A combination of the finite element analysis and experimental indentation via the cornea

Segmental biomechanics of the normal and glaucomatous human aqueous outflow pathway

The conventional aqueous outflow pathway, encompassing the trabecular meshwork (TM), juxtacanalicular connective tissue (JCT), and inner wall endothelium of Schlemm's canal (SC), governs intraocular pressure (IOP) regulation. This study targets the biomechanics of low-flow (LF) and high-flow (HF) regions within the aqueous humor outflow pathway in normal and glaucomatous human donor eyes, using a combined experimental and computational approach. LF and HF TM/JCT/SC complex tissues from normal and glaucomatous eyes underwent uniaxial tensile testing. Dynamic motion of the TM/JCT/SC complex was recorded using customized green-light optical coherence tomography during SC pressurization in cannulated anterior segment wedges. A hyperviscoelastic model quantified TM/JCT/SC complex properties. A fluid-structure interaction model simulated tissue-aqueous humor interaction. FluoSpheres were introduced into the pathway via negative pressure in the SC, with their motion tracked using two-photon excitation microscopy. Tensile test results revealed that the elastic moduli of the LF and HF regions in glaucomatous eyes are 3.5- and 1.5-fold stiffer than the normal eyes, respectively. The FE results also showed significantly larger shear moduli in the TM, JCT, and SC of the glaucomatous eyes compared to the normal subjects. The LF regions in normal eyes demonstrated larger elastic moduli compared to the HF regions in glaucomatous eyes. The resultant strain in the outflow tissues and velocity of the aqueous humor in the FSI models were in good agreement with the digital volume correlation and 3D particle image velocimetry data, respectively. This study uncovers stiffer biomechanical responses in glaucomatous eyes, with LF regions stiffer than HF regions in both normal and glaucomatous eyes. STATEMENT OF SIGNIFICANCE: This study delves into the biomechanics of the conventional aqueous outflow pathway, a crucial regulator of intraocular pressure and ocular health. By analyzing mechanical differences in low-flow and high-flow regions of normal and glaucomatous eyes, this research unveils the stiffer response in glaucomatous eyes. The distinction between regions' properties offers insights into aqueous humor outflow regulation, while the integration of experimental and computational methods enhances credibility. These findings have potential implications for disease management and present a vital step toward innovative ophthalmic interventions. This study advances our understanding of glaucoma's biomechanical basis and its broader impact on ocular health.

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.

Computational Modeling of Ophthalmic Procedures: Computational Modeling of Ophthalmic Procedures

PURPOSE

To explore how finite-element calculations can continue to contribute to diverse problems in ophthalmology and vision science, we describe our recent work on modeling the force on the peripheral retina in intravitreal injections and how that force increases with shorter, smaller gauge needles. We also present a calculation that determines the location and stress on a retinal pigment epithelial detachment during an intravitreal injection, the possibility that stress induced by the injection can lead to a tear of the retinal pigment epithelium.

BACKGROUND

Advanced computational models can provide a critical insight into the underlying physics in many surgical procedures, which may not be intuitive.

METHODS

The simulations were implemented using COMSOL Multiphysics. We compared the monkey retinal adhesive force of 18 Pa with the results of this study to quantify the maximum retinal stress that occurs during intravitreal injections.

CONCLUSIONS

Currently used 30-gauge needles produce stress on the retina during intravitreal injections that is only slightly below the limit that can create retinal tears. As retina specialists attempt to use smaller needles, the risk of complications may increase. In addition, we find that during an intravitreal injection, the stress on the retina in a pigment epithelial detachment occurs at the edge of the detachment (found clinically), and the stress is sufficient to tear the retina. These findings may guide physicians in future clinical research. NOTE: Publication of this article is sponsored by the American Ophthalmological Society.

Ocular biomechanics during improvised explosive device blast: A computational study using eye-specific models

BACKGROUND

Eye injuries comprise 10-13% of civilian improvised explosive device (IED) injuries. The bomb blast wave induces a normal and shear forces on the tissues, causing a large acute IOP elevation. This study calculated the biomechanical stresses and strains in the eye due to IED explosion via eye-specific fluid-structure interaction (FSI) models.

METHODS

Blast occurred at 2, 3, and 4 m from the front and side of the victim and the weights of the IED were 1 and 2 kg. The ground was covered with the deformable soil to mimic the realistic IED explosion condition and reflect the blast wave.

RESULTS

The IOP elevation of ∼6,000-48,000 mmHg was observed in the eyes while the highest IOP was occurred with the IED weight and distance of 2 kg and 2 m (front) and the lowest was occurred with the IED weight and distance of 1 kg and 4 m (side). Our findings suggest the importance of the victim location and orientation concerning the blast wave when it comes to ocular injury assessment. IOP elevation of ∼2900 and ∼2700 mmHg were observed in ∼1.6 ms after the blast for the IEDS weight of 2 kg and a victim distance of 2 m in front and side blasts, respectively, in consistence with the literature. Nonetheless, IOPs were considerably higher after ∼1.6 ms due to the merging of the bomb blast wave and its reflection off the ground.

CONCLUSIONS

The stresses and strains were highest for the frontal blast. Both side and frontal blasts caused higher stresses and strains at the rectus muscle insertions where the sclera is thinnest and prone to rupture. Blast angle has no considerable role in the resultant IOP. Front blast with a heavier IED resulted a higher stresses and deformations in the eye connective tissues compared to the side blast.

Trabecular Meshwork Motion Profile from Pulsatile Pressure Transients: A New Platform to Simulate Transitory Responses in Humans and Nonhuman Primates

Trabecular meshwork (TM) motion abnormality is the leading cause of glaucoma. With technique limitations, how TM moves is still an enigma. This study describes a new laboratory platform to investigate TM motion responses to ocular transients in ex vivo eyes. The anterior segments of human cadaver and primate eyes were mounted in a perfusion system fitting. Perfusion needles were placed to establish mean baseline pressure. A perfusion pump was connected to the posterior chamber and generated an immediate transient pressure elevation. A phase-sensitive optical coherent tomography system imaged and quantified the TM motion. The peak-to-peak TM displacements (ppTMD) were determined, a tissue relaxation curve derived, and a time constant obtained. This study showed that the ppTMD increased with a rise in the pulse amplitude. The ppTMD was highest for the lowest mean pressure of 16 mmHg and decreased with mean pressure increase. The pulse frequency did not significantly change ppTMD. With a fixed pulse amplitude, an increase in mean pressure significantly reduced the time constant of recoil from maximum distension. Our research platform permitted quantitation of TM motion responses to designed pulse transients. Our findings may improve the interpretation of new TM motion measurements in clinic, aiding in understanding mechanisms and management.

Ocular biomechanics due to ground blast reinforcement

BACKGROUND AND OBJECTIVE

Bomb blast injuries exerts a shearing force on the air-tissue interfaces, causing devastating ocular injury from the blast wave. Improvised explosive devices (IEDs) are usually placed at different heights from the ground to induce more severe injury through ground blast reinforcement (GBR). However, there is still a lack of knowledge of the role of GBR and IED height from the ground on ocular biomechanics, and how they can affect the intraocular pressure (IOP) in the eye. This study aimed to estimate the IOP due to frontal IED explosion at different heights from the ground using a fluid-structure interaction model with and without GBR effects.

METHODS

A 2 kg IED was placed within 5 m of the victim at 5 different heights from the ground, including 0, 0.42, 0.85, 1.27, and 1.70 m. Two different blast formulations were used to simulate the IED explosion: (a) spherical airburst, with no amplification of the initial shock wave due to interaction with the ground-surface, and (b) hemispherical surface-burst, where the initial blast wave is immediately reflected and reinforced by the ground (GBR).

RESULTS

Results revealed that the blast wave due to GBR reaches to the skull prior to the IED blast itself. The GBR also reached to the skull ∼ 0.6 ms earlier when the IED was on the ground compared to the height of 1.70 m. The highest and lowest IOPs of ∼ 17,000 and ∼ 15,000 mmHg were observed at the IED heights of 1.70 and 0 m from the ground considering GBR. However, when the role of the GBR is ignored, IOP of ∼ 9,000 mmHg was observed regardless of the IED height from the ground. The deformation in the apex of the cornea was higher when considering the GBR (∼ 0.75 cm) versus no GBR (∼ 0.65 cm). Considering GBR led to higher stresses and strains in the sclera.

CONCLUSIONS

When the role of GBR was ignored, the results showed similar patterns and magnitudes of stresses and deformations in the skull and eye regardless of the height of the IED from the ground, which was not the case when GBR was considered. The findings of this study suggest the critical role of GBR in ocular blast simulations.

Effective elastic modulus of an intact cornea related to indentation behavior: A comparison between the Hertz model and Johnson-Kendall-Roberts model

In this study, a macro-indentation test on the submillimeter scale was performed to analyze the indentation behavior of an intact cornea under physiological pressures. The Hertz and Johnson-Kendall-Roberts (JKR) models were employed to solve the elastic modulus (E) of the intact cornea. The relevant detailed analysis showed that the JKR model, which accounted for the contribution from the adhesion energy, could be used to obtain the E values that were more than two-folds of those obtained from the Hertz model, which only considered the external force. Compared with the uniaxial tension test in vitro, unlike the elastic Hertz-model, the E values under physiological pressures that were obtained with the JKR model were between the lower and upper limits of corneal material. This phenomenon indicated that the JKR model could be used to obtain reasonably effective E values of an intact cornea under physiological pressures.

Analysis of the effects of finite element type within a 3D biomechanical model of a human optic nerve head and posterior pole

BACKGROUND AND OBJECTIVE

Biomechanical stresses and strains can be simulated in the optic nerve head (ONH) using the finite element (FE) method, and various element types have been used. This study aims to investigate the effects of element type on the resulting ONH stresses and strains.

METHODS

A single eye-specific model was constructed using 3D delineations of anatomic surfaces in a high-resolution, fluorescent, 3D reconstruction of a human posterior eye, then meshed using our simple meshing algorithm at various densities using 4- and 10-noded tetrahedral elements, as well as 8- and 20-noded hexahedral elements. A mesh-free approach was used to assign heterogeneous, anisotropic, hyperelastic material properties to the lamina cribrosa, sclera and pia. The models were subjected to elevated IOP of 45 mmHg after pre-stressing from 0 to 10 mmHg, and solved in the open-source FE package Calculix; results were then interpreted in relation to computational time and simulation accuracy, using the quadratic hexahedral model as the reference standard.

RESULTS

The 10-noded tetrahedral and 20R-noded hexahedral elements exhibited similar scleral canal and laminar deformations, as well as laminar and scleral stress and strain distributions; the quadratic tetrahedral models ran significantly faster than the quadratic hexahedral models. The linear tetrahedral and hexahedral elements were stiffer compared to the quadratic element types, yielding much lower stresses and strains in the lamina cribrosa.

CONCLUSIONS

Prior studies have shown that 20-noded hexahedral elements yield the most accurate results in complex models. Results show that 10-noded tetrahedral elements yield very similar results to 20-noded hexahedral elements and so they can be used interchangeably, with significantly lower computational time. Linear element types did not yield acceptable results.

Accommodative tissues influence the shape of the cornea and potentially drive corneal morphogenesis

This study investigates whether the presence of accommodative tissues biomechanically influences the shape of the cornea and potentially drives corneal morphogenesis during embryonic ocular development. Porcine eyes were subjected to an internal pressure simulating intraocular pressure. Ocular geometry was evaluated using a corneal topographer and digital cameras before and after dissection of the accommodative tissues. A computational model of the porcine eye was constructed and loaded by an internal pressure representing intraocular pressure. Eye shape was evaluated in models with and without the ciliary body. The porcine model was generalized to the human model, simplified model, or embryonic model with different ocular tissue shapes, sizes, and stiffnesses. Experimental data showed that, even in the six-month-old pig eye, the average corneal radius of curvature increased after the removal of accommodative tissues compared to sham controls (p = 0.002). Computational results agreed with the experimental data and further suggested that the change in corneal radius is greater when the tissue stiffness is low and the intraocular pressure is high, regardless of the geometry and size of the eye components. Using a combined in vitro and in silico approach, this study explores the biomechanical influence of the accommodative tissues and related loads on the cornea and offers additional factors that might influence the shape of the cornea.

Influence of polydimethylsiloxane substrate stiffness on corneal epithelial cells

Many cell types are known to modulate their behaviour in response to changes in material stiffness; however, little is known about how stiffness affects corneal epithelial cells. This study aims to investigate the response of a corneal epithelial cell line to polydimethylsiloxane (PDMS) substrates with a range of Young's moduli from 10 to 1500 kPa. Cellular morphology, proliferation, differentiation and mechanobiology were examined. Cells grown on PDMS adopted the typical cobblestone morphology exhibited by the corneal epithelium. Proliferative markers pERK and Ki67 were higher in cells cultured on stiffer substrates compared with those on softer substrates. Material stiffness was also found to influence the cell phenotype with cells on stiffer substrates having higher cytokeratin 3 gene expression, a mature epithelial marker, while cells on softer substrates expressed more cytokeratin 14, a basal epithelial marker. Cells grown on softer substrates also displayed higher levels of focal adhesions and intermediate filaments compared with cells on stiff substrates. This research will aid in designing novel biomaterials for the culture and transplantation of corneal epithelial cells.