Depth-dependent mechanical properties of the human cornea by uniaxial extension.

The purpose of this study was to investigate the depth-dependent biomechanical properties of the human corneal stroma under uniaxial tensile loading. Human stroma samples were obtained after the removal of Descemet's membrane in the course of Descemet's membrane endothelial keratoplasty (DMEK) transplantation. Uniaxial tensile tests were performed at three different depths: anterior, central, and posterior on 2 × 6 × 0.15 mm strips taken from the central DMEK graft. The measured force-displacement data were used to calculate stress-strain curves and to derive the tangent modulus. The study showed that mechanical strength decreased significantly with depth. The anterior cornea appeared to be the stiffest, with a stiffness approximately 18% higher than that of the central cornea and approximately 38% higher than that of the posterior layer. Larger variations in mechanical response were observed in the posterior group, probably due to the higher degree of alignment of the collagen fibers in the posterior sections of the cornea. This study contributes to a better understanding of the biomechanical tensile properties of the cornea, which has important implications for the development of new treatment strategies for corneal diseases. Accurate quantification of tensile strength as a function of depth is critical information that is lacking in human corneal biomechanics to develop numerical models and new treatment methods.

Patient-specific finite element analysis of human corneal lenticules: An experimental and numerical study.

The number of elective refractive surgeries is constantly increasing due to the drastic increase in myopia prevalence. Since corneal biomechanics are critical to human vision, accurate modeling is essential to improve surgical planning and optimize the results of laser vision correction. In this study, we present a numerical model of the anterior cornea of young patients who are candidates for laser vision correction. Model parameters were determined from uniaxial tests performed on lenticules of patients undergoing refractive surgery by means of lenticule extraction, using patient-specific models of the lenticules. The models also took into account the known orientation of collagen fibers in the tissue, which have an isotropic distribution in the corneal plane, while they are aligned along the corneal curvature and have a low dispersion outside the corneal plane. The model was able to reproduce the experimental data well with only three parameters. These parameters, determined using a realistic fiber distribution, yielded lower values than those reported in the literature. Accurate characterization and modeling of the cornea of young patients is essential to study better refractive surgery for the population undergoing these treatments, to develop in silico models that take corneal biomechanics into account when planning refractive surgery, and to provide a basis for improving visual outcomes in the rapidly growing population undergoing these treatments.

Orientation and depth dependent mechanical properties of the porcine cornea: Experiments and parameter identification.

The porcine cornea is a standard animal model in ophthalmic research, making its biomechanical characterization and modeling important to develop novel treatments such as crosslinking and refractive surgeries. In this study, we present a numerical model of the porcine cornea based on experimental measurements that captures both the depth dependence and orientation dependence of the mechanical response. The mechanical parameters of the established anisotropic hyperelastic material models of Gasser, Holzapfel and Ogden (HGO) and Markert were determined using tensile tests. Corneas were cut with a femtosecond laser in the anterior (100 µm), central (350 µm), and posterior (600 µm) regions into nasal-temporal, superior-inferior, and diagonal strips of 150 µm thickness. These uniformly thick strips were tested at a low speed using a single-axis testing machine. The results showed that the corneal mechanical properties remained constant in the anterior half of the cornea regardless of orientation, but that the material softened in the posterior layer. These results are consistent with the circular orientation of collagen observed in porcine corneas using X-ray scattering. In addition, the parameters obtained for the HGO model were able to reproduce the published inflation tests, indicating that it is suitable for simulating the mechanical response of the entire cornea. Such a model constitutes the basis for in silico platforms to develop new ophthalmic treatments. In this way, researchers can match their experimental surrogate porcine model with a numerical counterpart and validate the prediction of their algorithms in a complete and accessible environment.

Novel biomarker of sphericity and cylindricity indices in volume-rendering optical coherence tomography angiography in normal and diabetic eyes: a preliminary study.

PURPOSE: Preliminary to evaluate geometric indices (vessel sphericity and cylindricity) for volume-rendered optical coherence tomography angiography (OCTA) in healthy and diabetic eyes. METHODS: Twenty-six eyes of 13 healthy subjects and 12 eyes of patients with central ischemic, non-proliferative diabetic retinopathy were included. OCTA volume and surface area of the foveal vessels were measured and compared to determine OCTA sphericity and cylindricity indices and surface efficiency (SE). RESULTS: The overall average OCTA volume in healthy was 0.49 ± 0.09 mm3 (standard deviation [SD]), compared to 0.44 ± 0.07 mm3 (SD) in the diabetic eyes (difference in means 0.06 mm3, p = 0.054). The overall average OCTA surface area in the healthy eyes was 87.731 ± 9.51 mm2 (SD), compared to 76.65 ± 13.67 mm2 (SD) in the diabetic eyes (difference in means 11.08 mm2, p = 0.021). In relation to total foveolar tissue volume, the proportion of blood vessels was 22% in healthy individuals and only 20% in diabetics. The difference between the groups was more pronounced with respect to the total OCTA surface area, with a decrease of 13% in diabetics. A diabetic eye was most likely using geometric vessel indices analysis if the sphericity value was ≥ 0.190, with a cylindricity factor of ≥ 0.001. Reproducibility of the method was good. CONCLUSIONS: A method for OCTA surface area and volume measurements was developed. The application of the novel OCTA sphericity and cylindricity indices could be suitable as temporal biomarker to characterize stable disease or disease progression and may contribute to a better understanding in the evolution of diabetic retinopathy.

Microstructure-based numerical simulation of the mechanical behaviour of ocular tissue.

This paper aims to present a novel full-eye biomechanical material model that incorporates the characteristics of ocular tissues at microstructural level, and use the model to analyse the age-related stiffening in tissue behaviour. The collagen content in ocular tissues, as obtained using X-ray scattering measurements, was represented by sets of Zernike polynomials that covered both the cornea and sclera, then used to reconstruct maps of collagen fibril magnitude and orientation on the three-dimensional geometry of the eye globe. Fine-mesh finite-element (FE) models with eye-specific geometry were built and supported by a user-defined material model (UMAT), which considered the regional variation of fibril density and orientation. The models were then used in an iterative inverse modelling study to derive the material parameters that represent the experimental behaviour of ocular tissues from donors aged between 50 and 90 years obtained in earlier ex vivo studies. Sensitivity analysis showed that reducing the number of directions that represented the anisotropy of collagen fibril orientation at each X-ray scattering measurement point from 180 to 16 would have limited and insignificant effect on the FE solution (0.08%). Inverse analysis resulted in material parameters that provided a close match with experimental intraocular pressure-deformation behaviour with a root mean square of error between 3.6% and 4.3%. The results also demonstrated a steady increase in mechanical stiffness in all ocular regions with age. A constitutive material model based on distributions of collagen fibril density and orientation has been developed to enable the accurate representation of the biomechanical behaviour of ocular tissues. The model offers a high level of control of stiffness and anisotropy across ocular globe, and therefore has the potential for use in planning surgical and medical procedures.

Interdevice variability of central corneal thickness measurement.

PURPOSE: To evaluate variability of central corneal thickness measurement (CCT) devices using a hitherto unprecedented number of CCT devices. METHODS: CCT was measured consecutively in 122 normal corneas of 61 subjects with seven different devices using three distinct measurement technologies: Scheimpflug, Ultrasound, and Optical Coherence Tomography (OCT). Per device deviation from the mean CCT value per eye was used to determine which of the devices performed best, compared to the mean value. RESULTS: Cirrus OCT yielded the lowest deviation. Deviations of the individual devices from the mean CCT of each eye were (OS/OD) 12.8±5.0/14.9±9.4 µm for Topcon noncontact specular microscopy (NCSM), 11.3±5.9/10.6±7.3 µm for Pentacam, 10.7±5.2/10.4±4.8 µm for Spectralis OCT, 6.0±3.9/6.2±4.9 µm for Topcon DRI OCT, 5.1±3.4/5.9±10.3 µm for AngioVue OCT, 4.8±4.1/5.7±4.6 µm for US pachymetry, and 4.2±3.2/5.7±4.6 µm for Cirrus OCT. The maximum differences between US pachymetry and the other devices were very high (up to 120 µm). CONCLUSION: Central corneal thickness may be under- or overestimated due to high interdevice variations. Measuring CCT with one device only may lead to inappropriate clinical and surgical recommendations. OCT showed superior results.

A viscoelastic anisotropic hyperelastic constitutive model of the human cornea.

A constitutive model based on the continuum mechanics theory has been developed which represents interlamellar cohesion, regional variation of collagen fibril density, 3D anisotropy and both age-related viscoelastic and hyperelastic stiffening behaviour of the human cornea. Experimental data gathered from a number of previous studies on 48 ex vivo human cornea (inflation and shear tests) enabled calibration of the constitutive model by numerical analysis. Wide-angle X-ray scattering and electron microscopy provided measured data which quantify microstructural arrangements associated with stiffness. The present study measures stiffness parallel to the lamellae of the cornea which approximately doubles with an increase in strain rate from 0.5 to 5%/min, while the underlying stromal matrix provides a stiffness 2-3 orders of magnitude lower than the lamellae. The model has been simultaneously calibrated to within 3% error across three age groups ranging from 50 to 95 years and three strain rates across the two loading scenarios. Age and strain-rate-dependent material coefficients allow numerical simulation under varying loading scenarios for an individual patient with material stiffness approximated by their age. This present study addresses a significant gap in numerical representation of the cornea and has great potential in daily clinical practice for the planning and optimisation of corrective procedures and in preclinical optimisation of diagnostic procedures.

A Novel Laser Refractive Surgical Treatment for Presbyopia: Optics-Based Customization for Improved Clinical Outcome.

Laser Assisted in Situ Keratomileusis (LASIK) is a proven treatment method for corneal refractive surgery. Surgically induced higher order optical aberrations were a major reason why the method was only rarely used to treat presbyopia, an age-related near-vision loss. In this study, a novel customization algorithm for designing multifocal ablation patterns, thereby minimizing induced optical aberrations, was used to treat 36 presbyopic subjects. Results showed that most candidates went from poor visual acuity to uncorrected 20/20 vision or better for near (78%), intermediate (92%), and for distance (86%) vision, six months after surgery. All subjects were at 20/25 or better for distance and intermediate vision, and a majority (94%) were also better for near vision. Even though further studies are necessary, our results suggest that the employed methodology is a safe, reliable, and predictable refractive surgical treatment for presbyopia.

Biomechanical Modeling of Pterygium Radiation Surgery: A Retrospective Case Study.

Pterygium is a vascularized, invasive transformation on the anterior corneal surface that can be treated by Strontium-/Yttrium90 beta irradiation. Finite element modeling was used to analyze the biomechanical effects governing the treatment, and to help understand clinically observed changes in corneal astigmatism. Results suggested that irradiation-induced pulling forces on the anterior corneal surface can cause astigmatism, as well as central corneal flattening. Finite element modeling of corneal biomechanics closely predicted the postoperative corneal surface (astigmatism error -0.01D; central curvature error -0.16D), and can help in understanding beta irradiation treatment. Numerical simulations have the potential to preoperatively predict corneal shape and function changes, and help to improve corneal treatments.

Gaussian process prediction of the stress-free configuration of pre-deformed soft tissues: Application to the human cornea.

Image-based modeling is a popular approach to perform patient-specific biomechanical simulations. One constraint of this technique is that the shape of soft tissues acquired in-vivo is deformed by the physiological loads. Accurate simulations require determining the existing stress in the tissues or their stress-free configurations. This process is time consuming, which is a limitation to the dissemination of numerical planning solutions to clinical practice. In this study, we propose a method to determine the stress-free configuration of soft tissues using a Gaussian process (GP) regression. The prediction relies on a database of pre-calculated results to enable real time predictions. The application of this technique to the human cornea showed a level of accuracy five to ten times higher than the accuracy of the topographic device used to obtain the patients' anatomy; results showed that for almost all optical indices, the predicted curvature error did not exceed 0.025 D, while the wavefront aberration percentage error did not overcome 5%. In this context, we believe that GP models are suitable for predicting the stress free configuration of the cornea and can be used in planning tools based on patient-specific finite element simulations. Due to the high level of accuracy required in ophthalmology, this approach is likely to be appropriate for other applications requiring the definition of the relaxed shape of soft tissues.

Geometrical aspects of patient-specific modelling of the intervertebral disc: collagen fibre orientation and residual stress distribution.

Patient-specific modelling of the spine is a powerful tool to explore the prevention and the treatment of injuries and pathologies. Albeit several methods have been proposed for the discretization of the bony structures, the efficient representation of the intervertebral disc anisotropy remains a challenge, especially with complex geometries. Furthermore, the swelling of the disc's nucleus pulposus is normally added to the model after geometry definition, at the cost of changes of the material properties and an unrealistic description of the prestressed state. The aim of this study was to develop techniques, which preserve the patient-specific geometry of the disc and allow the representation of the system anisotropy and residual stresses, independent of the system discretization. Depending on the modelling features, the developed approaches resulted in a response of patient-specific models that was in good agreement with the physiological response observed in corresponding experiments. The proposed methods represent a first step towards the development of patient-specific models of the disc which respect both the geometry and the mechanical properties of the specific disc.

Biomechanical Modeling of Femtosecond Laser Keyhole endokeratophakia Surgery.

PURPOSE: To apply a finite element model to endokeratophakia and evaluate anterior and posterior corneal surface changes. METHODS: Spatial elevation data (Pentacam HR; Oculus, Wetzlar, Germany) were obtained for the front and back corneal surfaces of an eye prior to undergoing an endokeratophakia procedure. These were used to warp a spherical template finite element model of the cornea to create a patient-specific finite element mesh and the initial stress distribution was computed with an iterative approach. The finite element model (Optimeyes; Integrated Scientific Services, Biel, Switzerland) included non-linear elastic characteristics of the stroma. The endokeratophakia procedure was recreated in the model: a donor lenticule (-10.50 diopters [D], 5.75-mm zone, 127-µm thick) was inserted into a lamellar pocket (180-µm deep, 6.25-mm diameter) and two 2-mm small incisions were made at 150° and 330°. Anterior and posterior surfaces, computed by the finite element model, were compared to clinical data to assess accuracy and reliability of finite element modeling. RESULTS: The postoperative axial curvature produced by the model closely resembled the patient data; average curvature was 48.01 D clinically and 48.23 D in the simulation, and corneal astigmatism was 3.01 D clinically and 2.88 D in the simulation. The posterior best-fit sphere elevation map also matched the patient data, replicating inward bulging of the posterior surface by approximately 40 µm. Stress distribution modeling predicted a stress increase by 159.94% ± 73% in the cap and a stress decrease by 32.41% ± 21% in the stromal bed. CONCLUSIONS: Finite element modeling of the cornea reproduced the clinically observed anterior and posterior corneal surface changes following an endokeratophakia procedure. This case sets the stage for further study to refine and yield predictive finite element modeling for the evaluation of corneal refractive surgical procedures.

Biomechanical model of the human cornea: considering shear stiffness and regional variation of collagen anisotropy and density.

A numerical model based on continuum mechanics theory has been developed which represents the 3D anisotropic behaviour of the corneal stroma. Experimental data has been gathered from a number of previous studies to provide the basis and calibration parameters for the numerical modelling. The resulting model introduces numerical representation of collagen fibril density and its related regional variation, interlamellar cohesion and age-related stiffening in an anisotropic model of the human cornea. Further, the model incorporates previous modelling developments including representation of lamellae anisotropy and stiffness of the underlying matrix. Wide angle X-ray scattering has provided measured data which quantifies relative fibril anisotropy in the 2D domain. Accurate numerical description of material response to deformation is essential to providing representative simulations of corneal behaviour. Representing experimentally obtained 2D anisotropy and regional density variation in the 3D domain is an essential component of this accuracy. The constitutive model was incorporated into finite element analysis. Combining with inverse analysis, the model was calibrated to an extensive experimental database of ex vivo corneal inflation tests and ex vivo corneal shear tests. This model represents stiffness of the underlying matrix which is 2-3 orders of magnitude than the mechanical response representing the collagen fibrils in the lamellae. The presented model, along with its age dependent material coefficients, allows finite element modelling for an individual patient with material stiffness approximated based on their age. This has great potential to be used in both daily clinical practice for the planning and optimisation of corrective procedures and in pre-clinical optimisation of diagnostic procedures.

Patient-specific finite-element simulation of the human cornea: a clinical validation study on cataract surgery.

The planning of refractive surgical interventions is a challenging task. Numerical modeling has been proposed as a solution to support surgical intervention and predict the visual acuity, but validation on patient specific intervention is missing. The purpose of this study was to validate the numerical predictions of the post-operative corneal topography induced by the incisions required for cataract surgery. The corneal topography of 13 patients was assessed preoperatively and postoperatively (1-day and 30-day follow-up) with a Pentacam tomography device. The preoperatively acquired geometric corneal topography - anterior, posterior and pachymetry data - was used to build patient-specific finite element models. For each patient, the effects of the cataract incisions were simulated numerically and the resulting corneal surfaces were compared to the clinical postoperative measurements at one day and at 30-days follow up. Results showed that the model was able to reproduce experimental measurements with an error on the surgically induced sphere of 0.38D one day postoperatively and 0.19D 30 days postoperatively. The standard deviation of the surgically induced cylinder was 0.54D at the first postoperative day and 0.38D 30 days postoperatively. The prediction errors in surface elevation and curvature were below the topography measurement device accuracy of ±5µm and ±0.25D after the 30-day follow-up. The results showed that finite element simulations of corneal biomechanics are able to predict post cataract surgery within topography measurement device accuracy. We can conclude that the numerical simulation can become a valuable tool to plan corneal incisions in cataract surgery and other ophthalmosurgical procedures in order to optimize patients' refractive outcome and visual function.

Importance of multiple loading scenarios for the identification of material coefficients of the human cornea.

A mechanical balance between intraocular pressure and tissue stiffness defines the refractive shape of the human cornea. More and more daily surgical procedures modify that shape to achieve vision correction, which increases the demand for a profound understanding of the tissue mechanics. The wide variety of published mechanical properties foreshadows the difficulty of this task. The aim of this study is to show that such problems may arise from using the inverse method for fitting material models with multiple coefficients to a limited number (usually one) of experimental data. Using multiple sets of experimental data for the fitting process is proposed as a possible solution.