During accommodation, the primate crystalline lens changes its shape and the gradient index of refraction redistributes, producing well-known changes in the optical properties of the crystalline lens: an increase of power and a shift of the spherical aberration toward more negative values. We have presented experimental measurements of the changes of both the geometry of the crystalline lens, and of the GRIN profile of nonhuman primate lenses (cynomolgus monkeys) with accommodation. Accommodation was simulated in vitro using a stretching device, a paradigm that has been previously demonstrated to mimic accurately the change in lens shape and power occurring in vivo.
41,43,45,53 These measurements have allowed us to quantify the role of the GRIN in accommodation, and to estimate the relative contribution of surface and GRIN to lens power—and most notably, to the spherical aberration, as a function of accommodation. All the results presented in this study were calculated using the group refractive index at 825 nm in both the crystalline lens and the preservation medium (DMEM, 1.345). To check the validity of the results in visible light, the ray tracing was repeated with the surface and nucleus refractive index converted to phase refractive index at 555 nm and assuming an aqueous and vitreous refractive index of 1.336. The differences between group refractive index and phase refractive index are around 1% (0.007 as a mean), producing average differences in power and spherical aberration below 3% (1.1 D and below 0.1 μm, respectively).
In agreement with previously reported in vivo and in vitro data in humans
8,9 and in rhesus monkey lenses,
11,61 we found a decrease in the lens surface radii of curvature with accommodation, larger for the anterior surface than for the posterior surface. The slightly smaller change per diopter of accommodation in cynomolgus monkeys may be due to interspecies differences, age differences, and the high asphericity of the anterior surface.
Very few studies have reported crystalline lens asphericity. We found that the anterior surface conic constant of the unaccommodated cynomolgus lens was consistently negative (although it varied significantly across individuals, ranging from −14 to −2) and decreased in most of the lenses toward a more spherical shape with accommodation. The posterior conic constant was also negative but close to zero and remained constant with accommodation. These data differ from reports in human lenses in vivo,
8 measured with Scheimpflug imaging, where both anterior and posterior surfaces had negative asphericity with similar mean values, although the intersubject variability was very large. Also, the change with accommodation differs, as in humans the anterior surface seems to become more curved with the peripheral areas of the lens remaining relatively flatter, and therefore the conic constant changes toward more negative values. However, the results in human lenses in vivo
8 show small changes in the anterior conic constant with accommodation, and no accommodation-related changes in the posterior surface conic constant due to limitations in the technique. Studies in in vitro–human crystalline lenses
58 reported a positive conic constant in the anterior surface and scattered values of approximately 0 for the posterior. The values of asphericity reported here for the fully accommodated state agrees well with those reported by a previous study in isolated cynomolgus monkey lenses,
33 where a wide range (from −6 to +4) was reported. The high value of lens anterior surface asphericity in monkeys in the unaccommodated state, never reported in humans, may be due to the differences in size between the species, to the young age of the monkey lenses compared with the humans from prior literature, and to the larger accommodative range of monkey lenses (up to 30 D) in comparison with the human lens (no more than 10 D).
We found that the lens thickness increased with accommodation at a rate of 0.036 ± 0.004 mm/D. This thickness variation is comparable to that reported in vivo in rhesus monkeys under stimulated accommodation, around 0.041 mm/D
11 and 0.063 mm/D,
62 and in vivo in humans, 0.045 mm/D
8 and 0.064 mm/D.
63
In agreement with previous findings, we have found that a rather constant value of the parameters defining the GRIN best fitted the experimental data
9,35 and that the equivalent refractive index did not change with accommodation.
9,34,35
Despite the simplicity of the GRIN model, the estimated parameters allow reproducing the experimental input data with great accuracy (mean RMS < 40 μm), for all accommodation levels, using our recently developed optimization method based on OCT imaging.
28 Previous studies with simpler GRIN models suggested that no change in the parameters of the model was needed to account for a change of power of the crystalline lens with accommodation.
9,35 We have found a slight trend for an increase in the power exponent parameter of our GRIN model (expansion of the central plateau in the GRIN distribution), although this was not statistically significant. This was in contrast with a report using MRI,
26 which suggested a decrease of this parameter (only significant in the meridional direction), and a 50% contribution of the lens thickness nucleus to the change of lens thickness with accommodation. Studies based on Scheimpflug imaging revealed a much higher contribution of the lens nucleus (90%) in humans
6,64,65 and rhesus monkey.
66 While differences arising from the definition of the lens nucleus and the data analysis are expected, our study on cynomolgus monkeys also supports a large contribution of the lens nucleus in thickness changes (69%, following the definition proposed by Kasthurirangan et al.
26 ). This conclusion is highly dependent of the adopted definition for the nucleus. While the current definition does not necessarily best describe the physiological area of the lens nucleus, it allows comparison with prior literature using this definition.
26 Nevertheless, the estimated nucleus thickness relative to the total thickness (73%) with that definition is only slightly larger than that obtained from direct imaging of the lens (65%, from Scheimpflug imaging in young human subjects in vivo
64 ; 57% from OCT imaging as an average in isolated human crystalline lenses of different ages [de Freitas C, et al.
IOVS 2013;52:ARVO E-Abstract 818]).
We found the spherical aberration of the unaccommodated cynomolgus lens to be negative (−2.3 μm, 6-mm pupil diameter), as reported in young human lenses (−0.16 μm, 6-mm pupil in vivo
67 ) and rhesus monkey (−1 μm, 7-mm in vitro
46 and −0.5 μm, 8-mm in vivo
41 ). Previous studies have reported a compensatory role of the GRIN in different species such as fish,
68 rat,
69 porcine lenses,
28,32,70 and also in humans (Birkenfeld J, et al.
IOVS 2011;52:ARVO E-Abstract 3404). With those lens geometries, and with a homogeneous index of refraction, the spherical aberration of the lens was positive, and the presence of GRIN shifted the lens toward less positive values (or close to zero, such as in fish) or toward negative values, which tended to compensate the positive spherical aberration of the cornea. In cynomolgus lenses, we have also found a compensatory role of GRIN. However, in this case, the GRIN did not reverse the sign of the spherical aberration, already negative with an equivalent refractive index, but rather doubled its magnitude. The spherical aberration value of the lens with an equivalent refractive index was on average 41% of that of the corresponding GRIN lens. Also, the presence of GRIN emphasized the change of spherical aberration with accommodation. The change in spherical aberration with accommodation estimated with the equivalent refractive index was on average 29% of the change for the corresponding GRIN lens. While there is a large intersubject variability (which we did not find to be correlated with age or postmortem time), we have found that the contribution of GRIN in the spherical aberration is slightly larger in the fully accommodated state.
As in rhesus monkeys,
41,46 we found a shift of the spherical aberration during accommodation toward more negative values. We found larger differences (unaccommodated to fully accommodative state) in spherical aberration in cynomolgus (3.3 μm for a 6-mm pupil) than in rhesus monkeys (around 2 μm, 8-mm, in vivo
41 ; 1.7 μm, 7-mm, in vitro
46 ). However, as the accommodation amplitude is larger in cynomolgus (20–30 D) than in rhesus (around 17 D), the shift of spherical aberration per diopter of accommodation appears relatively similar across species (−0.124 μm/D in the current study in cynomolgus monkeys; around −0.11 μm/D in vitro
46 and −0.19 and −0.24 μm/D in vivo
41 in rhesus). These values are higher than those reported in humans for 6-mm (−0.013 μm/D
5, −0.083 μm/D
3). The calculated spherical aberration value may be affected by errors in the calculation of the geometry of the surfaces of the crystalline lens, in the reconstruction of GRIN and in the accuracy of the GRIN model itself.
As in previous studies,
9,34,37,38,71 the contributions of the GRIN to the power and spherical aberration were computed by comparing the lens optical properties with those produced by refraction in the surfaces only. While previous publications assumed a fixed surface refractive index to estimate the contribution of the surfaces to the change of power of the lens, in this study the surface index was obtained directly for each lens from the GRIN reconstructed from the experimental data. The contribution of the GRIN to the power and accommodative amplitude of the lens reported is in agreement with previous studies in vitro in baboon and cynomolgus monkeys
34 and in humans.
34,53 For spherical aberration, we found that the surface contribution was around 20%, and that the contribution was larger in the fully accommodated state. These results are indicative of a large contribution (almost 80%) of the GRIN to the value of lens spherical aberration in the entire accommodative range. Also, the redistribution of the GRIN was found to be responsible for more than 70% of the change of spherical aberration through accommodation.
For these calculations, we defined the spherical aberration contribution of the GRIN as the difference between the spherical aberration of the reconstructed GRIN lens and the spherical aberration of a lens with a homogeneous refractive index equal to that of the surface, in a similar way as previously evaluated for the surface/GRIN contributions to the power of the lens.
9,34,53,71 There are other possible definitions or values of the index of the homogeneous lens that could be used, which may produce different numerical results, but we expect that the general finding regarding the importance of the GRIN will not change. For instance, our analysis shows that the change in spherical aberration of the lens with homogeneous index equal to the equivalent index (instead of the surface index) is still only 56% of the change found with the GRIN lens.
Theoretical analyses
72,73 have shown that model eyes that simulate the change of spherical aberration with accommodation can be designed using a lens model with a shape, and a homogeneous equivalent refractive index (
n = 1.429), based on the measurements of Dubbelman et al.
8 However, this lens model does not provide accurate predictions of the actual value of lens spherical aberration, most likely due to uncertainties in the lens surface asphericity values.
72 Our experimental study on monkey lenses is in disagreement with the conclusion of Lopez-Gil and Fernandez-Sanchez,
73 regarding the contribution of the GRIN to the change of spherical aberration with accommodation. We find that the equivalent homogeneous lens predicts the general trend of the change in spherical aberration with accommodation, but it does not reproduce the actual spherical aberration value and its change with accommodation, obtained with experimental measurements of the crystalline lens shape and GRIN.
The literature on the changes of the GRIN distribution with accommodation is scarce and to our knowledge, this is the first study that explores experimentally this redistribution in nonhuman primate lenses and studies its influence in the spherical aberration of the eye. This study has contributed to a deeper understanding of the role and relative importance of the gradient refractive index on the optics of the crystalline lens.