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From the Bascom Palmer Eye Institute, University of Miami School of Medicine, Miami, Florida.
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Abstract |
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n) depends on the density and composition of axonal organelles. The purpose of this study was to evaluate the distribution of birefringence around the optic nerve head (ONH) in normal subjects.
METHODS. Birefringence was calculated along circular scan paths around the ONH as n = R/T, where R is RNFL retardance measured by scanning laser polarimetry (SLP) and T is RNFL thickness measured by optical coherence tomography (OCT). OCT scans on a 3.4 mm diameter circle were obtained from 26 normal subjects aged 18 to 53 years. Scans on circles with various diameters were obtained from 17 of these subjects.
RESULTS. The average reproducibility of n measured on three separate days in four subjects was ±0.05 nm/µm. In most subjects n varied significantly along a circular path around the ONH, with maxima in superior and inferior bundles, minima temporally and nasally, and a mean of 0.32 ± 0.03 nm/µm. n profiles on circles of different diameter were similar, suggesting that n did not vary along nerve fiber bundles.
CONCLUSIONS. RNFL birefringence varies with position around the ONH. This variation may result from known structural differences among nerve fiber bundles that serve different retinal regions. Constant n along bundles is consistent with this hypothesis. Measurements of RNFL birefringence may provide a means to detect early subcellular changes in glaucoma.
Linear birefringence is an optical property of many materials, in which light polarized in a direction with higher refractive index travels more slowly than light polarized in the perpendicular direction. The difference in refractive index, n, gives the birefringence. For a homogenous material, retardance (R), the delay experienced by the slower component, is proportional to thickness (T), and birefringence can be calculated as retardance per unit thickness: n = R/T. (Birefringence is a dimensionless number; we, however, use units of nanometers per micrometer to acknowledge explicitly the relation between retardance and thickness.) An array of parallel cylinders in a medium of different refractive index exhibits a type of birefringence called form birefringence.6 Such an array behaves as a uniaxial crystal with the direction of highest refractive index parallel to the cylinders. The RNFL is generally assumed to exhibit form birefringence due to oriented cylinders at a spatial scale comparable to the wavelength of light (microtubules or axonal membranes, for example) and theoretical models of RNFL birefringence show that the volume fraction and relative refractive index of the relevant cylindrical organelles and the refractive index of the medium surrounding these organelles combine to determine n.7 8 On this assumption, therefore, differences in n must necessarily reflect differences in the density or composition of the axons that make up the RNFL.
Birefringence of the RNFL has been measured experimentally in several studies. Weinreb et al.9 used scanning Fourier ellipsometry at 514 nm to measure the retardance at many retinal locations in two fixed macaque eyes and histology to determine RNFL thickness at the same locations. Although individual points showed considerable variation in the ratio of thickness to retardance, data were fit with a straight line passing through zero to obtain a slope of 7.4 µm of thickness per degree of retardance. Recognizing that the retardance represents a double pass through the RNFL and converting retardance expressed as a phase difference (degrees at 514 nm) to retardance expressed as a path length (in nanometers) yields n = 0.19 nm/µm. Huang and Knighton10 measured the retardance of rat RNFL in vitro at multiple wavelengths (400–830 nm), and then measured the thickness of the same nerve fiber bundles in histologic sections. The calculated birefringence was similar across wavelength, averaging 0.23 nm/µm before and 0.19 nm/µm after glutaraldehyde tissue fixation. The wavelength invariance of birefringence justifies comparisons of studies performed at different wavelengths. Cense et al.11 used polarization-sensitive OCT (PS-OCT) at 830 nm to measure the birefringence of human RNFL in vivo. A study at one location in one subject found n = 0.45 nm/µm,11 and another study of several retinal locations in one subject found n ranging from 0.21 to 0.43 nm/µm.12 Measurements on a circular scan around the ONH in two subjects ranged from 0.12 to 0.4 nm/µm.13
The large difference in reported birefringence may mean that RNFL tissue properties differ between species and even between different areas of the RNFL in the same eye. Structurally, in fact, the RNFL does differ between retinal areas. In primate retina the proportion of small axons is lower in nerve fiber bundles nasal to the ONH, higher in arcuate bundles, and highest in papillomacular bundles.14 Furthermore, the glial content in the bundles varies across the retina.15 This leads immediately to the question: Does RNFL birefringence reveal these known variations in RNFL structure? If it does, measurement of n may provide a means of "optical biopsy"—the ability to detect changes in internal structure that may precede cell death in the early stages of glaucoma.
The preceding question motivated this study, which was based on the following two hypotheses: (1) birefringence varies across nerve fiber bundles—that is, n varies on circular paths around the ONH; and (2) birefringence does not vary along nerve fiber bundles—that is, axonal structure, and thus n, does not change rapidly with distance from the ONH. To test these hypotheses, we determined the variation of RNFL birefringence in the peripapillary retina by using SLP to measure RNFL retardance and OCT to measure RNFL thickness and then calculating n. A preliminary report of data obtained with a variety of OCT and SLP instruments (Huang et al., IOVS 2003;44:ARVO E-Abstract 3363) supported our hypotheses, as has a recent direct test with PS-OCT in two subjects.13 For this study we used two commercially available instruments, StratusOCT (Carl Zeiss Meditec, Dublin, CA) and GDx-VCC (Laser Diagnostic Technologies, San Diego, CA), to determine the variation of RNFL birefringence in the peripapillary retina of 26 normal human subjects.
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Materials and Methods |
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Extraction of Retardance along the OCT Scan Path
Image processing and data analysis were implemented in commercial software (MatLab, ver. 6.5; The MathWorks, Inc., Natick, MA).
SLP provides retardance values for a large area around the ONH, whereas OCT gives the RNFL thickness only along a circular scan path. To calculate birefringence, retardance along the corresponding scan path had to be extracted. To locate the OCT scan path in the SLP retardance image, the SLP fundus image (Fig. 2A) was registered to the OCT video image (Fig. 1C) by adjusting image scaling, rotation, and translation in custom software that used a combination of automatic algorithms with manual fine tuning.16 The size and position of the OCT scan circle were then transferred to the registered SLP fundus and retardance images.
We used blood vessel locations to check and adjust the image registration. A binary image of blood vessels in the SLP fundus image was obtained by applying a two-dimensional filter and threshold algorithm to the registered SLP fundus image (Fig. 3A) .17 In the OCT scan, major blood vessels in the retinal cross-sectional image (Fig. 3B , arrows) were identified by their shadows in the outer retina. Blood vessel positions along the scan path in the binary SLP image were plotted as a profile (Fig. 3B , solid line). With well-registered images, the vessel positions in the profile corresponded to the shadow positions, as demonstrated in Figure 3B . Otherwise, SLP image registration was adjusted until the blood vessel positions and shadows were well matched. The retardance profile was derived from the scan circle in the registered retardance image.
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Removal of the Residual Birefringence of the Compensated Anterior Segment
Although the variable compensator in SLP provided individualized compensation of anterior segment birefringence, residual birefringence existed in all subjects and typically appeared in a compensated image as a weak bow-tie pattern in the macula (Fig. 2B) . In a manner similar to the determination of anterior segment birefringence,3 residual birefringence was estimated from the macular pattern by fitting a smooth curve to the retardance profile on a circle around the fovea. The smooth curve varied above and below the average macular retardance by an amount equal to the residual retardance. Residual anterior retardance could change the values of measured RNFL retardance (either up or down) and affect the calculated n. We therefore used the macular retardance pattern to perform a correction on the RNFL profile. We assumed that the same variation of retardance seen in the macular profile also occurred in the RNFL profile—that is, we assumed that nerve fiber bundles were radially distributed around the ONH and simply subtracted from the RNFL profile the variation of the smooth curve fit to the macular profile. The assumption that nerve fiber bundles are radially oriented around the ONH is not strictly true, especially for the arcuate bundles, but calculations showed that a variation of ±10° had negligible effect for the small corrections used. This study used corrected RNFL retardance profiles for all birefringence calculations.
Calculation of n
In this study, the RNFL was assumed to be homogenous with depth, and birefringence was calculated as n = R/T, where R was the single-pass RNFL retardance measured by SLP and T was the RNFL thickness measured by OCT. Evidence for homogeneity comes from electron microscopy, which shows that although axon diameters range from 0.1 to 3 µm there is no obvious stratification of axons by size,14 15 and from PS-OCT, which shows linear variation of retardance with depth.11 12 13
Subjects
This research adhered to the tenets of the Declaration of Helsinki and was approved by the University of Miami Institutional Review Board. All subjects gave informed consent after the nature and possible consequences of the study were explained. Subjects were judged normal if they had no history of ocular disease, intraocular pressure less than or equal to 21 mm Hg by Goldmann applanation tonometry, normal optic disc appearance, normal perimetry, and refractive errors within ±6 D.
Subjects were recruited from two study sites, both having the same models and software versions of StratusOCT and GDx VCC. Thirteen subjects were studied at each site (Table 1) . There was no significant difference in age between the two groups, but the residual retardance of anterior chamber birefringence compensation was significantly larger in group 1 (P < 0.001, t-test). At study site 1, one eye of each subject was randomly selected for imaging. Nine eyes were imaged with OCT at a scan radius of 1.73 mm, and four eyes were imaged at scan radii of 1.44, 1.69, 1.90, and 2.25 mm. To determine the reproducibility of the measurements, imaging was repeated on two additional days for these latter four eyes. At study site 2, both eyes of each subject were measured, with five subjects imaged with OCT at scan radii of 1.44, 1.60, 1.70, and 1.85 mm and eight subjects imaged with an additional radius of 1.95 mm. Data from OCT scan circles with 1.69-, 1.70-, and 1.73-mm radii were considered equivalent (3.4 mm diameter). For all subjects, SLP and OCT were performed on the same day. For repeated SLP, the anterior segment birefringence was determined once and used for setting the VCC for all sessions. All images were obtained by experienced operators.
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Results |
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nn = R/T. To estimate measurement reproducibility, this subject was imaged on three different days over a 3-month period. The three T profiles, obtained by an experienced operator from a subject with good fixation, showed excellent reproducibility (Fig. 4A) . To show the variation in the SLP measurement alone, one OCT scan path was used to extract an R profile from each of the three SLP images. The three R profiles obtained also showed excellent reproducibility (Fig. 4B) . Finally, all nine combinations of OCT and SLP images were registered separately and used to calculate nine profiles of n. The mean ± SD of the nine profiles is shown in Figure 4C . Reproducibility measured in three additional subjects was similar (Figs. 4D 4E 4F) . To produce a summary measure of the reproducibility of n, the squares of the standard deviation (the variances) at each point were averaged across the n profiles from the four subjects. The square root of this average—that is, the average standard deviation for measurements of n—was 0.052 nm/µm.
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n shown in Figure 4C is that n was not constant, but rather varied significantly along a scan path that crossed nerve fiber bundles. That is, the variation of the n profile around the ONH was much larger than the variation of individual points. To explore further this variation across nerve fiber bundles, n profiles on a 3.4-mm diameter scan path were measured in 13 eyes of 13 subjects at one study site and 26 eyes of 13 subjects at the other site (Table 1) . For the subjects with both eyes measured, one eye of each subject was randomly selected for comparison.
Overall appearance of the n profiles was similar in most eyes (23/26), with peaks in superior and inferior RNFL and valleys in temporal and nasal RNFL. Figure 5 shows profiles for 12 of 13 eyes in group 1 (left column) and 11 of 13 eyes in group 2 (right column). For these 23 eyes the averages of T, R and n over the scan path (profile means) as well as the average n in four 60° (2-clock-hour) sectors are summarized in Table 2 . The average birefringence—that is, the profile mean of n—was similar within a group (low standard deviation); the sector means within a group, however, were significantly different from each other (P < 0.001, F-test), reflecting the peaks and valleys in Figure 5 . The average T in group 1 was significantly higher than in group 2, and the average R was somewhat lower. As a consequence, n in group 1 was significantly higher than in group 2, especially in the superior and inferior sectors.
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n variation than usual (Fig. 6 , left column). n did not show the superior and inferior maxima and the nasal and temporal minima typical of other eyes. Another eye in group 2 had higher than usual nasal values (Fig. 6 , right column).
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Radial Variation in RNFL Birefringence
To test the hypothesis that birefringence does not vary along nerve fiber bundles, in four eyes of four subjects in group 1 and all 26 eyes of 13 subjects in group 2 we measured n profiles on peripapillary circles of different diameters. Figure 7A displays T profiles for one subject on four circles around the ONH. As expected, the RNFL thinned with increasing scan radius. The four OCT scan circles were transferred to the SLP retardance image to yield R profiles along the corresponding scan paths (Fig. 7B) . Retardance also decreased with increasing scan radius. The calculated n profiles, however, did not show systematic variation with circle radius (Fig. 7C) . Rather, with the exception of the superior and inferior peaks of the largest circle (thinnest RNFL), the n profiles were nearly the same. The average SD of the four n profiles in Figure 7C , computed as for Figure 4C , was 0.059. Similar behavior was seen in the n profiles of the other three subjects of Figure 4 (Figs. 7D 7E 7F) as well as the 26 eyes in group 2. The average standard deviation across all subjects was 0.046 nm/µm, which is comparable to the reproducibility (Fig. 4) and much less than the magnitude of n variation among bundles (n ranged from approximately 0.24 to 0.40 nm/µm around the ONH). This result suggests that, at least for the distance covered by the scan circles, n does not change significantly along nerve fiber bundles.
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Discussion |
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TopAbstractMaterials and MethodsResultsDiscussionReferences |
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n should depend critically on details of tissue ultrastructure.7 8 This study combined SLP measurements of RNFL retardance (R) with OCT measurements of RNFL thickness (T) to test whether n = R/T would reveal the structural variation of the normal peripapillary RNFL. Profiles of n on circular paths around the ONH showed significant variation in most subjects (Figs. 4 5) , which quite plausibly may reflect the different distributions of axonal diameter and glial content seen histologically.14 15 Profiles on paths of different radii were similar (Fig. 7) , consistent with the concepts that axons, once bundled together, tend to stay together as they converge on the ONH and that the internal structure of axons varies slowly over the distances examined.
Because both T and R were measured by commercially available devices, the method used in the current study for determining RNFL birefringence can have widespread application. The SLP and OCT images are easily acquired in a clinical setting. Calculation of n, however, required postprocessing with custom software. The precision of T and R measurements affect the birefringence calculated, and in this study, although the pattern of n variation was similar, a bias existed between the two groups measured with different instruments (Table 2) . Calibration between devices, therefore, is necessary, to compare precisely data from different studies.
A legitimate concern in the derivation of n from measurements made with two different instruments is whether systematic inaccuracies in either could produce apparent variation in n when none actually exists. The similar peripapillary pattern in n across individuals (Fig. 5) means that any error would have to have a similar pattern, with T overestimated and/or R underestimated in nasal and temporal retina and T underestimated and/or R overestimated in superior and inferior retina. On the assumption that n was constant, we calculated that the systematic error in T would have to have been 40 µm to produce the observed variation in n, an error not consistent with the RNFL boundaries seen on visual inspection of the OCT images. (It is worth noting, however, that in some sectors of some subjects the RNFL intensity fell to values that made the posterior boundary of the RNFL difficult to distinguish from underlying tissue. This intensity decrease, which was probably caused by the directional reflectance of the RNFL,18 could have caused errors in T due to failure of the OCT analysis algorithm to detect the true RNFL border.) Similarly, the systematic error in R would have to have been 20 nm, well above the SLP measurement error. The residual retardance of an incompletely compensated anterior chamber produces a patterned retardance bias, but across all subjects the residual retardance was never more than 10.5 nm, and we used a procedure to correct for most of this bias. It seems likely, therefore, that we have measured a true property of the RNFL. Confidence in our conclusion that n varies around the ONH also comes from a few subjects measured with PS-OCT,11 12 13 a fundamentally different method in which n measured directly shows similar values and a similar magnitude of variation. Finally, the early in vitro data of Weinreb et al.9 showed significant scatter around the regression used to characterize RNFL birefringence. Although not suggested by those investigators, spatial variation in n of the magnitude found in the current study could explain the scatter that they observed.
The profiles of n around the ONH were similar in most subjects (Fig. 5) . The observed differences in profile shapes (e.g., Fig. 6 ) probably indicate anatomic variation in the spatial arrangement of the RNFL among individuals. Conversely, similar mean values reflected similar average tissue composition across subjects.
Our finding that n varies around the ONH has important consequences for the interpretation of SLP; although the commercial instrument (GDx-VCC; Laser Diagnostic Technologies, Inc.) measures retardance, it expresses these measurements as RNFL thickness—that is, it incorporates implicitly the assumption that n is constant. The reported thicknesses cannot be correct everywhere, and changes in SLP measurements could result from changes in either anatomic thickness or birefringence of RNFL. The clinical utility of SLP, however, does not depend on its reported units, and comparisons of SLP parameters with normal values and with individual baseline values remain valid.
RNFL birefringence may provide a means of "optical biopsy"—the ability to measure a property of the RNFL that characterizes its internal structure. The sensitivity of n to axonal ultrastructure suggests that an accurate measurement of n may be useful for detecting morphologic abnormalities caused by glaucoma. Such abnormalities may include gliosis or a partial loss of organelles, such as microtubules, that might cause n to decrease or shrinkage of ganglion cells,19 20 21 which might cause n to increase. If morphologic change precedes irreversible loss of axons, birefringence measurements may provide an early indicator of glaucoma that may open a therapeutic window during which damage might be prevented.
In summary, two commercially available technologies, OCT and SLP, have been used in combination to measure RNFL birefringence, an optical property that depends on the structure of nerve fiber bundles. We found that RNFL birefringence in normal subjects varies with position around the ONH, a variation that may result from known structural differences among nerve fiber bundles that serve different regions. Constant n along bundles is consistent with this idea. The dependence of n on structural variation offers hope that measurement of RNFL birefringence may be able to detect early subcellular changes in glaucoma. To explore this possibility, future studies must measure RNFL birefringence in patients with ocular hypertension and various degrees of glaucomatous damage.
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Footnotes |
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Submitted for publication February 4, 2004; revised May 11, 2004; accepted May 27, 2004.
Disclosure: X.-R. Huang, Laser Diagnostic Technologies, Inc. (F); H. Bagga, None; D.S. Greenfield, Laser Diagnostic Technologies, Inc. (F, R), Carl Zeiss Meditec (R); R.W. Knighton, Laser Diagnostic Technologies, Inc. (F)
The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked "advertisement" in accordance with 18 U.S.C. 
1734 solely to indicate this fact.
Corresponding author: Xiang-Run Huang, Bascom Palmer Eye Institute, University of Miami School of Medicine, 1638 NW Tenth Avenue, Miami, FL 33136;xhuang3{at}med.miami.edu.
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References |
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and ß retinal ganglion cells in cats with chronic glaucoma. Invest Ophthalmol Vis Sci. 2003;44:3005–3010.This article has been cited by other articles:
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  B. Fortune, G. A. Cull, and C. F. Burgoyne Relative Course of Retinal Nerve Fiber Layer Birefringence and Thickness and Retinal Function Changes after Optic Nerve Transection Invest. Ophthalmol. Vis. Sci., October 1, 2008; 49(10): 4444 - 4452. [Abstract] [Full Text] [PDF]
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B. Fortune, L. Wang, G. Cull, and G. A. Cioffi Intravitreal Colchicine Causes Decreased RNFL Birefringence without Altering RNFL Thickness Invest. Ophthalmol. Vis. Sci., January 1, 2008; 49(1): 255 - 261. [Abstract] [Full Text] [PDF]
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X.-R. Huang, R. W. Knighton, and L. N. Cavuoto Microtubule Contribution to the Reflectance of the Retinal Nerve Fiber Layer Invest. Ophthalmol. Vis. Sci., December 1, 2006; 47(12): 5363 - 5367. [Abstract] [Full Text] [PDF]
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N. J. Reus, Q. Zhou, and H. G. Lemij Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation. Invest. Ophthalmol. Vis. Sci., September 1, 2006; 47(9): 3870 - 3877. [Abstract] [Full Text] [PDF]
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L. M. Ventura, N. Sorokac, R. D. L. Santos, W. J. Feuer, and V. Porciatti The Relationship between Retinal Ganglion Cell Function and Retinal Nerve Fiber Thickness in Early Glaucoma. Invest. Ophthalmol. Vis. Sci., September 1, 2006; 47(9): 3904 - 3911. [Abstract] [Full Text] [PDF]
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 M Sehi, D C Guaqueta, and D S Greenfield An enhancement module to improve the atypical birefringence pattern using scanning laser polarimetry with variable corneal compensation Br. J. Ophthalmol., June 1, 2006; 90(6): 749 - 753. [Abstract] [Full Text] [PDF]
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X.-R. Huang and R. W. Knighton Microtubules Contribute to the Birefringence of the Retinal Nerve Fiber Layer Invest. Ophthalmol. Vis. Sci., December 1, 2005; 46(12): 4588 - 4593. [Abstract] [Full Text] [PDF]
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C. K.-s. Leung, K. K.-L. Chong, W.-m. Chan, C. K.-F. Yiu, M.-y. Tso, J. Woo, M.-K. Tsang, K.-k. Tse, and W.-h. Yung Comparative Study of Retinal Nerve Fiber Layer Measurement by StratusOCT and GDx VCC, II: Structure/Function Regression Analysis in Glaucoma Invest. Ophthalmol. Vis. Sci., October 1, 2005; 46(10): 3702 - 3711. [Abstract] [Full Text] [PDF]
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C. K.-s. Leung, W.-m. Chan, K. K.-L. Chong, W.-h. Yung, K.-t. Tang, J. Woo, W.-m. Chan, and K.-k. Tse Comparative Study of Retinal Nerve Fiber Layer Measurement by StratusOCT and GDx VCC, I: Correlation Analysis in Glaucoma Invest. Ophthalmol. Vis. Sci., September 1, 2005; 46(9): 3214 - 3220. [Abstract] [Full Text] [PDF]
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