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.

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. (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.

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 growth 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.

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.

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.

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. 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.

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 ($Z_4^0,\mu m)$ (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.

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.