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Optometry & Vision Science:
doi: 10.1097/OPX.0b013e31826c5dde
Original Articles

Corneal Refractive Index–Hydration Relationship by Objective Refractometry

Patel, Sudi*; Alió, Jorge L.

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*PhD, FAAO

MD, PhD

Research, Development and Innovation Department, VISSUM, Instituto Oftalmologico de Alicante, Alicante, Spain

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Abstract

Purpose. To compare an objective (VCH-1) with a manual subjective Abbé refractometer (MSAR) and evaluate the refractive index (RI)–hydration (H) relationship for the corneal stroma.

Methods. Epithelial and endothelial layers were removed from a fresh postmortem ovine corneal buttons. RI was measured at both surfaces using (i) MSAR then (ii) VCH-1. The sample was weighed, slowly dehydrated under controlled conditions (2 h), and RI measures were repeated. Sample was oven dried (90°C) for 3 d to obtain dry weight and hydration at each episode of RI measurement.

Results. Average difference between individual pairs of measurements obtained using the two refractometers (ΔRI) was 0.00071 (standard deviation ± 0.0029, 95% confidence interval ± 0.0058). Root mean square difference between measurements obtained by the refractometers was 0.0024. There was no relationship between ΔRI and the mean of each measurement pair (r = 0.201, n = 40, p = 0.214). Linear regression revealed a significant relationship between RI and reciprocal of H at both surfaces as follows: anterior (i) RI = 1.355 + 0.111/H (r = −0.852, n = 20, p = <0.001), (ii) RI = 1.357 + 0.105/H (r = −0.849, n = 20, p = <0.001) and posterior (i) RI = 1.353 + 0.085/H (r = −0.882, n = 20, p = <0.001), (ii) RI = 1.350 + 0.088/H (r = −0.813, n = 20, p = <0.001).

Conclusions. VCH-1 measurements are in good agreement with MSAR. RI at the anterior stroma was consistently higher suggesting hydration is lower by 1.10 units (6%) compared with the posterior stroma. Dehydration increased RI at both surfaces by similar rates. Current hypothetical models are useful for predicting RI from H for the posterior, but not the anterior, stroma.

Traditional Abbé refractometry requires the investigator to view down an observation tube and estimate the location of a dark-light boundary.1 The light scatter induced by a turbid medium, such as the corneal stroma, reduces the clarity of this dark-light boundary. This leads to uncertainty in judging the locus of the dark-light boundary and consequential systematic error and bias. A shift in stromal hydration from the normal physiological range is expected to further contribute to this uncertainty because such changes are associated with increased levels of stromal light scatter. The VCH-1 (Index Instruments, Huntington, UK) is an objective manual device for measuring the corneal refractive index based on the principles of Abbé refractometry.2 The instrument, designed for use in vivo, displays refractive index and an estimate of percentage water content based on theoretical models.4,5 The device has been calibrated, and its performance compared with more a traditional Abbé refractometer using appropriate liquids, hydrogel lenses, and turbid media such as pastes and creams.2,3 To date, the performance of the device has not been compared with a traditional Abbé refractometer using stromal tissue over a range of hydration values.

Several models link the refractive index of the stroma with hydration.4–8 Most of these models are based on the Gladstone-Dale law,9 assume the stroma is a single unit homogeneous medium and predict an inverse relationship between stromal refractive index and hydration. In contrast, the model according to Laing et al.6 is based on the empirical thickness-hydration relationship of the cornea10–12 These various derivations4–8 ignored the possible contribution of the stromal keratocytes on the overall refractive index. The influence of the keratocytes on the overall refractive index should be considered because of their significant contribution to the basic histology of the stroma13 The various models according to Maurice, Fatt and Harris, Laing et al.4–6 can be adapted allowing the possible effects of stromal keratocytes and variations in other stromal properties. These modifications are presented in the Appendix (the appendix is available online at http://links.lww.com/OPX/A108).

The direct evaluation of stromal hydration is a destructive process. Fortunately, measuring the refractive index is a rapid, convenient, economic, and non-destructive test that could be used to estimate, and monitor changes of hydration with the aid of a suitable empirical model. Model described by Eqs. 1 and 2 (the appendix is available online at http://links.lww.com/OPX/A108) can be used to predict the refractive index by suitably adjusting the values of the various components. The architecture of the corneal stroma alters along its depth13–19 leading to variations in the physiological properties between the anterior and posterior layers. The anterior stroma features tighter interwoven lamellae, a lower keratin sulfate:dermatan suphate ratio and a reduced propensity to swell when compared with the posterior stroma13–23 suggesting that, the refractive index may vary along the depth of the tissue. In comparison with the posterior surface, refractive index has been shown to be higher at the anterior surface of the stroma in bovine, porcine, and human models.8,24–27 In response to osmotic stress, the posterior corneal stroma is more susceptible and less resilient to changes in hydration when compared with the anterior stroma.8,16,17,19–23 Thus, we would expect changes of refractive index at the posterior corneal stroma to be more profoundly related to changes in the net overall hydration of the corneal stroma when compared with the anterior corneal stroma. This has been confirmed in the bovine corneal stroma when the refractive index was measured using a standard bench model, Abbé refractometer.8 However, we cannot be certain this holds true for other mammalian corneas.

The aim of this study was two fold. First, to compare the performance of the VCH-1 with a traditional subjective Abbé refractometer to estimate the effects of changes in overall hydration on the refractive index at the anterior and posterior surface of the ovine corneal stroma. Second, to identify whether a particular hypothetical model best describes the empirical relationship between refractive index and hydration in the ovine stroma.

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METHODS AND MATERIALS

Refractometry

Refractive index was measured using a subjective Abbé refractometer (Bellingham and Stanley, Waterford, UK) and the objective VCH-1 refractometer. The latter is a handheld automated contact device designed for the intraoperative measure of refractive index of the human cornea. The former is a handheld subjective Abbé refractometer designed for measuring the refractive index of liquid samples. The instrument was modified by removing part of the housing, revealing the contact testing surface of the refractometer, to facilitate measuring the refractive index of corneal samples. All measurements were taken using a sodium yellow light. The modus operandi of the VCH-1 has been thoroughly described in a previous publication.2 The device consists of an optically smooth circular flint glass contact plate of 12.6 mm2 connected to a light sensor transducer. On contact with the stroma, the device detects the relative position of the dark-light boundary that is a basic requirement of critical angle refractometry. The position of this boundary is directly related to the refractive index of the material under examination. The VCH-1 features a liquid crystal display noting the refractive index of the tissue. Once the dark-light boundary is detected by the instrument, a confirmatory sound signal is triggered by an internal device, and the results are displayed on screen.

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Calibration

During manufacture, the VCH-1 was calibrated using standard media listed under international standards certificates of calibration or standards traceable to National Institute of Science and Technology. Unlike the corneal stroma, these media are optically clear with minimal turbidity and relatively high light transmission properties. The subjective Abbé refractometer was calibrated using a standard test plate supplied by the manufacturer. The precision of our device was 0.0018 units of refractive index. The refractive index of each tissue sample was measured initially with the subjective Abbé refractometer and then with the objective VCH-1. The contact surfaces of the VCH-1 and subjective Abbé refractometer were cleaned with surgical grade alcohol before and after any measurement.

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Materials

Sheep eyes were obtained from the local slaughterhouse. The eyes10 were removed and transported in a sealed moist chamber with a conjunctival flap to prevent desiccation. The epithelium was scrapped off using a scalpel blade to reveal the stromal surface. The stromal button was cut from the globe by making a circumcorneal incision just within the limits of the limbus. The button was reversed, and the posterior surface was gently scraped to strip away the endothelium. A standard binocular surgical microscope with cold light illumination was used to facilitate dissection. The anterior surface of the button was placed on the measurement template of the subjective Abbé refractometer, and a reading for the refractive index was taken using a sodium lamp source. The sample was lifted, and a measurement was taken for the posterior surface of the button. Keeping the sample on the test plate of the subjective Abbé refractometer, the probe of the VCH-1 was introduced on to the anterior surface of the sample for the objective evaluation of refractive index. The sample was lifted and reversed, and the refractive index was estimated for the posterior surface of the sample. The sample was weighed immediately after this refractive index measurement to obtain the wet weight using a chemical balance. The sample was then placed in a sealed moist chamber for two hours to allow for passive dehydration from both surfaces. Refractive index of each surface was again measured twice using the subjective Abbé refractometer then VCH-1. The wet weight of the passively dehydrated sample was obtained by weighing the sample immediately after the last refractive index measurement. The sample was then dehydrated for up to 3 days at 90°C. The dry weight of the sample was obtained by weighing the sample using the same chemical balance after this period of desiccation. The hydration (H) of the sample at each session of refractive index measurement was calculated as follows: H = (wet weight −dry weight)/dry weight. Hydration is a ratio expressed in units mgm/mgm. All measurements were taken at room temperature 23°C and relative humidity 35%. Slaughterhouse ovine samples were used because this prevented unnecessary sacrifice of laboratory animals; they were available soon after death and inexpensive. Hydration is defined as the mass of water present in the stroma divided by the mass of dry material present in the stroma.

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Statistical Analysis

Data were stored on an Excel spread sheet (Microsoft Corp) and analyzed to determine whether (i) the results obtained using VCH-1 were comparable with results obtained using standard Abbé refractometer, (ii) there was any significance in apparent differences in the refractive index values obtained between the anterior and posterior surfaces, (iii) there was a correlation between stromal hydration and refractive index measured at the stromal surfaces (Pearson correlation coefficient, r). The significance level was set at a p value of <0.05. The two instruments were compared using the methods proposed by Bland and Altman.28

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RESULTS

Agreement Between Refractometers

Initially, 10 pairs of refractive index values were obtained from the anterior surface and 10 from the posterior surface. This was repeated after passive dehydration, leading to a final total of forty pairs of refractive index measurements. The data were pooled, analyzed according to the method of Bland and Altman,28 and shown in Fig. 1. There was no significant correlation between the difference of values obtained using the two instruments and the mean of each pair of values obtained using the two instruments (r = 0.201, n = 40, p = 0.214). The mean difference [Δ refractive index (RI)] between individual pairs of measurements was 0.00071 [standard deviation (SD) = ±0.0029, 95% confidence limit = ±0.0058], and the limits of agreement between the two instruments (ΔRI ± 1.96 SD) were 0.00071 ± 0.0058. The average root mean square difference between the 40 individual pairs of measurements obtained using the VCH-1 and subjective Abbé refractometer was 0.0024.

Figure 1
Figure 1
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Refractive Index, Anterior and Posterior Surfaces
First Set of Measurements Before Dehydration

The mean (±SD) results for the anterior and posterior surfaces using the subjective Abbé refractometer were 1.375 (±0.005) and 1.368 (±0.004). The differences were significant (t-test, p = 0.0019, n = 10). The mean (±SD) results for the anterior and posterior surfaces using the VCH-1 refractometer were 1.376 (±0.005) and 1.366 (±0.007). The differences were significant (t-test, p = 0.0018, n = 10). Apparent differences between the mean results obtained from the two instruments for the anterior and posterior surfaces were not significant (t-test, p = 0.079 and 0.066, respectively). The mean (±SD) hydration was 5.6 (±0.71, n = 10).

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Second Set of Measurements After Passive Dehydration

The mean (±SD) results for the anterior and posterior surfaces using the subjective Abbé refractometer were 1.390 (±0.011) and 1.379 (±0.008). The differences were significant (t-test, p = 0.0058, n = 10). The mean (±SD) results for the anterior and posterior surfaces using the VCH-1 refractometer were 1.390 (±0.011) and 1.378 (±0.008). The differences were significant (t-test, p = 0.0048, n = 10). Apparent differences between the mean results obtained from the two instruments for the anterior and posterior surfaces were not significant (t-test, p = 0.330 and 0.274, respectively). The mean (±SD) hydration was 3.3 (±0.74, n = 10).

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Refractive Index and Hydration

The refractive index and reciprocal hydration data are shown in Figs. 2 and 3 together with the Fatt and Harris model5 for comparison. A statistically significant correlation was revealed between stromal surface refractive index and the reciprocal of hydration using both refractometers. The least squares regression lines equating refractive index (RI) with hydration (H) were as follows:

Figure 2
Figure 2
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Figure 3
Figure 3
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Subjective Abbé Refractometer

Eqs. 1 and 2 can be found in the Appendix, available at http://links.lww.com/OPX/A108.

Equation (Uncited)
Equation (Uncited)
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VCH-1 Refractometer

Equation (Uncited)
Equation (Uncited)
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DISCUSSION

Differences Between Instruments

The average root mean square difference between the refractive index values estimated using the VCH-1, and manual subjective Abbé refractometer was 0.0024. This is favorable compared with the value of 0.003 reported for synthetic turbid media.3 The root mean square value is one indication of the agreement between the two instruments. Fig. 1 shows the Bland and Altman plot28 for the data obtained from both stromal surfaces. The mean difference between individual pairs of measurements was 0.00071. This is swamped by the 95% confidence interval for the differences between the measurements, which was ± 0.0058, obtained from the two instruments. There is a good agreement between the two instruments, with no obvious bias. The 95% confidence interval indicates the upper limits of agreement we can attach to measurements obtained using these two instruments. Some dehydration of the sample during a session of measurements could have introduced bias. The time taken to obtain one complete set of data from one sample, that is two measurements from the anterior and two from the posterior surfaces, was typically 3 minutes but never exceeded 5 minutes. The differences between the results obtained using the two instruments were not statistically significant. This indicates that there was no obvious bias of one instrument over the other when the order of data acquisition was controlled as described in the methods section.

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Difference in Refractive Index between Anterior and Posterior Stromal Surfaces

In general, stromal hydration tends to increase along the anteroposterior direction in mammals.21,29 Thus, the refractive index is expected to reduce along this axis, and this has been confirmed ex vivo in cow,8,24,27 human, and pig corneal stroma.25 In keeping with the other mammalian species, a fall in refractive index from the anterior to posterior surface was revealed in our ovine stromal samples. The similarity between our current and previous findings in other mammals suggests that the ovine stroma is a reasonable model for corneal stromal refractive index-hydration studies. The subjective refractometer revealed a significant drop in refractive index of 0.007 units between the anterior and posterior surfaces increasing to 0.011 units after passive dehydration. Similarly, the VCH-1 refractometer revealed a significant though slightly greater drop in refractive index of 0.011 units between the anterior and posterior surfaces increasing to 0.012 units after passive dehydration. If the structure of the anterior and posterior stroma was similar but the two regions differed in hydration alone, then Eqs. 3 to 6 can be used to estimate the likely difference in hydration between the two compartments. When the hydration at the posterior stroma is 4.0, the predicted hydration at the anterior stroma is approximately 2.9. In terms of percentage, the water content at the anterior stroma is 6% lower.

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Refractive Index and Hydration

The data, albeit from ex vivo samples, support the findings of previous studies where an inverse relationship was found between refractive index and hydration in the bovine stroma.8,26 We believe this is the first report of such a finding in the ovine stroma. The data in Figs. 2 and 3 show the relationship between the refractive index and hydration. The Fatt and Harris model5 in its basic form is a reasonable estimate for the posterior stroma but not for the anterior stroma. A better correlation between the empirical results and any hypothetical model could be achieved using suitable computer iterative techniques. Thus, the Laing et al. model6 closely fits the measured data for the posterior stroma when the refractive index and density of the ground substance are 1.336 and 1.30 g/cc, respectively. This model should be treated with caution because it is totally dependent on two constants, namely, the starting point values for both refractive index and hydration. For the Fatt and Harris model, a number of components could be adjusted to obtain a better fit to the actual data, for e.g., (i) differences in optical properties of prevailing collagen, (ii) refractive index and concentration of keratocytes, (iii) density of ground substance, etc. How these components affect refractive index are summarized in Eqs. 7 and 8 in the Appendix (the appendix is available online at http://links.lww.com/OPX/A108). Some examples of the various permutations are shown in Fig. 4 for comparison with the Laing et al. model. The Fatt and Harris model best fits the actual data for the posterior stroma when the concentration of keratocytes is near zero, the refractive index of dry collagen is 1.60, and density of dry material in the stroma is 1.20 gm/cc. These values are reasonable; however, for the anterior stroma, there are no logical values that best fit the actual data for refractive index and overall hydration. This leaves us to conclude that, the actual regional hydration of the anterior stroma is naturally lower in comparison with the overall hydration.

Figure 4
Figure 4
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We have already considered that, the relatively lower resistance to changes in hydration at the posterior stroma8,16,17,19–23 should lead to more pronounced changes in the refractive index in this region in response to a unit change in overall hydration when compared with the anterior region of the stroma. This trend does occur in bovine stroma where the slope of the regression line correlating refractive index with overall hydration is more pronounced for the posterior stroma.8 This trend was not apparent in our study. According to the data obtained using VCH-1 (Eqs. 7 and 8), for a shift in overall hydration from 5 to 3, the refractive index at the anterior stroma is predicted to increase by 0.014. In contrast, the refractive index at the posterior stroma is predicted to increase by 0.012. The data suggest there may be fundamental differences in the properties, involving both structure and biophysical characteristics, in the ovine corneal stroma compared with other mammalian species. If similar variations in response to hydration exist between the anterior and posterior corneal stroma in the human model, then this may impact on the outcome of corneal refractive procedures.

Jorge L. Alió

Research, Development and Innovation Department

VISSUM, Instituto Oftalmologico de Alicante

Avda. Denia s/n. Edificio Vissum, 03016 Alicante,

Spain

e-mail: jlalio@vissum.com

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ACKNOWLEDGMENTS

JLA is an employee at Vissum Corporación; SP is an Honorary Associate at Vissum Corporación. Both authors have a commercial interest in the VCH-1.

Received February 8, 2012; accepted July 9, 2012.

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APPENDIX

The appendix is available online at http://links.lww.com/OPX/A108.

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REFERENCES

1. Longhurst RS. Geometrical and Physical Optics, 2nd ed. London: Longman; 1967.

2. Patel S, Alió JL, Javaloy J, Perez-Santonja JJ, Artola A, Rodriguez-Prats J. Human cornea before and after refractive surgery using a new device: VCH-1. Cornea 2008; 27: 1042–9.

3. Patel S, Alió JL, Amparo F, Rodriguez-Prats JL. The influence of age on the refractive index of the human corneal stroma resected using a mechanical microkeratome. Cornea 2011; 30: 1353–7.

4. Maurice DM. The structure and transparency of the cornea. J Physiol 1957; 136: 263–86.

5. Fatt I, Harris MG. Refractive index of the cornea as a function of its thickness. Am J Optom Arch Am Acad Optom 1973; 50: 383–6.

6. Laing RA, Sanstrom MM, Berrospi AR, Leibowitz HM. Changes in the corneal endothelium as a function of age. Exp Eye Res 1976; 22: 587–94.

7. Worthington CR. The structure of cornea. Q Rev Biophys 1984; 17: 423–51.

8. Meek KM, Dennis S, Khan S. Changes in the refractive index of the stroma and its extrafibrillar matrix when the cornea swells. Biophys J 2003; 85: 2205–12.

9. Gladstone JM, Dale TP. Researches on the refraction dispersion and sensitiveness of liquids. Phil Trans Roy Soc (London) 1863; 153: 317–43.

10. Hedbys BO, Mishima S. Flow of water in the corneal stroma. Exp Eye Res 1962; 1: 262–75.

11. Ytteborg J, Dohlman CH. Corneal edema and intraocular pressure. II. Clinical results. Arch Ophthalmol 1965; 74: 477–84.

12. Fatt I, Hedbys BO. Flow conductivity of human corneal stroma. Exp Eye Res 1970; 10: 237–42.

13. Bron AJ. The architecture of the corneal stroma. Br J Ophthalmol 2001; 85: 379–81.

14. McTigue JW. The human cornea: a light and electron microscopic study of the normal cornea and its alterations in various dystrophies. Trans Am Ophthalmol Soc 1967; 65: 591–660.

15. Hogan MJ, Alvarado JA, Weddell J, eds. Histology of the Human Eye: An Atlas and Textbook. Philadelphia, PA: Saunders; 1971.

16. Castoro JA, Bettelheim AA, Bettelheim FA. Water gradients across bovine cornea. Invest Ophthalmol Vis Sci 1988; 29: 963–8.

17. Komai Y, Ushiki T. The three-dimensional organization of collagen fibrils in the human cornea and sclera. Invest Ophthalmol Vis Sci 1991; 32: 2244–58.

18. Bron AJ, Tripathi RC, Tripathi BJ. Wolff’s Anatomy of the Eye and Orbit, 8th ed. London: Chapman and Hall; 1997.

19. Müller LJ, Pels E, Vrensen GF. The specific architecture of the anterior stroma accounts for maintenance of corneal curvature. Br J Ophthalmol 2001; 85: 437–43.

20. Kikkawa Y, Hirayama K. Uneven swelling of the corneal stroma Invest Ophthalmol Vis Sci. 1970; 9: 735–41.

21. Turss R, Friend J, Reim M, Dohlman CH. Glucose concentration and hydration of the corneal stroma. Ophthalmic Res 1971; 2: 253–60.

22. Lee D, Wilson G. Non-uniform swelling properties of the corneal stroma. Curr Eye Res 1981; 1: 457–61.

23. Cristol SM, Edelhauser HF, Lynn MJ. A comparison of corneal stromal edema induced from the anterior or the posterior surface. Refract Corneal Surg 1992; 8: 224–9.

24. Patel S. Refractive index of the mammalian cornea and its influence during pachometry. Ophthalmic Physiol Opt 1987; 7: 503–6.

25. Patel S, Marshall J, Fitzke FW III. Refractive index of the human corneal epithelium and stroma. J Refract Surg 1995; 11: 100–5.

26. Patel S, Alió JL, Perez-Santonja JJ. Refractive index change in bovine and human corneal stroma before and after lasik: a study of untreated and re-treated corneas implicating stromal hydration. Invest Ophthalmol Vis Sci 2004; 45: 3523–30.

27. Vasudevan B, Simpson TL, Sivak JG. Regional variation in the refractive-index of the bovine and human cornea. Optom Vis Sci 2008; 85: 977–81.

28. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986; 1: 307–10.

29. Bauer NJ, Wicksted JP, Jongsma FH, March WF, Hendrikse F, Motamedi M. Noninvasive assessment of the hydration gradient across the cornea using confocal Raman spectroscopy. Invest Ophthalmol Vis Sci 1998; 39: 831–5.

30. Batsanov SS. Refractometry and Chemical Structure. Authorized Translation from the Russian by Paul Porter Sutton. Applied Science Library. Princetown: Von Nostrand; 1960.

Keywords:

corneal stroma; hydration; refractive index

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