In Vivo Study of Changes in Refractive Index Distribution in the Human Crystalline Lens with Age and Accommodation

Abstract

purpose. Magnetic resonance imaging (MRI) was used to map the refractive index distribution in human eye lenses in vivo and to investigate changes with age and accommodation.

methods. Whole-eye MR images were obtained for sagittal and transverse axial planes in one eye each of 15 young (19–29 years) and 15 older (60–70 years) subjects when viewing a far (∼6 m) target and at individual near points in the young subjects. Refractive index maps of the crystalline lens were calculated by using a procedure previously validated in vitro.

results. A central high refractive index plateau region and sharp decline in refractive index at the periphery were seen in all three groups. The peripheral decline was steepest in the older lenses and least steep in the young accommodated lenses. Average lens thickness increased (+0.27 mm; P < 0.05) and equatorial diameter decreased (−0.35 mm; P < 0.05) with accommodation. Axial thickness (+0.96 mm; P < 0.05) and equatorial diameter (+0.28 mm; P < 0.05) increased with age. The central index (1.409 ± 0.008) did not differ between groups. The axial thickness of the central plateau increased with age (+0.83 mm; P < 0.05) but not significantly with accommodation. The equatorial diameter of the central plateau increased with age (+0.56 mm; P < 0.01) and decreased with accommodation (−0.43 mm; P < 0.05).

conclusions. The refractive index of the central plateau region does not change significantly with accommodation or ageing, but its size increases with age and the peripheral decline in refractive index becomes steeper in older lenses.

A detailed understanding of the refractive index distribution in the human eye lens and how it changes with age and accommodation is essential to an understanding of the optical properties of the eye. The gradient refractive index (GRIN) structure of the lens increases its effective power and influences the optical aberrations of the eye. It has been suggested that changes in GRIN structure increase the effective power of the lens during accommodation. ¹ It has also been proposed that increases in lens thickness and surface curvature with age (which may be expected to increase lens power) are counteracted by age-dependent changes in the GRIN structure of the lens that prevent an older eye from becoming myopic. ² The GRIN structure, along with asphericity of the lens surfaces, has been invoked to explain accommodation-related changes in the spherical aberration of the eye. ³ Recently, it was shown that the change in higher-order ocular aberrations with accommodation is dependent on age, ⁴ a finding that was explained on the basis of proposed changes in the GRIN structure of the lens with age. Although the GRIN structure of the human eye lens is incorporated in various models of the optical properties of the eye, the refractive index distribution in the crystalline lens, let alone its dependence on age and accommodation, has not been measured in vivo 

The refractive index distribution in the lens has been inferred from optical measurements that are either invasive ^{5 6 7} or involve a priori assumptions concerning lens shape and internal structure (Barbero S, et al. IOVS 2004;45:ARVO E-Abstract 1732). ^{8 9} We have described a noninvasive method for measuring the refractive index distribution in the lens with the use of magnetic resonance imaging (MRI) ^{10 11} and have demonstrated its ability to measure age-dependent changes in the refractive index distribution of isolated human lenses in vitro. ¹² The MRI technique provides a relatively direct method of measuring refractive index of the lens without assumptions about the shape or optical characteristics of the lens. 

Important information has been obtained by measuring refractive index distribution in isolated lenses in vitro. ^{5 6 7 12} Advantages of in vitro experiments include the fact that the tissue can be carefully aligned and measurements performed over long durations to provide high-resolution data free of artifacts associated with blinking and fixation instability. However, postmortem changes in lens structure and shape may influence the measured refractive index distribution in the lens, ¹³ and in vitro measurements cannot adequately provide information on how the GRIN may vary with state of accommodation. The purpose of the present study was to use MRI to measure the refractive index distribution in the human lens in situ and in vivo, as a function of both age and accommodative state, and to compare the results with those in previous in vitro studies. 

Methods

Subjects

Fifteen young and 15 older subjects were recruited for the study. The age of the young subjects was 19 to 29 years (mean ± 1SD: 22.82 ± 3.13). The age of the older subjects was 60 to 70 years (mean ± 1SD: 64.26 ± 3.16). All subjects had good ocular and general health. A preliminary examination was conducted to ensure emmetropia (± 0.75 D sphere and up to 0.50 D cylinder) with 6/6 distance visual acuity in the tested eye. Only one eye of each subject was used: the right eye was chosen when both eyes satisfied the inclusion criteria, but otherwise the better eye was chosen if it satisfied the inclusion criteria. The research adhered to the tenets of the Declaration of Helsinki. The experimental protocol was approved by the Queensland University of Technology and The Prince Charles Hospital human ethics review boards. Informed consent was obtained from all subjects. 

MRI Technique

MR images were obtained on a clinical MR scanner operating at a field strength of 1.5 Tesla (Signa Twin Speed; GE Medical Systems, Milwaukee, WI). A 3.5-cm receive-only surface coil (Nova Medical, Wilmington, MA) was used to obtain high-resolution images from one eye of each subject. Two types of imaging pulse sequences were used. A fast spin echo (FSE) sequence was used to obtain high-resolution images with a relatively short acquisition time and a multi-spin echo (MSE) sequence was used to obtain the refractive index data. ^{10 12} In each case, the images were acquired with a 40-mm field of view and 3-mm slice thickness. The FSE images were acquired with an effective echo time (TE) = 19 ms, an echo train length of 4, a 320 × 320 matrix size (interpolated to 512 × 512 pixel images), and a recycle time (TR) = 400 ms giving a total image acquisition time of 2 minutes and 11 seconds. The FSE images were used for dimensional measurements within the eye and to estimate the eye rotation angle. The MSE images were acquired with four echoes, TE = 12, 24, 36, and 48 ms; a 256 × 256 matrix size; and TR = 400 ms, giving a total acquisition time of 3 minutes and 28 seconds. 

Experimental Procedure

In young subjects, MRI measurements were performed for far and near viewing, whereas in the older subjects, measurements were performed only for far viewing. The subject was positioned supine on a table, and the head was stabilized with foam pads (Fig. 1) . The MRI eye coil, with a viewing hole in the middle, was placed in front of and as close as possible to the measured eye (without touching the skin or eye lashes) and clamped in place. A mirror tilted vertically by 45° was placed 10 cm above the eye. The subject looked through the mirror at the center of a 31-mm-diameter spoke-wheel target on a wall 6.1 m away. 

The subject was instructed to look at the target during the measurements and to relax between measurements. The order of image acquisition was (1) a 16-second set of scout images, (2) an FSE image in the sagittal plane of the eye, (3) an FSE image in the transverse axial plane, (4) an MSE image in the sagittal plane, and (5) an MSE image in the transverse axial plane. If the eye appeared tilted in the sagittal scout images, the vertical tilt of the mirror was adjusted appropriately, and another set of scout images was obtained. The transverse axial scout images were used for manual selection of the slice plane for the first sagittal FSE image, to correspond with the geometric axis of the crystalline lens. The sagittal FSE image was used to determine the slice for the next transverse axial FSE image (i.e., in the sequence just mentioned, each image was used to set up the axis for the next image). 

In young subjects, MR images during near viewing were also obtained. A near spoke-wheel target was placed in a mount in front of the subject’s eye, and as close as possible to the eye, so that it could still be seen clearly and comfortably. The near target was removed from the mount to reveal a round hole in the mount. The subject was instructed to move the mount vertically and horizontally until the distant target appeared centered in the hole. The mount was locked in place, and the near target was replaced. In this manner, the near target was subjectively aligned with the distant target, to maintain similar gaze direction for far and near scans. The subject was instructed to look at the near target and keep it in focus. The range of near target distances for different subjects was 14.5 to 20.9 cm, which corresponds to 6.9 to 4.8 D of accommodative stimulus. The same sequence of MRI images was used as with the far target. 

Data Analysis

The MR images were analyzed with custom software (written in MatLab; The MathWorks, Natick, MA). The key steps in the image analysis were (1) estimation of the rotation angle of the eye, (2) identification of the pixels contained within the crystalline lens, (3) calculation of the refractive index associated with each identified pixel, and (4) noise reduction in the refractive index profiles. Raw and post processed MR images obtained during far viewing in one young subject are shown in Figure 2 . 

Estimation of the Eye Rotation Angle.

The orientation of the eyes in the images had to be adjusted to a common axis for further data analysis. This procedure involved software rotation of the images to correct for any deviation of the axis of the lens from the vertical. Also, in young subjects, even though the far and near targets were aligned during the experiment, it was important to estimate any eye turn between far and near viewing conditions. Therefore, a method to estimate the overall eye rotation angle was developed. 

The method used to estimate eye rotation angles defines a reference axis of the eye that connects the anterior edge of the cornea to the posterior edge of the sclera. This method is similar to that described previously for lower resolution MR images. ¹⁴ The performance of the algorithm was tested by rotating MR images of the eye by various angles and using the software to measure the induced eye rotation. In addition to the whole-eye rotation, the tilt of the crystalline lens was estimated based on the equatorial edge pixels of the lens. Because the clarity of the sclera in the MSE images was poor compared with that in the FSE images, the rotation angle of the eye obtained from the FSE images was used to orient the MSE images vertically with the cornea at the top and sclera below. 

Identification of Lens Pixels.

The pixels contained within the lens were identified automatically with minimal user interference. The user defined a region of interest around the crystalline lens by using a computer mouse in the first of the four images in the MSE sequence. Edge detection was performed with a Canny edge filter, to identify the crystalline lens edges. Unfortunately, the boundary between the crystalline lens and iris was indistinguishable in the images. The user therefore marked two regions on either side of the pupil around the contact between the iris and the lens. These regions were removed from further analysis. The remaining lens edge pixels were selected by the user with mouse clicks. In the custom software (MatLab; The MathWorks) a contiguous set of edge pixels could be selected with one mouse click. Once the edge pixels were identified, the anterior and posterior edges of the lens were individually smoothed with a conic curve (equation 1 ), as described by Dubbelman and van der Heijde ¹³ :  

\[y{=}\frac{c(x{-}x_{0})^{2}}{1{+}\sqrt{1{-}kc^{2}(x{-}x_{0})^{2}}}{+}y_{0}\]

where x ₀, y ₀ is the vertex position, c is the curvature at the vertex, and k is the conic constant. Vertical rows of pixels between and including the anterior and posterior smoothed surfaces from one equatorial edge of the lens to the other were recorded to identify all the pixels contained within the crystalline lens. The same pixel locations were used for the remaining three images acquired simultaneously in the MSE sequence. 

Calculation of Refractive Index.

The refractive index associated with each crystalline lens pixel was calculated as described by Jones et al. ^{11 12} The pixel intensity, I, from each of the four MSE images was fitted to a monoexponential decay function: I=I ₀ e ^{−R ₂ TE} where TE is the echo time (Fig. 2) . In this way, an estimate of R ₂ (the inverse of the spin-spin relaxation time T ₂) was obtained for each lens pixel. R ₂ is directly proportional to the concentration of macromolecules (notably crystallin proteins), which in the crystalline lens is related to the refractive index. ^{10 11 12} Using a refractive index versus R ₂ calibration equation obtained from human lens homogenate samples, ¹² the resulting R ₂ map was converted into a refractive index map of the lens corresponding to a 589-nm wavelength of light. The resolution of the refractive index maps is determined by that of the corresponding MSE images from which they are derived, although both may be affected by image blurring from eye movements and possibly also accommodative lens fluctuations in the young eyes. The MSE images had an in plane resolution of 0.156 mm and a slice thickness of 3 mm, resulting in a voxel size of 0.156 × 0.156 × 3 mm (height × width × depth) for refractive index measurements. 

Reduction of Noise in the Refractive Index Profile.

The two-dimensional (2-D) refractive index maps obtained from the MSE images were inherently noisy compared with previous in vitro data, ¹² due to the lower magnetic field strength of the clinical MRI instrument (1.5 Tesla) and the presence of motion artifacts in some images due to blinks and eye movements. Consequently, we decided to compute refractive index profiles along the axis and equatorial diameter of the lens, while simultaneously averaging the refractive index profile over a 5-pixel-wide band. For example, in each subject, the refractive indices of a band of five pixels perpendicular to the axial direction were averaged to compute the axial refractive index profile. Similarly, the refractive indices of a band of 5 pixels perpendicular to the equatorial direction were averaged to compute the equatorial refractive index profile. The 5-pixel averaging resulted in a voxel size of 0.78 × 0.156 × 3 mm (height × width × depth) for refractive index profile calculations. 

The data within the young and older groups were then averaged to obtain an average profile for each subgroup. Since this involved averaging profiles from lenses of different thickness and diameter, it was necessary first to scale the data for each subject to the median thickness and diameter calculated for their group. To ensure that averaging was performed for equivalent locations within the lens, each subject’s data were interpolated in 0.156-mm steps (i.e., 40 mm/256 pixels) over the average axial or equatorial length for the group. After group averaging, the lens thickness or diameter was normalized to extend from −1 to +1 to compare young unaccommodated, young accommodated, and old lenses of different sizes. 

Results

Of the 90 MSE images planned in the study, 4 were not completed due to subject fatigue, and 2 could not be analyzed due to image blur. Consequently, refractive index data from 84 MSE images for (1) far viewing in young subjects (15 transverse axial and 14 sagittal images), (2) near viewing in young subjects (14 transverse axial and 12 sagittal images), and (3) far viewing in older subjects (15 transverse axial and 14 sagittal images) are reported. 

The algorithm used to determine eye rotation angle was tested by calculating the eye rotation angle for MR images rotated artificially by known angles from −10° to +10°. Transverse axial images of an unaccommodated and an accommodated eye from two young subjects were used for this analysis. The algorithm performed very well in estimating the eye rotation angle, as indicated by a good correlation between induced and measured eye rotation angles (slope: 1.17; intercept: 0.13; r ² = 0.99). 

During the analysis of images to extract refractive index data, the software would indicate the measured eye rotation angle in the software window. The user would then run the image-rotation algorithm until the eye image was oriented vertically within ±0.25°, as measured by the software. Usually, one to two runs were necessary to align the image vertically within ±0.25°. The estimated eye rotation angles in all subjects ranged between 0.54° and 12.63° (mean ± SD: 6.08 ± 2.74°) for transverse axial images and between 0.41° and 4.20° (mean ± SD: 0.45 ± 2.62°) for sagittal images. In young subjects, the differences between eye rotation angles at far and near viewing were not significantly different for transverse axial (paired t-test; P = 0.99) and sagittal (paired t-test; P = 0.29) images. 

Two-dimensional maps of refractive index distribution (averaged over all subjects within a group) for the three groups of lenses (i.e. young unaccommodated, young accommodated, and old unaccommodated lenses) are shown in Figure 3 . A region of high refractive index (≥1.40) at the center and a relatively steep decline in refractive index near the periphery were seen in all three groups. For the younger lenses the decline in peripheral refractive index was more gradual in the accommodated state (Fig. 3B)than in the unaccommodated state (Fig. 3A) . An increase in the overall crystalline lens size and especially that of the central high refractive index region occurred with increase in age (Fig. 3C) . 

Average refractive index profiles along the axis and the equatorial diameter of the three groups of lenses are shown in Figures 4 and 5(see the Methods section for details on averaging). Figure 4shows the transverse axial profiles and Figure 5shows the sagittal profiles, with the left- and right-hand sides of the figures showing normalized and raw lens distances on the x-axis, respectively. As for the 2-D representations in Figure 3 , there were high refractive index plateaus at the center and sharp declines in refractive index toward the periphery. In the older lenses, the central plateau extended over a wider region, and the peripheral decline in refractive index was more abrupt than in the younger lenses. In the accommodated lenses, the peripheral decline in refractive index appeared to be less steep than in the unaccommodated lenses. Except for being a little noisier, the trends in the sagittal profiles (Fig. 5)were similar to the those in the axial profiles (Fig. 4) . 

To compare the sizes of the central region of uniform refractive index between different groups, this region was defined as the region encompassing refractive indices within 1% of the average central refractive index. The central refractive index was calculated as the mean refractive index over nine pixels in a 3 × 3 grid (0.468 × 0.468 × 3 mm voxel) at the lens center. The lengths of the central plateau region along the axis and equator of the lens were computed individually for each of the 84 lens images included in the final analysis. The mean dimensions of the central plateau for combined transverse axial and sagittal data were determined for each group and are given in Table 1and shown in Figure 6 . The overall lens dimensions are also provided in Table 1 . Overall lens axial thickness increased (4.05 vs. 3.78 mm; mean change: 0.27 mm; P < 0.05) and equatorial diameter decreased with accommodation (8.77 vs. 9.12 mm; mean change: 0.35 mm; P < 0.05). Lens axial thickness increased (4.75 vs. 3.78 mm; mean change: 0.96 mm; P < 0.05) and equatorial diameter also increased (9.39 vs. 9.12 mm; mean change: 0.28 mm; P < 0.05) with age. The average central refractive index of 1.409 ± 0.008 (mean ± SD) was not significantly different between the groups (Table 1) . The length of the central plateau along the axis increased significantly with age (3.95 vs. 3.12 mm; mean change: 0.83 mm or 27%; P < 0.01), but not with accommodation (P = 0.38). The length of the central plateau along the equator increased significantly with age (8.50 vs. 7.94 mm; mean change: 0.56 mm or 7%; P < 0.01) and decreased significantly with accommodation (7.51 vs. 7.94 mm; mean change: −0.43 mm or 6%; P < 0.05). 

The normalized refractive index profiles along the axis and equator of the crystalline lens derived from the transverse axial images (Fig. 4)were fitted to a power function as described elsewhere ^{2 12} :  

\[N(r){=}c_{0}{+}c_{\mathrm{p}}\ {_\ast}\ r^{p}\]

where N is refractive index, r is the normalized distance from lens center (r = 0 at the center and r = 1 at the periphery), c ₀ is the refractive index at the lens center, c _p is the change in refractive index between the lens center and periphery, and the exponent p characterizes the GRIN from center to periphery. ¹²  

Transverse axial images were chosen for this analysis as the data were less noisy and more symmetrical than the data from sagittal images (compare Figs. 4 and 5 ). To fit power functions, refractive index data from each semidiameter of the lens were averaged to provide a refractive index distribution corresponding to one half of the crystalline lens (i.e. from the geometric center to the edge of the lens; Fig. 7 ). Good power function fits, with r ² of at least 0.95 were obtained. Examination of the residuals indicated good fits to the data with no clear pattern of (or any large) residuals. 

Parameters obtained by fitting equation 2to the refractive index profiles are provided in Table 2 . These include the predicted central refractive index c ₀ and the refractive index at the lens edge (c ₀ + c _p). The exponent parameters (p) describing the shape of the refractive index distribution for the three groups of lenses were tested statistically with t-tests. The parameter p was significantly larger in older lenses than in the young unaccommodated lenses along both the axis (p = 6.7 vs. 4.9; t = 3.24, P < 0.05) and equatorial diameter (p = 10.3 vs. 6.3; t = 4.30, P < 0.05) of the lens. The parameter p was significantly smaller in young accommodated compared with unaccommodated lenses along the equatorial diameter (p = 5.1 vs. 6.3; t = 2.30, P < 0.05) and approached statistical significance along the axis (p = 4.0 vs. 4.9; t = 2.03, P = 0.05) of the lens. In all three groups of lenses, the parameter p was larger for the equatorial refractive index profile than for the corresponding axial refractive index profile (P < 0.05 for all three paired t-tests). In the older lenses, there appeared to be a small difference between the predicted central refractive index obtained from the equatorial data and both the mean of the axial and equatorial central refractive indices for the younger lenses and the corresponding value for the older lenses obtained from the axial data. However, this difference of 0.0014 (or 0.1%) from the mean central refractive index of the younger lenses probably reflects the effects of spatial averaging combined with the fact that this equation is only an approximation (albeit a reasonably good one) to the actual refractive index variation in the lens. Values for the predicted refractive index at the lens edge (c ₀ + c _p) do not differ significantly between the three groups or between axis and equator. 

Discussion

The MRI technique was successfully used for the first time to map the refractive index distribution of the crystalline lens in living human eyes in both the unaccommodated and accommodated states. As expected and despite the noise in the data, a central region of high refractive index with a sharp decline in refractive index toward the periphery can be seen in the average refractive index maps shown in Figure 3 . The refractive index distributions along the axis and equatorial diameter of the crystalline lens were well described by power functions (Fig. 7) . For normalized lens distances, although the overall patterns of refractive index distributions were similar along the axis and the equatorial diameter, the rate of decline in refractive index from center to periphery was sharper along the equatorial diameter as indicated by the larger values of parameter p (Table 2) . 

The central and peripheral refractive indices of the crystalline lens were 1.409 ± 0.008 and 1.380 ± 0.004, respectively (corresponding to a 589-nm wavelength of light), and these values did not change significantly with age or accommodation. The invariance of central refractive index with age has been reported previously using in vivo ¹⁵ and in vitro lens measurement techniques. ^{12 16 17} In their study, Jones et al. ¹² used higher resolution MRI measurements on isolated lens tissues, and the central and peripheral refractive indices were reported to be 1.418 and 1.371, respectively. The central refractive index obtained in the present study was slightly lower and the peripheral refractive index slightly higher compared with those reported by Jones et al., probably because of the poorer signal-to-noise ratio, lower spatial resolution, and spatial averaging techniques used in the current in vivo study. 

The size of the central plateau region of approximately uniform refractive index changed with both age and state of accommodation (Table 1 , Fig. 6 ). Past studies have suggested that the central region of high refractive index corresponds to the lens nucleus. ^{17 18} If so, the changes in the dimensions of the central region might be considered to reflect changes in the size of the lens nucleus with age and accommodation. The equatorial diameter of the central plateau decreased by approximately 6% with accommodation, whereas its axial thickness increased by approximately 5%, although the latter change was not statistically significant (P = 0.38). Previous studies in which Scheimpflug imaging was used identified the nucleus of the lens based on densitometry. ^{18 19 20 21 22} The findings in these studies suggested that the axial thickness of the lens nucleus increases ¹⁸ by approximately 6%, ²² 11%, ¹⁹ or 13% ²³ and the equatorial diameter of the lens nucleus decreases by approximately 8% ²³ for a 6-D accommodative stimulus. Based on the data of Hermans et al., ²³ this change equates to approximately 0.33 mm for an unaccommodated nucleus thickness of 2.5 and 0.48 mm for an unaccommodated nucleus diameter of 6 mm, corresponding to approximately 2 and 3 pixels, respectively, in the MR images of the present study. The predicted changes in axial thickness of the nucleus are therefore close to the resolution limits of the present study. 

In the studies mentioned, including the present study, accommodative response magnitude was not measured. Differences in accommodative response in individual subjects ²⁴ and between studies could partly account for the reported differences in lens nucleus changes with accommodation. In the present study, the change in overall axial lens thickness with accommodation was 0.26 ± 0.17 mm (mean ± SD), corresponding to approximately 3.99 ± 1.92 D (mean ± SD) of accommodation calculated using the lens thickness change to accommodation ratio of 0.067 mm/D reported by Ostrin et al. ²⁵ Therefore, the changes in nucleus and refractive index profile with accommodation reported herein would correspond to approximately 4 D of response accommodation. 

With increasing age, the axial thickness of the central plateau increased by 21%, and the equatorial diameter increased by 7%. Results in past studies in which Scheimpflug densitometry was used, suggest that the thickness of lens nucleus increases by 5% ¹⁹ or 12% ²¹ with age, although another study reported a decrease of 6%. ²⁰ The increase in thickness of the nucleus reported in this study is higher than in previous reports, whereas an in vivo change in equatorial diameter of the nucleus with age is reported herein for the first time. 

A common issue both with past Scheimpflug imaging studies and the current MRI study is the definition of the lens nucleus. Scheimpflug studies identify the lens nucleus based on light scattering in the lens, whereas in the present study the central plateau was described as the region encompassing refractive index values within 1% of the central maximum. These differences in definition therefore probably account for the discrepancies between the changes in dimensions of the lens nucleus with age and accommodation reported by these two techniques. However, both techniques confirm that the axial thickness of the nucleus increases with age and accommodation and the equatorial diameter of the nucleus decreases with accommodation and increases with age. 

The peripheral decline in refractive index was somewhat smoother in the accommodated lens compared with that in the unaccommodated lens. With age, the peripheral decline in refractive index became more abrupt (Fig. 7) . The pattern of changes in refractive index distribution with age is similar to that described previously in lenses in vitro, ^{12 17} although in the current in vivo study, the lower spatial resolution and spatial averaging techniques used may have artificially reduced the steepness of the peripheral decline in refractive index in all lens groups. However, the age-related changes in refractive index distribution reported in past in vitro studies are potentially influenced by the age dependence of the accommodative state of isolated lenses. ¹² Once the zonular tension is released, isolated lenses tend to become more spherical under the elastic influence of the lens capsule, adopting a state of maximum accommodation. ²⁶ The present study is the first to report changes in refractive index distribution in the lens with the state of accommodation and confirms that there are indeed changes in the refractive index distribution of the crystalline lens with accommodation, notably a decrease in the equatorial diameter of the central region (Table 1 , Fig. 6B ) and a smoother decline in peripheral refractive index (Figs. 4 5 7) . This study also clearly demonstrates changes in the refractive index distribution of the unaccommodated lens with age (Figs. 4 5 7) . 

In a previous study, it was reported that the normalized axial and equatorial refractive index profiles were different in young lenses but similar in older lenses. ⁷ In our study, the normalized axial and equatorial profiles were largely similar in the young and older lenses, albeit with a sharper decline in refractive index along the equatorial diameter. In the study by Pierscionek, ⁷ only a slight refractive index variation along the axial direction in both young and older lenses (a change of 1% or less based on a central refractive index of 1.403 and predictions of peripheral refractive indices for 25- and 65-year-old lenses using equations from Pierscionek’s Table 1 ⁷ ) or along the equatorial diameters of all but one of the older lenses was observed. In contrast, a much larger refractive index variation was reported along the equatorial diameter of young lenses (>3% change). In the present study, clear refractive index variations along both the axial and equatorial directions were observed (>2% change in refractive index from center to periphery in the young and older lenses). Given the paucity of young lenses in Pierscionek’s study, it can be concluded from our study that, within the overall experimental error (≤ ±0.01) of our refractive index measurements, the normalized axial and equatorial refractive index profiles followed a largely similar pattern of high refractive index at the center and a sharp decline in refractive index toward the periphery, and the asymmetry between axial and equatorial profiles (Figs. 4 5 7)was less pronounced than that suggested by Pierscionek. 

Our in vivo technique offers useful insights into the refractive index properties of the crystalline lens. The data were inherently noisy due primarily to the limited sensitivity of the clinical MRI scanner for this type of measurement and the need to minimize scan times to reduce motion artifacts and avoid fatiguing the subject. However, the clarity of the lens images was comparable between the young and older eyes, suggesting that accommodative lens fluctuations in the young subjects minimally affected image resolution. Systematic errors arising from conversion of the measured transverse relaxation rates R ₂ to refractive index values are more difficult to assess, due to the paucity of comparable data obtained by independent methods. However, we believe that these errors are likely to be smaller than the random errors arising from noise in the images. This supposition is supported by the fact that our values for both central and peripheral refractive indices fell within the range of values obtained in vitro when an optical (reflectometric) technique is used. ⁷ However, the thickness of the MRI slice (3 mm) could make the central refractive index estimate lower, the peripheral refractive index estimate higher, the length of the central plateau narrower, and the peripheral gradient less steep, although the magnitude of this averaging error is difficult to estimate. Issues related to available software and specific absorption rates (SARs) limited us to using only four echoes in the MSE sequence, compared with the 64 echoes used in our previous study of isolated human lenses. ¹² This limitation restricted the accuracy of the current in vivo technique in detecting refractive index variations, particularly in the center of the lens where the transverse relaxation times were shortest. Signal-to-noise ratio and resolution (spatial and refractive index) can be significantly improved with the use of higher field MRI systems (operating at field strengths of 3.0 T and above), which are becoming routinely available. In future, the use of higher field MRI instruments will help reduce measurement duration and provide high-clarity images that will help better understand individual variation and longitudinal trends. 

The primary objective of our study was to use MRI to measure the refractive index distribution of the human lens in vivo, as a function of both age and state of accommodation. By making use of careful image processing and averaging procedures we have been able to demonstrate characteristic changes in the refractive index distribution of the crystalline lens with both accommodation and ageing. The human crystalline lens is characterized by a central plateau region of high refractive index with a marked decline in refractive index at the periphery that is well described by a power law function (equation 2) . Although the central refractive index does not change with accommodation or ageing, the peripheral decline in refractive index is more gradual in accommodated lenses and steeper in older lenses. The size of the central high refractive index region increases with age. The age-related changes in the refractive index distribution agree well with those reported in past studies, whereas the accommodative changes provide fresh insight into the optical changes in the lens during accommodation. It will be interesting to model the impact of these changes in the refractive index distribution with age and accommodation on the optical properties of the eye. 

 Supported by National Health and Medical Research Council Grant 290500.

 Submitted for publication November 9, 2007; revised February 12, 2008; accepted April 9, 2008.

 Disclosure: S. Kasthurirangan, None; E.L. Markwell, None; D.A. Atchison, None; J.M. Pope, None

 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.

 

Figure 1.

 

Schematic of the MRI setup based on a cartoon from the Web site http://nobelprize.org/. The subject lay supine and looked through the central hole in the eye coil at far and near targets reflected off a 45° mirror. Care was taken to align the near target with the far target, to maintain eye position throughout imaging. The subject’s head was stabilized with foam pads for comfort and to prevent head movements during data acquisition.

Figure 2.

 

Schematic representation of the analysis procedure. (A–D) MSE images obtained at TEs of 12, 24, 36, and 48 ms, respectively. Note the progressive decrease in intensity of lens pixels with increasing echo time. (E) Custom software was used to identify the lens pixels (shown in saturated white for the MSE image at 12 ms) with minimal user input. (F) Intensity of a central lens pixel, plotted against echo time. The data were fitted with a mono-exponential decay function to obtain R ₂ and calculate the refractive index for each pixel. (G) A composite refractive index map of all pixels contained within the lens. Note the brighter areas of higher refractive index at the center and darker areas of lower refractive index at the periphery. Noise in the refractive index data necessitated use of spatial averaging procedures.

Figure 3.

 

Contour plots of refractive index distribution obtained from transverse axial images in the young unaccommodated (A), young accommodated (B), and older group (C) of lenses. The raw data from lenses within each group were averaged to obtain these distributions. In general, the refractive index was high (≥1.40) over a central region and steeply declined to a lower refractive index (∼1.37) in the periphery.

Figure 4.

 

Average refractive index profiles from transverse axial images plotted against normalized axial distance (A), axial distance based on median axial thickness for each group (B), normalized equatorial distance (C), and equatorial distance based on median equatorial diameter for each group (D). Data are shown for young unaccommodated, young accommodated, and older lenses. Error bars, ±1SE. With increasing age, the refractive index distribution appeared to be uniform over a wider central region and fall more sharply at the periphery. With accommodation, the peripheral decline in refractive index appeared to be less abrupt.

Figure 5.

 

Average refractive index profiles from sagittal images plotted against normalized axial distance (A), axial distance based on median axial thickness for each group (B), normalized equatorial distance (C), and equatorial distance based on median equatorial diameter for each group (D). Data are shown for young unaccommodated, young accommodated, and older lenses. Error bars, ±1SE. The refractive index profiles and pattern of changes with age and accommodation were similar to the transverse axial images.

Table 1.

 

Average Overall Lens Size, Central Refractive Index (RI), and Size of the Central Plateau of High RI

Lens Group	n	Age (y)	Target Dist.	Central RI	Lens Size (mm)			Central Plateau Size (mm)
										Axis	Equator	Axis	Equator
Young unaccommodated	29	22.8 ± 3.1	6.1 m	1.4097 ± 0.0080	3.78 ± 0.22	9.12 ± 0.33	3.12 ± 0.27	7.94 ± 0.64
Young accommodated	26	22.8 ± 3.1	16.4 ± 1.8 cm	1.4075 ± 0.0092	4.05 ± 0.23*	8.77 ± 0.31*	3.27 ± 0.42	7.51 ± 0.87*
Old unaccommodated	29	64.3 ± 3.2	6.1 m	1.4084 ± 0.0074	4.75 ± 0.38*	9.39 ± 0.34*	3.95 ± 0.49*	8.50 ± 0.30*

 Data are the mean ± SD, obtained from transverse axial and sagittal images for each of the three lens groups. n, number of images analyzed in each case. See the Results section for calculation of the central plateau size.

*  Data that are significantly different from the young unaccommodated lens.

Figure 6.

 

Average lengths of central plateau of high refractive index along the axis (A) and equator (B) of the crystalline lens for the three groups of lenses. Data from transverse axial and sagittal images were averaged. Error bars, ±1SE. With increasing age, the central plateau increased significantly both along the axis and the equator of the crystalline lens. With accommodation, the central plateau did not change significantly along the axis, but decreased significantly along the equator of the crystalline lens. ***Statistically significantly different data (P < 0.05), relative to the young unaccommodated group.

Figure 7.

 

Power function fits to refractive index profiles from the center to the periphery of the three groups of lenses are shown for normalized distances along the lens axis (A) and equatorial diameter (B). Only data from the transverse axial images were used for this analysis. Different symbols and the associated lines represent young unaccommodated, young accommodated, and older lenses. For clarity, error bars (±1SE) are provided only for the young unaccommodated lenses. Error bars were comparable between the three lens groups. Good fits with an r ² of at least 0.95 were obtained; the equations for each fit are shown in the figures. The pattern of refractive index distribution was different between the three groups of lenses, as indicated by the value of the exponent (shape) parameter p (see also Table 2 ).

Table 2.

 

Parameters of Exponential Fit to the Refractive Index Profiles along Axial and Equatorial Directions of the Three Groups of Lenses

Lens Group	Parameters of Exponential Fit N (r) = C 0 + C p · r P
		Axis (c 0)	Equator (c 0)	Axis (c 0 + c p)	Equator (c 0 + c p)	Axis (p)	Equator (p)
Young unaccommodated	1.4095 ± 4e-4	1.4090 ± 3e-4	1.3785 ± 11e-4	1.3820 ± 10e-4	4.90 ± 0.35	6.30 ± 0.45
Young accommodated	1.4094 ± 3e-4	1.4087 ± 3e-4	1.3812 ± 9e-4	1.3811 ± 10e-4	4.04 ± 0.24, †	5.09 ± 0.28*
Old unaccommodated	1.4096 ± 3e-4	1.4107 ± 3e-4*	1.3786 ± 9e-4	1.3804 ± 8e-4	6.71 ± 0.43*	10.28 ± 0.81*

 Data are expressed as the mean ± standard error. c ₀, the predicted central refractive index; c ₀ + c _p the predicted refractive index at the lens edge; p, the shape parameter of the power function fits. The power function fits to accommodated, and older lenses were compared with young unaccommodated lenses using t-tests, and significant differences are indicated.

*  Significantly different from the young unaccommodated data.

†   P = 0.05 for test of difference from young unaccommodated data.

The authors thank The Prince Charles Hospital for access to their MRI facility.