Inflation experiments and inverse finite element modelling of posterior human sclera

A simple computational model for scleral stiffness assessments via air-puff deformation OCT

Introduction: The mechanical properties of the sclera are related to its structural function, and changes to these properties are believed to contribute to pathologies such as myopia. Air-puff deformation imaging is a tool that uses an imaging system coupled with an air-puff excitation source to induce and measure deformation in a tissue in vivo. Typically used for the study of the cornea's mechanical properties and IOP, this tool has been proposed as a method to evaluate scleral stiffness. Methods: In this work, we present a computational model of the rabbit eye to assess scleral deformation under air-puff. Parametric studies were conducted to evaluate the effects of material properties, intraocular pressure, and other parameters on the deformation response. Output from the model was also compared to experimental measurements of air-puff deformation in rabbit eyes under varying IOP. Results: Central deformation response was found to be most influenced by material properties of the sclera (at site of air-puff and posterior), thickness, and IOP, whereas deformation profile was most influenced by material properties. Experimental and simulated IOP dependence were found to be similar (RMSE = 0.13 mm). Discussion: Scleral APDI could be a useful tool for quick in vivo assessment of scleral stiffness.

The Effect of Scleral Buckle Surgery on Tonographic Outflow Facility, Positional Intraocular Pressure, and Ocular Biomechanics

PURPOSE

To investigate the in vivo effect of scleral buckle surgery on ocular biomechanics and aqueous humor dynamics.

DESIGN

Prospective observational cross-sectional study.

PARTICIPANTS

Nine patients with unilateral 360 degree encircling scleral buckles without vitrectomy for rhegmatogenous retinal detachments, between 3 and 39 months postoperative.

METHODS

All measurements were performed in both eyes of all participants. Intraocular pressure (IOP) was measured in the seated and supine positions using pneumatonometry. Outflow facility was measured using 2-minute weighted pneumatonography. Ocular rigidity coefficient was determined from the Friedenwald equations based on the difference in IOP with and without a weighted tonometer tip. The percentage change in IOP upon transitioning from seated to supine was calculated. Measurements for buckled and nonbuckled eyes were compared using paired Student t test of means.

MAIN OUTCOME MEASURES

Sitting and supine IOP and percentage difference between the 2 positions; outflow facility; ocular rigidity coefficient.

RESULTS

Seated IOP was similar between buckled and nonbuckled eyes (16.1 ± 2.5 vs. 16.7 ± 2.7 mmHg; P = 0.5) whereas supine IOP was lower in buckled eyes compared with nonbuckled eyes (18.7 ± 2.6 vs. 21.3 ± 2.5 mmHg; P = 0.008). The percentage increase in IOP upon change in body position from seated to supine was greater in nonbuckled eyes (17.4 ± 9.4% vs. 27.6 ± 9.5%; P = 0.005). Ocular rigidity coefficient was lower in buckled (9.9 × 10-3 ± 1.4 × 10-3 μL-1) vs. nonbuckled eyes (14.4 × 10-3 ± 3.1 × 10-3 μL-1; P = 0.006). Outflow facility was not significantly different in buckled and nonbuckled eyes.

CONCLUSIONS

Scleral buckling decreases ocular rigidity but does not affect outflow facility. This change in ocular biomechanics likely results in the attenuated IOP change from seated to supine position. Decreased ocular rigidity may also reduce IOP fluctuations and potentially reduce the risk for glaucoma progression.

FINANCIAL DISCLOSURE(S)

Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Typical localised element-specific finite element anterior eye model

Purpose

The study presents an averaged anterior eye geometry model combined with a localised material model that is straightforward, appropriate and amenable for implementation in finite element (FE) modelling.

Methods

Both right and left eye profile data of 118 subjects (63 females and 55 males) aged 22-67 years (38.5 ± 7.6) were used to build an averaged geometry model. Parametric representation of the averaged geometry model was achieved through two polynomials dividing the eye into three smoothly connected volumes. This study utilised the collagen microstructure x-ray data of 6 ex-vivo healthy human eyes, 3 right eyes and 3 left eyes in pairs from 3 donors, 1 male and 2 females aged between 60 and 80 years, to build a localised element-specific material model for the eye.

Results

Fitting the cornea and the posterior sclera sections to a 5th-order Zernike polynomial resulted in 21 coefficients. The averaged anterior eye geometry model recorded a limbus tangent angle of 37° at a radius of 6.6 mm from the corneal apex. In terms of material models, the difference between the stresses generated in the inflation simulation up to 15 mmHg in the ring-segmented material model and localised element-specific material model were significantly different (p < 0.001) with the ring-segmented material model recording average Von-Mises stress 0.0168 ± 0.0046 MPa and the localised element-specific material model recording average Von-Mises stress 0.0144 ± 0.0025 MPa.

Conclusions

The study illustrates an averaged geometry model of the anterior human eye that is easy to generate through two parametric equations. This model is combined with a localised material model that can be used either parametrically through a Zernike fitted polynomial or non-parametrically as a function of the azimuth angle and the elevation angle of the eye globe. Both averaged geometry and localised material models were built in a way that makes them easy to implement in FE analysis without additional computation cost compared to the limbal discontinuity so-called idealised eye geometry model or ring-segmented material model.

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.

Real-time imaging of optic nerve head collagen microstructure and biomechanics using instant polarized light microscopy

Current tools lack the temporal or spatial resolution necessary to image many important aspects of the architecture and dynamics of the optic nerve head (ONH). We evaluated the potential of instant polarized light microscopy (IPOL) to overcome these limitations by leveraging the ability to capture collagen fiber orientation and density in a single image. Coronal sections through the ONH of fresh normal sheep eyes were imaged using IPOL while they were stretched using custom uniaxial or biaxial micro-stretch devices. IPOL allows identifying ONH collagen architectural details, such as fiber interweaving and crimp, and has high temporal resolution, limited only by the frame rate of the camera. Local collagen fiber orientations and deformations were quantified using color analysis and image tracking techniques. We quantified stretch-induced collagen uncrimping of lamina cribrosa (LC) and peripapillary sclera (PPS), and changes in LC pore size (area) and shape (convexity and aspect ratio). The simultaneous high spatial and temporal resolutions of IPOL revealed complex ONH biomechanics: i) stretch-induced local deformation of the PPS was nonlinear and nonaffine. ii) under load the crimped collagen fibers in the PPS and LC straightened, without torsion and with only small rotations. iii) stretch-induced LC pore deformation was anisotropic and heterogeneous among pores. Overall, with stretch the pores were became larger, more convex, and more circular. We have demonstrated that IPOL reveals details of collagen morphology and mechanics under dynamic loading previously out of reach. IPOL can detect stretch-induced collagen uncrimping and other elements of the tissue nonlinear mechanical behavior. IPOL showed changes in pore morphology and collagen architecture that will help improve understanding of how LC tissue responds to load.

Biomechanical properties of retina and choroid: a comprehensive review of techniques and translational relevance

Studying the biomechanical properties of biological tissue is crucial to improve our understanding of disease pathogenesis. The biomechanical characteristics of the cornea, sclera and the optic nerve head have been well addressed with an extensive literature and an in-depth understanding of their significance whilst, in comparison, knowledge of the retina and choroid is relatively limited. Knowledge of these tissues is important not only to clarify the underlying pathogenesis of a wide variety of retinal and vitreoretinal diseases, including age-related macular degeneration, hereditary retinal dystrophies and vitreoretinal interface diseases but also to optimise the surgical handling of retinal tissues and, potentially, the design and properties of implantable retinal prostheses and subretinal therapies. Our aim with this article is to comprehensively review existing knowledge of the biomechanical properties of retina, internal limiting membrane (ILM) and the Bruch’s membrane–choroidal complex (BMCC), highlighting the potential implications for clinical and surgical practice. Prior to this we review the testing methodologies that have been used both in vitro, and those starting to be used in vivo to aid understanding of their results and significance.

Compressive behaviour of soft contact lenses and its effect on refractive power on the eye and handling off the eye

PURPOSE

To investigate the stress-strain behaviour of 9 soft contact lens materials, that are commonly used in the market, under uniaxial compression loading.

METHODS

Seven types of hydrogel and two types of silicone-hydrogel soft contact lens materials were hydrated in phosphate-buffered saline (PBS) solution then subjected to uniaxial compression loads. The load rate was set to 16.0 N/min starting with two consecutive initial 5.0 N loading cycles followed by three relaxation periods of 4.0 min within which there were two more 5.0 N loading cycles and eventually, a full loading cycle that stopped at a load of 49.0 N. The load and contraction data obtained experimentally were analysed to derive the stress-strain behaviour. Finite Element (FE) analysis was then utilised to evaluate the performance of soft contact lenses on the human eye and handling lenses off the eye.

RESULTS

Unlike tensile tests, all tested materials showed nonlinear behaviour when tested under compression. When fitted to first-order Ogden hyperelastic model, parameter μ was found to be varying in the range 0.12 to 0.74 MPa and material parameter α was found to be varying in the range 8.2 to 20.326 among the nine tested materials. Compression modulus of elasticity was 2.2 times higher than the tensile modulus of elasticity on average. FE simulation with nonlinear Ogden constitutive model showed a limited change (8%~12%) in the optical performance when compared to other material models, however, it predicted higher stress when the lens was simulated under bending during off-eye handling.

CONCLUSIONS

Compression tests revealed slightly nonlinear behaviour when materials were strained under compression stress down to 15% ~ 30% of their nominal heights. Considering the physiological compression loading range of 8 mmHg, secant moduli of elasticity were 1.5% to 6.9% higher than the tension moduli of elasticity depending on the material. Tensile-based moduli of elasticity could be used in FE analysis as a step towards simulating the optical performance of soft contact lenses on-eye. However, nonlinear compression-based material models are recommended for FE analysis of soft contact lenses when lens-handling is investigated off-eye.

Viscoelastic characteristics of the canine cranial cruciate ligament complex at slow strain rates

Ligaments including the cruciate ligaments support and transfer loads between bones applied to the knee joint organ. The functions of these ligaments can get compromised due to changes to their viscoelastic material properties. Currently there are discrepancies in the literature on the viscoelastic characteristics of knee ligaments which are thought to be due to tissue variability and different testing protocols.

The aim of this study was to characterise the viscoelastic properties of healthy cranial cruciate ligaments (CCLs), from the canine knee (stifle) joint, with a focus on the toe region of the stress-strain properties where any alterations in the extracellular matrix which would affect viscoelastic properties would be seen. Six paired CCLs, from skeletally mature and disease-free Staffordshire bull terrier stifle joints were retrieved as a femur-CCL-tibia complex and mechanically tested under uniaxial cyclic loading up to 10 N at three strain rates, namely 0.1%, 1% and 10%/min, to assess the viscoelastic property of strain rate dependency. The effect of strain history was also investigated by subjecting contralateral CCLs to an ascending (0.1%, 1% and 10%/min) or descending (10%, 1% and 0.1%/min) strain rate protocol. The differences between strain rates were not statistically significant. However, hysteresis and recovery of ligament lengths showed some dependency on strain rate. Only hysteresis was affected by the test protocol and lower strain rates resulted in higher hysteresis and lower recovery. These findings could be explained by the slow process of uncrimping of collagen fibres and the contribution of proteoglycans in the ligament extracellular matrix to intra-fibrillar gliding, which results in more tissue elongations and higher energy dissipation. This study further expands our understanding of canine CCL behaviour, providing data for material models of femur-CCL-tibia complexes, and demonstrating the challenges for engineering complex biomaterials such as knee joint ligaments.

Which feature influences on-eye power change of soft toric contact lenses: Design or corneal shape?

PURPOSE

This study investigates how both the peripheral zone design and corneal shape affect the behaviour of soft contact lenses on-eye.

METHODS

In this study, soft contact lenses of varying nominal cylindrical powers and peripheral zone designs-a single-prism gravity-based stabilised lens (G1P), two-prism blink-based stabilised lens (B2P) and four-prism blink-based stabilised lens (B4P)-were generated as finite element models. The on-eye simulation results were analysed to identify the impact of each peripheral zone design (Each with different volume ratios) on the effective power change (EPC) when worn by a subject. Topographies of three eyes of varying average simulated anterior corneal curvature (flat, average & steep) were used in this study.

RESULTS

The volume of the lens's peripheral zone as a ratio of the total lens volume (Vp) recorded very weak correlations with the effective power change (EPC) among the three investigated designs when they were fitted to the flat eye (R = -0.19, -0.15 & -0.22 respectively), moderate correlations with the average eye (R = 0.42, 0.43 & 0.43 respectively) and strong correlations with the steep eye (R = 0.91, 0.9 & 0.9 respectively). No significant differences were noticed among the three investigated designs and none of the cylindrical lenses designed with axis 90° recorded EPC values outside the acceptance criteria range (ACR) of ±0.25 D. No significant differences in EPC were recorded among the three designs G1P, B2P and B4P (p>0.6) when they were designed with three axes at 90°, 45° and 0°. Moving the toric lens axis away from 90° dragged the EPC to the negative side and most of the investigated lenses with axes at 45° and 0° recorded EPCs outside the ±0.25D range.

CONCLUSIONS

In all cases, the shape of the cornea had a more dominant effect on EPC when compared to the peripheral zone design. Corneal shape influences the soft toric contact lens's on-eye power change more than the lens design.

Limbus misrepresentation in parametric eye models

Purpose

To assess the axial, radial and tangential limbus position misrepresentation when parametric models are used to represent the cornea and the sclera.

Methods

This retrospective study included 135 subjects aged 22 to 65 years (36.5 mean ±9.8 STD), 71 females and 64 males. Topography measurements were taken using an Eye Surface Profiler topographer and processed by a custom-built MATLAB code. Eye surfaces were freed from edge-effect artefacts and fitted to spherical, conic and biconic models.

Results

When comparing the radial position of the limbus, average errors of -0.83±0.19mm, -0.76±0.20mm and -0.69±0.20mm were observed within the right eye population for the spherical, conic and biconic models fitted up to 5mm. For the same fitting radius, the average fitting errors were -0.86±0.23mm, -0.78±0.23mm and -0.73±0.23mm for the spherical, conic and biconic models respectively within the left eye population. For the whole cornea fit, the average errors were -0.27±0.12mm and -0.28±0.13mm for the spherical models, -0.02±0.29mm and -0.05±0.27mm for the conic models, and -0.22±0.16mm and 0.24±0.17mm for the biconic models in the right and left eye populations respectively.

Conclusions

Through the use of spherical, conic and biconic parametric modelling methods, the eye’s limbus is being mislocated. Additionally, it is evident that the magnitude of fitting error associated with the sclera may be propagating through the other components of the eye. This suggests that a corneal nonparametric model may be necessary to improve the representation of the limbus.