·Investigation·
Image
registration of the human accommodating eye demonstrates equivalent increases
in lens equatorial radius and central thickness
Andrzej Grzybowski1,2, Ronald A Schachar3,
Magdalena Gaca-Wysocka2, Ira H Schachar4, Barbara K.
Pierscionek5
1Institute for Research in
Ophthalmology, Poznan 60-554, Poland
2Department of Ophthalmology,
University of Warmia and Mazury, Olsztyn 10-082, Poland
3Department of Physics, University of
Texas in Arlington, Arlington, Texas 76019, USA
4Department of Ophthalmology,
Horngren Family Vitreoretinal Center, Byers Eye Institute, Stanford University
School of Medicine, Palo Alto, California 94304, USA
5School of Science and Technology,
Nottingham Trent University, Nottingham NG1 4FQ, UK
Correspondence to: Ronald A Schachar. PO Box 8669, La Jolla, California
92038, USA. ron@2ras.com
Received:
Abstract
Aim: To compare the results of in vivo human high resolution image registration studies of the eye during
accommodation to the predictions of mathematical and finite element models of
accommodation.
Methods: Data from published high
quality image registration studies of pilocarpine induced accommodative changes
of equatorial lens radius (ELR) and central lens thickness (CLT) were
statistically analyzed.
Results: The mean changes in ELR and
CLT were 6.76 μm/diopter
and 6.51 μm/diopter,
respectively. The linear regressions, reflecting the association between ELR
and accommodative amplitude (AAELR) was: slope=6.58 μm/diopter, r2=0.98,
P<0.0001 and between CLT and AACLT was: slope=6.75 μm/diopter, r2=0.83,
P<0.001. On the basis of these relationships, the CLT slope and the
AAELR were used to predict the measured change in ELR (ELRpredicted).
There was no statistical difference between ELRpredicted and the
measured ELR as demonstrated by a Student’s paired t-test: P=0.96
and linear regression analysis: slope=0.97, r2=0.98, P<0.00001.
Conclusion: Image registration with invariant positional references demonstrates that
ELR and CLT equivalently minimally increase ~7.0 μm/diopter during accommodation.
The small equivalent increases in ELR and CLT are associated with a large
accommodative amplitude. These findings are consistent with the predictions of
mathematical and finite element models that specified the stiffness of the lens
nucleus is the same or greater than the lens cortex and that accommodation
involves a small force (<
Keywords: image registration;
accommodation; equatorial lens radius; central lens thickness
DOI:10.18240/ijo.2019.11.14
Citation: Grzybowski
A, Schachar RA, Gaca-Wysocka M, Schachar IH, Pierscionek BK. Image registration
of the human accommodating eye demonstrates equivalent increases in lens
equatorial radius and central thickness. Int J Ophthalmol
2019;12(11):1751-1757
Introduction
After over 160 years, the mechanism
of accommodation is still being examined. The Helmholtz theory predicts
that during accommodation all zonular tension decreases causing reduced
stability of the whole lens, a large decrease in equatorial lens radius (ELR;
>35 μm/diopter) with rounding of the lens and a large increase in central
optical power resulting in a shift of spherical aberration in the positive
direction. In contrast, the Schachar mechanism of accommodation predicts that
equatorial zonular tension increases causing the whole lens to remain stable, a
small increase in ELR (≤20 μm/diopter), flattening of the peripheral lens
surfaces with simultaneous steepening of the central lens surfaces resulting in
a shift of spherical aberration in the negative direction. Both theories
predict central lens thickness (CLT) will increase, however, Helmholtz predicts
a much larger increase than Schachar. The fundamental differences between these
two theories of accommodation are reflected by the magnitude of the change in
CLT and the extent and direction of the change in ELR (Figure 1)[1].
Figure 1 Schematic drawings of the lens
according to the two theories of accommodation A: Unaccommodated state, viewing
at distance; B: Accommodated states, focusing at near. Helmholtz mechanism of
accommodation, note that the equatorial lens diameter decreases; C: Schachar
mechanism of accommodation, note that the equatorial lens diameter increases.
Reproduced with permission from the American Physiological Society.
It has been difficult to evaluate
the mechanism of accommodation by observational techniques. Visualization of
the edge of the lens during accommodation is not possible due to the presence
of the iris. To overcome this obstacle, the change in ELR following
accommodation has been assessed photographically in patients with aniridic eyes
and in normal subjects using magnetic resonance imaging (MRI).
Unfortunately, the published MRI images in these studies are of low resolution
(>100 μm/pixels), and did not include stable unchanging positional
references for proper image registration. Even with one eye covered during
accommodation, the eye translates and cyclotorts non-randomly inducing
systematic bias that confounds data acquisition.
To minimize the effects of motion
artifact, image registration is standard practice. It significantly improves measurement
accuracy and detection of conformational changes. The advantages of image
registration became apparent in ophthalmology when it was incorporated into
commercially available optical coherent tomographic instruments designed for
examining the posterior segment of the eye. Measurements of the change in
retinal nerve fiber layer and central retinal thickness have become more
accurate. Detection of subtle retinal pathologies, not visible in the past, are
now routinely observed[2-3].
Currently, there is no commercially
available instrument that incorporates image registration for assessing the
anterior segment of the eye. If compared images are not precisely registered,
any resulting observations cannot be assessed for small changes at the
threshold required to determine the mechanism of accommodation. Because of the
lack of accurate image registration, the literature is replete with exaggerated
assessments of accommodative changes in the eye. For example, it has been
contended that the cornea changes shape during accommodation. However, with
image registration using limbal blood vessels, it has been documented that the
cornea does not change shape during accommodation.
Mathematical and finite element
analyses have been used to model the mechanism of accommodation. A basic
requirement for these analyses is incorporation of realistic material
properties, e.g., is the lens nucleus harder (stiffer) or softer than
the lens cortex. The physical parameters that characterize these properties of
the lens are the elastic and shear moduli. Unfortunately, many published finite
element analyses incorrectly assigned a lower elastic modulus for the lens
nucleus than the lens cortex based on estimates from Fisher’s spinning lens
test, which has been shown to be incorrect. Or, by relying on the results from
dynamic indentation on sections of previously frozen lenses, which makes the
findings flawed because freezing alters the material properties of the lens.
An in vivo Brillouin light
scattering study demonstrated that the longitudinal modulus, a measure of
compressibility, is higher in the lens nucleus than the lens cortex at all ages
and that the longitudinal modulus is linearly related to the shear modulus[4]. Consequently, the lens nucleus is less compressible
and stiffer than the lens cortex. This is verified by multiple studies
including in vitro conical probe indentation, shear rheometry, Brillouin
light scattering and bubble acoustic radiation force. In addition, from
clinical experience with clear lens phacoemulsification in patients <40
years of age, the nucleus has the same or greater hardness than the cortex.
When the stiffness of the nucleus
was specified to be the same or greater than the lens cortex in mathematical
models, only a small force, <
The purpose of this study is to
statistically assess the validity of the mathematical and finite element
predictions based upon clinically measured changes in ELR and CLT during
accommodation. Data were obtained from published studies of ELR and CLT during
accommodation, in which stable positional references for proper image
registration were employed.
Subjects and Methods
This is a retrospective analysis of
data from two accommodation clinical studies that used high resolution
techniques with strict image registration criteria. For the change in ELR
during accommodation, data from a high resolution ultrasound biomicroscopic
(UBM) publication was utilized[6]. For
the change in CLT during accommodation, a high resolution, swept-source
biometric (Zeiss IOLMaster 700) study of pilocarpine stimulated
accommodation was utilized[7]. These studies were
designed to provide data acquired by carefully executed image registration
achieved with invariant positional references. These are the only two clinical
studies in the current accommodative literature in which accommodation was
stimulated with pilocarpine and invariant positional references were
incorporated for image comparisons. Both of these studies had a small number of
enrolled subjects, reflecting the difficulty in obtaining properly registered
images (ELR study: n=7[6]; CLT study: n=8[7]).
Equatorial Lens Radius During
Accommodation A UBM 50 MHz probe was used to
measure the positional change of the lens equator during pharmacologically
controlled accommodation in 12 young healthy volunteer subjects (mean age 26y;
range: 20 to 34y) with correctable visual acuity of 20/20 and mean near point
of 9.5 diopters, which was within normal limits for the 12 enrolled subjects.
Tropicamide 1% was used to induce cycloplegia for the baseline measurements.
Then pilocarpine 2% was applied to induce accommodation and the near point was
measured 1h later with the pupils no smaller than
Central Lens Thickness During
Accommodation The data for the CLT change during
accommodation was obtained from the original swept-source biometric publication[7]. For inclusion in the CLT study, the subjects had to be
aged ≥18y and ≤25y. Each had a normal ophthalmological examination with best
corrected visual acuity of 20/
The following dosing regimen was
used to maximize accommodation while minimizing miosis[8].
Phenylephrine does not affect accommodative amplitude[9].
Thirty minutes after instillation of 10% phenylephrine, one drop every minute
for five applications in the right eye, the refraction of the right eye was
obtained while it was fixating on a non-accommodative target within an
auto-refractor. Then the CLT of the right eye was measured using a Zeiss IOL700
Master swept-source biometer. The left eye of the subject was occluded
during all measurements. Following these baseline measurements, pilocarpine 4%,
one drop every minute times 3, and after 5min phenylephrine 10%, one drop every
minute times 5, were instilled in the cul-de-sac of the right eye. One hour
later, auto-refraction was repeated and three additional biometric measurements
of the CLT were obtained. The change in the spherical equivalent, auto-refraction
measurement before and after pilocarpine was defined as the accommodative
amplitude.
Foveal registration was determined
by magnifying the biometric foveal images 400% and precisely superimposing the
post-pilocarpine image on the pre-pilocarpine image. Only 8 of 25 subjects
satisfied the inclusion criteria of registerable foveal images, central corneal
shifts ≤100 μm and ≥7 diopters of change in accommodative amplitude
post-pilocarpine. For enrollment, the foveal images had to be visually registerable
by superimposition and the subtracted images had to have a mean gray scale
value <25.
Statistical Analysis Descriptive statistics and linear
regression were performed to assess the change in ELR and CLT associated with
accommodation[10]. This was based upon prior
clinical studies that have established a linear relationship between
accommodative amplitude and the change in CLT and ELR[11-13]. A zero intercept was used for the linear regressions
because any change in CLT only occurs when there is an accommodative change and
the P-value of the intercept of the ordinary linear regression was not
statistically significant.
Results
The mean increase in ELR and CLT
associated with accommodation were 6.76 μm/diopter and 6.51 μm/diopter,
respectively (Tables 1 and 2).
Table 1 ELR study[6]
|
Subject |
Age (y) |
Iris color |
Baseline pupil (mm) |
Post-pilocarpine |
||
|
△Pupil (mm) |
△ELR (μm) |
AAELR (diopters) |
||||
|
1 |
29 |
Blue |
7 |
-2 |
40 |
5.5 |
|
2 |
34 |
Brown |
8 |
-2.5 |
45 |
6.0 |
|
3 |
27 |
Brown |
8 |
-3 |
43 |
6.0 |
|
4 |
30 |
Brown |
7.5 |
-2.5 |
42 |
6.5 |
|
5 |
20 |
Brown |
8 |
-2 |
66 |
8.5 |
|
6 |
23 |
Blue |
7.5 |
-2 |
66 |
10.0 |
|
7 |
20 |
Blue |
9 |
-2.5 |
58 |
11.0 |
|
Mean |
26.1 |
|
7.9 |
-2.4 |
51.4 |
7.6 |
|
SD |
5.3 |
|
0.6 |
0.4 |
11.5 |
2.2 |
ELR: Equatorial
lens radius; AAELR: Accommodative amplitude; △Pupil: Change in pupil; △ELR: Change in ELR; SD: Standard
deviation.
Table 2 CLT study[7]
|
Subject |
Age (y) |
Iris color |
Baseline |
Post-pilocarpine |
||||||
|
|
SER (diopters) |
Pupil (mm) |
CLT (mm) |
△Pupil (mm) |
△CLT (μm) |
AACLT (diopters) |
||||
|
1 |
20 |
Blue |
1.5 |
7.2 |
3.77 |
-0.1 |
100 |
11.25 |
||
|
2 |
20 |
Blue |
-0.62 |
8.4 |
3.59 |
-1.1 |
120 |
15.38 |
||
|
3 |
20 |
Green |
-4.25 |
7.8 |
3.33 |
-0.1 |
50 |
10.50 |
||
|
4 |
20 |
Hazel |
-0.75 |
8.3 |
3.26 |
-2.5 |
10 |
13.12 |
||
|
5 |
20 |
Green |
-0.37 |
8.5 |
3.45 |
-2.1 |
110 |
16.88 |
||
|
6 |
22 |
Brown |
-3.12 |
8.9 |
3.47 |
-2.5 |
170 |
16.25 |
||
|
7 |
22 |
Brown |
-1.25 |
7.7 |
3.45 |
-1.7 |
20 |
8.50 |
||
|
8 |
20 |
Blue |
-1.37 |
8.6 |
3.58 |
-1.2 |
70 |
7.75 |
||
|
Mean |
20.5 |
|
-1.28 |
8.2 |
3.49 |
-1.4 |
81 |
12.45 |
||
|
SD |
0.9 |
|
1.75 |
0.6 |
0.16 |
1.0 |
54 |
3.51 |
||
SER: Spherical equivalent
refraction; CLT: Central lens thickness; AACLT: Absolute value of
post- minus pre-pilocarpine SER; △Pupil: Change in pupil; △CLT: Change in CLT; SD: Standard deviation.
Linear regression analyses of the
changes in ELR and CLT were plotted as two independent linear regressions on
the same graph (Figure 2). For the change in ELR, the slope was 6.58 μm/diopter
[95% confidence interval (CI): 5.67 to 7.49 μm/diopter], r2=0.98
and the P<0.0001, and for the change in CLT, the slope was 6.75
μm/diopter (95%CI: 3.97 to 9.53 μm/diopter), r2=0.83 and the P<0.001.
Figure 2 The change in ELR and CLT versus
the change in accommodative amplitude for each subject Linear regression lines are shown
for ELR and CLT vs accommodative amplitude.
The mean change and slopes of the
regression lines for ELR and CLT were essentially the same. Based on this
commonality, accommodative amplitude can be used to predict the associated
change in CLT or ELR. The CLT slope and the AAELR were used to
predict the change in ELR. No statistical difference was found between ELRpredicted
(CLT×AAELR) and the measured ELR as demonstrated by a Student’s
paired t-test: P=0.96 and linear regression: slope =0.97, r2=0.98
with P<0.00001 (Figure 3).
Figure 3 The
measured change in ELR versus the predicted change in ELR The predicted change in ELR was
obtained by multiplying accommodative amplitude, AAELR given in
Table 1, by the change/diopter in CLT, 6.75 μm/diopter.
Discussion
Statistical analysis of lens changes
during accommodation, from the two, independent image registration studies,
indicates that for each diopter of change in accommodation there is only a 6.58
μm increase in ELR and a 6.75 μm increase in CLT. Accommodation is clearly a
small displacement phenomenon.
To assess the robustness of the
analysis of the CLT data, the regression was evaluated with and without
outliers. The regression analysis of CLT yielded a slope =6.75 μm/diopter with
a 95%CI of 3.97 to 9.53 μm/diopter. The change/diopter of subjects 4 and 6 were
both outside this 95%CI. However, when these two subjects were removed from the
analysis, the regression yielded essentially the same slope =6.80 μm/diopter.
In addition, the median for the subjects was 7.16 μm/diopter. When the two
outliers, subjects 4 and 6 are removed from the analysis, the median is
identical, 7.16 μm/diopter. Even if only subject 4, the largest outlier, is
removed, the median =7.80 μm/diopter and the regression yields a comparable
slope =7.64 μm/diopter. These analyses demonstrate that the outliers in the CLT
data did not significantly affect the outcome.
Consistent with these observations,
a swept-source biometric study of CLT found the accommodative change in CLT was
16 μm/diopter during voluntary stimulated accommodation[14].
In addition, an anterior segment optical coherence tomographic (OCT) clinical
study found that CLT changed less than 5% during accommodation[15]. Independently, another OCT study found that the mean
decrease in anterior chamber depth for 10 diopters of accommodation was 130 μm.
This decrease in anterior chamber depth is directly related to and similar in
magnitude to the change in CLT[7].
In further
support of these findings, published in vivo UBM nonhuman primate image
registration studies also demonstrated that accommodation was associated with a
small increase in ELR and a large increase in central lens optical power[1]. In addition, symmetrical stretching of the non-human
primate lens in vitro revealed that in response to a small force, <
For the lens equatorial radius to
increase, zonular tension must increase. This is caused by contraction of the
ciliary muscle. As OCT has demonstrated during human accommodation, the
anterior ciliary muscle fibers move toward the sclera, forming a notch in the
anterior ciliary muscle fibers (Figure
The analyses in the present study
confirm the predictions of both mathematical and finite element models of
accommodation[1]. In order for the
models to be valid, the mathematical and finite element analyses must
incorporate realistic material properties, with the stiffness of the lens
nucleus the same or greater than the lens cortex. That the nucleus
must be less compressible and stiffer than the cortex is confirmed by in
vivo Brillouin light scattering[4] and the
gradient refractive index (GRIN) of the lens. The lens refractive index
progressively increases from the surface of the cortex to the nucleus. Within
the nucleus the refractive index is maximum with a relatively constant value.
The lens GRIN is due to the progressive increase in protein concentration from
the surface of the cortex to the nucleus. Similar to other protein
solutions, the elastic modulus of the lens would be expected to be directly
related to its protein concentration. Therefore, it is not a coincidence that
the in vivo measurement of the longitudinal modulus within the lens
increases from a softer periphery toward a stiffer central (nuclear) plateau at
all ages[4] just like the lens refractive index
changes from a lower index to a higher index with a central (nuclear) plateau.
When the stiffness of the lens nucleus is the same or greater than the lens
cortex, these models accurately predict the small magnitude of increase in the
ELR and CLT associated with accommodation. As further evidence that the
designation of lens material properties is critical in finite element analysis,
some of the finite element models varied the cortical and nuclear elastic
moduli without changing the baseline lens geometry[1].
When the elastic modulus of the nucleus was the same or greater than the
cortex, the predictions of these finite element models were consistent with
those in the present study.
In contradiction to the results of
the present study, clinical studies[10-12]
and finite element models[1,23]
have found that the zonular tension causes both CLT and central optical power
to decrease, that a change in ELR is less than the change in CLT and that
changes in ELR and CLT are 3 to 10 times greater than found in the present study.
These clinical studies are subject to flawed conclusions, since they did not
utilize proper image registration, with invariant positional references for
image comparison. Extraocular movements can affect the accurate measurement of
ocular parameters during accommodation. Similarly, multiple finite element
models were in error because of the incorrect assumption that the lens cortex
was stiffer than the lens nucleus.
The present study has limitations.
Accommodative amplitude was calculated from the near point in the ELR study and
measured with an auto-refractor in the CLR study. However, a study of young
subjects[8] demonstrated that following
pilocarpine, accommodative amplitude measured with an auto-refractor is
comparable to reported near point accommodative amplitude. Clearly, the mean
accommodative amplitudes in the ELR and CLR studies were different. This can be
attributed to the mean age difference between the studies, the use of tropicamide
in the ELR study (which reduced the effect of pilocarpine), the use of
phenylephrine in the CLR study (which had no effect on accommodation) and the
much higher pilocarpine dose in the CLR study. Although the amplitudes were
different in the two studies, this would did not affect the results, since the
change in accommodative amplitude is linearly related to the changes in ELR and
CLR. As a consequence of the strict image registration requirements, data from
only a small number of subjects were available to both the UBM and CLT studies.
This small number of subjects is a limitation of the present analysis. Future
studies of accommodative lens changes from a large population of subjects are
needed, that incorporate high resolution techniques, with automatic
registration of the limbal and retinal vessels and fovea/optic nerve to
facilitate accurate, precise and repeatable measurements.
In conclusion, for accurate
mathematical and finite element modeling of accommodation, the elastic and
shear moduli of the lens nucleus must be specified as the same or greater than
the lens cortex. Valid measurements in accommodative experiments demand the use
of invariant positional references for proper image registration. When these
requisite methodologies are employed, as in this analysis of the mechanism of
accommodation, large increases in central lens optical power are associated
with small similar increases in ELR and CLT. These findings are consistent with
the Schachar mechanism of accommodation that the lens forms a “steep profile”
in response to equatorial tension similar to other negligibly compressible
objects, such as water/gel filled mylar/rubber balloons that have an aspect
ratio (minor/major) ≤0.6[1].
Acknowledgements
Presented at the Annual Meeting of the American Academy
of Ophthalmology, Chicago, Illinois, USA. October 28, 2018.
Conflicts of Interest: Grzybowski A, None; Schachar RA,
None; Gaca-Wysocka M, None; Schachar IH, None; Pierscionek
BK, None.
References