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Age-Related Changes in Human Ciliary Muscle and Lens:
A Magnetic Resonance Imaging Study
Susan A. Strenk,13 John L Semmlow,1'2 Lawrence M. Strenk? Paula Munoz,1'2
Judy Gronlund-Jacob,4 andj. Kevin DeMarco4
PURPOSE. TO use
high-resolution magnetic resonance (MR) images of the eye to directly measure the
relationship between ciliary muscle contraction and lens response with advancing age.
A General Electric, 1.5-Tesla MR imager and a custom-designed eye imaging coil were
used to collect high-resolution MR images from 25 subjects, 22 through 83 years of age. A
nonmagnetic binocular stimulus apparatus was used to induce both relaxed accommodation (0.1
diopter [D]) and strong accommodative effort (8.0 D). Measurements of the ciliary muscle ring
diameter (based on the inner apex), lens equatorial diameter, and lens thickness were derived from
the MR images.
METHODS.
RESULTS. Muscle contraction is present in all subjects and reduces only slightly with advancing age.
A decrease in the diameter of the unaccommodated ciliary muscle ring was highly correlated with
advancing age. Lens equatorial diameter does not correlate with age for either accommodative
state. Although unaccommodated lens thickness (i.e., lens minor axis length) increases with age,
the thickness of the lens under accommodative effort is only modestly age-dependent.
Ciliary muscle contractile activity remains active in all subjects. A decrease in the
unaccommodated ciliary muscle diameter, along with the previously noted increase in lens
thickness (the "lens paradox"), demonstrates the greatest correlation with advancing age. These
results support the theory that presbyopia is actually the loss in ability to disaccommodate due to
increases in lens thickness, the inward movement of the ciliary ring, or both. (Invest Ophthalmol
Vis Sci. 1999;40:l 162-1169)
CONCLUSIONS.
P
resbyopia, an inevitable consequence of growing older,
is generally believed to be caused, at least in part, by a
decrease in the ability of the lens to change its shape.
Both contemporary and classic theories for presbyopia are
based on the Gullstrand formulation of the accommodative
(i.e., focusing) mechanism,' a theory developed from concepts
first described by Helmholtz in the mid-19th century. Under
Gullstrand's theory, the ciliary muscle alters the balance of two
passive elastic elements: the elasticity of the lens and a restoring element thought to be the choroid. (This single muscle
mechanical process is unique. Perhaps the tight confines between the lens and the edge of the eye prohibit the typical
agonist-antagonist muscle mechanism. Evidence presented
later indicates that presbyopia may be the price paid for this
motor expedient.) These changes in balance alter the diameter
of a suspensory ring formed from the ciliary muscle that sur-
From the 'Department of Surgery (Bioengineering), UMDNJ-Robert Wood Johnson Medical School, New Brunswick, New Jersey; the
2
Department of Biomedical Engineering, Rutgers-The State University
of New Jersey, Piscataway, New Jersey; 3Diagnostics Instruments,
Aurora, Ohio; and the "'Laurie Imaging Center, New Brunswick, New
Jersey.
Supported in part by Grant EY-11529 from the National Eye
Institute, National Institutes of Health, Bethesda, Maryland.
Submitted for publication October 2, 1998; revised December 2,
1998; accepted December 21, 1998.
Proprietary interest category: N.
Reprint requests: John L. Semmlow, Department of Biomedical
Engineering, Rutgers University, 617 Bowser Road, Piscataway, NJ
08855.
1162
rounds and supports the lens. Decreases in ring diameter allow
the lens to round up, increasing its dioptric power. Conversely,
increasing ciliary ring diameter applies tension that flattens the
lens. (Recently, some modifications of these basic concepts
have been developed, in particular the essential role of the
vitreous in supporting the lens2'3 and a geometric model of
accommodation.4)
Changes in any of the three major accommodative processes, the lens, the ciliary muscle, or the restoring elasticity,
could alter the balance of forces in this system, which in turn
would change the equilibrium position of the ciliary ring and
influence the maximum accommodative response. Because all
these processes experience some change in their mechanical
properties with age, they have all been considered, at one time
or another, as potentially significant in the development of
presbyopia.
Two classic theories have evolved from a long-standing
debate to explain the mechanics of presbyopia.5'6 These theories differ with regard to ciliary muscle involvement and
predict different relationships between ciliary muscle contraction and lens shape changes. The earliest theory for presbyopia
placed all the responsibility on the lens: Presbyopia was believed to be caused by a decrease in the ability of the lens to
change its shape. Under this lenticular theory, developed from
early contributions by Hess7 and Gullstrand,' muscle changes
are not an important consideration in presbyopia. The muscle's
ability to modify lens shape is essentially normal in the region
where the lens is still capable of response (the "manifest"
region). Above this level, a latent region exists where the
Investigative Ophthalmology & Visual Science, May 1999, Vol. 40, No. 6
Copyright © Association for Research in Vision and Ophthalmology
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IOVS, May 1999, Vol. 40, No. 6
muscle, although still capable of contracting, cannot produce a
change in accommodation due to excessive stiffness.
In opposition to the lenticular theory of Hess-Gullstrand,
the extralenticular theory of Duane8'9 placed the responsibility
for presbyopia on the ciliary muscle. This theory was developed in response to experiments showing that the slightest
weakening of the ciliary muscle (by topical application of
diluted atropine) produced a decrease in maximum accommodative response.10"12 If a latent region existed as proposed by
Hess-Gullstrand, some muscle weakening should be possible
without a corresponding change in lens shape. In a modification of this theory by Alpern,1314 the muscle-lens relationship
has a latent region initially, but gradual atrophy through lack of
use eliminates this latent region. This modification results in an
essentially lenticular theory because muscle weakness becomes an effect not a cause of lens immobility.15
Fincham proposed a theory 1016 that falls between these
two extremes, suggesting that the decline in accommodation
was primarily lenticular but that the amount of ciliary muscle
contraction required for a given accommodative response also
increases with age over the entire response range. Although
the theories of Duane and Fincham postulate different underlying causes for presbyopia (muscle in the former, lens in the
latter), they both predict the same muscle-lens relationship.
Muscle activity should always produce some, however small,
lens response, and the maximum accommodative response
should always be associated with maximum muscle effort: If
additional muscle contraction was made possible, a greater
accommodative response should be achieved.
Although these early theories imply experimentally verifiable differences, none has gained unambiguous support. Under
the lenticular theory ascribed to Hess and Gullstrand, the
strength of the ciliary muscle (or other extralenticular processes) should not be diminished in the region where the lens
is still capable of fairly normal responses (the "manifest")
region. Above this level, a latent region should exist where the
muscle, although still capable of contracting, cannot produce a
change in accommodation due to limitations in mechanical
properties of the lens.14'17"19 Because the responsiveness, or
effectiveness, of the accommodative motor processes (both
lenticular and extralenticular) would be normal in the nonpresbyopic or "manifest" response region, variables that involve
accommodative responsiveness, such as AC/A stimulus ratio,
will be unchanged in this region. Conversely, because responsiveness is negligible within the presbyopic or "latent" region,
the AC/A stimulus ratio should be very large within this region.
Results from studies that track changes in the AC/A stimulus
ratio with age have been mixed: Some show little change or
even a gradual decrease with age,20"24 whereas others,25 including two longitudinal studies,2627 have shown a marked
increase in stimulus AC/A with age. After a long history of
conflicting findings, recent results28"30 clearly demonstrate
that from 30 to around 45 years of age, the response AC/A ratio
increases by approximately 0.1 prism diopter [D]/D. per year.
After 45 years of age, this measurement is no longer reliable
because of the small accommodative response. This modest
change in the response AC/A ratio is most consistent with the
Hess-Gullstrand theory.
The strongest support for the lenticular theory is found in
evidence that indicates that the ciliary muscle does not weaken
with age, a fundamental assumption of the extralenticular
theory. Several researchers8'31"33 have shown that loss of ac-
MRI of the Accommodated Lens and Ciliary Muscle
1163
commodation begins at an early age, and Sun et al.33 have
argued that this would be unusual for a disorder caused by
muscle weakness. In addition, Fisher34 has determined that the
strength of the ciliary muscle actually increases with age.
Additional support for the lenticular theory is found in impedance cyclography experiments, which provide a qualitative
measure of ciliary muscle activity. Saladin and Stark35 showed
ciliary activity in the absence of an accommodative response,
indicating a true latent region as required by the lenticular
theory. Similarly, Swegmark36 showed that the amount of ciliary muscle activity required for a given accommodative response within the manifest region does not change with age as
implied by the extralenticular theory.
Although it is commonly held that changes in the mechanical properties of the lens are an underlying cause of presbyopia, there is evidence that extralenticular processes do play a
significant role in the apparent violation of the Hess-Gullstrand
theory. For example, the lenticular theory assumes that maximum accommodation occurs well before maximum ciliary
muscle contraction; hence, a modest increase or decrease in
muscle contractile ability should have no effect on the maximum accommodative response. Careful studies by Fincham10
and later by Eskridge1 l l 2 show that if the ciliary muscle activity is augmented or diminished (e.g., through the use of a
parasympathomimetic or parasympatholytic drug) maximum
accommodation changes accordingly. Thisfindingimplies that
ciliary muscle weakness does contribute to the loss of accommodation. However, Semmlow et al.5 used computer simulations of the muscle-lens system to show that these results were
also compatible with the lenticular theory when the highly
nonlinear behavior of the presbyopic lens was taken into account.
Much of the controversy regarding the mechanism of
presbyopia (and accommodation) results from an inability to
directly measure the parameters in question. In this study,
high-resolution magnetic resonance imaging (MRI) has been
used to directly detect changes in the lens and the ciliary
muscle. Of primary interest in this study is the relationship
between the ciliary muscle and the lens. Specifically, we
wished to determine whether the contractile ability of the
ciliary muscle diminishes with age. We also examined changes
in the resting (unaccommodated) dimensions of the ciliary
muscle and age-related changes in lens equatorial diameter and
thickness.
METHODS
High-resolution MRI is an extremely useful modality with
which to study the relationship between ciliary muscle contraction and lens response, because it produces undistorted
images of the entire anterior portion of the eye. Additionally,
MRI offers excellent soft tissue contrast, thus the ciliary muscle
is well visualized. MRI offers the ability to directly image
intraocular structures during accommodation without obscuring vision and MR images can be acquired in any desired plane.
Finally, MRI uses no ionizing radiation and has no known
adverse effects. Nonetheless, to image structures as small as the
ciliary muscle and lens using MRI presents a number of challenges, including resolution limitations, signal-to-noise ratio
(SNR) limitations, image acquisition time constraints, the difficulty of presenting accommodative stimuli within the confines
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1164
Strenk et al.
IOVS, May 1999, Vol. 40, No. 6
of the imager, and the need to limit head and eye movements
during the scans.
Imaging Protocol
A 1.5-Testa MR imager (1.5T-Signa, General Electric Medical
Systems, Waukesha, WI) was used to obtain images from 26
subjects, 21 to 83 years of age. The research followed the
tenets of the Declaration of Helsinki, informed consent was
obtained after the nature and possible consequences of the
study were explained, and the research was approved by the
institutional review board of UMDNJ-Robert Wood Johnson
Medical School.
Images were acquired using a T,-weighted, single echo,
multislice, spin-echo technique. The imaging protocol consisted of acquiring a 2.5-minute sagittal scout scan to ensure
that the eye was properly positioned and that the axial scan
that followed would bisect the lens. Great care was taken to
position the eye so that it was not rotated with respect to the
axial plane. Multislice axial scans were collected with a 4-cm
field-of-view (FOV) and 256 X 256 pixel matrix, resulting in a
0.156 mm in-plane resolution. The contiguous 3-mm-thick axial
slices ensured that the center of the lens was captured and
allowed the desired slice and its adjacent neighbors to be
evaluated to measure slice-centering accuracy.
Standard clinical MRI rarely uses a FOV less than 8 cm. Yet
to obtain adequate in-plane resolution, a smaller FOV was
required. By using a 4-cm FOV and standard clinical MR imaging receiver coils, we attained sufficient in-plane resolution,
but the SNR of the resultant image was decreased to an unacceptable level. The SNR, which had been decreased by a factor
of 4 because of the increase in FOV, could be restored to its
original value by increasing the number of imaging averages by
a factor of 16; however, this would result in an unacceptable
increase the scan time from 5 to 80 minutes. We decided to
address these SNR and scan time limitations by designing a
custom receiver coil consisting of a two-turn solenoid with a
2.5-cm diameter. This small coil, positioned directly around the
eye, restored the SNR in the region of interest to an adequate
level and allowed high-resolution images of the ciliary muscle
and lens to be acquired.
Stimulus Apparatus
An accommodative stimulus apparatus device was designed to
present binocular (accommodative and disparity) stimuli and
to provide a fixation target to reduce eye movement during the
scan. The nonmagnetic apparatus consisted of a plastic frame
that allowed the position of the visual target to be varied, a
mirror to allow viewing of distant targets, and a simple black
crosshair target that was backlit by a small incandescent bulb.
The light was driven by a flasher circuit that periodically varied
the bulb intensity between 100% and 50% at a rate of 2 Hz.
Flashing the stimulus produced a compelling target and reduced the stabilized image phenomenon, which results in
target image fading. The flashing target stimulus was effective
in limiting eye movement during the scan. Standard MRI positioning cushions were used to limit head movement.
Visual targets were positioned at the appropriate distance
from the eye to provide either a strong (8.0 D) or minimal (0.1
D) binocular accommodative stimulus during the MR scans.
For presbyopic subjects, the near target was out of focus, but
the effort to fuse produces disparity drive to the accommoda-
FIGURE 1. High-resolution axial MR image of the eye. (A) Binocular fur
stimulus (0.1 D). (B) Binocular near stimulus (8 D). Both are from
subject EB.
tive system. 5 1 0 1 ' The initial scans were generally taken at the
minimum stimulus at -which point resting accommodation is
expected. Scans taken under the 8-D accommodative stimulus
followed. Images were acquired first with far target stimulation
followed by near target stimulation to reduce possible effects
from incomplete accommodative relaxation.
Image Analysis
The images were analyzed using the NIH Image 1.6 software
package. The pixel coordinates for the major and minor lens
axes were obtained. Within the ciliary body, the ciliary muscle
was identified as a roughly triangular hypointense pixel cluster
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MRI of the Accommodated Lens and Ciliary Muscle
IOVS, May 1999, Vol. 40, No. 6
TABLE
1. Repeatability Data
Condition
Ciliary Ring
Diameter
(mm)
Lens
Diameter
(mm)
Lens
Thickness
(mm)
JS-8 D
JS-8D
JS-8D
Average (SD)
12.30
13-27
13.27
13.28 (0.014)
8.96
8.89
8.90
8.92 (0.037)
4.44
4.49
4.41
4.45 (0.042)
extending posteriorly from the iris root. A pixel corresponding
to the medial apex of this triangle was identified for the nasal
and temporal ciliary muscle cross sections. The distance between these points is taken as the apparent ciliary muscle
diameter. Measurements of the apparent ciliary muscle diameter and those of the lens were corrected for finite slice thickness and slice-centering offsets to obtain the actual ciliary
muscle diameter (see the Appendix for a description of these
corrective algorithms).
RESULTS
Figure 1 shows representative images from one subject under
near and far binocular stimuli. To assess the accuracy of the
dimensional data extracted from these images, repeated images
were taken from one subject. Table 1 shows dimensional data
obtained from MR images of subject JS for three different trials
with 8-D accommodative stimulus. The relative consistency of
the data demonstrates that the dimensional measurements obtained from the MR images sets are repeatable to within the
image resolution (0.156 mm).
Figure 2 A shows the change in ciliary muscle ring diameter produced by accommodative effort. For all subjects, the
ciliary muscle continues to contract with accommodative effort, even for advanced presbyopes. Although some reduction
in muscle contractility may occur, particularly in early presbyopes (r2 = 0.26; P < 0.015), substantial contractile ability
remains even in advanced age (note data point at 86 years of
age). However, the most dramatic age-related change in the
muscle is the decrease in unaccommodated ring diameter (Figure 2B; r2 = 0.74; P < 0.0001).
The age-related loss in the ability of the lens to change
shape is shown in Figures 3A and 4A, which plot the changes
in lens thickness and lens equatorial diameter that occur with
accommodative effort. In both plots, the ability to change
diameter and thickness decreases to zero after 50 years of age.
(Note that the negative values are within the resolution limits
of the measurement process.) As noted previously, the accommodated lens thickens with age, 37 '' i0 as can be seen in Figure
3B, and a strong correlation was found between lens thickness
and age (r2 = 0.53; P < 0.0001). However, the maximum lens
thickness attained under accommodative effort showed only
modest correlation with age (r2 = 0.26; P < 0.12). Similarly,
the equatorial diameter of the unaccommodated lens is not a
function of age as seen in Figure 4B (r2 = 0.0; P > 0.10). For
subjects under 40 years of age, changes in lens dimensions are
age-independent; the diameter decreases an average of 5.7%,
and the thickness increases an average of 12% during maximum accommodative effort. Table 2 summarizes the dimensional data obtained from all subjects.
DISCUSSION
Data were obtained from a limited number of subjects of both
genders and varied races; consequently, significant individual
variations are expected. Because of the limited number of
subjects, ourfindingsare of a preliminary nature. Nonetheless,
a number of statistically significant findings are noted.
15
1.5
E
b
B
14
I
%
<D
1.0
E
~ 13
C
c
O
c
I
0
O)
c
cu
0.0
12
O
6
10 20 30 40 50 60 70 80 90
Age (years)
1165
11
10 20 30 40 50 60 70 80 90
Age (years)
FIGURE 2. (A) Change in the diameter of the ciliary muscle ring produced by an 8-D binocular accommodative stimulus as a function of age. Ciliary muscle activity continues to occur even in advanced
presbyopia. (B) Unaccommodated (relaxed) ciliary muscle ring diameter as a function of age. The ciliary
ring diameter decreases with age.
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1166
Strenk et al.
E
E
IOVS, May 1999, Vol. 40, No. 6
1.0
B
0
I 5
c
!§ 0.5
(D
c
o
c
0
0 0.0
CD
c
c
(D
O
20 30 40 50 60 70 80 90
20 30 40 50 60 70 80 90
Age (years)
Age (years)
FIGURE 3- (A) Change in the lens thickness produced by an 8-D binocular accommodative stimulus as a
function of age. The ability of the lens to change shape diminishes to zero with age. (B) Unaccommodated
(relaxed) lens thickness as a function of age. Lens thickness continues to increase with age as described
in the so-called lens paradox.
Maximum ciliary muscle contractile activity reduces only
slightly with age and the ciliary muscle remains active in all
subjects, well beyond the time when lens response is no longer
possible. Because the restoring force of the choroid is known
to increase with age,41 the contractile force of the ciliary
muscle may actually increase with age.42 Within the context of
classic theories of presbyopia, this finding supports the Hess-
Gullstrand, or lenticular, theory of presbyopia because the
extralenticular theory does not allow for muscle contraction in
the absence of lens response.
Although lens diameter did not show any significant
change with age, an age-related increase in the thickness of the
lens was observed. The increase in lens thickness has been
noted previously and has been termed the "lens paradox."37"40
11
1.0
B
If
E10
£
0
E 0.5
CD
CD
b
-1—1
c
0
to
c
0.0
0)
CD
C
05
sz
O
20 30 40 50 60 70 80 90
Age (years)
20 30 40 50 60 70 80 90
Age (years)
FIGURE 4. (A) Change in lens equatorial diameter produced by an 8-D binocular accommodative stimulus
as a function of age. The ability of the lens to decrease its equatorial diameter decreases to zero with age.
(B) Unaccommodated (relaxed) lens equatorial diameter as a function of age. The equatorial diameter of
the lens does not change with age.
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MRI of the Accommodated Lens and Ciliary Muscle
JOVS, May 1999, Vol. 40, No. 6
TABLE
2. Dimensional Data
Ciliary Muscle (mm)
Age (y)
22
23
24
25
25.5
26
29
29.2
29.4
31
37
37.5
38
38.5
41
42
42.5
44
41
48
49
50
54
62
83
1167
Lens Equ. (mm)
Lens Thickness (mm)
0.1 D
8D
0.1 D
8D
0.1 D
8D
13.88
14.33
13.91
13.34
13.62
13.46
13.87
1386
13.40
13.97
13.38
13.50
13.49
12.85
1361
13-86
12.72
12.73
13-00
13.01
13.30
13.47
13.26
12.52
12.39
13-33
13.27
13-24
12.41
13.07
12.37
13.16
12.71
12.87
13-38
13.04
12.57
12.80
12.61
13-20
13.24
12.44
12.47
12.04
12.46
12.24
13.14
13.04
12.02
12.01
8.90
9.36
9.22
8.56
9.24
9.36
8.44
8.80
8.72
7.91
8.31
8.69
8.75
9.19
8.48
8.74
8.76
8.75
8.85
8.29
8.64
9.36
8.46
8.89
9.29
8.85
8.96
9.37
8.80
3.77
3.61
3.38
3.93
3-52
3.93
3.91
3.46
3.98
4.10
This term relates to the fact that while the lens increases in
thickness and curvature, there is no increase in its refractive
power, presumably because of the action of some compensatory mechanism.43'44
The ciliary muscle also showed a significant decrease in
ring diameter for the unaccommodated state. It is possible that
this decrease in ciliary ring diameter is secondary to the increase in lens thickness. There is evidence to suggest that the
aging lens thickens due to increases in anterior and posterior
lens cortices.44'45 Such a process might lead to a shortening of
the equatorial dimension that would, in turn, pull the ciliary
muscle inward/'3 Although no statistically significant change
was found in lens equatorial dimension, such changes could be
missed because of our sample size. It is also possible that an
increase in lens thickness could exert an inward pull on the
ciliary muscle without altering lens diameter. Because a greater
number of zonulas are attached to the anterior surface of the
lens, an increase in the thickness of the anterior surface might
develop an inward pull caused by the relative position of the
muscle and lens. An inverse process is also possible: Lens
thickening might be the result of the decrease in ciliary ring
diameter. Under this scenario, the inward movement of the
ciliary muscle with age would reduce tension on the lens, and
this reduction in tension would enable processes that lead to
increased thickness. In this case, the decrease in ciliary muscle
ring diameter might be caused by an increase in the resting
length of the restoring elasticity (the choroid) as has been
previously proposed by Bito and Miranda.46 (Although the
choroid appears to increase its elasticity with age,4' there is no
evidence regarding changes in its resting length. An intriguing
analogy is the elasticity in old underwear, which becomes
942
9.58
9.25
9.22
9-40
9-08
9.17
8.75
9.16
9.67
8.97
9.30
9.85
8.98
9.05
9.37
8.82
8.99
8.77
909
8.84
318
3.60
3.75
4.33
3.14
3.64
3.62
4.10
3.47
3.80
4.06
4.39
4.46
3.78
4.13
4.22
5.31
362
4.51
3.87
4.30
4.38
4.09
3.40
4.21
392
4.76
3.66
3.90
4.20
4.40
3.91
4.22
4.31
4.38
4.44
3.63
4.20
4.22
5.33
stiffer but also expands in length. It is the latter feature that
usually leads to its demise.) Alternatively, the decrease in ciliary
ring diameter could be due to growth and/or realignment of
the muscle itself.47 These alternatives are being addressed in
another study.
Although data obtained from the limited number of subjects studied thus far indicate that the ciliary muscle remains
active well after accommodation is lost, a longitudinal study
would directly address this issue and is ongoing. Also, concerns
regarding subject fatigue, image resolution, and the cost of
imager time constrained us to acquire images only at the two
extreme levels of accommodative effort; however, age-related
effects on intermediate accommodative levels might well be of
interest. We are investigating the use of three-dimensional
(volume) MR imaging to obtain information about gradations of
ciliary muscle contraction. Volume MR imaging allows planes
of less than 1 mm to be acquired. If sufficient SNR and thus
in-plane resolution can be obtained, data will be collected at
several intermediate accommodative levels. An additional benefit of volume imaging is that the error due to the finite slice
thickness would become negligible, eliminating the need to
correct for partial volume averaging in the ciliary muscle measurement (see Appendix).
CONCLUSIONS
This study was structured to provide experimental differentiation between two long-standing theories of presbyopia: the
Hess-Gullstrand, or lenticular theory; and the Duane-Fincham,
or extralenticular theory. The approach used MR images to
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examine the relationship between the ciliary muscle and lens
during accommodative effort with advancing presbyopia. Experimental limitations (resolution, SNR, motion artifacts, and
the difficulty of controlling accommodative stimulation within
the confines of the imager) were addressed. MR images were
obtained and analyzed for of 25 subjects. Measurements of the
ciliary muscle ring diameter, lens thickness, and lens equatorial
diameter were obtained from MR images under minimum and
maximum accommodative efforts for each subject. The data
clearly show ciliary muscle activity with accommodative effort
for all ages studied. This finding supports the Hess-Gullstrand
theory and implies that lenticular changes underlie presbyopia.
However, a decrease in the unaccommodated ciliary muscle
diameter was also strongly correlated with age, opening the
possibility that lenticular changes are secondary to reductions
in tension applied by the ciliary ring.
References
1. Gullstrand A. Die optische abbildung in heterogenen medien die
clioptrik der kristallinse des menchen. K Sven Vetenskapsakad
Handl. 1908;43:l-28.
2. Coleman DJ. Unified model for accommodative mechanism. AmJ
Opbthalmol. 1970;69:1063-1079.
3. Coleman DJ. On the hydraulic suspension theory of accommodation. Trans Am Opbthalmol Soc. 1986;84:846-867.
4. Koretz JL, Handleman GH. How the human eye focuses. Sci Am.
1988;259:92-99.
5. Semmlow JL, Stark L, Vanderpol C, Nguyen A. The relationship
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APPENDIX
Correction of the Ciliary Muscle Ring Diameter
for Partial Volume Averaging and Slice-Centering
Offset
Partial volume averaging occurs because the finite slice thickness of 3 mm is projected onto a single image. Slice-centering
offset occurs if the center of the 3-mm slice is offset from the
center of the lens. During volume averaging, the largest object
dimension occurring in the slice is usually visualized in the
resultant image. Consequently, as long as the center of the lens
is captured somewhere within the 3-mm slice, its cross section
will be correctly displayed in the resulting image. Although the
lens dimensions in the resultant image are not altered by either
partial volume averaging or slice-centering offset, both effects
will cause the ciliary muscle ring diameter to appear smaller in
the resultant image. Nonetheless, the actual ciliary muscle ring
diameter is easily calculated from the apparent diameter measured in the image as described below.
Assuming radial symmetry of the lens and ciliary muscle, a
slice passing exactly through the center of the lens produces
an error in the diameter of the ciliary ring because of the finite
thickness of the slice. The actual ciliary ring diameter, Dc, is
given as Dc = \D,2 + (SLT)2]>/2, where Din is the measured
ciliary ring diameter and SLTis the slice thickness. The error in
the measured value of the ciliary ring is further increased if a
slice-centering offset (h) exists (i.e.,, if the center of the slice
MRI of the Accommodated Lens and Ciliary Muscle
1169
does not correspond exactly with the center of the lens).
Although slice-centering offset can be corrected, images that
displayed significant slice-centering offset were discarded. (Obvious lens cross-sectional asymmetry in the two slices flanking
the center slice was used as an indication of slice-centering
offset). Correcting for small slice-centering offsets (generally
<0.75 mm) was accomplished by calculating the width of the
lens in each flanking slice, the superior and inferior lens
chords, Cs and C,. Assuming lens symmetry, these cord lengths
should be equal. The perpendicular offset, h, of the center slice
can be determined from the difference in these chord lengths.
Let D, be the actual diameter of the lens and yg and y, be the
perpendicular distances from the center of the lens to the edge
of the adjacent superior and inferior slices, respectively. Partial
volume averaging results in the longest lens chord in an adjacent slice being visualized. This chord corresponds to the
boundary between the center slice and an adjacent slice. By
measuring chords C, and Cs of adjacent slices, a corresponding
distance^, and j / , can be foundy, = [(P,/2)2 - (C/2) 2 ] 1/2 and
ys = [(ZV2)2 ~ (C.v/2)2]l/2- From the geometry, the slice offset
h is found to be h = (1/2) (ys — y,y
By compensating for the partial volume-averaging error
subsequent to correcting for slice offset, the true diameter of
the ciliary muscle ring, Dc, can be found from the measured
diameter of the ciliary muscle ring, Dni, by the Pythagorean
2
2 l/2
theorem Dc = [D,n + (SLT + hi) ] .
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