Customized Finite Element Modelling of the Human Cornea

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.

Modeling biological growth of human keratoconus: On the effect of tissue degradation, location and size

Keratoconus is a non-inflammatory bilateral disease, that usually occurs in the inferior-temporal region, where the cornea bulges out and becomes thinner, due to the gradual loss of structural organization in corneal tissue. Degenerated extracellular matrix and fibers breakage have been observed in keratoconic corneas, that may promote the progression of the pathology. While keratoconus histopathology has been widely described in literature, its etiology is still not clear. Being able to fully understand keratoconus growing process could be crucial to detect its development and improve prevention strategies. This work proposes a novel continuum-based keratoconus growth model. The proposed framework accounts for the structural changes occurring in the underlying tissue during the progression of the disease, as indicated in experiments. The developed formulation is able to replicate the typical bulging and thinning of keratoconic corneas, as well as different forms in terms of shape, as they are commonly classified in clinics (nipple, oval and globus cones). The cone that is obtained constitutes a permanent deformed state, not pressure dependent. The resulting model may help to better understand the etiology of the behavior of this disease with the aim of improving the diagnosis and the treatment of the pathology.

Diagnostic ability of the corneal anterior and posterior surface area calculated by corneal modelling approach in early stage keratoconus patients

PURPOSE

To investigate the discrimination ability of the corneal anterior and posterior surface area between patients with keratoconus stage 1 and normal individuals.

METHODS

In this retrospective study, 116 eyes of 116 normal individuals and 366 eyes of 366 keratoconus patients were included. Keratoconus patients were divided into six groups according to the topographic keratoconus classification of Pentacam. Anterior and posterior surface data of sagittal (SM) and elevation maps (EM) were exported from Pentacam, and human corneal models were created employing the software utilizing the PyVista module of Python programming language. The anterior and posterior corneal surface area (a-CSA and p-CSA) of SM and EM were calculated by the software ranging from central 3 to 8mm diameter.

RESULTS

Anterior and posterior CSA values were higher in KC patients compared to normal individuals (p < 0.001). The p-CSA for SM and EM measured at the central 3mm was higher in patients with KC-1 compared to normal eyes (p = 0.002, p = 0.005, respectively), For both maps, a-CSA and p-CSA measured at the central 4 and 5mm were higher in KC-1 compared to normal individuals (p < 0.05). The highest area under the curve (AUC) values in the diagnosis patients with KC-1 were obtained from 3mm p-CSA for SM (AUC: 0.8338), 3mm p-CSA for EM (AUC: 0.7999), 4mm p-CSA for SM (AUC: 0.8531), 4mm p-CSA for EM (AUC:0.7948), 5mm p-CSA for SM (AUC: 0.8455), 5mm p-CSA for EM (AUC:0.7614).

CONCLUSION

The corneal surface area as a parameter, especially for central 3, 4, and 5mm, has a discrimination ability in diagnosing keratoconus disease and distinguishes normal eyes from KC-1 eyes.

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.

Experimental evaluation of corneal stress-optic coefficients using a pair of force test

BACKGROUND

Topography and tomography are valuable techniques for measuring the corneal shape, but they cannot directly assess its internal mechanical stresses. And nonuniform corneal stress plays a crucial biomechanical role in the progression of diseases and postoperative changes. Given the cornea's inherent transparency, analyzing corneal stresses using the photoelasticity method is highly advantageous. However, quantification of photoelasticity faces challenges in obtaining the stress-optic coefficient due to wrinkles caused by the non-spherical geometry during tensional experiments.

OBJECTIVE

In this study, we propose an innovative experimental setup aimed at generating a gradient field of simple shear stress and achieving surface flatness during corneal stretching experiments, enabling the acquisition of the stress-optic coefficient through comparison with numerical results.

METHODS

Our designed setup applies fluid pressure and force couples on the cornea. The internal fluid pressure maintains the corneal shape, preventing wrinkles, while the force couples create a stress field leading to isochromatic fringes.

RESULTS

We successfully measured the stress-optic coefficients of the porcine anisotropic cornea in ex-vivo as 1.87 × 10-9 (horizontal) and 1.97 × 10-9 (vertical) (m2/N). Each isochromatic fringe order represents a shear stress range of 6.05 × 104 Pa under a low tension.

CONCLUSIONS

This study establishes a significant connection between corneal photoelastic patterns and the quantification of corneal stress by enabling direct measurement through advanced photoelastic visualization technology for clinical applications.

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.

3D Bioprinting of Acellular Corneal Stromal Scaffolds with a Low Cost Modified 3D Printer: A Feasibility Study

PURPOSE

Loss of corneal transparency is one of the major causes of visual loss, generating a considerable health and economic burden globally. Corneal transplantation is the leading treatment procedure, where the diseased cornea is replaced by donated corneal tissue. Despite the rise of cornea donations in the past decade, there is still a huge gap between cornea supply and demand worldwide. 3D bioprinting is an emerging technology that can be used to fabricate tissue equivalents that resemble the native tissue, which holds great potential for corneal tissue engineering application. This study evaluates the manufacturability of 3D bioprinted acellular corneal grafts using low-cost equipment and software, not necessarily designed for bioprinting applications. This approach allows access to 3D printed structures where commercial 3D bioprinters are cost prohibitive and not readily accessible to researchers and clinicians.

METHODS

Two extrusion-based methods were used to 3D print acellular corneal stromal scaffolds with collagen, alginate, and alginate-gelatin composite bioinks from a digital corneal model. Compression testing was used to determine moduli.

RESULTS

The printed model was visually transparent with tunable mechanical properties. The model had central radius of curvature of 7.4 mm, diameter of 13.2 mm, and central thickness of 0.4 mm. The compressive secant modulus of the material was 23.7 ± 1.7 kPa at 20% strain. 3D printing into a concave mold had reliability advantages over printing into a convex mold.

CONCLUSIONS

The printed corneal models exhibited visible transparency and a dome shape, demonstrating the potential of this process for the preparation of acellular partial thickness corneal replacements. The modified printing process presented a low-cost option for corneal bioprinting.

Developing a Novel Platelet-Rich Plasma-Laden Bioadhesive Hydrogel Contact Lens for the Treatment of Ocular Surface Chemical Injuries

Permanent injury to corneal limbal stem cells after ocular surface chemical and thermal injuries is a major cause of corneal blindness. In this study, a PRP-laden GelMA hydrogel contact lens is manufactured which is aimed to support the limbal niche after ocular surface insults thereby preventing limbal stem cell failure. GelMA with varying platelet-rich plasma (PRP) concentrations (5%, 10%, and 20%) is photopolymerized using a visible light crosslinking system followed by characterizations of mechanical properties, growth factor release, enzymatic degradation, and in vitro cytotoxicity. The addition of 10% PRP into 10% GelMA hydrogel precursor solution results in the highest tensile and compressive modulus (38 and 110 kPa, respectively) and burst pressure (251±37.66 mmHg). Degradation time varies according to the concentration of the collagenase enzyme tested (0, 2.5, 5, and 40 µg/mL) and is most prolonged with 20% PRP. EGF and TGF-β release profiles suggest an initial burst release followed by sustained release, most consistent in the 10% PRP sample. Although cell viability decreases on day 1, rapid recovery is observed and is approximately 120% after day 21. PRP-laden GelMA in the form of a contact lens may be a promising biomaterial-based treatment approach for the maintenance of limbal epithelial stem cells after ocular surface insults.

Modeling the biomechanics of laser corneal refractive surgery

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

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.

Biomechanics of keratoconus: Two numerical studies

BACKGROUND

The steep cornea in keratoconus can greatly impair eyesight. The etiology of keratoconus remains unclear but early injury that weakens the corneal stromal architecture has been implicated. To explore keratoconus mechanics, we conducted two numerical simulation studies.

METHODS

A finite-element model describing the five corneal layers and the heterogeneous mechanical behaviors of the ground substance and lamellar collagen-fiber architecture in the anterior and posterior stroma was developed using the Holzapfel-Gasser-Ogden constitutive model. The geometry was from a healthy subject. Its stroma was divided into anterior, middle, and posterior layers to assess the effect of changing regional mechanical parameters on corneal displacement and maximum principal stress under intraocular pressure. Specifically, the effect of softening an inferocentral corneal button, the collagen-based tissues throughout the whole cornea, or specific stromal layers in the button was examined. The effect of simply disorganizing the orthogonally-oriented posterior stromal fibers in the button was also assessed. The healthy cornea was also subjected to eye rubbing-like loading to identify the corneal layer(s) that experienced the most tensional stress.

RESULTS

Conical deformation and corneal thinning emerged when the corneal button or the mid-posterior stroma of the button underwent gradual softening or when the collagen fibers in the mid-posterior stroma of the button were dispersed. Softening the anterior layers of the button or the whole cornea did not evoke conical deformation. Button softening greatly increased and disrupted the stress on Bowman's membrane while mid-posterior stromal softening increased stress in the anterior layers. Eye rubbing profoundly stressed the deep posterior stroma while other layers were negligibly affected.

DISCUSSION

These observations suggest that keratoconus could be initiated, at least partly, by mechanical instability/damage in the mid-posterior stroma that then imposes stress on the anterior layers. This may explain why subclinical keratoconus is marked by posterior but not anterior elevation on videokeratoscopy.

In Vivo Biomechanical Measurements of the Cornea

In early corneal examinations, the relationships between the morphological and biomechanical features of the cornea were unclear. Although consistent links have been demonstrated between the two in certain cases, these are not valid in many diseased states. An accurate assessment of the corneal biomechanical properties is essential for understanding the condition of the cornea. Studies on corneal biomechanics in vivo suggest that clinical problems such as refractive surgery and ectatic corneal disease are closely related to changes in biomechanical parameters. Current techniques are available to assess the mechanical characteristics of the cornea in vivo. Accordingly, various attempts have been expended to obtain the relevant mechanical parameters from different perspectives, using the air-puff method, ultrasound, optical techniques, and finite element analyses. However, a measurement technique that can comprehensively reflect the full mechanical characteristics of the cornea (gold standard) has not yet been developed. We review herein the in vivo measurement techniques used to assess corneal biomechanics, and discuss their advantages and limitations to provide a comprehensive introduction to the current state of technical development to support more accurate clinical decisions.

Effects of Laser In Situ Keratomileusis and Small-Incision Lenticule Extraction on Corneal Biomechanical Behavior: A Finite Element Analysis

Myopia, which is the result of the uncoordinated development of the eyeball, has become a major public health focus worldwide. Laser in situ keratomileusis (LASIK) and small-incision lenticule extraction (SMILE) have been successfully used in modern corneal refractive surgery. However, there are still controversies about postoperative results of LASIK and SMILE. In this study, a three-dimensional finite element model of the cornea was constructed based on the elevation and pachymetry data of a female volunteer. Surgical parameters, magnitudes of myopic correction, and intraocular pressure (IOP) were varied. Furthermore, an iterative algorithm was applied to retrieve the free-stress state of the intact corneal model, LASIK model, and SMILE model. To better evaluate the differences between LASIK and SMILE procedures, the displacement and Von Mises stress on the anterior and posterior corneal surface along the x- and y-axes were analyzed. Results for the zero-pressure model showed larger displacement compared to the image-based corneal model, suggesting that the initial corneal pre-stress stiffens the response of the cornea, both in the intact cornea and under refractive surgery. In addition, the displacement on the corneal surface in LASIK (both zero-pressure and image-based model) was obviously higher than that of the SMILE model. In contrast, SMILE increased Von Mises stress in the corneal cap and reduced Von Mises stress in the residual stromal bed compared with the LASIK model. However, the maximum Von Mises stress in the SMILE model was still smaller than that of the LASIK model. Moreover, the displacement and Von Mises stress on the residual stromal bed increased linearly with IOP. Overall, LASIK and SMILE refractive surgery could change biomechanical behaviors of the cornea. Compared to LASIK refractive surgery, SMILE may present a lower risk of ectasia. Creating a corneal cap rather than a corneal flap may have an advantage in improving corneal biomechanical stability.

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.

Novel vision restoration techniques: 3D bioprinting, gene and stem cell therapy, optogenetics, and the bionic eye

BACKGROUND

Vision restoration has been one of the most sought-after goals of ophthalmology because of its inception. Despite these problems being tackled from numerous different perspectives, a concrete solution has not yet been achieved. An optimal solution will have significant implications on the patient's quality of life, socioeconomic status, and mental health.

METHODS

This article will explore new and innovative approaches with one common aim-to restore functional vision for the visually impaired. These novel techniques include 3D bioprinting, stem cell therapy, gene therapy, implantable devices, and optogenetics.

RESULTS

While the techniques mentioned above show significant promise, they are currently in various stages of development ranging from clinical trials to commercial availability. Restoration of minimal vision in specific cases has already been achieved by the different methods but optimization of different parameters like biocompatibility, spatiotemporal resolution, and minimizing the costs are essential for widespread use.

CONCLUSION

The developments over the past decade have resulted in multiple milestones in each of the techniques with many solutions getting approved by the FDA. This article will compare these novel techniques and highlight the major advantages and drawbacks of each of them.

The combined importance of finite dimensions, anisotropy, and pre-stress in acoustoelastography

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties that are altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasistatic tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article, we review how prestress alters both bulk mechanical wave motion and wave motion in one- and two-dimensional waveguides. Key findings are linked to studies on skeletal muscle and the human cornea, as one- and two-dimensional waveguide examples. This study highlights the underappreciated combined acoustoelastic and waveguide challenge to elastography. Can elastography truly determine viscoelastic properties of a material when what it is measuring is affected by both these material properties and unknown prestress and other boundary conditions?

Finite Element Analysis of the Epiretinal Membrane Contraction

The epiretinal membrane is a thin sheet of fibrous tissue that can form over the macular area of the retina, and may result in the loss of visual acuity or metamorphopsia, due to superficial retinal folds. A vitrectomy surgery, the current treatment procedure for this pathology, is only performed after symptoms are present. However, sometimes the patients do not present any vision improvements after the surgery. The use of computational methods for a patient-specific biomechanical analysis can contribute to better understanding the mechanisms behind the success or failure of a vitrectomy. Using medical data from two patients who underwent a vitrectomy, one with substantial improvements and another with no improvements, an analysis of the retinal displacement due to the contraction of the epiretinal membrane was performed. Our results suggest a causal effect between the magnitude of the retinal displacements caused by the epiretinal membrane contraction and the outcome of the vitrectomy procedure.

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.

Is it Possible to Derive the Dresdner Correction Formula Using a Finite Element Program?

INTRODUCTION

The aim was to construct a model cornea by CAD and finite element software to find out how the intraocular pressure compares to the forces for applanation at the outside of the model cornea. These data were to be compared to the Dresdner correction formula. Thereby, it was possible to find out whether the model was plausible and to find hints as to why a correction for how the intraocular pressure depends on the corneal thickness is necessary at all.

METHODS

Using the open-source software FreeCad and geometrical data for the cornea of the literature, an average cornea was constructed. On this average cornea, a finite element analysis was performed using the free software z88aurora. The intraocular pressure was measured by applanation of the outer cornea. The necessary forces were analysed.

RESULTS

In this model, the intraocular pressure had to be corrected depending on the corneal thickness. The correction factor was k_{mean; finite elements} = 19.17 - 0.0334*corneal thickness. The necessary correction did not exclusively depend on the relation between the endothelial area and the area of the outer cornea: for this relation alone the correction would have been k_{area-relation} = 1.0361 - 0.0006*corneal thickness.

DISCUSSION

The model correction formula was close to the Dresdner formula. The relation between endothelial area and the area of the outer cornea could only explain about half of the necessary correction.

Simulated biomechanical effect of aspheric transition zone ablation profiles after conventional hyperopia refractive surgery

We studied the effects of the aspheric transition zone on the optical wavefront aberrations, corneal surface displacement, and stress induced by the biomechanical properties of the cornea after conventional laser in situ keratomileusis (LASIK) refractive surgery. The findings in this study can help improve visual quality after refractive surgery. Hyperopia correction in 1-5D was simulated using five types of aspheric transition zones with finite element modeling. The algorithm for the simulations was designed according to the optical path difference. Wavefront aberrations were calculated from the displacements on the anterior and posterior corneal surfaces. The vertex displacements and stress on the corneal surface were also evaluated. The results showed that the aspheric transition zone has an effect on the postoperative visual quality. The main wavefront aberrations on the anterior corneal surface are defocus, y-primary astigmatism, x-coma, and spherical aberrations. The wavefront aberrations on the corneal posterior surface were relatively small and vertex displacements on the posterior corneal surface were not significantly affected by the aspheric transition zone. Stress analysis revealed that the stress on the cutting edge of the anterior corneal surface decreased with the number of aspheric transition zone increased, and profile #1 resulted in the maximum stress. The stress on the posterior surface of the cornea was more concentrated in the central region and was less than that on the anterior corneal surface overall. The results showed that the aspheric transition zone has an effect on postoperative aberrations, but wavefront aberrations cannot be eliminated. In addition, the aspheric transition zone influences the postoperative biomechanical properties of the cornea, which significantly affect the postoperative visual quality.

Individualized Characterization of the Distribution of Collagen Fibril Dispersion Using Optical Aberrations of the Cornea for Biomechanical Models

Purpose

The spatial distribution of collagen fibril dispersion has a significant impact on both corneal biomechanical and optical behaviors. The goal of this study was to demonstrate a novel method to characterize collagen fibril dispersion using intraocular pressure (IOP)-induced changes in corneal optical aberrations for individualized finite-element (FE) modeling.

Methods

The method was tested through both numerical simulations and ex vivo experiments. Inflation tests were simulated in FE models with three assumed patterns of collagen fibril dispersion and experimentally on three rhesus monkey corneas. Geometry, matrix stiffness, and the IOP-induced changes in wavefront aberrations were measured, and the collagen fibril dispersion was characterized. An individualized corneal model with customized collagen fibril dispersion was developed, and the estimated optical aberrations were compared with the measured data.

Results

For the theoretical investigations, three assumed distributions of fibril dispersion were all successfully characterized. The estimated optical aberrations closely matched the measured data, with average root-mean-square (RMS) differences of 0.29, 0.24, and 0.10 µm for the three patterns, respectively. The overall features of the IOP-induced changes in optical aberrations were estimated for two ex vivo monkey corneas, with average RMS differences of 0.57 and 0.43 µm. Characterization of the fibril dispersion in the third cornea might have been affected by corneal hydration, resulting in an increased RMS difference, 0.8 µm.

Conclusions

A more advanced corneal model with individualized distribution of collagen fibril dispersion can be developed and used to improve our ability to understand both biomechanical and optical behaviors of the cornea.

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.

On the Connection Between Geometry and Statically Determined Membrane Stresses in the Human Cornea

Under the action of the intraocular pressure (IOP), the human cornea is stressed and deforms acquiring a quasi-spherical configuration. If the stressed configuration is known, and the cornea is regarded as a membrane, disregarding flexural behaviors with an equilibrium analysis only is possible to estimate the distribution of the average stress across the thickness. In the cornea, the action of the intraocular pressure is supported by collagen fibrils, immersed into an elastin-proteoglycan matrix, and organized in a very precise architecture to provide the necessary confinement and transparency to the light. With the goal of understanding the static consequences of shape modifications due to pathological dilatation (ectasia), we present a simplified stress analysis of the human cornea modeled as a membrane. A numerical investigation over 40 patient-specific corneas (20 normal and 20 ectatic) is carried out to establish a relationship between the physiological geometry and the distribution of the membrane stresses, and to assess the possibility to obtain information on the stress state based on topographic images only. Comparative analyses reveal that, with respect to normal corneas, in ectatic corneas the pattern of the principal stress lines is modified markedly showing a deviation from the hypothetical dominant orientation of the collagen fibrils. The rotation of the principal stress with respect to the fibril orientation can be thought as responsible of the transmission of a large amount of shear stresses onto the elastin-proteoglycan matrix. The anomalous loading of the matrix could be correlated to the evolution of time-dependent shape modifications leading to ectasia.

3D Printed Personalized Corneal Models as a Tool for Improving Patient’s Knowledge of an Asymmetric Disease

Additive manufacturing is a vanguard technology that is currently being used in several fields in medicine. This study aims to evaluate the viability in clinical practice of a patient-specific 3D model that helps to improve the strategies of the doctor-patient assistance. Data obtained from a corneal topographer were used to make a virtual 3D model by using CAD software, to later print this model by FDM and get an exact replica of each patient’s cornea in consultation. Used CAD and printing software were open-source, and the printing material was biodegradable and its cost was low. Clinic users gave their feedback by means of a survey about their feelings when perceiving with their senses their own printed cornea. There was 82 surveyed, 73.8% (9.74; SD: 0.45) of them considered that the model had helped them a lot to understand their disease, expressing 100% of them their intention of taking home the printed model. The majority highlighted that this new concept improves both quality and clinical service in consultation. Custom-made individualized printed models allow a new patient-oriented perspective that may improve the communication strategy from the ophthalmologist to the patient, easing patient’s understanding of their asymmetric disease and its later treatment.

Cornea modelling

Background

Biomechanics introduces numerous technologies to support clinical practice in ophthalmology, with the goal of improving surgical outcomes and to develop new advanced technologies with minimum impact on clinical training. Unfortunately, a few misconceptions on the way that computational methods should be applied to living tissues contributes to a lack of confidence towards computer-based approaches.

Methods

Corneal biomechanics relies on sound theories of mechanics, including concepts of equilibrium, geometrical measurements, and complex material behaviors. The peculiarities of biological tissues require the consideration of multi-physics, typical of the eye environment, and to adopt customized geometrical models constructed on the basis of advanced optical imaging and in-vivo testing.

Results

Patient-specific models are able to predict the outcomes of refractive surgery and to exploit the results of in-vivo test to characterize the material properties of the corneal tissue.

Conclusions

Corneal biomechanics can become an important support to clinical practice, provided that methods are based on the actual multi-physics and use customized geometrical and mechanical models.

Assessment of the Association between In Vivo Corneal Morphogeometrical Changes and Keratoconus Eyes with Severe Visual Limitation

Assessing changes suffered by the cornea as keratoconus progresses has proven to be vital for this disease diagnosis and treatment. This study determines the corneal biometric profile in eyes considered as affected by keratoconus (KC) showing severe visual limitation, by means of in vivo 3D modelling techniques. This observational case series study evaluated new objective indices in 50 healthy and 30 KC corneas, following a validated protocol created by our research group, which has been previously used for diagnosis and characterization of KC in asymptomatic (preclinical) and mild visually impaired eyes. Results show a statistically significant reduction of corneal volume and an increase of total corneal area in the severe KC group, being anterior and posterior corneal surfaces minimum thickness points the best correlated parameters, although with no discrimination between groups. Receiving operator curves were used to determine sensitivity and specificity of selected indices, being anterior and posterior apex deviations the ones which reached the highest area under the curve, both with very high sensitivity (96.7% and 90%, respectively) and specificity (94.0% and 99.9%, respectively). The results suggest that once severe visual loss appears, anterior corneal topography should be considered for a more accurate diagnosis of clinical KC, being anterior apex deviation the key metric discriminant. This study can be a useful tool for KC classification, helping doctors in diagnosing severe cases of the disease, and can help to characterize corneal changes that appear when severe KC is developed and how they relate with vision deterioration.

A microstructural model of cross-link interaction between collagen fibrils in the human cornea

We propose a simplified micromechanical model of the fibrous reinforcement of the corneal tissue. We restrict our consideration to the structural function of the collagen fibrils located in the stroma and disregard the other all-important components of the cornea. The reinforcing structure is modelled with two sets of parallel fibrils, connected by transversal bonds within the single fibril family (inter-cross-link) and across the two families (intra-cross-link). The particular design chosen for this ideal structure relies on the fact that its ability to sustain loads is dependent on the degree of the cross-link and, therefore, on the density and stiffness of the bonds. We analyse the mechanical response of the system according to the type of interlacing and on the stiffness of fibres and bonds. Results show that the weakening of transversal bonds is associated with a marked increase of the deformability of the system. In particular, the deterioration of transversal bonds due to mechanical, chemical or enzymatic reasons can justify the loss of stiffness of the stromal tissue resulting in localized thinning and bulging typically observed in keratoconus corneas. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.

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

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

Novel dynamic corneal response parameters in a practice use: a critical review

Background

Non-contact tonometers based on the method using air puff and Scheimpflug’s fast camera are one of the latest devices allowing the measurement of intraocular pressure and additional biomechanical parameters of the cornea. Biomechanical features significantly affect changes in intraocular pressure values, as well as their changes, may indicate the possibility of corneal ectasia. This work presents the latest and already known biomechanical parameters available in the new offered software. The authors focused on their practical application and the diagnostic credibility indicated in the literature.

Discussion

An overview of available literature indicates the importance of new dynamic corneal parameters. The latest parameters developed on the basis of biomechanics analysis of corneal deformation process, available in non-contact tonometers using Scheimpflug’s fast camera, are used in the evaluation of laser refractive surgery procedures, e.g. LASIK procedure. In addition, the assessment of changes in biomechanically corrected intraocular pressure confirms its independence from changes in the corneal biomechanics which may allow an intraocular pressure real assessment. The newly developed Corvis Biomechanical Index combined with the corneal tomography and topography assessment is an important aid in the classification of patients with keratoconus.

Conclusion

New parameters characterising corneal deformation, including Corvis Biomechanical Index and biomechanical compensated intraocular pressure, significantly extend the diagnostic capabilities of this device and may be helpful in assessing corneal diseases of the eye. Nevertheless, further research is needed to confirm their diagnostic pertinence.

Study and characterization of morphogeometric parameters to assist diagnosis of keratoconus

Background

In case of significant imperfections on the cornea, data acquisition is difficult and a significant level of missing data could require the interpolation of important areas of the cornea, resulting in a very ambiguous model. The development of methods to define in vivo customised geometric properties of the cornea based only on real raw data is extremely useful to diagnose and assess the progression of diseases directly related to the corneal architecture. The present work tries to improve the prognostic of corneal ectasia creating a 3D customised model of the cornea and analysing different geometric variables from this model to determine which variables or combination of them could be defined as an indicator of susceptibility to develop keratoconus.

Methods

A corneal geometric reconstruction was performed using zonal functions and retrospective Scheimpflug tomography data from 187 eyes of 187 patients. Morphology of healthy and keratoconic corneas was characterized by means of geometric variables. The performance of these variables as predictors of a new geometric marker was assessed and their correlations were analysed.

Results

The more representative variable to classify the corneal anomalies related to keratoconus was posterior apex deviation (area under receiver operating characteristic curve > 0.899; p < 0.0001). However, the strongest correlations in both healthy and pathological corneas were provided by the metrics directly related to the thickness, as deviations of the anterior/posterior minimum thickness points.

Conclusions

The presented morphogeometric approach based on the analysis and custom geometric modelling of the cornea demonstrates to be useful for the characterization and diagnosis of keratoconus disease, stating that geometrical deformation is an effective marker of the ectatic disease’s progression.

Assessment of Pattern and Shape Symmetry of Bilateral Normal Corneas by Scheimpflug Technology

Purpose: The aim of this study was to assess bilateral symmetry in normal fellow eyes by using optical and geometric morphometric parameters. Methods: All participants underwent complete biocular examinations. Scheimpflug tomography data from 66 eyes of 33 patients were registered. The interocular symmetry was based on five patterns: morphogeometric symmetry, axial symmetry at the corneal vertex, angular-spatial symmetry, direct symmetry (equal octants), and enantiomorphism (mirror octants). Results: No statistically significant differences were found between right and left eyes in corneal morphogeometric (p ≥ 0.488) and aberrometric parameters (p ≥ 0.102). Likewise, no statistically significant differences were found in any of the axial symmetry parameters analyzed (p ≥ 0.229), except in the surface rotation angle beta (p = 0.102) and translation coordinates X0 and Y0 (p < 0.001) for the anterior corneal surface, and the rotation angle gamma (p < 0.001) for the posterior surface. Similarly, no statistically significant differences were identified for direct symmetry (p ≥ 0.20) and enantiomorphism (p ≥ 0.75), except for some elevation data in the posterior surface (p < 0.01). Conclusions: The level of symmetry of both corneas of a healthy individual is high, with only some level of disparity between fellow corneas in rotation and translation references. Abnormalities in this pattern of interocular asymmetry may be useful as a diagnostic tool.

3D bioprinting of a corneal stroma equivalent

Corneal transplantation constitutes one of the leading treatments for severe cases of loss of corneal function. Due to its limitations, a concerted effort has been made by tissue engineers to produce functional, synthetic corneal prostheses as an alternative recourse. However, successful translation of these therapies into the clinic has not yet been accomplished. 3D bioprinting is an emerging technology that can be harnessed for the fabrication of biological tissue for clinical applications. We applied this to the area of corneal tissue engineering in order to fabricate corneal structures that resembled the structure of the native human corneal stroma using an existing 3D digital human corneal model and a suitable support structure. These were 3D bioprinted from an in-house collagen-based bio-ink containing encapsulated corneal keratocytes. Keratocytes exhibited high cell viability both at day 1 post-printing (>90%) and at day 7 (83%). We established 3D bio-printing to be a feasible method by which artificial corneal structures can be engineered.

Sensitivity of corneal biomechanical and optical behavior to material parameters using design of experiments method

The optical performance of the human cornea under intraocular pressure (IOP) is the result of complex material properties and their interactions. The measurement of the numerous material parameters that define this material behavior may be key in the refinement of patient-specific models. The goal of this study was to investigate the relative contribution of these parameters to the biomechanical and optical responses of human cornea predicted by a widely accepted anisotropic hyperelastic finite element model, with regional variations in the alignment of fibers. Design of experiments methods were used to quantify the relative importance of material properties including matrix stiffness, fiber stiffness, fiber nonlinearity and fiber dispersion under physiological IOP. Our sensitivity results showed that corneal apical displacement was influenced nearly evenly by matrix stiffness, fiber stiffness and nonlinearity. However, the variations in corneal optical aberrations (refractive power and spherical aberration) were primarily dependent on the value of the matrix stiffness. The optical aberrations predicted by variations in this material parameter were sufficiently large to predict clinically important changes in retinal image quality. Therefore, well-characterized individual variations in matrix stiffness could be critical in cornea modeling in order to reliably predict optical behavior under different IOPs or after corneal surgery.

Transient viscous response of the human cornea probed with the Surface Force Apparatus

Knowledge of the biomechanical properties of the human cornea is crucial for understanding the development of corneal diseases and impact of surgical treatments (e.g., corneal laser surgery, corneal cross-linking). Using a Surface Force Apparatus we investigated the transient viscous response of the anterior cornea from donor human eyes compressed between macroscopic crossed cylinders. Corneal biomechanics was analyzed using linear viscoelastic theory and interpreted in the framework of a biphasic model of soft hydrated porous tissues, including a significant contribution from the pressurization and viscous flow of fluid within the corneal tissue. Time-resolved measurements of tissue deformation and careful determination of the relaxation time provided an elastic modulus in the range between 0.17 and 1.43 MPa, and fluid permeability of the order of 10⁻¹³ m⁴/(N∙s). The permeability decreased as the deformation was increased above a strain level of about 10%, indicating that the interstitial space between fibrils of the corneal stromal matrix was reduced under the effect of strong compression. This effect may play a major role in determining the observed rate-dependent non-linear stress-strain response of the anterior cornea, which underlies the shape and optical properties of the tissue.

SyntEyes KTC: higher order statistical eye model for developing keratoconus

PURPOSE

To present and validate a stochastic eye model for developing keratoconus to e.g. improve optical corrective strategies. This could be particularly useful for researchers that do not have access to original keratoconic data.

METHODS

The Scheimpflug tomography, ocular biometry and wavefront of 145 keratoconic right eyes were collected. These data were processed using principal component analysis for parameter reduction, followed by a multivariate Gaussian fit that produces a stochastic model for keratoconus (SyntEyes KTC). The output of this model is filtered to remove the occasional incorrect topography patterns by either an automatic or manual procedure. Finally, the output of this keratoconus model is matched to that of the original model for normal eyes using the non-corneal biometry to obtain a description of keratoconus development.

RESULTS

The synthetic data generated by the model were found to be significantly equal to the original data (non-parametric Mann-Whitney equivalence test; 145/154 passed). The variability of the synthetic data, however, was often significantly less than that of the original data, especially for the higher order Zernike terms of corneal elevation (non-parametric Levene test; p < 0.05/154). These results remained generally the same after applying either filter procedure to remove the synthetic eyes with incorrect topographies. Interpolation between matched pairs of normal and keratoconic SyntEyes appears to provide an adequate model for keratoconus progression.

CONCLUSION

The synthetic data provided by the proposed keratoconus model closely resembles actual clinical data and may be used for a range of research applications when (sufficient) real data is not available.

Computational Biomechanical Analysis of Asymmetric Ectasia Risk in Unilateral Post-LASIK Ectasia

PURPOSE

To develop a computational approach to corneal biomechanical risk analysis in refractive surgery and to investigate its utility in an enigmatic case of unilateral ectasia after bilateral LASIK.

METHODS

Preoperative corneal elevation datasets from both eyes of a patient who developed unilateral post-LASIK ectasia were used to construct geometrically patient-specific, microstructurally motivated finite element models. Models were assessed before and after implementation of case-specific treatment parameters for interocular differences in corneal geometry and strain behavior under physiological loading conditions.

RESULTS

Standard clinical predictors of post-LASIK ectasia risk were similar for the affected and contralateral eyes, and no risk factor asymmetry was identified in tomographic screening that included posterior corneal elevation analysis. However, differences in the magnitude and distribution of strain and stress were observed that are consistent with greater predisposition to biomechanical instability in the affected eye. Load testing with simulated intraocular pressure increases provoked opposite trends in curvature change in the preoperative models representing affected and unaffected eyes, with steepening in the ectatic eye and flattening in the clinically stable eye.

CONCLUSIONS

Patient-specific computational analyses revealed differences in intrinsic biomechanical behaviors that may predispose a cornea to instability after refractive surgery. Strain and stress analyses elucidated differential risk not ascertained with current refractive surgery screening paradigms. This pilot study illustrates a risk analysis approach that implicitly considers the entire corneal three-dimensional geometry and can be performed a priori in a screening setting. [J Refract Surg. 2016;32(12):811-820.].

Computational Simulation of Scleral Buckling Surgery for Rhegmatogenous Retinal Detachment: On the Effect of the Band Size on the Myopization

A finite element model (FE) of the eye including cornea, sclera, crystalline lens, and ciliary body was created to analyze the influence of the silicone encircling bandwidth and the tightness degree on the myopia induced by scleral buckling (SB) procedure for rhegmatogenous retinal detachment. Intraocular pressure (IOP) was applied to the reference geometry of the FE model and then SB surgery was simulated with encircling bandwidths of 1, 2, and 2.5 mm. Different levels of tightening and three values of IOP were applied. The anterior segment resulted as unaffected by the surgery. The highest value of Cauchy stress appeared in the surroundings of the implant, whereas no increment of stress was observed either in anterior segment or in the optic nerve head. The initial IOP did not appear to play any role in the induced myopia. The wider the band, the greater the induced myopia: 0.44, 0.88, and 1.07 diopters (D) for the 1, 2, and 2.5 mm bandwidth, respectively. Therefore, patients become more myopic with a wider encircling element. The proposed simulations allow determining the effect of the bandwidth or the tightness degree on the axial lengthening, thus predicting the myopic increment caused by the encircling surgery.

Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions

The purpose of the present study was to develop a discriminant function departing from the biomechanical parameters provided by a non-contact tonometer (Corvis-ST, Oculus Optikgeräte, Wetzlar, Germany) to distinguish subclinical keratoconus from normal eyes. 212 eyes (120 patients) were divided in two groups: 184 healthy eyes of 92 patients aged 32.99 ± 7.85 (21-73 years) and 28 eyes of 28 patients aged 37.79 ± 14.21 (17-75 years) with subclinical keratoconus. The main outcome measures were age, sex, intraocular pressure (IOP), corneal central thickness (CCT) and other specific biomechanical parameters provided by the tonometer. Correlations between all biomechanical parameters and the rest of variables were evaluated. The biomechanical measures were corrected in IOP and CCT (since these variable are not directly related with the corneal structure and biomechanical behavior) to warrant an accurate comparison between both types of eyes. Two discriminant functions were created from the set of corrected variables. The best discriminant function created depended on three parameters: maximum Deformation Amplitude (corrected in IOP and CCT), First Applanation time (corrected in CCT) and CCT. Statistically significant differences were found between groups for this function (p=2·10(-10); Mann-Withney test). The area under the Receiving Operating Characteristic was 0.893 ± 0.028 (95% confidence interval 0.838-0.949). Sensitivity and specificity were 85.7% and 82.07% respectively. These results show that the use of biomechanical parameters provided by non-contact tonometry, previous normalization, combined with the theory of discriminant functions is a useful tool for the detection of subclinical keratoconus.

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

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