Elena Lanchares

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 Lindstroms nomogram [Chu, Y., Hardten, D., Lindquist, T., Lindstrom, R., 2005. Astigmatic keratotomy. Duanes 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 Lindstroms 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.

Evaluation of in vitro efficacy of combined riboflavin and ultraviolet a for Acanthamoeba isolates.

PURPOSE To evaluate in vitro the amoebicidal effects of riboflavin and ultraviolet A (UVA) collagen cross-linking. DESIGN Experimental study, laboratory investigation. METHODS Two different strains of Acanthamoeba species were tested identically. Four treatment groups were considered: group 1 consisted of 0.1% riboflavin and 30-minute UVA irradiation; group 2 consisted of 0.1% riboflavin and 60-minute UVA irradiation; group 3 consisted of no riboflavin and no UVA exposure; group 4 consisted of 0.1% riboflavin and no UVA exposure. The application of UVA was performed under the parameters used for in vivo corneal collagen cross-linking. RESULTS In all cases, cysts and trophozoites were detected 24 hours after treatment at a radial distance from the center of the seeding point more than 5 mm, indicating that the amoebae were viable. All treated and untreated groups of amoebae from the 2 strains exhibited growth (radii of 14 to 15 mm in groups 1, 3, and 4; radius of 12 mm in group 2). The final morphologic features of the 2 strains of trophozoites that received treatment were similar to those of the initial seeding group and the untreated control group. CONCLUSIONS The results obtained in our study show that a single dose (30 or 60 minutes) of cross-linking cannot achieve eradication in the 2 different Acanthamoeba strains examined. However, in vitro results do not always indicate in vivo efficacy, so future studies should test the validity of this treatment for Acanthamoeba keratitis.

Assessment of Corneal Biomechanical Properties and Intraocular Pressure in Myopic Spanish Healthy Population

Purpose. To examine biomechanical parameters of the cornea in myopic eyes and their relationship with the degree of myopia in a western healthy population. Methods. Corneal hysteresis (CH), corneal resistance factor (CRF), Goldmann correlated intraocular pressure (IOP), and corneal compensated IOP (IOPcc) were measured using the ocular response analyzer (ORA) in 312 eyes of 177 Spanish subjects aged between 20 and 56 years. Refraction was expressed as spherical equivalent (SE), which ranged from 0 to −16.50 diopters (D) (mean: −3.88 ± 2.90 D). Subjects were divided into four groups according to their refractive status: group 1 or control group: emmetropia (−0.50 ≤ SE < 0.50); group 2: low myopia (−0.75 ≤ SE < 3.00 D); group 3: moderate myopia (−3.00 ≤ SE ≤ −6.00 D); and group 3: high myopia (SE greater than −6.00 D). We analyzed the relationship between corneal biomechanics measured with ORA and SE. Results. CH in the emmetropia, low myopia, moderate myopia, and high myopia groups was 11.13 ± 0.98, 11.49 ± 1.25, 10.52 ± 1.54, and 10.35 ± 1.33 mmHg, respectively. CH in the highly myopic group was significantly lower than that in the emmetropic group (P = 0.07) and low myopic group (P = 0.035); however, there were no differences with the moderate myopic group (P = 0.872). There were no statistically significant differences regarding IOP among the four groups (P > 0.05); nevertheless, IOPcc was significantly higher in the moderately myopic (15.47 ± 2.47 mmHg) and highly myopic (16.14 ± 2.59 mmHg) groups than in the emmetropia (15.15 ± 2.06 mmHg) and low myopia groups (14.53 ± 2.37 mmHg). No correlation between age and the measured parameters was found. CH and IOPcc were weakly but significantly correlated with SE (r = 0.171, P = 0.002 and r = −0.131, P = 0.021, resp.). Conclusions. Present study showed only a very weak, but significant, correlation between CH and refractive error, with CH being lower in both moderately and highly myopic eyes than that in the emmetropic and low myopic eyes. These changes in biomechanical properties of the cornea may have an impact on IOP measurement, increasing the risk of glaucoma.

Lower- and higher-order aberrations predicted by an optomechanical model of arcuate keratotomy for astigmatism

PURPOSE: To develop a realistic model of the optomechanical behavior of the cornea after curved relaxing incisions to simulate the induced astigmatic change and predict the optical aberrations produced by the incisions. SETTING: ICMA Consejo Superior de Investigaciones Científicas and Universidad de Zaragoza, Zaragoza, Spain. METHODS: A 3‐dimensional finite element model of the anterior hemisphere of the ocular surface was used. The corneal tissue was modeled as a quasi‐incompressible, anisotropic hyperelastic constitutive behavior strongly dependent on the physiological collagen fibril distribution. Similar behaviors were assigned to the limbus and sclera. With this model, some corneal incisions were computer simulated after the Lindstrom nomogram. The resulting geometry of the biomechanical simulation was analyzed in the optical zone, and finite ray tracing was performed to compute refractive power and higher‐order aberrations (HOAs). RESULTS: The finite‐element simulation provided new geometry of the corneal surfaces, from which elevation topographies were obtained. The surgically induced astigmatism (SIA) of the simulated incisions according to the Lindstrom nomogram was computed by finite ray tracing. However, paraxial computations would yield slightly different results (undercorrection of astigmatism). In addition, arcuate incisions would induce significant amounts of HOAs. CONCLUSIONS: Finite‐element models, together with finite ray‐tracing computations, yielded realistic simulations of the biomechanical and optical changes induced by relaxing incisions. The model reproduced the SIA indicated by the Lindstrom nomogram for the simulated incisions and predicted a significant increase in optical aberrations induced by arcuate keratotomy.

The Effect of Intraocular Pressure on the Outcome of Myopic Photorefractive Keratectomy: A Numerical Approach

Photorefractive Keratectomy (PRK) is a surgical procedure widely performed to correct myopia. In this work, the effect of the intraocular pressure (IOP) on the refractive correction achieved by the PRK surgery was analyzed using a numerical model. Simulations of PRK surgery at 10, 15 and 21 mmHg of IOP were performed and the post-surgical diopters were estimated. For low and medium values of IOP (10 and 15 mmHg), the computed results were close to those used by clinicians based on experience and defined without considering the IOP, while an undercorrection was predicted for the highest value of IOP (21 mmHg). From these results, we suggest that IOP should be considered in the determination of the depth of ablation, in addition to other factors such as the level of myopia or the corneal central thickness.

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.

Immediate Effect of Ultraviolet-A Collagen Cross-linking Therapy on the Biomechanics and Histology of the Human Cornea

Wollensak et al. introduced corneal collagen crosslinking (CXL) using riboflavin and ultraviolet-A for the treatment of progressive keratoconus.1 Empirical in vitro studies evaluated the stiffening effect of CXL and some used human corneas to assess the stiffness achieved,2,3 but they did not present a histological analysis of the treated human cornea. To learn the immediate mechanical and histological effect induced by CXL in human corneal tissue, we performed tensile stress tests and histological comparative observation of cross-linked and untreated healthy human corneas. The corneas were retrieved from the local tissue bank. They were clear with normal epithelium, endothelium, and corneal thickness. One sample received a standard epithelium–off-riboflavin/ ultraviolet-A CXL treatment and the other was only deepithelialized. The stress-strain test showed a stiffer response of the treated tissue than that of the untreated tissue. The treated cornea resulted in 1.8, 1.6, 1.7, and 1.5 folds stiffer than the untreated sample at the 6%, 8%, 10%, and 12% stretches, respectively. Stiffness of the tissue after treatment was increased by 64% (factor of 1.64). Although Wollensak et al.2 initially found a 350% increase of stiffness in the treated tissue (greater than that of the current study), this value was later corrected and an increase in stiffness by a factor of 1.5 was given by Spoerl in the 7th Cross-linking Congress. The study by Raiskup and Spoerl4 gave a value of 70% increase (factor of 1.7), which matches our result. Besides increasing the biomechanical rigidity of the human cornea, CXL induces secondary effects such as keratocyte apoptosis.1 Therefore, the safety of the procedure must be guaranteed. The cytotoxicity of the riboflavin/ ultraviolet-A treatment on keratocytes and endothelium cells was studied by Wollensak et al.,2 who established a cytotoxic threshold of 5.4 J/cm2. However, the significance of the damage is not yet completely known and, to our knowledge, it has not been reported in in vivo studies with human corneas in the literature. Our histological analysis of the treated sample showed an immediate effect of the outermost stroma compacting with increased fibrillar density and decreased interlamellar space in comparison with the control. Dehydration reached approximately 65% of the thickness. Regarding the cellular population, the treated sample showed absence of keratocyte nuclei in the stroma even at a deep level, whereas the control sample showed intact keratocyte nuclei (Figure 1). Therefore, keratocyte apoptosis happens immediately after treatment in the cross-linked cornea and at a deeper level than expected, possibly due to immediately performing the histological analysis. Wollensak5 observed keratocytes in the posterior stroma 24 hours after CXL. We suppose keratocytes could have repopulated the deeper cornea during these hours. According to our results, CXL has an immediate biomechanical and histological effect. Stiffening of the tissue, stromal compacting, and a keratocyte apoptosis deeper than compacting were observed.

Use of 2% hydroxypropyl methylcellulose to prevent the corneal swelling during the in vitro mechanical characterization

The aim of this study was to assess the use of 2% HPMC during in vitro uniaxial tensile tests, with corneal strips immediately obtained or after storing the eyes for 24 h in 0.9% NaCl solution at 4 ℃. The purpose was to establish a standardized procedure to prevent phenomena which can modify the mechanical properties of the tissue. Rabbit eyes were divided into four groups. Group A had seven eyes that were preserved in NaCl solution for 24 h before testing. Group B had seven eyes that were immediately tested. In both groups, to prevent both swelling and dehydration, 2% hydroxypropyl methylcellulose (2% HPMC) was applied. Group C had seven eyes that were preserved in NaCl solution for 24 h before testing. Group D had seven eyes that were immediately tested. In both groups, HPMC was not applied. Regarding the mechanical response, groups with HPMC showed similar Cauchy stress–stretch curves and there were no statistically significant differences at 5%, 10% and 15% strain between them, which mean that both showed similar mechanical behavior. The same result was obtained between groups without HPMC. However, for coupled groups with and without HPMC, statistically significant differences at 10% and 15% strain were observed. On the other hand, when grouped by storage time, statistically significant differences were found between groups that had eyes preserved for 24 h with and without HPMC, respectively, as well as between groups immediately tested with and without HPMC, respectively, at 15% strain. Nevertheless, if coupled groups were considered, between groups that were preserved for 24 h in NaCl before testing and groups that were immediately tested, no statistically significant differences were obtained. In addition, the Cauchy stress–stretch curves of groups without HPMC showed a decreasing slope of the linear part (strain > 8%) of the graph during the experiment. In summary, the use of HPMC during the handling of the tissue from excision to testing seems to prevent both swelling and dehydration.

Patient-Specific Biomechanical Framework for Aiding Clinical Decisions in Eye Surgery

In this work we present the development of a patient-specific model of the eye for helping in different ophthalmologic surgical techniques. To build the model we use a simple general model on which we can add the patient specificities measured with proper equipment. The model of the eye is composed of several tissues that must be characterized to ensure that the model has a behavior similar to the real eye. Once the constitutive model is described and characterized for all the tissues included in the model, different surgical techniques can be accomplished. We present here the usefulness of this model to help in surgical planning of incisional surgery for the correction of astigmatism, the numerical analysis of the process of accommodation and the numerical simulation of the scleral buckling technique for retinal detachment.