Constant Volume of the Human Lens and Decrease in Surface Area of the Capsular Bag during Accommodation: An MRI and Scheimpflug Study

Abstract

purpose. A change in surface area of the capsular bag and a change in volume of the lens can indicate whether a change in the shape of the lens during accommodation is due to the compressibility or the elasticity of the lens material.

methods. 3D magnetic resonance imaging (MRI) was used to image the complete shape of the lens in a group of five healthy subjects between 18 and 35 years of age. A parametric representation of the cross-sectional shape was fitted to the edges of the lens, which were determined with a Canny edge filter. Based on a partition of the lens into eight parts, the parametric shape makes it possible to calculate the mean cross-sectional area, the volume, and the surface area as a function of accommodation. Corrected Scheimpflug imaging was used to validate the results obtained with MRI.

results. No significant difference in central anterior and posterior radius of curvature and thickness was found between the MRI and Scheimpflug measurements. In accordance with the Helmholtz accommodation theory, a decrease in the anterior and posterior radius of curvature and equatorial diameter and an increase in lens thickness occurred with accommodation. During accommodation, the mean cross-sectional area increased and the surface area decreased. However, no significant change in lens volume was found.

conclusions. The preservation of lens volume implies that the internal human lens material can be assumed to be incompressible and is undergoing elastic deformation. Furthermore, the change in surface area indicates that the capsular bag also undergoes elastic deformation.

During accommodation, the thickness of the lens increases and the radius of curvature of the anterior and posterior central area decreases, resulting in an increase in optical power. According to the Helmholtz accommodation theory, ¹ this deformation is caused by the ciliary muscle release of zonular tension. It is not exactly known whether the deformation of the lens is due to the elasticity or the compressibility of lens material. 

A change in surface area (SA) of the capsular bag could indicate that the elasticity of the capsular bag plays an important role in accommodation. On the other hand, a change in lens volume (VOL) could indicate that decompression of the internal lens material is responsible for the accommodative changes. The objective of the present study was to determine the VOL of the lens and SA of the capsular bag and to investigate whether there is a change in these quantities with accommodation. Therefore, the 3D geometry of the human lens was measured in vivo in a group of five healthy subjects. Furthermore, knowledge about human lens VOL and strain in the capsular bag could be used for refilling the capsular bag with a viscoelastic material to restore accommodation. ²  

Different methods have been applied to determine in vitro the VOL as a function of age. ^{3 4 5} In vivo, Strenk, et al. ⁶ used 2D magnetic resonance imaging (MRI) to measure the cross-sectional lens geometry. In one axial MRI slice the changes in thickness and equatorial diameter of the lens as a function of two different accommodation stimuli were measured in 25 healthy subjects. Furthermore, in another study, Strenk et al. ⁷ observed an increase in the cross-sectional area (CSA) of 25 human lenses, and they suggested that the lens may be compressed in the unaccommodated state. However, a change in the CSA does not necessarily imply a change in lens VOL. ⁸ In vitro, Gerometta et al. ⁹ placed bovine lenses in a stretching device, and based on lateral photographs of the CSA, the center of mass and VOL were determined during stretching. With accommodation, they measured an increase of 8% in bovine lens VOL. Based on data from the literature, they simulated a human lens during accommodation and expected that the human lens would undergo an increase of approximately 3% in lens VOL. It was suggested that compression of the lens material could play an important role in accommodation. However, the change in VOL of the human lens has not yet been measured in vivo as a function of accommodation. 

In vitro, Fisher ¹⁰ developed a method with which to estimate the energy released by the anterior part of the lens capsule during accommodation. He concluded that the elasticity of the surface of the capsule plays a major role in the loss of accommodation. In studies conducted in vitro, Krag et al. ¹¹ Krag and Andreassen, ¹² and Heistand et al. ¹³ also determined the mechanical properties of the human capsule, but no in vivo measurement of strain during accommodation has ever been performed. 

Chien et al. ¹⁴ used various analytical functions to describe the cross-sectional shape of the human crystalline lens. Using polar coordinates, they found that a parameterization with cosines appeared to result in the best fit for the surface of the human lens. Kasprzak ¹⁵ proposed an analytical function that describes the complete axisymmetric lens profile in an accommodated and a disaccommodated state. However, both descriptions contain many parameters with no physical meaning that have to be fit simultaneously. To compare Scheimpflug measurements of the central part of the lens with MRI measurements of the central and peripheral part of the lens, it is necessary to have a parametric geometry that can describe both parts separately. 

In the present study, 3D MRI was used to determine the complete shape of the lens as a function of accommodation in five healthy subjects. The shape of the lens was described by cross-sectional geometry, which contains five physical parameters. From this parametric geometry, the CSA, the SA of the capsular bag, and VOL of the lens were estimated. The changes in VOL and strain of the capsular bag were determined during accommodation. Finally, Scheimpflug imaging was used to validate the MRI results. 

Method

Subjects

The sample population consisted of five healthy subjects (two men, three women), between 18 and 35 years of age, who had no ocular abnormalities, diabetes mellitus, cataract, or previous ocular surgery. The study protocol was approved by the Medical Ethics Committee of the Vrije Universiteit (VU) Medical Center (Amsterdam, The Netherlands). The measurements were performed with the understanding and written consent of each subject, according to the tenets of the Declaration of Helsinki. 

System Setup

MRI was performed on a 1.5-T whole-body scanner (Magnetom Sonata; Siemens, Erlangen, Germany), using a small ring-shaped receiver coil (diameter, 3 cm) positioned close to the right eye, and the body coil as RF transmitter. 3D images of the lens were obtained with a T₁-weighted 3D MPRAGE (magnetization prepared rapid acquisition gradient echo) sequence, with repetition time (TR) 2300 ms, echo time (TE) 5.7 ms, inversion time TI 950 ms, flip angle 8°, and bandwidth 160 Hz/pixel. The small coverage of the receiver coil produced a rectangular field-of-view in the transverse plane of 75 mm (anterior–posterior) by 120 mm (left–right). With a 240 × 384 matrix, this resulted in an area of 0.31 × 0.31 mm pixels, which was interpolated to 0.15 × 0.15 mm during reconstruction. The 3D slab of 128 mm in head–foot direction consisted of 160 transverse slices of 0.8 mm. The time needed to acquire one 3D data set was 9 minutes 14 seconds. 

Subsequently, images of the anterior segment of the eye were obtained with a Scheimpflug camera (SL-45; Topcon, Tokyo, Japan) the film of which was replaced by a CCD camera (St-9XE; SBIG Astronomical Instruments, Santa Barbara, CA) with a dynamic range of 16 bits of gray values (512 × 512 pixels, pixel size 20 × 20 μm, magnification, 1×). Axial length was measured with an ocular biometer (IOL Master; Carl Zeiss Meditec, Oberkochen, Germany), which is based on partial-coherence interferometry, ¹⁶ and the ocular refractive error was measured with an aberrometer (IRX3; Imagine Eyes Optics, Orsay, France). 

Measurements

Accommodation Amplitude.

First, the right eye was covered, and the subject was asked to focus with the left eye on a black letter X projected on a white background, 2 m from the subject’s head. A lens was placed in a plastic trial frame 19 mm in front of the left eye to induce the unaccommodated state of the eye. Then, to induce accommodation, we increased the power of the lens in front of the left eye in steps of −1 D until the subject indicated that it was no longer possible to obtain a sharp image of the target. The preceding accommodated state was regarded as the maximum state of accommodation. 

Magnetic Resonance Imaging.

The subject was placed in a supine position in the MRI scanner, with head fixed, looking at a screen at the rear end of the scanner (2 m from the subjects head) via a mirror tilted at 45°. The targets projected onto the screen consisted of a black letter X and a black plus sign on a white background, which alternated every 2 seconds. The subject was asked to focus with the left eye on the center of the target during the MR imaging, while the right eye with the RF coil was covered. After the acquisition in the unaccommodated state, the lens positioned in the plastic trial frame in front of the left eye was changed to induce accommodation. A 3D MRI acquisition of the right eye was obtained in the unaccommodated and the maximum accommodated states. 

Scheimpflug Imaging.

The Scheimpflug image of the lens was captured by dilating the pupil of the right eye of each subject with two drops of 5% phenylephrine HCl. The same two accommodative states as for the MRI examination were again created, using a trial frame and lenses in front of the left eye. The subject was instructed to fixate on a fixation light in the Scheimpflug camera, whereas the slit of the camera was aligned along the optical axis of the right eye. The subject was then asked to fixate with the left eye on a Maltese star, the position of which could be adjusted horizontally and vertically by remote control until the subject reported that the fixation light of the Scheimpflug camera was superimposed on the center of the Maltese star. At this point, the internal fixation light of the camera was turned off, and the subject was asked to focus on the Maltese star while three images were obtained per accommodative state. 

Aberrometry.

To determine the accommodative response, we measured the refractive error of the right eye of each subject with the aberrometer. The same accommodative states were created as for the MRI and Scheimpflug measurements, with different lenses used in front of the left eye and a Maltese star as the fixation target. After alignment of the internal fixation light in the aberrometer with the Maltese star, the internal fixation light was turned off and the refractive error of the right eye was measured. Using a fixed 3-mm pupil, we transferred the effective refractive error in both accommodative states to accommodative response at the spectacle plane. 

Postprocessing

The shape of the lens was described as a parametric curve with a minimal set of parameters that had a physical meaning. It was assumed that the curve describing the cross-sectional shape of the lens and its derivative are continuous and that the derivative in axial direction is 0 at the equator and the radial derivative is 0 at the poles. Figure 1illustrates the geometric model that consists of anterior and posterior parabolas representing the central area of the lens  

\[x{=}\sqrt{\frac{2(y{-}y_{0\mathrm{ant}})}{c_{\mathrm{ant}}}}\ if\ x{\leq}2.5\ \mathrm{mm\ and}\ y{\geq}0\ \mathrm{mm\ with}\ c_{\mathrm{ant}}{=}\frac{1}{R_{\mathrm{ant}}}\]

 

\[x{=}\sqrt{\frac{2(y{-}y_{0\mathrm{post}})}{c_{\mathrm{post}}}}\ if\ x{\leq}2.0\ \mathrm{mm\ and}\ y{\leq}0\ \mathrm{mm\ with}\ c_{\mathrm{post}}{=}\frac{1}{R_{\mathrm{post}}}\]

with R as the central radius of curvature and (0, y ₀) as the apex position (all units in millimeters). 

With Scheimpflug imaging, the posterior central area of the lens is less visible than the anterior central area. Therefore, it is possible to fit the anterior parabola at an aperture of 5 mm and the posterior parabola at an aperture of only 4 mm. 

The ratio between anterior and posterior thicknesses, with respect to the equatorial plane and the total thickness (TT), was defined as  

\[\mathrm{ratio}{=}\left|\frac{y_{0\mathrm{ant}}}{y_{0\mathrm{post}}}\right|\]

 

\[TT{=}{\vert}y_{0\mathrm{ant}}{\vert}{+}{\vert}y_{0\mathrm{post}}{\vert}.\]

The two curves in the periphery that closed the lens were formed by conics, which can be described by the following formulas  

\[x{=}R_{\mathrm{eq}}{-}\frac{c_{\mathrm{ant}{-}\mathrm{eq}}y^{2}}{1{+}\sqrt{1{-}k_{\mathrm{ant}{-}\mathrm{eq}}c_{\mathrm{ant}{-}\mathrm{eq}}y^{2}}}\ if\ x{\geq}2.5\ \mathrm{mm\ and}\ y{\geq}0\ \mathrm{mm}\]

 

\[x{=}R_{\mathrm{eq}}{-}\frac{c_{\mathrm{post}{-}\mathrm{eq}}y^{2}}{1{+}\sqrt{1{-}k_{\mathrm{post}{-}\mathrm{eq}}c_{\mathrm{post}{-}\mathrm{eq}}y^{2}}}\ if\ x{\geq}2.0\ \mathrm{mm\ and}\ y{\leq}0\ \mathrm{mm}\]

with R _eq as the equatorial radius, c as the curvature, and k as the asphericity of the conic. 

To guarantee a continuous function, as well as a continuous derivative, we constrained the four parameters of the conics to the following expressions:  

\[c_{\mathrm{ant}{-}\mathrm{eq}}{=}\frac{R_{\mathrm{eq}}{-}x_{1}}{y_{1}{[}c_{\mathrm{ant}}(R_{\mathrm{eq}}{-}x_{1})x_{1}{+}y_{1}{]}}\]

 

\[k_{\mathrm{ant}{-}\mathrm{eq}}{=}\frac{y_{1}{[}2c_{\mathrm{ant}}(R_{\mathrm{eq}}{-}x_{1})x_{1}{+}y_{1}{]}}{(R_{\mathrm{eq}}{-}x_{1})^{2}}\]

 

\[c_{\mathrm{post}{-}\mathrm{eq}}{=}\frac{R_{\mathrm{eq}}{-}x_{2}}{y_{2}{[}c_{\mathrm{post}}(R_{\mathrm{eq}}{-}x_{2})x_{2}{+}y_{2}{]}}\]

 

\[k_{\mathrm{post}{-}\mathrm{eq}}{=}\frac{y_{2}{[}2c_{\mathrm{post}}(R_{\mathrm{eq}}{-}x_{2})x_{2}{+}y_{2}{]}}{(R_{\mathrm{eq}}{-}x_{2})^{2}}\]

with P1 (x ₁ = 2.5 mm, y ₁) and P2 (x ₂ = 2.0 mm, y ₂) as the position of the interception points between the anterior and posterior central parabolic and the conic curves in the periphery. 

CSA, SA, and VOL Calculation.

With f(y) as the axisymmetric cross-sectional curve as a function of the axial position (y) with respect to the axis of rotation, it is possible to compute the CSA, the SA of the capsular bag, and the VOL of the lens ¹⁷  

\[\mathrm{CSA}{=}2{{\int}_{y_{0\mathrm{post}}}^{y_{0\mathrm{ant}}}}f(y)dy\]

 

\[\mathrm{SA}{=}2{\pi}{{\int}_{y_{0\mathrm{post}}}^{y_{0\mathrm{ant}}}}f(y)\sqrt{f{^\prime}(y)^{2}}{+}1dy\]

 

\[\mathrm{VOL}{=}{\pi}{{\int}_{y_{0\mathrm{post}}}^{y_{0\mathrm{ant}}}}f(y)^{2}dy.\]

The integrals in equations 11 and 13were computed analytically, but the integral in equation 12had to be approximated numerically. 

Step I: Parameter Estimation from MR Images Assuming Axisymmetry.

The MR images were linearly interpolated to a spatial resolution of 0.1 × 0.1 × 0.1 mm, to determine the edge of the lens with subpixel accuracy. To determine the lens edges, a Canny edge filter ¹⁸ with automatic thresholding was applied to the interpolated MRI slices every 0.5 mm in the three principal directions. In every Canny edge–filtered slice, chains of edge points were selected manually by mouse to obtain the coordinates of the lens edge. Subsequently, these coordinates were translated (Δx, Δy, Δz), rotated (Δα, Δβ), and transformed to spherical coordinates. Under the assumption of an axisymmetric lens, the cross-sectional shape is independent of the circular direction. Therefore, all coordinate points were mapped to one cross-sectional plane (x, y) as can be seen in Figure 2 . 

Nonlinear least-squares curve-fitting with the reflective Newton method (available in the MatLab Optimization toolbox; The Mathworks Inc., Natick, MA), was performed to estimate the orientation (Δx, Δy, Δz, Δα, and Δβ) and shape parameters of the lens (R _{ant, R post} , ratio, TT, and R _eq). The orientation and geometry in which the lens showed most axisymmetry was determined. 

Step II: Parameter Estimation from MR Images Taking into Account Lens Nonaxisymmetry.

Because the lens is not completely axisymmetric, a better description of the geometry could perhaps be obtained by dividing the lens into eight parts (Fig. 3) . The choice of eight parts was a tradeoff between the number of data points per part and asymmetry. To obtain an accurate estimate of the SA and the VOL of the lens, the cross-sectional geometry, as proposed in Figure 1 , was fitted to each of the eight parts. The CSA, the SA, and the VOL were calculated for each part, and the mean of the CSAs of all parts was calculated for each subject. Finally, the SA and the VOL of the parts were summed to obtain an estimate of the total SA and VOL in each accommodative state. 

Step III: Parameter Estimation from Scheimpflug Images.

The inclined position of the CCD camera, according to the Scheimpflug principle, causes geometric distortion (type I). The light rays that form the image of the lens are also refracted by the cornea and the anterior side of the lens, causing refractive distortion (type II). The correction for both types of distortion was performed with custom-developed software written in C++. ¹⁹ The index of refraction of the lens is needed to determine the path of the light rays that originate from inside the lens and are refracted on the anterior lens surface. An equivalent index of refraction of the lens was estimated, using additional information on axial length and refractive error. After correction, the anterior and posterior central parabolics and total thickness were fitted at an aperture of 4 and 5 mm, respectively, with the Levenberg-Marquardt method. Because of the 2D Scheimpflug imaging technique, it has to be assumed that the lens is axisymmetric. The position of the axis of symmetry of the cross-sectional geometry inside the Scheimpflug object plane was also estimated. 

Figure 4summarizes the scheme used to estimate the geometry of the lens. A Bland-Altman plot was constructed to compare the central parameters (R _ant, R _post, and TT) obtained from MRI and Scheimpflug measurements to validate both techniques. The nonparametric Wilcoxon signed rank test was used to investigate whether there was a significant difference between the measurements in the unaccommodated and accommodated state, where P < 0.05 was considered to be statistically significant. 

Results

An example of two cross-sectional slices of the 3D MRI acquisition in unaccommodated and fully accommodated state are shown in Figure 5 . Although the subjects had to fixate on the target and were requested to stay immobile for nearly 10 minutes, no substantial artifacts due to motion were observed. The MR images showed high contrast between lens and vitreous, as well as aqueous humor, as can be seen in Figure 5and Movie 1 . 

Table 1shows the refractive error in the disaccommodated state and the accommodative amplitude of the subjects, measured with aberrometry. 

The central anterior and posterior radius of curvature and the lens thickness were measured with MRI and Scheimpflug imaging. Figures 6a 6b and 6cshow, respectively, the anterior and the posterior radius and thickness of the lens of the subjects as a function of accommodation (in diopters at the spectacle plane). The mean decrease in anterior and posterior radius of curvature and the mean increase in lens thickness per diopter accommodation are presented in Table 2 . The values obtained by Dubbelman et al. ^{20 21 22} and Jones et al. ²³ were based on a 29-year-old subject, and the results reported by Strenk et al. ⁶ were derived by applying linear regression to the reported data of subjects under 35 years of age. 

The ratio between the anterior and posterior thicknesses, with respect to the equatorial plane and the equatorial radius, were only obtained with MRI. Figures 7a and 7bshow the ratio between the anterior and posterior thicknesses and the equatorial diameter as a function of accommodation. This ratio varied slightly with accommodation for different subjects, the mean ratio (±SD) at 0 D accommodation was 0.718 ± 0.03 and at maximum accommodation was 0.744 ± 0.02. 

Based on eight lens parts, the mean CSA, SA, and VOL in the group of healthy subjects was determined. Figures 8a 8b and 8cshow the mean CSA, SA, and VOL of the lens as a function of accommodation. 

Figure 9shows the equatorial radius of the eight parts for each subject, obtained in steps I and II. The nonrotational symmetric shape of the lens results in different values per part in each subject. The value obtained in step I can therefore be under- or overestimated, depending on the nonrotational symmetric shape. 

The mean CSA increased with accommodation from 25.9 ± 0.2 to 27.1 ± 0.3 mm², with an average of 0.2 ± 0.1 mm²/D, which is significant according to the Wilcoxon signed rank test (P = 0.04). The mean SA of the capsular bag decreased significantly (P = 0.04) with accommodation from 175.9 ± 2.8 to 167.5 ± 2.9 mm², which is a difference of 8.4 mm². The mean decrease in SA per diopter accommodation was −1.4 ± 0.2 mm²/D. The decrease in SA is equivalent to a mean strain of 5.0% (the change in SA divided by the SA at maximum accommodation). The mean lens VOL was 160.1 ± 2.5 mm³ in the unaccommodated state and 160.2 ± 2.7 mm³ in the accommodated state, which does not represent a significant difference according to the Wilcoxon signed rank test (P = 0.9). The 95% confidence interval of the difference in VOL between the measurements in accommodated and unaccommodated state was −1.8 to +1.5 mm³, corresponding to ±1%. 

A typical estimate of the shape of the lens of the 20-year-old subject during accommodation is shown in Movies 2 and 3 . During accommodation, the lens becomes thicker, whereas there is a decrease in the equatorial diameter and also in both the anterior and the posterior central radii of curvature. 

Table 3shows the results of the comparison between the MRI and the Scheimpflug measurements. The small bias and 95% limits of agreement indicate that the MRI results are in accordance with the Scheimpflug measurements. 

Discussion

In the present study, a parametric geometric description of the cross-sectional shape of the human lens was fitted to 3D MRI and 2D Scheimpflug images of five healthy subjects of different ages. By dividing the lens into eight parts, it was possible to describe the changes in the geometry of the complete lens during accommodation. In accordance with the Helmholtz accommodation theory, the anterior and posterior radius of the lens decreased with accommodation. Furthermore, there was a decrease in the equatorial radius, whereas there was an increase in the thickness of the lens, which is in agreement with the results of the MRI study performed by Strenk et al. ⁶ and the Scheimpflug studies by Brown, ²⁴ Koretz et al., ²⁵ and Dubbelman et al. ¹⁹ The ratio between anterior and posterior thicknesses, with respect to the equatorial plane of the lens, was approximately 0.73, and in some cases, it changed slightly during accommodation. This ratio is in accordance with the ratio reported by Glasser and Campbell ²⁶ and Rosen et al. ⁵  

The parametric geometry of the entire lens made it possible to estimate the CSA, the SA, and the VOL of the lens. The mean CSA increased significantly with accommodation, but there was no change in lens VOL. This finding seems to be in contrast with the findings of Strenk et al., ⁷ who suggested that the VOL of the lens should increase with accommodation because of the increase in CSA that was measured. However, an increase in CSA does not necessarily imply a change in VOL. ⁸ Based on shape information from the literature and an assumed end cap for the shape of the lens in the equator, Gerometta et al. ⁹ built a geometric model of the human lens during accommodation and found an increase of approximately 2.6% in VOL during accommodation for a typical 20-year-old human subject. However, our in vivo 3D MRI measurements showed that there was no change in lens VOL during accommodation with a 95% confidence interval of ±1%. This makes it clear that the lens material can be assumed to be incompressible with a Poisson’s ratio of approximately 0.5 if no VOL is transported in or out of the lens. Moreover, the mean SA of the capsular bag showed a decrease during accommodation, resulting in a mean strain of 5.0%. The change in SA indicates that the capsular bag is elastically deformed during accommodation. 

In this study, a comparison was made between Scheimpflug and MR imaging for the central lens parameters. These two techniques produced no significant difference in the lens thickness or the anterior and posterior radius. Koretz et al. ²⁷ combined MRI measurements with geometrically corrected Scheimpflug imaging. Statistical agreement was found between the MRI and the Scheimpflug data sets, with the exception of the posterior lens radius of curvature. In a similar study, Fea et al. ²⁸ compared Orbscan II (Bausch & Lomb; Rochester, NY) and MRI measurements of the anterior chamber. The results indicated that there was no difference in the measurements of the anterior chamber depth (ACD). 

For the purpose of comparison, Table 2summarizes the results of the present study and the in vivo studies of Dubbelman et al., ^{19 20 22} Jones et al., ²³ and Strenk et al. ⁶ The results of the present study are consistent with the results of Dubbelman et al., ^{19 20 22} who measured the radii of curvature and central lens thickness as a function of accommodation stimulus, in a large group of subjects who varied in age. The changes in lens thickness and equatorial radius correspond well with the results reported by Jones et al. ²³ and Strenk et al. ⁶ The higher rate of increase in lens thickness is probably because the results of the present study are with respect to accommodative response. Dubbelman et al. ^{19 20 22} and Jones et al. ²³ reported their results with respect to the accommodative stimulus. Strenk et al., ^{6 7} Koretz et al., ²⁷ and Jones et al. ²³ made in vivo MRI measurements of one 3-mm-thick axial slice as a function of accommodation, but did not determine the VOL or SA of the lens. Rosen et al. ⁵ approximated the VOL of the lens based on Strenk’s MRI measurements and calculated that the VOL increases with age from 130 to 200 mm³ (20–62 years of age). Koretz et al. ²⁹ approximated the VOL of the lens by a solid of revolution of the central anterior and posterior boundaries. Assuming that the scale of Figure 2in Koretz et al. should be multiplied by a factor of 1000, they found a VOL of 200 mm³, increasing with age to 260 mm³. Compared to the mean VOL (160 mm³) found in the present study, the approximation of Koretz is higher; this difference can probably be explained by simplification of the lens geometry. 

No in vivo measurements of the strain of the capsular bag have yet been performed. However, in a previous study we built finite element models of the human lens at different ages and states of accommodation. ³⁰ In a typical 29-year-old subject we found a mean strain of 4.9% for the capsular bag, which is similar to the mean strain of 5.0% that was measured in the group of healthy subjects in the present study. 

In the present study the nonaxisymmetric lens was subdivided into eight parts, and the VOL of each part was calculated. The mean CSA increased, whereas the SA decreased with accommodation, but no significant change was found in total lens VOL. This finding indicates that the internal human lens material can be assumed to be incompressible and that it undergoes elastic deformation. Moreover, the change in SA indicates that the capsular bag also undergoes elastic deformation. Further research on the nonrotational symmetric properties of the human lens should be performed to obtain more insight into the 3D geometric changes during accommodation. 

 Supported by SenterNovem Grant IS 043081.

 Submitted for publication April 4, 2008; revised May 7, 2008; accepted October 27, 2008.

 Disclosure: E.A. Hermans, None; P.J.W. Pouwels, None; M. Dubbelman, None; J.P.A. Kuijer, None; R.G.L. van der Heijde, None; R.M. Heethaar, 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.

 

Geometric representation of the cross-sectional shape f(y) of the human lens; x-axis and y-axis represent the radial and the axial directions, respectively.

Figure 2.

 

Translation and rotation of the 3D MRI edge coordinate points, followed by transformation to spherical coordinates and mapping to one cross-sectional plane.

Figure 3.

 

Canny edge data points of the 20-year-old subject divided into eight parts.

Figure 4.

 

Estimation scheme for the MRI and Scheimpflug measurements.

Figure 5.

 

Example of two cross-sectional slices of the 3D MRI measurements of the 20-year-old subject in the unaccommodated and fully accommodated states.

Figure 10.

 

Example of a complete 3D MRI acquisition of the anterior segment of the eye of the 20-year-old subject in the fully accommodated state. Movie.

Table 1.

 

Spherical Equivalent of the Refractive Error at the Spectacle Plane and the Accommodative Amplitude of the Subjects, Measured with Aberrometry

Age (y)	Refractive Error (D)	Accommodative Amplitude (D)
18	−0.5	7.1
20	−1.4	4.9
25	−0.5	5.4
27	−3.0	6.0
35	−1.1	6.0

 Data were obtained with a 3-mm pupil.

Figure 6.

 

R _ant, R _post, and TT measured with MRI (step I) and Scheimpflug imaging (step III). Solid lines: MRI measurements; dashed lines: Scheimpflug measurements with a different gray value for each of the five subjects.

Table 2.

 

Values at 0 D Accommodation and Rate of Change of the Five Geometric Parameters in Step I Measured with MRI and Scheimpflug Techniques and Values from the Literature

Geometric Parameter	Present Study			Literature	Source
		MRI	Scheimpflug
R ant at 0 D (mm)	11.45 ± 1.7	12.15 ± 0.6	11.25 ± 0.4	Dubbelman et al. 20 29-year-old subjects
ΔR ant/A (mm/D)	−0.51 ± 0.5	−0.64 ± 0.1	−0.61 ± 0.15	Dubbelman et al. 19
R post at 0 D (mm)	6.11 ± 1.4	5.82 ± 0.6	6.01 ± 0.3	Dubbelman et al. 20 29-year-old subjects
ΔR post/A	−0.14 ± 0.13	−0.16 ± 0.1	−0.13 ± 0.06	Dubbelman et al. 19
TT at 0 D (mm)	3.66 ± 0.14	3.684 ± 0.06	3.63 ± 0.07	Dubbelman et al. 22 29-year-old subjects
			3.83 ± 0.1	Jones et al. 23 29-year-old subjects
			3.63 ± 0.08	Strenk et al. 6 on average for subjects under 35 years of age
ΔTT/A (mm/D)	0.061 ± 0.03	0.045 ± 0.01	0.045 ± 0.012	Dubbelman et al. 19
			0.050 ± 0.024	Jones et al. 23
			0.052 ± 0.006	Strenk et al. 6 on average for subjects under 35 years of age
Ratio at 0 D	0.718 ± 0.06	—
ΔRatio/A	0.005 ± 0.013	—
R eq at 0 D (mm)	4.79 ± 0.13	—	4.59 ± 0.15	Jones et al. 23
			4.61 ± 0.05	Strenk et al. 6 on average for subjects under 35 years of age
ΔR eq/A (mm/D)	−0.037 ± 0.004	—	−0.033 ± 0.015	Jones et al. 23
			−0.035 ± 0.005	Strenk et al. 6 on average for subjects under 35 years of age

 Data are expressed as the mean ± SD. A, the accommodative response amplitude.

Figure 7.

 

Ratio between anterior and posterior thickness and equatorial radius measured with MRI (step I).

Figure 8.

 

Mean CSA, summed SA and VOL based on eight parts measured with 3D MRI as a function of accommodation (step II).

Figure 9.

 

Equatorial radius of the lens parts at 0 D accommodation for all subjects computed in step II; dashed lines: the equatorial radius of the parts obtained in step I.

Figure 11.

 

Change in 3D geometry according to the MRI measurements of the 20-year-old subject in the disaccommodated and accommodated states (4.85 D). Movie.

Figure 12.

 

Change in geometry of the 20-year-old subject measured with Scheimpflug photography. Ratios in R_eq are obtained from the MRI results in the disaccommodated and accommodated states (4.85 D). Movie.

Table 3.

 

Data from the Bland-Altman Plot of R _ant, R _post, and TT Measured with MRI and Scheimpflug Imaging in the Accommodated and Unaccommodated States

	R ant (mm)	R post (mm)	TT (mm)
Bias	−0.24	0.32	0.02
SD of bias	1.39	1.16	0.11
95% Limits of agreement confidence interval	−2.97–2.49	−1.96–2.59	−0.19–0.24

 Bias is defined as the mean difference between the MRI and Scheimpflug measurements.

Supplementary Materials

Movie 1 - 1.3 MB (QuickTime movie) 

Movie 2 - 1.2 MB (QuickTime movie) 

Movie 3 - 4.5 MB (QuickTime movie) 

The authors thank Ype Henry, MD, for his role as an independent physician.