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Quantitative 3-D Optical Coherence Tomography was used to measure surface topography of 36 isolated human lenses, and to evaluate the relationship between anterior and posterior lens surface shape and their changes with age. All lens surfaces were fitted to 6th order Zernike polynomials. Astigmatism was the predominant surface aberration in anterior and posterior lens surfaces (accounting for ~55% and ~63% of the variance respectively), followed by spherical terms, coma, trefoil and tetrafoil. The amount of anterior and posterior surface astigmatism did not vary significantly with age. The relative angle between anterior and posterior surface astigmatism axes was on average 36.5 deg, tended to decrease with age, and was >45 deg in 36.1% lenses. The anterior surface RMS spherical term, RMS coma and 3rd order RMS decreased significantly with age. In general, there was a statistically significant correlation between the 3rd and 4th order terms of the anterior and posterior surfaces. Understanding the coordination of anterior and posterior lens surface geometries and their topographical changes with age sheds light into the role of the lens in the optical properties of the eye and the lens aging mechanism.
© 2014 Optical Society of America
1. Introduction
The crystalline lens of the eye is a fascinating optical element, which, together with the cornea, transmits and refracts light to form an image of the world on the retina. The elastic young crystalline lens changes shape via constriction and/or relaxation of the ciliary muscle, resulting in a change of the optical power of the eye which provides a focused image of objects both near and far. With aging, the human lens becomes thicker, relatively steeper, and looses the ability to accommodate [1–3]. In addition, the crystalline lens shows a gradient refractive index (GRIN) distribution, which also changes with age [4–8]. Recent work has shown that in human [9], as well as monkey [10] and porcine lenses [4], both the lens shape and the GRIN play a role in the negative spherical aberration of the lens.
Despite its important contribution to the optical quality of the eye, several aspects of the crystalline lens are not known. The lens surface radii of curvature, and their changes with age and accommodation have been extensively measured both ex vivo, using, among other techniques, shadowphotography [11] and Optical Coherence Tomography (OCT) [12,13], and in vivo, using Purkinje imaging [14–16], Scheimpflug imaging [14,17], magnetic Resonance Imaging [18,19] and OCT [20]. Data ex vivo and in vivo differ primarily because the isolated lens appears in its maximally accommodated state, and therefore the young lens shows large steepening ex vivo. Ex vivo, the anterior and posterior lens surface radii of curvature tend to increase with age (at least up to past the presbyopia onset) [9,21], while in vivo, both surfaces tend to steepen with age [22].
Measurements of other geometrical aspects of the lens surfaces, such as their asphericity, are scarce. Manns et al. reported, for the first time, measurements of the lens asphericity ex vivo [21]. Interaction effects between lens radius of curvature and asphericity in the lens profile fittings suggest that those values should not be interpreted separately [23]. Dubbelman et al. showed that the asphericity of human lenses in vivo tends to increase with age for both anterior and posterior surface [22]. These results are in agreement with the report by Birkenfeld et al. on ex vivo lenses [9].
Much of the knowledge on the optics of the crystalline lens comes from wavefront aberration measurements. Hartmann-Shack measurements of the crystalline lens in rhesus monkeys by Roorda et al. suggest the presence of high order aberrations beyond spherical aberration [24]. Artal et al. measured the wavefront aberration of the crystalline lens in vivo neutralizing the contribution of the cornea by the use of goggles filled with solution [25]. Several works estimate the internal optics obtained by subtraction of the corneal aberrations from the total aberrations [25,26]. These studies confirm the previously reported balance between the positive spherical aberration of the cornea and the negative spherical aberration of the crystalline lens [27]. However, this methodology does not permit identification of the relative contribution of irregular shape in the crystalline lens and ocular misalignments to the lens wavefront aberration. In particular, there is evidence that the balance between horizontal coma in the cornea and the crystalline lens arises primarily from the eccentric position of the fovea, resulting in an angular separation between the line of sight and the optical axis, known as angle lamda [28,29].
Given its high accessibility, the corneal topography is well characterized. Corneal irregularities in the elevation map and astigmatism are common. Interestingly, the posterior corneal surface appears to compensate part of the errors of the anterior cornea. In particular, the posterior cornea has been reported to compensate around 3.5% of the coma of the anterior surface [30]. There are also numerous reports of the compensation of the corneal astigmatism by the astigmatism of the crystalline lens using corneal and refractive parameters [28,31–33]. However, to our knowledge, there is little information on possible compensations within the crystalline lens itself, i.e. between anterior and posterior surface or between its surfaces and its GRIN.
Early attempts to measure the astigmatism of the internal ocular surfaces involved the use of videokeratography, A-scan ultrasonography, and autorefractometry along with multi-meridional phakometric measurements of Purkinje images [34]. As recognized by the authors [35], the ophthalmo-phakometric method was prone to considerable accumulated experimental errors. However, the work reports some interesting findings, such as predominance of inverse astigmatism (defined as the one where the steeper meridian is in the horizontal axis) in the posterior cornea and in the posterior lens surface, while the astigmatism of the anterior surface of the lens was direct (defined as the one where the steeper meridian is in the vertical axis).
We have presented recently a quantitative 3-D OCT system which allows profilometry of the ocular surfaces of the eye [36,37]. This technique was used for measurements of corneal elevation maps in vivo [38], biometry and lens alignment [39], dynamic measurement of crystalline lens radii of curvature with accommodation [20] and crystalline lens surfaces elevation maps in vivo [40].
In this study, we have measured the elevation maps of the anterior and posterior lens surfaces of 36 isolated human donor lenses of different ages with quantitative 3-D OCT. These measurements ex vivo allowed direct access to the posterior surface of the lens, without potential distortions produced by the GRIN of the lens. To our knowledge, this is the first systematic study of the lens topography (including high order irregularities) and its change with age. Knowledge of the full lens topography and its age-related changes is important in the understanding of the relative contribution of the lens properties to the optical quality of the eye, possible through the use of ray tracing on custom eye models, as well as in investigating the changes undergone by the lens with aging. This information is particularly relevant in the design of correcting strategies in the eye, and specifically in cataract surgery, in which the crystalline lens of the eye is replaced by an artificial intraocular lens. Novel designs aim at finding inspiration from the natural young lens.
2. Methods
2.1 Lens specimens and preparation
Thirty-six isolated human crystalline lenses from twenty-eight human donor eyes were obtained from the BST Eye bank (Banc de Sang i Teixits, Barcelona, Spain). In all cases the cornea had been previously removed by the eye bank for clinical use. All eyes were shipped in sealed vials at 4°C, moisturized in preservation medium (DMEM/F-12, HEPES). Crystalline lenses with evident cataract formation and lenses with obvious surface damage were exclusion criteria in the study. Methods for securing human tissue were in compliance with the Declaration of Helsinki. The handling and experimental procedures, described in detail in a prior publication [9], have been approved by the institutional Review Boards of BST and Consejo Superior de Investigaciones Científicas (CSIC). The post-mortem time varied between 1 and 3 days at the time of the experiment. A typical experimental session lasted 1-2 hours.
2.2 Experimental sOCT setup and experimental protocols
The crystalline lenses were placed in a cuvette filled with a preservation medium (DMEM/F-12, HEPES, no phenol red, GIBCO) [41]. The lenses were measured with a custom developed OCT system, described in more detail in [42]. The illumination source of the OCT is a super luminescent diode (840-nm central wavelength, 50 nm (FWHM)). One complete 3-D image was composed by 1668 A-scans and 60 B-scans on a 12x12 mm region. The axial resolution was calculated to 6.9 μm in tissue.
The lens was immersed in the cuvette and placed on a ring. Centration of the lens for image acquisition was done using the visualization mode provided by the OCT, which displayed on the computer screen every 0.5 seconds two perpendicular B-scans passing through the OCT axis. The lens axis was aligned with the OCT scan axis such that a specular reflection was seen from both surfaces of the lens. The lens was first imaged with the anterior surface facing the OCT beam, and was then flipped around a predetermined axis and imaged again with the posterior surface up. To produce a complete image of the crystalline lens, two images were captured in each position, one with the OCT focused in the first surface visible (anterior in the anterior-up image and posterior in the posterior-up image), and another with the OCT focused in the second surface and showing the image of the cuvette holding the lens and the preservation media. The procedure was described in more detail elsewhere [9].
2.3 Lens surface elevations
Only the first lens surface imaged in each condition was analyzed in terms of elevation: anterior surface in anterior-up images and posterior in posterior-up images. The distortions present in this surface arising from the scanning architecture of the OCT system (fan distortion [37]) and the refractive index of the preservation medium were corrected. The other two surfaces visible in the OCT image were the second surface of the lens (posterior in anterior-up images and anterior in posterior-up images) and the cuvette. These two surfaces are also distorted by the unknown optics of the crystalline lens. The second surface of the lens was not used in this study but the image of the cuvette was used for alignment and to avoid possible rotations between the anterior-up and posterior-up images produced while flipping the lens [9].
To obtain the shape of the lens surfaces, a surface segmentation algorithm previously described [4] was used. The segmented surfaces were fit to biconical surfaces and spheres. The apex of the lens was used as a reference to center each surface. Lens surface elevation maps (obtained by subtraction of the best fitting spheres from the segmented surfaces) were fitted to 6th order Zernike polynomials. All fittings were done for a 6-mm diameter optical zone. Descriptive parameters of the lens surface geometries are radii of curvature and asphericities. Descriptive parameters of the surface elevation maps include individual surface Zernike coefficients (up to 6th order), and the root mean square (RMS) of combination of some terms (RMS astigmatism, RMS trefoil, RMS tetrafoil, RMS spherical terms, RMS coma and RMS 4th order Astigmatism), or Zernike orders (from 2nd order to 6th order RMS). We studied the changes of those parameters with age as well as relationships between the anterior and the posterior surfaces.
2.4. Lens orientation
As the relative angle of the lens with respect to the cornea and the body is unknown, for convention, all lenses were aligned such that the astigmatic axis of the anterior lens was on the vertical meridian (direct astigmatism). The magnitude of astigmatism (C) of each lens surface was computed using Eq. (1)
Where, are the radii of curvature as obtained from the biconic fittings, and and are the refractive indices of the lens’ surrounding medium and the lens cortex, respectively. Lack of reports of the index of refraction of the capsular bag prevented us from using that value in the calculations. Instead, and in keeping with previous publications [11,12], we used a surface refractive index of 1.3709. The refractive index of aqueous was assumed to be equal to the refractive index of water (1.332 at 635 nm). The angle of astigmatism of each surface was given byWhere J180 is the power at axis α = 0° = 180° and J45 is the power at axis α = 45° [43]The image of the cuvette was used to align the anterior-up and posterior-up images [9]. All OCT images were processed to obtain the shape of the lens surfaces and the surface of the cuvette, using algorithms described in detail in previous publications [6]. We aligned the anterior and posterior surfaces using the astigmatism vector of the cuvette segmented surface. This adjustment guaranteed that the lens could be treated as a whole, and therefore a rotation of the entire lens preserved the relative angle between anterior and posterior surface astigmatic axes.
The entire lens was rotated so that = 90 deg for the anterior lens, while keeping the astigmatism relative angle (-) constant. Elevation maps and individual Zernike terms are provided following rotation according to this convention (i.e. = 0 in all anterior lenses). Posterior elevation maps are shown by flipping the horizontal coordinates (i.e. by moving the observation point to the back of the lens). Since the convention used still leaves the vertical orientation as an unknown (i.e. the lenses could be rotated 180 deg) and we cannot distinguish between right and left eyes, the relative angles of astigmatism between the anterior and posterior surfaces are given in a 0-90 deg range.
2.5 Power vector analysis
To illustrate the distribution of anterior and posterior astigmatism in the lens sample, we present the magnitude of astigmatism and the relative angle between anterior and posterior astigmatism in a power vector graph [43,44]. The length of the vectors represents the calculated magnitude of surface astigmatism (in diopters,) and the directions of the vectors correspond to the relative angle between anterior and posterior astigmatism axis. All vectors were represented in a polar coordinate system. We studied the age-dependence of the astigmatism magnitude of the anterior and posterior surfaces as well as of the relative angle of astigmatism between those surfaces.
2.6 Correlation analysis
Changes in lens surfaces with age and relationships between the anterior and posterior lens surfaces were studied by linear regressions between the parameters describing the lens surface shape (radii of curvature, conic constants, Zernike polynomial coefficients and high order RMS) and age, and between the descriptive parameters of the anterior and posterior lens surfaces. The statistical significance levels were adjusted by a Bonferroni correction, applied to avoid potential Type 1 errors arising from multiple comparisons Significance level was established at p<0.05 for radii of curvature and conic constants, p<0.008 for RMS terms, p<0.01 for RMS orders and p<0.00017 for individual Zernike terms.
3. Results
3.1. Lens surface elevation maps
Figure 1 shows the two raw central OCT images that needed to be merged to obtain a complete anterior-up image of one of the crystalline lens, and segmented 3-D lens and cuvette surfaces. The fan distortion and the optical distortion due to the DMEM were corrected, and the shape of the cuvette was used to avoid rotations between anterior-up and posterior-up image.
Fig. 1 Upper panels: Anterior-up OCT images corresponding to the anterior-up position of one of the crystalline lenses imaged, with (a) OCT focused on the anterior surface and (b) OCT focused on the posterior surface and the image of the cuvette. The detected surfaces are also marked in blue (anterior surface) red (posterior surface) and green (cuvette). Lower panels: 3-D OCT data from images of the crystalline lens with (c) the anterior surface up and (d) the posterior surface up. The blue and red points correspond to the segmented anterior and posterior surfaces of the lens, respectively. The green points and the black points correspond to the cuvette imaged through the lens, therefore distorted by the lens, and the cuvette without distortion respectively.
Figure 2 shows Zernike fittings to the anterior and posterior lens surface elevations (relative to the best fitting sphere) for all lenses of the study, sorted by age. The first and third columns show the astigmatic Zernike terms only, and the second and fourth columns represent astigmatism and high order aberrations (up to the 6th order terms) of anterior and posterior surface respectively. Since, by convention, the lenses have been aligned such that the anterior lens steepest meridian is vertical, the anterior maps show only astigmatic component. In many cases the astigmatic axis of the posterior lens surface is rotated with respect to the anterior lens surface. Astigmatism dominates in some, but not all eyes. In general, there is a good correspondence between anterior and posterior lens surface maps. Also, certain degree of similarity occurs in the high order aberration maps of both eyes from the same donor eyes, marked with asterisks (lens#7&8, lens#11&12, lens#15&16, lens#17&18, lens#23&24, lens #27&28, lens #35&36). On average, for eye pairs from the same donor (the average correlation coefficients for the high order Zernike between eyes are r = 0.78 (p = 0.002) for the anterior and r = 0.53 (p = 0.03) for the posterior lens surface, while the average correlation coefficients when compared to eyes from other eyes are r = 0.10 and r = 0.17 for the anterior and posterior lens surface, respectively.
Fig. 2 Lens surface elevation maps for all lenses, ordered by age. By convention, the maps are aligned so that the steepest meridian of the anterior lens surface lies in the vertical axis. Anterior and posterior images are shown as mirrored in the vertical axis. Asterisks indicate pairs of lenses from the same donor.
3.2. Lens radii of curvature and asphericity: anterior/posterior lens relationships and changes with age
Figure 3 shows the radii of curvature in the steepest and flattest meridians (and) in the anterior and posterior lens surface as a function age, obtained from biconic fittings. Per definition, the steepest meridian is aligned vertically in the anterior lens surface, and the steepest and flattest meridians are orthogonal in both surfaces.
Fig. 3 (a) Radii of curvature of anterior and posterior lens surface at their corresponding steepest meridian as a function of age (b) Radii of curvature of anterior and posterior lens surface at their corresponding flattest meridian as a function of age. Data were obtained from fits to biconic surfaces. Open circles represent data of the anterior lens surface and solid circles represent data of the posterior lens surface.
Similarly to earlier reports for the average radii of curvature, both the radii of curvature in the flattest and steepest meridian increase statistically significantly with age (p≤0.003). The steepest and flattest meridians change at a rate of 95µm/year and 94μm/year, respectively, in the anterior lens, and 20μm/year and 19μm/year in the posterior lens.
We also studied the change in conic constant (k) with age. Figure 4 shows the conic constants in the steepest and flattest meridians for the anterior and posterior lens surfaces, obtained from biconic fittings. Both anterior and posterior lens conic constants shift from negative values towards more positive (or less negative) values with age, although the change is not statistically significant.
Fig. 4 (a) Conic constants of anterior and posterior lens surface at their corresponding steepest meridian as a function of age. (b) Conic constants of the posterior lens surface at their corresponding flattest meridian as a function of age. Data were obtained from fits to biconic surfaces. Open triangles represent data of the anterior lens surface and solid triangles represent data of the posterior lens surface.
3.3. Changes of lens surface astigmatism and relative astigmatic angle with age
The magnitude of lens surface astigmatism (calculated from and in Eq. (1)) ranged from 0.046 to 1.185 D (average: 0.563 ± 0.347 D) in the anterior lens and from 0.013 to 1.118 D (average: 0.553 ± 0.320 D) in the posterior lens. Figure 5(a) shows the variation of anterior and posterior lens surface astigmatism with age. For both lens surfaces, the changes with age were not statistically significant (p = 0.29 and p = 0.23 for anterior and posterior surface respectively). For 52.78% (anterior surface) and 41.67% (posterior surface) of the lenses the magnitude of astigmatism was between 0.2 and 0.6 D. Figure 5(b) shows the correlation of anterior and posterior lens surface astigmatism, which did not reach statistical significance (p = 0.226).
Fig. 5 (a) Magnitude of lens surface astigmatism in the anterior and posterior lens surface as a function of age. (b) Correlation of the magnitude of astigmatism between anterior and posterior surfaces
Figure 6 shows the power vector analysis for anterior and posterior lens surface astigmatism. By convention, the anterior lens astigmatism is aligned with the vertical steepest meridian, as shown in Fig. 6(a). This convention is adopted as a consequence of the lack of information on the actual orientation of the lens in vivo (up, down, nasal, temporal), resulting in a relative angle of astigmatism in a range between 0 and 90 deg (see Fig. 6(b)).
Fig. 6 (a) Anterior astigmatism power vector polar plot with the steepest meridian aligned at 90 deg, by convention; (b) Posterior astigmatism power vector polar plot. The angle (from the vertical axis) represents the relative angle between the anterior and posterior astigmatic axis. Each arrow represents one lens, the length of the vectors represent the magnitude of the corresponding astigmatism in diopters.
The relative angle between anterior and posterior astigmatism was on average 36.46 deg. In 36.1% of the lenses the relative angle was > 45 deg. Figure 7 shows the change of the relative angle of the astigmatic axis between the anterior and posterior lens surface with age. The relative angle tends to decrease with age, although the correlation is low (r = 0.305, p = 0.071). We did not find that the relative angle was correlated with the amount of astigmatism of either surface (not shown).
Fig. 7 Relative angle between anterior and posterior lens surface astigmatic axis as a function of age (Slope: −0.53 deg/year; r = 0.305; p = 0.071);
3.4. Lens elevation high order Zernike terms: anterior and posterior lens relationships
We tested the similarity of anterior and posterior lens topographies by evaluating the correlation of the high order Zernike terms in the anterior and posterior lens surfaces. We found that several high order Zernike terms were statistically significantly correlated in anterior and posterior lens surfaces. As an example, Fig. 8 shows linear regressions between anterior and posterior surface for vertical trefoil (), 3rd order RMS, RMS Coma and 4th order RMS.
Fig. 8 (a) Trefoil-v : Anterior vs. Posterior (Slope = 0.387,r = 0.467, p = 0.004) (b) RMS 3th order terms: Anterior vs. Posterior (Slope = 0.019; r = 0.477, p = 0.003; (c) RMS Coma: Anterior vs. Posterior (Slope = 0.387; r = 0.617, p = 0.0001) (d) 4th order RMS: Anterior vs. Posterior (Slope = 0.387.; r = 0.423, p = 0.010.)
Table 1 shows the mean and standard deviation of different parameters describing the shape of the anterior and posterior surface in terms of RMS, and its level of correlation with age. Also the last column shows the correlation between anterior and posterior lens surface elevation. We have found a strong correlation between surfaces of the RMS for 3rd order, 4rd order, coma, trefoil and spherical terms.
Table 1. Mean and standard deviation of the RMS of high-order Zernike coefficients for anterior and posterior lens surfaces. The Pearson correlation coefficient and the p-value are shown for the correlation with age of these parameters in each surface and between surfaces.
3.5. Lens elevation high order Zernike terms: changes with age
Figure 9 shows several Zernike surface elevation terms (in terms of RMS) as a function of age: (a) RMS coma (b) RMS spherical (c) 3rd order RMS, and (d) 5th order RMS, both for the anterior and posterior lens surfaces. RMS coma (Fig. 9(a)) decreased highly statistically significantly with age at a rate of 0.087μm/year and 0.123 μm /year for anterior and posterior surface, respectively. RMS spherical (Fig. 9(b)) and 3rd order RMS (Fig. 9(c)) decrease significantly with age for the anterior surface, but not for the posterior surface (RMS spherical: slope = −0.175 μm /year for anterior surface, slope = −0.05 μm /year for posterior surface; 3rd order RMS: slope = −0.083μm/year for anterior surface). 5th and 6th order RMS do not show statistically significant changes with age. Table 1 (4th and 5th columns) shows the correlations with age for different RMS orders.
Fig. 9 Lens elevation high order RMS terms; RMS coma: slope = −0.087μm/year, r = 0.582 and p = 0.0001for anterior surface, slope = −0.123μm/year, r = 0.515and p = 0.001 for posterior surface; (b) RMS spherical: slope = −0.175 μm /year, r = 0.439, p = 0.007 for anterior surface only (c) 3rd order RMS: slope = −0.083μm/year, r = 0.564 and p = 0.0001 for anterior surface only
3.6 Relative contribution of different Zernike terms to the lens surface elevations
Figure 10 shows the average relative contribution of lower and higher order Zernike terms in both surfaces. Relative contributions are accounted for in terms of variance (RMS2). Astigmatism is the predominant term both in the anterior surface (54.96%) and in the posterior surface (62.95%), followed by spherical (25.10%, 17.85%), coma (10.91%, 6.38%), trefoil (6.01%, 8.73%), tetrafoil (1.76%, 2.80%) and 4th order astigmatism (1.27%, 1.30%), for anterior and posterior surface, respectively. We also studied the change of these relative contribution with age (not shown) and found that for the anterior surface, the two predominant terms, astigmatism and spherical, change with age. The relative proportion of astigmatism increased with age at a rate of 0.702 /year (r = 0.427, p = 0.009), while the percentage of spherical term decreased significantly with age at a rate of −0.616/year (r = 0.474, p = 0.004). For the posterior surface, we only found a significant change in the proportion of coma (slope = −0.307/year, r = 0.450, p = 0.006).
Fig. 10 Relative contribution of different Zernike terms to the overall surface elevation maps (in terms of RMS2) with an asterisk the terms that change statistically significantly with age.
4. Discussion
We have studied the 3-D surface topography of 36 isolated human crystalline lenses, obtained using quantitative 3-D OCT. The lens surface shape has been described with radii of curvature, asphericity, and Zernike polynomials up to the 6th order. We have evaluated the correlations between the anterior and posterior lens surface shape and their changes with age.
The anterior and posterior crystalline lens surfaces have been usually described by the fitting parameters of conic functions (radius of curvature, and less frequently radius of curvature and asphericity), using measurements normally obtained from single meridians [17,21,22]. However, the direct measurements of lens surface elevations in 3-D in our study reveal that the human crystalline lens shows in fact non-spherically symmetric surfaces. Our data show the presence of astigmatism and, to a lesser extent, other high order contributions (trefoil, spherical, coma and tetrafoil). Previous studies comparing corneal and total astigmatism predicted the presence of astigmatism in the lens, which in many cases, has a compensatory effect for corneal astigmatism [25,28].
Our study shows that both the anterior and posterior lens surfaces contribute to lens astigmatism. The surface astigmatic power in our lens sample ranged from 0.046 to 1.185 D in the anterior lens surface, and from 0.013 to 1.118 D in the posterior lens surface. However, the presence of a gradient refractive index (GRIN) distribution may play a role in the overall astigmatism of the lens. Whether GRIN has a compensatory role in lens astigmatism remains to be investigated. OCT-based measurements of lens GRIN in multiple meridians in isolated lenses [9] will help to get insights on the contribution of GRIN to astigmatism. We can only speculate on the factors contributing to lobular Zernike surface terms such as trefoil and tetrafoil, which might be related to suture branching. In a work by Gargallo et al. [45], lens aberrations in several species with Y-suture branches were analyzed for their relationship with suture distribution. A high degree of correlation between suture orientation and the axis of no rotationally symmetric wavefront aberrations was found.
In keeping with prior studies, we found changes in lens shape with aging for both, anterior and posterior lens surface. The increased steepness and negative asphericity in isolated young lenses is consistent with the fact that isolated lenses are maximally accommodated. The flattening (increased radius of curvature) and rounding (shift of asphericity towards less negative values) with age of the anterior lens surface is consistent with other studies in the literature using alternative techniques [11,17,46].
We did not find a strong correlation between surface astigmatism and age, but there were statistically highly significant correlations in the anterior lens surface for RMS 3rd and RMS 4th order Zernike term, RMS spherical, and RMS coma (p <0.008), which all decreased with age. No significant correlation was found with age for surface tetrafoil and high order lobular terms, in general. Although, if lobular terms are associated with the presence of lens sutures, we would have expected an increase of the higher order terms with age, as the number of suture branches increases with aging. However, it has been shown that the formation of new branching structures is highly slowed down at older ages [47]. Our OCT data did not provide a three-dimensional view of the lens branching, although more refined imaging modalities revealing these structures could allow modeling of the potential relationships between branching and trefoil and tetrafoil terms.
To our knowledge, this is the first comprehensive topographic study of the human lens with aging. A previous study from our laboratory showed the ability to measure crystalline lens anterior and posterior surface elevation maps in vivo using sOCT, and demonstrated it on three human young subjects in vivo. Besides the fully accommodated state of the isolated lens and potential changes post-mortem, there may be other differences between in vivo and ex vivo conditions. For example, the zonular tension in the un-accommodated condition may cause further high order contributions to lens surface elevation in vivo (besides the flattening of the lens). Also, the up-right orientation of the lens in vivo (as opposed to the horizontal one in our ex vivo measurements) may create some changes associated to gravity.
Two of the three eyes measured in vivo in our earlier study showed perpendicular astigmatism axes in the anterior and posterior lens, whereas the astigmatic axes in our study tended to differ on average only 36.46 deg. In 13 of the 36 lenses the relative angle was >45 deg, and 6 lenses had a relative angle >70 deg. The average relative angle was larger for younger lenses (41.74 deg for lenses <50 years) than for older lenses (28.1 deg for lenses ≥50 years), indicating a higher compensation of astigmatism between the lens surfaces at a younger age.
Finally, the lack of a reference for the lenses ex vivo prevented from analyzing the relative axis of astigmatism with corneal astigmatism (and therefore evaluation of potential compensatory effects between the surfaces of the cornea and lens and their changes with aging) and possible changes in the anterior lens surface astigmatic axis with aging. For example, it is well known that corneal astigmatism changes from with-the-rule to against-the-rule astigmatism with aging [48–50]. Previous studies suggested that the astigmatism axis of the anterior lens surface is vertical [51–53]. We did not find a significant correlation between anterior or posterior astigmatism axis and age. However, the tendency of the relative angle to decrease with age could be interpreted as a decrease of the anterior by posterior astigmatism balance with age.
Regardless potentially additional information provided by future in vivo studies of lens surface topography and its changes with age, our study shows that astigmatism and high order terms may be considered when trying to predict optical quality of a phakic eye at an individual level, based on anatomical information. This information could be used in a ray tracing analysis that incorporates data from cornea and lens GRIN distribution [21,52,54,55].
Acknowledgments
This study has been funded by Spanish Government Grant FIS2011-25637 (SM), European Research Council ERC-2011 AdG-294099 (SM), Marie Curie Actions-Networks of Initial Training (ITN) FP7-PEOPLE-2010-ITN 264605 (OpAL-Optical and adaptational limits of vision) (MS), Consejo Superior de Investigaciones Científicas Junta de Ampliación de Estudios (CSIC JAE)-Pre Program (JB). The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement 294099.
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