Changes in Corneal Wavefront Aberrations with Aging
Tetsuro Oshika,1 Stephen D. Klyce,2 Raymond A. Applegate,5 and Howard C. Howland4
PURPOSE. TO
investigate whether corneal wavefront aberrations vary with aging.
METHODS. One hundred two eyes of 102 normal subjects were evaluated with videokeratography.
The data were decomposed using Taylor and Zernike polynomials to calculate the monochromatic
aberrations of the cornea for both small (3-mm) and large (7-mm) pupils.
RESULTS. For
a 3-mm pupil, the amount of total aberrations (Spearman rank correlation coefficient
rs = 0.145; P = 0.103) and spherical-like aberrations (rs = -0.068; P = 0.448) did not change with
aging, whereas comalike aberrations exhibited a weak but statistically significant correlation with
age (rs = 0.256; P = 0.004). For a 7-mm pupil, total aberrations (rs = 0.552; P < 0.001) and
comalike aberrations (rs = 0.561; P < 0.001) significantly increased with aging, but spherical-like
aberrations showed no age-related changes (rs = 0.124; P = 0.166). Simulated pupillary dilation
from 3 mm to 7 mm caused a 38.0 ± 28.5-fold increase in the total aberrations, and the extent of
increases significantly correlated with age (rs = 0.354; P < 0.001). Pupillary dilation influenced the
comalike aberrations more in the older subjects than in the younger subjects (rs = 0.243; P =
0.006), but such age dependence was not found for spherical-like aberrations (rs = 0.141; P =
0.115).
Comalike aberrations of the cornea correlate with age, implying that the corneas
become less symmetrical along with aging. Spherical-like aberrations do not vary significantly with
aging. Pupillary dilation markedly increases wavefront aberrations, and those effects are more
prominent in older subjects than in younger subjects. (Invest Ophthalmol Vis Sci. 1999;40:
1351-1355)
CONCLUSIONS.
I
t has been well documented that naturally occurring astigmatism, in either keratometry1"7 or refraction,8"10 shifts
from a pattern of "with-the-rule" to "against-the-rule" with
aging. Age-related changes in chromatic aberrations of the eye
have been investigated.1 '~13 However, no studies are available
on the relationship between monochromatic aberrations and
age.
With an increasing number of keratorefractive surgical
procedures performed annually, their influence on the optical
quality of the cornea gathers more attention. Recent studies
have indicated that higher order monochromatic aberrations of
the cornea significantly increased after radial keratotomy,14-16
photorefractive keratectomy,17"20 and laser in situ keratom-
From the 'Department of Ophthalmology, University of Tokyo
School of Medicine, Japan; Louisiana State University Eye Center, New
Orleans; the 'Department of Ophthalmology, School of Medicine,
University of Texas Health Science Center at San Antonio; and the
"'Neurobiology and Behavior Section, Cornell University, Ithaca, New
York.
Supported in part by Grants EYO3311 (SDK) and EY02377 (Louisiana State University Eye Center) from the US Public Health Service,
Washington, D.C.; Grants EY08520 and EYO852O-O3S1 (RAA) and
EY02994 (HCH) from the National Eye Institute, National Institutes of
Health, Bethesda, Maryland; a San Antonio Area Foundation Grant
(RAA); and an unrestricted research grant to the Department of Ophthalmology, University of Texas Health Science Center at San Antonio,
from Research to Prevent Blindness, New York, New York.
Submitted for publication August 13, 1998; revised January 8,
1999; accepted February 18, 1999Proprietary interest category: Cl, C5 (SK); N (TO, TA, HH).
Reprint requests: Tetsuro Oshika, Department of Ophthalmology,
University of Tokyo School of Medicine, 7-3-1 Hongo, Bunkyo-ku,
Tokyo, 113-8655 Japan.
Investigative Ophthalmology & Visual Science, June 1999, Vol. 40, No. 7
Copyright © Association for Research in Vision and Ophthalmology
ileusis.20 Further, it has been shown that the increase in corneal aberrations is associated with a decrease in visual performance after radial keratotomy.21 Thus, the wavefront
aberrations of the cornea are now not only of investigational
interest, but also of clinical interest.22'23 In this situation, basic
data regarding monochromatic aberrations, such as changes
due to aging, are essential. We conducted the present study to
assess the influence of aging on the aberrations of the cornea.
SUBJECTS AND METHODS
The study was conducted according to the tenets of the Declaration of Helsinki. One hundred two eyes of 102 subjects
were evaluated. They did not have any ocular disease except
for age-related cataract and mild refractive errors, including
myopia, hyperopia, and regular forms of astigmatism (less than
1.5 D). None of them was wearing contact lenses. They were
selected from the patients who visited the Department of
Ophthalmology, University of Tokyo School of Medicine, for
ocular examination. Their ages ranged from 9 to 85 years
(Table 1). All the subjects were Japanese; there were 48 men
and 54 women.
Videokeratographic data were obtained with computerized videokeratography (TMS-1; Computed Anatomy, New
York, NY). For each eye, measurements were repeated at least
three times to obtain a well-focused, properly aligned image of
the eye. The files containing information about corneal elevation, curvature, power, and position of the pupil were downloaded on a removable media and used for the following
analysis.
The calculation of wavefront aberrations was performed
using the descriptive polynomial method of Howland and
1351
1352
Oshika et al.
IOVS, June 1999, Vol. 40, No. 7
TABLE 1. Age Range and Refractive Status of Subjects
Age
<20
21-30
31-40
41-50
51-60
61-70
^71
Total group
Eyes
16
15
14
15
14
15
13
102
Spherical
equivalent
(D)
-1.0 ±
-0.8 ±
-1.2 ±
-1.4 ±
-1.1 ±
-0.7 ±
-0.9 ±
-1.1 ±
1.3
1.4
2.0
0.8
1.6
1.1
1.2
1.6
Astigmatism
(D)
0.15
0.17
0.18
0.26
0.19
0.21
0.25
0.19
±0.19
± 0.24
± 0.37
± 0.26
± 0.36
± 0.44
± 0.35
± 0.37
Data are expressed as means ± SD.
Howland.24 The center of the pupil was identified on the
topography video screen, and its deviation from the videokeratographic axis was measured. Using the method of least
squares, the reference sphere for each eye was calculated by
determining the best-fit sphere to the elevation data over the
3-mm area centered on the pupil. The elevations of the best-fit
sphere were subtracted from the measured elevations to define
a surface termed the remainder lens. To calculate the optical
effects of the remainder lens, the elevations of that lens were
multiplied by 0.3375 (the keratometric index of refraction of
the cornea minus the refractive index of air). Using the method
of least squares, the resultant data were fit with the Taylor
polynomial of the form24 ~26:
W(x,y) = A + Bx + Cy + Dx2 + Exy + Fy2 + Gx5 + Hx2y
+ Ixy2 + Jy5 + Kx4 + Lx^y + Mx2y2 + Nxy* + Oy4
+ Px5 + Qx4y + Rx5y2 + SxY + Txy4 + Uy5 + Vx6
(7)
+ Wx^y + Xx4y2 + Yx*y* + Zx2y4 + A&y5 +
where (x(y) are Cartesian coordinates of the cornea in millimeters with their origin being taken on the pupil center. This is a
two-dimensional, sixth-order Taylor representation of the
wave-aberration surface with the positive axis pointing away
from the retina. The coefficients were scaled so that the function W(x j/) was expressed in micrometers when x and y were
expressed in millimeters. A represents a shift of the entire
wavefront along the optical axis; B and C represent the vertical
and horizontal prism components. D through E include the
conventional ophthalmic prescription: sphere, cylinder, and
axis. G through / express comalike aberration, and K through
O express spherical-like aberration.24 P through U are the
fifth-order Taylor coefficients, and V through A^ denote the
sixth-order Taylor coefficients.
The Taylor polynomial was then converted to the Zernike
polynomial to obtain orthogonal coefficients.24'27 Zernike coefficients 7 through 28 (Z7 through Z28) were calculated from
linear combinations of Taylor coefficients as described by Howland and Howland.23 Coefficients Z7 through Z10 correspond
to comalike aberration, Z n through Z l 5 correspond to spherical-like aberration, Z, 6 through Z2, express the fifth-order
Zernike coefficients, and Z22 through Z 28 are the sixth-order
Zernike coefficients.
These Zernike coefficients were then used to calculate the
global descriptors of monochromatic corneal aberrations,
which are represented by the terms, S3, S4, 55, and S6. Because
spherical and coma aberrations refer to symmetrical systems
and the eye is not rotationally symmetrical, the terms sphericallike and comalike aberrations are used in this article. The 5 3
(third-order component of the wavefront aberration) represents the mean squared wavefront variance from that of a
perfect spherocylinder caused by comalike aberration. Similarly, S4 (fourth-order component of the wavefront aberration)
represents the mean squared wavefront variance from that of a
perfect spherocylinder caused by spherical-like aberration. 55
and S6 are the fifth- and sixth-order components of the wavefront aberrations, respectively. Because the variances of each
term are independent, the total wavefront variance was computed by summing the individual variances and served as a
parameter of total wavefront aberrations (Su). The odd-order
aberrations (S3 + 55) were summed to examine the magnitude
of comalike aberrations, and the even-order aberrations (54 +
56) were summed to evaluate the changes in spherical-like
aberrations. These calculations were used for both 3-mm and
7-mm pupils.20
RESULTS
For a 3-mm pupil, the amount of total aberrations (Su) did not
change with aging (Spearman rank correlation coefficient rs —
0.145; P = 0.103; Fig. 1), whereas comalike aberrations (S3 +
55) exhibited a weak, but statistically significant correlation
with age (rs = 0.256; P = 0.004; Fig. 2). Spherical-like aberrations (S4 + 5g) did not correlate with age (rs = -0.068; P =
0.448; Fig. 3).
For a 7-mm pupil, total aberrations (rs = 0.552; P < 0.001;
Fig. 4) and comalike aberrations (rs = 0.561; P < 0.001; Fig. 5)
exhibited statistically significant positive correlations with age.
Even when two extremely large values in Figures 4 and 5 were
excluded from the analyses, the correlations remained statistically significant for total aberrations (rs = 0.533; P < 0.001)
and comalike aberrations (rs = 0.543; P < 0.001). Sphericallike aberrations showed no age-related changes (rs = 0.124;
P = 0.166; Fig. 6).
Simulated pupillary dilation from 3 mm to 7 mm caused a
38.0 ± 28.5-fold increase (mean ± SD) in total aberrations, and
0.10
40
60
100
Age (years)
FIGURE 1. Correlation between age and total wavefront aberrations
(Su) for a 3-mm pupil (nonsignificant; Spearman rank correlation coefficient r s = 0.145; P = 0.103).
Corneal Aberrations and Age
IOVS, June 1999, Vol. 40, No. 7
0.04
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•
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60
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FIGURE 2. Statistically significant correlation between age and comalike aberrations (5 3 + 55) for a 3-mm pupil (Spearman rank correlation coefficient rs = 0.256; P = 0.004).
FIGURE 4. Statistically significant correlation between age and total
wavefront aberrations (Su) for a 7-mm pupil (Spearman rank correlation coefficient rs = 0.552; P < 0.001).
the extent of increases by pupillary dilation showed statistically
significant correlation with age (rs = 0.354; P < 0.001; Fig. 7).
Similarly, pupillary dilation influenced the comalike aberrations more in the older subjects than in the younger subjects
(rs = 0.243; P = 0.006; Fig. 8), but such age dependence was
not found for spherical-like aberrations (rs = 0.141; P = 0.115;
Fig. 9).
did not show any age-related changes for both 3- and 7-mm
pupils, implying that the central-to-peripheral balance of the
corneal curvature is not significantly affected by increasing age.
It should be noted that increases in the corneal comalike
aberrations in the elderly do not directly indicate the deterioration of visual function in their eyes for several reasons. First,
the pupils of older subjects tend to be more miotic,28'29 resulting in a smaller influence of the corneal wavefront aberrations
on visual performance. Secondly, aberrations of the crystalline
lens were not considered in the present study. In contrast to
the spherical aberrations of the lens,30"32 little is known about
the lenticular coma aberrations. It was anticipated that comalike aberrations introduced by corneal asymmetries are similar in magnitude to those measured for the eye as a whole,
suggesting that these aberrations originate mainly in the cornea.33 However, proof of this hypothesis must wait until the
relative contributions of cornea and crystalline lens are elucidated. Thirdly, the Stiles-Crawford effect34 was not considered
in these calculations. However, the Stiles-Crawford effect is
retinal in origin and does not alter the aberration or the change
of aberration with age of the cornea or eye. Although it has
DISCUSSION
In our study population of 102 eyes, we found a weak but
statistically significant correlation (rs = 0.256; P = 0.004)
between age and comalike aberrations for a 3-mm pupil. For a
7-mm pupil, comalike aberrations exhibited significant positive
correlations with age (rs = 0.561; P < 0.001). Although we
may not be able to apply the current results to subjects of all
races and refractive status, it is suggested that comalike aberrations of the cornea tend to show age-related changes. Because comalike aberrations consist of tilt and/or asymmetry,
these results imply that the corneas become less symmetric
along with aging. On the contrary, spherical-like aberrations
0.04
.
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0.03
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t
Sphe
o
0.00
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*
20
40
60
•
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'v • : :ft:
80
o
100
Age (years)
FIGURE 3. Correlation between age and spherical-like aberrations (54
+ 56) for a 3-mm pupil (nonsignificant; Spearman rank correlation
coefficient r s = -0.068; P = 0.448).
40
60
80
100
Age (years)
FIGURE 5. Statistically significant correlation between age and comalike aberrations (5 3 + 55) for a 7-mm pupil (Spearman rank correlation coefficient r s = 0.561; P < 0.001).
1354
Oshika et al.
IOVS, June 1999, Vol. 40, No. 7
•
0.8
w
0.6
re
o.
re
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=
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•
•
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•
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in
20
•'*.:
40
.'#
60
80
40
100
80
60
100
Age (years)
Age (years)
FIGURE 6. Statistically significant correlation between age and spherical-like aberrations (SA + 56) for a 7-mrn pupil (Spearman rank correlation coefficient rs = 0.124; P - 0.166).
been claimed that the Stiles-Crawford effect reduces the impact of optical aberrations on vision, a recent analysis showed
that the effect on vision is very small.35
Simulated pupillary dilation from 3 mm to 7 mm markedly
increased the total aberrations and comalike aberrations; those
influences were significantly larger in the older subjects than in
the younger subjects (Figs. 7, 8). The data, especially in those
with a 7-mm pupil, may have been influenced by the limitations of the Placido-based videokeratography in accurately capturing data from the peripheral cornea, although the obvious
increases (38.0-fold increases) associated with pupillary dilation seemed to be sufficiently meaningful. These results have
clinical relevance in situations in which pupillary abnormalities
are encountered as a consequence of complications of intraocular surgery, such as atonic,36"38 eccentric,39'40 and overly
stretched pupils.41'42 It has been known that when the pupil is
made eccentric, spherical aberrations cause coma,43 which
adds to the preexisting comalike aberrations. Even under normal concessions, the pupillary size increases with dim illumination in all age groups.44 Applegate et al.21 have reported that
FIGURE 8. Statistically significant correlation between age and the
magnitude of increases in comalike aberrations (5 3 + 5 5 ) induced by
simulated pupillary dilation from 3 mm to 7 mm (Spearman rank
correlation coefficient rs = 0.243; P = 0.006).
a 1-log-unit change in wavefront variance induces a 0.23
change in the area under the log contrast-sensitivity function.
They also reported that a 1-log-unit change in wavefront variance induces a 0.22 logarithmic minimum angle of resolution
(logMAR) loss in high-contrast Bailey-Lovie visual acuity (2+
line) and a 0.32 logMAR loss in low-contrast Bailey-Lovie visual
acuity (3+ line) for a 7-mm pupil.45 With this in mind, it is
interesting that contrast sensitivity has been reported to be
stable through the fifth decade,46'47 followed by a monotonic
decrease from the sixth decade on.''5 In the present study, we
found little, if any, systemic changes in the aberration through
the fifth decade, with most large aberration values occurring
after the age of 60 (Fig. 4). Although this armchair analysis is
intriguing and worth noting in passing, it is likely that other
factors such as lens scattering may play a significant role in the
loss of visual function in the over-60 group. We offer the
current results as a reference for future studies on the monochromatic aberrations of the cornea and their contribution to
the total aberrations of the eye.
300
150
•
•S
re rr
£
0 CI
z
200
n
•
•
re ir
•
•="§•
Q.^" 100
•
re
cc
40
60
100
Age (years)
FIGURE 7. Statistically significant correlation between age and the
magnitude of increases in total wavefront aberrations (Su) induced by
simulated pupillary dilation from 3 mm to 7 mm (Spearman rank
correlation coefficient r s = 0.354; P < 0.001).
•
•
• •
•
20
•
•
•
s.
—-•—
40
• ••
••
60
•
e
80
100
Age (years)
FIGURE 9. Statistically significant correlation between age and the
magnitude of increases in spherical-like aberrations (5 4 + 56) induced
by simulated pupillary dilation from 3 mm to 7 mm (Spearman rank
correlation coefficient rs = 0.141; P = 0.115).
IOVS, June 1999, Vol. 40, No. 7
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