Anterior-posterior asymmetry in iris mechanics measured by indentation

The Structural Layers of the Porcine Iris Exhibit Inherently Different Biomechanical Properties

Purpose

The purpose of this study was to isolate the structural components of the ex vivo porcine iris tissue and to determine their biomechanical properties.

Methods

The porcine stroma and dilator tissues were separated, and their dimensions were assessed using optical coherence tomography (OCT). The stroma underwent flow test (n = 32) to evaluate for permeability using Darcy's Law (ΔP = 2000 Pa, A = 0.0391 mm2), and both tissues underwent stress relaxation experiments (ε = 0.5 with initial ramp of δε = 0.1) to evaluate for their viscoelastic behaviours (n = 28). Viscoelasticity was characterized by the parameters β (half width of the Gaussian distribution), τm (mean relaxation time constant), E0 (instantaneous modulus), and E∞ (equilibrium modulus).

Results

For the stroma, the hydraulic permeability was 9.49 ± 3.05 × 10-6 mm2/Pa · s, and the viscoelastic parameters were β = 2.50 ± 1.40, and τm = 7.43 ± 4.96 s, with the 2 moduli calculated to be E0 = 14.14 ± 6.44 kPa and E∞ = 6.08 ± 2.74 kPa. For the dilator tissue, the viscoelastic parameters were β = 2.06 ± 1.33 and τm = 1.28 ± 1.27 seconds, with the 2 moduli calculated to be E0 = 9.16 ± 3.03 kPa and E∞ = 5.54 ± 1.98 kPa.

Conclusions

We have established a new protocol to evaluate the biomechanical properties of the structural layers of the iris. Overall, the stroma was permeable and exhibited smaller moduli than those of the dilator muscle. An improved characterization of iris biomechanics may form the basis to further our understanding of angle closure glaucoma.

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.

In vivo biomechanical assessment of iridial deformations and muscle contractions in human eyes

The iris is a muscular organ whose deformations can cause primary angle-closure glaucoma (PACG), a leading cause of blindness. PACG risk assessment does not consider iridial biomechanical factors, despite their expected influence on iris deformations. Here, we exploited an existing biometric dataset consisting of near-infrared movies acquired during the pupillary light reflex (PLR) as a unique resource to study iris biomechanics. The PLR caused significant (greater than 100%) and essentially spatially uniform radial strains in the iris in vivo, consistent with previous findings. Inverse finite-element modelling showed that sphincter muscle tractions were ca fivefold greater than iridial stroma stiffness (range 4- to 13-fold, depending on sphincter muscle size). This muscle traction is greater than has been previously estimated, which may be due to methodological differences and/or to different patient populations in our study (European descent) versus previous studies (Asian); the latter possibility is of particular interest due to differential incidence rates of PACG in these populations. Our methodology is fast and inexpensive and may be a useful tool in understanding biomechanical factors contributing to PACG.

Numerical study of aqueous humor flow and iris deformation with pupillary block and the efficacy of laser peripheral iridotomy

BACKGROUND

Disclosing the mechanism of primary angle closure glaucoma with pupillary block is important to the diagnosis as well as treatments, such as the laser peripheral iridotomy. Comparing with abundant clinical researches, there have been fewer quantitative studies of the aqueous humor flows with synechia iris configurations, and the efficacy of laser peripheral iridotomy in treating glaucoma.

METHODS

Based on the mathematical models of aqueous humor flow and iris deformation, the flow fields were simulated by computational fluid dynamics with normal and synechia iris configurations (iris-lens gap of 30, 5 and 2 μm, respectively), and through one-way fluid-structure coupling technique the deformations of the iris under the flow field pressure were calculated by finite element analysis. The efficacy of glaucoma treatment with different orifice sizes was also investigated.

FINDINGS

Results show that the pressure difference between anterior and posterior chambers and iris deformation increase dramatically with the iris-lens gap distance less than 5 μm, and when further decreasing this gap may lead the iris touch the cornea causing angle closure glaucoma with noticeable iris bombé. Laser peripheral iridotomy simulation results show that iridotomy size of 0.2 mm can effectively decrease the pressure difference across the iris and relieve iris bombé.

INTERPRETATION

This is a biomechanical numerical study, and the results are reasonable compare to those of published works. It may shed additional light on the diagnosis and treatment of angle closure glaucoma with pupillary block.

Changes in Iris Stiffness and Permeability in Primary Angle Closure Glaucoma

Purpose

To evaluate the biomechanical properties of the iris by evaluating iris movement during pupil constriction and to compare such properties between healthy and primary angle-closure glaucoma (PACG) subjects.

Methods

A total of 140 subjects were recruited for this study. In a dark room, the anterior segments of one eye per subject were scanned using anterior segment optical coherence tomography imaging during induced pupil constriction with an external white light source of 1700 lux. Using a custom segmentation code, we automatically isolated the iris segments from the AS-OCT images, which were then discretized and transformed into a three-dimensional point cloud. For each iris, a finite element (FE) mesh was constructed from the point cloud, and an inverse FE simulation was performed to match the clinically observed iris constriction in the AS-OCT images. Through this optimization process, we were able to identify the elastic modulus and permeability of each iris.

Results

For all 140 subjects (95 healthy and 45 PACG of Indian/Chinese ethnicity; age 60.2 ± 8.7 for PACG subjects and 57.7 ± 10.1 for healthy subjects), the simulated deformation pattern of the iris during pupil constriction matched well with OCT images. We found that the iris stiffness was higher in PACG than in healthy controls (24.5 ± 8.4 kPa vs. 17.1 ± 6.6 kPa with 40 kPa of active stress specified in the sphincter region; P < 0.001), whereas iris permeability was lower (0.41 ± 0.2 mm2/kPa s vs. 0.55 ± 0.2 mm2/kPa s; p = 0.142).

Conclusions

This study suggests that the biomechanical properties of the iris in PACG are different from those in healthy controls. An improved understanding of the biomechanical behavior of the iris may have implications for the understanding and management of angle-closure glaucoma.

Indentation of the cornea: A Bi-layer contact problem

Histological observations of the cornea have identified the presence of multiple layers with differing thickness and function. The composition of the cornea consists primarily of collagen fibrils held together with proteoglycans but with an aqueous interstitial component being dominant. Indentation provides a means to quantify the spatial variation of the mechanical properties of the cornea, however the role of the different layers on the indentation response has barely been addressed. In addition, the response of the fluid content and its displacement during indentation has not been adequately considered. In this study indentation of the cornea with a relatively large spherical tipped indenter (R = 500 μm) is considered. It was observed that the initial phase of loading did not fit a classic Hertz elastic response but showed an initial steeper slope that gradually declines with increasing force and displacement. A relatively simple approach is developed that initially considers the cornea as a poro-elastic bi-layer contact problem, that is the presence of an outer thin stiffer Bowman's layer overlaying the thicker less stiff stroma.

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.

Iris stromal cell nuclei deform to more elongated shapes during pharmacologically-induced miosis and mydriasis

Nuclear shape alteration in ocular tissues, which can be used as a metric for overall cell deformation, may also lead to changes in gene expression and protein synthesis that could affect the biomechanics of the tissue extracellular matrix. The biomechanics of iris tissue is of particular interest in the study of primary angle-closure glaucoma. As the first step towards understanding the mutual role of the biomechanics and deformation of the iris on the activity of its constituent stromal cells, we conducted an ex-vivo study in freshly excised porcine eyes. Iris deformation was achieved by activating the constituent smooth muscles of the iris. Pupillary responses were initiated by inducing miosis and mydriasis, and the irides were placed in a fixative, bisected, and sliced into thin sections in a nasal and temporal horizontal orientation. The tissue sections were stained with DAPI for nucleus, and z-stacks were acquired using confocal microscopy. Images were analyzed to determine the nuclear aspect ratio (NAR) using both three-dimensional (3D) reconstructions of the nuclear surfaces as well as projections of the same 3D reconstruction into flat two-dimensional (2D) shapes. We observed that regardless of the calculation method (i.e., one that employed 3D surface reconstructions versus one that employed 2D projected images) the NAR increased in both the miosis group and the mydriasis group. Three-dimensional quantifications showed that NAR increased from 2.52 ± 0.96 in control group to 2.80 ± 0.81 and 2.74 ± 0.94 in the mydriasis and miosis groups, respectively. Notwithstanding the relative convenience in calculating the NAR using the 2D projected images, the 3D reconstructions were found to generate more physiologically realistic values and, thus, can be used in the development of future computational models to study primary angle-closure glaucoma. Since the iris undergoes large deformations in response to ambient light, this study suggests that the iris stromal cells are subjected to a biomechanically active micro-environment during their in-vivo physiological function.

Appropriate Objective Functions for Quantifying Iris Mechanical Properties Using Inverse Finite Element Modeling

Quantifying the mechanical properties of the iris is important, as it provides insight into the pathophysiology of glaucoma. Recent ex vivo studies have shown that the mechanical properties of the iris are different in glaucomatous eyes as compared to normal ones. Notwithstanding the importance of the ex vivo studies, such measurements are severely limited for diagnosis and preclude development of treatment strategies. With the advent of detailed imaging modalities, it is possible to determine the in vivo mechanical properties using inverse finite element (FE) modeling. An inverse modeling approach requires an appropriate objective function for reliable estimation of parameters. In the case of the iris, numerous measurements such as iris chord length (CL) and iris concavity (CV) are made routinely in clinical practice. In this study, we have evaluated five different objective functions chosen based on the iris biometrics (in the presence and absence of clinical measurement errors) to determine the appropriate criterion for inverse modeling. Our results showed that in the absence of experimental measurement error, a combination of iris CL and CV can be used as the objective function. However, with the addition of measurement errors, the objective functions that employ a large number of local displacement values provide more reliable outcomes.

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.

A simple basis for determination of the modulus and hydraulic conductivity of human ocular surface using nano-indentation

This paper presents a simple analysis based upon Darcy's Law and indentation contact mechanics to determine the effective hydraulic conductivity and elastic modulus of fluid filled tissues. The approach is illustrated with the mechanical response of the human ocular surface using a 500μm radius spherical tipped indenter. Indentations of various regions of the ocular surface including the corneal stroma, limbal region and sclera have been conducted. Force-control indentations were made to a maximum force, which was maintained before unloading. Measurements of the indentation response of cornea at three different loading rates were also made. Elastic like response was observed during loading, which was followed by extensive creep prior to unloading.

STATEMENT OF SIGNIFICANCE

This manuscript attempts to provide a relatively simply model for the contact loading of fluid containing tissues and materials. It shows that the response of such materials provides a basis for determining the effective modulus and effective hydraulic conductivity (permeability) in much the same manner that hardness and modulus do for the indentation of elastic-plastic materials. Eye tissue with its anisotropic elastic and permeability properties is used to illustrate the approach.

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.

Translating ocular biomechanics into clinical practice: current state and future prospects

Biomechanics is the study of the relationship between forces and function in living organisms and is thought to play a critical role in a significant number of ophthalmic disorders. This is not surprising, as the eye is a pressure vessel that requires a delicate balance of forces to maintain its homeostasis. Over the past few decades, basic science research in ophthalmology mostly confirmed that ocular biomechanics could explain in part the mechanisms involved in almost all major ophthalmic disorders such as optic nerve head neuropathies, angle closure, ametropia, presbyopia, cataract, corneal pathologies, retinal detachment and macular degeneration. Translational biomechanics in ophthalmology, however, is still in its infancy. It is believed that its use could make significant advances in diagnosis and treatment. Several translational biomechanics strategies are already emerging, such as corneal stiffening for the treatment of keratoconus, and more are likely to follow. This review aims to cultivate the idea that biomechanics plays a major role in ophthalmology and that the clinical translation, lead by collaborative teams of clinicians and biomedical engineers, will benefit our patients. Specifically, recent advances and future prospects in corneal, iris, trabecular meshwork, crystalline lens, scleral and lamina cribrosa biomechanics are discussed.

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

BACKGROUND

Understanding the mechanical properties of the iris can help to have an insight into the eye diseases with abnormalities of the iris morphology. Material parameters of the iris were simply calculated relying on the ex vivo experiment. However, the mechanical response of the iris in vivo is different from that ex vivo, therefore, a method was put forward to determine the material parameters of the iris using the optimization method in combination with the finite element method based on the in vivo experiment.

MATERIAL AND METHODS

Ocular hypertension was induced by rapid perfusion to the anterior chamber, during perfusion intraocular pressures in the anterior and posterior chamber were record by sensors, images of the anterior segment were captured by the ultrasonic system. The displacement of the characteristic points on the surface of the iris was calculated. A finite element model of the anterior chamber was developed using the ultrasonic image before perfusion, the multi-island genetic algorithm was employed to determine the material parameters of the iris by minimizing the difference between the finite element simulation and the experimental measurements.

RESULTS

Material parameters of the iris in vivo were identified as the iris was taken as a nearly incompressible second-order Ogden solid. Values of the parameters μ1, α1, μ2 and α2 were 0.0861 ± 0.0080 MPa, 54.2546 ± 12.7180, 0.0754 ± 0.0200 MPa, and 48.0716 ± 15.7796 respectively. The stability of the inverse finite element method was verified, the sensitivity of the model parameters was investigated.

CONCLUSION

Material properties of the iris in vivo could be determined using the multi-island genetic algorithm coupled with the finite element method based on the experiment.

Anterior and posterior corneal stroma elasticity assessed using nanoindentation

Corneal biomechanics is an essential parameter for developing diagnostic and treatment methods of corneal-related diseases. It is widely accepted that corneal mechanical strength stems from the stroma's collagenous composition. However, more comprehensive insight into the mechanical properties within the stroma is needed to improve current corneal diagnostic and treatment techniques. The purpose of this study was to perform elasticity characterization of anterior and posterior stromal regions of human corneas using atomic force microscopy (AFM). Nine pairs of human whole globes were placed in 20% Dextran solution, cornea side down, to restore the corneal thickness to physiological levels (400-600 μm). The epithelium and Bowman's membrane were removed from all eyes. Anterior stromal AFM elasticity testing was then performed on left (OS) eyes. Additional stroma was removed from right (OD) eyes to allow posterior stromal measurements at a depth of 50% of the original thickness. All experiments were performed with corneas submerged in 15% Dextran to maintain corneal hydration. The results of the study showed that the Young's modulus of elasticity of the anterior stroma (average: 281 ± 214 kPa; range: 59-764 kPa) was significantly higher than that of the posterior stroma (average: 89.5 ± 46.1 kPa; range: 29-179 kPa) (p = 0.014). In addition, a linear relationship was found between the posterior stromal elasticity and anterior stromal elasticity (p = 0.0428). On average, the elasticity of the posterior stroma is 39.3% of the anterior stroma. In summary, there appears to be an elasticity gradient within the corneal stroma, which should be considered in the design and development of corneal diagnostic and treatment methods to enhance efficacy.

Increased iris-lens contact following spontaneous blinking: mathematical modeling

The purpose of this work was to study in silico how iris root rotation due to spontaneous blinking alters the iris contour. An axisymmetric finite-element model of the anterior segment was developed that included changes in the iris contour and the aqueous humor flow. The model geometry was based on average values of ocular dimensions. Blinking was modeled by rotating the iris root posteriorly and returning it back to the anterior. Simulations with maximum rotations of 2°, 4°, 6°, and 8° were performed. The iris-lens contact distance and the pressure difference between the posterior and anterior chambers were calculated. When the peak iris root rotation was 2°, the maximum iris-lens contact increased gradually from 0.28 to 0.34mm within eight blinks. When the iris root was rotated by 6° and 8°, the pressure difference between the posterior and anterior chambers dropped from a positive value (1.23Pa) to negative values (-0.86 and -1.93Pa) indicating the presence of reverse pupillary block. Apparent iris-lens contact increased with steady blinking, and the increase became more pronounced as posterior rotation increased. We conclude that repeated iris root rotation caused by blinking could maintain the iris in a posterior position under normal circumstances, which would then lead to the clinically observed anterior drift of the iris when blinking is prevented.

The posterior location of the dilator muscle induces anterior iris bowing during dilation, even in the absence of pupillary block

PURPOSE

To examine the effect of the posterior location of the dilator on iris anterior curvature during dilation.

METHODS

An in vivo human study, an ex vivo porcine experiment, and an in silico computational model were performed in parallel. Iris anterior curvature was measured in vivo before and after dilation by time-domain slit lamp optical coherence tomography (SL-OCT). All patients (n = 7) had undergone laser peripheral iridotomy to eliminate any pupillary block due to primary angle-closure glaucoma. In the ex vivo experiments, isolated porcine irides (n = 30) were secured at the periphery and immersed in an oxygenated Krebs-Ringer buffer. Dilation was induced pharmaceutically by the addition of 2.5% phenylephrine and 1% tropicamide. An in-house optical coherence tomography (OCT) system was used to obtain iris images before and after dilation. A finite element model was also developed based on typical geometry of the iris from the initial OCT image. The iris was modeled as a neo-Hookean solid, and the active muscle component was applied only to the region specified as the dilator.

RESULTS

An increase in curvature and a decrease in chord length after dilation were observed in both experiments. In both the in vivo and ex vivo experiments, the curvature-to-chord length ratio increased significantly during dilation. Computer simulations agreed well with the experimental results only when the proper anatomic position of dilator was used.

CONCLUSIONS

The posterior location of the dilator contributes to the anterior iris bowing via a nonpupillary block dependent mechanism.