An inverse method to determine the mechanical properties of the iris in vivo

An Inverse Method to Determine Mechanical Parameters of Porcine Vitreous Bodies Based on the Indentation Test

The vitreous body keeps the lens and retina in place and protects these tissues from physical insults. Existing studies have reported that the mechanical properties of vitreous body varied after liquefaction, suggesting mechanical properties could be effective parameters to identify vitreous liquefaction process. Thus, in this work, we aimed to propose a method to determine the mechanical properties of vitreous bodies. Fresh porcine eyes were divided into three groups, including the untreated group, the 24 h liquefaction group and the 48 h liquefaction group, which was injected collagenase and then kept for 24 h or 48 h. The indentation tests were carried out on the vitreous body in its natural location while the posterior segment of the eye was fixed in the container. A finite element model of a specimen undertaking indentation was constructed to simulate the indentation test with surface tension of vitreous body considered. Using the inverse method, the mechanical parameters of the vitreous body and the surface tension coefficient were determined. For the same parameter, values were highest in the untreated group, followed by the 24 h liquefaction group and the lowest in the 48 h liquefaction group. For C₁₀ in the neo-Hookean model, the significant differences were found between the untreated group and liquefaction groups. This work quantified vitreous body mechanical properties successfully using inverse method, which provides a new method for identifying vitreous liquefactions related studies.

Soft Contact Mechanics with Gradient-Stiffness Surfaces

The stiffness in the top surface of many biological entities like cornea or articular cartilage, as well as chemically cross-linked synthetic hydrogels, can be significantly lower or more compliant than the bulk. When such a heterogeneous surface comes into contact, the contacting load is distributed differently from typical contact models. The mechanical response under indentation loading of a surface with a gradient of stiffness is a complex, integrated response that necessarily includes the heterogeneity. In this work, we identify empirical contact models between a rigid indenter and gradient elastic surfaces by numerically simulating quasi-static indentation. Three key case studies revealed the specific ways in which (I) continuous gradients, (II) laminate-layer gradients, and (III) alternating gradients generate new contact mechanics at the shallow-depth limit. Validation of the simulation-generated models was done by micro- and nanoindentation experiments on polyacrylamide samples synthesized to have a softer gradient surface layer. The field of stress and stretch in the subsurface as visualized from the simulations also reveals that the gradient layers become confined, which pushes the stretch fields closer to the surface and radially outward. Thus, contact areas are larger than expected, and average contact pressures are lower than predicted by the Hertz model. The overall findings of this work are new contact models and the mechanisms by which they change. These models allow a more accurate interpretation of the plethora of indentation data on surface gradient soft matter (biological and synthetic) as well as a better prediction of the force response to gradient soft surfaces. This work provides examples of how gradient hydrogel surfaces control the subsurface stress distribution and loading response.

Glaucoma and biomechanics

PURPOSE OF REVIEW

Biomechanics is an important aspect of the complex family of diseases known as the glaucomas. Here, we review recent studies of biomechanics in glaucoma.

RECENT FINDINGS

Several tissues have direct and/or indirect biomechanical roles in various forms of glaucoma, including the trabecular meshwork, cornea, peripapillary sclera, optic nerve head/sheath, and iris. Multiple mechanosensory mechanisms and signaling pathways continue to be identified in both the trabecular meshwork and optic nerve head. Further, the recent literature describes a variety of approaches for investigating the role of tissue biomechanics as a risk factor for glaucoma, including pathological stiffening of the trabecular meshwork, peripapillary scleral structural changes, and remodeling of the optic nerve head. Finally, there have been advances in incorporating biomechanical information in glaucoma prognoses, including corneal biomechanical parameters and iridial mechanical properties in angle-closure glaucoma.

SUMMARY

Biomechanics remains an active aspect of glaucoma research, with activity in both basic science and clinical translation. However, the role of biomechanics in glaucoma remains incompletely understood. Therefore, further studies are indicated to identify novel therapeutic approaches that leverage biomechanics. Importantly, clinical translation of appropriate assays of tissue biomechanical properties in glaucoma is also needed.

Sex Differences in Rate of Axial Elongation and Ocular Biometrics in Elementary School Students

Purpose

To determine the relationship between the ocular biometrics and axial length (AL) elongation and its rate in elementary school children.

Methods

This is a prospective observational study of 102 right eyes of third-grade elementary school students who were 8 to 9 years old. All participants underwent measurements of the AL, anterior chamber depth (ACD), and lens thickness (LT) annually for 3 years. The AL elongation during the first half and second half was calculated by subtracting the AL of the 1st year from that at the 2nd year, and AL of the 3rd year minus 2nd year. The total AL elongation (TALE) was obtained by summing up the first and second half AL elongations. The growth rate change (GRC) was obtained by subtracting the first half AL elongation from second half AL elongation. Spearman correlations were used to determine the correlation between the 1st year ocular biometrics and the TALE and GRC.

Results

The mean TALE was 0.54 ± 0.26 mm in boys and 0.46 ± 0.31 mm in girls. The mean GRC was 0.00 ± 0.16 mm in boys and −0.04 ± 0.14 mm in girls. In boys and girls, the TALE was significantly larger in the eyes with myopic ocular biometrics such as a deeper ACD, thinner LT, and longer AL during the 1st year (|r|=0.41 to 0.46, P < 0.05). The GRC was significantly accelerated in the eyes of only the girls with hyperopic ocular biometrics such as a shallower ACD, thicker LT, and shorter AL during the 1st year (|r|=0.31 to 0.41, P<0.05).

Conclusion

In boys and girls, the TALE tends to be larger in eyes with myopic biometrics at the 1st year examination. The GRC tended to accelerate in the eyes with hyperopic ocular biometry during the 1st year only in girls.

Adaptive finite element eye model for the compensation of biometric influences on acoustic tonometry

BACKGROUND AND OBJECTIVE

Glaucoma is currently a major cause for irreversible blindness worldwide. A risk factor and the only therapeutic control parameter is the intraocular pressure (IOP). The IOP is determined with tonometers, whose measurements are inevitably influenced by the geometry of the eye. Even though the corneal mechanics have been investigated to improve accuracy of Goldmann and air pulse tonometry, influences of geometric properties of the eye on an acoustic self-tonometer approach are still unresolved.

METHODS

In order to understand and compensate for measurement deviations resulting from the geometric uniqueness of eyes, a finite element eye model is designed that considers all relevant eye components and is adjustable to all physiological shapes of the human eye.

RESULTS

The general IOP-dependent behavior of the eye model is validated by laboratory measurements on porcine eyes. The difference between simulation and measurement is below 8 µm for IOP levels from 5 to 40 mmHg. The adaptive eye model is then used to quantify systematic uncertainty contributions of a variation of eye length and central corneal thickness based on input statistics of a clinical trial series. The adaptive eye model provides the required relation between biometric eye parameters and the corneal deflection amplitude, which here is the measured quantity to trace back to the IOP. Implementing the relations provided by the eye model in a Gaussian uncertainty propagation calculation now allows the quantification of the uncertainty contributions of the biometric parameters on the overall measurement uncertainty of the acoustic self-tonometer. As a result, a systematic uncertainty contribution resulting from deviations in eye length dominate stochastic deviations of the sensor equipment by a factor of 3.5.

CONCLUSION

As perspective, the proposed adaptive eye model provides the basis to compensate for systematic deviations of (but not only) the acoustic self-tonometer.

Experimental evaluation of the viscoelasticity of porcine vitreous

This study aims to estimate the material properties of the porcine vitreous while testing it in close to its natural physiological conditions. Eighteen porcine eyes were tested within 48 h post-mortem. A custom-built computer-controlled test rig was designed to support, load and monitor the behaviour of eye globes while being subjected to dynamic rotation cycles mimicking saccade eye movement. Specimens were glued to the base of a container, surrounded by gelatin, frozen and cut in half to expose the vitreous. After thawing, the container was subjected to concentric dynamic rotations of up to 5°, 10° or 15°, while taking 50 MP photos of the specimen every 2 ms. The images were analysed by a digital image correlation algorithm to trace the movement of marked points on the vitreous surface with different radii from the centre of the posterior chamber. The initial camera image was used in building a finite-element model of the test set-up, which was used in an inverse analysis exercise to estimate the material properties of the vitreous. Angular displacements of the monitored points were up to 3.3°, 4.1° and 3.9° in response to eye rotations of 5°, 10° and 15°, respectively. With the experimental relationships between eye rotation and angular displacements used as target behaviour, the inverse analysis exercise estimated the initial shear modulus, the long-term shear modulus and the viscoelastic decay constant of the porcine vitreous as 2.10 ± 0.15 Pa, 0.50 ± 0.04 Pa and 1.20 ± 0.09 s^-1, respectively. Consideration of the viscoelasticity of the vitreous was essential to represent its experimental behaviour. Testing the vitreous in close to its normal physiological conditions produced estimations of the initial shear modulus and long-term shear modulus that were, respectively, smaller and larger than reported values (Zimberlin et al. 2010 Soft Matter 6, 3632-3635. (doi:10.1039/b925407b), Liu et al. 2013 J. Biomech. 46, 1321-7. (doi:10.1016/j.jbiomech.2013.02.006), Rossi et al. 2011 Invest. Ophthalmol. Vis. Sci. 52, 3994-4002. (doi:10.1167/iovs.10-6477)).

In vivo estimation of murine iris stiffness using finite element modeling

The iris plays an important role in certain types of glaucoma, including primary angle-closure glaucoma and pigmentary glaucoma. Iris mechanics are also important in influencing trabecular meshwork deformation in response to intraocular pressure changes in some animal species. Although mice are widely used to study ocular disease, including glaucoma, the in vivo biomechanical properties of the murine iris are unknown. Thus, the primary objective of this study was to estimate murine iris biomechanical stiffness. We used optical coherence tomography (OCT) images of the anterior segment of living mice (n = 13, age = 7.3 ± 3.2 [mean ± SD] months) at sequentially increasing IOP levels, observing IOP-dependent iris deformations. We then used an inverse finite element model to predict iris deformations under the same conditions, estimating iris stiffness by maximizing agreement between OCT data and numerical simulations. Our results show an in vivo murine iris stiffness of 96.1 ± 54.7 kPa (mean ± SD), which did not correlate with age but was dependent on gender. Our results further showed strong evidence of reverse pupillary block, with mean posterior chamber pressure remaining at approximately 12 mmHg even as anterior chamber pressure was set to much higher levels. Our approach to monitoring iris stiffness in vivo is applicable to study potential changes of iris stiffness in various pathophysiological conditions and thus has significant potential for clinical care of ocular disease involving iris biomechanics.

Quantification of iris elasticity using acoustic radiation force optical coherence elastography

Careful quantification of the changes in biomechanical properties of the iris can offer insight into the pathophysiology of some ocular diseases. However, to date there has not been much information available regarding this subject because clinical detection for iris elasticity remains challenging. To overcome this limitation, we explore, for the first time to our knowledge, the potential of measuring iris elasticity using acoustic radiation force optical coherence elastography (ARF-OCE). The resulting images and shear wave propagation, as well as the corresponding shear modulus and Young's modulus from ex vivo and in vivo rabbit models confirmed the feasibility of this method. With features of noninvasive imaging, micrometer-scale resolution, high acquisition speed and real-time processing, ARF-OCE is a promising method for reconstruction of iris elasticity and may have great potential to be applied in clinical ophthalmology with further refinement.

Computational Study on the Biomechanics of Pupil Block Phenomenon

Pupil blocking force (PBF) can indicate the potential risk of pupil block (PB), which is considered as a main pathogenic factor of primary angle-closure glaucoma (PACG). However, the effect of PB on the PBF under different pupil diameters and iris-lens channel (ILC) distance was unknown. Besides, a simple and practical method to assess PBF has not been reported yet. In this study, 21 finite element models of eyes with various pupil diameters (2.4 mm–2.6 mm) and ILC (2 μm–20 μm) were constructed and were conducted to simulate aqueous humor flow by fluid-solid coupling numerical simulation. PBF in each model was calculated based on the numerical simulation results and was fitted using response surface methodology. The results demonstrated that ILC distance had a more significant effect than pupil diameter on PBF. With the decrease of ILC distance, the PBF increased exponentially. When the reduced distance was lower than 5 μm, the PBF exploded quickly, resulting in a high risk of iris bomb. The PBF also varied with pupil diameter, especially under the condition of narrow ILC. Both ILC distance and pupil diameter could explain more than 97% variation in PBF, and a second-order empirical model has been developed to be a good predictor of PBF. Based on the linear relationship between anterior chamber deformation and PBF, a threshold value of PBF was given to guide clinical decisions. This study could be used to investigate PACG pathological correlation and its pathogenesis, so as to provide a reference value for clinical diagnosis of PACG.

Numerical stress analysis of the iris tissue induced by pupil expansion: Comparison of commercial devices

Purpose

(1) To use finite element (FE) modelling to estimate local iris stresses (i.e. internal forces) as a result of mechanical pupil expansion; and to (2) compare such stresses as generated from several commercially available expanders (Iris hooks, APX dilator and Malyugin ring) to determine which design and deployment method are most likely to cause iris damage.

Methods

We used a biofidelic 3-part iris FE model that consisted of the stroma, sphincter and dilator muscles. Our FE model simulated expansion of the pupil from 3 mm to a maximum of 6 mm using the aforementioned pupil expanders, with uniform circular expansion used for baseline comparison. FE-derived stresses, resultant forces and area of final pupil opening were compared across devices for analysis.

Results

Our FE models demonstrated that the APX dilator generated the highest stresses on the sphincter muscles, (max: 6.446 MPa; average: 5.112 MPa), followed by the iris hooks (max: 5.680 MPa; average: 5.219 MPa), and the Malyugin ring (max: 2.144 MPa; average: 1.575 MPa). Uniform expansion generated the lowest stresses (max: 0.435MPa; average: 0.377 MPa). For pupil expansion, the APX dilator required the highest force (41.22 mN), followed by iris hooks (40.82 mN) and the Malyugin ring (18.56 mN).

Conclusion

Our study predicted that current pupil expanders exert significantly higher amount of stresses and forces than required during pupil expansion. Our work may serve as a guide for the development and design of next-generation pupil expanders.

Estimating Human Trabecular Meshwork Stiffness by Numerical Modeling and Advanced OCT Imaging

Purpose

The purpose of this study was to estimate human trabecular meshwork (hTM) stiffness, thought to be elevated in glaucoma, using a novel indirect approach, and to compare results with direct en face atomic force microscopy (AFM) measurements.

Methods

Postmortem human eyes were perfused to measure outflow facility and identify high- and low-flow regions (HF, LF) by tracer. Optical coherence tomography (OCT) images were obtained as Schlemm's canal luminal pressure was directly manipulated. TM stiffness was deduced by an inverse finite element modeling (FEM) approach. A series of AFM forcemaps was acquired along a line traversing the anterior angle on a radially cut flat-mount corneoscleral wedge with TM facing upward.

Results

The elastic modulus of normal hTM estimated by inverse FEM was 70 ± 20 kPa (mean ± SD), whereas glaucomatous hTM was slightly stiffer (98 ± 19 kPa). This trend was consistent with TM stiffnesses measured by AFM: normal hTM stiffness = 1.37 ± 0.56 kPa, which was lower than glaucomatous hTM stiffness (2.75 ± 1.19 kPa). None of these differences were statistically significant. TM in HF wedges was softer than that in LF wedges for both normal and glaucomatous eyes based on the inverse FEM approach but not by AFM. Outflow facility was significantly correlated with TM stiffness estimated by FEM in six human eyes (P = 0.018).

Conclusions

TM stiffness is higher, but only modestly so, in glaucomatous patients. Outflow facility in both normal and glaucomatous human eyes appears to associate with TM stiffness. This evidence motivates further studies to investigate factors underlying TM biomechanical property regulation.

Biomechanics of the sclera and effects on intraocular pressure

Accumulating evidence indicates that glaucoma is a multifactorial neurodegenerative disease characterized by the loss of retinal ganglion cells (RGC), resulting in gradual and progressive permanent loss of vision. Reducing intraocular pressure (IOP) remains the only proven method for preventing and delaying the progression of glaucomatous visual impairment. However, the specific role of IOP in optic nerve injury remains controversial, and little is known about the biomechanical mechanism by which elevated IOP leads to the loss of RGC. Published studies suggest that the biomechanical properties of the sclera and scleral lamina cribrosa determine the biomechanical changes of optic nerve head, and play an important role in the pathologic process of loss of RGC and optic nerve damage. This review focuses on the current understanding of biomechanics of sclera in glaucoma and provides an overview of the possible interactions between the sclera and IOP. Treatments and interventions aimed at the sclera are also discussed.

A novel suture retention test for scaffold strength characterization in ophthalmology

Sutures are a common way to attach scaffolds in patients. For tubular cardiac scaffolds, the 'suture retention strength' is commonly used to evaluate the resistance of a scaffold against the pull-out of a suture. In order to make this quantity accessible for ophthalmological scaffolds the test procedure has been modified in a novel way. Polycaprolactone (PCL) films of different thicknesses and an amniotic membrane (AM) were used for the experiments. Circular samples with a radius of 7mm were taken and a suture was passed through each sample and tied to a loop. The sample was clamped in a tensile tester and a bolt was passed through the loop. The suture was then pulled with a constant deformation rate until pull-out occurred. The suture retention strength, the deformation at the suture retention strength, and the deformation at rupture were determined for each sample. The presented modified suture retention test allows to measure the relevant parameters of samples on the scale of ophthalmological scaffolds in a reproducible way. A comparison between the first data on PCL and AM has been made.

Computing the stresses and deformations of the human eye components due to a high explosive detonation using fluid-structure interaction model

INTRODUCTION

In spite the fact that a very small human body surface area is comprised by the eye, its wounds due to detonation have recently been dramatically amplified. Although many efforts have been devoted to measure injury of the globe, there is still a lack of knowledge on the injury mechanism due to Primary Blast Wave (PBW). The goal of this study was to determine the stresses and deformations of the human eye components, including the cornea, aqueous, iris, ciliary body, lens, vitreous, retina, sclera, optic nerve, and muscles, attributed to PBW induced by trinitrotoluene (TNT) explosion via a Lagrangian-Eulerian computational coupling model.

MATERIALS AND METHODS

Magnetic Resonance Imaging (MRI) was employed to establish a Finite Element (FE) model of the human eye according to a normal human eye. The solid components of the eye were modelled as Lagrangian mesh, while an explosive TNT, air domain, and aqueous were modelled using Arbitrary Lagrangian-Eulerian (ALE) mesh. Nonlinear dynamic FE simulations were accomplished using the explicit FE code, namely LS-DYNA. In order to simulate the blast wave generation, propagation, and interaction with the eye, the ALE formulation with Jones-Wilkins-Lee (JWL) equation defining the explosive material were employed.

RESULTS

The results revealed a peak stress of 135.70kPa brought about by detonation upsurge on the cornea at the distance of 25cm. The highest von Mises stresses were observed on the sclera (267.3kPa), whereas the lowest one was seen on the vitreous body (0.002kPa). The results also showed a relatively high resultant displacement for the macula as well as a high variation for the radius of curvature for the cornea and lens, which can result in both macular holes, optic nerve damage and, consequently, vision loss.

CONCLUSION

These results may have implications not only for understanding the value of stresses and strains in the human eye components but also giving an outlook about the process of PBW triggers damage to the eye.

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.