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ABSTRACT _Purpose_ This paper briefly reviews current explanations for corneal transparency and uses a well-developed model to try to explain the increased light scattering either

accompanying corneal swelling or following phototherapeutic keratectomy (PTK). _Methods_ The direct summation of fields (DSF) method was used to compute light transmission as a function of

wavelength. The method requires input of a number of structural parameters. Some of these were obtained from electron micrographs and others were calculated from X-ray diffraction data.

_Results_ By swelling sections of stroma cut from different depths in the tissue, we have shown that fluid entering the cornea causes more swelling in the posterior lamellae than in the

anterior lamellae. Furthermore, posterior lamellae can reach a higher final hydration than anterior lamellae. Collagen-free regions (‘lakes’) exist in corneas swollen _in vitro_and in

Fuch's dystrophy corneas, many of which may be caused by the death of cells. The DSF method shows that local fibril disordering, increased refractive index mismatch, and increased

corneal thickness together can account for a 20% increase in light scattering in a Fuch's dystrophy cornea at _H_=5.8 compared to the normal cornea. Additional scattering is probably

caused by ‘lakes’. The DSF method applied to PTK rabbit stroma with high levels of haze suggests that the newly deposited collagen is not the cause of the increased light scattering.

_Conclusions_ Fluid is not uniformly distributed within the corneal stroma when the cornea swells. Increased hydration of posterior lamellae may be because of known differences in the

glycosaminoglycans between the anterior and posterior stroma. Lamellar interweave in the anterior stroma probably limits the extent to which the constituent lamellae can swell. The DSF

method can be used to account for increased light scattering in oedematous corneas but cannot account for haze following PTK. INTRODUCTION One of the most remarkable properties of the cornea

is its ability to transmit almost all the incident light in the visible part of the spectrum. The reasons for corneal transparency have occupied scientists for many decades and despite

considerable advances in our understanding, to date there is still no universally accepted explanation. Even more perplexing are the causes of increased light scattering in the cornea during

wound healing or in some pathological situations. In this paper, we briefly review some of the theories put forward to explain corneal transparency and use the most well tested of these to

try to model the light scattering expected from oedematous corneas and from corneas following phototherapeutic keratectomy (PTK). CORNEAL TRANSPARENCY Any system where the attenuation of

light is only caused by scattering (in other words there are no other losses such as might be due, for example, to absorption) can be described by where _F_t is the percentage of the

incident light transmitted without scattering, _α_s is the scattering attenuation coefficient, and _t_ is the thickness in the direction of the light path. In the case of a corneal lamella

consisting of parallel collagen fibrils, the scattering attenuation coefficient can be written as the product _ρσ_, where _ρ_ is the number of fibrils per unit area in a cross-section (often

called the bulk fibril number density or simply the number density) and _σ_ is the scattering cross-section. Over the years there have been many models put forward to explain transparency;

the difference between these models essentially depends on the mathematical formulation of the scattering cross-section term. Here we describe the most important of these models. All must

consider the structure of the cornea, that is, the size and shape of the stromal constituents and their refractive indices since each of these factors influences the amount of light

scattered by the structure. In particular, the refractive index of the collagen fibrils, the refractive index of the extrafibrillar material, and the ratio of these two refractive indices,

all play a major role in determining the extent of light scattered by the stroma. The simplest model1 proposes that all corneal components have a _uniform_ refractive index (which is

equivalent to a zero value for the scattering cross-section). This essentially means that light cannot distinguish between fibrils and the material between them, hence it can propagate

directly through the tissue unscattered. This model is generally rejected, partly because it fails to explain two important properties of the cornea, birefringence and transparency loss when

the structure is distorted. Also, recent X-ray diffraction data have unambiguously confirmed earlier evidence for a difference in the refractive indices of the collagen fibrils and of the

extrafibrillar material.2 Most modern models are based on the lattice theory put forward by Maurice.3 By approximating the collagen fibril to perfect, infinitely long cylinders, an estimate

of the scattering from an individual fibril can be calculated. The refractive index difference between the fibrils and interfibrillar matrix means that each fibril scatters a small amount of

light. However, if the fibrils are packed in a lattice arrangement, correlation in their relative positions leads to destructive interference of light scattered away from the forward

direction, all the light energy going into the constructive interference in the forward direction. However, both electron microscopy and X-ray diffraction do not show the presence of this

regular packing of collagen fibrils.4,5 Table 1 shows these two models alongside the other main models, which are all based on Maurice's early work. Hart and Farrell4 showed that only

short-range order in the positions of the collagen fibrils is necessary for the required destructive interference of scattered photons. Results from X-ray diffraction showed that the type of

short-range order in the packing seen in electron micrographs is indeed what is found in the tissue.5 Feuk6 developed a long-range order model based on small, random displacements of the

fibrils from ideal lattice sites. Twersky,7 assuming that the fibrils were arranged as in a two-dimensional fluid, expressed the distribution explicitly in terms of the volume fraction

occupied by the fibrils. Benedek8 considered the problem from the point of view of fluctuations in the fibril number density. These concepts were explored quantitatively by Vaezy and Clark,9

who examined fluctuations in the spatial arrangement of the collagen fibrils using Fourier methods. Recently, Ameen _et al_10 used photonic band structure methods to explain light

transmission through corneal lattices. Space is too limited to go into these models in greater detail, so, for a fuller account, the reader is directed to reviews by Farrell and McCally11

and Freegard.12 A more generalised mathematical review of transparency in biological tissues is by Tuchin.13 By way of a summary, it has been pointed out by Farrell and McCally11 that all

currently viable transparency theories agree with three points: * 1 each fibril is an ineffective scatterer; * 2 despite this, the large number of fibrils requires that destructive

interference of scattered light must occur; and * 3 the cornea is thin. DIRECT SUMMATION OF FIELDS METHOD In 1986, Freund _et al_14 published a method to compute light scattering from the

cornea, following on from the theoretical principles previously advanced by Hart and Farrell.4 The technique can be used to predict transmission by an arbitrary short-range order

distribution of different-sized fibrils. A full account of the approach, called the direct summation of fields (DSF) method, is found in the original papers.14,15 It is a statistical

technique in which the scattering from each individual fibril is computed, then the effects of interference are included and summed for the whole tissue using a method called ensemble

averaging. It is worth mentioning at this stage that, in this method, transmission is computed as a function of wavelength, ignoring the lamellar structure of the stroma and also the

presence of stromal cells. With these assumptions in mind, however, the DSF method has been tested and found to give reliable results in a number of situations.16,17,18 In order to use DSF

to compute the expected light transmission, it is necessary to measure a number of structural and physical properties of the stroma. The refractive index of the hydrated collagen fibrils,

the refractive index of the interfibrillar matrix, and the ratio of these have previously been obtained using X-ray diffraction measurements in a number of different species.2 The relative

positions of the individual fibrils, and the diameter of each fibril, are obtained from electron micrographs. There is a problem in using measurements from electron microscopy in that it has

been shown that a number of microscope preparation protocols result in considerable shrinkage of fibril diameters and, particularly, interfibril spacings.19 To overcome this problem, we

have used X-ray diffraction (a technique where corneas can be examined without the need for any processing20) to measure the mean values of these parameters in the same tissue as used for

microscopy, and then scaled the data from electron micrographs so as to compensate for this shrinkage. Table 2 gives the values for several of these parameters for human corneas. The corneas

were obtained from the Eye Bank in culture medium, and were dehydrated to close to physiological hydration using polyethylene glycol.21 It should be noted that the value for the fibril

number density is lower than previously reported, partly owing to the scaling procedure. Fibril diameters and spacings were measured by image analysis of selected electron micrographs where

collagen fibrils were sectioned in cross-section. The positions and diameters of collagen fibrils in a human cornea were obtained after image analysis of these micrographs and scaled using

X-ray data from the same samples as described above. By taking the corneal thickness as 0.52 mm and combining these data with the refractive index data in Table 2, the DSF method was used to

predict the transmission as a function of wavelength. As expected (Figure 1), transmission was predicted to exceed 90% throughout most of the visible spectrum. In their original paper4 and

later16,15,11 Farrell and co-workers made only limited reference to how changes in the individual parameters might affect transparency in abnormal conditions. It is of interest to examine

the theoretical effects of changing each of these parameters, keeping the rest constant, so as to gauge to which parameters light transmission is most sensitive. It should be remembered that

here we are testing a single model for transparency, which has certain implicit assumptions about the tissue. Note also that this is a theoretical situation; in practice, many of the

parameters are related, and a change in one is often accompanied by a change in one or more of the others. With these caveats, Figure 2a shows that increasing the fibril radius to 20 nm

reduces transmission, particularly in the blue end of the spectrum, whereas reducing the radius has the opposite effect. So why not have small collagen fibrils in humans, as is found in

fish? The answer is probably down to tissue mechanics — larger fibrils mean a stronger cornea. The independent effect of the fibril number density on light scattering is difficult to assess,

as altering the fibril number density by increasing the separation of the fibrils simultaneously changes the effects of interference. However, we find that keeping the relative positions of

the fibrils constant but moving the fibrils apart (Figure 2b) leads to less scattering (greater transmission). An important point to realise, however, is that, contrary to what is often

asserted, increased interfibril spacings (for example, when the cornea swells) are not _per se_ responsible for the increased light scattering that accompanies oedema. From Equation (1) it

is clear that light scattering will increase with increased corneal thickness (assuming the increased thickness is because of extra tissue mass rather than oedema). However, Figure 2c shows

that this effect is relatively small, the corneal thickness could almost double without seriously increasing scattering. This presumably accounts for why, for example, a bovine cornea has

similar transparency to a thinner human cornea. Light transmission through the cornea is very sensitive to an increased mismatch in the refractive indices of the collagen and the

extrafibrillar matrix. Theoretically, there are two ways of varying their ratio, either keep the refractive index of the fibrils constant and vary that of the matrix, or _vice versa_. Both

have a similar effect (Figure 2d). If the ratio is one, there is total transmission throughout the spectrum. This is the uniform refractive index condition. As we increase the ratio,

transmission reduces, once again, particularly at the blue end of the spectrum. In conclusion, the DSF method can be used to demonstrate that light scattering in the cornea will increase if:

* 1 order in the spatial arrangement of the fibrils is destroyed; * 2 fibril diameters increase; * 3 fibril number density increases; * 4 there is an increased refractive index imbalance

between the hydrated fibrils and the extrafibrillar matrix; * 5 corneal thickness increases. So far, we have imagined the cornea as a structure made only of collagen fibrils and

extrafibrillar matrix. Of course, there are a large number of keratocytes in the stroma, which gradually reduce in density from the anterior to the posterior stroma.22,23 Maurice3 believed

that there were insufficient of these to contribute significantly to scattering. Besides, they are relatively thin in the direction of the light path through the cornea. More recently,

Jester _et al_24 have suggested that these cells contain special proteins called corneal crystallins, which produce a uniform refractive index in the cells and may match the refractive index

of the cytoplasm to that of the surrounding matrix. This, together with the dimensions of the cells, renders them weak scatterers (except for their nuclei, which are readily visible in the

confocal microscope). However, if keratocytes change their shape or spill their contents, a different situation ensues, and they are capable of becoming very efficient scatterers.25,26

CORNEA OEDEMA An understanding of structure and transparency changes when the cornea swells is dependent on our knowledge of where imbibed water is situated, both at the level of the tissue

as a whole and within the lamellae themselves. In many animals, the anterior stroma is less ordered,15 less hydrated,27,28,29 has a higher keratocyte density,22,23 has a lower keratan

sulphate (KS) to chondroitin/dermatan sulphate (DS) ratio,28 and is less easily swollen29,30,31 than the posterior stroma. We have examined four frozen human corneas (two at physiological

hydration and two swollen in culture medium). These were sectioned at 100 _μ_m intervals from the anterior to posterior using a Mikrom sliding microtome. All sections were weighed and then

placed in dH2O. At fixed intervals, each section was reweighed and then returned to the dH2O to continue swelling until a constant weight was reached. The hydration of each section was

calculated for both the physiological and the swollen corneas. The results (Figure 3) confirm results from other species27,28,29 and show that hydration increases with tissue depth in both

the physiological and the swollen human corneas. This may be related to the gradual increase in the KS/DS ratio with depth, since KS is known to show greater water absorption than DS.32,33

However, as Bron34 has pointed out it is possible that there is a differential loss of proteoglycans between anterior and posterior stroma as the cornea swells and this, if it happens, would

affect the swelling at different stromal depths. The corneal sections were immersed in distilled water until they essentially stopped swelling. The final hydrations achieved were plotted as

a function of tissue depth (Figure 4). We found that the maximum achievable hydration increases as a function of depth. This means that the posterior stroma is capable of swelling much more

than the anterior. It is likely that anterior swelling is limited by lamellar interweaving and insertions into Bowman's layer, a phenomenon that may have considerable importance in

maintaining the correct shape of the cornea.31,34 Information on the distribution of imbibed water _within_ the lamellae has been obtained using X-ray diffraction methods. When the denuded

cornea swells, there is a linear relation between the fibril separation _squared_ and the hydration.35 Interfibrillar centre-to-centre spacings were determined for bovine corneas as a

function of hydration using X-ray diffraction, and the results are shown in Figure 5 (line a). By extrapolating this line to _H_=0, it is possible to plot a theoretical graph of the expected

interfibril spacing on the assumption that all the water entering the stroma has gone towards separating the constituent fibrils.5,21 This theoretical plot is shown in Figure 5 (line b).

The shading around the theoretical plot is the uncertainty owing to the uncertainty in determining the spacing at _H_=0 from the experimental data. The interesting point is that at a given

hydration, the interfibril spacing is lower than it should be considering the amount of water in the stroma. This must mean that some of the water is not between fibrils, and thus must be in

fibril-free regions. Some of these regions are probably places occupied by cells that have died post mortem. If we assume that keratocytes occupy 15% of the stromal volume, we can take this

into account in the theoretical calculation, and the match between theory and experiment becomes much better (Figure 6). So it appears that fibril-free regions (‘lakes’) form in swollen

corneas, and that when cells die, the spaces previously occupied by them might themselves become ‘lakes’ that could contribute to an increase in light scattering. LIGHT SCATTERING IN

OEDEMATOUS CORNEAS A full survey of the literature probing the causes of scattering when the cornea swells is beyond the scope of this article. From a theoretical standpoint, ‘lakes’ would

add a term to the total scattering cross-section that would vary as _B_/_λ_2.37,38 By measuring transmission as corneas swelled, Farrell _et al_ were able to compute the scattering

cross-section and demonstrated that it has a 1/_λ_2 dependence, as predicted by the presence of ‘lakes’.35 Lakes are not seen in the normal human cornea, but they are present in bullous

keratopathy and Fuch's dystrophy corneas.39 Some fibril-free regions appear to be because of matrix disorder (Figure 7), while others might reflect the presence of dead cells. The

question is, to what extent does the intralamellar disordering lead to light scattering? In principle, the summation of scattered fields approach could again be used to compute the

theoretical effects of disordering and/or lakes. The required structural information (fibril positions, diameters, number density) can be obtained from electron micrographs scaled according

to the X-ray diffraction measurements as described previously. However, as the cornea swells, the extra water will change the refractive indices of the interfibrillar matrix and also,

possibly, of the collagen fibrils themselves. However, we know from previous studies21 that collagen fibrils do not swell appreciably above physiological hydration, so their refractive index

is independent of tissue hydration and stays constant at 1.416. As water or electrolyte enters the interfibrillar matrix, it dilutes it and the refractive index falls. The amount by which

it falls can be estimated by measuring the change in the refractive index of the stroma as a function of tissue thickness or hydration (Figure 8) and then applying Gladstone and Dales's

law of refractive indices to the system.2 Since the imbibed fluid does not enter the fibrils themselves,21 this fall in the refractive index as the stroma swells leads to an increase in the

ratio of the refractive index of the fibrils to that of the interfibrillar matrix and to a corresponding increase in light scattering. We found that between physiological hydration and

_H_=3.8, there was a 0.15% reduction in the refractive index of the matrix and a corresponding 0.1% increase in the ratio of the refractive indices of the fibrils and the matrix (S Khan, S

Dennis, and K Meek, unpublished results). Between physiological hydration and _H_=5.8, these percentages were 0.59% and 0.58%, respectively. Armed with this quantitative information, it is

now possible to apply the summation of scattered fields method to Fuch's dystrophy corneas. The result is shown in Figure 9. It can be appreciated that the intralamellar disruption in

the spatial arrangement of fibrils, the increased mismatch in the refractive indices, and the increased thickness of the stroma together lead to the overall reduction in light transmission.

PHOTOTHERAPEUTIC KERATECTOMY It is well known that haze develops following laser ablation to the anterior stroma. The definition of haze is difficult because of the different methods used to

measure it, and even less certain is the origin of the haze.40 Various authors have ascribed the observed haze to irregularities in the epithelium,41,42 to subepithelial deposits,43 to the

presence of vacuoles,44 to the deposition of poorly organised collagen,45,46 or to the presence of activated keratocytes.25,26 However, none of these suggestions have been experimentally or

theoretically shown to account for increased light scattering. We have used PTK in rabbits to predict the percentage transmission of visible light through the newly deposited collagen using

the DSF method and hence to see if this collagen could account for the observed haze. All experimental procedures were carried out in accordance with the ARVO Resolution on the Use of

animals in Ophthalmic and Vision Research. PTK took place at St Thomas' Hospital London using an Omnimed excimer laser (Summit Technology, Boston, MA, USA) with a wavelength of 193 nm.

The pulse energy resulted in a radiant exposure of 180 mJ/cm2 at a pulse frequency of 10 Hz. The beam shape was circular with a fixed diameter of 6.0 mm. Wounds were allowed to heal for up

to 19 months. We used an objective measurement for corneal haze developed by Lohmann _et al_47 in which haze was determined using a slit-lamp-mounted charged-coupled device (CCD) system. The

results of the haze measurements are shown in Figure 10 and confirm that both a transitory haze (which peaks after a month) and a more persistent or late developing haze (which remains for

many months) occur. The question we address here is to what extent the persistent haze can be ascribed to the nature of the newly deposited collagen. After 8 months of healing, the rabbit

corneas had laid down a layer of newly deposited collagen that had almost compensated for the amount removed (approximately 100 _μ_m). Apart from the most superficial layer, most of this

collagen had formed a lamellar structure, although the order in the fibril packing was visibly poor. Micrographs were taken at different depths and typical ones were used in the DSF method

to predict light transmission. In this case, however, we had no information about refractive indices in the new matrix, so we made the assumption that these were normal. Figure 11 shows that

despite the fact that the fibril diameters and organisation had not returned to normal, only a very small drop in light transmission is predicted. This is probably due, in large part, to

the fact that the newly deposited layer extended to only about 100 _μ_m. The thinness of this collagenous layer, therefore, counteracts the increased scattering caused by the poor

organisation of the new collagen. It appears, therefore, that newly deposited collagen is not the cause of persistent haze following PTK. Electron microscopy of our rabbit corneas showed a

qualitative correlation between haze, the number of activated keratocytes, and the smoothness of the subepithelial basement lamina. We therefore believe that either or both of these

contribute more to post-PTK persistent haze than does the newly deposited collagen. CONCLUSIONS Despite the considerable effort that has been put into understanding corneal transparency,

there is still no universally accepted explanation and no model that has been thoroughly tested. Some progress has been made, particularly with respect to our understanding of what factors

govern corneal fibril size49,50 and organisation, including the roles of the ambient ions51 and of proteoglycans. The recent availability of gene-targeted mice with null mutations for

selected proteoglycans52,53,54 now makes it possible to correlate the structural effect of selected deletions with tissue transparency. For example, it is interesting that lumican-null mice

have cloudy corneas,52 decorin-null mice have clear corneas,53 and keratocan-null mice have mostly clear corneas.54 These and similar tissues open the possibility to greatly increase our

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Professor John Marshall and Anne Patmore for carrying out the PTK and making the haze measurements shown in Figure 10. We also thank Mr Nick Hawksworth for supplying postoperative

pathological corneas, Dr Val Smith for supplying normal human corneas from the Bristol Eye Bank, and Dr S Akhtar for assistance with electron microscopy. We are grateful to the staff at the

SRS Daresbury laboratory for their ongoing help with the data collection. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Cardiff Institute of Tissue Engineering and Repair and Department of

Optometry and Vision Sciences, Cardiff University, Cardiff, UK K M Meek, C J Connon, S Dennis & S Khan * The Open University, Oxford Research Unit, Oxford, UK D W Leonard Authors * K M

Meek View author publications You can also search for this author inPubMed Google Scholar * D W Leonard View author publications You can also search for this author inPubMed Google Scholar *

C J Connon View author publications You can also search for this author inPubMed Google Scholar * S Dennis View author publications You can also search for this author inPubMed Google

Scholar * S Khan View author publications You can also search for this author inPubMed Google Scholar CORRESPONDING AUTHOR Correspondence to K M Meek. ADDITIONAL INFORMATION This work was

funded by the Wellcome Trust and is currently funded by the Medical Research Council RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Meek, K., Leonard,

D., Connon, C. _et al._ Transparency, swelling and scarring in the corneal stroma. _Eye_ 17, 927–936 (2003). https://doi.org/10.1038/sj.eye.6700574 Download citation * Received: 28 February

2003 * Accepted: 28 February 2003 * Published: 20 November 2003 * Issue Date: 01 November 2003 * DOI: https://doi.org/10.1038/sj.eye.6700574 SHARE THIS ARTICLE Anyone you share the following

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SharedIt content-sharing initiative KEYWORDS * corneal transparency * stroma * swelling * oedema * phototherapeutic keratectomy