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Abstract
We investigated changes in ciliary body ring diameter, lens dimensions and lens refractive index distributions with accommodation in young adults. A 3T clinical magnetic resonance imaging scanner imaged right eyes of 38 18-29 year old participants using a multiple spin echo sequence to determine accommodation-induced changes along lens axial and equatorial directions. Accommodation stimuli were approximately 1 D and 5 D. With accommodation, ciliary body ring diameter, and equatorial lens diameter decreased (–0.43 ± 0.31 mm and –0.30 ± 0.23 mm, respectively), and axial lens thickness increased ( + 0.34 ± 0.16 mm). Lens shape changes cause redistribution of the lens internal structure, leading to change in refractive index distribution profiles. With accommodation, in the axial direction refractive index profiles became flatter in the center and steeper near the periphery of the lens, while in the equatorial direction they became steeper in the center and flatter in the periphery. The results suggest that the anatomical accuracy of lens optical models can be improved by accounting for changes in the refractive index profile during accommodation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The human lens is asymmetric, with its anterior surface being flatter than the posterior surface [1]. During accommodation the lens changes its shape due to contraction of the ciliary muscle, which reduces zonular and capsular tension. It adopts a more rounded shape, with both surfaces (but particularly the anterior surface), becoming more curved. The lens reduces in diameter, and becomes thicker axially accompanied by a similar reduction in anterior chamber depth and a small reduction in vitreous depth [2, 3]. Strenk et al. reported increase in cross-sectional area of the anterior portion of the lens with accommodation [4], but others had reported small decreases in cross-sectional area with accommodation [5, 6]. Small increases [5] or no changes [6, 7] in volume with accommodation have been reported. Accompanying the changes in the external geometry of the lens is a change in the gradient refractive index distribution (GRIN) inside the lens [8]. Gullstrand referred to this as the intracapsular mechanism of accommodation [9].
The distribution of the GRIN in the accommodating lens has remained relatively unexplored. Kasthurirangan et al. used 2-dimensional magnetic resonance imaging (MRI) to model the axial and equatorial GRIN profiles of the human lens by power functions, but did not take into account the asymmetry of the lens [8]. MRI offers the advantage over other imaging techniques, such as Scheimpflug photography, ultrasound biomicroscopy and anterior segment optical coherence tomography, that images are free from optical distortions [10].
In this study we used 3-D MRI to investigate accommodation-induced changes in ciliary body ring diameter, lens dimensions and refractive index distribution of the in-vivo lens. We took into account the asymmetry of the lens shape, while imaging with a larger number of people, better resolution and signal to noise ratio than Kasthurirangan et al. [8].
2. Methods
2.1 Participants
Right eyes of 38 healthy young participants (18 – 29 years, 22.7 ± 3.0 years) with spherical equivalent refractions ‒1. 7 ± 2.4 D (range + 1.0 to −8.0 D) underwent MRI scans. All had < 1.5 D astigmatism. These people were part of a larger group of 60 participants [11]; thirteen participants could not be included because accommodation images were not acquired, and for nine participants some images had significant motion artifacts (three without, and six with accommodation).
The research adhered to the tenets of the Declaration of Helsinki. The experimental protocol was approved by the Queensland University of Technology and University of Queensland human ethics review boards. All participants were required to give written consent and to complete a standard questionnaire in order to exclude participants with heart pacemakers, aneurysm clips or other metallic implants (whose function might be affected by the magnetic field of the MRI system and cause local radio-frequency heating or image distortion), and to exclude those who might have metal fragments in the eye or head.
2.2 MRI – basic procedures
MRI was used to measure the lens refractive index distribution and lens dimensions using a 3.0 Tesla (Siemens Trio) clinical scanner in the Centre for Advanced Imaging at the University of Queensland, Australia.
During the MRI procedure, participants were positioned supine on the instrument table and heads were stabilized with padding. Participants were asked to focus (via an adjustable mirror mounted at 45○ to vertical) on a white Maltese cross fixation target on a black background that was projected onto a translucent screen at the end of the magnet bore at approximately 0.93 m from the eye. A standard 4.0 cm (Siemens) circular receive-only surface coil was taped over the examined eye so that the target was visible through the hole in the center of the coil, as illustrated in Fig. 1 of reference 7). A thin spacer made from self-adhesive felt, glued to the surface of the coil body was used to minimize skin contact with the coil, in order to protect against localized radio-frequency heating. The non-examined eye was occluded using an eye patch. Participants were instructed to avoid head movement, focus on the fixation target and minimize blinking during data acquisition. They were advised to blink and/or close their eyes between data acquisitions to avoid eye dryness. Where refractions were outside the range ± 0.50 D, a lens was attached to the surface coil on the opposite side from the participant’s eye so that the target became clear and imaging was performed. The distance of lenses from the eye was estimated to be 25 mm. The power of the lens was determined from the distance refraction, assumed to apply at 12 mm vertex distance. To stimulate approximately 5 D accommodation a more negative powered lens was put in place based on adding a −5 D power to the distance refraction at the 12 mm vertex distance, the participant was asked once again to focus on the target and the imaging protocols were repeated. The mean change in accommodation stimulus was approximately 4.5 D.
Fig. 1 Dimensions for refractive index profiles. The red dot is the axial midpoint and the blue dot is the midpoint of the equatorial diameter.
2.3 MRI – imaging protocols
Following localizer scans to locate the position of the eye in the center of the field of view (FOV), multi-slice fast spin echo (FSE) images (64 mm FOV; 256 × 256 matrix; 2 mm slice thickness (no gaps); TR = 4000 ms; TE = 16 ms; echo train length 12, imaging time 128 s) were obtained in both axial and sagittal planes, giving in-plane resolution of 0.25 mm. A single slice multiple spin echo (MSE) sequence (64 mm FOV; 256 × 256 matrix; 2 mm slice thickness; TR = 2000 ms; 4 echoes: TE = 12.5/25/37.5/50 ms; imaging time 4.5 mins) was used to acquire data both for measuring lens dimensions and for calculating the refractive index distribution through the lens [8, 12]. The FSE images were used only to ensure that the single slice was placed through the symmetry axis of the lens, using the center slice from the sagittal FSE image to identify this axis.
In MRI of the eye lens, the proton transverse or spin-spin relaxation rate (R2 = 1/ T2) is proportional to the concentration of macro-molecules (mainly crystallin proteins) in the lens, which in turn determines the refractive index [12]. A MSE sequence was used to map the R2-distribution through the lens, by fitting the decay of pixel signal intensity S with echo time TE for each image voxel in the lens to the single exponential decay equation
where S0 is the signal intensity extrapolated to TE = 0 (the signal corresponding to the equilibrium or steady state magnetization). The R2 map can be transformed to a refractive index map at 589 nm equivalent wavelength of light, using the calibration equation [8, 12]where n is refractive index.A normalized refractive index distribution can be defined along the axis and equator of the lens according to
where r is the normalized distance from the lens center (r = 0 at the center and r = 1 at the periphery), C0 is the index at the lens center, Cp is the difference in refractive index between the lens center and periphery, and the exponent p characterizes the gradient refractive index rate of change.2.4 MRI – data processing
Image analysis was performed using custom built software written in Matlab (Mathworks, Natick, MA, version R2011). Full details of the image processing have been described elsewhere [13].
Due to motion and blinking in some participants, MSE images and hence refractive index maps suffered from artefacts. In order to improve signal to noise (S/N) and make comparisons between different subject groups, lens refractive index profiles were computed using the line of pixels closest to the lens axis or equatorial diameter, and also by averaging over a 3-pixel-wide band centered on these axes. Further details of this procedure together with typical examples of the refractive index profiles obtained for individual lenses can be found in Fig. 2 of our previous publication [13]. As MSE images had in-plane resolution of 0.25 mm and slice thickness of 2 mm, this gave an effective voxel size of 0.375 mm3 (3 × 0.25 × 0.25 × 2).
Fig. 2 Characteristic MSE images of a 21 year old male (a) without accommodation stimulus, and (b) with 5.0 D accommodation stimulus. Upon accommodation, ciliary body ring diameter and lens equatorial diameter decreased, and axial thickness increased.
The first axial MSE image (TE = 12.5 ms) with the best S/N and contrast was selected to determine the lens axial thickness, equatorial diameter and the ciliary body ring diameter manually using ImageJ software (developed at National Institutes of Health, available in the public domain at http://rsbweb.nih.gov/ij/index.html). The axial thickness was measured along the optical axis between the anterior and posterior edges of the lens and the equatorial diameter was measured along the equatorial diameter line between nasal and temporal edges of the lens. An anterior axial thickness was measured from the anterior edge of the lens to the center of the equatorial diameter line. Similarly, a posterior axial thickness was measured from the posterior edge to the center of the equatorial diameter line (Fig. 1). Ciliary body ring diameter was measured as the distance between innermost ciliary body tips. As the slice passes through the center of the lens in the MSE image, it produces an error in measurement of ciliary body ring diameter [14]. Therefore, a correction equation for the ciliary body ring diameter was employed:
where Dc is the corrected ciliary muscle diameter, Dm is the measured ciliary body ring diameter and S is the slice thickness.To analyze refractive index data, lens dimensions were normalized to extend from 0 to + 1 for each participant. For the equatorial axis, the normalized dimension extended from −1 to + 1 and the data were folded about the optical axis to give a normalized dimension 0 to 1. A similar approach was used for the axial dimension, with the midpoint between anterior and posterior points as the reference point (red dot in Fig. 1). In addition, separate analyzes were performed for the portions anterior and posterior to the midpoint of the equatorial diameter (blue dot in Fig. 1). Group data of each dimension were fitted according to Eq. (3).
3. Results
Table 1 shows lens and ciliary ring dimensions, and Fig. 2 shows images of a typical participant without and with accommodation. All dimensions changed significantly upon accommodation. Ciliary body ring diameter and equatorial lens diameter decreased by 0.43 ± 0.31 mm and 0.30 ± 0.23 mm, respectively. Total axial lens thickness and its anterior and posterior components increased by + 0.34 ± 0.16 mm, 0.25 ± 0.25 mm and + 0.10 ± 0.18 mm, respectively. As a measure of lens shape, the ratio of the total axial lens thickness to equatorial diameter without and with accommodation was calculated (Table 1). This ratio increased with accommodation by a mean of 0.05 (13%).
Table 1. Lens and ciliary ring dimensions without and with accommodation
The combined normalized refractive index profile data for different lens dimensions and each accommodation condition were fitted by the power Eq. (3) using Sigmaplot software. Table 2 shows the means and standard errors of the refractive index co-efficients for the anterior, posterior and total axial thicknesses, and Table 3 shows the means and standard errors of the refractive index co-efficients for the equatorial diameter. These parameters and the number of participants (38) were used to perform unpaired t-tests comparing unaccommodated and accommodated conditions using GraphPad (https://www.graphpad.com/quickcalcs/ttest1.cfm).
Table 2. Co-efficients of fit to normalized axial refractive index data. Numbers in brackets are standard errors.
Table 3. Co-efficients of fit to normalized equatorial refractive index data. Numbers in brackets are standard errors.
With accommodation, p values increased for both anterior (p = 2.14 vs p = 3.31, P = 0.03 and posterior axial segments (p = 2.79 vs p = 4.73, P = 0.04), while the equatorial p value decreased (p = 4.34 vs p = 3.66, P = 0.04). There were significant differences in Co and Cp for the total axial thickness with accommodation, and Co became slightly larger along the posterior axial direction (P = 0.04). Co and Cp changed significantly along the equatorial direction (P < 0.001 and 0.04, respectively), with Co becoming larger and Cp becoming smaller with accommodation.
Figure 3 shows the refractive index profiles of the lens anterior and posterior axial segments, plotted against normalized anterior and posterior axial distances respectively, both without and with accommodation. With accommodation, the axial refractive index profiles show increased steepness at the periphery.
Fig. 3 Normalized refractive index profiles for axial thickness with fits to Eq. (3): (a) anterior axial without accommodation; (b) anterior axial with accommodation; (c) posterior axial without accommodation; (d) posterior axial with accommodation. The origin for the fits corresponds to the mid-point of the equatorial plane (the blue dot in Fig. 1). The fits are determined by combining all data, but the means and standard errors are determined from refractive index data at each normalized distance. The dashed lines are the 95% confidence limits of the fits.
Figure 4 shows the refractive index profiles of the lens for the total axial dimension and for the equatorial direction for normalized equatorial distances, both without and with accommodation. With accommodation, the equatorial refractive index profiles become less steep at the periphery.
Fig. 4 Normalized refractive index profiles for the total axial and equatorial distances with fits to Eq. (3): (a), (c) without accommodation, and (b), (d) with accommodation. The origin for the axial profiles is the mid-point of the axis (red dot in Fig. 1) and that for the equatorial profiles is the mid-point of the equatorial plane (blue dot in Fig. 1). The fits are determined by combining all data and folding about the respective center points, but the means and standard errors are determined from refractive index data at each normalized distance. The dashed lines are the 95% confidence limits of the fits.
Figure 5 shows the refractive index profiles of the axial (anterior and posterior) and equatorial segments plotted against axial (anterior and posterior) and equatorial distances that are scaled by the mean axial (anterior and posterior) lens thickness and half the mean equatorial diameter, respectively.
Fig. 5 Refractive index profiles, for distances (in mm) from the lens center, without and with accommodation: (a) anterior axial; (b) posterior axial; (c) equatorial. The fits are scaled from those in Figs. 3 and 4 by the mean thicknesses (axial and posterior axial) and half the mean diameter (equatorial) as given in Table 1. The fits are determined by combining all data, but the means and standard error are determined from refractive index data at each normalized distance. The dashed lines are the 95% confidence limits of the fits.
4. Discussion
In agreement with previous studies, we report that, with accommodation, lens thickness increases [2, 5–7, 10, 14–20], while lens equatorial diameter [5–7, 10, 14–17] and ciliary body ring diameter decrease [14–17, 21]. Table 4 is a summary of changes in lens thickness, lens diameter and ciliary ring diameter for our study and for previous in vivo studies using various methodologies, together with a recent in-vitro study [22]. These changes are given per diopter of accommodation, with some studies using the accommodation stimulus as the measure of accommodation, while others used estimates of accommodation response. It would be expected that the latter would give the larger, and more reasonable estimates, as accommodation response is less than stimulus, particularly as the ages of participants increase. For lens thickness, the in-vivo studies ranged from means of + 0.04 to + 0.08 mm/D with our study near the top ( + 0.08 ± 0.04 mm/D); despite using the stimulus method, this may be in part because all participants were young adults. For lens diameter, the nine in-vivo studies ranged from −0.05 to −0.14 mm/D with the majority of studies including ours having values of −0.07 to −0.08 mm/D. All but one in vivo study used MRI, with the Martinez-Enriquez et al. [6] study giving by far the greatest results; this might be a consequence of the method involving considerable shape modelling when being unable to image much of the lens through the iris. For ciliary ring diameter, the studies gave results in the range −0.07 to −0.11 mm/D, with our study continuing the finding in four out of five of the previous studies that reduction in ciliary ring diameter with accommodation was greater than the corresponding reduction in lens diameter.
Table 4. Change in ocular parameters with accommodation from various in-vivo studies
For the in-vitro study involving lens stretching and laser raytracing [22], the rate of change for lens thickness at + 0.07 mm/D was similar to in-vivo studies, the rate for lens diameter at −0.05 mm/D was at the low end of in-vivo studies, and ciliary ring diameter was much higher than in-vivo studies at 0.16 mm/D. As changes in lens power are about 30% greater than accommodation measured at the front of the eye [23], correction to make them more comparable with the in vivo studies using accommodation response would give respective rates of approximately 0.06, 0.08 and 0.19 mm/D.
An important finding of our study is the change in lens GRIN profiles with accommodation, with the anterior and posterior axial refractive index profiles becoming steeper at the periphery (Fig. 3) and the equatorial refractive index profiles becoming flatter at the periphery (Fig. 4). This is reflected in changes in p values for the corresponding power equation fits, with increases from 2.14 to 3.31 for the anterior axis and from 2.79 to 4.73 for the posterior axis (Table 2) and decrease for the equatorial axis from 4.34 to 3.66 (Table 3). The total axial profile does not show an obvious change in steepness with accommodation towards the periphery (Fig. 4). While none of the profiles are ideal for considering spatial variation in index, we think that taking into account the lens axial asymmetry is preferable to ignoring it as in the total axial profile approach in which center points of the axial profiles with/without accommodation correspond to considerably different regions in the lens.
Interestingly, the accommodated results have less scatter than the unaccommodated results relative to fitted curves (Fig. 3). We have no explanation as to why this occurred.
Like us Kasthurirangan et al. [8] found similar changes in the decline in refractive index from center to the periphery along the equatorial diameter (p value changing from 6.30 ± 0.45 to 5.09 ± 0.28), but unlike us they found the axial refractive profiles become less steep at the periphery (4.90 ± 0.35 to 4.04 ± 0.24). The earlier study, which was carried out on an MRI system operating at 1.5T, used the total axial profile approach only and had poorer S/N and lower spatial resolution than the 3T data used in this study. Differences between the studies may also be due to a higher accommodation stimulus in the earlier study (between 6.9 and 4.8 D compared with a mean of 4.5 D in this study).
The current study has limitations. Firstly, accommodative response magnitude was not measured; about half the studies reported in Table 4 have this limitation, while the rest inferred response from refraction instruments at similar stimulus levels. Secondly as pointed out previously [8] “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.” With the growing availability of clinical MRI systems operating at higher magnetic fields of 7T and above, it should become possible to obtain high resolution refractive index profiles with good signal-to-noise ratio for individual lenses, similar to those that we have obtained ex-vivo [24], particularly with the advent of dedicated receiver coils for eye imaging at these fields.
5. Conclusion
We used magnetic resonance imaging to study ciliary body, lens dimensions and lens refractive index distributions in healthy young participants. With accommodation, ciliary body ring diameter and lens equatorial diameter decreased and lens thickness increased, with associated changes in refractive index profiles along axial and equatorial directions. This finding suggests that anatomically correct optical models of the crystalline lens would benefit from the changes in refractive index distribution that occur with accommodation e.g [25]. The geometrical parameters in Table 1 and power law fit parameters in Tables 2 and 3 may form a starting point for modeling such changes.
Acknowledgments
We thank the Centre for Advanced Imaging, University of Queensland, and in particular its radiographers Aiman Al Najjar and Anita Burns. This work was supported by Johnson & Johnson Vision.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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