Accurate refractive index measurements of the crystalline lens are important for the development of surgical treatments for presbyopia. Numerical modeling of the lens is being used more commonly to study the dynamics of accommodation and the effects of aging during presbyopia and these modeling methods rely on accurate measurements of the static optical properties of the lens. The OCT images of the isolated lenses were used to calculate the average value of the refractive index profile along the optic axis. These measurements resulted in a mean value of
= 1.408±0.005 for all of the eyes scanned in the age range 6 – 82 years. To the best of our knowledge, there is only one published report with measurements of the group refractive index of the crystalline lens with which we can compare our results. Drexler et al. (1998)
used multiple wavelength low-coherence interferometry to measure the group dispersion (Δng
/Δλ) of the crystalline lens and found g
= 1.4055 at λ = 855 nm which corresponds to an average phase index of
= 1.397 at λ = 589 nm (see sec. 2.3
). However, their method of calculating the average group index (g
) from the measured optical thickness involved using the dispersion of water instead of the crystalline lens, which can introduce significant errors.
The precision of the group refractive index measurement is limited by the axial resolution of the OCT system. Assuming we can reliably locate the peak intensity from a given surface within ±1 µm, we can estimate our group index measurement precision to ±0.0002. However, the conversion from group to phase index introduces two possible sources of error from the uncertainty in the central wavelength of our light source and in the value for the dispersion of the crystalline lens (see Eq. 5
). Our light source has a nearly Gaussian output spectrum with a specified central wavelength of 825 nm. We measured the spectrum with a spectrometer and fit the data with a Gaussian function which calculated a central wavelength of 828 nm. Assuming an error of 5 nm in the determination of the central wavelength, this only impacts the calculated index by < 0.0001, which is below our group index measurement precision. The value for the dispersion of the lens (dn/dλ) that was used in the calculation represents the best estimate available from a review of published literature (Atchison and Smith, 2005
). However, there is significant variation in published lens index data, due in part to the complexity of the lens index gradient. Assuming the published value is accurate within 20 %, the error in the phase index calculation is within ±0.001. If however, the dispersion is off by as much as 50 %, then error in the phase index may be as much as ±0.004.
The average refractive index measured with OCT was compared to the results of the MRI measurements from Jones et al. (2005)
by integrating the sagittal index profiles and dividing by the axial thickness of the section to calculate the average value of the index profile. This results in a mean value of
= 1.411 ± 0.006 for 21 lenses over the age range of 7 – 82 years. No significant age dependence was found (P
≈ 1.0) due to the large variability. However, there is good agreement between the OCT and MRI measurements; the mean average index over similar age ranges is well within the standard deviation of each technique. This would appear to validate the technique of using MRI to measure the refractive index distribution of the crystalline lens. Furthermore, the results from both the OCT and MRI measurements suggest that the peak refractive index in the nucleus is closer to nc
= 1.42 as suggested by Jones et al. (2005)
and Augusteyn et al. (2008)
, rather than the more commonly accepted value of ≈ 1.406 since the average value of the index profile (≈ 1.41) must be lower than the peak value.
A statistically significant decrease in the average index with age was found (−0.000159 year−1, P < 0.001). However, the age related changes in the average index are small compared to the precision of the measurement technique. If the slope of the regression line is assumed to represent the rate of change, over an entire life span (≈ 80 years), the total change in the average refractive index will only be ≈ 0.01. The precision of the refractive index measurement is limited by the axial resolution of the OCT system and the accuracy of the lens dispersion data, leading to an estimated precision of ±0.001. A very large sample size evenly distributed over the entire age range would therefore be required to determine a better model of the age dependence.
The increase in lens thickness with age seen in is consistent with previous measurements of the isolated lens thickness, including the MRI measurements by Jones et al. (2005)
, which reported an age dependent thickness of t
= 4.77 mm + 0.0042 × Age(mm/year). The lens thickness growth rate measured with OCT (0.0064 mm/year) is similar to the growth rate measured from the MRI imaging (0.0042 mm/year). It is also consistent with previous photographic measurements of the isolated lens by Rosen et al. (2006)
who found a growth rate of (0.0123 mm/year), and by Glasser and Campbell (1999)
who could not establish a statistically significant growth rate, but did note an increasing trend in the lens thickness with age.
One concern when performing measurements on ex vivo
tissue is whether its properties have been affected by storage and preservation. Isolated crystalline lenses have a tendency to swell, or absorb water when stored too long before experimentation and fluid tends to pool in ”discreet lakes” located near the capsule and around the axis (Augusteyn et al., 2006
). Indeed, of the 40 lenses measured in this study, 6 had visible capsule separations that clearly had fluid trapped between the capsule and the cortex. This raises a concern over whether the lens swelling had any effect on the measured refractive index. For each lens measured, the optical thickness that is used to calculated the refractive index was always chosen from the anterior cortical boundary to the posterior cortical boundary, neglecting the capsule and the fluid surrounding the lens cortex. This assures that the refractive index that is measured is due to the lens cell mass and is not influenced by possible tissue swelling. Since the capsule is believed to have a refractive index that is nearly equal to the surrounding aqueous or vitreous (Smith, 2003
), the capsule’s contribution to the optical thickness of the lens in negligible. Furthermore, fluid trapped in the capsular space has the same refractive index as the surrounding medium, therefore it does not contribute to the measured optical thickness of the lens, and as such, has no measurable effect on the refractive index.
The question remains of how measurements of the average refractive index relate to the development of presbyopia. It appears that as the human lens ages, the refractive index forms a distinct plateau in the central region (Jones et al., 2005
; Augusteyn et al., 2008
). Early in life there is a gradual change in the refractive index from the cortex to the nucleus. As new layers of protein are laid down in the cortex, the refractive index in the nucleus increases due to tissue compaction (Augusteyn, 2007
) until the peak refractive index is reached in the center of the lens. At that point, the refractive index in the surrounding layers increases until a large, optically homogeneous region of constant index is formed. This central region with constant index (plateau) grows faster than the overall lens thickness until the age of about 60 years (Augusteyn et al., 2008
). As the refractive index in the cortical layers is increasing during the plateau formation, the overall lens thickness is increasing as well, so the net result is that the average value of the index profile remains nearly constant through the age of about 60 years. This can be seen in the data in . After the age of about 60, the index plateau has been fully formed but the total lens thickness continues to increase, thereby decreasing the average value of the refractive index profile as the age increases. This suggests that some form of a biphasic model is more appropriate to model the age dependence of the average index.
Other studies of the crystalline lens support this picture as well. In a study of 100 isolated human lenses with an age range of 6–94 years, Borja et al. (2008)
measured the surface powers and equivalent refractive index using shadowphotography and lens power measurements. It was concluded that the contribution of the index gradient to the total lens power decreases until the age of about 60 years, at which point it is practically constant. This is consistent with the index plateau model since around the age of 60 years the plateau has fully developed and occupies the majority of the axial lens thickness, leaving only a small region of lower index cortical material. Viewed another way, the young lens could be thought of a single ‘thick’ lens (the nucleus) with high index surrounded by several ‘thin’ lenses (cortical layers) of decreasing index. Each of the thin lenses adds refractive power, but with increasing age, there are fewer refracting thin lenses to contribute to the total lens power. It is interesting to note that the relatively recent evidence supporting a refractive index plateau is consistent with Gullstrand’s original observations that a reflex from the lens nucleus can only be observed beyond the age of about 30 years since a sharp increase in the index gradient is required to create the reflex.