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.

Progressive high-fluence epithelium-on accelerated corneal crosslinking: a novel corneal photodynamic therapy for early progressive keratoconus.

Purpose: To assess the preliminary clinical results of a new, progressively higher fluence-pulsed light Epi-On accelerated crosslinking nomogram (PFPL M Epi-On ACXL) in the treatment of progressive keratoconus (KC). Setting: Siena Crosslinking Center, Siena, Italy. Methods: A prospective pilot open, non-randomized interventional study, including 32 eyes of 32 young-adult patients over 26 years old with Stages I-III progressive KC undergoing PFPL M Epi-On ACXL, was conducted. Riboflavin loading was performed by using Paracel I 0.25% for 4 min and Paracel II 0.22% for 6 min. The Avedro KXL System (Glaukos-Avedro, Burlington, USA) was used for pulsed-light accelerated crosslinking (ACXL) at air room 21% oxygenation and 13 min of UV-A irradiation. The treatment fluence was set at 7.2 J/cm2, 8.6 J/cm2, and 10.0 J/cm2 in corneas with baseline pachymetry <420 µm (group 1: 8 eyes), ≥ 420 µm <460 µm (group 2, 11 eyes), and ≥ 460 µm (group 3, 13 eyes), respectively. Uncorrected distance visual acuity (UDVA), best-spectacle corrected visual acuity (BSCVA), Scheimpflug corneal tomography, and anterior segment OCT (AS-OCT) data were collected at baseline and postoperatively at 1, 3, and 6 months. Results: UDVA and BSCVA improved in all groups (P ≤ 0.05). Maximum keratometry values (K max) showed a significant decrease in the 10.0 J/cm2 group (Δ -1.68 D). The coma (HOAs) value improved significantly by the sixth month in all groups. OCT average demarcation lines were 211 ± 19 µm in group 1, 245 ± 23 µm in group 2, and 267 ± 21 µm in group 3. Conclusions: The preliminary results show that pachymetry-based PFPL M Epi-On ACXL nomogram stabilizes ectasia progression. Higher fluence Epi-On ACXL increases CXL penetration, with better functional outcomes in the absence of complications.

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.

Evaluation of the Efficacy of Low-Particle-Size Toothpastes against Extrinsic Pigmentations: A Randomized Controlled Clinical Trial.

Stain-removing domiciliary protocols are focused on the elimination of dental extrinsic pigmentations by the application of abrasive toothpastes, extensively available in commerce. The goal of the present study is to evaluate the efficacy of two different stain removal molecule-formulated toothpastes by the reduction of clinical parameters: the micro-cleaning crystals and activated charcoal. A total of 40 participants with extrinsic dental pigmentations were enrolled and divided into two groups: a Control group, assigned to a toothpaste with micro-cleaning crystals (Colgate Sensation White); and a Trial group, with microparticle-activated charcoal toothpaste (Coswell Blanx Black). At T0 (baseline), T1 (10 days), T2 (1 month), and T3 (3 months), clinical parameters, including Lobene stain index calculated for intensity and extension, plaque control record, and bleeding on probing, were measured. Statistically significant differences were found in both groups (p < 0.05): a reduction of extrinsic pigmentation, both in intensity and extension, was obtained in the Control group, but their total elimination could be achieved only in the Trial group with the activated charcoal molecule, though without significant difference between the groups (p > 0.05). No intergroup differences were found for each timeframe for PCR, BoP, LSI-I, and LSI-E. Both tested toothpastes can be recommended for domiciliary oral hygiene of patients with extrinsic pigmentations.

Experimental in-vitro investigation on Epi-Off-Crosslinking on porcine corneas.

AIM: To evaluate quantitatively the effects of the Epi-Off-CXL irradiance dose on the stromal stiffening of pig corneas. SETTING: Laboratory of Biological structures (LaBS), Politecnico di Milano, Milano, Italy. METHODS: Inflation tests have been carried on 90 excised and de-epithelized pig corneas, monitoring the change of configuration of the corneal dome at specific pressures. Test have been carried out twice on each cornea, once before and once after Epi-Off-CXL performed at a constant irradiance of 9 mW/cm2 and variable UV-A exposure times. Corneas were grouped according to the exposure time (2.5, 5, 10, 15 and 20 min), proportional to the irradiation dose (1.35, 2.7, 5.4, 8.1, and 10.8 J/cm2). A theoretical model based on linearized shell theory has been used to estimate the increment of the corneal stiffness. RESULTS: The linearized shell theory allowed to establish a quantitative relation between the increment of the stiffness parameters and the irradiation dose. Relative to the pre-treatment values, in all experiments the post-treatment corneal stiffness revealed a pronounced increase. In general, the stiffness gain increased with the exposure time. No significant differences in stiffening was observed between tests conducted at 2.5, 5, and 10 min exposure. CONCLUSIONS: Qualitatively, the effectiveness of accelerated CXL treatments observed in pig corneas complies very well with in-vivo clinical results in humans, suggesting that experimental data in pigs can be very useful for the design of the procedure in humans. A larger irradiation dose provides a larger increment of the corneal stiffness. Due to the biological variability of the tissues, however, it is difficult to distinguish quantitatively the level of the reinforcement induced by accelerated protocols (low doses with < = 10 min exposure), less prone to induce damage in the corneal tissue. Therefore, the definition of personalized treatments must be related to the actual biomechanics of the cornea.

A numerical model of capsulorhexis to assess the relevance of size and position of the rhexis on the IOL decentering and tilt.

Finite element models of human crystalline capsular bag and zonular fibers are used to estimate the mechanical response of the capsule to the presence of a C-loop Intra-Ocular Lens (IOL) after cataract surgery, to assess the influence of capsulorhexis size, shape and location on IOL decentration and tilt. The model includes, in the anterior capsule, a hole with variable size, shape and position, which represents the rhexis obtained in a manual or laser-assisted manner. The IOL is not explicitly modelled, but its action is reproduced by means of a set of elastic ties, connecting the opposite sides of the bag and exerting the force corresponding to an expanded IOL. Numerical simulations show that IOL decentration and tilt are not related to the size of the rhexis. A decentered rhexis induces IOL decentration <40 µm and a tilt <12°; the combination of non-circular shape and decentering of the rhexis induces IOL decentration <47 µm. While the introduction of a circular central rhexis causes an increment of the stresses in the capsule up to 100% relative to the physiological state, the combination of rhexis decentering and non-circular shape causes an additional 10% stress change. The values of IOL decentering and IOL tilt obtained from simulations are of scarce relevance in the clinical practice.

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.

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.

Modelling with a meshfree approach the cornea-aqueous humor interaction during the air puff test.

The air puff test is an in-vivo investigative procedure commonly utilized in ophthalmology to estimate the intraocular pressure. Potentially the test, quick and painless, could be combined with inverse analysis methods to characterize the patient-specific mechanical properties of the human cornea. A rapid localized air jet applied on the anterior surface induces the inward motion of the cornea, that interacts with aqueous humor-the fluid filling the narrow space between cornea and iris-with a strong influence on the dynamics of the cornea. While models of human cornea reproduce accurately patient-specific geometries and have reached a considerable level of complexity in the description of the material, yet scant attention has been paid to the aqueous humor, and no eye models accounting for the physically correct fluid-solid interaction are currently available. The present study addresses this gap by proposing a fluid-structure interaction approach based on a simplified two-dimensional axis-symmetric geometry to simulate the anterior chamber of the eye undergoing the air puff test. We regard the cornea as a membrane described through an analytical model and discretize the fluid with a mesh-free particle approach. The membrane is assumed to be nonlinear elastic and isotropic, and the fluid weakly compressible Newtonian. Numerical analyses reveal a marked influence of the fluid on the dynamics of the cornea. We perform a parametric analysis to assess the quantitative influence of geometrical and material parameters on the mechanical response of the model. Additionally, we investigate the possibility to use the dynamics of the test to estimate the intraocular pressure.

Myopic Surface Ablation in Asymmetrical Topographies: Refractive Results and Theoretical Corneal Elastic Response.

PURPOSE: To evaluate refractive results and the theoretical elastic response of photorefractive keratectomy in eyes with asymmetrical corneal surface and to compare such outcomes with a control-matched group of normal topographies. DESIGN: Retrospective interventional case series with matched comparison group. METHODS: Thirty eyes with superior-inferior dioptric difference (SI index) > 1.40 diopter (D) were compared to 30 eyes with normal topographies. Both groups were matched for age, preoperative spherical equivalent (SE), mean keratometry, and percentage of tissue altered (PTA). Refractive results and the theoretical elastic modulus calculations were evaluated. RESULTS: The mean preoperative SI index in the asymmetrical group was 2.06 ± 0.56 D vs 0.14 ± 0.73 D in the control group (P < .001). From 3 to 12 months postoperatively, the asymmetrical group presented a mean re-steepening of 0.51 ± 0.39 D vs 0.19 ± 0.40 D in the control group (P = .014). The mean PTA of 14.42% generated a theoretical elastic modulus reduction of 10.25% in the asymmetrical group vs 2.45% in the control group (P = .006). The reduction of the theoretical elastic modulus correlated with the preoperative SI index (ρ = -0.387, P = .007). After 36 months, 90% of all eyes were within ±0.50 D of SE and the theoretical elastic modulus did not present a significant difference between both groups (P = .085). CONCLUSIONS: Asymmetrical-topography corneas treated with myopic surface ablation presented an increased short-term keratometric re-steepening and reduction of the theoretical elastic moduli. The long-term follow-up indicated that, in selected cases of asymmetrical topographies, myopic surface ablation could induce a premature biomechanical elastic response rather than a progressive pathologic process.

Coupled electro-mechanical models of fiber-distributed active tissues.

We discuss a constitutive model for stochastically distributed fiber reinforced tissues, where the active behavior of the fibers depends on the relative orientation of the electric field. Unlike other popular approaches, based on numerical integration over the unit sphere, or on the use of second order structure tensors, for the passive behavior we adopt a second order approximation of the strain energy density of the distribution. The purely mechanical quantities result to be dependent on two (second and fourth order, respectively) averaged structure tensors. In line with the approximation used for the passive behavior, we model the active behavior accounting for the statistical fiber distribution. We extend the Helmholtz free energy density by introducing a directional active potential, dependent on a stochastic permittivity tensor associated to a particular direction, and approximate the total active potential through a second order Taylor expansion of the permittivity tensor. The approximation allows us to derive explicitly the active stress and the active constitutive tensors, which result to be dependent on the same two averaged structure tensors that characterize the passive response. Active anisotropy follows from the distribution of the fibers and inherits its stochastic parameters. Examples of passive and active behaviors predicted by the model in terms of response to biaxial testing are presented, and comparisons with passive experimental data are provided.

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.

Customized Finite Element Modelling of the Human Cornea.

AIM: To construct patient-specific solid models of human cornea from ocular topographer data, to increase the accuracy of the biomechanical and optical estimate of the changes in refractive power and stress caused by photorefractive keratectomy (PRK). METHOD: Corneal elevation maps of five human eyes were taken with a rotating Scheimpflug camera combined with a Placido disk before and after refractive surgery. Patient-specific solid models were created and discretized in finite elements to estimate the corneal strain and stress fields in preoperative and postoperative configurations and derive the refractive parameters of the cornea. RESULTS: Patient-specific geometrical models of the cornea allow for the creation of personalized refractive maps at different levels of IOP. Thinned postoperative corneas show a higher stress gradient across the thickness and higher sensitivity of all geometrical and refractive parameters to the fluctuation of the IOP. CONCLUSION: Patient-specific numerical models of the cornea can provide accurate quantitative information on the refractive properties of the cornea under different levels of IOP and describe the change of the stress state of the cornea due to refractive surgery (PRK). Patient-specific models can be used as indicators of feasibility before performing the surgery.

A Newly Developed Tri-Leaflet Polymeric Heart Valve Prosthesis.

The potential of polymeric heart valves (PHV) prostheses is to combine the hemodynamic performances of biological valves with the durability of mechanical valves. The aim of this work is to design and develop a new tri-leaflet prosthetic heart valve (HV) made from styrenic block copolymers. A computational finite element model was implemented to optimize the thickness of the leaflets, to improve PHV mechanical and hydrodynamic performances. Based on the model outcomes, 8 prototypes of the designed valve were produced and tested in vitro under continuous and pulsatile flow conditions, as prescribed by ISO 5840 Standard. A specially designed pulse duplicator allowed testing the PHVs at different flow rates and frequency conditions. All the PHVs met the requirements specified in ISO 5840 Standard in terms of both regurgitation and effective orifice area (EOA), demonstrating their potential as HV prostheses.

The influence of the geometry of the porcine cornea on the biomechanical response of inflation tests.

To withstand the high probability of success, the growing diffusion of laser surgery for the correction of visual defects, corneal surgeons are regarding with interest numerical tools able to provide reliable predictions of the intervention outcomes. The main obstacle to the definition of a predictive numerical instrument is the objective difficulty in evaluating the in vivo mechanical properties of the human cornea. In this study, we assess the ability of a parametrised numerical model of the cornea (Pandolfi and Manganiello 2006) to describe individual pressurisation tests on whole porcine corneas once the mechanical parameters of the model have been calibrated over average data. We also aim at estimating the sensitivity of the mechanical response with the variation of basic geometrical parameters, such as the central corneal thickness, the curvature and the in-plane diameter. We conclude that the actual geometry of a cornea has a minor role in the overall mechanical response, and therefore the material properties must be considered carefully and individually in any numerical application. This study makes use of the data obtained from a wide experimental program, where a set of 21 porcine corneas has been fully characterised in terms of mechanical and geometrical properties (Boschetti et al. 2012).

Biomechanical and optical behavior of human corneas before and after photorefractive keratectomy.

PURPOSE: To evaluate numerically the biomechanical and optical behavior of human corneas and quantitatively estimate the changes in refractive power and stress caused by photorefractive keratectomy (PRK). SETTING: Athineum Refractive Center, Athens, Greece, and Politecnico di Milano, Milan, Italy. DESIGN: Retrospective comparative interventional cohort study. METHODS: Corneal topographies of 10 human eyes were taken with a scanning-slit corneal topographer (Orbscan II) before and after PRK. Ten patient-specific finite element models were created to estimate the strain and stress fields in the cornea in preoperative and postoperative configurations. The biomechanical response in postoperative eyes was computed by directly modeling the postoperative geometry from the topographer and by reproducing the corneal ablation planned for the PRK with a numerical reprofiling procedure. RESULTS: Postoperative corneas were more compliant than preoperative corneas. In the optical zone, corneal thinning decreased the mechanical stiffness, causing local resteepening and making the central refractive power more sensitive to variations in intraocular pressure (IOP). At physiologic IOP, the postoperative corneas had a mean 7% forward increase in apical displacement and a mean 20% increase in the stress components at the center of the anterior surface over the preoperative condition. CONCLUSION: Patient-specific numerical models of the cornea can provide quantitative information on the changes in refractive power and in the stress field caused by refractive surgery. FINANCIAL DISCLOSURES: No author has a financial or proprietary interest in any material or method mentioned.

Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations.

Experimental tests on human corneas reveal distinguished reinforcing collagen lamellar structures that may be well described by a structural constitutive model considering distributed collagen fibril orientations along the superior-inferior and the nasal-temporal meridians. A proper interplay between the material structure and the geometry guarantees the refractive function and defines the refractive properties of the cornea. We propose a three-dimensional computational model for the human cornea that is able to provide the refractive power by analyzing the structural mechanical response with the nonlinear regime and the effect the intraocular pressure has. For an assigned unloaded geometry we show how the distribution of the von Mises stress at the top surface of the cornea and through the corneal thickness and the refractive power depend on the material properties and the fibril dispersion. We conclude that a model for the human cornea must not disregard the peculiar collagen fibrillar structure, which equips the cornea with the unique biophysical, mechanical, and optical properties.