Changes in the refractive index of the stroma and its extrafibrillar matrix when the cornea swells

The transparency of the corneal stroma is critically dependent on the hydration of the tissue; if the cornea swells, light scattering increases. Although this scattering has been ascribed to the disruption caused to the arrangement of the collagen fibrils, theory predicts that light scattering could increase if there is an increased mismatch in the refractive indices of the collagen fibrils and the material between them. The purpose of this article is to use Gladstone and Dale's law of mixtures to calculate volume fractions for a number of different constituents in the stroma, and use these to show how the refractive indices of the stroma and its constituent extrafibrillar material would be expected to change as more solvent enters the tissue. Our calculations predict that solvent entering the extrafibrillar space causes a reduction in its refractive index, and hence a reduction in the overall refractive index of the bovine stroma according to the equation n'(s) = 1.335 + 0.04/(0.22 + 0.24 H'), where n'(s) is the refractive index and H' is the hydration of the swollen stroma. This expression is in reasonable agreement with our experimental measurements of refractive index versus hydration in bovine corneas. When the hydration of the stroma increases from H = 3.2 to H = 8.0, we predict that the ratio of the refractive index of the collagen fibrils to that of the material between them increases from 1.041 to 1.052. This change would be expected to make only a small contribution to the large increase in light scattering observed when the cornea swells to H = 8.     

X-ray diffraction study of the cornea

Low-angle X-ray diffraction patterns have been recorded from the cornea. A fibre diagram was obtained: the reflections from the axial period of collagen were on the equator while reflections from the collagen fibril lattice structure were on the meridian. Only the reflections from tha array of collagen fibrils have been studied. These reflections contain a primary first-order reflection and up to four subsidiary maxima. The first-order reflection from the array provides an estimate of the interfibril separation distance. Evidence is presented that the subsidiary maxima are consistent with the intensity transform of a uniform cylinder with a constant radius. Values for the fibril diameters and the interfibril distances are obtained for corneas from rabbit, cow and frog and from corneas of two marine fishes: toadfish and skate. Although the volume fraction of the collagen fibrils cannot be directly evaluated, an upper limit can be given. Thus, an upper limit of 0.28 was obtained for rabbit cornea.     

Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach

Extracellular bone material can be characterised as a nanocomposite where, in a liquid environment, nanometre-sized hydroxyapatite crystals precipitate within as well as between long fibre-like collagen fibrils (with diameters in the 100 nm range), as evidenced from neutron diffraction and transmission electron microscopy. Accordingly, these crystals are referred to as ‘interfibrillar mineral’ and ‘extrafibrillar mineral’, respectively. From a topological viewpoint, it is probable that the mineralisations start on the surfaces of the collagen fibrils (‘mineral-encrusted fibrils’), from where the crystals grow both into the fibril and into the extrafibrillar space. Since the mineral concentration depends on the pore spaces within the fibrils and between the fibrils (there is more space between them), the majority of the crystals (but clearly not all of them) typically lie in the extrafibrillar space. There, larger crystal agglomerations or clusters, spanning tens to hundreds of nanometers, develop in the course of mineralisation, and the micromechanics community has identified the pivotal role, which this extrafibrillar mineral plays for tissue elasticity. In such extrafibrillar crystal agglomerates, single crystals are stuck together, their surfaces being covered with very thin water layers. Recently, the latter have caught our interest regarding strength properties (Fritsch et al. 2009 J Theor Biol. 260(2): 230–252) – we have identified these water layers as weak interfaces in the extrafibrillar mineral of bone. Rate-independent gliding effects of crystals along the aforementioned interfaces, once an elastic threshold is surpassed, can be related to overall elastoplastic material behaviour of the hierarchical material ‘bone’. Extending this idea, the present paper is devoted to viscous gliding along these interfaces, expressing itself, at the macroscale, in the well-known experimentally evidenced phenomenon of bone viscoelasticity. In this context, a multiscale homogenisation scheme is extended to viscoelasticity, mineral-cluster-specific creep parameters are identified from three-point bending tests on hydrated bone samples, and the model is validated by statistically and physically independent experiments on partially dried samples. We expect this model to be relevant when it comes to prediction of time-dependent phenomena, e.g. in the context of bone remodelling.     

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.     

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.     

Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization

We model the elastic properties of bone at the level of mineralized collagen fibrils via step-by-step homogenization from the staggered arrangement of collagen molecules up to an array of parallel mineralized fibrils. A new model for extrafibrillar mineralization is proposed, assuming that the extrafibrillar minerals are mechanically equivalent to reinforcing rings coating each individual fibril. Our modeling suggests that no more than 30% of the total mineral content is extrafibrillar and the fraction of extrafibrillar minerals grows linearly with the overall degree of mineralization. It is shown that the extrafibrillar mineralization considerably reinforces the fibrils’ mechanical properties in the transverse directions and the fibrils’ shear moduli. The model predictions for the elastic moduli and constants are found to be in a good agreement with the experimental data reported in the literature.     

Electron tomography reveals multiple self-association of chondroitin sulphate/dermatan sulphate proteoglycans in Chst5-null mouse corneas

The spatial distribution of collagen fibrils in the corneal stroma is essential for corneal transparency and is primarily regulated by extrafibrillar proteoglycans, which are multi-functional polymers that interact with hybrid type I/V collagen fibrils. In order to understand more about proteoglycan organisation and collagen associations in the cornea, three-dimensional electron microscopy reconstructions of collagen-proteoglycan interactions in the anterior, mid and posterior stroma from a Chst5 knockout mouse, which lacks a keratan sulphate sulphotransferase, were obtained. Both longitudinal and transverse section show sinuous, oversized proteoglycans with near-periodic, orthogonal off-shoots. In many cases, these proteoglycans traverse over 400nm of interfibrillar space interconnecting over 10 collagen fibrils. The reconstructions suggest that multiple chondroitin sulphate/dermatan sulphate proteoglycans have aggregated laterally and, possibly, end-to-end, with orthogonal extensions protruding from the main electron-dense stained filament. We suggest possible mechanisms as to how sulphation differences may lead to this increase in aggregation of proteoglycans in the Chst5-null mouse corneal stroma and how this relates to proteoglycan packing in healthy corneas.     

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.     

A model for the human cornea: constitutive formulation and numerical analysis

The human cornea (the external lens of the eye) has the macroscopic structure of a thin shell, originated by the organization of collagen lamellae parallel to the middle surface of the shell. The lamellae, composed of bundles of collagen fibrils, are responsible for the experimentally observed anisotropy of the cornea. Anomalies in the fibril structure may explain the changes in the mechanical behavior of the tissue observed in pathologies such as keratoconus. We employ a fiber-matrix constitutive model and propose a numerical model for the human cornea that is able to account for its mechanical behavior in healthy conditions or in the presence of keratoconus under increasing values of the intraocular pressure. The ability of our model to reproduce the behavior of the human cornea opens a promising perspective for the numerical simulation of refractive surgery.     

A study of dense mineralized tissue by neutron diffraction

Neutron diffraction studies of mineralized tissue show a close relationship between the wet state equatorial diffraction spacing and wet tissue density expressable as a second-order polynomial. The molecular fractional shrinkage when the tissue is dried shows a straight line dependence on wet tissue density with a correlation of 0.98. Since the dry state equatorial diffraction spacing is much less than for the corresponding wet state, even in fully mineralized bone, the collagen molecules must be displaced through a mineral-free volume while drying. The mineral can only be located within the available volume of the dried tissue whether intra- or extrafibrillar. The dimension of the dry state equatorial spacing for each of the tissues examined is close to that of dried tendon collagen. It appears unlikely that hydroxyapatite crystallites can be accommodated radially between collagen molecules in bone if the packing is like that of dried tail tendon collagen. The only mineral within the fibrils must be in the intermolecular gaps. It is estimated on the basis of the volume of the axial intermolecular gaps and the minimum extrafibrillar volume that the intrafibrillar mineral can be no more than 20% of the total mineral and may be less than 10%.     

The mechanical properties of the rabbit and human cornea

The extensibility of rabbit and human corneas was measured by raising the pressure within the intact globe of the eye and measuring the displacements of two very small mercury drops on the corneal surface. The human cornea showed a negligible extensibility under low stresses. The rabbit tissue, however, underwent a 9% strain under low pressures with a curvilinear relationship between stress and strain. At higher pressures the relationship was linear, and the tissue showed some creep. The low pressure stress-strain relationship of the rabbit could not be explained on the basis that the collagen fibrils were being straightened out from an initial set in a sinusoidal wave. When the stroma was isolated from Descemet's membrane, it showed a negligible low pressure extensibility in rabbit and man. On the other hand, isolated Descemet's membrane was very extensible in both species. The difference between them in the behavior of the intact cornea seems to lie in the relative initial strain in the stroma and Descemet's membrane.     

Interpretation of the meridional X-ray diffraction pattern from collagen fibrils in corneal stroma

The low angle X-ray diffraction pattern from corneal stroma can be interpreted as arising from the equivalent of sharp meridional reflections due to the packing of molecules along the collagen fibrils and an equatorial pattern due to the packing of these fibrils within lamellae.Axial electron density profiles for corneal collagen fibrils have been produced by combining intensity data from the meridional pattern with two independent sets of phases. The first set was obtained using an electron microscopical technique, whereas the second set consisted of calculated tendon collagen phases given in the literature. Substantial agreement between the two electron density profiles was found.A quantitative analysis of the difference between the electron density profiles of rat tail tendon and corneal collagen showed that the step between the gap and overlap regions is smaller in cornea than in tendon. This is probably due to the binding of non-collagenous material in the gap region as occurs in bone and other tissue. Two peaks corresponding to regions where electron density is greater in the cornea are situated at the gap/overlap junctions. A third region where the corneal collagen is more electron dense is located near the centre of the gap region. The proximity of these peaks to the positions of hydroxylysine residues along the fibril axis suggests that they may be the major sites at which sugars are bound to corneal collagen.     

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

There is an ongoing discussion on how bone strength could be explained from its internal structure and composition. Reviewing recent experimental and molecular dynamics studies, we here propose a new vision on bone material failure: mutual ductile sliding of hydroxyapatite mineral crystals along layered water films is followed by rupture of collagen crosslinks. In order to cast this vision into a mathematical form, a multiscale continuum micromechanics theory for upscaling of elastoplastic properties is developed, based on the concept of concentration and influence tensors for eigenstressed microheterogeneous materials. The model reflects bone's hierarchical organization, in terms of representative volume elements for cortical bone, for extravascular and extracellular bone material, for mineralized fibrils and the extrafibrillar space, and for wet collagen. In order to get access to the stress states at the interfaces between crystals, the extrafibrillar mineral is resolved into an infinite amount of cylindrical material phases oriented in all directions in space. The multiscale micromechanics model is shown to be able to satisfactorily predict the strength characteristics of different bones from different species, on the basis of their mineral/collagen content, their intercrystalline, intermolecular, lacunar, and vascular porosities, and the elastic and strength properties of hydroxyapatite and (molecular) collagen.     

Average hydroxyapatite concentration is uniform in the extracollagenous ultrastructure of mineralized tissues: evidence at the 1–10-μm scale

At the ultrastructural observation scale of fully mineralized tissues (l=1-10 mum), transmission electron micrographs (TEM) reveal that hydroxyapatite (HA) is situated both within the fibrils and extrafibrillarly, and that the majority of HA lies outside the fibrils. The extrafibrillar amount of HA varies from tissue to tissue. By means of mathematical modeling, we here provide strong indications that there exists a physical quantity that is the same inside and outside the fibrils, for all different fully mineralized tissues. This quantity is the average mineral concentration in the non-collagenous space. This space is the sum of the extrafibrillar volume and of the volume of the fibrils that is not occupied by collagen molecules. Two independent sets of experimental observations covering a large range of tissue mass densities establish the relevance of our proposition: (i) mass density measurements and diffraction spacing measurements, re-analyzed through a dimensionally consistent packing model; (ii) optical density measurements of TEMs. The aforementioned average uniform HA-concentration in the extracollagenous space of the ultrastructure may emphasize the putative role played by a number of non-collagenous organic molecules in providing the chemical boundary conditions for mineralization of HA in the extracollagenous space. The probable existence of an average uniform extracollagenous HA concentration has far-reaching consequences for the mechanical behavior of mineralized tissues.     

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.     

X-ray diffraction studies on the structure of hydrated collagen

The temperature dependence of the humidity-sensitive spacing, d, related to the lateral packing of collagen molecules was measured for fully hydrated collagen. In the vicinity of 0°C, a sudden change in d was observed, which was reversible with temperature. In the diffraction profile, below 0°C, a set of diffraction peaks identified with the hexagonal crystalline form of ice was observed. With the reduction in water content, the intensity of the set of diffraction peaks decreased and was found to be zero at a water content of 0.38 g/g collagen. These results were considered to be caused by the frozen water in collagen fibril below 0°C. According to the water content dependence of d, it was considered that up to a certain water content water absorbed would be stowed in the intermolecular space of collagen and above that water content water molecules would aggregate to make pools, i. e., extrafibrillar spaces. The unfreezable bound water was considered to be located in the intermolecular space of collagen. Size of the extrafibrillar space, determined from the intensity analysis of a smallangle x-ray scattering pattern, corroborates the speculation that the water showed in the extrafibrillar space is freezable and free. The formation of the hexagonal crystalline form of ice in the extrafibrillar space was considered to cause the sudden change in d at 0°C.     

Collagen and mature elastic fibre organisation as a function of depth in the human cornea and limbus

A network of circumferentially oriented collagen fibrils exists in the periphery of the human cornea, and is thought to be pivotal in maintaining corneal biomechanical stability and curvature. However, it is unknown whether or not this key structural arrangement predominates throughout the entire corneal thickness or exists as a discrete feature at a particular tissue depth; or if it incorporates any elastic fibres and how, with respect to tissue depth, the circumcorneal annulus integrates with the orthogonally arranged collagen of the central cornea. To address these issues we performed a three-dimensional investigation of fibrous collagen and elastin architecture in the peripheral and central human cornea using synchrotron X-ray scattering and non-linear microscopy. This showed that the network of collagen fibrils circumscribing the human cornea is located in the posterior one-third of the tissue and is interlaced with significant numbers of mature elastic fibres which mirror the alignment of the collagen. The orthogonal arrangement of collagen in the central cornea is also mainly restricted to the posterior stromal layers. This information will aid the development of corneal biomechanical models aimed at explaining how normal corneal curvature is sustained and further predicting the outcome of surgical procedures.     

Role of Decorin Core Protein in Collagen Organisation in Congenital Stromal Corneal Dystrophy (CSCD)

The role of Decorin in organising the extracellular matrix was examined in normal human corneas and in corneas from patients with Congenital Stromal Corneal Dystrophy (CSCD). In CSCD, corneal clouding occurs due to a truncating mutation (c.967delT) in the decorin (DCN) gene. Normal human Decorin protein and the truncated one were reconstructed in silico using homology modelling techniques to explore structural changes in the diseased protein. Corneal CSCD specimens were also examined using 3-D electron tomography and Small Angle X-ray diffraction (SAXS), to image the collagen-proteoglycan arrangement and to quantify fibrillar diameters, respectively. Homology modelling showed that truncated Decorin had a different spatial geometry to the normal one, with the truncation removing a major part of the site that interacts with collagen, compromising its ability to bind effectively. Electron tomography showed regions of abnormal stroma, where collagen fibrils came together to form thicker fibrillar structures, showing that Decorin plays a key role in the maintenance of the order in the normal corneal extracellular matrix. Average diameter of individual fibrils throughout the thickness of the cornea however remained normal.     

Collagen organization in the chicken cornea and structural alterations in the retinopathy, globe enlarged (rge) phenotype--an X-ray diffraction study

An investigation into the collagenous structure of the mature avian cornea is presented. Wide-angle X-ray diffraction is employed to assess collagen organization in 9-month-old chicken corneas. The central 2-4mm corneal region features a preponderance of fibrils directed along the superior-inferior and nasal-temporal orthogonal meridians. More peripherally the orientation of fibrils alters in favor of a predominantly tangential arrangement. The chicken cornea appears to be circumscribed by an annulus of fibrils that extends into the limbus. The natural arrangement of collagen in the chicken cornea is discussed in relation to corneal shape and the mechanical requirements of avian corneal accommodation. Equivalent data are also presented from age-matched blind chickens affected with the retinopathy, globe enlarged (rge) mutation, characterized by an abnormally thick and flat cornea. The data indicate considerable realignment and redistribution of collagen lamellae in the peripheral rge cornea. In contrast to normal chickens, no obvious tangential collagen alignment was evident in the periphery of rge corneas. In mammals, the presence of a limbal fibril annulus is believed to be important in corneal shape preservation. We postulate that corneal flattening in rge chickens may be related to biomechanical changes brought about by an alteration in collagen arrangement at the corneal periphery.     

Mechanical properties of mineralized collagen fibrils as influenced by demineralization

Dentin and bone derive their mechanical properties from a complex arrangement of collagen type-I fibrils reinforced with nanocrystalline apatite mineral in extra- and intrafibrillar compartments. While mechanical properties have been determined for the bulk of the mineralized tissue, information on the mechanics of the individual fibril is limited. Here, atomic force microscopy was used on individual collagen fibrils to study structural and mechanical changes during acid etching. The characteristic 67 nm periodicity of gap zones was not observed on the mineralized fibril, but became apparent and increasingly pronounced with continuous demineralization. AFM-nanoindentation showed a decrease in modulus from 1.5 GPa to 50 MPa during acid etching of individual collagen fibrils and revealed that the modulus profile followed the axial periodicity. The nanomechanical data, Raman spectroscopy and SAXS support the hypothesis that intrafibrillar mineral etches at a substantially slower rate than the extrafibrillar mineral. These findings are relevant for understanding the biomechanics and design principles of calcified tissues derived from collagen matrices.