Download Volume change of the ocular lens during accommodation

Am J Physiol Cell Physiol 293: C797–C804, 2007.
First published May 30, 2007; doi:10.1152/ajpcell.00094.2007.
Volume change of the ocular lens during accommodation
R. Gerometta,1,2 A. C. Zamudio,3 D. P. Escobar,1 and O. A. Candia3
1
Departamento de Farmacologı́a and 2Departamento de Oftalmologı́a, Facultad de Medicina, Universidad Nacional Del
Nordeste, Corrientes, Argentina; and 3Department of Ophthalmology, Mount Sinai School of Medicine, New York, New York
Submitted 8 March 2007; accepted in final form 23 May 2007
a clear image on the retina from objects
situated within a wide range of distances due to a process
called accommodation. In higher vertebrates, including humans, accommodation results from changes in crystalline lens
shape and surface radii of curvature (13).
When the ciliary muscle is relaxed and flattened against
the sclera, the zonulae adjoining the ciliary body and the
lens capsule are under tension and thus pulling eccentrically
on the lens equator. This action causes the lens to adopt a
relatively flattened shape with a larger equatorial diameter
and a shorter A-P length, which allows focusing on virtual
infinity (zero accommodation). When an individual focuses
on a near object, the ciliary muscle contracts (shortening its
distance to the lens equator), the zonulae relax, and the lens
as a whole adopts a relatively rounded shape, which is its
normal tendency. Physically, these changes in lens shape
inevitably must involve changes in either capsular surface
area or lens volume, or both.
Classic theories of lenticular accommodation suggest that
the volume of the intraocular crystalline lens remains constant
during the accommodation process (16, 17, 30). No empirical
studies have demonstrated that the volume actually stays constant. Because of the physical principle mentioned above, an
assumption for a constant volume implies that the surface area
of the lens must change during accommodation.
Furthermore, most of the anterior capsule, where the main
changes in curvature occur during accommodation (11, 24),
both covers and serves as the basement membrane for the
single layer of epithelial cells, which could be disrupted if the
capsule surface area changed extensively. Only the epithelial
cells in the equatorial region are arranged in a multilayered
configuration (18). It is also well known that the capsule and
the internal fiber cells are freely permeable to fluid. In vitro
experiments have demonstrated that osmotic forces can swell
and shrink crystalline lenses (10).
Thus we decided to examine the possibility that it is
primarily the lens volume that changes during accommodation with relatively limited associated changes in surface
area. For this purpose, we characterized 1) an in vitro
model: the isolated iris-ciliary body-zonulae-lens complex
dissected from bovines, and 2) a theoretical model: the
graphical construction of human lenses from structural parameters acquired from the literature.
The bovine lens was chosen because of the following
reasons: its ability to be obtained fresh, its large size that
allows for determination of small volume changes, and its
abundance at a low cost. We are aware that the bovine lens
has limited accommodation amplitude given its internal
fibers structure (19). However, it serves our purpose,
namely, to show that deformation of a mammalian lens
results in volume changes.
Given the complex geometric shape of the lens, an accurate
measurement of its volume is not easy to determine with
certainty. Hence, we developed a method to compute the
volume of the lens from lateral photographs. The approach
takes advantage of the topology of the lens as detailed in
METHODS. Our results suggest that during the accommodative
process, the lens gains or looses ⬃2– 8% of its volume as it
gets rounder or flatter, respectively. Our findings also suggest
that fluid must move in and out of the lens during
this process, possibly aided by the numerous aquaporins connecting the fiber cells (1, 31, 32). With preliminary calculations
we determined that this volume flow could occur within the
time frame of the rapid accommodation process.
Address for reprint requests and other correspondence: O. A. Candia, Dept.
of Ophthalmology, Mount Sinai School of Medicine, Box 1183, One Gustave
L. Levy Place, New York, NY 10029 (e-mail: [email protected]).
The costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked “advertisement”
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
lens volume calculation; intralenticular fluid movement; presbyopia;
mammalian lens
THE EYE IS ABLE TO FORM
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Gerometta R, Zamudio AC, Escobar DP, Candia OA. Volume change of the ocular lens during accommodation. Am J
Physiol Cell Physiol 293: C797–C804, 2007. First published May
30, 2007; doi:10.1152/ajpcell.00094.2007.—During accommodation, mammalian lenses change shape from a rounder configuration
(near focusing) to a flatter one (distance focusing). Thus the lens
must have the capacity to change its volume, capsular surface area,
or both. Because lens topology is similar to a torus, we developed
an approach that allows volume determination from the lens
cross-sectional area (CSA). The CSA was obtained from photographs taken perpendicularly to the lenticular anterior-posterior
(A-P) axis and computed with software. We calculated the volume
of isolated bovine lenses in conditions simulating accommodation
by forcing shape changes with a custom-built stretching device in
which the ciliary body-zonulae-lens complex (CB-Z-L) was
placed. Two measurements were taken (CSA and center of mass)
to calculate volume. Mechanically stretching the CB-Z-L increased
the equatorial length and decreased the A-P length, CSA, and lens
volume. The control parameters were restored when the lenses
were stretched and relaxed in an aqueous physiological solution,
but not when submerged in oil, a condition with which fluid leaves
the lens and does not reenter. This suggests that changes in lens
CSA previously observed in humans could have resulted from fluid
movement out of the lens. Thus accommodation may involve
changes not only in capsular surface but also in volume. Furthermore, we calculated theoretical volume changes during accommodation in models of human lenses using published structural
parameters. In conclusion, we suggest that impediments to fluid
flow between the aquaporin-rich lens fibers and the lens surface
could contribute to the aging-related loss of accommodative
power.
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LENS VOLUME CHANGE DURING ACCOMMODATION
METHODS
Determination of Lens Volume From Lateral (Sagittal) Photographs
Fig. 1. A: view of how the cross-sectional area (CSA) of a torus would look
(lined area) in a perpendicular cut. R and r, radius; d, diameter. B: a cylinder
that is deformed to form a torus. CM, center of mass; h, height. C: horn torus
and its CSAs touching each other. A horn torus can be deformed to look like
a lens without losing its topological qualities.
AJP-Cell Physiol • VOL
Fig. 2. Sagittal view of a lens showing its total cross-sectional surface area.
This is divided into 2 identical CSAs for the right (CSAR) and left (CSAL)
sides. The 2 CMs are indicated. A perpendicular circle going through the CMs
(solid and dashed lines) is also shown. A-P thickness, length of anterior-toposterior axis.
Dissection, Isolation, and Mounting of the Bovine Ciliary
Body-Zonulae-Lens Complex
Bovine eyes were obtained within 30 min of death, from a local
slaughterhouse in Argentina, where experiments were done. Each eye
was dissected by making a circular cut around the sclera 10 mm
posterior to the limbus. The vitreous was completely removed from
the lens. The entire ciliary body was carefully separated from the
sclera by microdissection and then scooped out with a Teflon spatula.
At this point, the zonulae relaxed and the lens acquired its most
rounded shape, not different from a completely isolated one. The
stromal side of the iris-ciliary body (ICB) was attached with cyanoacrylate glue to a rubber washer with an external diameter of 45 mm
and a central aperture of 20 mm in diameter so that the lens was
suspended within the opening of the washer. The washer with the
glued ICB-zonulae-lens complex was then placed horizontally on an
aluminum platform of a custom-built stretching device. Subsequently,
eight small metal hooks arranged symmetrically around the whole
circumference were used to clasp the prepierced outer edge of the
washer (Fig. 3). The hooks were connected to a rotating flywheel with
unstretchable strings. Turning the round dial elongated the washer
radially, uniformly augmenting its central opening while maintaining
its circularity. This maneuver applied tension to the zonulae, which in
turn transmitted the tension to the lens and changed its shape in a
manner simulating the unaccommodative state (i.e., maximal reduction in the A-P sagittal thickness). Relaxing the tension simulated the
opposite, or accommodative, state (i.e., minimal equatorial length).
Experiments were performed in several conditions: 1) the setup
was completely submerged in a bath with Tyrode solution (composition elsewhere, Ref. 7), while the stretching and relaxing maneuvers
were performed reversibly; 2) similar to the previous condition, but
immersed in corn oil, instead; and 3) combinations of the first two
protocols described. The whole arrangement was temporarily exposed
to air, as needed, for mechanical measurements and digital photographing in each of the two oppositely imposed accommodative
states. The visual axis of the photographic camera was on a perpendicular plane with respect to the A-P axis of the lens, validated by
determining that the two CSAs were symmetrically identical and that
each CSA was a minimum.
With the use of graphics software (Photoshop), the sagittal outline
of the lens was obtained from the digital images, and this outline was
further cut exactly in half for subsequent analysis of both photographs
as described later. A depiction of such outlines in the stretched (no
accommodation) and relaxed (maximum accommodation) positions is
shown in Fig. 4.
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The torus is a topological body similar to a doughnut. Its volume
can be calculated from the cross-sectional area (CSA), where CSA ⫽
␲ ⫻ r2, and from the diameter of the circle (d ) that perpendicularly
crosses the center of mass (CM) of the CSA (Fig. 1A) such that
volume of torus ⫽ ␲2 ⫻ r2 ⫻ d.
The following example could aid in illustrating this concept: the
volume of a cylinder is calculated by multiplying the CSA (of the
circle) by its height (h). The center of the circle is also the CM. If we
bend the cylinder so that the base joins its top, we create a doughnut,
with the length h along the CM remaining constant. The volume of the
body is also constant, even though the inner ring diameter of the
resulting doughnut is relatively compressed and its outer ring diameter
expanded (Fig. 1B).
The horn torus is considered the same topological body as the
torus, but without the center hole (Fig. 1C). The lens can be
compared with a horn torus. When the lens is observed from the
side (sagittal view), 90° from the anterior-posterior (A-P) axis that
crosses the center, a deformed oval can be seen (Fig. 2); rotating
the lens around the A-P axis does not change the image. The total
area of this shape is the CSA of the two sides of the horn torus.
Therefore, the volume of the lens will be obtained by multiplying
the CSA of one of the halves of this area (that is separated by the
A-P axis) times ␲ times the length between the CMs of the two
symmetrical halves of the lens, which corresponds to the diameter
of the circle that rotates around the A-P axis, as volume of lens ⫽
CSA ⫻ ␲ ⫻ d (Fig. 2).
LENS VOLUME CHANGE DURING ACCOMMODATION
C799
divided by 2. These compared values were less than 0.5% of each
other (in this case there was no difference), so the half lens picture was
kept for further study. If the error was larger than 0.5%, the half lens
would be disregarded and a new half lens outline would be cut, until
it fell within the error set as standard. The A-P thickness of the whole
lens and the halves had to match precisely.
3. In the half lens, the location of the CM, perpendicularly measured from the A-P axis, was 84.43 pixels, or 3.95 mm. This length is
the radius r; therefore, 2r equals 7.90 mm, the value for d. Applying
the volume equation, 94.1 mm2 ⫻ ␲ ⫻ 7.90 mm ⫽ 2,334.7 mm3, or
2.33 ml.
The method was corroborated both by weighing a custom-made
acrylic lens (of known density) and by determining its volume with a
volume displacement apparatus with a capillary. Furthermore, with a
machined plastic lens of known volume, the photographic method
described yielded values within 1%.
Fig. 3. Stretching apparatus showing 1) iris-ciliary body with lens in its center
still attached with zonulae. A spatula is used to flatten the ciliary body against
the rubber washer. 2) Expandable rubber washer. 3) Hooks piercing the rubber
washer with its strings. 4) Aluminum plate that supports the rubber-lens
complex horizontally. 5) Aperture in the aluminum plate to permit lateral
photography of the lens. 6) Sliding plastic plate. 7) Rotating plastic wheel. Its
rotation changes the distance between the aluminum plate and the sliding
plastic plate, exerting a tension on the string-rubber washer-ciliary-zonulaelens continuum. 8) Set of plastic washers used to measure the equatorial
diameter of the lens.
Calibration for Conversion of Pixels Into Millimeters and
Volume Determination
Construction of Human Lenses
Before photographs were taken, the equatorial diameter was determined by placing a plastic (acetal copolymer) washer that corresponded to the closest fit around the equator of the bovine lens. The
internal diameter of this plastic washer (custom-milled with a precision of 0.1 mm) indicated the equatorial length. Similarly, a vernier
caliper was used to determine the A-P thickness (length from anterior
to posterior poles through the A-P axis) with resolution of 0.1 mm.
The needed dimensions and surfaces of the whole lens and its
symmetrical halves, in both accommodative states, were obtained
with ImageJ software (http://rsb.info.nih.gov/ij/) in pixels, and the
pixel values were converted to millimeters for volume calculations.
An example of such step-by-step analysis follows.
1. From the outline obtained with Photoshop of one complete lens,
equator length and A-P thickness were determined. The equator length
of this representative lens was 389.4 pixels, and the value obtained
from the measurement with the plastic washer was 18.2 mm; therefore, the conversion was 21.39 pixels/mm. The A-P thickness was
276.0 pixels, which upon conversion yielded 12.9 mm, a value that
corresponded exactly to that obtained with the vernier caliper for the
length of the A-P axis. As for the CSA of the entire lens, the CSA of
the half lens was first obtained (43,063.0 squared pixels). The square
root of this value converted to millimeters (by dividing by the
conversion factor) was squared and multiplied by two to get 188.2
mm2.
2. In the photograph of the same lens, but cut exactly in half along
the A-P axis, the CSA and the distance from the A-P axis to the
equator pole were found to be 21,531.5 and 194.7 pixels, respectively,
and were compared with the pixel values obtained for the whole lens
AJP-Cell Physiol • VOL
Adolescent human eyes can attain up to 14 diopters (D) of accommodation, a property that declines with aging (a diopter measures the
power of a lens and is equal to the reciprocal of the focal length of the
lens in meters).
Human crystalline lenses of 20 and 45 yr of age were chosen to be
depicted in their unaccommodative (0 D) and in their purported
maximal accommodative states (10 and 4 D, respectively). The
resulting drawings represented a sagittal cut from the A-P side
through the A-P axis. The final outlined schematics were drawn in
Photoshop. The resulting CSAs from both accommodative states, at
both ages, were used to calculate their volumes as was done with the
images of the bovine lens.
Most parameters needed for the sketches of the lenses were obtained or calculated from information available in the literature (4, 5,
12, 25, 28). Stepwise description of the construction from the available data is shown below. An assumption in the present study is that
lenses change the CSA and the volume with minimal or no CSA
perimeter change. Therefore, the perimeters of the constructed lens
CSAs were kept constant.
Accommodated lenses from in vitro data. Isolated postmortem
human lenses presumably manifest their most rounded conformation
because they are devoid of any tension from zonulae and ciliary body.
Fig. 4. Images of the bovine lens after being processed with the software
ImageJ and Photoshop.
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Calculation of Volumes on the Theoretical Human Lens
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LENS VOLUME CHANGE DURING ACCOMMODATION
UCM R a ⫽ ACM R a ⫹ (0.62 mm ⫻ D of ACM lens),
UCM R p ⫽ ACM R p ⫹ (0.13 mm ⫻ D of ACM lens)
and
Fig. 6. Images of all created human crystalline lenses. Whole and half lenses
at each age and accommodative state are shown. Unaccommodated lens is
choosen as zero diopter.
UCM A-P ⫽ ACM A-P ⫺ [(0.058⫺0.00048⫻age)
⫻D of ACM lens].
After the circles were drawn with the calculated curvatures, they
were symmetrically approached in a fashion similar to the maximally
accommodated lenses from the in vitro data to the specified A-P
thickness. Since there are no reliable studies on equator lengths of
unaccommodated in vivo lenses, the equator and the end caps were
fitted into the shape via trial-and-error method, until the equator and
the end caps joined the edges of the outlined anterior and posterior
lines, respecting the previously mentioned ratio of 8.28 ⫽ radius of
equator/radius of end cap.
All of the human lenses diagramed (Fig. 6) were analyzed in a
manner similar to that described earlier for the bovine lenses by
using ImageJ to obtain the measurements needed and by applying
the modified horn torus formula to calculate the volumes.
RESULTS
The Bovine Lens
Fig. 5. Procedure to create a model human lens from circles of various
curvatures. See text for details. D, diopter.
AJP-Cell Physiol • VOL
Tables 1 and 2 list the data obtained with the bovine lens. Of
the three parameters presented, A-P length and equator diameters were actual mechanical measurements, included to
demonstrate differences during relaxing (set as “control” for
our purposes) and stretching of the lens, akin to accommodative changes within the in vivo eye, and were used in the
calibration process to convert pixels to millimeters. Both factors are discussed later for their implication in dioptric power
changes as a result of their different curvatures and thicknesses. The third parameter, the volume, was a value calculated
from the analysis of the digital pictures.
Change in shape and volume of the lens submerged in
Tyrode solution. Two sets of experiments were performed in
which the whole experimental setup was submerged in
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Therefore, it was assumed that the shape of such lenses corresponds
to the largest ocular accommodation for its age. For example, for a
20-yr-old, an overall eye accommodation of 10 D was assumed to be
the maximum for that age (4, 15), even though the eye could in
principle accommodate slightly more or less at age 20 (15).
Rosen et al. (25), in their research on excised human lenses from
cadavers (ages 20 to 99 yr), developed a linear regression analysis of
curvatures of the anterior and posterior surfaces, as well as A-P
sagittal thickness and equator diameter. Most of the formulas for
creating the accommodated lenses were extracted from this study.
As an example, for the creation of the 20-yr-old lens in Photoshop, from an eye that accommodated 10 D, the radius of curvature
of the anterior aspect (Ra) was obtained from Rosen’s formula:
Ra ⫽ 0.046 mm ⫻ age ⫹ 7.5. A circle with d ⫽ 16.9 mm was then
depicted (Fig. 5). In the aforementioned study it was found that the
posterior aspect radius of curvature (Rp) does not change with age;
therefore, the reported Rp value of 5.5 mm was doubled to draw a
circle with d ⫽ 11.0 mm, which corresponded to the posterior aspect
of the accommodated 20-yr-old lens.
The next step was to find the A-P thickness using the formula A-P
thickness ⫽ 0.0123 mm ⫻ age ⫹ 3.97. A value of 4.22 mm was
obtained.
The two circles were then superimposed with their centers aligned
on the same axis, until the maximal distance between the portion of
the circle (arc) that represented the anterior aspect was at 4.22 mm of
distance from the arc representing the posterior aspect. Subsequently,
the equator length was calculated as 0.0138 ⫻ age ⫹ 8.7. The value
calculated for the equator was 8.98 mm.
Near the equatorial periphery (the bow zone), the curvature radii on
the anterior and posterior sides of the equator become smaller.
Therefore, as a final step, two smaller circles were sketched to adjoin
both surfaces at each end of the equator. The circles with a radius that
was 8.28 times smaller than the equator’s radius, called “end caps,”
were placed to join tangentially the anterior and posterior at certain
angles as proposed and modeled by Burd et al. (5) and Schachar et al.
(27). The resulting outline was cropped and analyzed as described
above for the bovine lens.
Information from in vivo lenses. For drawing the lenses with 0 D
accommodation, linear regression analysis developed by Dubbelman
et al. (12) from corrected Scheimpflug images on live subjects were
mainly used. Values for Ra, Rp, and A-P thickness, as well as the total
diopters of the accommodated lenses (ACM) were needed to calculate
the curvatures of the unaccommodated lenses (UCM) as follows:
C801
LENS VOLUME CHANGE DURING ACCOMMODATION
Table 1. Changes in bovine lens dimensions and volume upon simulated accommodative changes in Tyrode submersion
A-P Length, mm
Relaxed
Stretched
12.9
12.1
13.1
12.1
12.6
12.5
12.1
12.5
0.15
12.8
11.8
12.3
11.8
12.2
12.2
11.9
12.1
0.13
⫺3.2*
11.9
12.2
12.6
11.1
12.5
12.3
12.1
0.22
11.7
12.0
12.4
10.4
12.1
12.0
11.8
0.29
⫺2.5*
Equator Diameter, mm
Relaxed
Relaxed
Stretched
Volume, ml
Relaxed
Relaxed
Stretched
2.33
1.94
2.25
1.86
2.08
2.05
1.89
2.06
0.07
2.25
1.87
2.00
1.81
1.98
1.91
1.83
1.95
0.06
⫺5.3*
1.76
1.80
2.11
1.38
2.04
1.92
1.83
0.11
1.54
1.77
1.99
1.25
1.94
1.80
1.72
0.11
⫺6.0†
Relaxed
Set 1
Mean
SE
%Change
18.2
18.1
17.8
17.2
18.8
18.0
17.6
18.0
0.19
18.8
18.4
18.6
17.7
19.0
18.2
18.0
18.4
0.17
⫹2.2*
Set 2
17.4
17.5
19.0
16.8
17.4
17.8
17.7
0.30
17.7
18.0
19.3
17.0
17.8
18.1
18.0
0.31
⫹1.7*
17.8
17.7
18.8
16.6
17.6
17.8
17.7
0.29
⫺1.7†
1.84
1.80
2.09
1.37
1.94
2.06
1.85
0.11
⫹7.6†
A-P length, length of anterior-posterior axis. *P ⬍ 0.01. †P ⬍ 0.05.
Tyrode solution (Table 1). In set 1 (n ⫽ 7), the naturally
relaxed lens (with no imposed tension) had an A-P length of
12.5 mm, and a 3.2% reduction was achieved when the lens
was stretched (unaccommodated). On the same maneuver,
the equator increased 2.2% from 18.0 to 18.4 mm. Analyzed
sagittal photographs yielded a volume reduction of 5.3%
(2.06 to 1.95 ml) when the lens was stretched.
In set 2 (n ⫽ 6), an extra step was added at the end to show
reversible changes when going back to the relaxed control
state. A-P length and equator diameter first decreased and
increased, respectively, and then recovered their initial values
upon relaxation, whereas the volume decreased 6% during
stretching and recovered to 1.6% above its control value when
the lens was relaxed at the end.
Change in shape and volume of the lens submerged in oil.
Candia et al. (8) reported that lenses compressed in an oil
bath lose volume that is not recovered when the lens is
relaxed in this medium. With this rationale, a set of experiments consisting of seven lenses was done in which they
were submerged in oil and subsequently stretched and
relaxed with the stretching device used above (Table 2). The
results show that, unlike relaxation in Tyrode solution, the
lenses did not regain their initial parameters. Upon stretching, lenses yielded a 5.6% reduction of the mean volume
(1.77 to 1.67 ml), and subsequent relaxation, still under oil,
gave a small, insignificant increase to 1.70 ml.
However, when four of those lenses were removed from the
oil (last 4 experiments in Table 2) and further exposed to
Tyrode solution, they recovered their initial values that were
determined under the relaxed state. Changes in the A-P thickness and equator diameter were significantly different when the
lenses were stretched under oil; however, there was a marginally significant recovery of the control values when lenses were
relaxed while still under oil, probably due to the natural shape
of the lens somehow being distorted in the oil maneuvers.
AJP-Cell Physiol • VOL
Nonetheless, there was a clear restoration of both parameters
when lenses were returned to control conditions in Tyrode
solution.
The Human Lens
The results shown in Table 3 demonstrate that in a 20-yr-old
lens changing from the fully accommodated state (10 D) to the
unaccommodated state (0 D), the A-P thickness decreases
13.1%, equator diameter increases 2.9%, and CSA decreases
7.1%, and these changes result in a 2.6% decrease of the
volume from 0.155 to 0.151 ml.
The lens parameters that were obtained from the sketches of
the 45-yr-old lens at 4 and 0 D are, respectively, as follows:
A-P thickness of 4.52 and 4.38 mm (3.2% reduction), equator
diameter of 9.32 and 9.41 mm (1% augmentation), CSA of
15.45 and 15.14 mm2 (2% decrease), and finally, a volume
decrease of 1.7%, from 0.183 to 0.180 ml.
DISCUSSION
Our results confirm in two different mammalian models, the
in vitro bovine crystalline lens and the modeled human lens,
the hypothesis that lenses gain and lose volume during accommodation and unaccommodation, respectively. In the bovine, a
reversible 6 – 8% change was observed, and in the human, a
2–3% increase of volume was calculated with increased accommodation.
The bovine accommodative amplitude has not been studied
previously but is estimated to be low, less than in primates and
more than in rodents, perhaps no more than 2 D (3, 23). To
approximate the modification in dioptric power that the
changes in volume in our experiments represent, the bovine
lens photographs were further analyzed. The radii of curvatures
at the two accommodative states were measured, and together
with the A-P thickness (previously measured) plus the refrac-
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Mean
SE
%Change
12.2
12.1
12.7
10.8
12.2
12.3
12.1
0.26
⫹2.5*
C802
1.90
0.01
⫹6.1*
A-P Length, mm Equator Diameter, mm CSA, mm2 Volume, ml
1.79
0.03
2.2
20-yr-old lens
ACM (10 D)
UCM (0 D)
%Change
45-yr-old lens
ACM (4 D)
UCM (0 D)
%Change
1.86
0.02
In the last 4 experiments, lenses were removed from the oil and further exposed to Tyrode solution. *P ⬍ 0.01. †P ⬍ 0.05.
17.7
0.13
⫹0.6*
17.6
0.14
⫺0.7†
17.7
0.13
0.4*
17.6
0.13
12.3
0.13
⫹1.6*
12.1
0.15
⫹1.7†
11.9
0.21
⫺3.5*
12.3
0.13
Mean
SE
%Change
Mean of last 4
experiments
SE
%Change
11.6
11.2
11.4
12.1
12.4
11.7
11.4
11.7
0.16
⫺3.3*
12.1
11.7
11.8
12.7
12.4
12.3
12.0
12.1
0.12
4.22
3.73
⫺13.1
8.98
9.17
⫹2.1
13.66
12.66
⫺7.9
0.155
0.151
⫺2.6
4.52
4.38
⫺3.2
9.32
9.41
⫹1.0
15.45
15.14
⫺2.0
0.183
0.180
⫺1.7
CSA, cross-sectional area; ACM, accommodated (relaxed) lenses; UCM,
unaccommodated (stretched) lenses; D, diopter, a measure of the power of a
lens.
1.75
0.05
⫺5.8*
1.87
1.93
1.91
1.87
17.4
17.5
17.9
17.9
12.4
12.7
12.1
12.1
Relaxed in Oil
1.66
1.49
1.59
1.79
1.80
1.85
1.71
1.70
0.05
⫹1.8
1.65
1.51
1.56
1.77
1.82
1.78
1.62
1.67
0.05
⫺5.6*
Stretched in Oil
Relaxed
Relaxed in Tyrode
1.74
1.57
1.63
1.86
1.88
1.90
1.80
1.77
0.05
16.9
16.1
16.7
17.3
17.3
17.8
17.8
17.1
0.23
⫺1.7†
Relaxed in Oil
Stretched in Oil
17.2
16.5
17.1
17.5
17.4
17.9
17.9
17.4
0.18
⫹1.2*
16.9
16.2
16.8
17.5
17.3
17.9
17.7
17.2
0.22
Stretched in Oil
Relaxed
Relaxed in Oil
Relaxed in Tyrode
Relaxed
Equator Diameter, mm
A-P Length, mm
Table 2. Changes in bovine lens dimensions and volume upon simulated accommodative changes in oil submersion
Table 3. Dimensions and volumes of 20- and 45-yr-old
human lenses during extremes in accommodative states
AJP-Cell Physiol • VOL
tive indexes for the lens, aqueous, and vitreous humor (21, 22),
the equivalent dioptric power of the bovine lens was computed
using the Gullstrand’s equation for thick lenses. From 11
bovine lenses, a mean value of 14.8 ⫾ 0.25 D was calculated
for the unaccommodated (stretched) lens, whereas the value for
the accommodated (relaxed) lens was 16.3 ⫾ 0.23 D. These
values probably represent only a fraction of the total equivalent
power for the whole simplified eye. However, with other
factors being constant, the change was statistically significant
(P ⬍ 0.01 as paired data), representing the lens contribution to
accommodation, although we clearly cannot say with certainty
what the real dioptric powers of the lens within the in vivo eye
actually are. The fact that with a change of 1.5 D in lens
equivalent power there was an 8% change of volume means
that the magnitude of the changes of accommodation and
volume in vivo could be even higher if the range of accommodation were larger. We did not measure the force that we
applied to deform the lens simulating the natural accommodation.
Nevertheless, the process was reversible and the anatomical
structures remained intact, indicating that they could withstand
an equivalent or even larger force in vivo. Even if the bovine
eye does not accommodate, it serves as a model to show that
lens deformation is associated with volume change. In the
Fig. 7. Anterior surface depictions of accommodated and unaccommodated
lenses, showing increased surface area circumferentially (in white), in proximity to the equator with unaccommodation, while maintaining outside anterior
pole-to-equator length constant.
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11.9
11.4
11.7
12.4
12.2
12.2
11.7
11.9
0.13
⫹1.7†
Volume, ml
Relaxed in Tyrode
LENS VOLUME CHANGE DURING ACCOMMODATION
LENS VOLUME CHANGE DURING ACCOMMODATION
AJP-Cell Physiol • VOL
seconds to stretch the lens, but we felt no particular resistance.
Thus we believe that with a more advanced technology, the
same volume change can be attained in less than a second.
Although we have clearly demonstrated a change in volume of
the lens, our model and interpretation also require changes in
its surface area (see Fig. 7). We assume that the lens capsule
may not stretch radially in the pole-to-equator direction. As the
lens is pulled by the zonulae, the A-P distance decreases and
the region closest to the equator opens up the most, like a
Spanish abanico (ladies fan). This is not different from trying
to flatten an upside-down cup. One needs to make radial cuts
and fill in the triangular areas between cuts with additional
surface. Little change in area occurs at the poles.
In humans, equivalent dioptric powers of 60 D for the eye
with the unaccommodated lens and 71 D for the eye with the
accommodated lens are typical values for about 10 D of in vivo
accommodation. The unaccommodated crystalline lens equivalent power is 22 D; in an eye with 10 D of accommodation,
the lens equivalent power is 35 D. Therefore, a change of 10 D
change for the whole eye represents a change of 13 D in the
equivalent powers of the lens (22).
To validate whether our modeled human lenses (Table 1)
were close to the in vivo values, we also calculated the
equivalent powers. In the case of the 20-yr-old lens, the 2.6%
decrease in volume represented a change of lens equivalent
power from 27.1 to 20.6 D. For the 45-yr-old lens, the 1.7%
decrease in volume correlated with an equivalent lens power
change from 26.3 to 22.6 D.
Furthermore, using magnetic resonance imaging of the human eye in vivo at 0.1 and 8 D, Strenk et al. (30) found that the
lens CSA increased with accommodation. They realized that
the changes in lens CSA that they observed during accommodation reflected changes in lens volume and suggested that the
lens material must be slightly compressed when the lens is
stretched (i.e., unaccommodated). Moreover, they also emphasized that their results challenge a long-held belief that the lens
is incompressible, based on the fact that it contains a large
amount of water, which is incompressible. However, Strenk
et al. did not consider the possibility that fluid could leave the
lens when it is compressed, as our results indicate. Nevertheless, both our data and those of Strenk et al. are in accord on
the point that the CSA increases with accommodation.
Presbyopia, a condition that affects humans as they age, is
characterized as a decline in accommodation. Most believe that
the presbyopic changes are mainly due to the growth of the lens
throughout life and an associated increase in capsular and
lenticular stiffness. Several theories have been advanced to
explain this change (2, 14, 15, 29). We suggest, in addition,
that defective and less permeable AQPs within the lens may
inhibit the movement of fluid between the fibers that would be
necessary for a rapid deformation of the lens.
ACKNOWLEDGMENTS
We thank Lawrence Alvarez and Brian Wu for contributions toward the
preparation of the manuscript.
GRANTS
This work was supported by National Eye Institute Grants EY00160 and
EY01867 and by an unrestricted grant from Research to Prevent Blindness,
Inc., New York, NY.
293 • AUGUST 2007 •
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experiments performed under oil, stretching also produced a
decrease in volume. The lost fluid was dispersed in the oil, and
upon release of the stretching forces, the lens did not regain its
volume and its shape was distorted. Obviously, when the lens
is perturbed from its natural relaxed, rounded state by stretching, internal forces develop that are probably only dissipated
by fluid absorption. This springlike behavior of the lens fibers
has been described by Kuszak et al. (19). They compared the
tension developed inside the lens fibers to a springlike phenomenon that tends to return the lens to its lower energy
natural accommodated state. They also pointed out that aquaporins (AQPs) and gap junctions predominantly connect the
fibers to each other in their central parts, leaving the end of the
fibers, which form the lens sutures, free for a limited displacement when the lens changes shape during the accommodation
process. They noted as well that the cortex participates in the
accommodation process. Although the fibers’ structure of the
bovine lens may not allow a wide range of accommodation,
findings by Kuszak et al. can be applied to the internal changes
that occur in our model.
When an aqueous medium is not bathing the surface of the
lens, the lens cannot regain its natural volume and shape, and
its sagittal image deforms. When the lens is transferred to
Tyrode solution, the lens spontaneously recovers its volume
and shape. We could not determine whether the fluid interchange occurs at the anterior or posterior surface, or both, or
what were the relative contributions of the lens compartments.
Knowing that most of the change in curvature occurs at the
anterior face, which is bathed by the aqueous humor, we expect
this to be the side of most of the interchange.
An extensive network of water channels (AQP0) communicates the internal lens fibers to each other (31, 32). Furthermore, Mathias et al. (20) proposed a model for an internal
circulating system within the avascular lens that results in fluid
movement internally within the organ. Fluid is thought to enter
the lens at the poles and leave at the equator, facilitated by the
syncytial nature of the lens with its extensive internal communication via gap junctions and AQPs. We demonstrated a
current distribution in the rabbit lens consistent with the current
flows that support the fluid movement in the model by Mathias
et al., as well as evidence for an internal fluid movement within
the bovine lens (6, 9). Although the natural fluid flow is slow
and driven by osmotic forces, the same channels may allow
rapid fluid flow during accommodation driven by the external
mechanical force. Thus any external force that deforms the lens
will force water movement within the lens, as will happen
when a sponge full of water is squeezed. The fluid that comes
to the outside represents the contribution of multiple compartments that get realigned, with the cortex fibers possibly contributing the most. Eventually, the fluid has to flow across the
epithelium and the capsule. The capsule (as a collagen matrix)
is highly permeable to water, and the epithelium contains
AQPs (26).
Although the lens can swell or shrink under the influence of
osmotic forces, there are no studies showing that a few microliters can be expelled across the anterior face in less than a
second (2), which is the time required in accommodation. We
do not know the force developed inside the lens when
stretched, but it should be sufficient to move fluid at the rate
required. For technical reasons related to the design of our
“stretching apparatus” (rotating the wheel), it took several
C803
C804
LENS VOLUME CHANGE DURING ACCOMMODATION
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