Biomechanical modeling of refractive corneal surgery

The aim of refractive corneal surgery is to modify the curvature of the cornea to improve its dioptric properties. With that goal, the surgeon has to define the appropriate values of the surgical parameters in order to get the best clinical results, i.e., laser and geometric parameters such as depth and location of the incision, for each specific patient. A biomechanical study before surgery is therefore very convenient to assess quantitatively the effect of each parameter on the optical outcome. A mechanical model of the human cornea is here proposed and implemented under a finite element context to simulate the effects of some usual surgical procedures, such as photorefractive keratectomy (PRK), and limbal relaxing incisions (LRI). This model considers a nonlinear anisotropic hyperelastic behavior of the cornea that strongly depends on the physiological collagen fibril distribution. We evaluate the effect of the incision variables on the change of curvature of the cornea to correct myopia and astigmatism. The obtained results provided reasonable and useful information in the procedures analyzed. We can conclude from those results that this model reasonably approximates the corneal response to increasing pressure. We also show that tonometry measures of the IOP underpredicts its actual value after PRK or LASIK surgery.     

人眼波前像差表示、测量及矫正研究

目的:波前像差引导的准分子激光角膜消融是屈光手术的新方法,研究人眼波前像差的测量原理、方法、表示、人眼波前像差准分子激光矫正的原理,以此理论用于准分子激光人眼像差矫正系统。方法:采用理论研究、计算机模拟、实验室实验等手段。分析人眼像差的概念和产生的原因,用数学的Zern ike多项式来表示像差,理论上定量分析Zern ike多项式表示的波前像差与角膜切削深度的关系,研究准分子激光切削角膜的机理,研究准分子激光进行矫正人眼像差的原理框图。结果:通过计算机模拟和实验室实验,用准分子激光矫正低阶和高阶像差是可行的。结论:用波前像差来引导屈光手术,使人眼的视力能够达到20/10上,并能避免当前PRK、LASIK屈光手术前后像差增大而引起的对视觉质量的影响。     

Reversible Femtosecond Laser-Assisted Myopia Correction: A Non-Human Primate Study of Lenticule Re-Implantation after Refractive Lenticule Extraction

LASIK (laser-assisted in situ keratomileusis) is a common laser refractive procedure for myopia and astigmatism, involving permanent removal of anterior corneal stromal tissue by excimer ablation beneath a hinged flap. Correction of refractive error is achieved by the resulting change in the curvature of the cornea and is limited by central corneal thickness, as a thin residual stromal bed may result in biomechanical instability of the cornea. A recently developed alternative to LASIK called Refractive Lenticule Extraction (ReLEx) utilizes solely a femtosecond laser (FSL) to incise an intrastromal refractive lenticule (RL), which results in reshaping the corneal curvature and correcting the myopia and/or astigmatism. As the RL is extracted intact in the ReLEx, we hypothesized that it could be cryopreserved and re-implanted at a later date to restore corneal stromal volume, in the event of keratectasia, making ReLEx a potentially reversible procedure, unlike LASIK. In this study, we re-implanted cryopreserved RLs in a non-human primate model of ReLEx. Mild intrastromal haze, noted during the first 2 weeks after re-implantation, subsided after 8 weeks. Refractive parameters including corneal thickness, anterior curvature and refractive error indices were restored to near pre-operative values after the re-implantation. Immunohistochemistry revealed no myofibroblast formation or abnormal collagen type I expression after 8 weeks, and a significant attenuation of fibronectin and tenascin expression from week 8 to 16 after re-implantation. In addition, keratocyte re-population could be found along the implanted RL interfaces. Our findings suggest that RL cryopreservation and re-implantation after ReLEx appears feasible, suggesting the possibility of potential reversibility of the procedure, and possible future uses of RLs in treating other corneal disorders and refractive errors.     

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.     

Involvement of pigment epithelium-derived factor,docosahexaenoic acid and neuroprotectin D1 in corneal inflammation and nerve integrity after refractive surgery

Alterations in corneal innervations result in impaired corneal sensation, severe dry eye and damage to the epithelium that may in turn lead to corneal ulcers, melting and perforation. These alterations can occur after refractive surgery. We have discovered that pigment epithelium-derived factor (PEDF) plus docosahexaenoic acid (DHA or the docosanoid bioactive neuroprotectin D1 (NPD1)) induces nerve regeneration after corneal surgery that damages the stromal nerves. We found that PEDF is released from corneal epithelial cells after injury, and when DHA is provided to the cells it stimulates the biosynthesis of NPD1 by an autocrine mechanism. The combination of PEDF plus DHA also decreased the production of leukotriene B4 (LTB4), a neutrophil chemotactic factor, thereby decreasing the inflammation induced after corneal damage. These studies suggest that PEDF plus DHA and its derivative NPD1 hold promise as a future treatment to restore a healthy cornea after nerve damage.     

Prevalence and associations of steep cornea/keratoconus in Greater Beijing. The Beijing Eye Study

Purpose

To evaluate the prevalence and associated factors of steep cornea/keratoconus in the adult Chinese population.

Methods

The population-based Beijing Eye Study 2011 included 3468 individuals with a mean age of 64.6±9.8 years (range: 50–93 years). A detailed ophthalmic examination was performed including optical low-coherence reflectometry. Steep cornea/keratoconus were defined as an anterior corneal refractive power exceeding 48 diopters.

Results

Mean refractive power of the cornea was 43.16±1.45 diopters (range: 36.51 to 48.46 diopters; flattest meridian) and 43.98±1.52 diopters (range: 37.00 to 52.88 diopters; steepest meridian). A steep cornea/keratoconus defined as corneal refractive power of ≥48 diopters and ≥49 diopters was detected in 27 subjects (prevalence rate: 0.9±0.2%) and 6 (0.2± 0.1%) subjects, respectively. Presence of steep cornea/keratoconus was associated with shorter axial length (P<0.001), smaller interpupillary distance (P = 0.038), lower best corrected visual acuity (P = 0.021), higher cylindrical refractive error (P<0.001) and more myopic refractive error (P<0.001). It was not significantly associated with gender, body height, psychic depression, cognitive function, blood concentrations of glucose, lipids, creatinine and C-reactive protein, blood pressure and quality of life score, nor with intraocular pressure, dry eye feeling, and lens thickness.

Conclusions

A steep cornea/keratoconus defined as corneal refractive power of 48+ diopters has a prevalence of 0.9±0.2% among Chinese aged 50 years and above. Its prevalence was significantly associated with the ocular parameters of shorter axial length, smaller interpupillary distance, higher cylindrical and myopic refractive error and lower best corrected visual acuity, however, with none of the systemic parameters tested.     

Corneal donor tissue preparation for endothelial keratoplasty

Over the past ten years, corneal transplantation surgical techniques have undergone revolutionary changes. Since its inception, traditional full thickness corneal transplantation has been the treatment to restore sight in those limited by corneal disease. Some disadvantages to this approach include a high degree of post-operative astigmatism, lack of predictable refractive outcome, and disturbance to the ocular surface. The development of Descemet's stripping endothelial keratoplasty (DSEK), transplanting only the posterior corneal stroma, Descemet's membrane, and endothelium, has dramatically changed treatment of corneal endothelial disease. DSEK is performed through a smaller incision; this technique avoids 'open sky' surgery with its risk of hemorrhage or expulsion, decreases the incidence of postoperative wound dehiscence, reduces unpredictable refractive outcomes, and may decrease the rate of transplant rejection. Initially, cornea donor posterior lamellar dissection for DSEK was performed manually resulting in variable graft thickness and damage to the delicate corneal endothelial tissue during tissue processing. Automated lamellar dissection (Descemet's stripping automated endothelial keratoplasty, DSAEK) was developed to address these issues. Automated dissection utilizes the same technology as LASIK corneal flap creation with a mechanical microkeratome blade that helps to create uniform and thin tissue grafts for DSAEK surgery with minimal corneal endothelial cell loss in tissue processing. Eye banks have been providing full thickness corneas for surgical transplantation for many years. In 2006, eye banks began to develop methodologies for supplying precut corneal tissue for endothelial keratoplasty. With the input of corneal surgeons, eye banks have developed thorough protocols to safely and effectively prepare posterior lamellar tissue for DSAEK surgery. This can be performed preoperatively at the eye bank. Research shows no significant difference in terms of the quality of the tissue or patient outcomes using eye bank precut tissue versus surgeon-prepared tissue for DSAEK surgery. For most corneal surgeons, the availability of precut DSAEK corneal tissue saves time and money, and reduces the stress of performing the donor corneal dissection in the operating room. In part because of the ability of the eye banks to provide high quality posterior lamellar corneal in a timely manner, DSAEK has become the standard of care for surgical management of corneal endothelial disease. The procedure that we are describing is the preparation of the posterior lamellar cornea at the eye bank for transplantation in DSAEK surgery (Figure 1).     

Patient-specific modeling of corneal refractive surgery outcomes and inverse estimation of elastic property changes

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

A triphasic analysis of corneal swelling and hydration control.

Physiological studies strongly support the view that hydration control in the cornea is dependent on active ion transport at the corneal endothelium. However, the mechanism by which endothelial ion transport regulates corneal thickness has not been elaborated in detail. In this study, the corneal stroma is modeled as a triphasic material under steady-state conditions. An ion flux boundary condition is developed to represent active transport at the endothelium. The equations are solved in cylindrical coordinates for confined compression and in spherical coordinates to represent an intact cornea. The model provides a mechanism by which active ion transport at the endothelium regulates corneal hydration and provides a basis for explaining the origin of the "imbibition pressure" and stromal "swelling pressure." The model encapsulates the Donnan view of corneal swelling as well as the "pump-leak hypothesis."     

Artificial Cornea: Towards a Synthetic Onlay for Correction of Refractive Error

Synthetic onlays that are implanted onto the surface of the cornea have the potential to become an alternative to spectacles and contact lenses for the correction of refractive error. A successful corneal onlay is dependent on development of a biocompatible polymer material that will maintain a healthy cornea after implantation and that will promote growth of corneal epithelial cells over the onlay, and development of a method for attachment of the onlay with minimal surgical invasiveness. The ideal onlay should be made of a material that is highly permeable yet has sufficient surface characteristics to stimulate stable and firm attachment of the corneal epithelium over the onlay. Recent research indicates that collagen I coated polymer materials that mimic the basement membrane of the corneal epithelium promote the most favorable growth of epithelial cells in vivo in comparison to wholly biological or synthetic materials.     

Influence of needling conditions on the corneal insertion force

Abstract

Needle insertion plays an important part in the process of corneal graft surgery. In this paper, a three-dimensional symmetry model of the human cornea is constructed using the finite element method. Simplification of specific optic physiology is defined for the model: The cornea constrained by the sclera is presented as two layers consisting of epithelium and stroma. A failure criterion based on the distortion energy theory has been proposed to predict the insertion process of the needle. The simulation results show a good agreement with the experimental data reported in the literature. The influence of needling conditions (e.g. insertion velocity, rotation parameters and vibration parameters) on the insertion force are then discussed. In addition, a multi-objective optimization based on particle swarm optimization (PSO) is applied to reduce the insertion force. The numerical results provide guidelines for selecting the motion parameters of the needle and a potential basis for further developments in robot-assisted surgery.     

Spatial mapping of collagen fibril organisation in primate cornea-an X-ray diffraction investigation

New insights are presented into the collagenous structure of the primate cornea. Wide-angle X-ray diffraction was used to map the fibrillar arrangement and distribution of collagen over three common marmoset corneas. The maps provide a point of reference to help interpret data from pathological corneas or primate models of refractive surgery. The results herein disclose a circum-corneal annulus of highly aligned collagen, 0.5-1.5 mm wide, where the cornea and sclera fuse at the limbus; a feature similar to that observed in human tissue. As in humans, the annulus is not uniform, varying in width, fibril angular spread, and collagen density around its circumference. However, more centrally the marmoset cornea exhibits a preferred lamella orientation in which proportionally more fibrils are oriented along the superior-inferior corneal meridian. This observation is in striking contrast with the situation in human cornea, where there is an orthogonal arrangement of preferentially aligned fibrils. Investigation of a further 16 corneas confirmed that approximately 33% (+/-1%) (n = 76) of fibrils in the central marmoset cornea lie within a 45 degrees sector of the superior-inferior meridian. Implications for the mechanical and optical properties of the cornea are discussed.     

Analysis of the reasons for not undergoing laser corneal refractive surgery in 611 patients

To determine and analyze the reasons for patients not undergoing laser corneal refractive surgery. A retrospective observational study was conducted to analyze the reasons for not undergoing laser corneal refractive surgery in 611 patients. In this study, 611 (14.34%) among 4,262 enrolled patients did not undergo laser corneal refractive surgery. Among these 611 patients, the common reasons for not undergoing laser corneal refractive surgery were concern about the surgery (366 patients, 59.90%), insufficient corneal thickness (72 patients, 11.78%), too high corneal refractive power (36 patients, 5.89%), dry eye (33 patients, 5.40%), high intraocular pressure (22 patients, 3.60%), poor corrected visual acuity (25 patients, 4.09%), retinal diseases (23 patients, 3.76%) and others (34 patients, 5.56%). The concern about surgery is the primary factor for the patients not undergoing laser corneal refractive surgery.     

Finite element simulation of arcuates for astigmatism correction

In order to simulate the corneal incisions used to correct astigmatism, a three-dimensional finite element model was generated from a simplified geometry of the anterior half of the ocular globe. A hyperelastic constitutive behavior was assumed for cornea, limbus and sclera, which are collagenous materials with a fiber structure. Due to the preferred orientations of the collagen fibrils, corneal and limbal tissues were considered anisotropic, whereas the sclera was simplified to an isotropic one assuming that fibrils are randomly disposed. The reference configuration, which includes the initial strain distribution that balances the intraocular pressure, is obtained by an iterative process. Then the incisions are simulated. The final positions of the nodes belonging to the incised meridian and to the perpendicular one are fitted by both radii of curvature, which are used to calculate the optical power. The simulated incisions were those specified by Lindstrom's nomogram [Chu, Y., Hardten, D., Lindquist, T., Lindstrom, R., 2005. Astigmatic keratotomy. Duane's Ophthalmology. Lippincott Williams and Wilkins, Philadelphia] to achieve 1.5, 2.25, 3.0, 4.5 and 6.0D of astigmatic change, using the next values for the parameters: length of 45 degrees , 60 degrees and 90 degrees , an optical zone of 6mm, single or paired incisions. The model gives results similar to those in Lindstrom's nomogram [Chu et al., 2005] and can be considered a useful tool to plan and simulate refractive surgery by predicting the outcomes of different sorts of incisions and to optimize the values for the parameters involved: depth, length, position.     

Terrestrial optics in an aquatic eye: The sandlance,Limnichthytes fasciatus (Creediidae,Teleostei)

The sandlance, Limnichthyes fasciatus (Creediidae, Teleostei), behaves like a marine chameleon, with independent movements of its turret-like eyes, highly-effective camouflage and rapid strikes for isolated, mobile prey at close quarters. The optical system has a fixed circular pupil, a deep pit fovea and a flattened lens unlike any other teleost lens so far described. The convex, laminated structure of the cornea is also unparalleled in a teleost which suggests that the cornea may play a refractive role that might compensate for the reduced power of the flattened lens. This suggestion has been supported in the present investigation by four independent sets of observations:- i. Purkinje images formed underwater by the cornea; ii. Measurements of the magnification of intra-corneal iridophores viewed through the corneal lenticle; iii. Measurements of the magnification produced by the dissected corneal lenticle and lens when viewed over a grating; iv. Ray tracing experiments comparing the degree of refraction produced by the lens and by the corneal lenticle. All experimental observations confirm that the cornea of the sandlance has a significant refractive role, with a power of approximately 200 D compared with a power of 550 D for the lens. This is the first report of a significant refractive role played by the cornea in a teleost. The optical system of lens plus cornea, in combination with a deep pit fovea, may be more suitable for the detection and visual localisation of small, moving, underwater prey than the conventional wide-field spherical lens system of other teleosts. The evolutionary convergence of this marine optical system and lifestyle with those of the chameleon is remarkable, given the constraints imposed by underwater optics.     

Two-photon collagen crosslinking in ex vivo human corneal lenticules induced by near-infrared femtosecond laser

Myopia and keratoconus have become common corneal diseases that threaten the quality of human vision, and keratoconus is one of the most common indications for corneal transplantation worldwide. Collagen crosslinking (CXL) using riboflavin and ultraviolet A (UVA) light is an effective approach for treating ophthalmic disorders and has been shown clinically not only to arrest further progression of keratoconus but also to improve refractive power for cornea. However, CXL surgery irradiated by UVA has various potential risks such as surface damage and endothelial cell damage. Here, near-infrared femtosecond laser-based two-photon CXL was first applied to ex vivo human corneal stroma, operating at low photon energy with high precision and stability. After two-photon CXL, the corneal stiffness can be enhanced by 300% without significantly reducing corneal transparency. These findings illustrate the optimized direction that depositing high pulses energy in corneal focal volume (not exceeding damage threshold), and pave the way to 3D CXL of in vivo human cornea with higher safety, precision, and efficacy.     

The Semaphorin 3A Inhibitor SM-345431 Accelerates Peripheral Nerve Regeneration and Sensitivity in a Murine Corneal Transplantation Model

Background

Peripheral nerve damage of the cornea is a complication following surgery or infection which may lead to decreased visual function. We examined the efficacy of the semaphorin 3A inhibitor, SM-345431, in promoting regeneration of peripheral nerves in a mouse corneal transplantation model.

Methodology/Principal Findings

P0-Cre/Floxed-EGFP mice which express EGFP in peripheral nerves cells were used as recipients of corneal transplantation with syngeneic wild-type mouse cornea donors. SM-345431 was administered subconjunctivally every 2 days while control mice received vehicle only. Mice were followed for 3 weeks and the length of regenerating nerves was measured by EGFP fluorescence and immunohistochemistry against βIII tubulin. Cornea sensitivity was also measured by the Cochet-Bonnet esthesiometer. CD31 staining was used to determine corneal neovascularization as a possible side effect of SM-345431. Regeneration of βIII tubulin positive peripheral nerves was significantly higher in SM-345431 treated mice compared to control. Furthermore, corneal sensitivity significantly improved in the SM-345431 group by 3 weeks after transplantation. Neovascularization was limited to the peripheral cornea with no difference between SM-345431 group and control.

Conclusions/Significance

Subconjunctival injections of SM-345431 promoted a robust network of regenerating nerves as well as functional recovery of corneal sensation in a mouse keratoplasty model, suggesting a novel therapeutic strategy for treating neurotrophic corneal disease.     

The eye of the hooded seal,Cystophora cristata,in air and water

Summary Multiple refractive state measurements were made on a male and female hooded seal (Cystophora cristata) when the eyes were exposed to air and to water. The measures, made by conventional retinoscopy and by photorefraction, show that the seals are moderately hyperopic (2–3 diopters) in water and moderately myopic (2–4 diopters) in air. No significant astigmatism was noted in either medium. The absence of refractive state variation over time suggests that an accommodative mechanism is insignificant or absent, although histological study indicates that the ciliary muscle is well developed.Photokeratoscopy, carried out on two animals with two keratoscopic instruments, show that the cornea is relatively flat (30 mm, or about one-half the diameter of the eye). Furthermore the cornea is only slightly astigmatic (less than 1 diopter). The refractive power of the external corneal surface (in air), calculated from a measurement of corneal refractive index of 1.378, amounts to only 10 or 11 diopters.As in the typical fish eye, hooded seal lenses are spherical or nearly spherical in shape (24–23 mm), and have short focal lengths (30–32 mm). Focal measures for rays at varying distances from the lens center indicate that spherical aberration is well corrected.There is no indication in this seal species, of a previously reported adaptation involving a highly astigmatic cornea which together with a slit pupil can minimize the optical effect of movement from water to air.     

Studies on the Effect of the Adhesion Protein Isolated from Bovine Eye on Cell Proliferation in the Newt Cornea

The effect of the adhesion protein isolated from the bovine cornea was studied on the model of mechanical injury (cross cutting of the cornea). In the concentration of 10^?12 mg/ml, the protein influenced the proliferation of corneal epithelial cells in newt Pleurodeles waltl in vivo. Experiments were conducted using autoradiography, and the nuclear labeling index (NLI) was determined at different times after surgery and in different corneal regions. This adhesion protein significantly induced proliferation of corneal epithelial cells relative to control groups with the injured eyes treated with the serum adhesion protein at the same concentration or water. The differences between the experimental and control animals were most pronounced 7 days after surgery. By day 14, they were less pronounced but still significant. On day 28, no significant differences in NLI were observed between the three groups, although these values remained higher than in intact animals. An increased pool of proliferating cells in the corneal epithelium was observed both in the affected and intact areas. The data obtained indicate that the biological activity of this protein is not species specific and that it can be a proliferation factor for corneal epithelial cells.     

A model for the human cornea: constitutive formulation and numerical analysis

The human cornea (the external lens of the eye) has the macroscopic structure of a thin shell, originated by the organization of collagen lamellae parallel to the middle surface of the shell. The lamellae, composed of bundles of collagen fibrils, are responsible for the experimentally observed anisotropy of the cornea. Anomalies in the fibril structure may explain the changes in the mechanical behavior of the tissue observed in pathologies such as keratoconus. We employ a fiber-matrix constitutive model and propose a numerical model for the human cornea that is able to account for its mechanical behavior in healthy conditions or in the presence of keratoconus under increasing values of the intraocular pressure. The ability of our model to reproduce the behavior of the human cornea opens a promising perspective for the numerical simulation of refractive surgery.