Use and Misuse of Laplace's Law in Ophthalmology

Biomechanical changes of tree shrew posterior sclera during experimental myopia, after retrobulbar vehicle injections, and crosslinking using genipin

Myopia is a common ocular condition characterized by biomechanical weakening revealed by increasing creep rate, cyclic softening scleral thinning, change of collagen fibril crimping, and excessive elongation of the posterior sclera resulting in blurred vision. Animal studies support scleral crosslinking as a potential treatment for myopia control by strengthening the weakened sclera and slowing scleral expansion. While multiple studies investigated aspects of the biomechanical weakening and strengthening effects in myopia and after scleral crosslinking, a comprehensive analysis of the underlying mechanical changes including the effect of vehicle injections is still missing. The purpose of this study was to provide a comprehensive analysis of biomechanical changes by scleral inflation testing in experimental myopia, after retrobulbar vehicle injections and scleral crosslinking using genipin in tree shrews. Our results suggest that biomechanical weakening in myopia involves an increased creep rate and higher strain levels at which collagen fibers uncrimp. Both weakening effects were reduced after scleral crosslinking using genipin at doses that were effective in slowing myopia progression. Vehicle injections increased mechanical hysteresis and had a small but significant effect on slowing myopia progression. Also, our results support scleral crosslinking as a potential treatment modality that can prevent or counteract scleral weakening effects in myopia. Furthermore, vehicle solutions may cause independent biomechanical effects, which should be considered when developing and evaluating scleral crosslinking procedures.

Anterior Chamber Air Bubble Dynamics With Decreases in Atmospheric Pressure

PURPOSE

To evaluate the effect of decreasing barometric pressure on intracameral bubble size and intraocular pressure (IOP) in eyes with varying air fills in the anterior chamber.

METHODS

A total of 36 human donor eyes received 30%, 50%, or 90% anterior chamber air fill. The eyes were subjected to decreases in atmospheric pressure down to 750 hPa, equal to 2400 m in altitude, and were repeatedly imaged using anterior segment OCT while IOP was measured continuously.

RESULTS

Eyes with 30% air fill initially showed moderate increases in IOP yet rising to an average of 30.83 mm Hg at 850 hPa (mimicking 1400 m altitude) and 42.08 mm Hg at 750 hPa. Eyes with larger air bubbles showed more acute increases in IOP with increases to an average of 47.25 mm Hg in eyes with 50% air fill at 850 hPa and 63.33 mm Hg at 750 hPa. In eyes with 90% air fill in the anterior chamber, IOP readings with an average of 113.42 mm Hg were observed already at 850 hPa, at which point additional pressure reduction was not performed.

CONCLUSIONS

While severe increases in IOP were observed with decreased atmospheric pressure in eyes with large air bubbles in the anterior chamber, small and moderately sized bubbles seem to allow for travel over modest changes in altitude.

Who bears the load? IOP-induced collagen fiber recruitment over the corneoscleral shell

Collagen is the main load-bearing component of cornea and sclera. When stretched, both of these tissues exhibit a behavior known as collagen fiber recruitment. In recruitment, as the tissues stretch the constitutive collagen fibers lose their natural waviness, progressively straightening. Recruited, straight, fibers bear substantially more mechanical load than non-recruited, wavy, fibers. As such, the process of recruitment underlies the well-established nonlinear macroscopic behavior of the corneoscleral shell. Recruitment has an interesting implication: when recruitment is incomplete, only a fraction of the collagen fibers is actually contributing to bear the loads, with the rest remaining "in reserve". In other words, at a given intraocular pressure (IOP), it is possible that not all the collagen fibers of the cornea and sclera are actually contributing to bear the loads. To the best of our knowledge, the fraction of corneoscleral shell fibers recruited and contributing to bear the load of IOP has not been reported. Our goal was to obtain regionally-resolved estimates of the fraction of corneoscleral collagen fibers recruited and in reserve. We developed a fiber-based microstructural constitutive model that could account for collagen fiber undulations or crimp via their tortuosity. We used experimentally-measured collagen fiber crimp tortuosity distributions in human eyes to derive region-specific nonlinear hyperelastic mechanical properties. We then built a three-dimensional axisymmetric model of the globe, assigning region-specific mechanical properties and regional anisotropy. The model was used to simulate the IOP-induced shell deformation. The model-predicted tissue stretch was then used to quantify collagen recruitment within each shell region. The calculations showed that, at low IOPs, collagen fibers in the posterior equator were recruited the fastest, such that at a physiologic IOP of 15 mmHg, over 90% of fibers were recruited, compared with only a third in the cornea and the peripapillary sclera. The differences in recruitment between regions, in turn, mean that at a physiologic IOP the posterior equator had a fiber reserve of only 10%, whereas the cornea and peripapillary sclera had two thirds. At an elevated IOP of 50 mmHg, collagen fibers in the limbus and the anterior/posterior equator were almost fully recruited, compared with 90% in the cornea and the posterior sclera, and 70% in the peripapillary sclera and the equator. That even at such an elevated IOP not all the fibers were recruited suggests that there are likely other conditions that challenge the corneoscleral tissues even more than IOP. The fraction of fibers recruited may have other potential implications. For example, fibers that are not bearing loads may be more susceptible to enzymatic digestion or remodeling. Similarly, it may be possible to control tissue stiffness through the fraction of recruited fibers without the need to add or remove collagen.

Delayed reorganisation of F-actin cytoskeleton and reversible chromatin condensation in scleral fibroblasts under simulated pathological strain

Mechanical loading regulates the functional capabilities of the ocular system, particularly in the sclera (‘white of the eye’) – the principal load-bearing tissue of the ocular globe. Resident fibroblasts of the scleral eye wall are continuously subjected to fluctuating mechanical strains arising from eye movements, cerebrospinal fluid pressure and, most influentially, intra-ocular pressure (IOP). Whilst fibroblasts are hypothesised to actively participate in scleral biomechanics, to date limited information has been reported on how the macroscopic stresses and strains are transmitted via their cytoskeletal networks. In this study, the effect of applying either a ‘physiological load’ (simulating healthy IOP) or a ‘pathological load’ (simulating an elevated glaucomatous IOP) to bovine scleral fibroblasts, as a model of human glaucoma, was conducted to characterise cytoskeletal organisation, chromatin condensation and cell dimensions using immunofluorescence confocal microscopy. Quantification of cell parameters and cytoskeletal element anisotropy were subsequently performed using FibrilTool, and chromatin condensation parameter assessment through a bespoke MATLAB script. The novel findings suggest that physiological load-induced F-actin rearrangement is transient, whereas pathological load, recapitulating in vivo glaucomatous IOP levels, had a reversible and inhibitory influence on remodelling of the cytoskeletal architecture and, further, induction of chromatin condensation. Ultimately, this could compromise cell behaviour. These findings could provide valuable insight into the mechanism(s) used by scleral fibroblasts to mechanically adapt to support biomechanical tissue integrity, and how it could be potentially modified for therapeutic avenues targeting mechanically mediated ocular pathologies such as glaucoma.

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Physiological strain induced a transient F-actin rearrangement in scleral fibroblasts.

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In contrast, pathological strain reversibly delayed F-actin rearrangement.

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Vimentin and β-tubulin networks were largely unaffected by strain regimens.

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Pathological strain reversibly increased chromatin condensation parameter.

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Pathological strain may induce ‘inhibition delay’ to confer cytoprotection.

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.

Optical coherence elastography for assessing the influence of intraocular pressure on elastic wave dispersion in the cornea

The cornea is a highly specialized organ that relies on its mechanical stiffness to maintain its aspheric geometry and refractive power, and corneal diseases such as keratoconus have been linked to abnormal tissue stiffness and biomechanics. Dynamic optical coherence elastography (OCE) is a clinically promising non-contact and non-destructive imaging technique that can provide measurements of corneal tissue stiffness directly in vivo. The method relies on the concepts of elastography where shear waves are generated and imaged within a tissue to obtain mechanical properties such as tissue stiffness. The accuracy of OCE-based measurements is ultimately dependent on the mathematical theories used to model wave behavior in the tissue of interest. In the cornea, elastic waves propagate as guided wave modes which are highly dispersive and can be mathematically complex to model. While recent groups have developed detailed theories for estimating corneal tissue properties from guided wave behavior, the effects of intraocular pressure (IOP)-induced prestress have not yet been considered. It is known that prestress alone can strongly influence wave behavior, in addition to the associated non-linear changes in tissue properties. This present study shows that failure to account for the effects of prestress may result in overestimations of the corneal shear moduli, particularly at high IOPs. We first examined the potential effects of IOP and IOP-induced prestress using a combination of approximate mathematical theories describing wave behavior in thin plates with observations made from data published in the OCE literature. Through wave dispersion analysis, we deduce that IOP introduces a tensile hoop stress and may also influence an elastic foundational effect that were observable in the low-frequency components of the dispersion curves. These effects were incorporated into recently developed models of wave behavior in nearly incompressible, transversely isotropic (NITI) materials. Fitting of the modified NITI model with ex vivo porcine corneal data demonstrated that incorporation of the effects of IOP resulted in reduced estimates of corneal shear moduli. We believe this demonstrates that overestimation of corneal stiffness occurs if IOP is not taken into consideration. Our work may be helpful in separating inherent corneal stiffness properties that are independent of IOP; changes in these properties and in IOP are distinct, clinically relevant issues that affect the cornea health.

Lowering Intraocular Pressure: A Potential Approach for Controlling High Myopia Progression

High myopia is among the most common causes of vision impairment, and it is mainly characterized by abnormal elongation of the axial length, leading to pathologic changes in the ocular structures. Owing to the close relationship between high myopia and glaucoma, the association between intraocular pressure (IOP) and high myopia progression has garnered attention. However, whether lowering IOP can retard the progression of high myopia is unclear. On reviewing previous studies, we suggest that lowering IOP plays a role in progressive axial length elongation in high myopia, particularly in pathologic myopia, wherein the sclera is more remodeled. Based on the responses of the ocular layers, we further proposed the potential mechanisms. For the sclera, lowering the IOP could inhibit the activation of scleral fibroblasts and then reduce scleral remodeling, and a decrease in the scleral distending force would retard the ocular expansion like a balloon. For the choroid, lowering IOP results in an increase in choroidal blood perfusion, thereby reducing scleral hypoxia and slowing down scleral remodeling. The final effect of these pathways is slowing axial elongation and the development of scleral staphyloma. Further animal and clinical studies regarding high myopia with varied degree of IOP and the changes of choroid and sclera during IOP fluctuation in high myopia are needed to verify the role of IOP in the pathogenesis and progression of high myopia. It is hoped that this may lead to the development of a prospective treatment option to prevent and control high myopia progression.

Collagen V insufficiency in a mouse model for Ehlers Danlos-syndrome affects viscoelastic biomechanical properties explaining thin and brittle corneas

Ehlers–Danlos syndrome (EDS) is a genetic disease leading to abnormalities in mechanical properties of different tissues. Here we quantify corneal biomechanical properties in an adult classic EDS mouse model using two different measurement approaches suited for murine corneal mechanical characterization and relate differences to stromal structure using Second Harmonic Generation (SHG) microscopy. Quasi-static Optical Coherence Elastography (OCE) was conducted non-invasively during ambient pressure modulation by − 3 mmHg. 2D-extensometry measurements was conducted invasively consisting of a pre-conditioning cycle, a stress-relaxation test and a rupture test. In a total of 28 eyes from a Col5a1^+/− mouse model and wild-type C57BL/6 littermates (wt), Col5a1^+/− corneas were thinner when compared to wt, (125 ± 11 vs 148 ± 10 μm, respectively, p < 0.001). Short-term elastic modulus was significantly increased in OCE (506 ± 88 vs 430 ± 103 kPa, p = 0.023), and the same trend was observed in 2D-extensometry (30.7 ± 12.1 kPa vs 21.5 ± 5.7, p = 0.057). In contrast, in stress relaxation tests, Col5a1^+/− corneas experienced a stronger relaxation (55% vs 50%, p = 0.01). SHG microscopy showed differences in forward and backward scattered signal indicating abnormal collagen fibrils in Col5a1^+/− corneas. We propose that disturbed collagen fibril structure in Col5a1^+/− corneas affects the viscoelastic properties. Results presented here support clinical findings, in which thin corneas with global ultrastructural alterations maintain a normal corneal shape.

Effect of different preconditioning protocols on the viscoelastic inflation response of the posterior sclera

Preconditioning by repeated cyclic loads is routinely used in ex vivo mechanical testing of soft biological tissues. The goal of preconditioning is to achieve a steady and repeatable mechanical response and to measure material properties that are representative of the in vivo condition. Preconditioning protocols vary across studies, and their effect on the viscoelastic response of tested soft tissue is typically not reported or analyzed. We propose a methodology to systematically analyze the preconditioning process with application to inflation testing. We investigated the effect of preconditioning on the viscoelastic inflation response of tree shrew posterior sclera using two preconditioning protocols: (i) continuous cyclic loading-unloading without rest and (ii) cyclic loading-unloading with 15-min rest between cycles. Posterior scleral surface strain was measured using three-dimensional Digital Image Correlation (3D-DIC). We used five variables of characterizing features of the stress-strain loop curve to compare the two preconditioning protocols. Our results showed protocol-dependent differences in the tissue response during preconditioning and at the preconditioned state. Incorporating a resting time between preconditioning cycles significantly decreased the number of cycles (10.5 ± 2.9 cycles vs. 3.1 ± 0.5 cycles, p < 0.001) but increased the total time (15.8 ± 4.4 min vs. 51.2 ± 8.3 min, p < 0.001) needed to reach preconditioned state. At the preconditioned state, 2 of 5 characteristic variables differed significantly between protocols: hysteresis loop area (difference=0.023 kJ/m³, p = 0.0020) and elastic modulus at high IOPs (difference=24.0 MPa, p = 0.0238). Our results suggest that the analysis of the preconditioning process is an essential part of inflation experiments and a prerequisite to properly characterize the tissue viscoelastic response. Furthermore, material properties obtained at the preconditioned state can be impacted by the resting time used during preconditioning and may not be directly compared across studies if the resting time varies by 15 min between studies. STATEMENT OF SIGNIFICANCE: Although applying a preconditioning protocol by repeated cyclic loads is common practice in ex vivo mechanical characterization of soft tissues, the tissue response is typically not reported or analyzed, and the protocol's potential effect on the response remains unclear. This is partially caused by lack of a standardized methodology to precondition soft tissues. We present the first systematic analysis of two representative preconditioning protocols used during inflation testing in ocular biomechanics. Our results show protocol-dependent differences in the viscoelastic response during the preconditioning process and at the preconditioned state. Consequently, the analysis of the preconditioning response represents an essential part of mechanical testing and a prerequisite to properly characterize the tissue viscoelastic response. The effect of preconditioning on the preconditioned state response must be considered when comparing results across studies with different preconditioning protocols.

So-Called Lamina Cribrosa Defects May Mitigate IOP-Induced Neural Tissue Insult

Purpose

The prevailing theory about the function of lamina cribrosa (LC) connective tissues is that they provide structural support to adjacent neural tissues. Missing connective tissues would compromise this support and therefore are regarded as “LC defects”, despite scarce actual evidence of their role. We examined how so-called LC defects alter IOP-related mechanical insult to the LC neural tissues.

Methods

We built numerical models incorporating LC microstructure from polarized light microscopy images. To simulate LC defects of varying sizes, individual beams were progressively removed. We then compared intraocular pressure (IOP)-induced neural tissue deformations between models with and without defects. To better understand the consequences of defect development, we also compared neural tissue deformations between models with partial and complete loss of a beam.

Results

The maximum stretch of neural tissues decreased non-monotonically with defect size. Maximum stretch in the model with the largest defect decreased by 40% in comparison to the model with no defects. Partial loss of a beam increased the maximum stretch of neural tissues in its adjacent pores by 162%, compared with 63% in the model with complete loss of a beam.

Conclusions

Missing LC connective tissues can mitigate IOP-induced neural tissue insult, suggesting that the role of the LC connective tissues is more complex than simply fortifying against IOP. The numerical models further predict that partial loss of a beam is biomechanically considerably worse than complete loss of a beam, perhaps explaining why defects have been reported clinically but partial beams have not.

The Shape of Posterior Sclera as a Biometric Signature in Open-angle Glaucoma: An Intereye Comparison Study

Supplemental Digital Content is available in the text.

Purpose:

To characterize intereye differences in posterior segment parameters and determine their significance in open-angle glaucoma patients with unilateral damage.

Methods:

Both eyes from 65 subjects without any nerve damage and 43 patients undergoing treatment for unilateral open-angle glaucoma were included in this study. A 12.0×9.0×2.6 mm volume of the posterior segment in each eye was scanned with swept-source optical coherence tomography. Coronally reconstructed optical coherence tomography images were analyzed to determine the deepest point of the eye (DPE), which we then calculated the distance (Disc-DPE distance), depth (Disc-DPE depth), angle (Disc-DPE angle) from the optic disc center to the DPE. Posterior pole shape was analyzed measuring the posterior pole-cross-sectional area, posterior pole-horizontal width (PP-HW), and posterior pole-vertical width) of the posterior pole. These measurements and their intereye absolute difference (IAD; absolute difference in measurements between the right and left eyes) values were compared between the healthy and unilateral glaucomatous patients.

Results:

The posterior sclera measurements, including the Disc-DPE distance, Disc-DPE depth, and posterior pole-cross-sectional area, were significantly different between the unilateral glaucoma eyes and contralateral healthy eyes (P=0.043, P=0.035, and P=0.049, respectively). By contrast, none of the intereye differences in optic nerve head parameters were significant in the unilateral glaucoma patients. In comparison with the IAD values, the baseline intraocular pressure and PP-HW of the posterior segment showed significant differences between the healthy and the unilateral glaucoma patients (P=0.019 and P=0.036, respectively). A multivariate analysis showed that a larger baseline intraocular pressure IAD [odds ratio (OR), 1.381; P=0.009)] and larger PP-HW IAD (OR, 1.324; P=0.032) were significantly associated with the presence of glaucoma.

Conclusions:

Compared with the fellow healthy eyes, glaucomatous eyes had larger and more steeply curved posterior poles, which represent a structural variation of the posterior sclera that might be associated with glaucomatous optic neuropathy.

Heartbeat-Induced Corneal Axial Displacement and Strain Measured by High Frequency Ultrasound Elastography in Human Volunteers

Purpose

The purpose of this study was to establish in vivo data acquisition and processing protocols for repeatable measurements of heartbeat-induced corneal displacements and strains in human eyes, using a high-frequency ultrasound elastography method, termed ocular pulse elastography (OPE).

Methods

Twenty-four volunteers with no known ocular diseases were recruited for this study. Intraocular pressure (IOP) and ocular pulse amplitude (OPA) were measured using a PASCAL Dynamic Contour Tonometer (DCT). An in vivo OPE protocol was developed to measure heartbeat-induced corneal displacements. Videos of the central 5.7 mm of the cornea were acquired using a 50-MHz ultrasound probe at 128 frames per second. The radiofrequency data of 1000 frames were analyzed using an ultrasound speckle tracking algorithm to calculate corneal displacements and quantify spectral and temporal characteristics. The intrasession and intersession repeatability of OPE- and DCT-measured parameters were also analyzed.

Results

The in vivo OPE protocol and setup were successful in tracking heartbeat-induced corneal motion using high-frequency ultrasound. Corneal axial displacements showed a strong cardiac rhythm, with good intrasession and intersession repeatability, and high interocular symmetry. Corneal strain was calculated in two eyes of two subjects, showing substantially different responses.

Conclusions

We demonstrated the feasibility of high-frequency ultrasound elastography for noninvasive in vivo measurement of the cornea's biomechanical responses to the intrinsic ocular pulse. The high intrasession and intersession repeatability suggested a robust implementation of this technique to the in vivo setting.

Translational Relevance

OPE may offer a useful tool for clinical biomechanical evaluation of the cornea by quantifying its response to the intrinsic pulsation.

Descemetocele

A corneal descemetocele, the anterior herniation of an intact Descemet membrane through an overlying stromal defect, is a rare, but serious outcome of progressive corneal ulceration and mandates urgent intervention owing to the imminent risk of perforation. Various ocular and systemic abnormalities that can lead to the formation of descemetocele include microbial keratitis, neurotrophic keratopathy, dry eye disorders, and corneal inflammation associated with immune-mediated disorders. The primary aim of management of a descemetocele remains prompt restoration of ocular integrity to prevent the rupture of the Descemet membrane and further complications. Medical therapy is instituted immediately while deciding on the most suitable operative modality for an individual case. Commonly available treatment options include therapeutic bandage contact lenses, tissue adhesives, amniotic membrane transplantation, corneal patch grafts, penetrating or lamellar keratoplasty, and conjunctival flaps. Infrequently, platelet-rich fibrin membrane grafting and umbilical cord patch transplantation have also been tried with success. The surgical strategy and the outcome are commonly determined by the size, location, and etiology of descemetoceles. Despite the availability of all these treatment options, ambiguity remains about management. We review the available literature on pathogenesis, causes, presentation, differential diagnoses, and management of this disorder and also discuss our experience.

Comparison of Lamina Cribrosa Morphology in Eyes with Ocular Hypertension and Normal-Tension Glaucoma

Purpose

To characterize differences in the lamina cribrosa (LC) morphology between healthy, ocular hypertension (OHT), and naive normal-tension glaucoma (NTG) eyes.

Methods

Each group consisted of 80 eyes of 80 participants who were matched for age, sex, and axial length. The participants underwent enhanced-depth-imaging volume scanning of the optic nerve head using spectral-domain optical coherence tomography. The lamina cribrosa curvature index (LCCI) and lamina cribrosa thickness (LCT) were measured in horizontal B-scan images spaced equidistantly across the vertical diameter of the optic disc.

Results

The LCCIs in all seven planes were smaller in both OHT and healthy eyes than in NTG eyes (all P < 0.001), and did not differ significantly between the OHT and healthy eyes. The LCTs in all three planes were greatest in OHT eyes followed by healthy and then NTG eyes (all P < 0.001). Overall, the larger LCCI was associated with smaller LCT (P < 0.001).

Conclusions

The LC was thin and steeply curved in NTG eyes than in healthy and OHT eyes. In OHT eyes, the LC was thick, and its curvature was comparable to healthy eyes. Longitudinal studies are required to examine whether the straight and thickened LCs in OHT eyes precede the onset of OHT or are a protective response to elevated intraocular pressure.

Connective Tissue Remodeling in Myopia and its Potential Role in Increasing Risk of Glaucoma

Myopia and glaucoma are both increasing in prevalence and are linked by an unknown mechanism as many epidemiologic studies have identified moderate to high myopia as an independent risk factor for glaucoma. Myopia and glaucoma are both chronic conditions that lead to connective tissue remodeling within the sclera and optic nerve head. The mechanobiology underlying connective tissue remodeling differs substantially between both diseases, with different homeostatic control mechanisms. In this article, we discuss similarities and differences between connective tissue remodeling in myopia and glaucoma; selected multi-scale mechanisms that are thought to underlie connective tissue remodeling in both conditions; how asymmetric remodeling of the optic nerve head may predispose a myopic eye for pathological remodeling and glaucoma; and how neural tissue deformations may accumulate throughout both pathologies and increase the risk for mechanical insult of retinal ganglion cell axons.

Peripapillary sclera architecture revisited: A tangential fiber model and its biomechanical implications

The collagen fiber architecture of the peripapillary sclera (PPS), which surrounds the scleral canal, is a critical factor in determining the mechanical response of the optic nerve head (ONH) to variations in intraocular pressure (IOP). Experimental and clinical evidence point to IOP-induced deformations within the scleral canal as important contributing factors of glaucomatous neural tissue damage and consequent vision loss. Hence, it is imperative to understand PPS architecture and biomechanics. Current consensus is that the fibers of the PPS form a closed ring around the canal to support the delicate neural tissues within. We propose an alternative fiber architecture for the PPS, in which the scleral canal is supported primarily by long-running fibers oriented tangentially to the canal. We present evidence that this tangential model is consistent with histological observations in multiple species, and with quantitative measurements of fiber orientation obtained from small angle light scattering and wide-angle X-ray scattering. Using finite element models, we investigated the biomechanical implications of a tangential fiber PPS architecture. We found that the tangential arrangement of fibers afforded better mechanical support to the tissues within the scleral canal as compared to a simple circumferential ring of fibers or a combination of fibers oriented radially and circumferentially. We also found that subtle variations from a tangential orientation could reproduce clinically observed ONH behavior which has yet to be explained using current theories of PPS architecture and simulation, namely, the contraction of the scleral canal under elevated IOP.

STATEMENT OF SIGNIFICANCE

It is hypothesized that vision loss in glaucoma is due to excessive mechanical deformation within the neural tissue inside the scleral canal. This study proposes a new model for how the collagen of the peripapillary sclera surrounding the canal is organized to support the delicate neural tissue inside. Previous low-resolution studies of the peripapillary sclera suggested that the collagen fibers are arranged in a ring around the canal. Instead, we provide microscopic evidence suggesting that the canal is also supported by long-running interwoven fibers oriented tangentially to the canal. We demonstrate that this arrangement has multiple biomechanical advantages over a circular collagen arrangement and can explain previously unexplained experimental findings including contraction of the scleral canal under elevated intraocular pressure.

Lamina Cribrosa Pore Shape and Size as Predictors of Neural Tissue Mechanical Insult

Purpose

The purpose of this study was to determine how the architecture of the lamina cribrosa (LC) microstructure, including the shape and size of the lamina pores, influences the IOP-induced deformation of the neural tissues within the LC pores using computational modeling.

Methods

We built seven specimen-specific finite element models of LC microstructure with distinct nonlinear anisotropic properties for LC beams and neural tissues based on histological sections from three sheep eyes. Changes in shape (aspect ratio and convexity) and size (area and perimeter length) due to IOP-induced hoop stress were calculated for 128 LC pores. Multivariate linear regression was used to determine if pore shape and size were correlated with the strain in the pores. We also compared the microstructure models to a homogenized model built following previous approaches.

Results

The LC microstructure resulted in focal tensile, compressive, and shear strains in the neural tissues of the LC that were not predicted by homogenized models. IOP-induced hoop stress caused pores to become larger and more convex; however, pore aspect ratio did not change consistently. Peak tensile strains within the pores were well predicted by a linear regression model considering the initial convexity (negative correlation, P < 0.001), aspect ratio (positive correlation, P < 0.01), and area (negative correlation, P < 0.01). Significant correlations were also found when considering the deformed shape and size of the LC pores.

Conclusions

The deformation of the LC neural tissues was largely dependent on the collagenous LC beams. Simple measures of LC pore shape and area provided good estimates of neural tissue biomechanical insult.

Estimation of the mechanical properties of the eye through the study of its vibrational modes

Measuring the eye's mechanical properties in vivo and with minimally invasive techniques can be the key for individualized solutions to a number of eye pathologies. The development of such techniques largely relies on a computational modelling of the eyeball and, it optimally requires the synergic interplay between experimentation and numerical simulation. In Astrophysics and Geophysics the remote measurement of structural properties of the systems of their realm is performed on the basis of (helio-)seismic techniques. As a biomechanical system, the eyeball possesses normal vibrational modes encompassing rich information about its structure and mechanical properties. However, the integral analysis of the eyeball vibrational modes has not been performed yet. Here we develop a new finite difference method to compute both the spheroidal and, specially, the toroidal eigenfrequencies of the human eye. Using this numerical model, we show that the vibrational eigenfrequencies of the human eye fall in the interval 100 Hz-10 MHz. We find that compressible vibrational modes may release a trace on high frequency changes of the intraocular pressure, while incompressible normal modes could be registered analyzing the scattering pattern that the motions of the vitreous humour leave on the retina. Existing contact lenses with embebed devices operating at high sampling frequency could be used to register the microfluctuations of the eyeball shape we obtain. We advance that an inverse problem to obtain the mechanical properties of a given eye (e.g., Young's modulus, Poisson ratio) measuring its normal frequencies is doable. These measurements can be done using non-invasive techniques, opening very interesting perspectives to estimate the mechanical properties of eyes in vivo. Future research might relate various ocular pathologies with anomalies in measured vibrational frequencies of the eye.

Eye retraction and rotation during Corvis ST 'air puff' intraocular pressure measurement and its quantitative analysis

PURPOSE

The aim of this study was to analyse the indentation and deformation of the corneal surface, as well as eye retraction, which occur during air puff intraocular pressure (IOP) measurement.

METHODS

A group of 10 subjects was examined using a non-contact Corvis ST tonometer, which records image sequences of corneas deformed by an air puff. Obtained images were processed numerically in order to extract information about corneal deformation, indentation and eyeball retraction.

RESULTS

The time dependency of the apex deformation/eye retraction ratio and the curve of dependency between apex indentation and eye retraction take characteristic shapes for individual subjects. It was noticed that the eye globes tend to rotate towards the nose in response to the air blast during measurement. This means that the eye globe not only displaces but also rotates during retraction. Some new parameters describing the shape of this curve are introduced. Our data show that intraocular pressure and amplitude of corneal indentation are inversely related (r₈  = -0.83, P = 0.0029), but the correlation between intraocular pressure and amplitude of eye retraction is low and not significant (r₈  = -0.24, P = 0.51).

CONCLUSIONS

The curves describing corneal behaviour during air puff tonometry were determined and show that the eye globe rotates towards the nose during measurement. In addition, eye retraction amplitudes may be related to elastic or viscoelastic properties of deeper structures in the eye or behind the eye and this should be further investigated. Many of the proposed new parameters present comparable or even higher repeatability than the standard parameters provided by the Corvis ST.