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Experimental evaluation of corneal stress-optic coefficients using a pair of force test
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Purpose:
To identify the characteristic corneal biomechanical properties of osteogenesis imperfecta (OI), and to compare the corneal biomechanical properties between OI and keratoconus.
Methods:
We included 46 eyes of 23 patients with OI, 188 eyes of 99 keratoconus patients, and 174 eyes of 92 normal controls to compare corneal biomechanical parameters between OI corneas, keratoconus, and normal controls by using Corneal Visualization Scheimpflug Technology (Corvis ST).
Results:
Patients with OI had significantly higher Corvis biomechanical index (CBI) (P < 0.001), higher tomographic and biomechanical index (TBI) (P = 0.040), lower Corvis Biomechanical Factor (CBiF) (P = 0.034), and lower stiffness parameter at first applanation (SP-A1) (P < 0.001) compared with normal controls. In contrast, OI group showed lower CBI (P < 0.001), lower TBI (P < 0.001), higher CBiF (P < 0.001), and higher SP-A1 (P = 0.020) than keratoconus group. Notably, the stress-strain index (SSI) was not significantly different between the OI and normal controls (P = 1.000), whereas keratoconus showed the lowest SSI compared with OI group (P = 0.025) and normal controls (P < 0.001).
Conclusions:
Although the corneal structures of OI patients are less stable and easier to deform as compared to those of the control group, there is no significant difference in material stiffness observed between the OI and normal controls. In contrast, the corneas of keratoconus showed not only lower structural stability and higher deformability but also lower material stiffness compared with those of OI cornea and normal controls.
Translational relevance:
The biomechanical alterations are different between OI corneas and keratoconus.
Purpose
Discover the associations of force of applanation on the eye with the plunging depth of the cornea and quantify them. The results will be utilized as the feedback parameter in the new prototype development of eye care instruments as additional force may damage the internal structure of the eye or may result in erroneous output.
Method
A finite element-based eye model is designed utilizing the actual dimensions of the human eye. A standardized tonometer is designed and the simulation is carried out at predetermined deformation of the cornea to find the force of applanation on the cornea during tonometry. Adding on, the influence of IOP during tonometry is analyzed for a range of plunging depths of the cornea.
Results
The graphical results inferred the linear relation between the force of applanation with the deformation of the cornea and the results are quantified. The resulting deformation and stress plot of FEM based simulation approach is analyzed and observations regarding deformations and stress are made.
Conclusion
The human eye is successfully developed and also computed force on the cornea during tonometry is validated. The inference drawn from the deformation plot and stress plot is that the junction of cornea–sclera along with cornea-tonometer periphery undergo maximum deformation and experiences the highest stress compared to other areas of the eye while during tonometry.
Load-bearing tissues are typically fortified by networks of protein fibers, often with preferential orientations. This fiber structure imparts the tissues with direction-dependent mechanical properties optimized to support specific external loads. To accurately model and predict tissues’ mechanical response, it is essential to characterize the anisotropy on a microstructural scale. Previously, it has been difficult to measure the mechanical properties of intact tissues noninvasively. Here, we use Brillouin optical microscopy to visualize and quantify the anisotropic mechanical properties of corneal tissues at different length scales. We derive the stiffness tensor for a lamellar network of collagen fibrils and use angle-resolved Brillouin measurements to determine the longitudinal stiffness coefficients (longitudinal moduli) describing the ex vivo porcine cornea as a transverse isotropic material. Lastly, we observe significant mechanical anisotropy of the human cornea in vivo, highlighting the potential for clinical applications of off-axis Brillouin microscopy. Here, Brillouin optical microscopy noninvasively visualizes microscale anisotropy of the porcine cornea owing to its lamellar fiber structure and quantifies the longitudinal moduli of the bulk tissue. Anisotropy is also detected in angle-resolved measurement of the human cornea in vivo.
This study aimed to compare the values of new corneal visualization Scheimpflug technology (Corvis ST) parameters in normal, subclinical keratoconus (SKC) and keratoconus (KC) eyes, and evaluate the diagnostic ability to distinguish SKC and KC eyes from normal eyes. One-hundred normal, 100 SKC and 100 KC eyes were included in the study. Corvis ST parameters containing dynamic corneal response parameters were measured by one ophthalmologist. The receiver operating characteristic curve was used to evaluate the diagnostic ability of new Corvis ST parameters. The new Corvis ST parameters in KC eyes were different from those in the control and SKC eyes after adjusting for IOP and CCT, and stiffness parameter at the first applanation (SP-A1) and Corvis biomechanical index (CBI) were significantly different between the control and SKC eyes (all P < 0.05). The parameter with the highest diagnostic efficiency was SP-A1 (Youden index = 0.40, AUC = 0.753), followed by CBI (Youden index = 0.38, AUC = 0.703), and Integrated Radius (Youden index = 0.33, AUC = 0.668) in diagnosing SKC from control eyes. New Corvis ST parameters in SKC eyes were significantly different from normal control and KC eyes, and could be considered to distinguish SKC and KC eyes from normal eyes.
Corneal biomechanics play a fundamental role in the genesis and progression of corneal pathologies, such as keratoconus; in corneal remodeling after corneal surgery; and in affecting the measurement accuracy of glaucoma biomarkers, such as the intraocular pressure (IOP). Air-puff induced corneal deformation imaging reveals information highlighting normal and pathological corneal response to a non-contact mechanical excitation. However, current commercial systems are limited to monitoring corneal deformation only on one corneal meridian. Here, we present a novel custom-developed swept-source optical coherence tomography (SSOCT) system, coupled with a collinear air-puff excitation, capable of acquiring dynamic corneal deformation on multiple meridians. Backed by numerical simulations of corneal deformations, we propose two different scan patterns, aided by low coil impedance galvanometric scan mirrors that permit an appropriate compromise between temporal and spatial sampling of the corneal deformation profiles. We customized the air-puff module to provide an unobstructed SSOCT field of view and different peak pressures, air-puff durations, and distances to the eye. We acquired multi-meridian corneal deformation profiles (a) in healthy human eyes in vivo, (b) in porcine eyes ex vivo under varying controlled IOP, and (c) in a keratoconus-mimicking porcine eye ex vivo. We detected deformation asymmetries, as predicted by numerical simulations, otherwise missed on a single meridian that will substantially aid in corneal biomechanics diagnostics and pathology screening.
Purpose:
To assess corneal stiffening of standard (S-CXL) and accelerated (A-CXL) cross-linking
protocols by dynamic corneal response parameters and corneal bending stiffness
(Kc[mean/linear]) derived from Corvis (CVS) Scheimpflug-based tonometry. These
investigations were validated by corneal tensile stiffness (K[ts]), derived from stress-strain extensiometry in ex-vivo porcine eyes.
Methods:
Seventy-two fresh-enucleated and de-epithelized porcine eyes were soaked in 0.1%-riboflavin-solution including 10% dextran for 10 min. Eyes were separated into four groups: controls (n=18), S-CXL(intensity in mW/cm² * time in min; 3*30) (n=18), A-CXL(9*10) (n=18) and A-CXL(18*5) (n=18), respectively. CXL was performed using CCL Vario. CVS measurements were performed on all eyes. Subsequently, corneal strips were extracted by a double-bladed scalpel and used for stress-strain measurements. K[ts] was calculated from a force-displacement curve. Mean corneal stiffness (Kc[mean]) and constant corneal stiffness (Kc[linear]) were calculated from raw CVS data.
Results:
In CVS, biomechanical effects of cross-linking were shown to have a significantly decreased deflection amplitude as well as integrated radius, an increased IOP, and SP A1 (P < 0.05). Kc[mean]/Kc[linear] were significantly increased after CXL (P < 0.05). In the range from 2% to 6% strain, K[ts] was significantly higher in S-CXL(3*30) compared to A-CXL(9*10), A-CXL(18*5) and controls (P < 0.05). At 8% to 10% strain, all protocols induced a higher stiffness than controls (P < 0.05).
Conclusion:
Several CVS parameters and Kc[mean] as well as Kc[linear] verify corneal stiffening effect
after CXL on porcine eyes. S-CXL seems to have a higher tendency of stiffening than A-CXL protocols have, which was demonstrated by Scheimpflug-based tonometry and stress-strain extensiometry
Optical coherence tomography (OCT) is a non-invasive depth resolved optical imaging modality, that enables high resolution, cross-sectional imaging in biological tissues and materials at clinically relevant depths. Though OCT offers high resolution imaging, the best ultra-high-resolution OCT systems are limited to imaging structural changes with a resolution of one micron on a single B-scan within very limited depth. Nanosensitive OCT (nsOCT) is a recently developed technique that is capable of providing enhanced sensitivity of OCT to structural changes. Improving the sensitivity of OCT to detect structural changes at the nanoscale level, to a depth typical for conventional OCT, could potentially improve the diagnostic capability of OCT in medical applications. In this paper, we demonstrate the capability of nsOCT to detect structural changes deep in the rat cornea following superficial corneal injury.
Background
To develop a method, using current clinical instrumentation, to estimate the Young’s modulus of the human cornea in vivo.
Methods
Central corneal curvature (CCC), central corneal thickness(CCT), intraocular pressure (IOP) was measured with the Goldmann tonometer (IOPG) and the Pascal Dynamic Corneal Tonometer(PDCT) in one eye of 100 normal young human subjects (21.07 ± 2.94 years) in vivo. The Orssengo and Pye algorithm was used to calculate the Young’s modulus of the corneas of these subjects.
Results
The Young’s modulus(E) of the corneas of the subjects using the PDCT and IOPG results (Ecalc) was 0.25 ± 0.10MPa, and without the PDCT results (Eiopg) was 0.29 ± 0.06MPa. The difference in these results is due to the difference in tonometry results between the two instruments, as the mean PDCT result for the subjects was 16.89 ± 2.49mmHg and the IOPG result 15.06 ± 2.71mmHg. E was affected by the CCC of the subjects but more particularly by the CCT and IOP measurements. Corneal stiffness results are also presented.
Conclusion
Two methods have been developed to estimate the Young’s modulus of the human cornea in vivo using current clinical instrumentation. One method (Ecalc) is applicable to the general corneal condition, and Eiopg to the normal cornea, and these results can be used to calculate corneal stiffness.
Current intraocular pressure (IOP) measurement using air puff could be erroneous without applying proper corrections. Although noncontact tonometry is not considered to be accurate, it is still popularly used by eye clinics. It is thus necessary to extract the correct information from their results. This study proposes a practical approach to correctly measure IOP in vivo . By embedding a new model-based correction to the Corvis® ST, we can extract the corneal Young’s modulus from the patient data. This Young’s modulus can be used to correct the IOP readings. The tests were applied to 536 right eyes of 536 healthy subjects (228 male and 308 female) between March of 2012 and April of 2016. The tests were applied to patients at the Department of Ophthalmology, National Taiwan University Hospital and the Hung-Chuo Eye Clinics. The statistical analysis showed that the value for the Young’s modulus was independent of all the other parameters collected from the Corvis ST, including the corneal thickness and the intraocular pressure. Therefore, it is important to independently measure the Young’s modulus instead of depending on the correlation with the other parameters. This study adds the methodology of measuring corneal stiffness in vivo for ophthalmologists’ reference in diagnosis.
Recent advances in the analysis of corneal biomechanical properties remain difficult to predict the structural stability before and after refractive surgery. In this regard, we applied the finite element method (FEM) to determine the roles of the Bowman’s membrane, stroma, and Descemet’s membrane in the hoop stresses of cornea, under tension (physiological) and bending (nonphysiological), for patients who undergo radial keratotomy (RK), photorefractive keratectomy (PRK), laser-assisted in situ keratomileusis (LASIK), or small incision lenticule extraction (SMILE). The stress concentration maps, potential creak zones, and potential errors in intraocular pressure (IOP) measurements were further determined. Our results confirmed that the Bowman’s membrane and Descemet’s membrane accounted for 20% of the bending rigidity of the cornea, and became the force pair dominating the bending behaviour of the cornea, the high stress in the distribution map, and a stretch to avoid structural failure. In addition, PRK broke the central linking of hoop stresses and concentrated stress on the edge of the Bowman’s membrane around ablation, which posed considerable risk of potential creaks. Compared with SMILE, LASIK had a higher risk of developing creaks around the ablation in the stroma layer. Our FEM models also predicted the postoperative IOPs precisely in a conditional manner.
Purpose: To evaluate performance of waveform derived variables in distinguishing normal, suspect and keratoconus eyes
Setting: Narayana Nethralaya Eye Hospital, Bangalore, India
Design: Retrospective, observational, cross-sectional study
Methods: Pentacam and Corvis-ST (OCULUS Optikgerate Gmbh, Germany) of 253 normal (253 patients) eyes and 205 keratoconus (205 patients) were evaluated. Among the 205 patients, 62 patients had keratoconus in one eye, while the unaffected eye was "suspect". From deformation amplitude (DA), deflection amplitude and whole eye movement were extracted. A biomechanical model was used to derive a linear [kc (constant)] and non-linear measure [kc (mean)] of corneal stiffness. Multivariate logistic regression was performed to determine sensitivity and specificity. The analysis was validated in another data set of 59 normal, 45 suspect and 160 keratoconus eyes.
Results: DA maximum, applanation 1 time and deformation amplitude, applanation 2 time, kc (constant), kc (mean) and deflection amplitude maximum were significantly different between normal and keratoconus eyes (p<0.001). The deformation characteristics of the suspect eyes were similar to the keratoconus group, particularly grade 1 (p>0.05). kc (constant) and kc (mean) had the highest area under curve (>0.98), sensitivity and specificity greater than 90% and 91%, respectively. Logistic regression using kc (constant) and kc (mean) improved the area to 1.0 with a sensitivity and specificity equal to 99.6 % and 100.0%, respectively. In the validation data set, the same cut-off yielded a sensitivity, specificity and accuracy of 99.5%, 100% and 99.6%, respectively.
Conclusions: Corneal stiffness and waveform analyses could be a reliable differentiator of suspect and keratoconus eyes from normal eyes.
Background
The eye globe exhibits significant regional variation of mechanical behaviour. The aim of this present study is to develop a new experimental technique for testing intact eye globes in a form that is representative of in vivo conditions, and therefore suitable for determining the material properties of the complete outer ocular tunic. MethodsA test rig has been developed to provide closed-loop control of either applied intra-ocular pressure or resulting apical displacement; measurement of displacements across the external surface of the eye globe using high-resolution digital cameras and digital image correlation software; prevention of rigid-body motion and protection of the ocular surface from environmental drying. The method has been demonstrated on one human and one porcine eye globe, which were cyclically loaded. Finite element models based on specimen specific tomography, free from rotational symmetry, were used along with experimental pressure-displacement data in an inverse analysis process to derive the mechanical properties of tissue in different regions of the eye’s outer tunic. ResultsThe test method enabled monitoring of mechanical response to intraocular pressure variation across the surface of the eye globe. For the two eyes tested, the method showed a gradual change in the sclera’s stiffness from a maximum at the limbus to a minimum at the posterior pole, while in the cornea the stiffness was highest at the centre and lowest in the peripheral zone. Further, for both the sclera and cornea, the load–displacement behaviour did not vary significantly between loading cycles. Conclusions
The first methodology capable of mechanically testing intact eye globes, with applied loads and boundary conditions that closely represent in vivo conditions is introduced. The method enables determination of the regional variation in mechanical behaviour across the ocular surface.
This work presents a novel methodology for building a three-dimensional patient-specific eyeball model suitable for performing a fully automatic finite element (FE) analysis of the corneal biomechanics. The reconstruction algorithm fits and smooths the patient's corneal surfaces obtained in clinic with corneal topographers and creates an FE mesh for the simulation. The patient's corneal elevation and pachymetry data is kept where available, to account for all corneal geometric features (central corneal thickness-CCT and curvature). Subsequently, an iterative free-stress algorithm including a fiber's pull-back is applied to incorporate the pre-stress field to the model. A convergence analysis of the mesh and a sensitivity analysis of the parameters involved in the numerical response is also addressed to determine the most influential features of the FE model. As a final step, the methodology is applied on the simulation of a general non-commercial non-contact tonometry diagnostic test over a large set of 130 patients-53 healthy, 63 keratoconic (KTC) and 14 post-LASIK surgery eyes. Results show the influence of the CCT, intraocular pressure (IOP) and fibers (87%) on the numerical corneal displacement [Formula: see text] the good agreement of the [Formula: see text] with clinical results, and the importance of considering the corneal pre-stress in the FE analysis. The potential and flexibility of the methodology can help improve understanding of the eye biomechanics, to help to plan surgeries, or to interpret the results of new diagnosis tools (i.e., non-contact tonometers).
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).
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.
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.
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.
The mechanical response of the cornea subjected to a non-contact air-jet tonometry diagnostic test represents an interplay between its geometry, the corneal material behavior and the loading. The objective is to study this interplay to better understand and interpret the results obtained with a non-contact tonometry test. A patient-specific finite element model of a healthy eye, accounting for the load free configuration, was used. The corneal tissue was modeled as an anisotropic hyperelastic material with two preferential directions. Three different sets of parameters within the human experimental range obtained from inflation tests were considered. The influence of the IOP was studied by considering four pressure levels (10–28 mmHg) whereas the influence of corneal thickness was studied by inducing a uniform variation (300–600 microns). A Computer Fluid Dynamics (CFD) air-jet simulation determined pressure loading exerted on the anterior corneal surface. The maximum apex displacement showed a
Healthy eyes are vital for a better quality of human life. Historically, for man-made materials, scientists and engineers use stress concentration factors to characterise the effects of structural non-homogeneities on their mechanical strength. However, such information is scarce for the human eye. Here we present the shear stress distribution profiles of a healthy human cornea surface in vivo using photo-stress analysis tomography, which is a non-intrusive and non-X-ray based method. The corneal birefringent retardation measured here is comparable to that of previous studies. Using this, we derive eye stress concentration factors and the directional alignment of major principal stress on the surface of the cornea. Similar to thermometers being used for monitoring the general health in humans, this report provides a foundation to characterise the shear stress carrying capacity of the cornea, and a potential bench mark for validating theoretical modelling of stresses in the human eye in future.
Corneal biomechanical properties are usually measured by strip extensiometry or inflation methods. We developed a two-dimensional (2D) flap extensiometry technique, combining the advantages of both methods, and applied it to measure the effect of UV-Riboflavin cross-linking (CXL).
Corneal flaps (13 pig/8 rabbit) from the de-epithelialized anterior stroma (96 μm) were mounted on a custom chamber, consisting of a BK7 lens, a reflective retina, and two reservoirs (filled with Riboflavin and silicone oil). Stretching the corneal flap during five pressure increase/decrease cycles (0-30 mm Hg) changed the refractive power of the system, whose Zernike aberrations were monitored with a ray-tracing aberrometer. Porcine flaps were used to test the system. Rabbits were treated with CXL unilaterally in vivo following standard clinical procedures. Flaps were measured 1 month postoperatively. An analytical model allowed estimating Young's modulus from the change in surface (strain) and pressure (stress). Confocal microscopy examination was performed before, and at different times after CXL.
Flap curvature changed with increased function of IOP in pig flaps (23.4 × 10⁻³ D/mm Hg). In rabbit flaps curvature changed significantly less in 1 month post CXL (P = 0.026) than in untreated corneas [17.0 vs. 6.36 millidiopter (mD)/mm Hg]. Young's modulus was 2.29 megapascals (MPa) in porcine corneas, 1.98 MPa in untreated rabbit corneas, and 4.83 MPa in 1 month post CXL rabbit corneas. At the same time, highly reflective structures were observed in the rabbit midstroma after treatment.
2D flap extensiometry allows estimating corneal elasticity in vitro. The measurements are spatially resolved in depth, minimize the effects of corneal hydration, and preserve the integrity of the cornea. The method proved the efficacy of CXL in increasing corneal rigidity after 1 month in rabbits.
We present a case series of cornea and anterior segment disorders investigated by an office-based polarization-sensitive optical coherence tomography (PS-OCT). Blebs of glaucoma patients treated by trabeculectomy, and corneas of keratoconus and keratoplasty patients were measured by PS-OCT. Birefringence formations in trabeculectomy bleb were measured in 1 control eye and 3 eyes of trabeculectomy model rabbits. Polarization insensitive scattering OCT and the depth-resolved birefringence were measured simultaneously by PS-OCT. Abnormal birefringence was observed in keratoconus cases with advanced thinning and with a rupture of Descemet's membrane. The graft-host interface of the keratoplasty case showed abnormal birefringence. The appearance of abnormal birefringence in the cornea was likely to be an indication of cross-linking of collagen fibrils. The measurement of rabbit showed abnormal birefringence in the scarring eyes. Wide regions of strong birefringence were observed in the eyes of trabeculectomy patients who had high intraocular pressure. Visualization of scarring in bleb by PS-OCT may be useful for the planning of secondary surgery. PS-OCT showed promising for the study and diagnosis diseases related to abnormal fibrous tissues of the cornea and anterior eye segment.
An experimental study has been conducted to determine the stress-strain behaviour of human corneal tissue and how the behaviour varies with age. Fifty-seven well-preserved ex vivo donor corneas aged between 30 and 99 years were subjected to cycles of posterior pressure up to 60 mm Hg while monitoring their behaviour. The corneas were mechanically clamped along their ring of scleral tissue and kept in physiological conditions of temperature and hydration. The tissue demonstrated hyper-elastic pressure-deformation and stress-strain behaviour that closely matched an exponential trend. Clear stiffening (increased resistance to deformation) with age was observed in all loading cycles, and the rate of stiffness growth was nonlinear with bias towards older specimens. With a strong statistical association between stiffness and age (p < 0.05), it was possible to develop generic stress-strain equations that were suitable for all ages between 30 and 99 years. These equations, which closely matched the experimental results, depicted corneal stiffening with age in a form suitable for implementation in numerical simulations of ocular biomechanical behaviour.
The bulk of the corneal stroma is comprised of a layered network of fibrillar collagen. Determining the architecture of this unique structure may help us to better understand the cornea's biomechanical and optical function. The analysis of diffraction patterns obtained when X-rays are passed through the regularly arranged collagen molecules and fibrils of the stromal matrix yields quantitative data on fibrillar organisation, including the orientation and distribution of collagen lamellae within the corneal plane. In recent years, by exploiting the radiation from powerful synchrotron sources, techniques have been developed to enable the mapping of collagen fibril, and therefore lamellar, directions across whole corneas. This article aims to summarise the use of X-ray diffraction to map the orientation and distribution of collagen in the corneal stroma. The implications of the knowledge gained so far are discussed in relation to the optical and biomechanical properties of the cornea, and their alteration due to disease and surgical intervention.
Stress-induced birefringence is used in engineering to determine the distribution of mechanical stress in experimental models. The phenomenon has previously been reported in the cat cornea but no data for the human exists. A qualitative description of stress-induced birefringence in the human cornea in vitro is presented. Circularly polarised light is then used to detect the phenomenon in the post-operative human cornea in vivo.
To determine the biomechanical deformation of the cornea resulting from tissue cutting and removal by use of a new computational model and to investigate the effect of mechanical anisotrophy resulting from the fibrillar architecture.
Department of Mechanical Engineering, Stanford University, Stanford, California, USA.
A mathematical model for a typical lamella that explicitly accounts for the strain energy of the collagen fibrils, extrafibrillar matrix, and proteoglycan cross-linking was developed. A stromal model was then obtained by generalized averaging of the lamella properties through the stromal thickness, taking into account the preferred orientations of the collagen fibrils, which were obtained from x-ray scattering data.
The model was used to predict astigmatism induced by a tunnel incision in the sclera, such as is used for cataract extraction and intraocular lens implantation. The amount of induced cylinder was in good agreement with published clinical data. Results show it is important for the model to incorporate preexisting corneal physiological stress caused by intraocular pressure.
The mathematical model described appears to provide a framework for further development, capturing the essential features of mechanical anisotropy of the cornea. The tunnel incision simulation indicated the importance of the anisotropy in this case.
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.
The elastic moduli of the cornea, sclera, and limbus for different corneal eccentricities (e) and varying levels of intraocular pressure (IOP) were modelled in order to determine how the rheological properties, especially those of the limbus, need to alter to maintain optical image quality when the eye is subjected to small variations in IOP. Methods: Finite element analysis (FEA) was used to construct eyeball models with four different corneal eccentricities (e=0, 0.33, 0.5, 0.65). Three values for Young's modulus of the cornea were tested in all models (0.2 megapascal (MPa), 1.2 and 10 MPa). For each corneal modulus, scleral moduli of 3, 4, 5, 7, and 10 times that of the corneal modulus were selected. The limbal modulus was varied to optimise image quality of the eye model subjected to IOP variations of +/-0.8 mmHg for three different levels of IOP (8, 16, and 32 mmHg).
The elastic modulus of the limbal ring increases with an increase in corneal modulus and rises to a peak when the ratio of scleral to corneal moduli is between 5 and 7 depending on corneal eccentricity. Different levels of IOP produce only slight differences in the relative moduli required to maintain optical image quality.
The significance of a peak in the value of Young's modulus of the limbus is not clear but suggests that there may be an optimal limbal modulus that must be balanced with the moduli of cornea and sclera for preservation of image quality.
To determine the variation of corneal biomechanical properties with anatomical orientation.
Strip specimens extracted from fresh porcine corneas were tested under uniaxial tension with strain rates representing static and dynamic loading conditions. The specimens were extracted from the vertical, horizontal, and 45 degrees diagonal directions. The load elongation results were used to derive the stress-strain behavior of each specimen. The average behavior for specimens taken in each anatomical direction was determined along with the effect of strain rate. Specimens from a small number of human corneas were included in the study to verify the findings.
Specimens extracted from the vertical direction of porcine and human corneas demonstrated the highest strength (fracture stress) followed by horizontal then diagonal specimens. Vertical specimens were 10% to 20% stronger than horizontal specimens in porcine and human corneas. At low strain rates (1%/min), vertical specimens displayed similar stiffness (resistance to deformation) to horizontal specimens but greater stiffness than diagonal specimens. On increasing the strain rate to 500%/min, the stiffness behavior matched that of strength with vertical specimens being 10% to 20% stiffer than horizontal specimens in porcine and human corneas.
The corneal anisotropic behavior is compatible with the preferential orientation of stromal fibrils in the vertical and horizontal directions. Quantifying the effect of this nonuniform fibril organization on corneal anisotropic behavior will be useful in developing numerical models of the cornea for applications where its integrity is compromised such as in simulating refractive surgery procedures.
Orthokeratology (OK) is becoming a mainstream modality for myopia correction and control, but its underlying mechanism is not yet fully understood. In this study, the biomechanical response of cornea under the OK lens was investigated to further understand the mechanism of OK therapy. Numerical models of the cornea and OK lens with different corneal refractive powers and myopia degrees were established to analyze features and differences of the spatial displacement and stress distribution in different areas of the anterior corneal surface by finite element method. Displacement distributions on the anterior cornea surface with refractive powers of 39.5, 43, 46 D, and myopia degrees of -1.0, -3.0, -6.0 D demonstrate similar deformation trends and nearly rotationally symmetrical attributes of different corneal parameters. Displacement of mid-peripheral cornea was significantly high compared with that of the central and peripheral cornea, peaking at ~2.4 mm off the corneal apex. The stress increased with the increase in myopia degrees and was significantly large for the myopia degrees of -6.0 D at S1; the stress at S2 and S6 was low and stable and did not differ much at S3; the stress at S4 and S5, however, was extremely high. In summary, simulation result of orthokeratology can effectively evaluate the performance of OK lens and it properly associates with the differential map of the corneal topography. The base curve of the OK lens may also play a role in mid-peripheral corneal steepening. The design around the OK lens' alignment curve needs to be optimized.
Background
Pre and post-operative clinical assessment of the patients is generally based on the corneal tomographic data. However, techniques are required to assess the patient-specific structural and pathological changes for better therapeutic and surgical interventions. The birefringence of the human cornea is the manifestation of mechanics-structure interrelationship and is an important property to quantify corneal abnormalities.Objective
The present paper aims to understand the mechanics-structure interrelationship of the human cornea.Methods
For the first time, the birefringence behavior of the human cornea is explored using the digital photoelasticity technique and finite element method. The experimentally obtained phase maps of twenty corneas were analyzed at 0 and 20 mm Hg pressure. Finally, a qualitative comparison of the results from experiments and simulations was carried out.ResultsFeatures like isotropic points, retardation maps, etc., were extracted from the photoelastic phase maps. The pressure loading did not create a statistically significant change in the average retardation of the central 4 mm cornea. However, the isotropic points were distributed differently in the tested corneas, depicting inter-individual variability in corneal birefringence. The authors found that the steepness or flatness of the corneal curvature decides the location of the isotropic points.Conclusions
The inter-individual variability in corneal birefringence arises from the complex interplay of the cornea's microstructure, curvature, and stress distribution. The authors foresee the applicability of digital photoelasticity in clinics for diagnostic and monitoring purposes due to its operational simplicity and data accuracy.
An acoustic tonometer that measures shifts in resonance frequencies associated with intraocular pressure (IOP) could provide an opportunity for a type of tonometer that can be operated at home or worn by patients. However, there is insufficient theoretical background, especially with respect to the uncertainty in operating frequency ranges and the unknown relationships between IOPs and resonance frequencies. The purpose of this paper is to develop a frequency function for application in an acoustic tonometer. A linear wave theory is used to derive an explicit frequency function, consisting of an IOP and seven other physiological parameters. In addition, impulse response experiments are performed to measure the natural frequencies of porcine eyes to validate the provided function. From a real-time detection perspective, explicitly providing a frequency function can be the best way to set up an acoustic tonometer. The theory shows that the resonance oscillation of the eyeball is mainly dominated by liquid inside the eyeball. The experimental validation demonstrates the good prediction of IOPs and resonance frequencies. The proposed explicit frequency function supports further modal analysis not only of the dynamics of eyeballs, but also of the natural frequencies, for further development of the acoustic tonometer.
Purpose:
To simultaneously extract the corneal Young's modulus and the damping ratio from Scheimpflug imaging data.
Methods:
A spherical diaphragm model can better represent the geometry and physics of an eyeball than the popular mass-spring-damper model. This research derived the dynamic model of a water-filled spherical diaphragm based on the hydrodynamics and wave propagation theories. By applying modal analysis on the model, one can decouple the cornea vibration into individual modes and reconstruct the air puff vibration from the decoupled responses. By matching this response with the Scheimpflug imaging data from the Corvis(®) ST, it was then possible to extract multiple physiological properties as desired.
Results:
The dynamic modal analysis was employed to extract the corneal physiological properties of 25 Taiwanese normal subjects. Specifically, the corneal Young's moduli and damping ratios were estimated. In fact the model is dependent on the physiological parameters such as cornea thickness, densities, and intraocular pressure. It is thus also possible to extract these parameters through multi-goal minimisation processes.
Conclusions:
The spherical diaphragm model was able to better describe the dynamic response of the eyeball. The model analysis also provides additional corneal physiological properties that were not available through other means.
The determination of isoclinic parameter from photoelastic fringe patterns is a key problem in photoelasticity. However, it is not a simple task due to the influence of the isochromatic parameter. The purpose of this paper is to achieve the full-field isoclinic parameter measurement automatically by six-step digital phase shifting photoelasticity. However, there are several key problems, such as the range of the isoclinic parameter, the isoclinic-isochromatic interaction, and the influence of special points such as free corner point, singular point and isotropic point. Through analyzing these problems, we present an appropriate algorithm to get the correct full-field isoclinic parameter automatically which is validated by simulation and experiment. This method is simple and effective to solve the problems of the isoclinic-isochromatic interaction and the isoclinic parameter error around the special points.
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.
The mechanical response of the cornea subjected to a non-contact air-jet tonometry diagnostic test represents an interplay between its geometry, the corneal material behavior and the loading. The objective is to study this interplay to better understand and interpret the results obtained with a non-contact tonometry test. A patient-specific finite element model of a healthy eye, accounting for the load free configuration, was used. The corneal tissue was modeled as an anisotropic hyperelastic material with two preferential directions. Three different sets of parameters within the human experimental range obtained from inflation tests were considered. The influence of the IOP was studied by considering four pressure levels (10–28 mmHg) whereas the influence of corneal thickness was studied by inducing a uniform variation (300–600 microns). A Computer Fluid Dynamics (CFD) air-jet simulation determined pressure loading exerted on the anterior corneal surface. The maximum apex displacement showed a
Automatic methods of photoelasticity have had a significant progress with the development of automatic acquisition and image processing methods. This article concerns RGB photoelasticity, which allows the determination of the photoelastic retardation using, usually, a single acquisition of the isochromatic fringes in white light by a colour camera. In particular, the article presents an overview of the main characteristics of RGB photoelasticity that is influence of the quarter-wave plate error, number of acquisitions, type of light source, determination of low and high fringe orders, methods for searching the retardation, scanning procedures, calibration on a material different from that under test, combined use of the RGB and phase shifting methods. A short section on the applications of RGB photoelasticity completes the article.
Freshly enucleated andin vivo eyes of cats were analyzed to determine the detailed distribution of birefringence across the cornea and through its thickness, and to determine the change of birefringence with intraocular pressure. Scattered light and oblique-incidence photoelasticity were used. The experiments are summarized and special considerations are discussed. These include the necessity for a laser-light source; diffraction limitation in producing a narrow ribbon of light; rotation of the plane of polarization; inequalities in reflected components of polarized light.
The feasibility for utilizing transparent filament-resin composites for photoelastic stress analysis was investigated. Satisfactory photoelastic stress patterns were demonstrated in simple models with undirectional and bidirectional fiber orientations. A stress-optic law was formulated, based on the concept that the birefringence components contributed by each component of plane stress are combined according to a Mohr circle of birefringence. Applying this concept, the difference of the physical and optical principal directions was accounted for, and a general method of photoelastic solution for the plane-stress problem in orthotropic sheets was developed. The method of analysis is little more complex than the well-known procedures for isotropic materials, but at least three experimental measurements are required to characterize the optical response of the material to plane stress.Partial confirmation of the proposed stress-optic law was obtained by comparison of the theory to limited experimental data obtained in uniaxial-stress samples. It remains to establish a more positive verification by experiments in a variety of biaxial-stress conditions.
TV technology combined with a modern video-frame store is used to store the complete fringe pattern in digitized form in real
time. A minicomputer connected to the store has direct access to any picture point in the store. In this manner, it is possible
to evaluate the photoelastic-fringe pattern in the computer by special developed software.
The cornea is birefringent, and the birefringence can be easily observed in a living eye. For observation, a reflection polariscope is used, the iris serving as a reflector. Some sick people have grossly different and easily identifiable photoelastic patterns from the patterns observed in healthy subjects. The possibilities of a new clinical diagnostic method through the use of photoelasticity is discussed.
The values of the biomechanical human eyeball model parameters reported in the literature are still being disputed. The primary motivation behind this work was to predict the material parameters of the cornea through numerical simulations and to assess the applicability of the ubiquitously accepted law of applanation tonometry - the Imbert-Fick equation.
Numerical simulations of a few states of eyeball loading were run to determine the stroma material parameters. In the computations, the elasticity moduli of the material were related to the stress sign, instead of the orientation in space.
Stroma elasticity secant modulus E was predicted to be close to 0.3 MPa. The numerically simulated applanation tonometer readings for the cornea with the calibration dimensions were found to be lower by 11 mmHg then IOP = 48 mmHg.
This discrepancy is the result of a strictly mechanical phenomenon taking place in the tensioned and simultaneously flattened corneal shell and is not related to the tonometer measuring accuracy. The observed deviation has not been amenable to any GAT corrections, contradicting the Imbert-Fick law. This means a new approach to the calculation of corrections for GAT readings is needed.
To propose a new noncontact tonometer based on corneal photoelasticity.
In this study, we experimented with 18 enucleated porcine eyes. The anterior chamber was infused with a physiological solution. A circular polarizing filter was attached to an ophthalmic surgical microscope. Color fringe changes at the peripheral cornea related to its photoelasticity were recorded using an ophthalmic surgical microscope equipped with a charge-coupled device camera while intraocular pressure (IOP) changes were determined by the height of the physiological solution bottle. A peak intensity of the color fringes was determined by Image J software.
Circular, rainbow-like color fringes, a phenomenon that is the basis of photoelasticity, were detected in the peripheral cornea. When IOP increased from 7 to 29 mm Hg, the color fringes moved more peripherally becoming narrower with their peak intensity increasing. At an IOP of 7, 15, 22 and 29 mm Hg, the mean peak intensity of the color fringes had a gray value of 113.6, 114.2, 114.7 and 115.5, respectively. Correlation analysis between IOP and peak intensity of the color fringes in these porcine eyes showed a significant positive correlation with a Pearson correlation coefficient of 0.993 (p < 0.01).
The proposed noncontact tonometer based on photoelasticity of the cornea could become a true noncontact device that could be used for the screening of glaucoma or as an IOP follow-up for glaucoma patients.
The goal of this study was to determine age-related variation in the elasticity of the human cornea using nondestructive means.
Organ cultured human corneoscleral buttons were studied. Changes in strain were measured with a radial shearing speckle pattern interferometer after an increase in intraocular pressure from 15.0 to 15.5 mm Hg. Changes in central corneal displacement were calculated by integration, and a bulk corneal Young's modulus was derived by mathematical analysis.
Fifty corneas, including 17 pairs, were studied. Donors were aged between 24 and 102 years (mean, 73.1); 29 (58%) specimens were from male donors and 21 from female donors. Young's modulus of the cornea increased with age, with the line of best fit indicating an approximate doubling from 0.27 MPa at age 20 years (95% confidence interval, 0.22-0.31) to 0.52 (0.50-0.54) MPa at age 100 years (R² = 0.70).
The stiffness of the human cornea increases by a factor of approximately two between the ages of 20 and 100 years. This variation is relevant to the algorithms used to predict the response to incisional and ablative refractive surgery and will also affect the formulas used to calculate intraocular pressure by applanation.
To determine in a longitudinal study whether there is correlation between videokeratography and clinical signs of keratoconus that might be useful to practicing clinicians.
Cornea-Genetic Eye Institute, Cedars-Sinai Medical Center, Los Angeles, California, USA.
Eyes grouped as keratoconus, early keratoconus, keratoconus suspect, or normal based on clinical signs and videokeratography were examined at baseline and followed for 1 to 8 years. Differences in quantitative videokeratography indices and the progression rate were evaluated. The quantitative indices were central keratometry (K), the inferior-superior (I-S) value, and the keratoconus percentage index (KISA). Discriminant analysis was used to estimate the classification rate using the indices.
There were significant differences at baseline between the normal, keratoconus-suspect, and early keratoconus groups in all indices; the respective means were central K: 44.17 D, 45.13 D, and 45.97 D; I-S: 0.57, 1.20, and 4.44; log(KISA): 2.49, 2.94, and 5.71 (all P<.001 after adjusting for covariates). Over a median follow-up of 4.1 years, approximately 28% in the keratoconus-suspect group progressed to early keratoconus or keratoconus and 75% in the early keratoconus group progressed to keratoconus. Using all 3 indices and age, 86.9% in the normal group, 75.3% in the early keratoconus group, and 44.6% in the keratoconus-suspect group could be classified, yielding a total classification rate of 68.9%.
Cross-sectional and longitudinal data showed significant differences between groups in the 3 indices. Use of this classification scheme might form a basis for detecting subclinical keratoconus.
We describe a dual, second harmonic generation (SHG) and third harmonic generation (THG) microscope, with the aim to obtain large-scale images of the cornea that can simultaneously resolve the micron-thick thin layers. We use an Ytterbium femtosecond laser as the laser source, the longer wavelength of which reduces scattering and allows simultaneous SHG and THG imaging. We measure one-dimensional SHG and THG profiles across the entire thickness of pig cornea, detected in both the forward and backward directions. These profiles allow us to clearly distinguish all the porcine corneal layers (epithelium, stroma, Descemet's membrane and endothelium). From these profiles, longitudinal cross sectional images of the corneal layers are generated, providing large scale topographic information with high-spatial resolution. The ability to obtain both SHG and THG signals in epi-detection on fresh eyes gives promising hopes for in vivo applications.
To investigate Vogt striae in keratoconus using confocal microscopy.
The central cornea of 51 eyes of 29 subjects with keratoconus was observed using a slit-lamp biomicroscope, slit-scanning confocal microscope (TOMEY Confoscan 1), and corneal topographer (EyeSys 2000).
Alternating dark and light bands were seen in the stromal images of 23 eyes examined. The bands corresponded with the appearance of Vogt striae on slit-lamp biomicroscopy examination. Bands were found most commonly in the posterior stroma. Posterior bands varied in width, ran mainly in a nearly vertical direction, and appeared to run a straight course through individual image frames. Keratocyte nuclei were located in between the bands. Posterior keratocyte density was unaffected by the presence of bands. Nerve fibers appeared to run a straight course through the bands. When present, bands in the anterior stroma showed greater variability in width and direction within a single frame. Bands were only present in the anterior stroma in more severe levels of keratoconus. The difference in banding pattern noted between the anterior and posterior stroma parallels the known collagen fiber arrangement in the anterior and posterior stroma.
The bands apparent on confocal microscopy of the stroma of the keratoconic cornea correspond with Vogt striae on slit-lamp microscopy. It appears that these bands (and hence Vogt striae) represent collagen lamellae under stress. The stress pattern appears to radiate from the center of the cone and is consistent with the direction of striae when viewed with the confocal microscope.
In keratoconus, the cornea becomes progressively ectactic resulting in severe visual impairment. Here, we use a combination of videokeratography and synchrotron X-ray diffraction to investigate the relationship between corneal shape and thickness, and the distribution and predominant orientation of stromal fibrillar collagen in five keratoconus corneas. In all but the least advanced case, the thinning and ectasia measured in vivo using corneal videokeratography was accompanied by corresponding changes in the relative distribution and orientation of stromal collagen in the excised corneal buttons. Although the most severe case of keratoconus possessed the most pronounced stromal collagen alterations, and only a minor disruption to stromal collagen arrangement was seen in the least advanced case, a variability in the extent of stromal collagen alteration was seen between these clinical extremes. The observed abnormalities in collagen distribution and orientation are consistent with a mechanism of keratoconus progression that involves inter-fibrillar or inter-lamellar slippage causing a redistribution of tissue within the cornea.
This study is a comparative study of the relationship between corneal structure, morphology, and function in a range of mammalian species. X-ray scattering patterns were gathered at regular spatial intervals over the excised cornea (and in most cases also the scleral rim) of humans, marmosets, horses, cows, pigs, rabbits, and mice. All patterns were analyzed to produce quantitative information regarding the predominant orientation of fibrillar collagen throughout the tissue. The predominant direction of corneal collagen varies between mammals. This variation is not related to the size, shape, or thickness of the cornea or the frequency with which the animal blinks. A relationship does, however, appear to exist between corneal collagen arrangement and visual acuity. An excess of collagen directed toward one or both sets of opposing rectus muscles is a feature of animals that have an intermediate to high level of visual acuity. There is a significant variation in the arrangement of corneal collagen between different mammalian species. This finding may be related to differences in the frequency of action and the forces generated by the various extraocular muscles during eye movement and image fixation.
Birefringence measurement of cornea and anterior segment by office-based polarization-sensitive optical coherence tomography
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