The aim of this study was to determine the contribution of the lens gradient refractive index to the change in lens back vertex power during simulated accommodation in primate lenses. The main findings of the study are:
- The power, in D, of the lens surfaces and gradient linearly increases with increasing lens power during accommodation.
- The contribution, in D/D, of the anterior lens surface to the accommodation amplitude is greater than the contribution of the posterior surface for all lenses.
- The gradient contributes significantly to the accommodation amplitude, corresponding on average to 65% for cynomolgus monkeys and 66% for hama-dryas baboons.
- The lens back vertex power and the power of the surfaces and gradient decrease with age.
- The relative contribution of the gradient to the accommodative amplitude remains constant with age.
Clearly, the calculated gradient contribution depends on the value of the outer cortex refractive index. We used an outer cortex refractive index of 1.365, derived from measurements of protein concentrations (Moffat et al., 2002
; Pierscionek, Smith, & Augusteyn, 1987
). This value is also the median of published data, which ranges from 1.34 to 1.39 (Jones et al., 2005
; Moffat et al., 2002
; Nakao, Ono, Nagata, & Iwata, 1969
; Pierscionek & Chan, 1989
; Pomerantzeff, Pankratov, Wang, & Dufault, 1984
). In any case, independent of the refractive index value selected within this range, we find that our main conclusion that the gradient contributes to the accommodative power of the lens remains valid. In the extreme cases, n
= 1.34 results in a gradient power contribution of 94% and n
= 1.39 results in a gradient power contribution of 21%.
Our results are comparable to the in vivo
human results of Dubbelman et al. (2005)
, which measured the changes in lens shape in response to an accommodative stimulus. Dubbelman et al. (2005)
found a curvature change of 6.7 mm−1
/D for the anterior surface and 3.7 mm−1
/D for the posterior surface, which corresponds to power changes of 0.19 D/D for the anterior surface and 0.11 D/D for the posterior surface assuming a surface refractive index of 1.365. The combined contribution of the surfaces is therefore 30%, which is comparable to our findings (−34%). Furthermore, we compared our results with those obtained in vivo
with Rhesus monkeys by Rosales, Wendt, Marcos, and Glasser (2008)
. For this comparison, we performed a linear fit on their average anterior and posterior lens curvatures (Ra
= 11.11 mm − 6.4 mm/D; Rp
= −6.64 mm + 0.17 mm/D) and used the methods from our study to calculate the surface contributions. The resulting contributions were 18.2% for the anterior surface and 14.5% for the posterior surface, which gives a combined surface contribution of 32.7%. This is also in good agreement with our data and the human results of Dubbelman. In addition, our finding that the gradient power (D) decreases with age is in agreement with in vitro
and in vivo
studies on human, cynomolgus, rhesus, and baboon lenses (Borja et al., 2008
; Borja, Manns et al., 2010
; Dubbelman & Van der Heijde, 2001
; Jones et al., 2005
). These studies show that this decrease in the gradient power is the main contribution to the loss of power in isolated lenses with age.
To further compare our results with previous studies, which quantified the power of the internal structure of the lens using an equivalent refractive index, we first need to determine the relation between the power of the gradient and the equivalent refractive index. To simplify the analysis, we used a thin lens model. With some arithmetic manipulation, one can show that the relation between equivalent refractive index and power of the gradient is
= 1.336 is the refractive index of the aqueous, n
= 1.365 is the refractive index of lens outer cortex, P
is the lens power, and Pg
is the contribution of the gradient. Equation 3
shows that equivalent refractive index is a measure of the relative contribution of the gradient to the total lens power (ratio Pg
). Our finding that the relative contribution of the gradient remains constant with accommodation is therefore in agreement with previous studies, which found that the equivalent refractive index of the lens does not change with accommodation (Garner & Smith, 1997
; Hermans et al., 2008
The finding that the gradient contributes significantly to the accommodation amplitude is consistent with Gullstrand’s intracapsular theory of accommodation and the previous observation by Garner and Smith (1997)
based on a gradient model of the lens. Gullstrand used a higher value for the equivalent refractive index for his schematic lens in the accommodated state to take into account the contribution of the gradient. Our results, together with the simplified model of Equation 3
, show that a constant value for the equivalent index with accommodation can be assumed since the relative contribution of the gradient remains constant.
Our observation that the relative contribution of the gradient remains constant with age is consistent with the results of a previous study on isolated cynomolgus and rhesus monkey lenses (Borja, Manns et al., 2010
), where the gradient contribution was found to be 62% on average for cynomolgus monkeys. The values in the present study are slightly higher (65%) mainly because of differences in the value for the cortex refractive index (1.371 versus 1.365) and different methodology to calculate the lens power (effective power versus back vertex power). On the other hand, the previous study found a decrease in the relative contribution of the gradient with age in baboon lenses. However, the study only had two older baboon lenses (above 20 years) and had a smaller sample size. With the additional data and broader age range, the present study shows that the relative gradient contribution is constant with age.
Age-related changes in gradient power (D) seem to be primarily due to changes in the axial refractive index profile of the lens (Augusteyn, 2010
; Augusteyn et al., 2008
; Jones et al., 2005
). On the other hand, the fact that the relative contribution of the gradient remains constant with accommodation suggests that the changes in gradient power with accommodation are not due to changes in the axial distribution but rather to changes of the iso-indicial curvatures with accommodation. This observation is consistent with in vivo
MRI studies showing that the axial gradient profile changes much less with accommodation than with age (Kasthurirangan et al., 2008
In all lenses, we observed only a small change in posterior lens curvature during accommodation, consistent with previous in vivo
studies on human and rhesus monkey lenses (Brown, 1974
; Dubbelman et al., 2005
; Koretz, Bertasso, Neider, True-Gabel, & Kaufman, 1987
; Koretz, Handelman, & Brown, 1984
). However, there is always some uncertainty in the measurement of the posterior lens curvature because the posterior lens is imaged through the anterior surface and gradient (Borja et al., 2008
, Dubbelman & Van der Heijde, 2001
). In the present study, there are two potential sources of error. First, the OCT images were scaled by dividing the optical path length by an estimate of the group refractive index based on previous measurements (Uhlhorn et al., 2008
). Second, the OCT images were corrected for distortions due to refraction assuming a uniform refractive index equal to the average index of the lens. We performed an analysis to determine how the value of the group refractive index used to scale the lens and correct posterior distortions affects the posterior lens power. For average group refractive indices ranging from 1.39 to 1.42 (Uhlhorn et al., 2008
), we found a variation of less than 0.5 D (5%) for the posterior surface power. Therefore, the uncertainty on the value of the average refractive index has only a minimal effect on the final results.
In conclusion, we find that the gradient contributes on average 65 ± 3% of the total lens power change during accommodation for cynomolgus monkeys and 66 ± 3% for hamadryas baboons, assuming an outer cortex refractive index of 1.365. The relative contribution of the gradient (or equivalent refractive index) remains constant with accommodation. These findings show that accommodation-dependent optical models of the lens can assume a constant equivalent refractive index. They also suggest that a material of uniform refractive index could serve as a lens substitute for lens refilling procedures to restore accommodation (Kessler, 1964
; Koopmans, Terwee, Barkhof, Haitjema, & Kooijman, 2003
; Nishi, Mireskandari, Khaw, & Findl, 2009
; Parel, Gelender, Trefers, & Norton, 1986
). Overall, our findings lend support to the intracapsular theory of accommodation of Gullstrand.