Peripapillary and posterior scleral mechanics--part II: experimental and inverse finite element characterization

Capturing sclera anisotropy using direct collagen fiber models. Linking microstructure to macroscopic mechanical properties

Because of the crucial role of collagen fibers on soft tissue mechanics, there is great interest in techniques to incorporate them in computational models. Recently we introduced a direct fiber modeling approach for sclera based on representing the long-interwoven fibers. Our method differs from the conventional continuum approach to modeling sclera that homogenizes the fibers and describes them as statistical distributions for each element. At large scale our method captured gross collagen fiber bundle architecture from histology and experimental intraocular pressure-induced deformations. At small scale, a direct fiber model of a sclera sample reproduced equi-biaxial experimental behavior from the literature. In this study our goal was a much more challenging task for the direct fiber modeling: to capture specimen-specific 3D fiber architecture and anisotropic mechanics of four sclera samples tested under equibiaxial and four non-equibiaxial loadings. Samples of sclera from three eyes were isolated and tested in five biaxial loadings following an approach previously reported. Using microstructural architecture from polarized light microscopy we then created specimen-specific direct fiber models. Model fiber orientations agreed well with the histological information (adjusted R2's>0.89). Through an inverse-fitting process we determined model characteristics, including specimen-specific fiber mechanical properties to match equibiaxial loading. Interestingly, the equibiaxial properties also reproduced all the non-equibiaxial behaviors. These results indicate that the direct fiber modeling method naturally accounted for tissue anisotropy within its fiber structure. Direct fiber modeling is therefore a promising approach to understand how macroscopic behavior arises from microstructure.

Postmortem Digital Image Correlation and Finite Element Modeling Demonstrate Posterior Scleral Deformations during Optic Nerve Adduction Tethering

Postmortem human eyes were subjected to optic nerve (ON) traction in adduction and elevated intraocular pressure (IOP) to investigate scleral surface deformations. We incrementally adducted 11 eyes (age 74.1 ± 9.3 years, standard deviation) from 26° to 32° under normal IOP, during imaging of the posterior globe, for analysis by three-dimensional digital image correlation (3D-DIC). In the same eyes, we performed uniaxial tensile testing in multiple regions of the sclera, ON, and ON sheath. Based on individual measurements, we analyzed eye-specific finite element models (FEMs) simulating adduction and IOP loading. Analysis of 3D-DIC showed that the nasal sclera up to 1 mm from the sheath border was significantly compressed during adduction. IOP elevation from 15 to 30 mmHg induced strains less than did adduction. Tensile testing demonstrated ON sheath stiffening above 3.4% strain, which was incorporated in FEMs of adduction tethering that was quantitatively consistent with changes in scleral deformation from 3D-DIC. Simulated IOP elevation to 30 mmHg did not induce scleral surface strains outside the ON sheath. ON tethering in incremental adduction from 26° to 32° compressed the nasal and stretched the temporal sclera adjacent to the ON sheath, more so than IOP elevation. The effect of ON tethering is influenced by strain stiffening of the ON sheath.

Direct measurements of collagen fiber recruitment in the posterior pole of the eye

Collagen is the main load-bearing component of the peripapillary sclera (PPS) and lamina cribrosa (LC) in the eye. Whilst it has been shown that uncrimping and recruitment of the PPS and LC collagen fibers underlies the macro-scale nonlinear stiffening of both tissues with increased intraocular pressure (IOP), the uncrimping and recruitment as a function of local stretch have not been directly measured. This knowledge is crucial to understanding their functions in bearing loads and maintaining tissue integrity. In this project we measured local stretch-induced collagen fiber bundle uncrimping and recruitment curves of the PPS and LC. Thin coronal samples of PPS and LC of sheep eyes were mounted and stretched biaxially quasi-statically using a custom system. At each step, we imaged the PPS and LC with instant polarized light microscopy and quantified pixel-level (1.5 μm/pixel) collagen fiber orientations. We used digital image correlation to measure the local stretch and quantified collagen crimp by the circular standard deviation of fiber orientations, or waviness. Local stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers than the LC at the low levels of stretch. At 10% stretch the curves crossed with 75% bundles recruited. The PPS had higher uncrimping rate and waviness remaining after recruitment than the LC: 0.9º vs. 0.6º and 3.1º vs. 2.7º. Altogether our findings support describing fiber recruitment of both PPS and LC with sigmoid curves, with the PPS recruiting faster and at lower stretch than the LC, consistent with a stiffer tissue. STATEMENT OF SIGNIFICANCE: Peripapillary sclera (PPS) and lamina cribrosa (LC) collagen recruitment behaviors are central to the nonlinear mechanical behavior of the posterior pole of the eye. How PPS and LC collagen fibers recruit under stretch is crucial to develop constitutive models of the tissues but remains unclear. We used image-based stretch testing to characterize PPS and LC collagen fiber bundle recruitment under local stretch. We found that fiber-level stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers at a low stretch, but at 10% bundle stretch the two curves crossed with 75% bundles recruited. We also found that PPS and LC fibers had different uncrimping rates and non-zero waviness's when recruited.

Myopia: Histology, clinical features, and potential implications for the etiology of axial elongation

Myopic axial elongation is associated with various non-pathological changes. These include a decrease in photoreceptor cell and retinal pigment epithelium (RPE) cell density and retinal layer thickness, mainly in the retro-equatorial to equatorial regions; choroidal and scleral thinning pronounced at the posterior pole and least marked at the ora serrata; and a shift in Bruch's membrane opening (BMO) occurring in moderately myopic eyes and typically in the temporal/inferior direction. The BMO shift leads to an overhang of Bruch's membrane (BM) into the nasal intrapapillary compartment and BM absence in the temporal region (i.e., parapapillary gamma zone), optic disc ovalization due to shortening of the ophthalmoscopically visible horizontal disc diameter, fovea-optic disc distance elongation, reduction in angle kappa, and straightening/stretching of the papillomacular retinal blood vessels and retinal nerve fibers. Highly myopic eyes additionally show an enlargement of all layers of the optic nerve canal, elongation and thinning of the lamina cribrosa, peripapillary scleral flange (i.e., parapapillary delta zone) and peripapillary choroidal border tissue, and development of circular parapapillary beta, gamma, and delta zone. Pathological features of high myopia include development of macular linear RPE defects (lacquer cracks), which widen to round RPE defects (patchy atrophies) with central BM defects, macular neovascularization, myopic macular retinoschisis, and glaucomatous/glaucoma-like and non-glaucomatous optic neuropathy. BM thickness is unrelated to axial length. Including the change in eye shape from a sphere in emmetropia to a prolate (rotational) ellipsoid in myopia, the features may be explained by a primary BM enlargement in the retro-equatorial/equatorial region leading to axial elongation.

Finite Deformation of Scleral Tissue under Electrical Stimulation: An Arbitrary Lagrangian-Eulerian Finite Element Method

The sclera is considered as the principal load-bearing tissue within the eye. The sclera is negatively charged; thus, it exhibits mechanical response to electrical stimulation. We recently demonstrated the electroactive behavior of sclera by performing experimental measurements that captured the deformation of the tip of scleral strips subjected to electric voltage. We also numerically analyzed the electromechanical response of the tissue using a chemo-electro-mechanical model. In the pre-sent study, we extended our previous work by experimentally characterizing the deformation profile of scleral strips along their length under electrical stimulation. In addition, we improved our previous mathematical model such that it could numerically capture the large deformation of samples. For this purpose, we considered the transient variability of the fixed charge density and the coupling between mechanical and chemo-electrical phenomena. These improvements in-creased the accuracy of the computational model, resulting in a better numerical representation of experimentally measured bending angles.

A direct fiber approach to model sclera collagen architecture and biomechanics

Sclera collagen fiber microstructure and mechanical behavior are central to eye physiology and pathology. They are also complex, and are therefore often studied using modeling. Most models of sclera, however, have been built within a conventional continuum framework. In this framework, collagen fibers are incorporated as statistical distributions of fiber characteristics such as the orientation of a family of fibers. The conventional continuum approach, while proven successful for describing the macroscale behavior of the sclera, does not account for the sclera fibers are long, interwoven and interact with one another. Hence, by not considering these potentially crucial characteristics, the conventional approach has only a limited ability to capture and describe sclera structure and mechanics at smaller, fiber-level, scales. Recent advances in the tools for characterizing sclera microarchitecture and mechanics bring to the forefront the need to develop more advanced modeling techniques that can incorporate and take advantage of the newly available highly detailed information. Our goal was to create a new computational modeling approach that can represent the sclera fibrous microstructure more accurately than with the conventional continuum approach, while still capturing its macroscale behavior. In this manuscript we introduce the new modeling approach, that we call direct fiber modeling, in which the collagen architecture is built explicitly by long, continuous, interwoven fibers. The fibers are embedded in a continuum matrix representing the non-fibrous tissue components. We demonstrate the approach by doing direct fiber modeling of a rectangular patch of posterior sclera. The model integrated fiber orientations obtained by polarized light microscopy from coronal and sagittal cryosections of pig and sheep. The fibers were modeled using a Mooney-Rivlin model, and the matrix using a Neo-Hookean model. The fiber parameters were determined by inversely matching experimental equi-biaxial tensile data from the literature. After reconstruction, the direct fiber model orientations agreed well with the microscopy data both in the coronal plane (adjusted R2 = 0.8234) and in the sagittal plane (adjusted R2 = 0.8495) of the sclera. With the estimated fiber properties (C10 = 5746.9 MPa; C01 = -5002.6 MPa, matrix shear modulus 200 kPa), the model's stress-strain curves simultaneously fit the experimental data in radial and circumferential directions (adjusted R2's 0.9971 and 0.9508, respectively). The estimated fiber elastic modulus at 2.16% strain was 5.45 GPa, in reasonable agreement with the literature. During stretch, the model exhibited stresses and strains at sub-fiber level, with interactions among individual fibers which are not accounted for by the conventional continuum methods. Our results demonstrate that direct fiber models can simultaneously describe the macroscale mechanics and microarchitecture of the sclera, and therefore that the approach can provide unique insight into tissue behavior questions inaccessible with continuum approaches.

Direct measurements of collagen fiber recruitment in the posterior pole of the eye

Collagen is the main load-bearing component of the peripapillary sclera (PPS) and lamina cribrosa (LC) in the eye. Whilst it has been shown that uncrimping and recruitment of the PPS and LC collagen fibers underlies the macro-scale nonlinear stiffening of both tissues with increased intraocular pressure (IOP), the uncrimping and recruitment as a function of local stretch have not been directly measured. This knowledge is crucial for the development of constitutive models associating micro and macro scales. In this project we measured local stretch-induced collagen fiber bundle uncrimping and recruitment curves of the PPS and LC. Thin coronal samples of PPS and LC of sheep eyes were mounted and stretched biaxially quasi-statically using a custom system. At each step, we imaged the PPS and LC with instant polarized light microscopy and quantified pixel-level (1.5 μm/pixel) collagen fiber orientations. We used digital image correlation to measure the local stretch and quantified collagen crimp by the circular standard deviation of fiber orientations, or waviness. Local stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers than the LC at the low levels of stretch. At 10% stretch the curves crossed with 75% bundles recruited. The PPS had higher uncrimping rate and waviness remaining after recruitment than the LC: 0.9° vs. 0.6° and 3.1° vs. 2.7°. Altogether our findings support describing fiber recruitment of both PPS and LC with sigmoid curves, with the PPS recruiting faster and at lower stretch than the LC, consistent with a stiffer tissue.

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.

Anatomic Peculiarities Associated with Axial Elongation of the Myopic Eye

PURPOSE

To describe anatomical peculiarities associated with axial elongation in the human myopic eye.

METHODS

Reviewing the results of previous histomorphometrical investigations of enucleated human globes, as well as reviewing findings obtained in population-based studies and hospital-based clinical investigations of myopic patients and non-myopic individuals.

RESULTS

Myopic axial elongation is associated with a change from a mostly spherical eye shape to a prolate ellipsoid form. It is combined with choroidal and scleral thinning, most pronounced at the posterior pole and less pronounced in the fundus midperiphery. In the fundus midperiphery, the retina and density of the retinal pigment epithelium (RPE) and photoreceptors decrease with a longer axial length, while in the macular region, retinal thickness, RPE cell density, and choriocapillaris thickness are not related to axial length. With axial elongation, a parapapillary gamma zone develops, leading to an enlargement of the optic disc-fovea distance and a decrease in angle kappa. Axial elongation is also correlated with an increase in the surface and volume of Bruch's membrane (BM), while BM thickness remains unchanged. Axial elongation causes moderately myopic eyes to show a shift of BM opening to the foveal direction so that the horizontal disc diameter becomes shorter (with a consequent vertical ovalization of the optic disc shape), a temporal gamma zone develops, and the optic nerve exit takes an oblique course. Features of high myopia are an enlargement of the RPE opening (myopic parapapillary beta zone) and BM opening (secondary macrodisc), elongation and thinning of the lamina cribrosa, peripapillary scleral flange (parapapillary delta zone) and peripapillary choroidal border tissue, secondary BM defects in the macular region, myopic maculoschisis, macular neovascularization, and cobblestones in the fundus periphery.

CONCLUSIONS

These features combined may be explained by a growth in BM in the fundus midperiphery leading to axial elongation.

Finite element modeling of effects of tissue property variation on human optic nerve tethering during adduction

Tractional tethering by the optic nerve (ON) on the eye as it rotates towards the midline in adduction is a significant ocular mechanical load and has been suggested as a cause of ON damage induced by repetitive eye movements. We designed an ocular finite element model (FEM) simulating 6° incremental adduction beyond the initial configuration of 26° adduction that is the observed threshold for ON tethering. This FEM permitted sensitivity analysis of ON tethering using observed material property variations in measured hyperelasticity of the anterior, equatorial, posterior, and peripapillary sclera; and the ON and its sheath. The FEM predicted that adduction beyond the initiation of ON tethering concentrates stress and strain on the temporal side of the optic disc and peripapillary sclera, the ON sheath junction with the sclera, and retrolaminar ON neural tissue. However, some unfavorable combinations of tissue properties within the published ranges imposed higher stresses in these regions. With the least favorable combinations of tissue properties, adduction tethering was predicted to stress the ON junction and peripapillary sclera more than extreme conditions of intraocular and intracranial pressure. These simulations support the concept that ON tethering in adduction could induce mechanical stresses that might contribute to ON damage.

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.

A Review of Potential Novel Glaucoma Therapeutic Options Independent of Intraocular Pressure

Glaucoma, a progressive optic neuropathy characterized by retinal ganglion cell degeneration and visual field loss, is the leading cause of irreversible blindness worldwide. Intraocular pressure (IOP) is presently the only modifiable risk factor demonstrated to slow or halt disease progression; however, glaucomatous damage persists in almost 50% of patients despite significant IOP reduction. Many studies have investigated the non-IOP-related risk factors that contribute to glaucoma progression as well as interventions that can prevent or delay glaucomatous neurodegeneration and preserve vision throughout life, independently of IOP. A vast number of experimental studies have reported effective neuroprotection in glaucoma, and clinical studies are ongoing attempting to provide strong evidence of effectiveness of these interventions. In this review, we look into the current understanding of the pathophysiology of glaucoma and explore the recent advances in non-IOP related strategies for neuroprotection and neuroregeneration in glaucoma.

Method for the biomechanical analysis of aqueous veins and perilimbal sclera by three-dimensional photoacoustic imaging and strain field calculation

A method motivated by the eye's aqueous veins is described for the imaging and strain calculation within soft biological tissues. A challenge to the investigation of the biomechanics of the aqueous vein-perilimbal sclera tissue complex is resolution of tissue deformations as a function of intraocular pressure and the subsequent calculation of strain (a normalized measure of deformation). The method involves perfusion of the eye with a contrast agent during conduction of non-invasive, optical resolution photoacoustic microscopy. This imaging technique permits three-dimensional displacement measurements of tracked points on the inner walls of the veins which are used in a finite element model to determine the corresponding strains. The methods are validated against two standard strain measurement methods. Representative porcine globe perfusion experiments are presented that demonstrate the power of the method to determine complex strain fields in the veins dependent on intraocular pressure as well as vein anatomy. In these cases, veins are observed to move radially outward during increases in intraocular pressure and to possess significant spatial strain variation, possibly influenced by their branching patterns. To the authors' knowledge, these are the only such quantitative, data driven, calculations of the aqueous vein strains available in the open literature.

Material properties and effect of preconditioning of human sclera, optic nerve, and optic nerve sheath

The optic nerve (ON) is a recently recognized tractional load on the eye during larger horizontal eye rotations. In order to understand the mechanical behavior of the eye during adduction, it is necessary to characterize material properties of the sclera, ON, and in particular its sheath. We performed tensile loading of specimens taken from fresh postmortem human eyes to characterize the range of variation in their biomechanical properties and determine the effect of preconditioning. We fitted reduced polynomial hyperelastic models to represent the nonlinear tensile behavior of the anterior, equatorial, posterior, and peripapillary sclera, as well as the ON and its sheath. For comparison, we analyzed tangent moduli in low and high strain regions to represent stiffness. Scleral stiffness generally decreased from anterior to posterior ocular regions. The ON had the lowest tangent modulus, but was surrounded by a much stiffer sheath. The low-strain hyperelastic behaviors of adjacent anatomical regions of the ON, ON sheath, and posterior sclera were similar as appropriate to avoid discontinuities at their boundaries. Regional stiffnesses within individual eyes were moderately correlated, implying that mechanical properties in one region of an eye do not reliably reflect properties of another region of that eye, and that potentially pathological combinations could occur in an eye if regional properties are discrepant. Preconditioning modestly stiffened ocular tissues, except peripapillary sclera that softened. The nonlinear mechanical behavior of posterior ocular tissues permits their stresses to match closely at low strains, although progressively increasing strain causes particularly great stress in the peripapillary region.

Individual-Specific Modeling of Rat Optic Nerve Head Biomechanics in Glaucoma

Glaucoma is the second leading cause of blindness worldwide and is characterized by the death of retinal ganglion cells (RGCs), the cells that send vision information to the brain. Their axons exit the eye at the optic nerve head (ONH), the main site of damage in glaucoma. The importance of biomechanics in glaucoma is indicated by the fact that elevated intraocular pressure (IOP) is a causative risk factor for the disease. However, exactly how biomechanical insult leads to RGC death is not understood. Although rat models are widely used to study glaucoma, their ONH biomechanics have not been characterized in depth. Therefore, we aimed to do so through finite element (FE) modeling. Utilizing our previously described method, we constructed and analyzed ONH models with individual-specific geometry in which the sclera was modeled as a matrix reinforced with collagen fibers. We developed eight sets of scleral material parameters based on results from our previous inverse FE study and used them to simulate the effects of elevated IOP in eight model variants of each of seven rat ONHs. Within the optic nerve, highest strains were seen inferiorly, a pattern that was consistent across model geometries and model variants. In addition, changing the collagen fiber direction to be circumferential within the peripapillary sclera resulted in more pronounced decreases in strain than changing scleral stiffness. The results from this study can be used to interpret data from rat glaucoma studies to learn more about how biomechanics affects RGC pathogenesis in glaucoma.

Collagen fiber interweaving is central to sclera stiffness

The mechanical properties of the microstructural components of sclera are central to eye physiology and pathology. Because these parameters are extremely difficult to measure directly, they are often estimated using inverse-modeling matching deformations of macroscopic samples measured experimentally. Although studies of sclera microstructure show collagen fiber interweaving, current models do not account for this interweaving or the resulting fiber-fiber interactions, which might affect parameter estimates. Our goal was to test the hypothesis that constitutive parameters estimated using inverse modeling differ if models account for fiber interweaving and interactions. We developed models with non-interweaving or interweaving fibers over a wide range of volume fractions (36-91%). For each model, we estimated fiber stiffness using inverse modeling matching biaxial experimental data of human sclera. We found that interweaving increased the estimated fiber stiffness. When the collagen volume fraction was 64% or less, the stiffness of interweaving fibers was about 1.25 times that of non-interweaving fibers. For higher volume fractions, the ratio increased substantially, reaching 1.88 for a collagen volume fraction of 91%. Simulating a model (interweaving/non-interweaving) using the fiber stiffness estimated from the other model produced substantially different behavior, far from that observed experimentally. These results show that estimating microstructural component mechanical properties is highly sensitive to the assumed interwoven/non-interwoven architecture. Moreover, the results suggest that interweaving plays an important role in determining the structural stiffness of sclera, and potentially of other soft tissues in which the collagen fibers interweave. STATEMENT OF SIGNIFICANCE: The collagen fibers of sclera are interwoven, but numerical models do not account for this interweaving or the resulting fiber-fiber interactions. To determine if interweaving matters, we examined the differences in the constitutive model parameters estimated using inverse modeling between models with interweaving and non-interweaving fibers. We found that the estimated stiffness of the interweaving fibers was up to 1.88 times that of non-interweaving fibers, and that the estimate increased with collagen volume fraction. Our results suggest that fiber interweaving is a fundamental characteristic of connective tissues, additional to anisotropy, density and orientation. Better characterization of interweaving, and of its mechanical effects is likely central to understanding microstructure and biomechanics of sclera and other soft tissues.

Role of radially aligned scleral collagen fibers in optic nerve head biomechanics

Collagen fibers organized circumferentially around the canal in the peripapillary sclera are thought to provide biomechanical support to the sensitive tissues within the optic nerve head (ONH). Recent studies have demonstrated the existence of a family of fibers in the innermost sclera organized radially from the scleral canal. Our goal was to determine the role of these radial fibers in the sensitivity of scleral canal biomechanics to acute increases in intraocular pressure (IOP). Following the same general approach of previous parametric sensitivity studies, we created nonlinear generic finite element models of a posterior pole with various combinations of radial and circumferential fibers at an IOP of 0 mmHg. We then simulated the effects of normal and elevated IOP levels (15 and 30 mmHg). We monitored four IOP-induced geometric changes: peripapillary sclera stretch, scleral canal displacement, lamina cribrosa displacement, and scleral canal expansion. In addition, we examined the radial (maximum tension) and through-thickness (maximum compression) strains within the ONH tissues. Our models predicted that: 1) radial fibers reduced the posterior displacement of the lamina, especially at elevated IOP; 2) radial fibers reduced IOP-induced radial strain within the peripapillary sclera and retinal tissue; and 3) a combination of radial and circumferential fibers maintained strains within the ONH at a level similar to those conferred by circumferential fibers alone. In conclusion, radial fibers provide support for the posterior globe, additional to that provided by circumferential fibers. Most importantly, a combination of both fiber families can better protect ONH tissues from excessive IOP-induced deformation than either alone.

Long-term morphologic fundus and optic nerve head pattern of progressive myopia in congenital glaucoma distinguished by age at first surgery

The purpose of this study was to investigate the preservation of round optic nerve head (ONH) shape in myopic eyes of surgically treated congenital glaucoma patients, with regard to factors associated with intraocular pressure (IOP) elevation-induced peripapillary scleral (PPS) deformation. Using optical coherence tomography (OCT) on the ONH and macula, we identified myopic eyes with round ONH and internally oblique border tissue and those with non-round ONH. We investigated differences in clinical factors between the two groups. We included 51 eyes of 34 patients. Age at first surgery (2.8 vs. 15.2 months, P < 0.001) was significantly different between the two groups. Axial length was also significantly longer (P = 0.004) in the non-round group, but multiple logistic regression analysis revealed age as the only significant factor (P < 0.05) in ONH roundness. Interestingly, the round ONH group also had non-curved fundus morphology and a thick choroid, while the non-round ONH group showed diverse degrees of disc tilt and posterior pole curvature, and a thin choroid. In conclusion, in eyes with congenital glaucoma, age at first surgery, particularly when older than 6 months, was associated with round ONH and emmetropia-like fundus despite high myopia. The findings may indicate two different changes in the posterior sclera and the neural canal in response to the increased IOP.

In vivo measures of anterior scleral resistance in humans with rebound tonometry

PURPOSE

To measure regional variations in anterior scleral resistance (ASR) using a ballistic rebound tonometer (RBT) and examine whether the variations are significantly affected by ethnicity and refractive error (RE).

METHODS

ASR was measured using a RBT (iCare TA01) following calibration against the biomechanical properties of agarose biogels. Eight scleral regions (nasal, temporal, superior, inferior, inferior-nasal, inferior-temporal, superior-nasal and superior-temporal) were measured at locations 4mm from the limbus. Subjects were 130 young adults comprising three ethnic groups whose RE distributions [MSE (D) ± S.D.] incorporated individuals categorised as without-myopia (NM; MSE ≥ -0.50) and with-myopia (WM; MSE < -0.50); British-White (BW): 26 NM + 0.52 ± 1.15D; 22 WM -3.83 ± 2.89D]; British-South-Asian (BSA): [9 NM + 0.49 ± 1.06D; 11 WM -5.07 ± 3.76D; Hong-Kong-Chinese (HKC): [11 NM + 0.39 ± 0.66D; 49 WM -4.46 ± 2.70D]. Biometric data were compiled using cycloplegic open-field autorefraction and the Zeiss IOLMaster. Two- and three-way repeated measures analysis of variances (anovas) tested regional differences for RBT values across both refractive status and ethnicity whilst stepwise forward multiple linear regression was used as an exploratory test.

RESULTS

Significant regional variations in ASR were identified for the BW, BSA and HKC (p < 0.001) individuals; superior-temporal region showed the lowest levels of resistance whilst the inferior-nasal region the highest. Compared to the BW and BSA groups, the HKC subjects displayed a significant increase in mean resistance for each respective region (p < 0.001). With the exception of the inferior region, ethnicity was found to be the chief predictor for variation in the scleral RBT values for all other regions. Mean RE group differences were insignificant.

CONCLUSIONS

The novel application of RBT to the anterior sclera confirm regional variation in ASR. Greater ASR amongst the HKC group than the BW and BSA individuals suggests that ethnic differences in anterior scleral biomechanics may exist.

Biomechanical properties of the rat sclera obtained with inverse finite element modeling

It is widely accepted that biomechanics plays an important role in glaucoma pathophysiology, but the mechanisms involved are largely unknown. Rats are a common animal model of glaucoma, and finite element models are being developed to provide much-needed insight into the biomechanical environment of the posterior rat eye. However, material properties of rat ocular tissues, including the sclera, are currently unknown. Since the sclera plays a major role in posterior ocular biomechanics, our goal was to use inverse finite element modeling to extract rat scleral material properties. We first used digital image correlation to measure scleral surface displacement during whole-globe inflation testing. We modeled the sclera as a nonlinear material with embedded collagen fibers and then fit modeled displacements to experimental data using a differential evolution algorithm. Subject-specific models were constructed in which 3 parameters described the stiffness of the ground substance and collagen fibers in the posterior eye, and 16 parameters defined the primary orientation and alignment of fibers within eight scleral sub-regions. We successfully extracted scleral material properties for eight rat eyes. Model displacements recreated general patterns of the experimental displacements but did not always match local patterns. The fiber directions and fiber concentration parameters were highly variable, but on average, fibers were aligned circumferentially and were more aligned in the peripapillary sclera than in the peripheral sclera. The material properties determined here will be used to inform future finite element models of the rat posterior eye with the goal of elucidating the role of biomechanics in glaucoma pathophysiology.

Factors affecting optic nerve head biomechanics in a rat model of glaucoma

Glaucoma is the leading cause of irreversible blindness and is characterized by the death of retinal ganglion cells, which carry vision information from the retina to the brain. Although it is well accepted that biomechanics is an important part of the glaucomatous disease process, the mechanisms by which biomechanical insult, usually due to elevated intraocular pressure (IOP), leads to retinal ganglion cell death are not understood. Rat models of glaucoma afford an opportunity for learning more about these mechanisms, but the biomechanics of the rat optic nerve head (ONH), a primary region of damage in glaucoma, are only just beginning to be characterized. In a previous study, we built finite-element models with individual-specific rat ONH geometries. Here, we developed a parametrized model of the rat ONH and used it to perform a sensitivity study to determine the influence that six geometric parameters and 13 tissue material properties have on rat optic nerve biomechanical strains due to IOP elevation. Strain magnitudes and patterns in the parametrized model generally matched those from individual-specific models, suggesting that the parametrized model sufficiently approximated rat ONH anatomy. Similar to previous studies in human eyes, we found that scleral properties were highly influential: the six parameters with highest influence on optic nerve strains were optic nerve stiffness, IOP, scleral thickness, the degree of alignment of scleral collagen fibres, scleral ground substance stiffness and the scleral collagen fibre uncrimping coefficient. We conclude that a parametrized modelling strategy is an efficient approach that allows insight into rat ONH biomechanics. Further, scleral properties are important influences on rat ONH biomechanics, and additional efforts should be made to better characterize rat scleral collagen fibre organization.

In Vivo Measurements of Prelamina and Lamina Cribrosa Biomechanical Properties in Humans

Purpose

To develop and use a custom virtual fields method (VFM) to assess the biomechanical properties of human prelamina and lamina cribrosa (LC) in vivo.

Methods

Clinical data of 20 healthy, 20 ocular hypertensive (OHT), 20 primary open-angle glaucoma, and 16 primary angle-closure glaucoma eyes were analyzed. For each eye, the intraocular pressure (IOP) and optical coherence tomography (OCT) images of the optic nerve head (ONH) were acquired at the normal state and after acute IOP elevation. The IOP-induced deformation of the ONH was obtained from the OCT volumes using a three-dimensional tracking algorithm and fed into the VFM to extract the biomechanical properties of the prelamina and the LC in vivo. Statistical measurements and P values from the Mann-Whitney-Wilcoxon tests were reported.

Results

The average shear moduli of the prelamina and the LC were 64.2 ± 36.1 kPa and 73.1 ± 46.9 kPa, respectively. The shear moduli of the prelamina of healthy subjects were significantly lower than those of the OHT subjects. Comparisons between healthy and glaucoma subjects could not be made robustly due to a small sample size.

Conclusions

We have developed a methodology to assess the biomechanical properties of human ONH tissues in vivo and provide preliminary comparisons in healthy and OHT subjects. Our proposed methodology may be of interest for glaucoma management.

A Mesh-Free Approach to Incorporate Complex Anisotropic and Heterogeneous Material Properties into Eye-Specific Finite Element Models

Commercial finite element modeling packages do not have the tools necessary to effectively incorporate the complex anisotropic and heterogeneous material properties typical of the biological tissues of the eye. We propose a mesh-free approach to incorporate realistic material properties into finite element models of individual human eyes. The method is based on the idea that material parameters can be estimated or measured at so called control points, which are arbitrary and independent of the finite element mesh. The mesh-free approach approximates the heterogeneous material parameters at the Gauss points of each finite element while the boundary value problem is solved using the standard finite element method. The proposed method was applied to an eye-specific model a human posterior pole and optic nerve head. We demonstrate that the method can be used to effectively incorporate experimental measurements of the lamina cribrosa micro-structure into the eye-specific model. It was convenient to define characteristic material orientations at the anterior and posterior scleral surface based on the eye-specific geometry of each sclera. The mesh-free approach was effective in approximating these characteristic material directions with smooth transitions across the sclera. For the first time, the method enabled the incorporation of the complex collagen architecture of the peripapillary sclera into an eye-specific model including the recently discovered meridional fibers at the anterior surface and the depth dependent width of circumferential fibers around the scleral canal. The model results suggest that disregarding the meridional fiber region may lead to an underestimation of local strain concentrations in the retina. The proposed approach should simplify future studies that aim to investigate collagen remodeling in the sclera and optic nerve head or in other biological tissues with similar challenges.

Association between peripapillary scleral deformation and choroidal microvascular circulation in glaucoma

Peripapillary vessel density, which is reduced in eyes with glaucoma, has been proposed as a diagnostic tool for the desease and peripapillary choroidal microvasculature dropout(MvD) is considered one of pathophysiological manifestation of glaucomatous damage. However, little is known about the underlying pathogenic mechanism of dropout. According to recent studies, MvD is associated with structural changes in ONH structures. Therefore, we investigated the association between peripapillary scleral deformation and MvD. Data from 62 open-angle glaucoma (OAG) eyes with MvD and 36 eyes without MvD were analyzed in this study. And eyes with MvD were classified into two groups based on location: a juxtapapillary group and a non-juxtapapillary group for further analysis. More eyes with MvD had focal scleral deformation than did those without MvD (64.5% versus 2.8%; P < 0.001). Peripapillary choroidal thickness and focal scleral deformation were significantly associated with MvD. And juxtapapillary group was more associated with focal scleral deformation and coincidental RNFL defects than non-juxtapapillary groups. Peripapillary choroidal MvD was associated with the presence of scleral deformation, especially with juxtapapillary MvD, which was related to corresponding RNFL defects.

Full-field displacement measurement of corneoscleral shells by combining multi-camera speckle interferometry with 3D shape reconstruction

Changes in the biomechanical properties of the connective tissue of the eye occur with age and underlie the development of several ocular diseases, such as glaucoma, myopia, and keratoconus. The biomechanical dynamics of ocular connective tissue are measured by ex vivo inflation testing, in which intraocular pressure (IOP) is varied and optical methods are used to produce maps of corneal and scleral displacement. Current optical methods are limited by acquisition rate, occlusions, poor spatial resolution, and insufficient 3D mapping. We developed an interferometric optical method integrates four-camera electronic speckle pattern interferometry (ESPI) and a novel three-dimensional (3D) shape reconstruction process to measure shape and full-field mechanical deformations of corneal and scleral shells during ex vivo inflation testing. Each camera provides accurate measurements of the laser beam phase related to deformations of the specimen surface; a multi-view stereovision method generates the shape of the specimen and a functional form that links every pixel of a given camera to 3D points on the specimen's visible surface. In this way, dynamic deformations of the specimen are localized, with quantification of the time-dependent 3D displacements of the specimen at nanometric accuracy. The ESPI-3D system is suitable for analyzing scleral deformation and morphological changes caused by time-varying IOP.

Inflation experiments and inverse finite element modelling of posterior human sclera

The complexity of inverse finite element modelling methods used in ocular biomechanics research has significantly increased in recent years in order to produce material parameters that capture microscale tissue behaviour. This study presents a more accessible method for researchers to optimise sclera material parameters for use in finite element studies where macroscale sclera displacements are required. Five human donor sclerae aged between 36 and 72 years were subjected to cycles of internal pressure up to 61 mmHg using a custom-built inflation rig. Displacements were measured using a laser beam and two cameras through a digital image correlation algorithm. Specimen-specific finite element models incorporating regional thickness variation and sclera surface topography were divided into six circumferential regions. An inverse finite element procedure was used to optimise Ogden material parameters for each region. The maximum root mean squared (RMS) error between the numerical and experimental displacements within individual specimens was 17.5 µm. The optimised material parameters indicate a gradual reduction in material stiffness (as measured by the tangent modulus) from the equator to the posterior region at low-stress levels up to 0.005 MPa. The variation in stiffness between adjacent regions became gradually less apparent and statistically insignificant at higher stresses. The study demonstrated how inflation testing combined with inverse modelling could be used to effectively characterise regional material properties capable of reproducing global sclera displacements. The material properties were found to vary between specimens, and it is expected that age could be a contributing factor behind this variation.

The Relationship Between Scleral Strain Change and Differential Cumulative Intraocular Pressure Exposure in the Nonhuman Primate Chronic Ocular Hypertension Model

Purpose

To determine the relationship between peripapillary scleral strain change and cumulative differential IOP exposure in nonhuman primates (NHPs) with unilateral chronic ocular hypertension.

Methods

Posterior scleral shells from 6 bilaterally normal and 10 unilateral chronic ocular hypertension NHPs were pressurized from 5 to 45 mm Hg, and the resulting full-field, three-dimensional, scleral surface deformations were acquired using laser speckle interferometry. Scleral tensile strain (local tissue deformation) was calculated by analytical differentiation of the displacement field; zero strain was assumed at 5 mm Hg. Maximum principal strain was used to represent the scleral strain, and strains were averaged over a 15°-wide (∼3.6-mm) circumpapillary region adjacent to the ONH. The relative difference in mean strain was calculated between fellow eyes and compared with the differential cumulative IOP exposure within NHPs during the study period. The relationship between the relative difference in scleral strain and the differential cumulative IOP exposure in fellow eyes was assessed using an F test and quadratic regression model.

Results

Relative differential scleral tensile strain was significantly associated with differential cumulative IOP exposure in contralateral eyes in the chronic ocular hypertension NHPs, with the bilaterally normal NHPs showing no significant strain difference between fellow eyes. The sclera in the chronic ocular hypertension eyes was more compliant than in their fellow eyes at low levels of differential cumulative IOP exposure, but stiffer at larger differential IOPs (P < 0.0001).

Conclusions

These cross-sectional findings suggest that longitudinal IOP-induced changes in scleral mechanical behavior are dependent on the magnitude of differential cumulative IOP exposure.

Scleral structure and biomechanics

As the eye's main load-bearing connective tissue, the sclera is centrally important to vision. In addition to cooperatively maintaining refractive status with the cornea, the sclera must also provide stable mechanical support to vulnerable internal ocular structures such as the retina and optic nerve head. Moreover, it must achieve this under complex, dynamic loading conditions imposed by eye movements and fluid pressures. Recent years have seen significant advances in our knowledge of scleral biomechanics, its modulation with ageing and disease, and their relationship to the hierarchical structure of the collagen-rich scleral extracellular matrix (ECM) and its resident cells. This review focuses on notable recent structural and biomechanical studies, setting their findings in the context of the wider scleral literature. It reviews recent progress in the development of scattering and bioimaging methods to resolve scleral ECM structure at multiple scales. In vivo and ex vivo experimental methods to characterise scleral biomechanics are explored, along with computational techniques that combine structural and biomechanical data to simulate ocular behaviour and extract tissue material properties. Studies into alterations of scleral structure and biomechanics in myopia and glaucoma are presented, and their results reconciled with associated findings on changes in the ageing eye. Finally, new developments in scleral surgery and emerging minimally invasive therapies are highlighted that could offer new hope in the fight against escalating scleral-related vision disorder worldwide.

A Subdomain Method for Mapping the Heterogeneous Mechanical Properties of the Human Posterior Sclera

Although strongly correlated with elevated intraocular pressure, primary open-angle glaucoma (POAG) occurs in normotensive eyes. Mechanical properties of the sclera around the optic nerve head (ONH) may play a role in this disparity. The purpose of this study is to present an automated inverse mechanics based approach to determine the distribution of heterogeneous mechanical properties of the human sclera as derived from its surface deformations arising from pressure inflation experiments. The scleral shell of a 78 year old European Descent male donor eye was utilized to demonstrate the method; the sclera was coated with a speckle pattern on the outer surface and was subjected to inflation pressures of 5, 15, 30, and 45 mmHg. The speckle pattern was imaged at each pressure, and a displacement field was calculated for each pressure step using a previously described sequential digital image correlation (S-DIC) technique. The fiber splay and fiber orientation of the sclera collagen were determined experimentally, and the thickness across the scleral globe was determined using micro CT images. The displacement field from the inflation test was used to calculate the strain and also used as an input for inverse mechanics to determine the heterogeneity of material properties. The scleral geometry was divided into subdomains using the first principal strain. The Holzapfel anisotropic material parameters of matrix and fiber stiffness were estimated within each individual subdomain using an inverse mechanics approach by minimizing the sum of the square of the residuals between the computational and experimental displacement fields. The mean and maximum error in displacement across all subdomains were 8.9 ± 3.0 μm and 13.2 μm, respectively. The full pressure-inflation forward mechanics experiment was done using subdomain-specific mechanical properties on the entire scleral surface. The proposed approach is effective in determining the distribution of heterogeneous mechanical properties of the human sclera in a user-independent manner. Our research group is currently utilizing this approach to better elucidate how scleral stiffness influences those at high risk for POAG.

Radial and Circumferential Collagen Fibers Are a Feature of the Peripapillary Sclera of Human, Monkey, Pig, Cow, Goat, and Sheep

Purpose

To test the hypothesis that human, monkey, pig, sheep, cow, and goat eyes exhibit circumferential, radial, and interweaving collagen architecture in the posterior sclera.

Methods

We analyzed 1,327 cryosections from the posterior poles of 4 human, 4 monkey, 5 pig, 8 sheep, 1 goat, and 2 cow eyes. Images were acquired using polarized light microscopy and processed to obtain polar fiber orientations relative to the center of the canal. Circumferential, radial, and interweaving regions were identified and analyzed for mean fiber orientation and anisotropy and region width and thickness.

Results

Every eye exhibited circumferential, radial, and interweaving fibers in consistent locations. Radial fibers extended out from near the canal into the peripapillary and peripheral sclera in the innermost sclera. Circumferential fibers were directly adjacent to the canal and most prevalent in the outermost, posterior sclera. Interweaving fibers were found throughout the sclera thickness. Across all species, median anisotropy in the radial, circumferential, and interweaving regions were 0.95, 0.96, and 0.28, respectively.

Conclusions

Regions of radial, circumferential, and interweaving fibers occur in the posterior pole sclera of human, monkey, pig, sheep, cow, and goat eyes. The consistency across species in scleral architecture suggests that they are primary organizational components whose functions should be better understood.

Optic nerve head damage relation to intracranial pressure and corneal properties of eye in glaucoma risk assessment

This work presents results from numerical simulations of optic nerve head's (ONH) biomechanical behavior during exposure to elevated intraocular (IOP) and/or intracranial pressure (ICP) for ocular hypertension conditions. At the same time, a range of geometric and material properties of the eye structure and their interrelation with elevated IOP and ICP values are investigated. These simulations are performed on a generic model of the eye, which allows parametrical modification of geometric and material properties. Our main interest is in measuring ONH's potential damage in ocular hypertension due to intracranial pressure. Simulation results indicate a significant role of ICP in post-laminar neural tissue failure and a possible role of central corneal thickness (CCT) and scleral modulus in clinical assessment and treatment of patients with ocular hypertension (OHT). Specifically, CCT was found to affect ONH at early stages of damage in ocular hypertension conditions, and high scleral modulus seems to result in reduced shear failure in lamina cribrosa in a similar OHT state. These findings suggest that CCT could be a risk factor for glaucoma in OHT patients at initial stage along with cornea stiffness. Graphical abstract Graphical abstract.

Biomechanical Properties of Bruch's Membrane-Choroid Complex and Their Influence on Optic Nerve Head Biomechanics

Purpose

The purpose of this study was to measure the rupture pressure and the biomechanical properties of porcine Bruch's membrane (BM)-choroid complex (BMCC) and the influences of BM on optic nerve head (ONH) tissues.

Methods

The biomechanical properties of BMCC were extracted through uniaxial tensile tests of 10 BMCC specimens from 10 porcine eyes; the rupture pressures of BMCC were measured through burst tests of 20 porcine eyes; and the influence of BM on IOP-induced ONH deformations were investigated using finite element (FE) analysis.

Results

Uniaxial experimental results showed that the average elastic (tangent) moduli of BMCC samples at 0% and 5% strain were 1.60 ± 0.81 and 2.44 ± 1.02 MPa, respectively. Burst tests showed that, on average, BMCC could sustain an IOP of 82 mm Hg before rupture. FE simulation results predicted that, under elevated IOP, prelamina tissue strains increased with increasing BM stiffness. On the contrary, lamina cribrosa strains showed an opposite trend but the effects were small.

Conclusions

BMCC stiffness is comparable or higher than those of other ocular tissues and can sustain a relatively high pressure before rupture. Additionally, BM may have a nonnegligible influence on IOP-induced ONH deformations.

Bulk changes in posterior scleral collagen microstructure in human high myopia

Purpose

We aimed to characterize any bulk changes in posterior scleral collagen fibril bundle architecture in human eyes with high myopia.

Methods

Wide-angle X-ray scattering (WAXS) was employed to map collagen orientation at 0.5 mm × 0.5 mm spatial intervals across the posterior sclera of seven non-myopic human eyes and three eyes with high myopia (>6D of refractive error). At each sampled point, WAXS provided thickness-averaged measures of the angular distribution of preferentially aligned collagen fibrils within the tissue plane and the anisotropic proportion (the ratio of preferentially aligned to total collagen scatter).

Results

Non-myopic specimens featured well-conserved microstructural features, including strong uniaxial collagen alignment along the extraocular muscle insertion sites of the mid-posterior sclera and a highly anisotropic annulus of collagen circumscribing the nerve head in the peripapillary sclera. All three myopic specimens exhibited notable alterations in the peripapillary sclera, including a partial loss of circumferential collagen alignment and a redistribution of the normally observed regional pattern of collagen anisotropic proportion. Linear mixed-model analysis indicated that the mean fiber angle deviation from the circumferential orientation in the peripapillary sclera of highly myopic eyes (23.9° ± 18.2) was statistically significantly higher than that of controls (17.9° ± 12.0; p<0.05).

Conclusions

Bulk alterations in the normal posterior scleral collagen microstructure occur in human eyes with high myopia. These changes could reflect remodeling of the posterior sclera during axial lengthening and/or a mechanical adaption to tissue stresses induced by fluid pressure or eye movements that may be exacerbated in enlarged eyes.

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.

Cerebrospinal Fluid Pressure: Revisiting Factors Influencing Optic Nerve Head Biomechanics

Purpose

To model the sensitivity of the optic nerve head (ONH) biomechanical environment to acute variations in IOP, cerebrospinal fluid pressure (CSFP), and central retinal artery blood pressure (BP).

Methods

We extended a previously published numerical model of the ONH to include 24 factors representing tissue anatomy and mechanical properties, all three pressures, and constraints on the optic nerve (CON). A total of 8340 models were studied to predict factor influences on 98 responses in a two-step process: a fractional factorial screening analysis to identify the 16 most influential factors, followed by a response surface methodology to predict factor effects in detail.

Results

The six most influential factors were, in order: IOP, CON, moduli of the sclera, lamina cribrosa (LC) and dura, and CSFP. IOP and CSFP affected different aspects of ONH biomechanics. The strongest influence of CSFP, more than twice that of IOP, was on the rotation of the peripapillary sclera. CSFP had similar influence on LC stretch and compression to moduli of sclera and LC. On some ONHs, CSFP caused large retrolamina deformations and subarachnoid expansion. CON had a strong influence on LC displacement. BP overall influence was 633 times smaller than that of IOP.

Conclusions

Models predict that IOP and CSFP are the top and sixth most influential factors on ONH biomechanics. Different IOP and CSFP effects suggest that translaminar pressure difference may not be a good parameter to predict biomechanics-related glaucomatous neuropathy. CON may drastically affect the responses relating to gross ONH geometry and should be determined experimentally.

Collagen fiber recruitment: A microstructural basis for the nonlinear response of the posterior pole of the eye to increases in intraocular pressure

Our goal was to quantify and characterize how the collagen fiber crimp waviness of the lamina cribrosa (LC) and peripapillary sclera (PPS) changes with intraocular pressure (IOP). Thirteen sheep (ovine) eyes were immersion and perfusion fixed while maintaining IOP at 0, 10, 15, 20, or 50 mmHg. Coronal optic nerve head (ONH) sections (30 µm) were imaged with polarized light microscopy (PLM) and analyzed for collagen fiber orientation and waviness (SD of fiber orientation). In the LC, the waviness of every LC beam was measured. In the PPS, at least 900 collagen bundles were measured per eye. Using the waviness at 50 mmHg IOP, we defined tissue-specific thresholds to determine the fraction of loaded or recruited fibers. We found that fiber waviness decreased with IOP (P < 0.001). At every IOP, the waviness of the collagen fibers, and the fraction of fibers recruited in the LC were smaller or equal than those of the PPS (P < 0.001). At 15 mmHg IOP, both LC and PPS had ¾ recruited fibers and ¼ left in reserve. The decreased waviness with IOP and associated fiber recruitment is experimental evidence of fiber-based nonlinear biomechanical behavior of the ONH. At all IOPs the PPS had an equal or larger fraction of fibers recruited than the LC. That both LC and PPS had the same fraction of recruited and reserve fibers at normal IOP suggests that this may be an optimal fraction of recruitment for healthy eyes. Whether this extends to human eyes remains unknown.

STATEMENT OF SIGNIFICANCE

Collagen fibers exhibit a natural waviness or crimp that largely determine the nonlinear biomechanics of soft tissue. Experimental measurements of crimp morphology in the sheep eye, and how it changes with intraocular pressure (IOP), however, are exceedingly sparse. We quantified how posterior eye crimp changes with increasing IOP. We found that the lamina cribrosa and peripapillary sclera have fundamentally different crimp, and with increasing IOP, have different proportions of fibers that straighten, or get recruited, versus remaining wavy, or in reserve. Interestingly, at physiologic IOP of 15 mmHg, both tissues had about ¾ fibers recruited and ¼ fibers in reserve, indicating there may be an optimal fraction of fibers.

In vivo assessment of changes in corneal hysteresis and lamina cribrosa position during acute intraocular pressure elevation in eyes with markedly asymmetrical glaucoma

Purpose

To investigate the biomechanical response of the cornea, lamina cribrosa (LC), and prelaminar tissue (PT) to an acute intraocular pressure (IOP) increase in patients with markedly asymmetrical glaucoma and in healthy controls.

Patients and methods

A total of 24 eyes of 12 patients with markedly asymmetrical primary open-angle glaucoma (POAG) and 12 eyes of 12 healthy patients were examined with spectral-domain optical coherence tomography (SD-OCT) and ocular response analyzer (ORA) at baseline and during acute IOP elevation by means of an ophthalmodynamometer. The displacement of the LC and PT and the change in corneal hysteresis (CH) and corneal resistance factor (CRF) were evaluated.

Results

Following a mean IOP increase of 12.3±2.4 mmHg, eyes with severe glaucoma demonstrated an overall mean anterior displacement of the LC (−6.58±26.09 µm) as opposed to the posterior laminar displacement in eyes with mild glaucoma (29.08±19.28 µm) and in healthy eyes (30.3±10.9; p≤0.001 and p=0.001, respectively). The PT displaced posteriorly during IOP elevation in all eyes. The CH decreased in eyes with severe glaucoma during IOP elevation (from 9.30±3.65 to 6.92±3.04 mmHg; p=0.012), whereas the CRF increased markedly in eyes with mild glaucoma (from 8.61±2.30 to 12.38±3.64; p=0.002) and in eyes with severe glaucoma (from 9.02±1.48 to 15.20±2.06; p=0.002). The increase in CRF correlated with the anterior displacement of the LC in eyes with severe glaucoma.

Conclusion

Eyes with severe glaucoma exhibited a mean overall anterior displacement of the anterior laminar surface, while eyes with mild glaucoma and healthy eyes showed a posterior displacement of the LC during IOP elevation. The CH decreased significantly from baseline only in eyes with severe glaucoma, but the CRF increased significantly in all glaucomatous eyes. The CRF increase correlated with the anterior displacement of the LC in eyes with severe glaucoma.

Modeling the effect of collagen fibril alignment on ligament mechanical behavior

Ligament mechanical behavior is primarily regulated by fibrous networks of type I collagen. Although these fibrous networks are typically highly aligned, healthy and injured ligament can also exhibit disorganized collagen architecture. The objective of this study was to determine whether variations in the collagen fibril network between neighboring ligaments can predict observed differences in mechanical behavior. Ligament specimens from two regions of bovine fetlock joints, which either exhibited highly aligned or disorganized collagen fibril networks, were mechanically tested in uniaxial tension. Confocal microscopy and FiberFit software were used to quantify the collagen fibril dispersion and mean fibril orientation in the mechanically tested specimens. These two structural parameters served as inputs into an established hyperelastic constitutive model that accounts for a continuous distribution of planar fibril orientations. The ability of the model to predict differences in the mechanical behavior between neighboring ligaments was tested by (1) curve fitting the model parameters to the stress response of the ligament with highly aligned fibrils and then (2) using this model to predict the stress response of the ligament with disorganized fibrils by only changing the parameter values for fibril dispersion and mean fibril orientation. This study found that when using parameter values for fibril dispersion and mean fibril orientation based on confocal imaging data, the model strongly predicted the average stress response of ligaments with disorganized fibrils ([Formula: see text]); however, the model only successfully predicted the individual stress response of ligaments with disorganized fibrils in half the specimens tested. Model predictions became worse when parameters for fibril dispersion and mean fibril orientation were not based on confocal imaging data. These findings emphasize the importance of collagen fibril alignment in ligament mechanics and help advance a mechanistic understanding of fibrillar networks in healthy and injured ligament.

Racioethnic Differences in Human Posterior Scleral and Optic Nerve Stump Deformation

Purpose

The purpose of this study was to quantify the biomechanical response of human posterior ocular tissues from donors of various racioethnic groups to better understand how differences in these properties may play a role in the racioethnic health disparities known to exist in glaucoma.

Methods

Sequential digital image correlation (S-DIC) was used to measure the pressure-induced surface deformations of 23 normal human posterior poles from three racioethnic groups: African descent (AD), European descent (ED), and Hispanic ethnicity (HIS). Regional in-plane principal strains were compared across three zones: the optic nerve stump (ONS), the peripapillary (PP) sclera, and non-PP sclera.

Results

The PP scleral tensile strains were found to be lower for ED eyes compared with AD and HIS eyes at 15 mm Hg (P = 0.024 and 0.039, respectively). The mean compressive strains were significantly higher for AD eyes compared with ED eyes at 15 mm Hg (P = 0.018). We also found that the relationship between tensile strain and pressure was significant for those of ED and HIS eyes (P < 0.001 and P = 0.004, respectively), whereas it was not significant for those of AD (P = 0.392).

Conclusions

Our results suggest that, assuming glaucomatous nerve loss is caused by mechanical strains in the vicinity of the optic nerve head, the mechanism of increased glaucoma prevalence may be different in those of AD versus HIS. Our ONS strain analysis also suggested that it may be important to account for ONS geometry and material properties in future scleral biomechanical analysis.

Variation in the Three-Dimensional Histomorphometry of the Normal Human Optic Nerve Head With Age and Race: Lamina Cribrosa and Peripapillary Scleral Thickness and Position

Purpose

This study quantified the thickness and depth of the lamina cribrosa (LC) and peripapillary scleral thickness in high-resolution three-dimensional (3D) fluorescent reconstructions of the optic nerve head (ONH) in eyes from donors of African (AD) and European descent (ED).

Methods

A total of 64 eyes (45 ED, 19 AD) from 51 normal donors were obtained within 6 hours of death and fixed at 10 mm Hg of pressure. The optic nerve head was trephined from the globe and digitally reconstructed at 1.5 × 1.5 × 1.5 μm voxel resolution with an automated episcopic fluorescence technique. The load-bearing ONH connective tissue surfaces were manually delineated in 3D using custom software.

Results

The lamina cribrosa and peripapillary sclera were significantly thinner in AD eyes adjusting for age and sex (LC was 24 ± 11 μm thinner; P = 0.0350; scleral was 56 ± 22 μm thinner; P = 0.0097). The lamina cribrosa was significantly thinner in females (23 ± 11 μm thinner; P = 0.0425). Age was not significantly associated with any morphologic parameter in the ED group. However, increasing age was associated with an increase in scleral thickness (1.3 μm/year, P = 0.0499) and an increase in LC depth (2.3 μm/year, P = 0.0035) in the AD group. The sclera was thickest in the superior and temporal regions while the LC was thinnest superiorly.

Conclusions

Substantial sectorial and racial differences in LC and scleral morphology were observed, as well as increasing LC depth and scleral thickness with age in the AD group. Results suggest greater age-related remodeling of the load-bearing ONH connective tissues in eyes from AD individuals that could explain, in part, the greater predilection to glaucomatous injury seen in aged AD populations.

The connective tissue phenotype of glaucomatous cupping in the monkey eye - Clinical and research implications

In a series of previous publications we have proposed a framework for conceptualizing the optic nerve head (ONH) as a biomechanical structure. That framework proposes important roles for intraocular pressure (IOP), IOP-related stress and strain, cerebrospinal fluid pressure (CSFp), systemic and ocular determinants of blood flow, inflammation, auto-immunity, genetics, and other non-IOP related risk factors in the physiology of ONH aging and the pathophysiology of glaucomatous damage to the ONH. The present report summarizes 20 years of technique development and study results pertinent to the characterization of ONH connective tissue deformation and remodeling in the unilateral monkey experimental glaucoma (EG) model. In it we propose that the defining pathophysiology of a glaucomatous optic neuropathy involves deformation, remodeling, and mechanical failure of the ONH connective tissues. We view this as an active process, driven by astrocyte, microglial, fibroblast and oligodendrocyte mechanobiology. These cells, and the connective tissue phenomena they propagate, have primary and secondary effects on retinal ganglion cell (RGC) axon, laminar beam and retrolaminar capillary homeostasis that may initially be "protective" but eventually lead to RGC axonal injury, repair and/or cell death. The primary goal of this report is to summarize our 3D histomorphometric and optical coherence tomography (OCT)-based evidence for the early onset and progression of ONH connective tissue deformation and remodeling in monkey EG. A second goal is to explain the importance of including ONH connective tissue processes in characterizing the phenotype of a glaucomatous optic neuropathy in all species. A third goal is to summarize our current efforts to move from ONH morphology to the cell biology of connective tissue remodeling and axonal insult early in the disease. A final goal is to facilitate the translation of our findings and ideas into neuroprotective interventions that target these ONH phenomena for therapeutic effect.

Collagen Architecture of the Posterior Pole: High-Resolution Wide Field of View Visualization and Analysis Using Polarized Light Microscopy

Purpose

The purpose of this study was to leverage polarized light microscopy (PLM) to visualize the collagen fiber architecture of posterior pole and optic nerve head with micrometer-scale resolution and to identify and quantify major organizational components.

Methods

Eight sheep posterior poles were cryosectioned and imaged using PLM. Collagen fiber orientation was determined by using custom scripts, and the resulting orientation maps were inspected and quantified to identify major structural elements and tested for differences in mean fiber orientation and anisotropy, using linear mixed effect models.

Results

Images revealed an intricate organization of collagen fibers in the posterior pole. In the lamina cribrosa, interweaving fibers formed large knots and wrapped around nerve fiber pores, with beam insertions into the scleral canal wall that were either narrow and straight or wide. In the peripapillary sclera, three significantly different (P < 0.0001) components were identified: fibers oriented circumferentially proximal to the canal, radially in the innermost sclera, and unaligned with interweaving fibers. The radial fibers were between 60 and 180 μm thick, extending at least 3 mm from the canal.

Conclusions

PLM revealed structural aspects of the lamina cribrosa and sclera that may have important biomechanical roles but that were previously unreported or not characterized quantitatively. In the lamina cribrosa, these roles included wide and narrow beam insertions and details of collagen fibers interweaving and wrapping around the pores. In the sclera, we described regions of circumferential, radial, and unaligned “random” fibers. Although there is consensus that circumferential fibers protect neural tissues by resisting canal expansion, the role of the radial fibers remains unclear.

A numerical-experimental protocol to characterize corneal tissue with an application to predict astigmatic keratotomy surgery

Tonometers are intended to determine the intraocular pressure (IOP) and the quality of corneal tissue. In contrast to the physiological state of stress of the cornea, tonometers induce non-physiological bending stress. Recently, the use of a single experiment to calibrate a set of corneal mechanical properties was suggested to be an ill-posed problem. Thus, we propose a numerical-experimental protocol that uses inflation and indentation experiments simultaneously, restricting the optimization space to circumvent the ambiguity of the fitting. For the first time, both corneal behaviors, i.e., biaxial tension (physiological) and bending (non-physiological), are taken into account. The experimental protocol was performed using an animal model (New Zealand rabbit's cornea). The patient-specific geometry and IOP were registered using a MODI topographer (CSO, Italy) and an applanation tonometer, respectively. The mechanical response was evaluated using inflation and indentation experiments. Subsequently, the optimal set of material properties is identified via an inverse finite element method. To validate the methodology, an in vivo incisional refractive surgery (astigmatic keratotomy, AK) is performed on four animals. The optical outcomes showed a good agreement between the real and simulated surgeries, indicating that the protocol can provide a reliable set of mechanical properties that enables further applications and simulations. After a reliable ex vivo database of inflation experiments is built, our protocol could be extended to humans.

Displacement of the Lamina Cribrosa in Response to Acute Intraocular Pressure Elevation in Normal Individuals of African and European Descent

Purpose

To assess if the in vivo mechanical displacement of the anterior laminar cribrosa surface (ALCS) as a response of an acute elevation in intraocular pressure (IOP) differs in individuals of European (ED) and African descent (AD).

Methods

Spectral-domain optical coherence tomography (SDOCT) scans were obtained from 24 eyes of 12 individuals of AD and 18 eyes of 9 individuals of ED at their normal baseline IOP and after 60 seconds IOP elevation using ophthalmodynamometry. Change in depth (displacement) of the LC and to the prelaminar tissue (PLT) were computed in association with the change (delta) in IOP (Δ IOP), race, age, corneal thickness, corneal rigidity (ocular response analyzer [ORA]), and axial.

Results

In the ED group for small IOP elevations (Δ IOP < 12 mm Hg), the ALCS initially displaced posteriorly but for larger increase of IOP an anterior displacement of the lamina followed. Inversely, in the AD group the ALCS did not show a significant posterior displacement for small Δ IOP, while for larger IOP increases the ALCS significantly displaced posteriorly. Posterior displacement of the lamina cribrosa (LC) was also significantly correlated with longer axial length, higher corneal thickness, and ORA parameters. Prelaminar tissue posteriorly displaced for any magnitude of Δ IOP, in both groups.

Conclusions

The African descent group demonstrated a greater acute posterior bowing of the LC after adjustment for age, axial length, Bruch's membrane opening (BMO) area, and ORA parameters. Greater PLT posterior displacement was also seen in the AD group with increasing IOP, which was tightly correlated with the displacement of the LC.

The impact of ocular hemodynamics and intracranial pressure on intraocular pressure during acute gravitational changes

Exposure to microgravity causes a bulk fluid shift toward the head, with concomitant changes in blood volume/pressure, and intraocular pressure (IOP). These and other factors, such as intracranial pressure (ICP) changes, are suspected to be involved in the degradation of visual function and ocular anatomical changes exhibited by some astronauts. This is a significant health concern. Here, we describe a lumped-parameter numerical model to simulate volume/pressure alterations in the eye during gravitational changes. The model includes the effects of blood and aqueous humor dynamics, ICP, and IOP-dependent ocular compliance. It is formulated as a series of coupled differential equations and was validated against four existing data sets on parabolic flight, body inversion, and head-down tilt (HDT). The model accurately predicted acute IOP changes in parabolic flight and HDT, and was satisfactory for the more extreme case of inversion. The short-term response to the changing gravitational field was dominated by ocular blood pressures and compliance, while longer-term responses were more dependent on aqueous humor dynamics. ICP had a negligible effect on acute IOP changes. This relatively simple numerical model shows promising predictive capability. To extend the model to more chronic conditions, additional data on longer-term autoregulation of blood and aqueous humor dynamics are needed.NEW & NOTEWORTHY A significant percentage of astronauts present anatomical changes in the posterior eye tissues after spaceflight. Hypothesized increases in ocular blood volume and intracranial pressure (ICP) in space have been considered to be likely factors. In this work, we provide a novel numerical model of the eye that incorporates ocular hemodynamics, gravitational forces, and ICP changes. We find that changes in ocular hemodynamics govern the response of intraocular pressure during acute gravitational change.

Effect of acute intraocular pressure elevation on the minimum rim width in normal, ocular hypertensive and glaucoma eyes

BACKGROUND

To estimate and compare changes in the Bruch's membrane opening-minimum rim width (BMO-MRW) and area in normal, ocular hypertensive and glaucoma eyes following acute elevations in intraocular pressure (IOP).

METHODS

The optic nerve heads (ONHs) of 104 subjects (31 normals, 20 ocular hypertension (OHT) and 53 with primary glaucoma) were imaged using Spectral-domain optical coherence tomography (OCT; Spectralis, Heidelberg Engineering, Germany). IOP was raised twice by applying a force (0.64 n then 0.9 n) to the anterior sclera using an ophthalmo-dynamometer. After each IOP increment, IOP was held constant, measured with a Tonopen (AVIA applanation tonometer, Reichert, Depew, New York, USA), and ONH was rescanned with OCT. In each OCT volume, BMO-MRW and area were calculated and at each IOP increment.

RESULTS

The baseline MRW was significantly smaller in glaucoma subjects (174.3±54.3 µm) compared with normal (287.4±42.2 µm, p<0.001) and OHT subjects (255.4±45.3 µm, p<0.001). MRW of glaucoma subjects was significantly thinner at the first and second IOP elevations than that at baseline (both p<0.01), but no significant change was noted in normal and OHT subjects. There was no significant change of BMO area at acute IOP elevations from baseline in all diagnoses (all p>0.05).

CONCLUSION

Acute IOP elevation leads to compression of the nerve fibre layers of neuroretinal rim in glaucoma subjects only without changing ONH size. This suggests that the neural and connective tissues at ONH level in glaucoma subjects are more susceptible to acute IOP episodes than OHT or normal controls.

Anisotropic Finite Element Modeling Based on a Harmonic Field for Patient-Specific Sclera

Purpose. This study examined the influence of anisotropic material for human sclera. Method. First, the individual geometry of patient-specific sclera was reproduced from a laser scan. Then, high quality finite element modeling of individual sclera was performed using a convenient automatic hexahedral mesh generator based on harmonic field and integrated with anisotropic material assignment function. Finally, comparison experiments were designed to investigate the effects of anisotropy on finite element modeling of sclera biomechanics. Results. The experimental results show that the presented approach can generate high quality anisotropic hexahedral mesh for patient-specific sclera. Conclusion. The anisotropy shows significant differences for stresses and strain distribution and careful consideration should be given to its use in biomechanical FE studies.

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.