Age-Dependent Changes in the Water Content and Optical Power of the In Vivo Mouse Lens Revealed by Multi-Parametric MRI and Optical Modeling

Abstract

Purpose: The purpose of this study was to utilize in vivo magnetic resonance imaging (MRI) and optical modeling to investigate how changes in water transport, lens curvature, and gradient refractive index (GRIN) alter the power of the mouse lens as a function of age.

Methods: Lenses of male C57BL/6 wild-type mice aged between 3 weeks and 12 months (N = 4 mice per age group) were imaged using a 7T MRI scanner. Measurements of lens shape and the distribution of T2 (water-bound protein ratios) and T1 (free water content) values were extracted from MRI images. T2 values were converted into the refractive index (n) using an age-corrected calibration equation to calculate the GRIN at different ages. GRIN maps and shape parameters were inputted into an optical model to determine ageing effects on lens power and spherical aberration.

Results: The mouse lens showed two growth phases. From 3 weeks to 3 months, T2 decreased, GRIN increased, and T1 decreased. This was accompanied by increased lens thickness, volume, and surface radii of curvatures. The refractive power of the lens also increased significantly, and a negative spherical aberration was developed and maintained. Between 6 and 12 months of age, all physiological, geometrical, and optical parameters remained constant, although the lens continued to grow.

Conclusions: In the first 3 months, the mouse lens power increased as a result of changes in shape and in the GRIN, the latter driven by the decreased water content of the lens nucleus. Further research into the mechanisms regulating this decrease in mouse lens water could improve our understanding of how lens power changes during emmetropization in the developing human lens.

The quality of our vision is critically dependent on the ability of the cornea and lens to correctly focus light on the retina, and any subsequent mismatch between the optical power of the eye and its axial length results in refractive errors that affect overall vision quality.¹ The refractive power of the lens is dependent on its shape, or geometric factors, and its material property manifested in its gradient refractive index (GRIN). The key geometric properties of the lens are its anterior and posterior surface curvatures. At the same time, the water-to-protein ratio determines the magnitude of the refractive index and shape of the GRIN. In all species, the refractive index is lowest in the lens periphery and rises to a maximum in the central lens nucleus.² During embryonic development, intrinsic genetic factors drive the establishment of the structural features of the lens that determine its initial optical properties and, therefore, the initial contribution of the lens to the overall refractive properties of the eyes. However, after eye-opening, visual input becomes an additional external input that also contributes to the coordination of the continual growth of the lens to ensure that light is correctly focused on the retina in a process called emmetropization.^3,4 During emmetropization an increase in the equatorial diameter and a decrease in sagittal thickness of the lens causes it to flatten, become thinner, and lose refractive power in parallel to the increase in axial length of the eye that occurs during eye growth.^5–7 

In addition to these initial changes in lens shape observed during childhood and puberty when the eye is still growing, the ongoing growth of the adult lens in the absence of additional axial growth of the eye continues to produce increases in both the sagittal thickness and equatorial diameter of the adult lens that has two effects on the optical properties of the lens. The first is associated with an age-dependent increase in the overall stiffness of the lens,⁸ that results in a loss of the ability of the lens to accommodate during middle age.⁹ Whereas the second is caused by the continued growth of the lens throughout life that should theoretically produce a more powerful lens that focuses light in front of the retina.^10–13 However, rather than a myopic shift, a loss of lens power, and a hyperopic shift is observed in the adult eye as we age.^14–20 Thus there is a discrepancy in the relationship between lens shape and refractive power, such that an increase in lens power does not accompany the steepening of lens curvatures with age. This phenomenon is known as the “lens paradox”^21–23 and has proposed to be caused by an age-dependent reduction in refractive index variation, a flattening of the GRIN profile, or a combination of these two factors.^24–27 Experimental studies have subsequently confirmed these predictions and shown that a gradual flattening of the GRIN profile through the formation of a central plateau of the constant index (see Ref. 28) and a decline in lens nuclear refractive index^13,29 both occur with advancing age. However, what is not known is how changes to the underlying structure and function of the lens are coordinated across our lifetime to affect the necessary remodeling of lens shape and GRIN required to produce these observed age-related changes to lens power. 

The lens is a living biological tissue with a unique structure and function to establish and maintain its transparency and refractive properties.³⁰ The lens operates an internal microcirculation system that generates circulating fluxes of ions and water that enter the lens at both poles via an extracellular route and return to the lens surface via an intracellular pathway mediated by gap junction channels.^1,31 This outflow of water from the lens nucleus generates a substantial hydrostatic pressure gradient,³² which is intrinsically regulated by a dual feedback system.³³ To establish a link between the cellular physiology that regulates lens water transport and the optical properties of whole lenses, we have used a number of magnetic resonance imaging (MRI) protocols to measure the longitudinal relaxation time (T1) that is proportional to the free water content,^34,35 and transverse relaxation time (T2) which is related to the bound water-to-protein ratio, and therefore, is inversely proportional to the refractive index.^36,37 Because an MRI allows measurements of lens shape to be extracted in the absence of any optical distortions,^38,39 we have all the parameters (shape and GRIN) necessary to build optical models of the lens that allow lens power and spherical aberrations to be readily calculated.^38,40,41 Furthermore, experiments performed on ex vivo bovine lenses using this approach have shown that inhibiting water transport compromises the ability of the lens to maintain its volume and water-to-protein ratio (GRIN) and hence the refractive power of the lens.^40,42 These findings suggest that actively removing water can control the refractive power of the lens.¹ Therefore, we speculate that the observed age-dependent changes in lens optics may be driven at least partly by lens water transport changes. 

In support of this contention, we have shown that an increase in the free water content of human lenses with age is associated with a decrease in GRIN, which accounts for the loss of lens power associated with the lens paradox.^23,35,43 However, these studies did not address the mechanism responsible for these water changes to occur and were limited to subjects over the age of 20 years, and hence did not shed any light on whether changes in lens water content were driving the remodeling of lens power observed in young lenses during the process of emmetropization. To investigate a complete range of lens aging, we have now applied our MRI-based computer modeling approach to study the role of water transport on lens remodeling in the in vivo mouse. Mice are a commonly used model for studying lens ageing due to their relatively shortened lifespan and reduced individual variation.^44,45 Although the effects of aging on the electrophysiology, cellular morphologies, biomechanics, and GRIN have been extensively studied in the ex vivo mouse lens,^45–50 how these changes impact the physiological optics of the mouse lens in vivo has not been comprehensively investigated. 

Here, we have used our optimized MRI protocols to image C57BL/6 mice at different ages, from 3 weeks to 12 months. Moreover, we utilized a modeling platform to calculate the optical properties of the lens from MRI data for mouse imaging. By combining these technologies, we elucidated the age-related changes in lens curvature, lens optics, and lens water content in mice in vivo, which may now provide a new experimental avenue to further understand the mechanisms behind ageing processes in the human lens. 

Methods

Animal Preparation

Animal use adhered to the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research. C57BL/6 male mice (Taconic Biosciences, Germantown, NY, USA) of 3 and 6 weeks, and 3, 6, 8, 10, and 12 months of age (N = 4 for each age group, all male mice) were studied using procedures approved by the Stony Brook University IACUC. Within these age groups, 2 cohorts of mice were followed longitudinally from 6 weeks to 3 months and from 10 months to 12 months. Animals were initially anesthetized with 5% isoflurane, followed by a bolus of xylazine (6 mg/k, IP) to reduce eye motion and then maintained with 1% to 1.5% isoflurane.^51,52 In addition, a topical mydriatic eye drop of 1% tropicamide was applied to limit anterior eye motion,⁵³ and lubricant eye ointment was used to maintain corneal hydration. Animals were placed in a prone position in a cradle with a circulating warm water pad to maintain body temperature, and their heads were fixed with ear and tooth bars. During the scan, mice were continuously given 1% to 1.5% isoflurane from a nose cone under spontaneous breathing. The respiration rate and rectal temperature (approximately 37°C) were monitored to ensure physiological homeostasis. 

MRI Scan Protocols

The MRI scans were performed using a 7T horizontal pre-clinical scanner (Biospec; Brucker, Billerica, MA, USA) equipped with a 650 mT/m BGA12S-HP gradient at the Stony Brook University preclinical MRI facility. The left eye of each mouse was studied using a customized circular surface coil transceiver.^54,55 The imaging plane was set on the central axis of the lens by visually positioning the slice to bisect the eye into superior and inferior halves using previously optimized protocols.³⁹ Briefly, T1 and T2 parametric mapping was acquired with a field of view (FOV) = 6.4 × 6.4 mm and matrix size = 64 × 64, with a slice thickness of 0.5 mm. Balanced steady-state free precession (bSSFP) images with higher resolution (FOV = 6.4 × 6.4 mm and matrix size = 128 × 128) were acquired using echo time (TE) = 2.5 ms, repetition time (TR) = 5 ms, and 4 RF phase cycling angles (0, 90, 180, and 270 degrees) to combine to generate a banding-free image to assess lens and eye curvatures.⁵⁵ T1 mapping used a rapid acquisition with refocused echoes (RARE) sequence with variable TRs (TR = 200, 380, 620, 950, 1500, and 4000 ms) and TE = 2.62 ms to ensure rapid acquisition. Whereas T2 mapping utilized a multi-echo spin-echo sequence with twelve TEs (minimum TE = 2.78 ms and echo spacing = 2.78 ms), with TR = 1600 ms and 10 repetitions. 

Extraction of Lens Shape

Following acquisition, images were processed using custom-written routines in Matlab (Math-Works, Natick, MA, USA). The phase-cycled bSSFP images were combined by nonlinear averaging, and the corrected bSSFP image was used to measure the lens shape.^39,56 The anterior and posterior lens radii of curvatures (R_a and R_p) and conic constants (Q_a and Q_p) were calculated from the elliptic shape as R_{a, p} = a²/b and Q_{a, p} = (a/b)² – 1, where a and b are major and minor axes of the fitted ellipse.³⁷ Lens volume (LV) was estimated by computing the solid revolution of the cross-sectional plane around the optical axis using a discrete integration formula⁵⁷:  

\begin{equation}V = \pi \mathop \smallint \nolimits_{ - {T_P}}^{{T_A}} {\left[ {h\left( x \right)} \right]^2}dx\end{equation}

(1)

where T_a is the lens anterior thickness, T_p is the lens posterior thickness, and h(x) is the elliptical fitting of the lens (Fig. 1A). 

Figure 1.

 

Construction of the optical model of the mouse lens. (A) Geometric parameters of the lens anterior surfaces (Ra and Qa), posterior surfaces (Rp and Qp), lens thickness (LT), and equatorial diameter (ED) were processed from the bFFSP image. (B) The lens GRIN map was converted from the T2 map using a calibration, which was subsequently split into the anterior and posterior portions by the equatorial plane defined in our previous publication.³⁹ (C) The GRIN maps were fitted into the GRIN 3 model provided in the ZEMAX optical modelling package. Both shape and GRIN parameters of anterior and posterior surfaces were input into the ZEMAX interface to create an optical model of the lens that allowed lens power and spherical aberration to be calculated.

T1 and T2 Calculations

Pixel-wise T1 values were fit from the signal intensity, S, at an array of TRs as:  

\begin{equation}{\rm{S}}\left( {{\rm{TR}}} \right) = {{\rm{S}}_0}(1 - {{\rm{e}}^{ - \frac{{{\rm{TR}}}}{{{\rm{T}}1}}}})\end{equation}

(2)

where S₀ is the signal at infinite TR. 

In a previous study, pixel-wise T2 values were calculated using data sets that had values below the noise floor removed.³⁹ Although this method worked well for the 3-month-old mice used in this initial study, the T2 measured from the nucleus became increasingly shorter for older mice, which meant that the calculation of T2 in the lens nucleus of older mice became increasingly biased by the inherent noise, which resulted in an overestimation of T2 values produced by this fitting method. To correct this problem, we utilized a phase-correction method that estimates a Gaussian-distributed real dataset from the complex data instead of the magnitude data.⁵⁸ The phase-correction method used in this study was based on a maximum likelihood estimator because only one coil channel was used to image the mouse eye.⁵⁸ 

The phase-corrected signals (S_pc) were then fit to a signal equation to calculate T2 values:  

\begin{equation}{{\rm{S}}_{{\rm{pc}}}}\left( {{\rm{TE}}} \right) = {{\rm{S}}_0}{e^{ - \frac{{TE}}{{T2}}}}\end{equation}

(3)

where S₀ is the signal at TE = 0 ms. 

Extraction of GRIN

To convert T2 measurements into the refractive index (n), calibration curves of GRIN profiles of the mouse lens obtained by X-ray Talbot interferometry were used.^39,45 The sagittal n measurements at ages of 3 weeks, 6 weeks, 3 months, 6 months, 8 months, and 12 months obtained from X-ray Talbot interferometry⁴⁵ were plotted against the reciprocal of T2 (in s⁻¹) from the same plane calculated from the phase-correct method.⁵⁹ The resultant T2-n calibration at each age point was fit with a first order and a second polynomial of the form:  

\begin{equation}{\rm{First\;order}}:{\rm{\;}}n = {\beta _0} + {\beta _1} \times \left( {\frac{1}{{{T_2}}}} \right)\end{equation}

(4)

 

\begin{equation}{\rm{Second\;order}}:{\rm{\;}}n = {\rm{\;}}{\beta _0} + {\beta _1} \times \left( {\frac{1}{{{T_2}}}} \right) + {\beta _2} \times {\left( {\frac{1}{{{T_2}}}} \right)^2}\end{equation}

(5)

 

Both fittings were evaluated by their sample correlation coefficients, R², to choose the optimal fit for each age group to convert T2 to n (see the Table). Because no n data for the 10-month-old age group were previously measured,⁴⁵ calibration coefficients for this age had to be estimated. We observed a linear dependency of β₀ and β₁ in the period within the steady phase (approximately 3 to 12 months). Hence, we fit these two coefficients with respective mouse ages to model two equations:  

\begin{equation}{\beta _0} = 1.373 + 6.32\; \times {10^{ - 4}} \times Age\end{equation}

(6)

 

\begin{equation}{\beta _1} = 6.61\; \times {10^{ - 4}} - 2.61\; \times {10^{ - 6}} \times Age\end{equation}

(7)

Where age is the mouse age in weeks. These sets of the equation are used to extrapolate a T2 to n calibration on a 10-month-old group, and the converted n values were used for subsequent studies:  

\begin{equation}{n_{10m}} = 1.398 + 5.56\; \times {10^{ - 4}} \times {T_2}_{10m}\end{equation}

(8)

 

Table.

 

Correlation Coefficients for the First order and Second Order T2 to n Calibrations

 

Optical Modeling

An MRI-based computational platform used previously to measure lens power in ex vivo bovine⁴⁰ and in vivo human eyes³⁸ was adapted to measure the optical properties of the mouse lens. Lens shape and GRIN were combined in the ZEMAX optical software platform to create an optical model of the mouse lens for each age group. The lens was modeled as a doublet design that consisted of an anterior and posterior GRIN surface. The boundary between these two surfaces was defined as the equatorial plane,³⁸ as illustrated in Figure 1B. In brief, the GRIN is presented as a map of contours (see Fig. 1B), fitted to the second order polynomials. The contours from the anterior and posterior parts of the lens meet at the equatorial plane.³⁸ 

Lens thickness and GRIN were split at this plane (see Figs. 1A, 1B). The “Gradient 3” model (GRIN 3) was used to characterize the lens in ZEMAX, which formulated rotational symmetry of GRIN distribution based on the Liou Brennan model⁶⁰:  

\begin{equation}n\left( {w,z} \right) = {n_0} + {n_{01}}{w^2} + {n_{02}}{z^1} + {n_{03}}{z^2}\end{equation}

(9)

And  

\begin{equation}{w^2} = {x^2} + {y^2}\end{equation}

(10)

where x is the equatorial direction (y = 0), and z is the optical axis. The respective anterior and posterior lens shape and GRIN profiles were input into these two surfaces to create a lens optical model (Fig. 1C). Other parameters used to formulate the model included a pupil diameter of 2 mm,⁶¹ a polychromatic light source (wavelengths = 486, 587, and 656 nm), and field weighting of 0 degrees = 100%, 2.5 degrees = 40%, and 5 degrees = 20%. The optical power of the lens in diopters (D) was extracted from the model using the power field map function in ZEMAX. The spherical aberration was calculated by ZEMAX in the form of a fourth-order Zernike coefficient (\(Z_4^0\), µm). 

Statistical Analysis

To facilitate comparison between age groups, T1, T2, and n values were extracted from the equatorial axis using an averaging band of three pixels in width and then plotted against relative distance, r/a,³⁹ or the actual lens thickness. On the r/a scale, 0 refers to the lens center (mid-point of the equatorial axis), and +/−1 refers to the lens boundary. For each nominated location, we set a searching window of 0.01 r/a in order to collect data from all mice and allow an analysis of grouped data. The data from nominated locations in four murine samples were averaged; error bars represent the standard error of the mean at each r/a location for each age group. 

Statistical comparisons were performed by 1-way analysis of variance (ANOVA). Tukey's post hoc testing was used to identify the pair-wise differences between age groups. The P values < 0.05 were considered significant. 

Results

In this study, we have optimized our in vivo MRI protocols, originally developed to study lens shape, water content, and water-to-protein ratio in 3-month-old wild-type and transgenic mice, to a broader age range to observe how these properties change as a function of age in wild-type lenses.³⁹ To achieve this, we have purposely chosen age groups similar to those used in a previous study⁴⁵ that used ex vivo lenses of different ages to quantify the changes in lens shape and GRIN that occurred in the wild-type mouse lens as a function of aging. The MRI-based method allows us to investigate all these aspects in vivo with active physiological support, an advance from previous ex vivo wild-type mouse studies.^45,50 Adopting this approach allows us to not only compare our in vivo data obtained for lens shape with that obtained previously from ex vivo lenses, but also allows us to convert our T2 measurements into refractive index values. 

Age-Related Changes in Lens Shape

For each age group, lens thickness (LT), equatorial diameter (ED), anterior (R_a, Q_a), and posterior (R_p, Q_p) surface curvatures, and conic constants were all directly extracted from corrected bFFSP images (see Fig. 1A), whereas LV was calculated using Equation 1, and all parameters were plotted against age. As indicated by the age-dependent changes in LT (Fig. 2A), ED (Fig. 2B), and LV (Fig. 2C), lens size increased with age, with the fastest growth rate occurring from 3 weeks to 3 months of age. LT and LV increased by 8% and 23% during this period. Then from 3 to 8 months, the rate of increase in LT (7%) and LV (14%) slowed, and no significant increases in either LT or LV were observed from 8 months to 12 months, the maximum age used in this study. 

Figure 2.

 

Age-related changes in lens size. The lens thickness (LT) (A), the equatorial diameter (ED) (B), and lens volume (LV) (C), were processed from the bFFSP images and plotted against age to illustrate the lens size changes. In panel B, a model of lens growth⁶⁶ that predicts the effect of lens growth on ED as a function of age (red line) is superimposed on our MRI-based measures of ED. The deviation of the model prediction for changes in ED with age from the experimental data shows the effect of fiber cell compaction on the increase in ED with age. Data are mean ± SD. Open symbols show raw data. SD, standard deviation. Open symbols show raw data.

These changes in lens size were also accompanied by changes in lens shape and surface curvature, as characterized by the aspect ratio (AR), the radius of curvature (R) and the conic constants (Q) for the anterior and posterior surfaces (Fig. 3). The AR, which is calculated as the ratio of ED/LT, did not change significantly over the period of observation (see Fig. 3A) but was always greater than 1, as previously reported.⁴⁴ Because an AR equal to 1 indicates a round lens, this suggests that the lens maintained a similar aspheric shape across all age groups used in this study. In contrast to the overall shape of the lens, the curvatures of the anterior and posterior surfaces that make up the lens did change with age (see Figs. 3B, 3C). R_a increased sharply from 3 weeks to 6 weeks of age. R_a then steadily increased from 3 months until it reached the highest R_a observed in the 12-month-old mice (see Fig. 3B). R_p showed a significant increase from 3 weeks to 3 months, and was stable from 3 to 8 months. R_p then increased further from 8 months to 12 months of age (see Fig. 3B). The conic constant is used to describe the surface shapes; Q_a and Q_p both decreased progressively in magnitude (see Fig. 3C). These results suggest that the two surfaces of the aspheric mouse lens flatten gradually with advancing age. These geometric properties not only define how lens size, shape, and surface curvature change as a function of age, but can also be used in the construction of an optical model of the lens to observe changes in lens refractive power with age. 

Figure 3.

 

Age-related changes in the lens shape and surface curvature. (A) The change in lens shape with age is quantified as the changes in the aspect ratio (AR = ED/LT taken from Fig. 2), where an AR of 1 represents a perfectly round lens. (B, C) The effect of age on the surface curvature is quantified by fitting the lens surface with elliptic equations to extract the radii of surface curvature, R_a, and R_p (B), and conic constants, Qa, and Qp (C), for each age group. Data are mean ± SD. Open symbols show raw data.

Age-Related Changes in Lens T2 and GRIN

Because T2 gradients reflect the bound water-to-protein ratio in the lens,¹³ their values are inversely related to the refractive index and can be converted to absolute values of n using appropriate calibration curves.^37,38,59 In our previous study on 3 month old mice, any echo signals that fell below the noise threshold were discarded during the data fitting to ensure T2 measurements in the lens nucleus were unbiased by the noise while preserving the fitting accuracy for the lens cortex that requires longer TEs. In the lens nucleus of 3-month-old mice, 3 to 4 echoes exhibited signal intensities that were above the noise threshold, and these data points proved sufficient for T2 fitting. T2 maps were computed by fitting the magnitude and phase-corrected signal data using a 3-month and 8-month-old mice (Fig. 4) to illustrate the improvement of the T2 calculations. The sagittal plane of the T2 maps are presented here. For the younger lens, both datasets produced the same quality of T2 map (see Fig. 4A) and fitting (see Fig. 4B). Figures 4C and 4D compare an example of the older lens using the magnitude data fitting and the phase-correction method. At 8 months, the extremely low T2 values present in the lens nucleus led to significant overestimation when using magnitude data. However, after using the phase-corrected signal data, the quality and accuracy of the T2 fitting and map for the older samples were improved dramatically (see Fig. 4D). This optimized T2 fitting approach was used to generate T2 maps of the lens across the different age groups (Figs. 5A–H). To facilitate the comparison between age groups, T2 profiles were extracted across the equatorial radius of the lens and plotted against radial distance (Fig. 5I). The nuclear region of the lens showed a decrease in T2 values from 3-weeks to 3-month of age and then stabilized from 3 months to 12 months of age. Furthermore, the plateau of the lowest T2 values widened with advancing age. 

Figure 4.

 

Technical improvement of the T2 mapping. A phase correction method was implemented to improve the signal quality biased by noise. The imaging plane for this comparison is sagittal. For a 3 month old lens, using both magnitude data and phase-corrected data yielded similar T2 mapping quality (A) and fitting accuracy (B). For an 8 month old lens, the T2 was shortened significantly and biased the T2 calculations in the nucleus region (C). The phase-correction method improved the signal quality biased by noise to provide reliable T2 calculations (D).

Figure 5.

 

Age-related changes in the lens T2. Representative T2 maps obtained from mice at 3 weeks (A), 6 weeks (B), 3 months (C), 6 months (D), 8 months (E), 10 months (F), and 12 months (G) of age. (H) T2 scale bar. Trend analysis was performed for each mouse lens and group averaged to generate (I). The nucleus T2 decreased from 3 weeks to 3 months of age and then stabilized from 6 months until 12 months. The central plateau extended towards the periphery with increasing age. Data are mean ± SEM.

We previously converted T2 measurements to refractive index (n) by a calibration based on data from 3-month-old mice.³⁹ Figure 6A shows the reciprocal of minimum T2 (extracted from r/a = 0) against mouse age. The pattern correlates well with the age-related changes in the maximum n reported by Cheng et al.,⁴⁵ as presented in Figure 6B. Thus, to better characterize the conversion between T2 and n, we performed the T2 to n calibration for each reported age group. To choose the optimal equations for calibration, first and second polynomials equations were compared. Figures 6C and 6D compare the two fits of mice aged 6 weeks and 12 months, respectively, as examples. For the other age groups, both the first and second order polynomial fittings yielded high R² values for the T2 to n calibration, and the differences in R² between the two sets of the equation were minor (see the Table). Therefore, the first order polynomial form was chosen (Equation 4) for simplicity. The lens GRIN maps were calculated using the new sets of calibrations, and the resultant trends are presented in Figure 7. 

Figure 6.

 

Comparison of the reciprocal of T2 and the maximum refractive index. The reciprocals of T2 values extracted at radial distance = 0 were plotted against age (A). The trend is consistent with the maximum refractive index data (B) calculated based on conversion of the X-ray interferometry data from Cheng et al.⁴⁴ Representative fittings using first order and second rder polynomials are presented for two age groups: 6 weeks (C) and 12 months (D). Data are mean ± SD. Open symbols show raw data.

Figure 7.

 

Age-related changes in the lens GRIN. GRIN maps were derived from the T2 maps using our T2 to n calibrations. Representative GRIN maps were obtained from 3 week (A), 6 week (B), 3 month (C), 6 month (D), 8 month (E), 10 month (F), and 12 month (G) old mice. (H) Refractive index scale bar. Trend analysis was performed for each mouse lens and averaged for each age group to generate the plot (I). Both the shape and the value of GRIN changed significantly with ageing. Data are mean ± SEM.

After transforming the lens T2 maps into GRIN maps, we observed that the lens GRIN exhibited a rapid development phase from 3 weeks to 3 months (see Fig. 7). To further characterize this change, GRIN profiles were extracted and plotted against radial distance (see Fig. 7I). These plots show that the maximum n increased significantly from 3 weeks to 6 weeks of age (1.45 to 1.52) to form a characteristic parabolic GRIN profile. There was only a slight increase in the maximum n value between 3 months and 6 months and then an increase from 1.53 to 1.56 from 6 to 12 months. In parallel to the observed age-dependent increase in maximum n, a central plateau emerged in the profile in older lenses (see Fig. 7I). 

Age-Related Changes in the Lens Optics

Because the optical properties of the lens are a product of its shape and GRIN, we next investigated what effect the observed age-dependent changes in these parameters have on lens optical power (Fig. 8A) and spherical aberration (Fig. 8B). Using our computer-based optical model of the mouse lens, we were able to show that lens optical power increased significantly by 35% from 3 to 6 weeks and rose slightly by 7.75% from 6 weeks to 3 months, after which the power remained constant (see Fig. 8A). Although the maximum refractive index still changed, the combinational changes in the lens shape resulted in constant lens power. The spherical aberration, expressed in terms of the Zernike coefficients, was more negative at young ages (3 weeks and 6 weeks) but became less negative with advancing age (see Fig. 8B). Taken together, our in vivo MRI scans and computer modeling have shown that post eye-opening changes to lens shape and GRIN of the growing eye combine to increase the power of the lens over the first 3 months of life. 

Figure 8.

 

Age-related changes in lens optics. Lens optical power values were calculated from the lens model in ZEMAX and plotted against mouse age (A). The lens power increased dramatically from 3 to 6 weeks of age and then remained stable. The spherical aberrations were in the form of a fourth-order Zernike coefficient (\(Z_4^0,{\rm{\;}}\mu m)\) (B). The lens had more negative spherical aberrations at 3 and 6 weeks, which shifted positively with advancing age. Data are mean ± SD. Open symbols show raw data.

Age-Related Changes in the Lens Water Drive the Change in GRIN

To test this idea, we used T1 imaging to map lens water content in lenses from each age group (Figs. 9A–H), then extracted profiles of T1 values across the equatorial radius of the lens and plotted them against radial distance (Fig. 9I). This analysis showed that 3-week-old mice had the highest T1 values across all lens regions. With increasing age, there was a downward trend in T1 values from 6 weeks to 6 months within the lens nuclear region (radial distance = 0), after which it remained relatively constant up to 12 months of age (Fig. 9J). Furthermore, the shape of the T1 profile changed with age. Initially parabolic in lenses from 3- and 6-week-old mice, the profile developed a central plateau in which the central maximum T1 value extended toward the periphery with advancing age. 

Figure 9.

 

Age-related changes in lens T1 values. Representative T1 maps were obtained from 3 week (A), 6 week (B), 3 month (C), 6 month (D), 8 month (E), 10 month (F), and 12 month (G) old mice. (H) T1 scale bar. Trend analysis was performed for each mouse lens and group averaged to generate the plot (I). The minimum T1 (ms) extracted from R/A = 0 was plotted against the age (J). The nuclear T1 values decreased from 3 weeks to 6 months of age, then stabilized between 6 and 12 months. The central plateau extended towards the periphery with ageing. Data in panel I are mean ± SEM. Data in panel J are mean ± SD. Open symbols show raw data.

Discussion

In this study, we have further optimized our in vivo MRI protocols, initially used to study lenses in 3 months old mouse lenses,³⁹ to extract changes in lens shape and GRIN over a wider range of ages that overlapped with a recent study performed on ex vivo lenses by Cheng et al.⁴⁵ Consistent with the ex vivo study, our use of MRI to noninvasively monitor lens growth showed similar changes in lens size (LT, ED, and LV) and surface curvature (R_a, R_p, Q_a, and Q_p) with age. It should be noted that the ex vivo lenses lack zonular tension which is relevant in lenses that accommodate. The mouse lens is less malleable than many accommodating lenses, thus the zonular tension plays less of a role on its shape and symmetry.⁶² Hence, curvatures obtained from our in vivo mouse study are comparable to the ex vivo study. 

By adopting a phase-correction method to extract T2 values from older lenses,^58,63 we optimized our methods to accurately extract T2 values from the nucleus of older mouse lenses, which exhibit very short transverse relaxation times.^39,47 Having accurately extracted T2 values from lenses across ages, we used the GRIN measurements obtained by Cheng et al. using X-ray interferometry to create age-dependent calibration curves. These equations using first order polynomial fits allowed us to convert our T2 results to n and generate GRIN maps for lenses of different ages. We then used an optical model incorporating the MRI-measured shape and GRIN to calculate how these age-dependent lens geometries and GRIN changes affect overall lens power and spherical aberration. Finally, we used T1 mapping, which is related to the free water content of the lens,^35,64 to show that these age-dependent changes to lens structure and optical properties appear to be driven by the active removal of water from the lens nucleus. 

Because the most significant change in GRIN was associated with a dramatic increase in the central n, a region of the lens that has lost the ability to undergo de novo protein synthesis, we reasoned that this change was most likely driven by the active removal of water from the lens nucleus to increase the protein concentration. The greatest reduction in the free water content of the lens nucleus occurred from 3 weeks to 3 months of age and was associated with a flattened anterior radius of curvature, which was observed in our study and a previous report.⁶⁵ After this initial change in lens shape, the subsequent removal of water from the lens nucleus did not seem to result in any further change in lens shape or an appreciable change in lens volume, despite the continued growth of the lens.⁶⁵ These observations are supported by a quantitative model developed by Sikic et al. that incorporated the proliferation and differentiation of the lens fiber cells to predict the growth of the lens from C57BL/6 J mice.⁶⁶ We have used this model to calculate the rate of the growth of the lens as an increase in ED and have superimposed this predicted rate of growth on in vivo measurements of ED obtained by MRI (see Fig. 2B). This exercise shows that over the first 3 months of life, our experimental data on the age-dependent increase in ED, is well described by the theoretical rate of lens growth. However, the theoretical and actual lens growth deviated from each other after 6 months of age. This observation indicates that fiber cell compaction may be occurring, and, if so, this would explain the slower increase in lens volume. 

The removal of lens water and potential subsequent lens compaction is also associated with an increase in the central n and the development of a central plateau in the GRIN profile. The development of a central plateau in GRIN has also been observed in ageing models of the bovine lens⁶⁷ and in clinical studies of the human lens.⁶⁸ It has been attributed to the continuous addition of fiber cells to the lens and may indicate compaction,³⁰ although this remains contentious. Because the age-related changes in the magnitude and profile of T1 values mirrored the changes in the GRIN, we postulate that the increase in the GRIN, and therefore lens power, observed in young lenses is due to the active removal of water from the lens nucleus. In the absence of de novo protein synthesis in the lens nucleus, removal of water from this region should lead to an increased n in the lens nucleus because of the increase in protein concentration. The magnitude of the GRIN is determined by the protein concentration and distribution.² The maintenance of the GRIN profile, which requires adequate water transport may also have subtle localized fluctuations reflecting the exchange of proteins and biomolecules in the different parts of the lens, which warrants further investigation. The proportional increase in the magnitude of n from 3 weeks to 6 weeks of age appeared to be greater than the rate of change in T1 values in the same period, suggesting that other mechanisms may also work to increase the magnitude of n in the lens nucleus. In this regard, it is important to note that a protein's primary amino acid sequence will determine its higher-order structure and, therefore, its refractive index increment (dn/dc), which in turn is affected by the hydration shell around a protein.^69–72 Furthermore, it has been shown that changes in protein surface solvation can increase the dn/dc of γ-crystallin, the principle crystallin in the lens nucleus, above that obtained from the component amino acids of the protein alone.^73,74 Thus, as well as simply increasing the concentration of lens proteins in the lens nucleus, the removal of water may also effect an increase in the lens GRIN by increasing the dn/dc of proteins in this region of the lens. 

Using an optical modeling approach, we have shown that the observed age-dependent changes in lens shape and GRIN profiles, driven by water removal from the lens nucleus, alter lens power and spherical aberration. Although the values produced from our model are hard to validate in vivo using other optical equipment due to the relatively small size of the lens and potential optical distortions,⁷⁵ similar measurements of lens power of approximately 450 D have been obtained for 3 month old ex vivo lenses using laser ray tracing.⁷⁶ Our calculations showed that lens power increased dramatically from 3 to 6 weeks of age and then remained relatively constant from 3 to 12 months of age, despite the continued growth of the lens (see Figs. 2, 3) and associated changes in the shape of the GRIN. Our optical modeling approach also allowed spherical aberration to be calculated. These measurements show that the mouse lens generates and maintains a negative spherical aberration across the full age range examined in this current study. This negative spherical aberration is caused by the GRIN and functions to improve not only the optical quality of the lens itself but it also corrects the positive spherical aberrations introduced by the cornea.² Thus, it appears that age-related changes to lens water drive changes to lens shape and GRIN that alter the optical properties of the lens over the first 3 months of life. Then, after this initial period, changes in lens water content, shape, and GRIN appear to interact to maintain lens power and spherical aberration despite the continued growth of the lens. These optical changes correspond to mice that reach adulthood at approximately 3 months of age, are considered middle-aged by 8 months of age and elderly after 18 months,⁷⁷ an age not examined in the current study. The two distinctive changes in water transport and optical properties observed in the mouse from 3 weeks up to 3 months may indicate a process of refractive optimization which may be akin to the process of emmetropization in the human eye. Consistent with this view, others have reported that a process of refractive optimization that occurs in mice between 4 and 6 weeks of age and results in a change in lens shape from spheroid to lentoid and a decrease in lens power^78–80 that is accompanied by an increase in the GRIN.⁸⁰ To confirm this association, in future work, we will extend our MRI-optical modeling approach to include the whole mouse eye so that we can determine how an age-dependent change in lens power alters the overall refractive power of the mouse eye by using similar protocols to those developed for the human eye.^43,68 

Our finding that changes in lens water transport can alter the optical properties of the mouse lens is consistent with experiments performed on bovine lenses, which demonstrated that inhibiting the ionic and water fluxes generated by the lens microcirculation system also modulated lens optics.⁶⁴ However, our current results do not offer any insights into the mechanisms that coordinate the rate of removal of water to the modulation of lens power observed during the distinctively different phases of lens growth. In this regard, it is interesting that the pharmacological modulation of the contractility of the ciliary muscle, which alters the tension applied to the lens via the zonules, can regulate the signaling pathways that regulate water transport in the mouse lens.⁸¹ Because the ciliary muscle receives innervation from the retina via the ciliary nerve,⁸² it is conceivable that the de-focus signals, which are sensed by the retina and transduced into signaling pathways that coordinate the growth of the eye, are also conveyed to the lens as changes in zonular tension that affect the water transport which in turn modulates lens power. It is already known that signaling pathways activated by this retinal de-focus signal modulate growth and tissue remodeling of the back of the eye so that the axial length matches the focal length generated by the refractive tissues in the front of the eye.⁴ Here, we propose that, in parallel to these well-characterized changes in axial length, the lens responds to the retinal de-focus signal to coordinate the water transport that remodels the internal structure of the lens fiber cells. Consequently, the observed changes to lens shape and GRIN that determine the lens power are matched to the phase of both eye and lens growth. 

In summary, by applying our in vivo MRI-based optical modeling approach to mice of different ages, we have shown that changes to lens water content are associated with changes to lens shape and GRIN that modulate the power of the lens during two distinct phases of lens growth. Water is an essential driving factor for these changes, however, other factors, such as changes in protein solubility or post translational modifications, could also contribute to changes in the lens shape and GRIN. Extending these measurements to even older mice, it should be possible to determine whether changes in lens water transport are also involved in forming age-related cataracts. Finally, these studies also provide essential baseline information on how the lens water transport and optical power change as a function of age, which will be invaluable for future studies that utilize different strains of transgenic mice lacking key lens proteins known to modulate lens structure and function. 

Acknowledgments

Supported by the National Institutes of Health grants EY026911 (T.W.W.) and EY032056 (C.C.). 

Disclosure: X. Pan, None; E.R. Muir, None; C. Sellitto, None; K. Wang, None; C. Cheng, None; B. Pierscionek, None; P.J. Donaldson, None; T.W. White, None