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

Revealing regional variations in scleral shear modulus in a rabbit eye model using multi-directional ultrasound optical coherence elastography

The mechanical properties of the sclera play a critical role in supporting the ocular structure and maintaining its shape. However, non-invasive measurements to quantify scleral biomechanics remain challenging. Recently introduced multi-directional optical coherence elastography (OCE) combined with an air-coupled ultrasound transducer for excitation of elastic surface waves was used to estimate phase speed and shear modulus in ex vivo rabbit globes (n = 7). The scleral phase speed (12.1 ± 3.2 m/s) was directional-dependent and higher than for corneal tissue (5.9 ± 1.4 m/s). In the tested locations, the sclera proved to be more anisotropic than the cornea by a factor of 11 in the maximum of modified planar anisotropy coefficient. The scleral shear moduli, estimated using a modified Rayleigh-Lamb wave model, showed significantly higher values in the circumferential direction (65.4 ± 31.9 kPa) than in meridional (22.5 ± 7.2 kPa); and in the anterior zone (27.3 ± 9.3 kPa) than in the posterior zone (17.8 ± 7.4 kPa). The multi-directional scanning approach allowed both quantification and radial mapping of estimated parameters within a single measurement. The results indicate that multi-directional OCE provides a valuable non-invasive assessment of scleral tissue properties that may be useful in the development of improved ocular models, the evaluation of potential myopia treatment strategies, and disease characterization and monitoring.

Iris Morphological and Biomechanical Factors Influencing Angle Closure During Pupil Dilation

Purpose

To use finite element (FE) analysis to assess what morphologic and biomechanical factors of the iris and anterior chamber are more likely to influence angle narrowing during pupil dilation.

Methods

The study consisted of 1344 FE models comprising the cornea, sclera, lens, and iris to simulate pupil dilation. For each model, we varied the following parameters: anterior chamber depth (ACD = 2-4 mm) and anterior chamber width (ACW = 10-12 mm), iris convexity (IC = 0-0.3 mm), iris thickness (IT = 0.3-0.5 mm), stiffness (E = 4-24 kPa), and Poisson's ratio (v = 0-0.3). We evaluated the change in (△∠) and the final dilated angles (∠f) from baseline to dilation for each parameter.

Results

The final dilated angles decreased with a smaller ACD (∠f = 53.4° ± 12.3° to 21.3° ± 14.9°), smaller ACW (∠f = 48.2° ± 13.5° to 26.2° ± 18.2°), larger IT (∠f = 52.6° ± 12.3° to 24.4° ± 15.1°), larger IC (∠f = 45.0° ± 19.2° to 33.9° ± 16.5°), larger E (∠f = 40.3° ± 17.3° to 37.4° ± 19.2°), and larger v (∠f = 42.7° ± 17.7° to 34.2° ± 18.1°). The change in angles increased with larger ACD (△∠ = 9.37° ± 11.1° to 15.4° ± 9.3°), smaller ACW (△∠ = 7.4° ± 6.8° to 16.4° ± 11.5°), larger IT (△∠ = 5.3° ± 7.1° to 19.3° ± 10.2°), smaller IC (△∠ = 5.4° ± 8.2° to 19.5° ± 10.2°), larger E (△∠ = 10.9° ± 12.2° to 13.1° ± 8.8°), and larger v (△∠ = 8.1° ± 9.4° to 16.6° ± 10.4°).

Conclusions

The morphology of the iris (IT and IC) and its innate biomechanical behavior (E and v) were crucial in influencing the way the iris deformed during dilation, and angle closure was further exacerbated by decreased anterior chamber biometry (ACD and ACW).

A discrete-to-continuum model for the human cornea with application to keratoconus

We introduce a discrete mathematical model for the mechanical behaviour of a planar slice of human corneal tissue, in equilibrium under the action of physiological intraocular pressure (IOP). The model considers a regular (two-dimensional) network of structural elements mimicking a discrete number of parallel collagen lamellae connected by proteoglycan-based chemical bonds (crosslinks). Since the thickness of each collagen lamella is small compared to the overall corneal thickness, we upscale the discrete force balance into a continuum system of partial differential equations and deduce the corresponding macroscopic stress tensor and strain energy function for the micro-structured corneal tissue. We demonstrate that, for physiological values of the IOP, the predictions of the discrete model converge to those of the continuum model. We use the continuum model to simulate the progression of the degenerative disease known as keratoconus, characterized by a localized bulging of the corneal shell. We assign a spatial distribution of damage (i.e. reduction of the stiffness) to the mechanical properties of the structural elements and predict the resulting macroscopic shape of the cornea, showing that a large reduction in the element stiffness results in substantial corneal thinning and a significant increase in the curvature of both the anterior and posterior surfaces.

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.

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.

A novel intraocular pressure predicting method based on hyperelastic mechanical model of cornea

Measuring intraocular pressure (IOP) is crucial and remains challenging in diagnosing glaucoma, as it is associated with cornea deformation during inflation. In this study, a three-dimensional analytical model based on hyperelastic constitutive relationship to predict correlation between cornea vertex displacement and the IOP is proposed. The analytical model is validated by rigorous experiments. Rabbit corneas were selected for this study and their mechanical properties were obtained using uniaxial tensile tests. To mimic the environment in which the cornea exists, an artificial anterior chamber equipped with water-injection pipelines was constructed to study the relationship between the corneal vertex displacement with IOP value in practical situation. The experimental results of rabbits corneas prove that the IOP can be deduced based on the measured corneal vertex displacement by the analytical model. Furthermore, subtle difference occurs when comparing the calculated human IOPs with those measured by medical equipment, demonstrating that the proposed method is suitable for monitoring the IOP of human. This novel IOP predicting method provides new inspiration for the design of eyepieces, as well as the preoperative preparation for laser surgery and evaluation of corneal damage.

Structural control of corneal transparency, refractive power and dynamics

The cornea needs to be transparent to visible light and precisely curved to provide the correct refractive power. Both properties are governed by its structure. Corneal transparency arises from constructive interference of visible light due to the relatively ordered arrangement of collagen fibrils in the corneal stroma. The arrangement is controlled by the negatively charged proteoglycans surrounding the fibrils. Small changes in fibril organisation can be tolerated but larger changes cause light scattering. Corneal keratocytes do not scatter light because their refractive index matches that of the surrounding matrix. When activated, however, they become fibroblasts that have a lower refractive index. Modelling shows that this change in refractive index significantly increases light scatter. At the microscopic level, the corneal stroma has a lamellar structure, the parallel collagen fibrils within each lamella making a large angle with those of adjacent lamellae. X-ray scattering has shown that the lamellae have preferred orientations in the human cornea: inferior-superior and nasal-temporal in the central cornea and circumferential at the limbus. The directions at the centre of the cornea may help withstand the pull of the extraocular muscles whereas the pseudo-circular arrangement at the limbus supports the change in curvature between the cornea and sclera. Elastic fibres are also present; in the limbus they contain fibrillin microfibrils surrounding an elastin core, whereas at the centre of the cornea, they exist as thin bundles of fibrillin-rich microfibrils. We present a model based on the structure described above that may explain how the cornea withstands repeated pressure changes due to the ocular pulse.

The potential influence of the ligament of Wieger on the crystalline lens shape

This research uses mathematical modelling to evaluate the influence of the ligament of Wieger on the crystalline lens shape at rest, and during accommodation. An axisymmetric model of the anterior segment, including the ligament of Wieger, was created using the finite element method. Different conditions including variations of stiffness and positions of the ligament, with and without the ligament, were tested to see how they affected lens curvature and optical power. Adding the ligament of Wieger to the simulation had a noticeable impact on the optical power of the lens, particularly on the posterior surface power and total power. Ligament stiffness and width significant influenced the accommodative range of the eye by - 0.95D and - 2.39D for ligaments with the same and 3× the stiffness of the capsular bag, respectively. Ligament width and inner diameter had negligible effects on lens thickness but did have significant effects on posterior surface power and accommodation. In this simulation, we found that the ligament of Wieger can significantly affect the lens shape, both at rest and during accommodation, and may need to be considered in lens models.

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.

Patient-specific finite element analysis of human corneal lenticules: An experimental and numerical study

The number of elective refractive surgeries is constantly increasing due to the drastic increase in myopia prevalence. Since corneal biomechanics are critical to human vision, accurate modeling is essential to improve surgical planning and optimize the results of laser vision correction. In this study, we present a numerical model of the anterior cornea of young patients who are candidates for laser vision correction. Model parameters were determined from uniaxial tests performed on lenticules of patients undergoing refractive surgery by means of lenticule extraction, using patient-specific models of the lenticules. The models also took into account the known orientation of collagen fibers in the tissue, which have an isotropic distribution in the corneal plane, while they are aligned along the corneal curvature and have a low dispersion outside the corneal plane. The model was able to reproduce the experimental data well with only three parameters. These parameters, determined using a realistic fiber distribution, yielded lower values than those reported in the literature. Accurate characterization and modeling of the cornea of young patients is essential to study better refractive surgery for the population undergoing these treatments, to develop in silico models that take corneal biomechanics into account when planning refractive surgery, and to provide a basis for improving visual outcomes in the rapidly growing population undergoing these treatments.

Assessment of age-related change of the ocular support system

To estimate the material stiffness of the orbital soft tissue in human orbits using an inverse numerical analysis approach, which could be used in future studies to understand the behaviour under dynamic, non-contact tonometry or simulate various ophthalmological conditions. Clinical data were obtained for the left eye of 185 Chinese participants subjected to a complete ophthalmic examination, including tests by the Corvis ST and Pentacam. 185 numerical models of the eye globes were built with idealised geometry of the sclera while considering the corneal tomography measured by the Pentacam. The models were extended to include representations of the orbital soft tissue (OST), which were given idealised geometry. The movement of the whole eye in response to an air-puff directed at the central cornea was examined and used in an inverse analysis process to estimate the biomechanical stiffness parameters of the OST. The results indicated a weak correlation of E _t with the progression of age, regardless of the stress at which E _t was calculated. However, there was evidence of significant differences in E _t between some of the age groups. There was statistical evidence of significant differences between E _t in the age range 20< years < 43 relative to E _t in OST with age ranges 43< years < 63 (p = 0.022) and 63< years < 91 (p = 0.011). In contrast, E _t in OST with age ranges 43< years < 63 and 63< years < 91 were not significantly different (p = 0.863). The optimised mechanical properties of the OST were found to be almost four times stiffer than properties of fatty tissue of previous experimental work. This study consolidated previous findings of the role of extraocular muscles on the ocular suppor system. In addition, the rotation of the globe during corvis loading is suggested to be of posterior components of the globe and shall be further investigated.

Predictability of Astigmatism Correction by Arcuate Incisions with a Femtosecond Laser Using the Gaussian Approximation Calculation

Planning astigmatic correction is a complex task. Biomechanical simulation models are useful for predicting the effects of the physical procedure on the cornea. Algorithms based on these models allow preoperative planning and simulate the outcome of patient-specific treatment. The objective of this study was to develop a customised optimisation algorithm and determine the predictability of astigmatism correction by femtosecond laser arcuate incisions. In this study, biomechanical models and Gaussian approximation curve calculations were used for surgical planning. Thirty-four eyes with mild astigmatism were included, and corneal topographies were evaluated before and after femtosecond laser-assisted cataract surgery with arcuate incisions. The follow-up time was up to 6 weeks. Retrospective data showed a significant reduction in postoperative astigmatism. A total of 79.4% showed a postoperative astigmatic value less than 1 D. Clinical refraction was significantly reduced from -1.39 ± 0.79 D preoperatively to -0.86 ± 0.67 D postoperatively (p 0.02). A positive reduction in topographic astigmatism was also observed (p < 0.00). The best-corrected visual acuity increased postoperatively (p < 0.001). We can conclude that customised simulations based on corneal biomechanics are a valuable tool for correcting mild astigmatism with corneal incisions in cataract surgery to improve postoperative visual outcomes.

Typical localised element-specific finite element anterior eye model

Purpose

The study presents an averaged anterior eye geometry model combined with a localised material model that is straightforward, appropriate and amenable for implementation in finite element (FE) modelling.

Methods

Both right and left eye profile data of 118 subjects (63 females and 55 males) aged 22-67 years (38.5 ± 7.6) were used to build an averaged geometry model. Parametric representation of the averaged geometry model was achieved through two polynomials dividing the eye into three smoothly connected volumes. This study utilised the collagen microstructure x-ray data of 6 ex-vivo healthy human eyes, 3 right eyes and 3 left eyes in pairs from 3 donors, 1 male and 2 females aged between 60 and 80 years, to build a localised element-specific material model for the eye.

Results

Fitting the cornea and the posterior sclera sections to a 5th-order Zernike polynomial resulted in 21 coefficients. The averaged anterior eye geometry model recorded a limbus tangent angle of 37° at a radius of 6.6 mm from the corneal apex. In terms of material models, the difference between the stresses generated in the inflation simulation up to 15 mmHg in the ring-segmented material model and localised element-specific material model were significantly different (p < 0.001) with the ring-segmented material model recording average Von-Mises stress 0.0168 ± 0.0046 MPa and the localised element-specific material model recording average Von-Mises stress 0.0144 ± 0.0025 MPa.

Conclusions

The study illustrates an averaged geometry model of the anterior human eye that is easy to generate through two parametric equations. This model is combined with a localised material model that can be used either parametrically through a Zernike fitted polynomial or non-parametrically as a function of the azimuth angle and the elevation angle of the eye globe. Both averaged geometry and localised material models were built in a way that makes them easy to implement in FE analysis without additional computation cost compared to the limbal discontinuity so-called idealised eye geometry model or ring-segmented material model.

Keratoconus: A Biomechanical Perspective

PURPOSE

The relevance of corneal biomechanics and the importance of including it in the clinical assessment of corneal ectasias are being increasingly recognized. The connection between corneal ultrastructure, biomechanical properties, and optical function is exemplified by a condition like keratoconus. Biomechanical instability is seen as the underlying basis for the secondary morphological changes in the cornea. Asymmetric biomechanical weakening is believed to drive progressive corneal steepening and thinning. Biomechanical strengthening is the principle of collagen crosslinking that has been shown to effectively arrest progression of the keratoconus. Corneal biomechanics has therefore ignited the interest of researchers and clinicians alike and has given us new insights into the cause and course of the disease. This article is an overview of the extensive work published, predominantly in the last two decades, on the biomechanical aspect of keratoconus.

METHODS

Published articles on corneal biomechanics in the specific context of keratoconus were reviewed, based on an electronic search using PubMed, Elsevier, and Science Direct. The search terms used included "Corneal Biomechanics," "Mechanical properties of the cornea," "Corneal ultrastructure," "Corneal Collagen," and "Keratoconus". Articles pertaining to refractive surgery, keratoplasty, collagen crosslinking, or intrastromal rings were excluded.

RESULTS

The electronic search revealed more than 500 articles, from which 80 were chosen for this article.

CONCLUSIONS

The structural and organizational pattern of the corneal stroma determines its mechanical properties and are responsible for the maintenance of the normal shape and function of the cornea. Changes in the ultrastructure are responsible for the biomechanical instability that leads to corneal ectasia. As non-invasive methods for evaluating corneal biomechanics in vivo evolve, our ability to diagnose subclinical keratoconus will improve, allowing identification of patients at risk to develop ectasia and to allow early treatment to arrest progression of the disease.

Investigation on forced vibration characteristics of Nitinol tracheal stent

BACKGROUND

Tracheal stents can be placed in a narrow position in the human trachea to ensure smooth breathing. And the stent will deform during service by the influence of the physiological environment or random excitations, such as coughing.

METHODS

This paper divides the vibration into periodic and random vibrations according to the different pressures. And a coupling vibration model was established by analyzing the contact relationship between the stent and the trachea tissue. And this study discusses the influence of tracheal diameter, respiratory pressure, and frequency on the stent vibration characteristics through Ansys simulation. In addition, the nonlinear equations were solved by the Matlab numerical analysis method, which could help analyze the influence of cough intensity on the stability of the tracheal stent system.

RESULTS

The results showed that when tracheal stenosis occurred in the trachea's more significant grade, the trachea stent was more likely to fall off when treated with a tracheal stent. With the increase in respiratory frequency and pressure, the deformation of the tracheal stent is more considerable. Moreover, the frequency of normal cough hardly affects the stability of the stent system, while the excitation force and damping coefficient value greatly influence the system. When the excitation force of the cough exceeds the critical importance of 20 N, the tracheal stent is prone to fall off. This study comprehensively obtained the forced vibration characteristics of the stent under service conditions, which could make up for the shortage of the vibration theory of the stent.

CONCLUSION

The results can provide a theoretical basis for predicting the possibility of stent loss in clinical treatment.

Orientation and depth dependent mechanical properties of the porcine cornea: Experiments and parameter identification

The porcine cornea is a standard animal model in ophthalmic research, making its biomechanical characterization and modeling important to develop novel treatments such as crosslinking and refractive surgeries. In this study, we present a numerical model of the porcine cornea based on experimental measurements that captures both the depth dependence and orientation dependence of the mechanical response. The mechanical parameters of the established anisotropic hyperelastic material models of Gasser, Holzapfel and Ogden (HGO) and Markert were determined using tensile tests. Corneas were cut with a femtosecond laser in the anterior (100 μm), central (350 μm), and posterior (600 μm) regions into nasal-temporal, superior-inferior, and diagonal strips of 150 μm thickness. These uniformly thick strips were tested at a low speed using a single-axis testing machine. The results showed that the corneal mechanical properties remained constant in the anterior half of the cornea regardless of orientation, but that the material softened in the posterior layer. These results are consistent with the circular orientation of collagen observed in porcine corneas using X-ray scattering. In addition, the parameters obtained for the HGO model were able to reproduce the published inflation tests, indicating that it is suitable for simulating the mechanical response of the entire cornea. Such a model constitutes the basis for in silico platforms to develop new ophthalmic treatments. In this way, researchers can match their experimental surrogate porcine model with a numerical counterpart and validate the prediction of their algorithms in a complete and accessible environment.

Modification of Collagen Film via Surface Grafting of Taurine Molecular to Promote Corneal Nerve Repair and Epithelization Process

Corneal defects can seriously affect human vision, and keratoplasty is the most widely accepted therapy method for visual rehabilitation. Currently, effective treatment for clinical patients has been restricted due to a serious shortage of donated cornea tissue and high-quality artificial repair materials. As the predominant component of cornea tissue, collagen-based materials have promising applications for corneal repair. However, the corneal nerve repair and epithelization process after corneal transplantation must be improved. This research proposes a new collagen-based scaffold with good biocompatibility and biological functionality enhanced by surface chemical grafting of natural taurine molecular. The chemical composition of collagen-taurine (Col-Tau) material is evaluated by Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy, and its hydrophilic properties, light transmittance, swelling performance and mechanical tensile properties have been measured. The research results indicate that the Col-Tau sample has high transmittance and good mechanical properties, and exhibits excellent capacity to promote corneal nerve cell growth and the epithelization process of corneal epithelial cells. This novel Col-Tau material, which can be easily prepared at a low cost, should have significant application potential for the treating corneal disease in the future.

Collagen Film with Bionic Layered Structure and High Light Transmittance for Personalized Corneal Repair Fabricated by Controlled Solvent Evaporation Technique

Corneal blindness is a common phenomenon, and corneal transplantation is an effective treatment for corneal defects. However, there is usually a mismatch between the corneal repair material and the degree of the patient’s corneal defect. Therefore, patients with different corneal defects need suitable corneal repair materials with a specific microstructure for personalized treatment. In this research, collagen films with bionic structures were fabricated through ethanol evaporation technique by regulating the volume ratios of collagen solution: ethanol = 10:0(Col)/9:1(CC91)/8:2(CC82)/CC73(CC73). Under various preparation conditions, the obtained collagen films contain layered structures of different density. SEM photos show that the CC73 film with a dense layer arrangement has a microstructure similar to that of the corneal epithelial layer, whereas the Col film has a loose layered structure similar to that of the corneal stroma layer. Four kinds of collagen films showed different optical properties and water absorption ability. A more ordered arrangement of internal layer structure leads to better mechanical properties of the collagen film. In view of this, we think that these collagen films with different microstructures and different interlayer spacing may have huge potential applications for personalized corneal repair.

A new method for the in vivo identification of degenerated material property ranges of the human eye: feasibility analysis based on synthetic data

This paper proposes a new method for in vivo and almost real-time identification of biomechanical properties of the human cornea based on non-contact tonometer data. Further goal is to demonstrate the method's functionality based on synthetic data serving as reference. For this purpose, a finite element model of the human eye is constructed to synthetically generate full-field displacements from different data sets with keratoconus-like degradations. Then, a new approach based on the equilibrium gap method combined with a mechanical morphing approach is proposed and used to identify the material parameters from virtual test data sets. In a further step, random absolute noise is added to the virtual test data to investigate the sensitivity of the new approach to noise. As a result, the proposed method shows a relevant accuracy in identifying material parameters based on full-field displacements. At the same time, the method turns out to work almost in real time (order of a few minutes on a regular workstation) and is thus much faster than inverse problems solved by typical forward approaches. On the other hand, the method shows a noticeable sensitivity to rather small noise amplitudes rendering the method not accurate enough for the precise identification of individual parameter values. However, analysis show that the accuracy is sufficient for the identification of property ranges which might be related to diseased tissues. Thereby, the proposed approach turns out promising with view to diagnostic purposes.

Optical coherence elastography for assessing the influence of intraocular pressure on elastic wave dispersion in the cornea

The cornea is a highly specialized organ that relies on its mechanical stiffness to maintain its aspheric geometry and refractive power, and corneal diseases such as keratoconus have been linked to abnormal tissue stiffness and biomechanics. Dynamic optical coherence elastography (OCE) is a clinically promising non-contact and non-destructive imaging technique that can provide measurements of corneal tissue stiffness directly in vivo. The method relies on the concepts of elastography where shear waves are generated and imaged within a tissue to obtain mechanical properties such as tissue stiffness. The accuracy of OCE-based measurements is ultimately dependent on the mathematical theories used to model wave behavior in the tissue of interest. In the cornea, elastic waves propagate as guided wave modes which are highly dispersive and can be mathematically complex to model. While recent groups have developed detailed theories for estimating corneal tissue properties from guided wave behavior, the effects of intraocular pressure (IOP)-induced prestress have not yet been considered. It is known that prestress alone can strongly influence wave behavior, in addition to the associated non-linear changes in tissue properties. This present study shows that failure to account for the effects of prestress may result in overestimations of the corneal shear moduli, particularly at high IOPs. We first examined the potential effects of IOP and IOP-induced prestress using a combination of approximate mathematical theories describing wave behavior in thin plates with observations made from data published in the OCE literature. Through wave dispersion analysis, we deduce that IOP introduces a tensile hoop stress and may also influence an elastic foundational effect that were observable in the low-frequency components of the dispersion curves. These effects were incorporated into recently developed models of wave behavior in nearly incompressible, transversely isotropic (NITI) materials. Fitting of the modified NITI model with ex vivo porcine corneal data demonstrated that incorporation of the effects of IOP resulted in reduced estimates of corneal shear moduli. We believe this demonstrates that overestimation of corneal stiffness occurs if IOP is not taken into consideration. Our work may be helpful in separating inherent corneal stiffness properties that are independent of IOP; changes in these properties and in IOP are distinct, clinically relevant issues that affect the cornea health.

On the Relationship between Corneal Biomechanics, Macrostructure, and Optical Properties

Optical properties of the cornea are responsible for correct vision; the ultrastructure allows optical transparency, and the biomechanical properties govern the shape, elasticity, or stiffness of the cornea, affecting ocular integrity and intraocular pressure. Therefore, the optical aberrations, corneal transparency, structure, and biomechanics play a fundamental role in the optical quality of human vision, ocular health, and refractive surgery outcomes. However, the inter-relationships of those properties are not yet reported at a macroscopic scale within the hierarchical structure of the cornea. This work explores the relationships between the biomechanics, structure, and optical properties (corneal aberrations and optical density) at a macro-structural level of the cornea through dual Placido–Scheimpflug imaging and air-puff tonometry systems in a healthy young adult population. Results showed correlation between optical transparency, corneal macrostructure, and biomechanics, whereas corneal aberrations and in particular spherical terms remained independent. A compensation mechanism for the spherical aberration is proposed through corneal shape and biomechanics.

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.

Biomechanical properties of retina and choroid: a comprehensive review of techniques and translational relevance

Studying the biomechanical properties of biological tissue is crucial to improve our understanding of disease pathogenesis. The biomechanical characteristics of the cornea, sclera and the optic nerve head have been well addressed with an extensive literature and an in-depth understanding of their significance whilst, in comparison, knowledge of the retina and choroid is relatively limited. Knowledge of these tissues is important not only to clarify the underlying pathogenesis of a wide variety of retinal and vitreoretinal diseases, including age-related macular degeneration, hereditary retinal dystrophies and vitreoretinal interface diseases but also to optimise the surgical handling of retinal tissues and, potentially, the design and properties of implantable retinal prostheses and subretinal therapies. Our aim with this article is to comprehensively review existing knowledge of the biomechanical properties of retina, internal limiting membrane (ILM) and the Bruch’s membrane–choroidal complex (BMCC), highlighting the potential implications for clinical and surgical practice. Prior to this we review the testing methodologies that have been used both in vitro, and those starting to be used in vivo to aid understanding of their results and significance.

Fibril density reduction in keratoconic corneas

This study aims to estimate the reduction in collagen fibril density within the central 6 mm radius of keratoconic corneas through the processing of microstructure and videokeratography data. Collagen fibril distribution maps and topography maps were obtained for seven keratoconic and six healthy corneas, and topographic features were assessed to detect and calculate the area of the cone in each keratoconic eye. The reduction in collagen fibril density within the cone area was estimated with reference to the same region in the characteristic collagen fibril maps of healthy corneas. Together with minimum thickness and mean central corneal refractive power, the cone area was correlated with the reduction in the cone collagen fibrils. For the corneas considered, the mean area of keratoconic cones was 3.30 ± 1.90 mm². Compared with healthy corneas, fibril density in the cones of keratoconic corneas was lower by as much as 35%, and the mean reduction was 17 ± 10%. A linear approximation was developed to relate the magnitude of reduction to the refractive power, minimum corneal thickness and cone area (R² = 0.95, p < 0.001). Outside the cone area, there was no significant difference between fibril arrangement in healthy and keratoconic corneas. The presented method can predict the mean fibril density in the keratoconic eye's cone area. The technique can be applied in microstructure-based finite-element models of the eye to regulate its stiffness level and the stiffness distribution within the areas affected by keratoconus.

Experimental evaluation of stiffening effect induced by UVA/Riboflavin corneal cross-linking using intact porcine eye globes

UVA/riboflavin corneal cross-linking (CXL) is a common used approach to treat progressive keratoconus. This study aims to investigate the alteration of corneal stiffness following CXL by mimicking the inflation of the eye under the in vivo loading conditions. Seven paired porcine eye globes were involved in the inflation test to examine the corneal behaviour. Cornea-only model was constructed using the finite element method, without considering the deformation contribution from sclera and limbus. Inverse analysis was conducted to calibrate the non-linear material behaviours in order to reproduce the inflation test. The corneal stress and strain values were then extracted from the finite element models and tangent modulus was calculated under stress level at 0.03 MPa. UVA/riboflavin cross-linked corneas displayed a significant increase in the material stiffness. At the IOP of 27.25 mmHg, the average displacements of corneal apex were 307 ± 65 μm and 437 ± 63 μm (p = 0.02) in CXL and PBS corneas, respectively. Comparisons performed on tangent modulus ratios at a stress of 0.03 MPa, the tangent modulus measured in the corneas treated with the CXL was 2.48 ± 0.69, with a 43±24% increase comparing to its PBS control. The data supported that corneal material properties can be well-described using this inflation methods following CXL. The inflation test is valuable for investigating the mechanical response of the intact human cornea within physiological IOP ranges, providing benchmarks against which the numerical developments can be translated to clinic.

Multi-meridian corneal imaging of air-puff induced deformation for improved detection of biomechanical abnormalities

Corneal biomechanics play a fundamental role in the genesis and progression of corneal pathologies, such as keratoconus; in corneal remodeling after corneal surgery; and in affecting the measurement accuracy of glaucoma biomarkers, such as the intraocular pressure (IOP). Air-puff induced corneal deformation imaging reveals information highlighting normal and pathological corneal response to a non-contact mechanical excitation. However, current commercial systems are limited to monitoring corneal deformation only on one corneal meridian. Here, we present a novel custom-developed swept-source optical coherence tomography (SSOCT) system, coupled with a collinear air-puff excitation, capable of acquiring dynamic corneal deformation on multiple meridians. Backed by numerical simulations of corneal deformations, we propose two different scan patterns, aided by low coil impedance galvanometric scan mirrors that permit an appropriate compromise between temporal and spatial sampling of the corneal deformation profiles. We customized the air-puff module to provide an unobstructed SSOCT field of view and different peak pressures, air-puff durations, and distances to the eye. We acquired multi-meridian corneal deformation profiles (a) in healthy human eyes in vivo, (b) in porcine eyes ex vivo under varying controlled IOP, and (c) in a keratoconus-mimicking porcine eye ex vivo. We detected deformation asymmetries, as predicted by numerical simulations, otherwise missed on a single meridian that will substantially aid in corneal biomechanics diagnostics and pathology screening.

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.

A full-field 3D digital image correlation and modelling technique to characterise anterior cruciate ligament mechanics ex vivo

It is limiting to use conventional methods when characterising material properties of complex biological tissues with inhomogeneous and anisotropic structure, such as the anterior cruciate ligament (ACL) in the knee joint. This study aims to develop and utilise a three-dimensional digital image correlation method (3D DIC) for the purpose of determining material properties of femur-ACL-tibia complex across the surface without any contact between the tissue and the loading equipment. A full-field (360° view) 3D DIC test setup consisting of six digital single-lens reflex cameras was developed and ACL specimens from skeletally mature dog knee joints were tested. The six cameras were arranged into three pairs and the cameras within each pair were positioned with 25° in between to obtain the desired stereovision output. The test setup was calibrated twice: first to obtain the intrinsic and extrinsic parameters within camera pairs, and second to align the 3D surfaces from each camera pair in order to generate the full view of the ACLs. Using the undeformed 3D surfaces of the ligaments, ACL-specific finite element models were generated. Longitudinal deformation of ligaments under tensile loads obtained from the 3D DIC, and this was analysed to serve as input for the inverse finite element analysis. As a result, hyperelastic coefficients from the first-order Ogden model that characterise ACL behaviour were determined with a marginal error of <1.5%. This test setup and methodology provides a means to accurately determine inhomogeneous and anisotropic material properties of ACL. The methodology described in this study could be adopted to investigate other biological and cultured tissues with complex structure. STATEMENT OF SIGNIFICANCE: Determining the material properties of soft tissues with complex anatomical structure, such as the anterior cruciate ligament (ACL), is important to better understand their contribution to musculoskeletal biomechanics. Current conventional methods for characterising material properties of the ACL are often limited to a contact measurement approach, however an improved understanding of the mechanics of this complex tissue is vital in terms of preventing injury and developing novel therapies. This article reports the development and utilisation of non-contact optical methodology involving full-field three-dimensional digital image correlation and finite element analysis to accurately investigate material properties of the ACL, in a controlled environment. This technique reduces inaccuracies due to specimen clamping and more importantly considers the inhomogeneous nature of the examined tissue.

Microstructure-based numerical simulation of the mechanical behaviour of ocular tissue

This paper aims to present a novel full-eye biomechanical material model that incorporates the characteristics of ocular tissues at microstructural level, and use the model to analyse the age-related stiffening in tissue behaviour. The collagen content in ocular tissues, as obtained using X-ray scattering measurements, was represented by sets of Zernike polynomials that covered both the cornea and sclera, then used to reconstruct maps of collagen fibril magnitude and orientation on the three-dimensional geometry of the eye globe. Fine-mesh finite-element (FE) models with eye-specific geometry were built and supported by a user-defined material model (UMAT), which considered the regional variation of fibril density and orientation. The models were then used in an iterative inverse modelling study to derive the material parameters that represent the experimental behaviour of ocular tissues from donors aged between 50 and 90 years obtained in earlier ex vivo studies. Sensitivity analysis showed that reducing the number of directions that represented the anisotropy of collagen fibril orientation at each X-ray scattering measurement point from 180 to 16 would have limited and insignificant effect on the FE solution (0.08%). Inverse analysis resulted in material parameters that provided a close match with experimental intraocular pressure-deformation behaviour with a root mean square of error between 3.6% and 4.3%. The results also demonstrated a steady increase in mechanical stiffness in all ocular regions with age. A constitutive material model based on distributions of collagen fibril density and orientation has been developed to enable the accurate representation of the biomechanical behaviour of ocular tissues. The model offers a high level of control of stiffness and anisotropy across ocular globe, and therefore has the potential for use in planning surgical and medical procedures.

Keratoconus prognosis study for patients with corneal external mechanical stress mode

PURPOSE

To demonstrate the correlation between excessive eye rubbing and corneal degeneration for Keratoconus patients.

MATERIALS AND METHODS

Keratoconus (KC) patients who regularly rub their eyes had shown a rapid degeneration rate of their affected corneas. This observation is experimentally and numerical discussed and developed based on clinical data of 8 of KC Patients with a mean age of 26.5 ± 9.4 years old, and four healthy individuals with a mean age of 24.33 ± 5 years old at the baseline. Corneal topography was used to measure both central corneal thickness (CCT) and its total refractive power. The registered data had been exploited to assess the progression of the disease, and the final results were embedded in a finite element model of human corneas to simulate their response to eye rubbing at different stages of the pathology. Corneal lifetime prognosis using multi-layer perceptron was then established to estimate the number of eye rubbing cycles for each stage of KC.

RESULTS

The survey of KC patients who declared stopping eye rubbing had shown a decrease in CCT loss rate, followed by a durable stability. Mechanical stresses numerical simulations had shown different corneal behaviours in term of shape deformity, apical raise and corneal applanation between healthy and KC stages models. Apical rise ranged from 0.122 to 0.389 mm for an applied intraocular pressure that equals to 15 mmHg. A normal stress of 5 kPa provoked a corneal applanation that ranged from 0.27 mm in healthy cases to 1.173 mm in severe stages of the disease. The application of 2.5 kPa biaxial stress had resulted normal and tangential applanations that successively ranged from 0.152 and 0.173 mm in healthy corneas to 0.446 mm and 0.458 mm in severe KC stages. An adopted prognosis algorithm was able to predict the current stage of the disease and to estimate the remaining number of eye rubbing cycles before failure.

CONCLUSION

Eye rubbing was proven to be a considerable contributing factor in KC patient's corneal degeneration. The progression of this pathology could be decreased or halted by stopping eye rubbing at early stages.

Effects of the LASIK flap thickness on corneal biomechanical behavior: a finite element analysis

Background

It is well known that the biomechanical properties change after LASIK refractive surgery. One reason is the impact of flap creation on the residual stroma. The results have revealed that the change is closely related with the flap thickness in several studies. However, the quantitative relationships between the distributions of displacement and stress on the corneal surface and flap thickness have not been studied. The aim of the study was to quantify evaluate the biomechanical change caused by the LASIK flap.

Methods

By building a finite element model of the cornea, the displacement, the stress and the strain on the corneal surface were analyzed.

Results

The results showed that the corneal flap could obviously cause the deformation of the anterior corneal surface. For example, the displacement of the corneal vertex achieved 15 μm more than that without corneal flap, when the thickness of corneal flap was 120 μm thick. This displacement was enough to cause the change of aberrations in the human eyes. In the central part of the cornea, the stress on the anterior corneal surface increased with flap thickness. But the change in the stress on the posterior corneal surface was significantly less than that on the anterior surface. In addition, the stress in the central part of the anterior corneal surface increased significantly as the intra-ocular pressure (IOP) increase. Furthermore the increase of IOP had a clearly less effect on stress distribution at the edge of the cornea. Distributions of strain on the corneal surface were similar to those of stress.

Conclusions

The changes in the biomechanical properties of cornea after refractive surgery should not be ignored.

New parameters for evaluating corneal biomechanics and intraocular pressure after small-incision lenticule extraction by Scheimpflug-based dynamic tonometry

PURPOSE

To evaluate parameters and dynamic corneal densitometry with a new dynamic Scheimpflug analyzer (Corvis ST) in eyes having small-incision lenticule extraction (SMILE).

SETTING

Qvision, Vithas Virgen del Mar Hospital, Almería, Spain.

DESIGN

Retrospective case series.

METHODS

The study comprised eyes from the same institution having small-incision lenticule extraction surgery. Preoperative and 1-month postoperative measurements were taken.

RESULTS

Forty-three eyes were evaluated. The mean difference in intraocular pressure (IOP) and biomechanically corrected IOP before and after surgery was 2.24 mm Hg ± 1.26 mm (SD) (P = .001) and 0.57 ± 1.77 mm Hg (P = .04), respectively. All dynamic Scheimpflug analyzer parameters changed significantly after surgery (P < .05). The variation in each parameter was correlated with the removed corneal thickness (P < .05), except the stiffness parameter at the first applanation (P = .15). None of the 4 dynamic corneal densitometry parameters changed significantly as a result of surgery (P ≥ .29). A new sign, described as an inclined brightness fringe moving through the corneal periphery, appeared preoperatively in eyes with higher dynamic corneal densitometry. This sign was more prevalent postoperatively (48.8% versus 72.1%) (P = .04).

CONCLUSIONS

The biomechanically corrected IOP measured after surgery with the dynamic Scheimpflug analyzer showed better agreement with the preoperative values than IOP. The stiffness parameter was not dependent on the amount of removed corneal thickness. A new sign correlated with dynamic corneal densitometry was found and might be related to changes in corneal hydration and biomechanics.

Numerical Simulation of Corneal Fibril Reorientation in Response to External Loading

Purpose: To simulate numerically the collagen fibril reorientation observed experimentally in the cornea. Methods: Fibril distribution in corneal strip specimens was monitored using X-ray scattering while under gradually increasing axial loading. The data were analysed at each strain level in order to quantify the changes in the angular distribution of fibrils with strain growth. The resulting relationship between stain and fibril reorientation was adopted in a constitutive model to control the mechanical anisotropy of the tissue material. The outcome of the model was validated against the experimental measurements before using the model in simplified representations of two surgical procedures. Results: The numerical model was able to reproduce the experimental measurements of specimen deformation and fibril reorientation under uniaxial loading with errors below 8.0%. With tissue removal simulated in a full eye numerical model, fibril reorientation could be predicted around the affected area, and this change both increased with larger tissue removal and reduced gradually away from that area. Conclusion: The presented method can successfully simulate fibril reorientation with changes in the strain regime affecting cornea tissue. Analyses based on this method showed that fibrils tend to align parallel to the tissue cut following keratoplasty operations. With the ability to simulate fibril reorientation, numerical modelling can have a greater potential in modelling the behaviour following surgery and injury to the cornea.

Determination of Corneal Biomechanical Behavior in-vivo for Healthy Eyes Using CorVis ST Tonometry: Stress-Strain Index

Purpose: This study aims to introduce and clinically validate a new algorithm that can determine the biomechanical properties of the human cornea in vivo.

Methods: A parametric study was conducted involving representative finite element models of human ocular globes with wide ranges of geometries and material biomechanical behavior. The models were subjected to different levels of intraocular pressure (IOP) and the action of external air puff produced by a non-contact tonometer. Predictions of dynamic corneal response under air pressure were analyzed to develop an algorithm that can predict the cornea's material behavior. The algorithm was assessed using clinical data obtained from 480 healthy participants where its predictions of material behavior were tested against variations in central corneal thickness (CCT), IOP and age, and compared against those obtained in earlier studies on ex-vivo human ocular tissue.

Results: The algorithm produced a material stiffness parameter (Stress-Strain Index or SSI) that showed no significant correlation with both CCT (p > 0.05) and IOP (p > 0.05), but was significantly correlated with age (p < 0.01). The stiffness estimates and their variation with age were also significantly correlated (p < 0.01) with stiffness estimates obtained earlier in studies on ex-vivo human tissue.

Conclusions: The study introduced and validated a new method for estimating the in vivo biomechanical behavior of healthy corneal tissue. The method can aid optimization of procedures that interfere mechanically with the cornea such as refractive surgeries and introduction of corneal implants.

A novel numerical modelling approach for keratoplasty eye procedure

Objective of the work is to investigate stress and deformation that conrneal tissue and donor graft undergo during endothelial keratoplasty. In order to attach the donor graft to the cornea, different air bubble pressure profiles acting on the graft are considered. This study is carried out by employing a three-dimensional nonlinear finite element methodology, combined with a contact algorithm. The ocular tissues are treated as isotropic, hyper-elastic and nearly-incompressible materials. The contact algorithm, based on the penalty-based node-to-surface approach, is used to model the donor graft-corneal interface region. First, the proposed computational methodology is tested against benchmark data for bending of the plates over a cylinder. Then, the influence of geometrical and material parameters of the graft on the corneal contact-structural response is investigated. The results are presented in terms of Von Mises stress intensity, displacement and mean contact force. Results clearly indicate that the air bubble pressure plays a key role in the corneal stress and strain, as well as graft stiffness and thickness.

Quantification of collagen fiber structure using second harmonic generation imaging and two-dimensional discrete Fourier transform analysis: Application to the human optic nerve head

Second harmonic generation (SHG) microscopy is widely used to image collagen fiber microarchitecture due to its high spatial resolution, optical sectioning capabilities and relatively nondestructive sample preparation. Quantification of SHG images requires sensitive methods to capture fiber alignment. This article presents a two-dimensional discrete Fourier transform (DFT)-based method for collagen fiber structure analysis from SHG images. The method includes integrated periodicity plus smooth image decomposition for correction of DFT edge discontinuity artefact, avoiding the loss of peripheral image data encountered with more commonly used windowing methods. Outputted parameters are as follows: the collagen fiber orientation distribution, aligned collagen content and the degree of collagen fiber dispersion along the principal orientation. We demonstrate its application to determine collagen microstructure in the human optic nerve head, showing its capability to accurately capture characteristic structural features including radial fiber alignment in the innermost layers of the bounding sclera and a circumferential collagen ring in the mid-stromal tissue. Higher spatial resolution rendering of individual lamina cribrosa beams within the nerve head is also demonstrated. Validation of the method is provided in the form of correlative results from wide-angle X-ray scattering and application of the presented method to other fibrous tissues.

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.

Evaluation of corneal elastic modulus based on Corneal Visualization Scheimpflug Technology

BACKGROUND

Corneal biomechanical properties are important for the diagnosis of corneal diseases, individualized design and prognosis of corneal surgery. Clinical available devices such as Ocular Response Analyzer (ORA) and Corneal Visualization Scheimpflug Technology (Corvis ST) can provide corneal biomechanics related parameters, while corneal elastic modulus cannot be extracted directly from them at present. The aim of this study is to suggest a method to determine corneal elastic modulus based on the results of Corvis ST test according to Reissner's theory on the relation between stress and small displacement in shallow spherical shell.

RESULTS

Five rabbits (10 eyes) and 10 healthy humans (20 eyes) were measured with Corvis ST to obtain the normal range of corneal elastic modulus. Results showed Corneal elastic modulus of rabbit was 0.16 MPa to 0.35 MPa, human corneal elastic modulus was 0.16-0.30 MPa. Rabbit corneas were also measured at different intraocular pressures (IOP), and results showed corneal elastic modulus, first applanation time (A1T) and stiffness parameter (SP-A1) were positively correlated with IOP. Deformation amplitude (DA), the second applanations time (A2T), and peak distance (PD) were negatively correlated with IOP. Finite element method was used to simulate the Corvis measurements according to the calculated elastic modulus and the simulated corneal apical displacements were agreement with experimental results in general.

CONCLUSIONS

The method to determine corneal elastic modulus based on Corvis test according to the relationship between force and displacements of shallow spherical shell is convenient and effective.

Analysis of X-ray scattering microstructure data for implementation in numerical simulations of ocular biomechanical behaviour

This study aimed to analyse microstructure data on the density and orientation of collagen fibrils in whole eye globes and to propose an effective method for the preparation of data for use in numerical simulations of the eye’s biomechanical performance. Wide-angle X-ray scattering was applied to seven healthy ex-vivo human eyes. Each eye was dissected into an anterior and a posterior cup, and radial incisions were used to flatten the tissue before microstructure characterisation. A method was developed to use the microstructure data obtained for the dissected tissue to build realistic 3D maps of fibril density and orientation covering the whole eye globe. At the central cornea, 61.5±2.3% of fibrils were aligned within 45° sectors surrounding the two orthogonal directions. In contrast, more than one-third of the total fibril content was concentrated along the circumferential direction at the limbus (37.0±2.4%) and around the optic nerve head (34.8±2.1%). The insertion locations of the four recti muscles exhibited a preference in the meridional direction near the equator (38.6±3.9%). There was also a significant difference in fibril density between the limbus and other regions (ratio = 1.91±0.45, p <0.01 at the central cornea and ratio = 0.80±0.21, p <0.01 at the posterior pole). Characterisation of collagen fibril density and orientation across the whole ocular surface has been possible but required the use of a technique that involved tissue dissection and hence caused tissue damage. The method presented in this paper aimed to minimise the effect of dissection on the quality of obtained data and was successful in identifying fibril distribution trends that were compatible with earlier studies, which concentrated on localised areas of the ocular globe.

STUDY OF THE TRANSVERSAL DEFORMATION OF CORNEAL STRIP UNDER UNIAXIAL LOADING

Uniaxial test is easy to access and to obtain accuracy data, but it is difficult to acquire two-dimensional deformation information. We investigated the relationship between the two strain components of corneal strip in uniaxial tests, which is the basis for determining of anisotropic strain energy function of cornea via uniaxial tests. Nine rabbits were taken. The left and right corneas were cut along superior-inferior (SI) and nasal-temporal (NT) direction, respectively. For each strip the uniaxial test was carried out, and the tensile displacements, strip images and loads were recorded. Then the stretching strain, the transversal strains and stress were obtained. Optimization based inverse analysis was utilized to find the best among six fitting models that characterizes the relationship between two strain components in uniaxial tests. All models fitted well the experimental data gathered for corneal strips ([Formula: see text]). According to the model selection index, the power model achieved the best performance index: 0.1268 for SI strips and 0.1063 for NT strips versus 0.151 (SI strips) and 0.107 (NT strips) found at most by other models. Thus, it is the most suitable one for describing the relationship between the two strain components of corneal strip during uniaxial stretching.

The Relationship Between Mechanical Properties, Ultrastructural Changes, and Intrafibrillar Bond Formation in Corneal UVA/Riboflavin Cross-linking Treatment for Keratoconus

PURPOSE

To determine the relationship between mechanical behavior in cross-linked corneas and changes in the corneal ultrastructure after corneal cross-linking (CXL).

METHODS

Porcine corneas were treated following the "Dresden" protocol, the current gold standard for clinical treatment, consisting of dropwise application of 0.1% riboflavin in 20% dextran followed by 30 minutes of ultraviolet-A (UVA) irradiation. The effect of CXL was assessed using uniaxial tensile testing, transmission electron microscopy, and Fourier transform infrared spectroscopy, with results compared against corneas treated with each of the treatment solution components individually.

RESULTS

UVA/riboflavin cross-linked corneas displayed 28% ± 17% increase in the material tangent modulus compared with dextran treatment alone, and altered collagen architecture within the first 300 µm of stromal depth consisting of 5% increase in the thickness of collagen fibrils, no significant changes to interfibrillar spacing, and an 8% to 12% decrease in number of fibrils per unit area. Fourier transform infrared spectroscopy confirmed formation of interfibrillar bonds (P = .012) induced by UVA-mediated CXL.

CONCLUSIONS

The data support a model wherein collagen fibril diameter and structural density are fundamental parameters in defining tissue stiffening following UVA/riboflavin CXL and provide benchmarks against which modifications to the Dresden CXL protocol can be evaluated. [J Refract Surg. 2018;34(4):264-272.].

Development and clinical verification of numerical simulation for laser in situ keratomileusis

To develop and validate numerical models of the laser in situ keratomileusis (LASIK) procedure through considering its effect on corneal biomechanical behavior. 3D finite element models of the human eye were developed to simulate LASIK. The models' predictions of post-operative corneal elevation, corneal refractive power with vector decomposition (M_-c-pos, J_0-c-pos, J_45-c-pos) and refractive error correction (M_-rec, J_0-rec, J_45-rec) were compared against clinical data obtained for 28 eyes of 28 patients. A parallel exercise was conducted to estimate the post-operative corneal shape using a shape subtraction method (SSM) - which does not consider the effects of LASIK on corneal mechanical behavior - and the results are compared with the finite element method (FEM). A significant decrease in elevation differences between FEM predictions and clinical data was found compared with the differences between SSM results and clinical data (p = 0.000). In addition, there were no significant differences in post-operative equivalent sperical corneal refractive power between FEM results and corresponding clinical data (M_-c-pos: p = 0.501), while SSM showed significant differences with clinical data (M_-c-pos: p = 0.000). Further, FEM achieved a predicted value of M_-c-pos within ± 1.00D accuracy in 100% of cases, compared with 57% achieved by the SSM. M_-rec predicted by FEM was not significantly different from clinical results (p = 0.085), while SSM overestimated it (p = 0.000). The match between LASIK numerical model predictions with clinical measurements improved significantly when the procedure's effect on corneal biomechanical behavior was considered. This outcome has important implications on efforts to develop planning tools for refractive surgery.