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Vision Research 43 (2003) 2363–2375
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Changes in the internal structure of the human crystalline lens
with age and accommodation
M. Dubbelman a, G.L. Van der Heijde
a
a,*
, H.A. Weeber b, G.F.J.M. Vrensen
c
Department of Physics and Medical Technology, VU Medical Centre, P.O. Box 7057, 1007 MB, Amsterdam, The Netherlands
b
Applied Research, Pharmacia, P.O. Box 901, 9700 AX Groningen, The Netherlands
c
Department of Ophthalmology, Leiden University Medical Centre, P.O. Box 9600, 2300 RC Leiden, The Netherlands
Received 29 August 2002; received in revised form 29 January 2003
Abstract
Scheimpflug images were made of the unaccommodated and accommodated right eye of 102 subjects ranging in age between 16
and 65 years. In contrast with earlier Scheimpflug studies, the images were corrected for distortion due to the geometry of the
Scheimpflug camera and the refraction of the cornea and the lens itself. The different nuclear and cortical layers of the human
crystalline lens were determined using densitometry and it was investigated how the thickness of these layers change with age and
accommodation. The results show that, with age, the increase in thickness of the cortex is approximately 7 times greater than that of
the nucleus. The increase in thickness of the anterior cortex was found to be 1.5 times greater than that of the posterior cortex. It was
also found that specific parts of the cortex, known as C1 and C3, showed no significant change in thickness with age, and that the
thickening of the cortex is entirely due to the increase in thickness of the C2 zone. With age, the distance between the sulcus (centre
of the nucleus) and the cornea does not change. With accommodation, the nucleus becomes thicker, but the thickness of the cortex
remains constant.
Ó 2003 Elsevier Ltd. All rights reserved.
Keywords: Aging; Accommodation; Crystalline lens; Scheimpflug photography; Cortex; Nucleus
1. Introduction
The Scheimpflug camera provides high-contrast images that contain detailed information about the internal structure of the human crystalline lens, which makes
it possible to determine changes within the lens with age
and accommodation. Knowledge about these changes is
of importance in understanding how the human eye is
able to focus on near or far objects (the mechanism of
accommodation) and why this ability deteriorates with
age (presbyopia). Furthermore, knowledge about the
change in the internal structure of the lens is necessary
for optical modelling of the human eye and mechanical
modelling of the accommodation system.
The human lens continues to grow throughout life,
due to the addition of new lens fibres. With age, the lens
becomes more convex (Dubbelman & Van der Heijde,
*
Corresponding author. Fax: +31-20-4444147.
E-mail address: [email protected] (G.L. Van der Heijde).
0042-6989/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/S0042-6989(03)00428-0
2001) and thicker in the sagittal direction at a rate of
approximately 0.024 mm/years (Dubbelman, Van der
Heijde, & Weeber, 2001). The various anatomic regions
within the human lens are generally divided into two
main regions: the nucleus and the cortex. It is convenient
to take the dividing line between cortex and nucleus as
the point of sudden reduction in brightness on the
Scheimpflug image (Fig. 1). Several authors have used
Scheimpflug photography to measure the increase in
thickness of the cortex and nucleus of the normal human
lens. Brown (1976) found that the growth of the cortex
was three times the growth of the nucleus. According to
Shibata, Hockwin, Weigelin, Kleifeld, and Dragomirescu (1984) and Kashima, Trus, Unser, Edwards, and
Datiles (1993), this growth of the cortex would be 1.5
and 1.75 times the growth of the nucleus. Cook, Koretz,
Pfahnl, Hyun, and Kaufman (1994) even measured a
decrease of 3 lm/years in the thickness of the nucleus
with age.
Studies that are more detailed showed that alternating light and dark zones could be distinguished within
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M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
Fig. 1. Scheimpflug image of the eye of a 51 year-old female. Using the
densitogram above the image, 8 different zones can be distinguished.
Using the local maximums of the gradient of the densitogram under
the picture, three different cortical zones (C1–C3) can be defined according to the Oxford system.
the anterior and posterior cortex (Goldmann, 1964).
According to the zone system developed by Sparrow,
Bron, Brown, Ayliffe, and Hill (1986), these cortical
zones could be sub-divided into four zones: C1–C4.
Zone C1, which is located behind the anterior and just in
front of the posterior capsule, and C3 are zones of high
light scatter, whereas C2 and C4 are dark zones of low
light scatter (Fig. 1). The thickness of zone C4 can
usually not be determined accurately. The changes with
age in the thickness of zones C1–C3 of the anterior
cortex have been measured by Smith, Smith, Brown,
Bron, and Harris (1992). It appeared that most of the
growth of the lens occurred in zone C2, while C3 showed
little increase in thickness after it had been established
during the second decade of life. The thickness of zone
C1 showed a tendency to decrease with age.
It is suggested that the growth of the lens is slowed
down by the process of compaction (the compression of
existing fibres) (Bron, Vrensen, Koretz, Maraini, &
Harding, 2000). This term was used by Brown (1976) to
explain why glaucoma flecks and traumatic cataracts
sank into the cortex of the lens at a faster rate than
could be expected on account of the average growth of
the lens due the addition of new lens fibres. Support for
nuclear compaction has also come from the earlier
mentioned study carried out by Cook et al. (1994), in
which a decrease in nuclear thickness with age was
found. Further support came from the measurement of
a small group of patients with lamellar cataract, in
whom shrinkage of the lamellar shell of opacity could be
determined, particularly in the sagittal plane (Brown,
Sparrow, & Bron, 1988). In vitro, compaction in the
embryonic nucleus with age has been demonstrated (AlGhoul et al., 2001). The process of compaction has,
however, been questioned by Pierscionek and Weale
(1995).
The change in the internal structure of the lens during
accommodation has been measured in three studies
(Brown, 1973; Koretz, Cook, & Kaufman, 1997; Patnaik, 1967), from which it appeared that the accommodative increase in the sagittal lens thickness could be
attributed to an increase in the thickness of the lens
nucleus, while the thickness of the cortex remained almost unchanged.
Using optical techniques, such as Scheimpflug imaging, the internal structure of the lens is observed through
the preceding refractive surfaces, i.e. the cornea and the
anterior lens surface. The refraction at these surfaces
will distort the shape of the internal structure of the lens
(Richards, Russell, & Andersson, 1988; Dubbelman &
Van der Heijde, 2001). Up till now, in all studies measuring the internal structure of the lens with age or accommodation no attempt has been made to correct the
Scheimpflug images for this type of distortion. In most
studies, a correction was made for the distortion due to
the geometry of the Scheimpflug imaging system, in
which the object and/or image plane is tilted (Ray,
1995). However, correction for the refraction of cornea
and lens is also necessary to obtain accurate measurements of the internal structure of the lens and to determine age-related trends.
The purpose of the present investigation was therefore to correct for both types of distortion and to
measure the change in the internal structure of the
crystalline eye lens with age and accommodation.
Scheimpflug images were made of the eyes of subjects of
various ages at different accommodation levels. Individual ray tracing was applied to correct for the refraction of the front and back surface of the cornea and
the front surface of the lens. However, to make it possible to correct for the latter, the refractive index of the
lens is needed. Therefore, axial length was measured to
calculate the equivalent refractive index of the crystalline lens. Using this method to correct the Scheimpflug
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
images, it is possible to exclude artefacts that are due to
optical distortions and to provide an accurate measurement of the changes that take place in the internal
structure of the aging and accommodating lens.
2. Methods
2.1. Measurements
The sample population and the experimental design
have been described elsewhere in detail (Dubbelman &
Van der Heijde, 2001; Dubbelman et al., 2001). Briefly,
Scheimpflug images were made of the right eye of 102
healthy subjects aged between 16 and 65 years, who had
no history of eye injury or systemic disorders. Experiments were performed with the understanding and
written consent of each subject. After full pupil dilation
of the right eye (phenylephrine HCl 5%), refractive error
and astigmatism of both eyes was measured with a
Topcon KR-3500 autokerato-refractometer and subjects
with astigmatism larger than 1.5 D were excluded. A
topogram of the cornea of the right eye was made with
the Keratron corneal analyser (Optikon, 2000). Images
of the anterior segment of the right eye were made with
the Nidek Eas-1000 Scheimpflug camera (Nidek Co.
Ltd., Japan) (Sakamoto & Sasaki, 1994; Sasaki, Sakamoto, Shibata, & Emori, 1990), which was equipped
with a black and white CCD camera. The subject was
seated with the head in an upright position, and the slit
beam of the Scheimpflug was vertically oriented.
The left eye was used to focus on an accommodation
stimulus, while the right eye was photographed. The
accommodation stimulus was an illuminated black
Maltese star, which was located 1m from the left eye. To
obtain the unaccommodated state of the eye, a +1 D
lens and the refractive correction were placed in a lensholder directly in front of the left eye. The subject
concentrated first with the right eye on the fixation light
in the Scheimpflug camera and the camera was adjusted
along the optical axis of the eye by positioning the
corneal reflex in the centre of the pupil. Subsequently,
the subject fixated with the left eye on the accommodation stimulus, of which the position could be varied
by remote control until the subject confirmed that the
fixation light was superimposed on the centre of the
Maltese star. When the subject indicated that the Maltese star was clearly in focus, a Scheimpflug image was
made of the right eye. The subject was then asked to try
to maintain focus on the Maltese star, while negative
lenses in steps of )1 D were placed in front of the left eye
until the subject indicated that it was no longer possible
to focus sharply on the star. Each time, the front surface
of the cornea was imaged real time on the monitor
screen, and convergence was corrected by changing the
position of the Maltese star until the corneal reflex re-
2365
turned to the centre of the pupil. Because of limited
range of movement of the Maltese star, it was not possible to correct for convergence when accommodation
levels were higher than 8 D, and consequently, those
levels were not measured. Using the position and power
of the different lenses placed in front of the eye, the
accommodation stimulus was converted to the accommodation at the corneal plane (Rabie, Steele, & Davies,
1986). For this moment, we will not distinguish between
the real accommodative response of the eye and the
accommodative stimulus presented, but we will come
back to this at the end of paragraph 4.1. Finally, in
subjects whose posterior lens surface was clearly visible
on the Scheimpflug images, axial length was measured
with the IOL Master â Zeiss. This made it possible to
calculate the equivalent refractive index of the lens,
which was needed to correct for the refraction of the lens
itself. If this was not possible, correction was made with
the age-dependent equivalent refractive index (Dubbelman & Van der Heijde, 2001; Dubbelman et al., 2001).
2.2. Analysis of measurements
The initial stage of the analysis was to identify the
different zones within the lens. Fig. 1 shows a Scheimpflug image of an unaccommodated eye of a 51 yearold female. Two different classifications systems were
used, to distinguish the different zones on the Scheimpflug image. Firstly, a system often used in cataract
research (Hockwin, Dragomirescu, & Laser, 1982; Shibata et al., 1984; Wegener & Laser, 1996), which specifically distinguishes between the nuclear and the
cortical zones. This system makes use of the densitogram of the lens indicated in the upper part of Fig. 1,
which consists of the grey values along a sagittal strip
measuring 8 pixels (1 pixel ¼ ±0.025 mm) on either side
of the line through the vertex of the anterior lens surface. The densitograms were sub-divided into eight
zones, according to the course of the curve (local minima) representing: (1) anterior capsule and superficial
anterior cortex, (2) anterior cortex, (3) anterior supranuclear region, (4) anterior nucleus, (5) posterior nucleus, (6) posterior supranuclear region, (7) posterior
cortex, (8) posterior capsule and superficial posterior
cortex. The second system distinguishes different layers
in the anterior and posterior cortex, and is part of the
ÔOxford clinical cataract classification and grading systemÕ (Brown & Bron, 1996; Sparrow et al., 1986).
Strictly speaking, zone C1 consists of two narrow zones
behind the capsule: the low scatter zone behind the
narrow high scatter peak of the capsule (C1 a) and of
the subsequent high scatter zone (C1 b), which has also
been called the line of disjunction (Niesel, Krauchi, &
Bachmann, 1976). Because C1 a and C1 b could often
not be resolved accurately in this study, no distinction
was made between these two zones, and the C1 width
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
measurement therefore represented the sum of the capsule and C1. C2 is a zone of low light scatter, and its
width is determined by the maxima in the gradient of a
densitogram, the latter being a curve representing the
rate of change of the densitogram. The same applies to
the subsequent high scatter zone C3. Because zone C4
was difficult to distinguish from the anterior and posterior nuclear layers, this layer was not further analysed.
In the Scheimpflug image, the cursor of the mouse was
used to indicate the various zones depicted in Fig. 1.
When the cursor was moved across the Scheimpflug
image, its position in the densitogram and in the gradient of the densitogram could be observed on the
computer screen allowing determination of the various
zones with an error of maximal one pixel. Only those
zones which could be distinguished clearly were indicated.
After determination of the various zones, the Scheimpflug image was corrected for distortion. It was assumed that each intraocular surface is rotationally
symmetric and could be described by a conic of revolution. Using ray tracing through aspherical surfaces,
each Scheimpflug image was corrected for the two types
of distortion. This method has been validated by measuring an artificial eye and pseudophakic patients with
intraocular lenses of known dimensions (Dubbelman &
Van der Heijde, 2001; Dubbelman et al., 2001).
After correction of the Scheimpflug images, the
thickness of the various zones that were manually
marked was measured. For the total group of 102 subjects, the changes in the width of the different zones with
age were measured. To investigate the changes with
accommodation, measurements were made of a group of
65 subjects, who had an accommodation range of at
least 1 D. These subjects were selected because analysis
of their Scheimpflug images showed significant changes
in the anterior chamber depth, the lens thickness and the
radius of the anterior lens surface with accommodation
(results will be reported elsewhere). Subjects in this
group were between 16 and 51 years of age (mean ± s.d.:
32 ± 9) and had a mean equivalent refractive error of
)1.4 D. The group consisted of 31 myopes, 30 emmetropes and 4 hypermetropes. Two different methods
were used to analyse the different zones with accommodation. The first method is straightforward, and
measures the thickness of the different zones in the lens
at different accommodation levels. To calculate the
change per diopter in each zone, regression analysis was
performed for each subject. Because there is uncertainty
in the data in both parameters, orthogonal regression
was applied (Press, Flannery, Teukolski, & Vetterling,
1994). On the x-axis, the accommodation level of the
unaccommodated state (0 D) was given an error of ±0.5
D, because of the uncertainty in the determination of the
refractive error (±0.5 D), which might create an offset of
the zero accommodation level. As this offset does not
produce any error in the relative difference between the
higher accommodation levels, these levels were given an
error of ±0.25 D to account for possible focusing errors.
The borders of the different zones could be determined
with an accuracy of approximately 1 pixel (25 lm).
Therefore, an error of 40 lm in the determination of the
different zones was assumed, and further analysis confirmed that this value seemed to be realistic. The change
in thickness of the zones per diopter was determined by
means of orthogonal regression, but because the accommodation range is not the same for all 65 subjects,
each measurement is subject to a different error.
Therefore, the weighted mean, the weighted standard
deviation (s.d.) and the weighted standard errors
(S.E.M.) will be presented (Bevington, 1969).
A second method was used to investigate the changes
with accommodation. This method, compared the difference in the densitogram of the unaccommodated and
the accommodated lens, both shown in Fig. 2. The figure shows that the profiles of these two densitograms are
very similar, except for the fact that the densitogram of
the accommodated lens is more stretched, due to
thickening of the lens with accommodation. To determine which parts of the lens account for this accommodative increase in lens thickness, the profile of the
densitogram of the unaccommodated lens was stretched,
using a non-linear function in the horizontal direction,
to match the profile of the accommodated lens in a least
square sense (Fig. 3). The horizontal dashed line represents zero stretch, while the line indicated by the arrow
represents the parts of the unaccommodated lens that
have been stretched (or contracted). The amount of
stretch is indicated on the right y-axis. Positive values
indicate stretch, while negative values indicate shrink,
i.e. contraction. Thus, for this subject the most stretch is
found in the nucleus. The method was applied to all
110
100
Grey value (au)
2366
90
80
70
60
50
0D
40
4.6D
30
3.2
4.2
5.2
6.2
7.2
Distance from cornea (mm)
Fig. 2. The thick line represents the densitogram of the unaccommodated lens (0 D) of a 34 year-old male. The densitogram at 4.6 D accommodation is indicated by the thinner line. It can be seen that except
for the 0.21 mm longer densitogram of the accommodated lens, the
shape of the two densitograms is quite similar.
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
2367
1
110
100
0.8
Nucleus
0.6
80
0.4
70
60
0.2
post.
cortex
ant. cortex
50
Stretch
Grey values
90
0
40
stretch
30
-0.2
0
0.5
1
1.5
2
2.5
3
3.5
4
Distance from anterior lens vertex (mm)
Fig. 3. The two densitograms of Fig. 2 after non-uniform stretching of the densitogram of the unaccommodated lens. The horizontal dashed line
represents zero stretch. The solid line indicated by the arrow represents the parts of the unaccommodated lens which had to be stretched to match the
densitogram of the accommodated lens as accurately as possible. The higher this line is above the line of the zero stretch, the more the densitogram of
the unaccommodated lens has been stretched. It can be seen that it is mainly the nucleus which is stretched.
densitograms representing the different accommodative
states of the lens of each subject. Thus if a subject was
able to accommodate 3 diopters, 6 stretch-functions
could be obtained.
The stretching was performed with the Mathematica
Package Software (Version 4.0, Wolfram Research,
Inc.), including the Digital Image Processing toolbox as
an add-on. For optimisation, part of the programme
was written in C++. Before stretching, both densitograms were smoothed using a Block Lee filter (a nonlinear noise reducing operator), after which a set of 12
equidistant points was chosen in each densitogram. The
points of both sets had a one-to-one correspondence
with each other and the pairs of points define a smooth
stretch function, which maps points from one densitogram to the other. The first and the last point of the
stretch function are fixed, because after stretching these
points should match in both densitograms. In between
those points, the stretch function is represented by a
spline function, which connects all 12 points together.
Using the Powell minimisation method, the distance
between the points of the densitogram of the unaccommodated lens was varied to find the optimal stretch
function, with which it should be modified to match the
densitogram of the accommodated lens in a least square
sense. With a uniform stretch, the 12 points of the
densitogram of the unaccommodated lens remain equidistant. Because the pupil constricts during accommodation, the intensity of the scattered light of the lens
reduces in particular the posterior part of the lens. As a
result, the amplitude, but usually not the shape, of the
accommodated densitogram becomes smaller in comparison with the unaccommodated densitogram. To
compensate for this difference in density, another func-
tion was introduced with which the accommodated
densitogram should be multiplied. To avoid large
changes in the separate peaks of the accommodated
densitogram, this function is chosen to be more smooth
(less detailed) and is defined as a spline fitted to 4
equidistant points in the densitogram of the accommodated lens. As a result, the amplitude of the peaks of the
two densitograms will often not be identical, because of
the smoothness of this function. This function and the
stretch function were simultaneously included in the
minimisation procedure. To avoid confusion, this
function is not shown in Fig. 3.
3. Results
3.1. Optical correction of the Scheimpflug images
Fig. 4 shows the influence of the correction on the
densitogram of a 35 year-old male (upper part) and a 64
year-old male (lower part). The thick lines represent the
uncorrected densitograms, and the thin lines represent
the densitograms after correction for the geometry of the
Scheimpflug imaging system and the refraction of the
cornea and anterior lens surface. The correction influences the dimensions of the different zones in the lens,
and this influence is particularly dependent on the agedependent anterior chamber depth.
3.2. Changes with age
It was not possible to determine each zone in the lens
accurately for all 102 subjects, and therefore the number
of measurements differs for each zone. This was mainly
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M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
1.6
110
Anterior cortex (mm)
Grey value (au)
130
uncorrected
corrected
90
70
50
35 yrs
30
1.2
1
0.8
0.6
ACT=0.51 + 0.012 * Age
r = 0.80; n=102; p<0.0001
0.4
0.2
180
2.8
uncorrected
150
corrected
Nucleus (mm)
Grey value (au)
(a)
1.4
120
90
60
64 yrs
2.4
2.2
2
1.8
NT=2.11 + 0.003 * Age
r = 0.25; n=98; p=0.01
1.6
30
0
(b)
2.6
1
2
3
4
5
1.4
Fig. 4. Two examples of a densitogram (upper part: 35 year-old male,
lower part: 64 year-old male) to indicate the influence of correction of
the Scheimpflug images. The thick line represents the densitogram
before correction, and the thin line represents the densitogram after
correction. Note that the influence of the correction is not constant
with age.
because the posterior region of the crystalline lens
showed less contrast, or could sometimes not be seen,
because the pupil was small. Fig. 5 shows the change in
thickness of the cortex and nucleus with age according
to the classification of Hockwin et al. (1982), as indicated in the upper part of Fig. 1. With age, a small, but
significant (p ¼ 0:01) increase in nuclear thickness could
be measured, but the lens thickness increases primarily
due to the increase in thickness of the anterior and
posterior cortex. The increase of the anterior cortex is
approximately 1.5 times greater than that of the posterior cortex. Table 1 shows the mean thickness and
possible age-dependency of zones 1–8.
Using the Oxford system (lower part of Fig. 1), zones
C1–C3 can be differentiated within the anterior and
posterior cortex. Fig. 6 shows the change in thickness of
these three zones, and it can clearly be seen that the
increase in both the anterior and posterior cortex with
age is entirely due to zone C2 (Fig. 6b and e). Zones C1
and C3 of both the anterior and the posterior cortex
show no significant change in thickness with age
(p > 0:05). In the posterior cortex, zones C1–C3 could
often not be determined accurately, and the number of
measurements is therefore lower than for the anterior
cortex. Fig. 7 shows a schematic drawing of the aging
lens. The increase in thickness of the lens is mainly due
to the increase of the anterior and posterior C2 zone.
The curvature and thickness of the young and the old
lens are in correct proportion, according to the Scheimpflug measurements. However, because the more pe-
Posterior cortex (mm)
Distance from anterior lens vertex (mm)
1.4
(c)
1.2
1
0.8
0.6
0.4
PCT=0.33 + 0.0082 * Age
r = 0.71; n=89; p<0.0001
0.2
0
10
20
30
40
50
60
70
Age (years)
Fig. 5. The change in thickness of the cortex and nucleus with age. See
Fig. 1 for the determination of the different zones. (a) The anterior
cortex (zones 1 and 2). There was a highly significant increase with age:
ant.cortex ¼ 0.51 (±0.04) + 0.0116 (±0.007) age; n ¼ 102; r ¼ 0:8;
p < 0:0001. (b) The nucleus (zones 3–6). Significant increase with age:
nucleus ¼ 2.11 (±0.04) + 0.003 (±0.001) age; n ¼ 98; r ¼ 0:25;
p ¼ 0:01. (c) The posterior cortex (zones 7 and 8). Highly significant
increase with age: post.cortex ¼ 0.33 (±0.04) + 0.0082 (±0.007) age;
n ¼ 89; r ¼ 0:71; p < 0:0001.
ripheral parts of the lens are obscured by the iris, a
hypothetical lens equator has been added for convenience, indicated by a dotted line.
The age-dependency of the position of the sulcus with
respect to the cornea was investigated. The sulcus is well
defined in the densitogram as the dip in the centre of the
nucleus. Fig. 8 shows the position of the sulcus with
respect to the cornea, which showed no significant
change with age (p ¼ 0:12).
3.3. Changes with accommodation
In a first analysis, the different zones in the lens of
every subject were marked, and the rate of change per
diopter in the different zones was determined by means
of orthogonal regression. Fig. 9 shows the age-dependency of the change in the anterior cortex, nucleus and
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
2369
Table 1
Zones 1–8 with age (see upper part Fig. 1)
Zone
Regression (equation)
1
2
3
4
5
6
7
8
¼ 0.23(±0.03) + 0.012(±0.0008) age
¼ 0.73(±0.03) + 0.0016(±0.0008) age
¼ 0.74(±0.02) + 0.0011(±0.0006) age
¼ 0.18(±0.03) + 0.0076(±0.0008) age
n
r
p
Mean
s.d.
102
99
102
102
101
100
87
85
)0.03
0.84
)0.04
0.21
0.19
0.14
0.72
0.07
0.73
<0.0001
0.66
0.04
0.055
0.15
<0.0001
0.55
0.28
0.7
0.34
0.79
0.78
0.31
0.5
0.17
0.05
0.2
0.07
0.10
0.07
0.06
0.13
0.04
Simple linear regression was applied and results for each zone are indicated in mm: regression equation, number of measurements ðnÞ, correlation
coefficient ðrÞ, probability for rðpÞ, mean and standard deviation (s.d.). If there was no significant age-dependency, the equation is not given.
1
Anterior
(a)
C1 (mm)
0.8
Posterior
(d)
C1=0.20 + 0.0005 * Age
r = 0.14; n=100; p=0.17
C1=0.13 + 0.00026 * Age
r = 0.06; n=57; p=0.59
0.6
0.4
0.2
0
1
C2 (mm)
0.8
(b)
(e)
C2 = -0.15 + 0.012 * Age
r = 0.89; n=100; p<0.0001
C2= -0.06 + 0.0065 * Age
r = 0.73; n=56; p<0.0001
0.6
0.4
0.2
0
1
(c)
(f)
C3 =0.32 - 0.0007 * Age
r = -0.15; n=101; p=0.14
C3 (mm)
0.8
C3=0.19 + 0.0005 * Age
r = 0.10; n=81; p=0.37
0.6
0.4
0.2
0
10
20
30
40
50
60
Age (years)
70 10
20
30
40
50
60
70
Age (years)
Fig. 6. The change in thickness (mm) of the C1, C2 and C3 zones in the anterior cortex (a–c) and posterior cortex (d–f). See Fig. 1 for the determination of the different zones. The C2 zones of the anterior and posterior cortex increased significantly in thickness with age. (a) Mean thickness
C1 anterior: 0.22 (±0.04). (b) C2 anterior ¼ )0.15 (±0.04) + 0.012 (±0.001) Age. (c) Mean thickness C3 anterior: 0.30 (±0.06). (d) Mean thickness C1
posterior: 0.14 (±0.04). (e) C2 posterior ¼ )0.06 (±0.04) + 0.0065 (±0.001) Age. (f) Mean thickness C3 posterior: 0.21 (±0.06).
posterior cortex during accommodation labeled according to Hockwin et al. (1982) and the Oxford system.
It can be seen that there is no significant change per
diopter in the cortex, and that the thickening of the lens
with accommodation is primarily due to a change in the
thickness of the nucleus. Furthermore, it appears that
the results are dependent on the definition of the cortex
and nucleus. Labeling the zones according the system of
Hockwin et al. (1982), there is a minimal increase in
thickness in the cortex with accommodation. However,
defining the cortex and nucleus according to the Oxford
system, there is even a suggestion of a reduction in
cortical thickness with accommodation. Table 2 shows
the mean values for the change in the cortical and nuclear zones with accommodation according to both
systems.
Furthermore, the movement of the sulcus, or nuclear
dip during accommodation was investigated. During
2370
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
Change in thickness (mm)/D
0.06
20 yrs
a
C1β
C3
Nucleus
C2
Change in thickness (mm)/D
C1α
p
Sulcus
C2
0.05
17
0.04
4
0.03
0.02
0.01
8
5
18
17
8
8
7
5
9
8
4
4
0
-0.01
ant. cortex
nucleus
post. cortex
using the system of Hockwin et al. (1982)
-0.02
-0.03
0.06
3
14
7
9
0.05
9
3
0.04
0.03
3
0.02
0.01
8
3
18
16
10
9
9
5
8
3
8
0
-0.01
ant. cortex
nucleus
post. cortex
using the Oxford system
-0.02
-0.03
19
65 yrs
25
31
37
43
49
Age (years)
Fig. 7. Schematic drawing of the zones in the lens of a 20 year-old
subject (upper part) and a 65 year-old subject to indicate the growth
with aging. The increase in thickness of the lens is primarily due to the
anterior and posterior C2 zone.
Cornea ~ Sulcus (mm)
9
7
7
6
Fig. 9. Change in the anterior cortex, nucleus and posterior cortex in
mm per diopter with age. The data are grouped in 6 bins. The number
of measurements is indicated above each bin. In the upper part, the
cortex and nucleus were labeled according to Hockwin et al. (1982). In
the lower part, they were labeled according the Oxford system, in
which the cortex consists of zones C1–C3 and the nucleus is defined as
the area between the anterior and posterior C3 zone. Using the Oxford
system, the increase in lens thickness is entirely due to the nucleus.
7
whole nucleus is uniformly stretched (indicated by the
plateau of constant stretch in the nucleus, see Fig. 3).
Thus, we were not able to detect significant recurrent
dips, or peaks in the stretch-function, which would indicate that certain parts of the nucleus show a smaller or
greater increase in thickness during accommodation.
6.5
6
5.5
5
Thick=5.47 + 0.003 * Age
r = 0.15; n=102; p=0.12
4.5
4
10
20
30
40
50
60
70
Age (years)
Fig. 8. The distance between the anterior vertex of the cornea and the
sulcus. There is no significant change with age: cornea sulcus ¼ 5.47
(±0.08) + 0.003 (±0.002) age; n ¼ 102; r ¼ 0:15; p ¼ 0:12.
accommodation there appeared to be a significant
movement of the sulcus towards the cornea: mean
(±s.d.) ¼ 0.011/D (±0.010), n ¼ 55, p < 0:0001.
The results presented in Fig. 9 were obtained by
manually marking the different zones of the lens and are
consistent with those of the second method, in which the
densitogram of the unaccommodated lens was stretched
to match that of a lens in a higher accommodative state.
These results also show that with accommodation, it is
the nucleus that becomes thicker, while the thickness of
the cortex generally remains constant. Using this
method, it also becomes clear that, for the most part, the
4. Discussion
4.1. Correction of the Scheimpflug images
Scheimpflug imaging can be used to determine different dark and lighter zones in the crystalline lens,
which have been referred to as the zones of discontinuity. In the present study, the change in thickness of
these zones with age and accommodation was investigated. In contrast with earlier Scheimpflug studies,
correction was made for distortion due to the geometry
of the Scheimpflug imaging system and the refraction of
the cornea and lens. The method used to correct the
Scheimpflug images has been described and validated in
earlier publications (Dubbelman & Van der Heijde,
2001; Dubbelman et al., 2001).
To correct the internal structure of the lens for the
refraction of the lens itself, a simplification was made.
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
2371
Table 2
Change in cortical and nuclear thickness per diopter according the classification of Hockwin et al. (1982) and the Oxford system
Mean
According to Hockwin et al.:
D anterior cortex (mm/D)
D nucleus (mm/D)
D posterior cortex (mm/D)
0.004
0.040
0.0006
S.D.
S.E.M.
n
0.005
0.011
0.007
0.001
0.0014
0.0006
54
50
47
According the Oxford system
D anterior cortex (mm/D)
D nucleus (mm/D)
D posterior cortex (mm/D)
)0.001
0.046
)0.002
0.007
0.013
0.005
0.001
0.0015
0.0014
56
46
44
Total lens thickness (mm/D)
0.045
0.012
0.0015
58
Parameters are the weighted mean, standard deviation, standard error of the mean and the number of measurements ðnÞ of the change per diopter
with accommodation.
The crystalline lens was assumed to consist of one homogeneous medium with one equivalent refractive index (nl ), whereas it is generally assumed that the lens
has a gradient refractive index (GRIN) structure, with a
maximum value in the centre of approximately 1.40 and
a minimum value of approximately 1.37 in the periphery of the lens (Campbell, 1984; Pierscionek & Chan,
1989; Pierscionek, 1997). Thus, the nl is not intermediate between the index of the shell and the index of the
nucleus, but greater than the maximum index found in
the lens. However, the precise refractive structure of the
human lens is still unknown, and can therefore not
easily be implemented in the ray tracing procedure to
correct the Scheimpflug images. Because the change in
the refractive index is mainly found in the anterior and
posterior cortex, the major errors are made in the determination of the dimensions of these zones. However,
the values of these errors are small, because the correction for the refraction of the lens itself plays only a
minor part in distorting the shape of the lens, compared
to the influence of the anterior chamber depth and the
refraction of the anterior corneal surface. An estimation
of the size of these errors was made by correcting the
images, using different values for the nl . Lowering the
value for the nl with 0.01 will decrease the thickness of
the anterior and posterior cortex no more than 10 and 1
lm, respectively. The nucleus will decrease approximately 12 lm. Thus, if the gradient refractive index of
the lens is not taken into account, the size of the anterior and posterior cortex will be underestimated.
However, this underestimation will probably not exceed
25 lm, a value that is negligible compared to the interindividual variation of the cortical thickness. For the
measurements during accommodation, the effect can be
ignored if no great changes in the gradient refractive
index will occur during accommodation. In that case,
the gradient index will, nevertheless, cause an error in
the absolute thickness of the zones, but will hardly influence the measurement of the rate of change in
thickness per diopter.
It must be noted that the results with accommodation
have been obtained by presenting an accommodative
stimulus, which is not necessarily the same as the accommodative response of the eye. It has been reported
that for a zero accommodation stimulus, the accommodation is not completely relaxed leading to accommodative lead, while for higher accommodation levels,
the accommodative response is lower than the accommodative stimulus leading to accommodative lag (Abbott, Schmid, & Strang, 1998; Goss & Zhai, 1994). The
implications for the results with accommodation will be
that the absolute change in thickness of the whole lens
and the various layers per diopter given in Fig. 9 and
Table 2 will be slightly underestimated. Obviously, this
accommodation lag does not influence the results of the
relative change during accommodation of the various
zones with respect to each other.
4.2. Origin of the scattering
The different zones within the human lens that are
visible on the Scheimpflug images result from the different light scattering properties of each zone. However,
the exact origin of the scattering is still unclear. The light
scattering observed with the slit lamp or Scheimpflug
camera is known as backward scattering, and must be
distinguished from forward scattering in the direction of
the retina, which in fact is much more important for
vision. The intensity of the backward light scattering is
strongly dependent on the angle of illumination and
observation (Van den Berg & Spekreijse, 1999). The
protein concentration, which varies within the lens, is an
important parameter for light scatter. Nevertheless, such
a variation did not explain the different light scattering
properties of the various lens zones (Yaroslavsky et al.,
1994). Therefore, it is likely that factors such as the
configurations of the lens proteins and the orientation or
size of the lens fibres contribute to the appearance of the
zones of discontinuity. In addition, it has been shown
that the lens fibre membranes or extracellular spaces
2372
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
also act as sources for the scattering of light (Bettelheim,
1985). Furthermore, a large part of the light scattering
is, in fact, not real light scatter, but specular reflection
(Weale, 1986a, 1986b). This would suggest that there are
ragged surfaces within the lens, which separate areas of
different refractive index (Goldmann, 1964; Huggert,
1948).
It is also highly probable that the lens sutures play a
role in the explanation of the existence of the zones of
discontinuity (Kuszak, Deutch, & Brown, 1994). New
lens fibres formed from the cells at the equator extend
anteriorly and posteriorly to join with other fibres to
form the lens sutures, which become more complex as
the lens cells form successive layers throughout life
(Kuszak & Brown, 1994). According to Koretz, Cook,
and Kuszak (1994), the location of the zones of discontinuity is directly correlated with the development of
the lens sutures. Furthermore, it has been demonstrated
that there is a relationship between optical lens quality
and the lens sutures (Kuszak, Peterson, Sivak, & Herbert, 1994; Kuszak, Sivak, & Weerheim, 1991).
4.3. Changes with age
Because of the lack of a clear definition of the
boundary between nucleus and cortex, it is obvious that
the lens nucleus is not a uniform concept, but has to be
carefully defined each time it is used. In the present
study, two different definitions were used (Fig. 1): zones
3 to 6 (Hockwin et al.) and the area between the anterior
and posterior C3 zones (according to the Oxford system). The results with age show that for both definitions
of the nucleus the change in thickness of the cortex is
approximately 7 times greater than that of the nucleus,
which is significantly more than the value reported by
other Scheimpflug studies in which no correction was
made for the refraction of the cornea and lens. In contrast with the findings of Cook et al. (1994), i.e. a decrease in nuclear thickness with age, in the present study
a small increase in nuclear thickness of approximately 3
lm/years was found, which was entirely due to thickening in the central nuclear zone (zones 4 and 5). The
thickness of the anterior and posterior cortex increased
at a rate of approximately 12 and 8 lm/years, respectively. The increase in thickness of the anterior cortex is
thus 1.5 times greater than that of the posterior cortex,
which is less than the values of 3 and 2.4 times reported
by Kashima et al. (1993) and Cook et al. (1994).
Classification according the Oxford system makes it
possible to discern which layers of the cortex increase in
thickness with age. For the first time, the change in
thickness of zones C1–C3 of the posterior lens cortex
has been measured. For both the anterior and the posterior cortex, it appeared that C1 and C3 do not significantly change in thickness with age and that the
increase of the cortex is entirely due to the increase in
thickness of the C2 zone. Thus, the nucleus and the
adjacent C3 zones change little in width with age. This
implies that after appearance of the C3 zone during the
second decade of life, the process of compaction would
solely be restricted to the C1 and C2 zones. This is
consistent with the observation made by Brown and
Bron (1996), that nuclear compaction only occurs during the first 20 years of life, while cortical compaction
occurs throughout the entire life span. The latter was
supported by the study carried out by Brown (1976) in
which it was observed that cortical cataracts sank into
the lens at a faster rate than the rate at which the lens
was growing. Calculations make it clear that this finding
cannot be explained by the distortion due to refraction
of the cornea and lens. Nuclear compaction in the first
two decades of life could explain why there is almost no
increase in lens thickness, and that even thinning of the
lens has been observed up to 15 years of age (Mutti et al.,
1998).
New fibres are added to the surface of C1 a, but no
increase in the thickness of C1 was observed. The underlying fibres will therefore enter the C2 zone, which
implies a change in their light scattering properties. These
fibres pass through a phase of increased light scatter as
they enter C1 b, followed by a phase of decreased light
scatter when they are regarded to belong to the subsequent C2 zone. A possible explanation for this change of
the light scattering properties could be the process of
denucleation of the fibres associated with the formation
of the nuclear bow and the breakdown of the mitochondria, which lead to the dispersal of particulate material
and Ca2þ within the fibre (Bron et al., 2000).
There is no evident relationship of the zones observed
in vivo using a slit lamp or Scheimpflug camera and the
various lens regions distinguished in certain in vitro
studies on lens morphology. Taylor et al. (1996) analysed the fibres in five lens regions: deep cortex, adult
nucleus (fibre cells formed since puberty), juvenile nucleus (fibre cells formed from birth until the onset of
puberty), fetal nucleus (fibre cells formed from the seventh week of development until birth), and embryonic
nucleus (formed in the 6 weeks after fertilisation). Each
region appeared to have characteristic cell shapes and
sizes, and the approximate thickness of each zone was
given for an average age of 61 years. Comparing their
results with the measurements of the different lens zones
in the present study shows that the embryonic nucleus
corresponds to the sulcus, and the fetal nucleus (thickness: ±2.14 mm) corresponds well to the nucleus defined
according to Hockwin et al. (zone 3–6: ±2.2 mm) and
the area between the C4 zones according to the Oxford
system (±2.2 mm). This is consistent with the fact that
the Oxford system reserves the term nucleus only for
that part of the lens, which is present at birth (Brown &
Bron, 1996). Thus, only cortical layers are added postnatally. This avoids the confusing of regarding a set of
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
lens fibres as cortex at one period, but as nucleus at a
later period when they occupy a deeper position in the
lens. For the cortex, it becomes more difficult. Zones 2
and 7, defined by Hockwin et al. as the anterior (±1 mm)
and posterior cortex (±0.65 mm), roughly correspond to
the adult and juvenile nucleus combined (±1.25 mm)
according Taylor et al. (1996). As a result, zones 1 and 8
(±0.22 mm) should therefore be identical to what Taylor
et al. define as the deep cortex (±0.7 mm). The difference
in thickness, however, is large. The C4 zone (±0.2 mm)
according to the Oxford system corresponds to the juvenile nucleus (±0.19 mm), but relating zones C1–C3 to
the remaining adult nucleus and deep cortex is difficult.
This might be explained by the fact that zones C1–C3
correspond to zones in the lens with different light
scattering properties, whereas in the in vitro study carried out by Taylor et al. (1996) several regions were
distinguished on account of the shape and size of the
cells. It can be expected that there is a relationship between the former and the latter, but this does not need to
be obligatory, especially because the exact origin of the
scattering is still unclear.
According to Koretz, Kaufman, Neider, and Goeckner (1989a, 1989b), the anterior chamber shallows
with age at a rate equal to the increase in thickness of
the lens, i.e. the anterior segment length (distance from
the cornea to the posterior lens surface) remains constant. Consequently, in a subsequent analysis of the
change in the internal structure with age (Cook et al.,
1994), their results showed that the nucleus is gradually
translated anteriorly (towards the cornea) with increasing age at the rate of posterior cortical thickening.
However, in an earlier study (Dubbelman et al., 2001), it
was shown that correction of the Scheimpflug images
leads to significantly different results with regard to the
change in the anterior segment length with age. It appeared that the posterior lens surface receded from the
cornea with age, and that this backward movement did
not differ significantly from the forward movement of
the anterior lens surface. In the present study, it was
found that the distance between the cornea and the
sulcus, which can be regarded as the centre of the nucleus, did not change with age. Thus, the nucleus is not
gradually translated anteriorly (towards the cornea)
with increasing age, but stays in the same position.
4.4. Changes with accommodation
The results of the change in the internal structure of
the lens with accommodation are consistent with earlier
Scheimpflug studies measuring accommodation: the increase in lens thickness is mainly due to an increase in
the thickness of the nucleus. The magnitude of this
thickening depends on the definition of the nucleus. The
anterior and posterior C3 zone are zones of high light
scatter, and in between is the rather dark zone of low
2373
light scatter, which is regarded as the nucleus. According
to Hockwin et al. (1982), the peri-nuclear zone (zones 3
and 6) begins and ends when the side of the C3 zone
orientated towards the centre of the lens reaches a local
minimum in the densitogram. According to the Oxford
system, the nucleus was defined at the steepest part
(maximum gradient) of the side of the C3 zone (actually,
behind the C3 zone there is first the low scatter C4 zone
that is considered to precede the nucleus, but because
this C4 zone is difficult to determine, the nucleus was
defined as the area between the C3 zones). According to
this definition, the thickening of the lens with accommodation is entirely due to a change in the thickness of
the nucleus and there is even a suggestion of a reduction
in cortical thickness with accommodation. Defined according to the system of Hockwin et al. (1982), there is
still a slight increase in cortical thickness with accommodation. This indicates that there is a small accommodative increase in width between the position of the
highest gradient of the side of the C3 zone adjacent to
the nucleus and the point where this side reaches a local
minimum. It must be noted that the differences between
the two systems are smaller than the pixel size, which is
approximately the precision with which a transition
between the lens zones can be determined. Nevertheless,
it can be concluded that the anterior and posterior
cortex, defined as zones C1–C3, show no change in
thickness with accommodation. This finding is also
supported by the non-uniform stretching of the densitogram of the unaccommodated lens. The stretching
generally shows a plateau of constant stretch within the
nucleus, which makes it clear that with accommodation
there is a uniform thickening of the nucleus. This can
also be observed from the Scheimpflug images: the nuclear dip in the centre of the lens, of which the minimum
represents the position of the sulcus, becomes wider with
accommodation. The stretch could provide insight into
the stiffness profile within the lens. The sudden change in
stretch at the transition between anterior cortex and
nucleus indicates an abrupt change in the stiffness of the
lens. However, the subsequent plateau of constant
stretch in the nucleus does not necessarily reflect constant nuclear stiffness. There is a complex distribution of
forces within the lens, and it is possible that uniform
stiffness in the lens does not result in uniform stretch.
The fact, however, that there is a uniform stretch in the
nucleus can be used to model the forces within the lens
during accommodation. Furthermore, the growth of the
cortex with age also alters the distribution of the accommodative forces within the lens. The zonular forces
must be transmitted through the capsule and the cortex
to influence the nuclear shape with accommodation.
This transmission could be more difficult if the nucleus is
surrounded during the growth of the lens by a continuously increasing cortex, and this could possibly be a
factor in the occurrence of presbyopia.
2374
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
Acknowledgements
This research was partially supported by a grant from
Pharmacia Groningen, The Netherlands.
We wish to thank T.J.T.P. van den Berg, PhD, and
J.C. Coppens, MSc, from the Netherlands Ophthalmological Research Institute and AMC/Department of
Medical Physics in Amsterdam, for their helpful comments and for giving us the opportunity to use their
Nidek EAS-1000 Scheimpflug camera.
References
Abbott, M. L., Schmid, K. L., & Strang, N. C. (1998). Differences in
the accommodation stimulus response curves of adult myopes and
emmetropes. Ophthalmic Physiological Optics, 18(1), 13–20.
Al-Ghoul, K. J., Nordgren, R. K., Kuszak, A. J., Freel, C. D.,
Costello, M. J., & Kuszak, J. R. (2001). Structural evidence of
human nuclear fiber compaction as a function of ageing and
cataractogenesis. Experimental Eye Research, 72(3), 199–214.
Bettelheim, F. A. (1985). Physical basis of lens transparency. In E.
Maisel (Ed.), The ocular lens. Structure, function and pathology (pp.
265–300). New York: Marcel Dekker.
Bevington, P. R. (1969). Data reduction and error analysis for the
physical sciences. New York: McGraw-Hill, pp. 77–80.
Bron, A. J., Vrensen, G. F., Koretz, J., Maraini, G., & Harding, J. J.
(2000). The ageing lens. Ophthalmologica, 214(1), 86–104.
Brown, N. (1973). The change in shape and internal form of the lens of
the eye on accommodation. Experimental Eye Research, 15(4), 441–
459.
Brown, N. (1976). Dating the onset of cataract. Transactions of the
Ophthalmological Society of UK, 96(1), 18–23.
Brown, N. P., & Bron, A. J. (1996). Lens disorders: a clinical manual of
cataract diagnosis. Oxford: Butterworth-Heinemann, pp. 23–26.
Brown, N. A. P., Sparrow, J. M., & Bron, A. J. (1988). Central
compaction in the process of lens growth as indicated by lamellar
cataract. British Journal of Ophthalmology, 72, 538–544.
Campbell, M. C. (1984). Measurement of refractive index in an intact
crystalline lens. Vision Research, 24, 409–415.
Cook, C. A., Koretz, J. F., Pfahnl, A., Hyun, J., & Kaufman, P. L.
(1994). Aging of the human crystalline lens and anterior segment.
Vision Research, 34(22), 2945–2954.
Dubbelman, M., & Van der Heijde, G. L. (2001). The shape of the
aging human lens: curvature, equivalent refractive index and the
lens paradox. Vision Research, 41, 1867–1877.
Dubbelman, M., Van der Heijde, G. L., & Weeber, H. A. (2001). The
thickness of the aging human lens obtained from corrected
Scheimpflug images. Optometry and Vision Science, 78(6), 411–416.
Goldmann, H. (1964). Senile changes of the lens and the vitreous.
American Journal of Ophthalmology, 57, 1–13.
Goss, D. A., & Zhai, H. (1994). Clinical and laboratory investigations
of the relationship of accommodation and convergence function
with refractive error. A literature review. Documenta Ophthalmologica, 86(4), 349–380.
Hockwin, O., Dragomirescu, V., & Laser, H. (1982). Measurements of
lens transparency or its disturbances by densitometric image
analysis of Scheimpflug photographs. Graefes Archives of Clinical
and Experimental Ophthalmology, 219(6), 255–262.
Huggert, A. (1948). On the form of the iso-indicial surfaces of the
human crystalline lens. Acta Ophthalmologica (Suppl. 30), 1–128.
Kashima, K., Trus, B. L., Unser, M., Edwards, P. A., & Datiles, M. B.
(1993). Aging studies on normal lens using the Scheimpflug slitlamp camera. Investigative Ophthalmology and Visual Science,
34(1), 263–269.
Koretz, J. F., Cook, C. A., & Kaufman, P. L. (1997). Accommodation
and presbyopia in the human eye. Changes in the anterior segment
and crystalline lens with focus. Investigative Ophthalmology and
Visual Science, 38(3), 569–578.
Koretz, J. F., Cook, C. A., & Kuszak, J. R. (1994). The zones of
discontinuity in the human lens: development and distribution with
age. Vision Research, 34(22), 2955–2962.
Koretz, J. F., Kaufman, P. L., Neider, M. W., & Goeckner, P. A.
(1989a). Accommodation and presbyopia in the human eye, aging
of the anterior segment. Vision Research, 29, 1685–1692.
Koretz, J. F., Kaufman, P. L., Neider, M. W., & Goeckner, P. A.
(1989b). Accommodation and presbyopia in the human eye. 1:
Evaluation of in vivo measurement techniques. Applied Optics, 28,
1097–1102.
Kuszak, J. R., & Brown, H. G. (1994). Embryology and anatomy of
the lens. In D. A. Albert, & F. A. Jacobiec (Eds.), The principles
and Practice of ophthalmology. Basic sciences (pp. 82–96). Philadelphia: W.B. Saunders.
Kuszak, J. R., Deutch, T. A., & Brown, H. G. (1994). Anatomy of
aged and senile cataractous lenses. In D. A. Albert, & F. A.
Jacobiec (Eds.), The principles and practice of ophthalmology.
Clinical practice, vol.1 (pp. 564–575). W.B. Saunders: Philadelphia.
Kuszak, J. R., Peterson, K. L., Sivak, J. G., & Herbert, K. L. (1994).
The interrelationship of lens anatomy and optical quality II.
Primate lenses. Experimental Eye Research, 59(5), 521–535.
Kuszak, J. R., Sivak, J. G., & Weerheim, J. A. (1991). Lens optical
quality is a direct function of lens sutural architecture. Investigative
Ophthalmology and Visual Science, 32(7), 2119–2129.
Mutti, D. O., Zadnik, K., Fusaro, R. E., Friedman, N. E., Sholtz, R.
I., & Adams, A. J. (1998). Optical and structural development of
the crystalline lens in childhood. Investigative Ophthalmology and
Visual Science, 39(1), 120–133.
Niesel, P., Krauchi, H., & Bachmann, E. (1976). Der Abspaltungsstreifen in der Spaltlampenphotographie der alternden Linse.
Albrecht Von Graefes Archiv fur Klinische und Experimentelle
Ophthalmologie, 199(1), 11–20.
Patnaik, B. (1967). A photographic study of accommodative mechanisms: Changes in the lens nucleus during accommodation.
Investigative Ophthalmology, 6, 601–611.
Pierscionek, B. K. (1997). Refractive index contours in the human lens.
Experimental Eye Research, 64(6), 822–829.
Pierscionek, B. K., & Chan, D. Y. (1989). Refractive index gradient of
the human lens. Optometry and Vision Science, 66, 822–829.
Pierscionek, B. K., & Weale, R. A. (1995). The optics of the eye-lens and
lenticular senescence. Documenta Ophthalmologica, 89, 321–335.
Press, W. H., Flannery, B. P., Teukolski, S., & Vetterling, W. T.
(1994). Numerical recipes in C. Cambridge: Cambridge University
Press, pp. 666–670.
Rabie, E. P., Steele, C., & Davies, D. E. (1986). Anterior chamber
pachymetry during accommodation in emmetropic and myopic
eyes. Ophthalmic and Physiological Optics, 6(3), 283–286.
Ray, S. F. (1995). Applied photographic optics (p. 452). Oxford: Focal
Press.
Richards, D. W., Russell, S. R., & Anderson, D. R. (1988). A method
for improved biometry of the anterior chamber with a Scheimpflug
technique. Investigative Ophthalmology and Visual Science, 29(12),
1826–1835.
Sakamoto, Y., & Sasaki, K. (1994). Accuracy of biometrical data
obtained from the Nidek Eas-1000. Ophthalmic Research,
26(Suppl. 1), 26–32.
Sasaki, K., Sakamoto, Y., Shibata, T., & Emori, Y. (1990). The multipurpose camera: a new anterior eye segment analysis system.
Ophthalmic Research, 22(Suppl. 1), 3–8.
Shibata, T., Hockwin, O., Weigelin, E., Kleifeld, O., & Dragomirescu,
V. (1984). Biometrie der Linse in Abh€angigkeit vom Lebensalter
und von der Kataraktmorphologie. Klinische Monatsbl€atter f€ur
Augenheilkunde, 185(1), 35–42.
M. Dubbelman et al. / Vision Research 43 (2003) 2363–2375
Smith, G. T., Smith, R. C., Brown, N. A., Bron, A. J., & Harris, M. L.
(1992). Changes in light scatter and width measurements from the
human lens cortex with age. Eye, 6, 55–59.
Sparrow, J. M., Bron, A. J., Brown, N. A., Ayliffe, W., & Hill, A. R.
(1986). The oxford clinical cataract classification and grading
system. International Ophthalmology, 9(4), 207–225.
Taylor, V. L., Al-Ghoul, K. J., Lane, C. W., Davis, V. A., Kuszak, J.
R., & Costello, M. J. (1996). Morphology of the normal human
lens. Investigative Ophthalmology and Visual Science, 37(7), 1396–
1410.
Van den Berg, T. J., & Spekreijse, H. (1999). Light scattering model for
donor lenses as a function of depth. Vision Research, 39(8), 1437–
1445.
2375
Weale, R. A. (1986a). Real light scatter in the human crystalline lens.
Graefes Archive for Clinical and Experimental Ophthalmology,
224(5), 463–466.
Weale, R. A. (1986b). New method for visualising discontinuities in
the crystalline lens. British Journal of Ophthalmology, 70(12), 925–
930.
Wegener, A., & Laser, H. (1996). Imaging of the spatial density
distribution on the capsule of the lens with Scheimpflug photography. Ophthalmic Research, 28(Suppl. 2), 86–91.
Yaroslavsky, I. V., Yaroslavsky, A. N., Otto, C., Puppels, G. J.,
Vrensen, G. F., Duindam, H., & Greve, J. (1994). Combined elastic
and Raman light scattering of human eye lenses. Experimental Eye
Research, 59(4), 393–399.