Scleral anisotropy and its effects on the mechanical response of the optic nerve head

This paper presents a computational modeling study of the effects of the collagen fiber structure on the mechanical response of the sclera and the adjacent optic nerve head (ONH). A specimen-specific inverse finite element method was developed to determine the material properties of two human sclera subjected to full-field inflation experiments. A distributed fiber model was applied to describe the anisotropic elastic behavior of the sclera. The model directly incorporated wide-angle X-ray scattering measurements of the anisotropic collagen structure. The converged solution of the inverse method was used in micromechanical studies of the mechanical anisotropy of the sclera at different scales. The effects of the scleral collagen fiber structure on the ONH deformation were evaluated by progressively filtering out local anisotropic features. It was found that the majority of the midposterior sclera could be described as isotropic without significantly affecting the mechanical response of the tissues of the ONH. In contrast, removing local anisotropic features in the peripapillary sclera produced significant changes in scleral canal expansion and lamina cribrosa deformation. Local variations in the collagen structure of the peripapillary sclera significantly influenced the mechanical response of the ONH.     

Age-related changes in human peripapillary scleral strain

To test the hypothesis that mechanical strain in the posterior human sclera is altered with age, 20 pairs of normal eyes from human donors aged 20 to 90 years old were inflation tested within 48-h postmortem. The intact posterior scleral shells were pressurized from 5 to 45 mmHg, while the full-field three-dimensional displacements of the scleral surface were measured using laser speckle interferometry. The full strain tensor of the outer scleral surface was calculated directly from the displacement field. Mean maximum principal (tensile) strain was computed for eight circumferential sectors ( $45^{\circ }$ wide) within the peripapillary and mid-peripheral regions surrounding the optic nerve head (ONH). To estimate the age-related changes in scleral strain, results were fit using a functional mixed effects model that accounts for intradonor variability and spatial autocorrelation. Mechanical tensile strain in the peripapillary sclera is significantly higher than the strain in the sclera farther away from the ONH. Overall, strains in the peripapillary sclera decrease significantly with age. Sectorially, peripapillary scleral tensile strains in the nasal sectors are significantly higher than the temporal sectors at younger ages, but the sectorial strain pattern reverses with age, and the temporal sectors exhibited the highest tensile strains in the elderly. Overall, peripapillary scleral structural stiffness increases significantly with age. The sectorial pattern of peripapillary scleral strain reverses with age, which may predispose adjacent regions of the lamina cribrosa to biomechanical insult. The pattern and age-related changes in sectorial peripapillary scleral strain closely match those seen in disk hemorrhages and neuroretinal rim area measurement change rates reported in previous studies of normal human subjects.     

Quantification of collagen organization in the peripheral human cornea at micron-scale resolution

The collagen microstructure of the peripheral cornea is important in stabilizing corneal curvature and refractive status. However, the manner in which the predominantly orthogonal collagen fibrils of the central cornea integrate with the circumferential limbal collagen is unknown. We used microfocus wide-angle x-ray scattering to quantify the relative proportion and orientation of collagen fibrils over the human corneolimbal interface at intervals of 50 μm. Orthogonal fibrils changed direction 1–1.5 mm before the limbus to integrate with the circumferential limbal fibrils. Outside the central 6 mm, additional preferentially aligned collagen was found to reinforce the cornea and limbus. The manner of integration and degree of reinforcement varied significantly depending on the direction along which the limbus was approached. We also employed small-angle x-ray scattering to measure the average collagen fibril diameter from central cornea to limbus at 0.5 mm intervals. Fibril diameter was constant across the central 6 mm. More peripherally, fibril diameter increased, indicative of a merging of corneal and scleral collagen. The point of increase varied with direction, consistent with a scheme in which the oblique corneal periphery is reinforced by chords of scleral collagen. The results have implications for the cornea's biomechanical response to ocular surgeries involving peripheral incision.     

Lamellar orientation in human cornea in relation to mechanical properties

We have applied wide-angle X-ray scattering to the human cornea in order to quantify the relative number of stromal collagen fibrils directed along the two preferred corneal lamellar directions: superior-inferior and nasal-temporal. The data suggest that, on average, the two directions are populated in equal proportion at the corneal centre. Here, approximately one-third of the fibrils throughout the stromal depth tend to lie within a 45 degrees sector of the superior-inferior meridian, and similarly for the nasal-temporal direction. However, in some eyes we have measured significant differences between the two preferential fibril populations, with some corneas exhibiting as much as 25% more collagen in one direction than the other. Based on these findings, a mechanical model of the normal cornea may be envisaged, whereby the fibril tension in the underlying "background" of isotropically arranged collagen helps to balance the intraocular pressure; while the extra preferentially aligned fibrils take up the additional tensile stress along the superior-inferior and nasal-temporal meridians exerted by the rectus muscles and the orbicularis. It is possible that, through a direct impact on the elastic modulus of the tissue, an imbalance of superior-inferior and nasal-temporal fibrils in some eyes might affect corneal shape.     

X-ray scattering used to map the preferred collagen orientation in the human cornea and limbus

Many properties of connective tissues are governed by the organization of the constituent collagen. For example, the organization of collagen in the cornea and the limbus, where the cornea and sclera meet, is an important determinant of corneal curvature and hence of the eye's focusing power. We have used synchrotron X-ray scattering to map the orientation of the collagen fibrils throughout the human cornea, limbus, and adjacent sclera. We demonstrate a preferred orientation of collagen in the vertical and horizontal directions that is maintained to within about 1 mm from the limbus, where a circular or tangential disposition of fibrils occurs. The data are also used to map the relative distribution of both the total and the preferentially aligned collagen in different parts of the tissue, revealing considerable anisotropy. The detailed structural information provided is an important step toward understanding the shape and the mechanical properties of the tissue.     

Viscoelastic characterization of peripapillary sclera: material properties by quadrant in rabbit and monkey eyes

In this report we characterize the viscoelastic material properties of peripapillary sclera from the four quadrants surrounding the optic nerve head in both rabbit and monkey eyes. Scleral tensile specimens harvested from each quadrant were subjected to uniaxial stress relaxation and tensile ramp to failure tests. Linear viscoelastic theory, coupled with a spectral reduced relaxation function, was employed to characterize the viscoelastic properties of the tissues. We detected no differences in the stress-strain curves of specimens from the four quadrants surrounding the optic nerve head (ONH) below a strain of 4 percent in either the rabbit or monkey. While the peripapillary sclera from monkey eyes is significantly stiffer (both instantaneously and in equilibrium) and relaxes more slowly than that from rabbits, we detected no differences in the viscoelastic material properties (tested at strains of 0-1 percent) of sclera from the four quadrants surrounding the ONH within either species group.     

New insight into the shortening of the collagen fibril D-period in human cornea

Collagen fibrils type I display a typical banding pattern, so-called D-periodicity, of about 67 nm, when visualized by atomic force or electron microscopy imaging. Herein we report on a significant shortening of the D-period for human corneal collagen fibrils type I (21 ± 4 nm) upon air-drying, whereas no changes in the D-period were observed for human scleral collagen fibrils type I (64 ± 4 nm) measured under the same experimental conditions as the cornea. It was also found that for the corneal stroma fixed with glutaraldehyde and air-dried, the collagen fibrils show the commonly accepted D-period of 61 ± 8 nm. We used the atomic force microscopy method to image collagen fibrils type I present in the middle layers of human cornea and sclera. The water content in the cornea and sclera samples was varying in the range of .066–.085. Calculations of the D-period using the theoretical model of the fibril and the FFT approach allowed to reveal the possible molecular mechanism of the D-period shortening in the corneal collagen fibrils upon drying. It was found that both the decrease in the shift and the simultaneous reduction in the distance between tropocollagen molecules can be responsible for the experimentally observed effect. We also hypothesize that collagen type V, which co-assembles with collagen type I into heterotypic fibrils in cornea, could be involved in the observed shortening of the corneal D-period.     

Experimental surface strain mapping of porcine peripapillary sclera due to elevations of intraocular pressure

To experimentally characterize 2D surface mapping of the deformation pattern of porcine peripapillary sclera following acute elevations of intraocular pressure (IOP) from 5 mm Hg to 45 mm Hg. Four porcine eyes were obtained within 48 h postmortem and dissected to the sclera. After the anterior chamber was removed, each posterior scleral shell was individually mounted at the equator on a custom-built pressurization device, which internally pressurized the scleral samples with isotonic saline at 22 degrees C. Black polystyrene microspheres (10 microm in diameter) were randomly scattered and attached to the scleral surface. IOP was incrementally increased from 5 mm Hg to 45 mm Hg (+/-0.15 mm Hg), and the surface deformation of the peripapillary sclera immediately adjacent to the dural insertion was optically tracked at a resolution of 2 micrompixel one quadrant at a time, for each of four quadrants (superior, nasal, inferior, and temporal). The 2D displacement data of the microsphere markers were extracted using the optical flow equation, smoothed by weighting function interpolation, and converted to the corresponding Lagrangian finite surface strain. In all four quadrants of each eye, the principal strain was highest and primarily circumferential immediately adjacent to the scleral canal. Average maximum Lagrangian strain across all quadrants for all eyes was 0.013+/-0.005 from 5 mm Hg to 10 mm Hg, 0.014+/-0.004 from 10 mm Hg to 30 mm Hg and 0.004+/-0.001 from 30 mm Hg to 45 mm Hg, demonstrating the nonlinearity in the IOP-strain relationship. For each scleral shell, the observed surface strain mapping implied that the scleral stiffness was relatively low between 5 mm Hg and 10 mm Hg, but dramatically increased for each IOP elevation increment beyond 10 mm Hg. Peripapillary deformation following an acute IOP elevation may be governed by the underlying scleral collagen microstructure and is likely in the high-stiffness region of the scleral stress-strain curve when IOP is above 10 mm Hg.     

Spatial mapping of collagen fibril organisation in primate cornea-an X-ray diffraction investigation

New insights are presented into the collagenous structure of the primate cornea. Wide-angle X-ray diffraction was used to map the fibrillar arrangement and distribution of collagen over three common marmoset corneas. The maps provide a point of reference to help interpret data from pathological corneas or primate models of refractive surgery. The results herein disclose a circum-corneal annulus of highly aligned collagen, 0.5-1.5 mm wide, where the cornea and sclera fuse at the limbus; a feature similar to that observed in human tissue. As in humans, the annulus is not uniform, varying in width, fibril angular spread, and collagen density around its circumference. However, more centrally the marmoset cornea exhibits a preferred lamella orientation in which proportionally more fibrils are oriented along the superior-inferior corneal meridian. This observation is in striking contrast with the situation in human cornea, where there is an orthogonal arrangement of preferentially aligned fibrils. Investigation of a further 16 corneas confirmed that approximately 33% (+/-1%) (n = 76) of fibrils in the central marmoset cornea lie within a 45 degrees sector of the superior-inferior meridian. Implications for the mechanical and optical properties of the cornea are discussed.     

Opto-mechanical characterization of sclera by polarization sensitive optical coherence tomography

Polarization sensitive optical coherence tomography (PSOCT) is an interferometric technique sensitive to birefringence. Since mechanical loading alters the orientation of birefringent collagen fibrils, we asked if PSOCT can be used to measure local mechanical properties of sclera.Infrared (1300 nm) PSOCT was performed during uniaxial tensile loading of fresh scleral specimens of rabbits, cows, and humans from limbal, equatorial, and peripapillary regions. Specimens from 8 human eyes were obtained. Specimens were stretched to failure at 0.01 mm/s constant rate under physiological conditions of temperature and humidity while birefringence was computed every 117 ms from cross-sectional PSOCT. Birefringence modulus (BM) was defined as the rate of birefringence change with strain, and tensile modulus (TM) as the rate of stress change between 0 and 9% strain.In cow and rabbit, BM and TM were positively correlated with slopes of 0.17 and 0.10 GPa, and with correlation coefficients 0.63 and 0.64 (P < 0.05), respectively, following stress-optic coefficients 4.69, and 4.20 GPa⁻¹. In human sclera, BM and TM were also positively correlated with slopes of 0.24 GPa for the limbal, 0.26 GPa for the equatorial, and 0.31 GPa for the peripapillary regions. Pearson correlation coefficients were significant at 0.51, 0.58, and 0.69 for each region, respectively (<0.001). Mean BM decreased proportionately to TM from the limbal to equatorial to peripapillary regions, as stress-optic coefficients were estimated as 2.19, 2.42, and 4.59 GPa⁻¹, respectively.Since birefringence and tensile elastic moduli correlate differently in cow, rabbit, and various regions of human sclera, it might be possible to mechanically characterize the sclera in vivo using PSOCT.     

The collagen fibril architecture in the lamina cribrosa and peripapillary sclera predicted by a computational remodeling approach

The biomechanics of the optic nerve head is assumed to play an important role in ganglion cell loss in glaucoma. Organized collagen fibrils form complex networks that introduce strong anisotropic and nonlinear attributes into the constitutive response of the peripapillary sclera (PPS) and lamina cribrosa (LC) dominating the biomechanics of the optic nerve head. The recently presented computational remodeling approach (Grytz and Meschke in Biomech Model Mechanobiol 9:225–235, 2010) was used to predict the micro-architecture in the LC and PPS, and to investigate its impact on intraocular pressure–related deformations. The mechanical properties of the LC and PPS were derived from a microstructure-oriented constitutive model that included the stretch-dependent stiffening and the statistically distributed orientations of the collagen fibrils. Biomechanically induced adaptation of the local micro-architecture was captured by allowing collagen fibrils to be reoriented in response to the intraocular pressure–related loading conditions. In agreement with experimental observations, the remodeling algorithm predicted the existence of an annulus of fibrils around the scleral canal in the PPS, and a predominant radial orientation of fibrils in the periphery of the LC. The peripapillary annulus significantly reduced the intraocular pressure–related expansion of the scleral canal and shielded the LC from high tensile stresses. The radial oriented fibrils in the LC periphery reinforced the LC against transversal shear stresses and reduced LC bending deformations. The numerical approach presents a novel and reasonable biomechanical explanation of the spatial orientation of fibrillar collagen in the optic nerve head.     

Collagen type I and type V are present in the same fibril in the avian corneal stroma

The distribution, supramolecular form, and arrangement of collagen types I and V in the chicken embryo corneal stroma were studied using electron microscopy, collagen type-specific monoclonal antibodies, and a preembedding immunogold method. Double-label immunoelectron microscopy with colloidal gold-tagged monoclonal antibodies was used to simultaneously localize collagen type I and type V within the chick corneal stroma. The results definitively demonstrate, for the first time, that both collagens are codistributed within the same fibril. Type I collagen was localized to striated fibrils throughout the corneal stroma homogeneously. Type V collagen could be localized only after pretreatment of the tissue to partially disrupt collagen fibril structure. After such pretreatments the type V collagen was found in regions where fibrils were partially dissociated and not in regions where fibril structure was intact. When pretreated tissues were double labeled with antibodies against types I and V collagen coupled to different size gold particles, the two collagens colocalized in areas where fibril structure was partially disrupted. Antibodies against type IV collagen were used as a control and were nonreactive with fibrils. These results indicate that collagen types I and V are assembled together within single fibrils in the corneal stroma such that the interaction of these collagen types within heterotypic fibrils masks the epitopes on the type V collagen molecule. One consequence of the formation of such heterotypic fibrils may be the regulation of corneal fibril diameter, a condition essential for corneal transparency.     

A computational remodeling approach to predict the physiological architecture of the collagen fibril network in corneo-scleral shells

Organized collagen fibrils form complex networks that introduce strong anisotropic and highly nonlinear attributes into the constitutive response of human eye tissues. Physiological adaptation of the collagen network and the mechanical condition within biological tissues are complex and mutually dependent phenomena. In this contribution, a computational model is presented to investigate the interaction between the collagen fibril architecture and mechanical loading conditions in the corneo-scleral shell. The biomechanical properties of eye tissues are derived from the single crimped fibril at the micro-scale via the collagen network of distributed fibrils at the meso-scale to the incompressible and anisotropic soft tissue at the macro-scale. Biomechanically induced remodeling of the collagen network is captured on the meso-scale by allowing for a continuous re-orientation of preferred fibril orientations and a continuous adaptation of the fibril dispersion. The presented approach is applied to a numerical human eye model considering the cornea and sclera. The predicted fibril morphology correlates well with experimental observations from X-ray scattering data.     

The Expression of Tenascin-X in Developing and Adult Rat and Human Eye

Tenascin-X has been studied in developing and adult rat eye and in foetal and adult human eyes, using immunohistochemistry and frozen sections. The data were compared with the distribution of tenascin-C. The immunoreactivity for tenascin-X was seen in a basement membrane-like feature in different structures of embryonic (E) day 16–17 rat eyes. Postnatal (P) day 2 and older rat eyes showed immunoreactivity for tenascin-X in different connective tissues. In the epithelial basement membrane zone of the cornea, immunostaining was positive in P5 eyes, negative in P10 and P15 eyes and again positive in P30 and adult eyes. In the 20-week-old human foetus, immunoreactivity for the tenascin was seen in the posterior parts of the conjunctival stroma adjacent to the sclera and in a basement membrane-like fashion in anterior conjunctiva. In the adult human eye, immunoreactivity for tenascin-X was seen in the anterior one-third stroma of cornea as thin fibrils, in the stroma of the limbus and conjunctiva, and in blood vessels. Immunostaining for tenascin-C was seen in the posterior aspect of the further cornea, and in mesenchyme adjacent to cornea in E16–17 rat eyes. Corneal keratocytes and Descemet's membrane showed immunoreactivity for tenascin-C in P2–P15 rat eyes. Sclera and the junction of the cornea, and sclera expressed tenascin-C in P2 and older rat eyes. In human foetal eyes, immunostaining for tenascin-C was seen in the anterior parts of the corneal stroma, in the basement membrane zone and Bowman's membrane of the corneal epithelium, in the posterior one-fifth of the corneal stroma and the sclera starting from the junction of the cornea and sclera. In normal human adult eyes, immunostaining for tenascin-X was seen in the anterior one-third stroma of cornea, in the stroma of limbus and conjunctiva, and in blood vessels. The association of tenascin-X and basement membranes in early development evokes a question of its potential function in the development of the basement membrane. The results also suggest the association of tenascin-X with connective tissue development as well as the association of tenascin-C with the migration of keratocytes during the development of the corneal stroma.     

The integration of the corneal and limbal fibrils in the human eye.

The precise orientation of the collagen fibrils in human cornea and sclera and the method by which these two areas fuse together at the limbus have never been determined, despite the importance of this information. From a consideration of the mechanics of the system, fibril orientation in the tissue has the potential to affect the curvature of the cornea so, by inference, refractive problems such as astigmatism involving an incorrect curvature of the cornea may be related to fibril orientation. The high intensity and small beam size of a synchrotron x-ray source has enabled us to study fibril orientation in post-mortem human cornea and sclera. Previously we have revealed two preferred directions of orientation in the cornea (Meek, K. M., T. Blamires, G. F. Elliot, T. Y. Gyi, and C. J. Nave. 1987. Curr. Eye Res. 6:841-846) and a circumcorneal annulus in the limbus (Newton, R. H., and K. M. Meek. 1998. Invest. Ophthalmol. & Visual Sci. 39: 1125-1134). Here we present the results of our investigation into the relationship between these two features. Our measurements indicate that the corneal fibrils oriented in the two preferred directions bend at the limbus to run circumferentially. On the basis of these results we propose a model as to how the human cornea and sclera fuse together.     

Modeling of bone at a single lamella level

This paper focuses on the ultrastructure of bone at a single lamella level. At this scale, collagen fibrils reinforced with apatite crystals are aligned preferentially to form a lamella. At the next structural level, such lamella are stacked in different orientations to form either osteons in cortical bone or trabecular pockets in trabecular bone. We use a finite element model, which treats small strain elasticity of a spatially random network of collagen fibrils, and compute anisotropic effective stiffness tensors and deformations of such a single lamella as a function of fibril volume fractions (or porosities), prescribed microgeometries, and fibril geometric and elastic properties.     

Polarization-resolved second-harmonic generation in tendon upon mechanical stretching

Collagen is a triple-helical protein that forms various macromolecular organizations in tissues and is responsible for the biomechanical and physical properties of most organs. Second-harmonic generation (SHG) microscopy is a valuable imaging technique to probe collagen fibrillar organization. In this article, we use a multiscale nonlinear optical formalism to bring theoretical evidence that anisotropy of polarization-resolved SHG mostly reflects the micrometer-scale disorder in the collagen fibril distribution. Our theoretical expectations are confirmed by experimental results in rat-tail tendon. To that end, we report what to our knowledge is the first experimental implementation of polarization-resolved SHG microscopy combined with mechanical assays, to simultaneously monitor the biomechanical response of rat-tail tendon at macroscopic scale and the rearrangement of collagen fibrils in this tissue at microscopic scale. These experiments bring direct evidence that tendon stretching corresponds to straightening and aligning of collagen fibrils within the fascicle. We observe a decrease in the SHG anisotropy parameter when the tendon is stretched in a physiological range, in agreement with our numerical simulations. Moreover, these experiments provide a unique measurement of the nonlinear optical response of aligned fibrils. Our data show an excellent agreement with recently published theoretical calculations of the collagen triple helix hyperpolarizability.     

Spatial distribution and orientation of dermatan sulfate in human medial collateral ligament

The proteoglycan decorin and its associated glycosaminoglycan (GAG), dermatan sulfate (DS), regulate collagen fibril formation, control fibril diameter, and have been suggested to contribute to the mechanical stability and material properties of connective tissues. The spatial distribution and orientation of DS within the tissue are relevant to these mechanical roles, but measurements of length and orientation from 2D transmission electron microscopy (TEM) are prone to errors from projection. The objectives of this study were to construct a 3D geometric model of DS GAGs and collagen fibrils, and to use the model to interpret TEM measurements of the spatial orientation and length of DS GAGs in the medial collateral ligament of the human knee. DS was distinguished from other sulfated GAGs by treating tissue with chondroitinase B, an enzyme that selectively degrades DS. An image processing pipeline was developed to analyze the TEM micrographs. The 3D model of collagen and GAGs quantified the projection error in the 2D TEM measurements. Model predictions of 3D GAG orientation were highly sensitive to the assumed GAG length distribution, with the baseline input distribution of 69+/-23 nm providing the best predictions of the angle measurements from TEM micrographs. The corresponding orientation distribution for DS GAGs was maximal at orientations orthogonal to the collagen fibrils, tapering to near zero with axial alignment. Sulfated GAGs that remained after chondroitinase B treatment were preferentially aligned along the collagen fibril. DS therefore appears more likely to bridge the interfibrillar gap than non-DS GAGs. In addition to providing quantitative data for DS GAG length and orientation in the human MCL, this study demonstrates how a 3D geometric model can be used to provide a priori information for interpretation of geometric measurements from 2D micrographs.