a spherical, pre-stressed elastic shell containing a viscoelastic material and accounts for the interaction between the elastic corneoscleral shell and the viscoelastic vitreous humor. We investigate the natural frequencies of the system and the corresponding vibration modes, expanding the solution in terms of scalar and vector spherical harmonics. From a quantitative point of view, our findings reveal that the eyebulb vibration frequencies significantly depend on IOP. This dependency has two origins: "geometric" stiffening, due to an increase of the pre-stress, and "material" stiffening, due to the nonlinearity of the stress-strain curve of the sclera. The model shows that the second effect is by far dominant. We also find that the oscillation frequencies depend on ocular rigidity, but this dependency is important only at relatively large values of IOP. Thus close to physiological conditions, IOP is the main determinant of ocular vibration frequencies. The vitreous rheological properties are found to mostly influence vibration damping. This study contributes to the understanding of the mechanical behavior of the eye under dynamic conditions and thus has implications for non-contact intraocular pressure measurement techniques, such as acoustic tonometry. The model can also be relevant for other ocular pathological conditions, such as traumatic retinal detachment, which are believed to be influenced by the dynamic behavior of the eye.

Simultaneous tensile and shear measurement of the human cornea in vivo using S0- and A0-wave optical coherence elastography

Understanding corneal stiffness is valuable for improving refractive surgery, detecting corneal abnormalities, and assessing intraocular pressure. However, accurately measuring the elastic properties, particularly the tensile and shear moduli that govern mechanical deformation, has been challenging. To tackle this issue, we have developed guided-wave optical coherence elastography that can simultaneously excite and analyze symmetric (S0) and anti-symmetric (A0) elastic waves in the cornea at frequencies around 10 kHz and allows us to extract tensile and shear properties from measured wave dispersion curves. By applying acoustoelastic theory that incorporates corneal tension and a nonlinear constitutive tissue model, we verified the technique using elastomer phantoms and ex vivo porcine corneas and investigated the dependence on intraocular pressure. For two healthy human subjects, we measured a mean tensile modulus of 3.6 MPa and a mean shear modulus of 76 kPa in vivo with estimated errors of < 4%. This technique shows promise for the quantitative biomechanical assessment of the cornea in a clinical setting.

How can machine learning and multiscale modeling benefit ocular drug development?

The eyes possess sophisticated physiological structures, diverse disease targets, limited drug delivery space, distinctive barriers, and complicated biomechanical processes, requiring a more in-depth understanding of the interactions between drug delivery systems and biological systems for ocular formulation development. However, the tiny size of the eyes makes sampling difficult and invasive studies costly and ethically constrained. Developing ocular formulations following conventional trial-and-error formulation and manufacturing process screening procedures is inefficient. Along with the popularity of computational pharmaceutics, non-invasive in silico modeling & simulation offer new opportunities for the paradigm shift of ocular formulation development. The current work first systematically reviews the theoretical underpinnings, advanced applications, and unique advantages of data-driven machine learning and multiscale simulation approaches represented by molecular simulation, mathematical modeling, and pharmacokinetic (PK)/pharmacodynamic (PD) modeling for ocular drug development. Following this, a new computer-driven framework for rational pharmaceutical formulation design is proposed, inspired by the potential of in silico explorations in understanding drug delivery details and facilitating drug formulation design. Lastly, to promote the paradigm shift, integrated in silico methodologies were highlighted, and discussions on data challenges, model practicality, personalized modeling, regulatory science, interdisciplinary collaboration, and talent training were conducted in detail with a view to achieving more efficient objective-oriented pharmaceutical formulation design.

[Analysis of the results of modified personalized topographically and tomographically oriented technique of ultraviolet corneal collagen crosslinking]

PURPOSE

The study aims to develop a modified personalized topographically and tomographically oriented technique of ultraviolet corneal collagen cross-linking (UVCXL) to affect the area of the cornea with weakest biomechanical properties as determined by mathematical modeling.

MATERIAL AND METHODS

Modeling of the biomechanics of keratoconic cornea under conditions of external diagnostic action was done using COMSOL Multiphysics® software. Finite-element analysis procured 3D images of stress/deformation distribution pattern throughout the cornea. Matching these 3D images with primary topographic and tomographic Pentacam AXL maps and Corvis ST findings allowed determining localization and dimensions of impaired regions of the cornea. The acquired data helped develop the modified corneal collagen cross-linking technique, which was applied in the treatment of 36 persons (36 eyes) with degrees I and II keratoconus.

RESULTS

Uncorrected and best-corrected visual acuity (UCVA and BCVA logMAR) in all patients after modified UVCXL increased after the follow-up period lasting 6-12 months by 0.2±0.19 (23%) and 0.1±0.14 (29%) (p<0.05), respectively, in comparison with preoperative values. Maximum keratometry (Kmax) decreased by 1.35±1.63% (3%; p<0.05) in all cases at 6-12 months follow-up. Improvement of corneal biomechanical strength was determined by statistically significant increase in corneal stiffness index (SP-A1) and corneal stress-strain index (SSI) measured with Pentacam AXL and Corvis ST at 6-12 months follow-up by 15.1±5.04 (18%) and 0.21±0.20 (23%) (p<0.05), respectively. Effectiveness of the developed UVCXL technique is also confirmed by the appearance of a characteristic morphological marker - «demarcation line» at the cross-linking site in keratoconus projection at the depth of 240±10.2 µm.

CONCLUSION

The developed personalized topographically and tomographically oriented UVCXL technique provides an evident stabilizing effect on the cornea in the form of an increase in its biomechanical strength, improvement of clinical, functional indicators and safety of keratoconus treatment.

Biomechanical analysis of ocular diseases and its in vitro study methods

Ocular diseases are closely related to the physiological changes in the eye sphere and its contents. Using biomechanical methods to explore the relationship between the structure and function of ocular tissue is beneficial to reveal the pathological processes. Studying the pathogenesis of various ocular diseases will be helpful for the diagnosis and treatment of ocular diseases. We provide a critical review of recent biomechanical analysis of ocular diseases including glaucoma, high myopia, and diabetes. And try to summarize the research about the biomechanical changes in ocular tissues (e.g., optic nerve head, sclera, cornea, etc.) associated with those diseases. The methods of ocular biomechanics research in vitro in recent years are also reviewed, including the measurement of biomechanics by ophthalmic equipment, finite element modeling, and biomechanical analysis methods. And the preparation and application of microfluidic eye chips that emerged in recent years were summarized. It provides new inspiration and opportunity for the pathogenesis of eye diseases and personalized and precise treatment.

Estimations of Critical Clear Corneal Incisions Required for Lens Insertion in Cataract Surgery: A Mathematical Aspect

In a routine cataract operation cornea tissue may be damaged when an intra-ocular lens (IOL) injector of diameter between 1.467 and 2.011 mm is inserted through an empirically designed 2.2 mm corneal incision. We aimed to model and estimate the minimal length of the incision required to avoid wound tear. It was assumed that the damage was caused by tissue fracture at the tips of the incision, and this fracture could be studied using damage and fracture mechanics. The criterion of the damage was caused by a tear governed by the critical energy release rate (ERR) Gc, which is tissue dependent. Analytical and numerical studies were both conducted indicating the possibility of a safe and effective incision in cataract surgery. Six commonly used IOL injection systems were examined. Our results suggested that the recommended 2.2 mm incision cannot be treated as a universal threshold. Quicker IOL insertion may reduce wound damage. It was also recommended to advance IOL injector via its minor axis, and to cut the tear preferably along the circumferential direction due to tissue orthotropy. This study provides useful information and a deeper insight into the potential for mechanical damage to the corneal wound in cataract surgery.

Numerical Study of Customized Artificial Cornea Shape by Hydrogel Biomaterials on Imaging and Wavefront Aberration

The blindness caused by cornea diseases has exacerbated many patients all over the world. The disadvantages of using donor corneas may cause challenges to recovering eye sight. Developing artificial corneas with biocompatibility may provide another option to recover blindness. The techniques of making individual artificial corneas that fit the biometric parameters for each person can be used to help these patients effectively. In this study, artificial corneas with different shapes (spherical, aspherical, and biconic shapes) are designed and they could be made by two different hydrogel polymers that form an interpenetrating polymer network for their excellent mechanical strength. Two designed cases for the artificial corneas are considered in the simulations: to optimize the artificial cornea for patients who still wear glasses and to assume that the patient does not wear glasses after transplanting with the optimized artificial cornea. The results show that the artificial corneas can efficiently decrease the imaging blur. Increasing asphericity of the current designed artificial corneas can be helpful for the imaging corrections. The differences in the optical performance of the optimized artificial corneas by using different materials are small. It is found that the optimized artificial cornea can reduce the high order aberrations for the second case.

Delineating Corneal Elastic Anisotropy in a Porcine Model Using Noncontact OCT Elastography and Ex Vivo Mechanical Tests

Purpose

To compare noncontact acoustic microtapping (AμT) OCT elastography (OCE) with destructive mechanical tests to confirm corneal elastic anisotropy.

Design

Ex vivo laboratory study with noncontact AμT-OCE followed by mechanical rheometry and extensometry.

Participants

Inflated cornea of whole-globe porcine eyes (n = 9).

Methods

A noncontact AμT transducer was used to launch propagating mechanical waves in the cornea that were imaged with phase-sensitive OCT at physiologically relevant controlled pressures. Reconstruction of both Young's modulus (E) and out-of-plane shear modulus (G) in the cornea from experimental data was performed using a nearly incompressible transversely isotropic (NITI) medium material model assuming spatial isotropy of corneal tensile properties. Corneal samples were excised and parallel plate rheometry was performed to measure shear modulus, G. Corneal samples were then subjected to strip extensometry to measure the Young's modulus, E.

Main Outcome Measures

Strong corneal anisotropy was confirmed with both AμT-OCE and mechanical tests, with the Young's (E) and shear (G) moduli differing by more than an order of magnitude. These results show that AμT-OCE can quantify both moduli simultaneously with a noncontact, noninvasive, clinically translatable technique.

Results

Mean of the OCE measured moduli were E = 12 ± 5 MPa and G = 31 ± 11 kPa at 5 mmHg and E = 20 ± 9 MPa and G = 61 ± 29 kPa at 20 mmHg. Tensile testing yielded a mean Young's modulus of 1 MPa - 20 MPa over a strain range of 1% to 7%. Shear storage and loss modulus (G'/G'') measured with rheometry was approximately 82/13 ± 12/4 kPa at 0.2 Hz and 133/29 ± 16/3 kPa at 16 Hz (0.1% strain).

Conclusions

The cornea is confirmed to be a strongly anisotropic elastic material that cannot be characterized with a single elastic modulus. The NITI model is the simplest one that accounts for the cornea's incompressibility and in-plane distribution of lamellae. AμT-OCE has been shown to be the only reported noncontact, noninvasive method to measure both elastic moduli. Submillimeter spatial resolution and near real-time operation can be achieved. Quantifying corneal elasticity in vivo will enable significant innovation in ophthalmology, helping to develop personalized biomechanical models of the eye that can predict response to ophthalmic interventions.

Effects of intracorneal ring segments implementation technique and design on corneal biomechanics and keratometry in a personalized computational analysis

The implementation of intracorneal ring segments (ICRS) is one of the successfully applied refractive operations for the treatment of keratoconus (kc) progression. The different selection of ICRS types along with the surgical implementation techniques can significantly affect surgical outcomes. Thus, this study aimed to investigate the influence of ICRS implementation techniques and design on the postoperative biomechanical state and keratometry results. The clinical data of three patients with different stages and patterns of keratoconus were assessed to develop a three-dimensional (3D) patient-specific finite-element model (FEM) of the keratoconic cornea. For each patient, the exact surgery procedure definitions were interpreted in the step-by-step FEM. Then, seven surgical scenarios, including different ICRS designs (complete and incomplete segment), with two surgical implementation methods (tunnel incision and lamellar pocket cut), were simulated. The pre- and postoperative predicted results of FEM were validated with the corresponding clinical data. For the pre- and postoperative results, the average error of 0.4% and 3.7% for the mean keratometry value ([Formula: see text]) were predicted. Furthermore, the difference in induced flattening effects was negligible for three ICRS types (KeraRing segment with arc-length of 355, 320, and two separate 160) of equal thickness. In contrast, the single and double progressive thickness of KeraRing 160 caused a significantly lower flattening effect compared to the same type with constant thickness. The observations indicated that the greater the segment thickness and arc-length, the lower the induced mean keratometry values. While the application of the tunnel incision method resulted in a lower [Formula: see text] value for moderate and advanced KC, the induced maximum Von Mises stress on the postoperative cornea exceeded the induced maximum stress on the cornea more than two to five times compared to the pocket incision and the preoperative state of the cornea. In particular, an asymmetric regional Von Mises stress on the corneal surface was generated with a progressive ICRS thickness. These findings could be an early biomechanical sign for a later corneal instability and ICRS migration. The developed methodology provided a platform to personalize ICRS refractive surgery with regard to the patient's keratoconus stage in order to facilitate the efficiency and biomechanical stability of the surgery.

Influence of the eye globe design on biomechanical analysis

PURPOSE

To assess the mechanical contribution of inner eye components on corneal deformation during a finite element analysis.

METHODS

A finite element model of an eye globe was implemented to examine the corneal response under various mechanical conditions. The model incorporates the cornea, limbus, sclera, iris, lens, muscles, anterior chamber and vitreous. The Ogden hyperelastic model was used for the corneo-limbal region and the Yeoh isotropic model for the sclera. The anterior chamber was modelled as a cavity and other eye components were incorporated as linear elastic material. A fluid dynamic simulation was implemented to determine the spatial air puff velocity and pressure profiles around corneal surface.

RESULTS

The maximal apical displacement under IOP = 15 mmHg was 0.22 mm with a stress of 0.013 MPa. An unrestrained limbus slightly increases the apical displacement, while an unrestrained equatorial sclera largely increases the displacement by 10%, resulting in reduced stiffness. The iris slightly decreases the displacement but increases stress in the corneal periphery. Meanwhile, the joint contribution of muscle and lens cannot be neglected as it reduces corneal displacement by 50%. Incorporation of the remaining eye components results in nearly similar results. Under air puff loading, a free equatorial sclera raised the dynamic deformation amplitude by nearly 2%, while the dynamic profile remained similar for all remaining study cases considered.

CONCLUSION

In a finite element analysis, the lens, iris, and muscle each provide major mechanical contributions to corneal deformation, and it is highly recommended that the internal contributions are considered.

Interferometric Ex Vivo Evaluation of the Spatial Changes to Corneal Biomechanics Introduced by Topographic CXL: A Pilot Study

PURPOSE

To determine the efficacy of interferometry for examining the spatial changes to the corneal biomechanical response to simulated intraocular pressure (IOP) fluctuations that occur after corneal cross-linking (CXL) applied in different topographic locations.

METHODS

Displacement speckle pattern interferometry (DSPI) was used to measure the total anterior surface displacement of human and porcine corneas in response to pressure variations up to 1 mm Hg from a baseline pressure of 16.5 mm Hg, both before and after CXL treatment, which was applied in isolated topographic locations (10-minute riboflavin soak [VibeX-Xtra; Avedro, Inc], 8-minute ultraviolet-A exposure at 15 mW/cm²). Alterations to biomechanics were evaluated by directly comparing the responses before and after treatment for each cornea.

RESULTS

Before CXL, the corneal response to loading indicated spatial variability in mechanical properties. CXL treatments had a variable effect on the corneal response to loading dependent on the location of treatment, with reductions in regional displacement of up to 80% in response to a given pressure increase.

CONCLUSIONS

Selectively cross-linking in different topographic locations introduces position-specific changes to mechanical properties that could potentially be used to alter the refractive power of the cornea. Changes to the biomechanics of the cornea after CXL are complex and appear to vary significantly depending on treatment location and initial biomechanics. Hence, further investigations are required on a larger number of corneas to allow the development of customized treatment protocols. In this study, laser interferometry was demonstrated to be an effective and valuable tool to achieve this. [J Refract Surg. 2021;37(4):263-273.].

Indentation of the cornea: A Bi-layer contact problem

Histological observations of the cornea have identified the presence of multiple layers with differing thickness and function. The composition of the cornea consists primarily of collagen fibrils held together with proteoglycans but with an aqueous interstitial component being dominant. Indentation provides a means to quantify the spatial variation of the mechanical properties of the cornea, however the role of the different layers on the indentation response has barely been addressed. In addition, the response of the fluid content and its displacement during indentation has not been adequately considered. In this study indentation of the cornea with a relatively large spherical tipped indenter (R = 500 μm) is considered. It was observed that the initial phase of loading did not fit a classic Hertz elastic response but showed an initial steeper slope that gradually declines with increasing force and displacement. A relatively simple approach is developed that initially considers the cornea as a poro-elastic bi-layer contact problem, that is the presence of an outer thin stiffer Bowman's layer overlaying the thicker less stiff stroma.