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Progress in Retinal and Eye Research 47 (2015) 86e106
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Progress in Retinal and Eye Research
journal homepage: www.elsevier.com/locate/prer
Crystalline lens and refractive development
Rafael Iribarren*, 1
Department of Ophthalmology, San Luis Medical Center, Buenos Aires, Argentina
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 1 November 2014
Received in revised form
30 January 2015
Accepted 2 February 2015
Available online 13 February 2015
Individual refractive errors usually change along lifespan. Most children are hyperopic in early life. This
hyperopia is usually lost during growth years, leading to emmetropia in adults, but myopia also develops
in children during school years or during early adult life. Those subjects who remain emmetropic are
prone to have hyperopic shifts in middle life. And even later, at older ages, myopic shifts are developed
with nuclear cataract.
The eye grows from 15 mm in premature newborns to approximately 24 mm in early adult years, but,
in most cases, refractions are maintained stable in a clustered distribution. This growth in axial length
would represent a refractive change of more than 40 diopters, which is compensated by changes in
corneal and lens powers. The process which maintains the balance between the ocular components of
refraction during growth is still under study.
As the lens power cannot be measured in vivo, but can only be calculated based on the other ocular
components, there have not been many studies of lens power in humans. Yet, recent studies have
confirmed that the lens loses power during growth in children, and that hyperopic and myopic shifts in
adulthood may be also produced by changes in the lens. These studies in children and adults give a
picture of the changing power of the lens along lifespan. Other recent studies about the growth of the
lens and the complexity of its internal structure give clues about how these changes in lens power are
produced along life.
© 2015 Elsevier Ltd. All rights reserved.
Keywords:
Lens power
Refractive development
Gradient refractive index
Contents
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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ocular biometric components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calculation of crystalline lens power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Studies in preterm and full term infants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nicholas Brown and the lens paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The lens during early growth in chickens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The shape and the power of the lens during childhood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Anterior segment growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Change in lens shape during childhood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The anterior segment in premature children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The lens power in school years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theories for lens thinning during childhood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Change in ocular components at myopia onset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The lens power loss during university study years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The lens in adulthood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Longer eyes of taller subjects have lower powered lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
How can the lens change its power? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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* Department of Ophthalmology, Centro Medico San Luis, San Martin de Tours 2980, CABA 1428, Argentina. Tel./fax: þ54 11 4393 1844.
E-mail address: [email protected].
1
Percentage of work contributed by each author in the production of the manuscript is as follows: Rafael Iribarren: 100%.
http://dx.doi.org/10.1016/j.preteyeres.2015.02.002
1350-9462/© 2015 Elsevier Ltd. All rights reserved.
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Is the rate of lens power loss an actively regulated process? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Conclusions and future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
1. Introduction
The refractive status of the eye usually changes throughout life.
Children are born with a mean spherical equivalent refraction in
the moderate hyperopic range with a Gaussian distribution of refractions, and then move towards mild hyperopia with a narrower,
leptokurtic distribution of refractions over the first year or two after
birth. After this early stage, some children then progress in a
myopic direction through an increased rate of axial elongation
which is, at least in part, controlled by environmental exposures
(Wallman and Winawer, 2004). This developmental phase may
continue into the third decade after birth, when myopia prevalence
reaches its maximum. During school years, many hyperopic children come to be emmetropic. After this, there is a slow shift in the
hyperopic direction which may continue over several decades. This
hyperopic shift with ageing can be disrupted by the formation of
cataract which may lead to quite rapid and pronounced myopic
shifts. Two early clinical cross-sectional studies which involved
cycloplegia with atropine, characterized this change in refraction
with age from birth to senescence (Brown, 1938; Slapater, 1950).
This pattern of change appears to be very general but has never
been fully characterized with longitudinal data, because the study
would inevitably last longer than the working life of most chief
investigators and clinicians (except, perhaps, for the case of the
1958 British Cohort; Rahi et al., 2011). Another limitation of the
existing literature is that much of the evidence is based on clinical
samples, and has generally been measured without cycloplegia
(except for the two early clinical studies mentioned above), even
though it is generally recognized that the gold standard for measurement of refractive status requires cycloplegia, at least in children. This requirement may continue into adult life, since
accommodation is powerful well until the ages of 40e50. As a
result, some overestimation of myopia and major underestimation
of hyperopia can occur (Fotouhi et al., 2012; Krantz et al., 2010;
Morgan et al., 2015).
For this reason, we have chosen to illustrate the typical pattern
of change in refractive status with data from the Tehran Eye Study
(Hashemi et al., 2003, 2004), which involved a cross-sectional
study of refraction using cycloplegia over a wide age range, from
5 to over 75 years of age. Three of the major developmental phases
can be clearly seen. It should also be noted that while these data are
cross-sectional, strong evidence of longitudinal change has been
obtained for each of these phases (Fotedar et al., 2008;
Gudmundsdottir et al., 2005; Wu et al., 2005; Lee et al., 2002;
Saunders, 1986; Jones et al., 2005b; Mutti et al., 2005).
Fig. 1 of the above mentioned Tehran cross-sectional study
shows a complex change with age (Hashemi et al., 2003, 2004). The
conservative cut-off point for myopia or hyperopia at ±1 diopter
(spherical equivalent) was chosen because most subjects with that
amount of refractive error wear glasses on a permanent basis; a
cut-off point of ±0.50 diopters would make the prevalence of
refractive error appear much higher in comparison with this more
conservative cut-off point. Myopia is rare at age 5 and increases
steadily up to age 25 when it reaches its maximum prevalence of
18% (in this study under this cut-off point). Then myopia prevalence
remains stable along adulthood up to age 70, when it increases
again. In the meantime hyperopia is very frequent (50%) at age 5
and decreases steadily reaching a minimum (10%) at age 25, the
same age when myopia reaches its maximum prevalence (possibly
the age at which axial elongation stops). From then on the prevalence of hyperopia increases slowly during adult life, reaching a
value of 50% at age 70, and from that age it decreases abruptly, by
the same time as myopia prevalence increases.
These changes in the prevalence of refractive error in the Tehran
Eye Study, if confirmed prospectively in a long prospective study,
would mean that subjects are passing from one category to the
other. This is seen many times in the clinic. Hyperopic school
children become emmetropic during adolescence. Emmetropic
children develop myopia during school and university years.
Emmetropic young adults develop hyperopia during their 40e50's
and cataract patients in their 70's lose their hyperopia or develop
myopia (Duke-Elder and Abrams, 1970a; Saunders, 1984).
2. The ocular biometric components
From a clinical perspective, refractive status is the key parameter, because clinical correction of refractive error, whether with
glasses, contact lenses, refractive surgery, or intraocular lenses, is
the key to ensuring good visual acuity. However, from a biological
perspective, the ocular components of refraction, specifically
corneal and lens power, as well as anterior chamber depth, lens
thickness and vitreous chamber depth are optically more important, since it is the balance between these components which determines refractive status. For most of this period, refractive status
appears to be a passive player, but early in development, refractive
status does appear to act as a regulatory factor controlling the rate
of axial elongation in particular. For example, infantile high hyperopic eyes tend to grow faster, such that this refractive error is
compensated to some extent during the first years of life (Saunders
et al., 1995; Mutti et al., 2005).
Since the first classical studies (Tron, 1940; Stenstrom, 1948;
Sorsby et al., 1957, 1961; van Alphen, 1961; Sorsby and Leary,
1969; Sorsby, 1971), many studies have examined the relationship
between these biometric components and the refractive status. All
studies showed that the major biometric correlate/determinant of
refractive status was axial length, and that increased axial length
was the major cause of myopia. Where the issue has been examined, the ratio of the axial length to the corneal radius of curvature
was found to correlate even more strongly with refractive status
than with the axial length itself. This is not hard to understand in
principle, because while it is often stated that myopic eyes are
longer (and it is known that in the emmetropic range longer eyes
have flatter corneas, from Sorsby et al., 1957), strictly speaking,
myopia results from an axial length that is longer than the image
plane for distant objects, which is set by the optical power of the
cornea and the lens. The axial length/corneal radius ratio correlates
more strongly with refractive status because it partially adjusts for
corneal power (Grosvenor and Scott, 1994).
The changes in refractive error prevalence seen in Fig. 1 should
be associated with changes in the mentioned ocular components of
refraction (mainly: corneal power, crystalline lens power and axial
length). The cornea has been shown to develop small changes with
ageing, mainly an against-the-rule change in astigmatism (Liu et al.,
2011; Gudmundsdottir et al., 2005), but maintains constant power
88
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
Fig. 1. Prevalence of refractive error along lifespan, with a þ1/1 diopter cut off point in the Tehran Eye Study (Hashemi et al., 2004). Age 10 stands for 6e10 years, age 15 stands for
11e15 years and so on (Reanalysis of data published in Hashemi et al. (2004) and in Fotouhi et al. (2012).
for most subjects along life (except for the uncommon progressive
keratoconus cases). So the lens power and the axial length should
be responsible for the observed changes. Mainly we can say that
growth in axial length up to age 25e30 may be responsible for the
development of myopia and for the decreasing prevalence of hyperopia. From that age on, the changes in prevalence of refractive
error are surely driven by changes in the power of the lens
(Iribarren et al., 2012b).
3. Calculation of crystalline lens power
The crystalline lens power cannot be simply measured with a
lensmeter since it is inside the eye. The same accounts for corneal
power: usually only its anterior radius is measured, for example by
a keratometer. The contribution of the posterior corneal power is
assumed by an ideal index, which is calculated to obtain the power
of the whole cornea only with the measured anterior radius and
that ideal index (Olsen, 1986). Recently, using Scheimflug imaging it
has been possible to measure the power of the whole cornea with
the anterior and posterior radii, showing that the ideal index
should be even lower than that calculated by Olsen (Dubbelman
et al., 2006; Saad et al., 2013). Similarly, calculation of the power
of the lens inside the eye is not straightforward: its power must be
obtained from the other ocular components. Stenstrom's formula
based on refraction, keratometry, anterior chamber depth and axial
length calculated lens power as if it were a thin lens placed at its
anterior vertex. Later, intraocular lens power formulas were
developed, but these also calculate the lens as if it were a thin lens
placed at an estimated postoperative anterior chamber depth
(effective lens position) (Olsen et al., 2007; Gordon and Donzis,
1985). By the end of the 80's, Bennett and Rabbetts presented an
in vivo crystalline lens power formula that, as Stenstrom's, calculated lens power based on distance refraction, corneal power,
anterior chamber depth and axial length (Bennett and Rabbetts,
1989). This formula, of which certain constants were recently
revised (Rozema et al., 2011), can be used for calculating mean
values of crystalline lens power in case of studies with biometry
performed with the IOLMaster. When refraction, keratometry and
A-Scan biometry or LENSTAR are available, then another Bennett's
formula including lens thickness can be used (Bennett, 1988;
Dunne et al., 1989; Rozema et al., 2011).
Phakometric imaging of the crystalline lens in vivo has some
problems (Mutti et al., 1992; Dubbelman and Van der Heijde, 2001;
Rosales and Marcos, 2006). The Purkinje or Scheimpflug images of
the anterior lens curvature are magnified and distorted because
they are seen through the optics of the cornea. The posterior lens
surface is distorted by both the optics of the cornea and the lens
structure itself. The lens itself has a complex gradient of refractive
index which makes the problem even more challenging. This
gradient of refractive index is produced because the lens grows
from the surface, sinking fibers in its deeper layers, and the newly
laid fibers have greater water content and lower refractive index
than the older ones. Thus a gradient of refractive index is produced,
increasing from the cortex to the center of the lens. This complex
structure is generally solved by modeling the lens as if it were a
uniform thick lens, with an “equivalent” or “effective” index of
refraction equal to that necessary to explain the whole power of the
lens. This equivalent refractive index is greater than the peak index
at the center of the lens, because the gradient refractive index,
regardless of its profile, makes the rays bend incrementally as they
go through the changing multilayer structure of the lens, thus
giving what is called an internal power of the lens.
This gradient structure gives the lens another important property. Spherical lenses with uniform index have positive spherical
aberration, produced as rays in the peripheral (equatorial) sections
of the uniform lens bend more than those that go through the
central part of the lens. But gradient spherical lenses can elegantly
compensate this aberration because rays passing through the periphery are not bent as much because they pass through progressively lower refractive index sections. This was clearly shown
bending laser rays through lenses in vitro for fish and mammals by
Sivak and Warburg (1983) (Sivak and Kreuzer, 1983; Sivak, 1985)
and later by Jagger and Sands (1996). Fig. 2 shows that the spherical
fish lens has no spherical aberration and that the laser rays are bent
while passing through the lens structure because of the gradual
index change.
The phakometric measurements of the lens posterior curvature
have to be iteratively corrected calculating an ideal equivalent index, in a recursive manner such that it agrees with the measured
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
89
Fig. 2. Parallel laser beams seen from the side refracted by a trout lens. See the short
focal length of the fish lens and how the beams are bent inside the lens structure by
the gradient index, with no spherical aberration. Reprinted from Jagger and Sands
(1996). Copyright (1996), with permission from Elsevier.
refraction. With these recalculated lens curvatures, its thickness
and the calculated equivalent index, the lens power can be also
calculated using Gullstrand's well known thick lens formula to find
the total lens power. This iterative method allows the accurate
calculation of the lens curvatures and the equivalent refractive index. So, this phakometric method can be used when the objective is
to calculate the equivalent index and the lens curvatures, as has
been done in monkeys and humans (Jones et al., 2005b; Mutti et al.,
2005; Dubbelman and Van der Heijde, 2001; Qiao-Grider et al.,
2007).
When only biometric and refractive data are available, Bennett's
formula can be used to calculate the lens power alone. Two recent
papers have shown that there is good agreement between phakometry and Bennett's methods when the values of mean lens power are calculated in a given sample (Dunne et al., 1989; Rozema
et al., 2011). In this review, we have calculated lens power with
Bennett's method when data available in the literature allowed this
calculation and we have thus compared the data on lens power
obtained in different biometric studies along the lifespan.
If lens radii are available, and the cortical index is used in
Gullstrand's thick lens formula, then the surface contribution of
the lens curvatures can be calculated (as if the lens were homogeneous with the cortical index), and thus this surface power can
be subtracted from the total lens power to find the gradient
refractive index power contribution. In this way, the surface power
was found to contribute to about half of total lens power (Borja
et al., 2010). The rest was due to the internal or gradient power
of the lens. The problem with this approach is that the cortex
index has been measured in vitro and then calculated with magnetic resonance studies in vitro and in vivo, with different studies
giving different results for this cortical index (Pierscionek and
Chan, 1989; Moffat et al., 2002a; Jones et al., 2005b; Borja et al.,
2010). So the calculation of the surface power is somewhat inaccurate, but taken prospectively or with successive measurements
under different accommodative demands, this calculation can
show differences in the contribution of the surface and internal
powers of the lens both with age and accommodation (Borja et al.,
2010; Maceo et al., 2011).
Using these approaches we calculated the lens power for a
number of published studies which included refraction and biometry, from preterm infants to adult years. We used 1.3315 as the
ideal index for corneal power in all cases (Olsen, 1986), for consistency with our previous published data. These calculations give a
picture of the change in lens power along life.
4. Studies in preterm and full term infants
Cook et al. (2003) showed prospective changes in the ocular
components of refraction in premature children (without
Fig. 3. First, to the left, calculated lens power in premature infants from the data of
Cook et al. (2003) for premature infants from months 1 to 5 (white circles); second in
the middle, lens power data for full term infants from Mutti et al. (2005) aged 3 and 9
months (black circles), and last to the right, lens power data for schoolchildren from Ip
et al. (2007) (black circles).
retinopathy) from birth to 5 months of age, performing cycloplegic
refractions. From the data in their published table (Cook et al.,
2003), the crystalline lens power was calculated using Bennett's
formula (Bennett, 1988). Fig. 3 shows how the lens power decreases
steadily in premature infants from nearly 60 diopters at birth to 45
diopters by 5 months. Mutti et al. (2005) prospectively studied full
term infants at ages 3 and 9 months with cycloplegic refraction,
biometry and phakometry, calculating the crystalline power, and
they give decreasing lens power values of 41.01 D and 37.40 D for 3
and 9 months respectively (Fig. 3). Fig. 4 shows lens thickness in
both studies (premature and full term). In premature children the
lens becomes thicker during the first two months of life, and then
begins to thin (Cook et al., 2003). In full term infants the lens thins
from 3 to 9 months (Mutti et al., 2005). Besides, the lens has been
reported to thin in schoolchildren from age 6 to 10 years (Larsen,
1971; Jones et al., 2005b; Shih et al., 2009; Wong et al., 2010).
As we mentioned earlier, the calculated equivalent refractive
index is the index the lens would have considering its whole power
and surface curvatures as if it were a lens with uniform index of
refraction. While the lens thins and loses power, the Mutti et al.
study of full term infants reported that the calculated equivalent
refractive index of those lenses increased from 1.4526 to 1.4591
from 3 to 9 months (Mutti et al., 2005). Using similar methods,
Jones et al. (2005b) showed that, on the contrary, the lens equivalent index decreased in school years (from age 6 to 14) while the
Fig. 4. Lens thickness in premature infants from months 1 to 5 (Cook et al., 2003)
(white circles) and for full term infants aged 3 and 9 months (Mutti et al., 2005) (black
circles). The lens thickness increases in the first three months of life in premature
infants, perhaps following the high fetal rate of lens growth.
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R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
lens consistently thins and loses power. They also showed prospectively that the curvatures of the lens flatten at these school
ages, and they explained this loss of power by a scleral expansion
theory in which the lens thins by the forces of zonular traction
induced by eye growth in the anterior segment. This theory
explained that as the lens thins, its curvatures flatten, and in
consequence, the lens power decreases (Zadnik et al., 1995; Mutti
et al., 1998). These authors also proposed, alternatively, that
changing lens shape could modify the internal gradient index
structure, but did not explore further this idea.
However, what remained unclear was the decrease in the
equivalent refractive index at a time when the actual peak index in
the center of the lens is increasing (Augusteyn et al., 2008). Besides,
that scleral expansion based theory cannot explain why the lens of
premature children becomes thicker in the first months of life,
while it is steadily losing power. Furthermore, why is the equivalent
refractive index increasing in full term babies while the lens loses
power? Interestingly, a longitudinal study of the change in the
ocular components during growth in monkeys has also shown that
the lens increases in thickness and equivalent index during the first
months of life, then changing these growth patterns in the opposite
direction with further growth, but consistently flattening curvatures and losing power during both periods (Qiao-Grider et al.,
2007).
It must be noted that the lens has a complex multilayer structure
of progressive index that increases from a low index in the surface
to the peak index in the center (Augusteyn, 2008, Review;
Pierscionek and Regini, 2012, Review). As said, this is produced by
the apposition of new cortical fibers with greater water content
than those that are deeper, older, mature and full of protein content, or even deeper with less water, as they age and become
compacted in the center of the lens. This gradient of index increases
the power of the lens because rays going through the gradient are
curved incrementally at each step. Thus the total power of the lens
is composed of the surface power given by its curvatures, and an
internal power given by its gradient index of refraction.
The profile of this gradient index structure gives differential
power to the lens. This profile climbs from low index at the periphery to high index in the center of the lens, developing a central
plateau with ageing. As the profile of the peripheral gradient becomes more abrupt and the plateau develops, the gradient structure loses effective power. An in vivo magnetic imaging study has
shown that the profile of the peripheral gradient becomes more
abrupt with older age and smoother during accommodation in
young subjects (Kasthurirangan et al., 2008). These changes in the
gradient had been shown previously in in vitro studies and were
related to the maintenance of emmetropia (Brown et al., 1999) or
even before to the changes in lens power leading to presbyopia
(Pierscionek, 1990). Changes in the gradient index have also been
proposed as a cause of the hyperopic shifts leading to the development of hyperopic refractive errors in ageing adults (Brown et al.,
1999; Moffat et al., 2002b; Glasser and Campbell, 1988; Hashemi
et al., 2010).
One possible explanation for the loss of lens power during infant
life is that the profile of the peripheral refractive index gradient is
becoming more abrupt with age. As the peak index is becoming
greater by fiber maturation and compaction, then the climbing
index from the surface to the higher peak index in the center should
have a more abrupt profile (with less power) even more so if the
lens axial thickness is decreasing, as a thinner lens should also have
a more abrupt profile to reach the same peak. Besides, the increase
in peak index could drive the equivalent index up, as has been
found in infants (Mutti et al., 2005), but the net change could be
decreasing lens power produced both by flattening of curvatures
and changing gradient profile.
5. Nicholas Brown and the lens paradox
The idea that changes in the internal power of the lens could
have importance in refractive error began to gain acceptance in the
70's when Nicholas Brown described the “lens paradox” consisting
of an increment in lens thickness with a steepening of the surface
and internal curvatures of the ageing lens that would produce
systematic myopia at adult ages in which hyperopia and presbyopia
are the norm (Brown, 1974; Koretz and Handelman, 1988; Brown
et al., 1999). He introduced Scheimpflug photography in Ophthalmology to study the lens, and soon discovered that the anterior lens
surface was becoming steeper with ageing, just the opposite to
current thinking of those days (Brown, 1974). He also studied eyes
under accommodative effort and saw that older eyes at rest had
steeper anterior lens surfaces compared to younger accommodated
eyes (Brown, 1973). Then, Koretz & Handelman, studying his photographs with mathematical approaches, showed that the steepening of the lens curvatures with ageing should be accompanied by
changes inside the lens. They suggested that the lens equivalent
refractive index should be higher in younger subjects in order that
the eye could be maintained in focus according to differences in
lens shape (Koretz and Handelman, 1988).
Dubbelman then showed, with cross-sectional data, that the
equivalent refractive index of the lens really decreases with age in
adults, thus explaining the lens paradox (Dubbelman and Van der
Heijde, 2001). A lens with decreasing equivalent index would
maintain a constant power while its curvatures become steeper if
both changes were matched in ageing subjects (Brown et al., 1999),
but in subjects who develop hyperopia, the net change could be loss
of power if the loss of gradient power is greater than the increase in
curvatures (Brown et al., 1999; Hashemi et al., 2010; Iribarren et al.,
2012b). Experimental studies on refractive development in animal
models can provide information on the underlying mechanisms, as
we will see in the next section.
6. The lens during early growth in chickens
Interestingly, the lens also loses power in growing chicken eyes.
A recent re-analysis of the chick schematic eye model that was
originally developed by Schaeffel and Howland (1988) showed that
Bennett's equation could be used for calculation of lens power in
chick eyes (Iribarren et al., 2014a). As the original data included
refraction, biometry and lens radii measurements, the lens power
and equivalent index could be calculated for growing chicken eyes
from age 10e90 days. While axial length increased in chicken eyes
from 8 to 14 mm in this period, the cornea and the lens lost power
accordingly, such that refractions were maintained in the low hyperopic range. The lens thickness increased in chicken eyes during
this period, and as the lens possibly grew in all directions (axially
and equatorially), the curvatures flattened (Fig. 5). In the meantime,
the equivalent index decreased slowly with age. Thus, with all these
changes, the lens lost 30 diopters of power in these 80 days of eye
growth in chickens (Iribarren et al., 2014a).
To calculate the contribution of the gradient refractive index to
the total power of the lens at rest, we used the method proposed by
Borja et al. (2008). As said, in this method the total lens power is
calculated, based on Gullstrand's thick lens equation, from its radii
of curvature, thickness and equivalent refractive index, while for
the surface power the cortical refractive index is used. The cortex
index is lower than the equivalent index, as the cortex consists of
new fibers with higher water content and a lower refractive index.
The cortical refractive index has been measured in vitro in chicken
lenses by Sivak and Mandelman (1982), giving a value of 1.374.
Following Borja et al. (2008), we then derived the gradient power as
the total Gullstrand thick lens power (calculated with the
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
Fig. 5. Schematic drawing of the change in lens thickness and front and back curvatures of the 15 day old chick lens (inner lines) inside the 80 day old lens (outer lines). It
can be seen that the lens becomes thicker with flatter curvatures as it grows. Reprinted
from Iribarren et al. (2014a). Copyright (2014), with permission from Elsevier.
equivalent refractive index found for chick schematic eyes equal to
1.4502 for day 15 and 1.4409 for day 90) minus the surface power
(calculated using 1.374 as the cortical refractive index).
Table 1 shows the change in total lens power, surface lens power
and gradient lens power in the period from 15 to 80 days. It can be
seen that both surface and internal power change with age in
chicken eyes. As said, the total lens power decreases by some 30
diopters, of which 20 diopters are accounted for by changes in the
internal power, so the change in gradient power accounts for about
70% of the total change in power. Fig. 5 shows the front and back
curvatures of the 15 day old chick lens (inner lines) inside the 80
day old lens (outer lines). The increase in axial thickness and the
flattening of the curvatures can be seen as the lens expands in all
directions by growth of new layers of fibers. The equator was not
drawn since lens surfaces are not spherical (and we only had front
and back surface lens radii for the schematic drawings).
We have then showed that the equivalent refractive index and
the gradient index power are decreasing while the lens grows and
loses power in chicken eyes.
7. The shape and the power of the lens during childhood
Although there are studies reporting changes in lens thickness
in babies and schoolchildren (Larsen, 1971; Jones et al., 2005b;
Mutti et al., 2005; Shih et al., 2009; Wong et al., 2010) the literature shows less data on lens equatorial diameter growth as the lens
Table 1
Comparison of the surface and gradient contribution to the decrease in chicken lens
power.
Complete lens power (diopters)
Surface lens power (diopters)
Internal (gradient index)
power (diopters)
15 days
old
80 days
old
Difference
% Change
79.9
27.5
52.4
50.7
18.7
32.0
29.3
8.8
20.5
100.0%
30.0%
70.0%
91
equator is not visible in vivo by slit lamp observation because it is
behind the iris, even after pupil dilation. Augusteyn (2010) has
recently reviewed the data of lens equatorial growth. Duke-Elder
and Abrams (1961) gave values for in vitro measurements of
6.5 mm for newborns, 7.5 mm at the end of the first year, and
8.2 mm by 2e3 years. Similar in vitro values were presented by
Augusteyn et al. at the ARVO meeting (Augusteyn et al., 2012)
showing that the main growth of lens equatorial diameter is achieved during the first two years of life (see also Brown and Bron,
1996). Adult values are around 9 mm, increasing slightly and very
slowly with ageing (Augusteyn, 2010, Review). These in vitro data
have the problem that the lens is fully accommodated when free of
zonular tension, especially in children's lenses. This would make
the equatorial diameter in a 20e40 year lens about 0.6 mm shorter
according to in vivo data obtained by Strenk with magnetic resonance images (Strenk et al., 1999, calculated from their data with
lenses younger than 40). This difference between in vivo and in vitro
measurements could be more pronounced in infant lenses, which
have more spherical shape, capable of many diopters of accommodation. So these in vitro measurements in infant lenses are
possibly biased as if they were smaller. It is very possible that the
lens equatorial diameter increases in babies while the anterior
segment is growing steadily during the first months of life. A recent
magnetic resonance image study (Ishii et al., 2013) involving 26
children aged 1month to 6 years, showed that the lens equatorial
diameter in children under general anesthesia (tonic resting accommodation) increased steadily after birth reaching a value of
8 mm in by age 3. Thus, 90% of lens equatorial diameter growth is
achieved in the first 2e3 years of life.
Mutti et al. (2005) reported that the anterior lens radius
changed from 7.21 mm at three months to 8.97 mm at 9 months,
becoming flatter with lens thinning. If the lens were growing as
much in equatorial diameter as in axial thickness, as may be the
case in the first months of life in premature infants, then the
decrease in curvature of the anterior surface would be much less
(the lens would maintain a constant shape while it thickens in the
first two months). But it is still steadily losing power as we have
shown (Fig. 3). This also happens in growing chicken eyes, where
the lens grows both in axial and equatorial diameter, flattens curvatures, and also loses power (Iribarren et al., 2014a, Fig. 5). Then,
ellipsoidal lenses with flat front surfaces can flatten anterior curvature as they thin or as they grow, depending on the change in lens
shape.
The changes in the lens are rather complex, especially in infants
who have very powerful lenses, with a more rounded shape, and
possibly, with a newly developed very smooth climbing gradient
profile. The actual index of refraction is given by the concentration
of the crystalline proteins within the fibers' cytoplasm, and this
concentration is a function of the amount of fiber differentiation
and compaction. Fiber differentiation is rapidly established in such
a manner that even embryonic lenses have a gradient in a few
weeks (Peetermans et al., 1987). On the other hand, compaction,
demonstrated originally by Brown in adult lenses with cortical
cataracts (Brown, 1976), is a process that takes years to develop. It is
well known that after birth there are changes in the synthesis of the
different crystalline proteins that compose the lens, such that the
fetal nucleus (that part of the lens formed prenatally) has greater
content of gamma crystallin than the cortex (Augusteyn, 2007). It is
possible that the different types of crystallines have different time
constants for losing water and compacting (Augusteyn et al., 2008).
It is also known that the rate of synthesis of new layers decreases
drastically after birth (Augusteyn, 2007). Proof of this is the fact that
the lens develops approximately 4.0 mm axial thickness during
prenatal life in only 8 months, and then only 1.5 mm more from
birth to senescence (Brown and Bron, 1996).
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R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
Little is known about the compaction of the crystalline proteins
and fibers in the lens of babies and schoolchildren. It is possible that
they become slowly compacted in the nucleus during the following
years after birth, probably beginning from the older fibers in the
center. But one has to consider that those fibers were laid in a few
months during gestation and they may be compacting at a relatively uniform rate during the first years after birth. Evidence of this
compaction is given in the Mutti et al. (2005) study in babies which
shows an increase in equivalent refractive index from 3 to 9 months
of age. That would increase the power of the lens, but as the lens at
this time is losing much power, we propose that both surface and
internal powers are changing. Mutti et al. (2005) have demonstrated that the anterior lens curvature flattens during development in babies. We propose that the gradient index power is
decreasing by compaction of the nucleus with a more abrupt
climbing gradient profile (before the adult index plateau is developed). Furthermore, compaction inside the nucleus, with a slow
rate of addition of new fibers in the newly developed cortex after
birth could also explain the lens thinning in the first 10 years of life
(Brown and Bron, 1996).
The 6 year old lens studied in vitro in the Augusteyn et al. (2008)
paper (Fig. 6A & B) has not yet achieved the peak index found in
adult years, so it is probable that compaction of the nuclear fibers is
still not finished by age 6. As the cortex grows at a very slow rate
compared to the prenatal growth of the nucleus, one would expect
lens thinning until the rate of compaction in the nucleus equals the
rate of growth in the newly developed cortex. The idea that lens
cortical growth was balanced by nuclear compaction during
childhood was originally proposed by Nicholas Brown, who had
studied prospectively the lens in a few subjects with congenital
lamellar cataracts, finding that children had compaction in the
nucleus, and that this compaction declined its rate with ageing
(Brown et al., 1988). He suggested that lens growth was due to a
balance between epithelial growth and fiber compaction, and that
the nucleus became compacted up to age 30, and afterward, only
the deep cortex became compacted for the rest of life. This was also
discussed by other members of his team (Cook et al., 1994) and
during the presentation of Scheimpflug data in normal growing
children by Forbes et al. (1992).
So compaction may explain lens thinning found until age 10 in
different studies. Besides, while the gradient becomes compacted,
if its climbing profile becomes less smooth as can be seen in the
Augusteyn in vitro lenses (Fig. 6A & B, Augusteyn et al., 2008), then
the lens should lose internal power, explaining the loss of power
that has been shown in the different studies. In fact, the gradient
index in Fig. 6A & B is smoother in the child lens compared to the
abrupt climbing profile with a plateau of index developed in the
center of adult lenses. It is noted that the plateau section has no
gradient (less power). The schematic drawing of Fig. 6C shows how
a thinner lens has a more abrupt climbing gradient index profile
that reaches a higher peak index, as may be happening while the
lens thins and compacts from birth to school age, losing internal
power (before the central plateau is developed).
8. Anterior segment growth
The analysis of the anterior segment growth can help understanding lens growth. The anterior segment growth has been
measured by the increase in white to white corneal diameter
ze and Zobor, 2007) and by the
(Ronneburger et al., 2006; Lagre
anterior segment distance from the corneal apex to the posterior
pole of the lens (anterior segment length) (Larsen, 1971;
Dubbelman et al., 2001; Koretz et al., 2004). It is well known that
white to white diameter reaches adult values during the first year
of life and that the corneal power also reaches adult values by age
Fig. 6. Three gradient index profiles reconstructed from mri images of human lenses
in vitro. Fig. 6A equatorial axis, Fig. 6B saggital axis, (with permission from Augusteyn
(2008)). In gray dots a 7 year old lens, with a smooth climbing gradient profile and a
lower peak index compared to the other adult lenses. In white dots a 27 year old lens
with adult peak index and more abrupt gradient that is developing a central plateau. In
black dots a 82 year old human lens with a very abrupt climbing gradient and an
extended central plateau. Fig. 6C. Schematic drawing of the gradient index profile of
two lenses, one of which is thinner and has a more abrupt climbing profile to reach a
higher peak index. Although the thinner lens may have a higher peak index, the
change in gradient profile could make it have lower power. The younger lens is 4.0 mm
thick and the older 3.6 mm thick, representing the compaction achieved since birth up
to age 10.
1e2 (Gordon and Donzis, 1985; Ronneburger et al., 2006; Inagaki,
1986). It looks like the cornea does not change much in diameter
and power after year 2.
The anterior segment length up to the lens posterior pole has
been calculated from the data of Cook et al. (2003) and Mutti et al.
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
(2005) (Fig. 7) (adding anterior chamber depth þ lens thickness). In
full term and premature babies the anterior chamber grows during
the first months, while the lens thickness fluctuates, increasing in
prematures during months 1e3 and decreasing in full term babies
from months 3e9. Yet the anterior segment length increases
steadily as shown in Fig. 7, almost reaching adult values of
7e7.5 mm by the end of year 1 (Koretz et al., 2004; Dubbelman
et al., 2001; Larsen, 1971). In the follow up of emmetropic children, Zadniks's data (Zadnik et al., 2004) show little change in
anterior segment length at the time of lens thinning between ages 6
to 10 (Table 2), showing that the anterior chamber deepening at
these ages is a consequence of lens thinning and not merely growth
of the anterior segment. This was originally shown by Larsen (1971)
who stated that the anterior segment length growth “stagnated by
age 2e3 years”.
At ARVO 2013, Bailey et al. presented cross sectional data obtained with Visante images showing that the “anterior segment
chord” located behind the iris, from sclera to sclera, did not change
with age in schoolchildren (Bailey et al., 2013). So we think that the
anterior segment growth is completed in the first year or two of life
with no further change in dimensions after this age, but with internal and external changes in the lens. It is also difficult to explain
the scleral expansion theory (Zadnik et al., 1995; Mutti et al., 1998)
if the anterior segment does not grow between ages 6 and 14, when
the lens is thinning.
To estimate the equatorial diameter of the relaxed lens in vivo,
we drew the lenses in Fig. 8, using the mean anterior and posterior
curvatures and the mean lens thickness for the lens at rest given in
Mutti's and Zadnik's papers (Mutti et al., 1998, 2005). These curvature radii were drawn spherical although it is known that the real
lens has aspheric curvatures and thus should have even greater
equatorial diameter, so these data may be negatively biased. The
rounded edges at the equator were drawn following the shadowgraphs of in vitro lenses (Borja et al., 2010). From these drawings the
lens equatorial diameter was estimated to be 7.44 mm for the three
month old babies' lens, 7.99 mm for the 9 month old babies and
8.82 mm for the 14 year old lens in schoolchildren. With the same
data (Mutti et al., 2005) and the formula given by Rozema et al.
(2012), the lens diameter is estimated to be 7.38 mm in 9 month
babies and 7.77 mm in 9 month babies. These measurements may
be biased by the method used, but they show that the lens at rest
(under cycloplegia) reaches equatorial diameter values similar to
the 9 mm adult lens very early in life. The same holds for the other
described parameters of the anterior segment of the eye.
Fig. 7. Anterior segment length calculated from data in Cook et al. (2003) in premature
infants from months 1 to 5 (white circles), then for full term infants in Mutti et al.
(2005) aged 3 and 9 months (black circles), and for emmetropic schoolchildren at
ages 6 and 12 years from Zadnik et al. (2004) (black circles).
93
Table 2
Anterior Chamber (ACD), Lens Thickness (LT) and Anterior Segment Length (ASL) in
emmetropic children.a
Age (years)
ACD (mm)
LT (mm)
ASL (mm)
6
7
8
9
10
11
12
3.62
3.68
3.71
3.73
3.75
3.76
3.75
3.53
3.5
3.45
3.43
3.43
3.41
3.43
7.15
7.18
7.16
7.16
7.18
7.17
7.18
a
Calculated from Zadnik et al. (2004).
Fig. 8. Auto Cad drawings made with the data of curvatures and axial thickness given
by Mutti et al. in their studies for 3 months, 9 months and 14 year old children (Mutti
et al., 2005, 1998). Curvatures were assumed as spherical. The equatorial curvatures
were drawn following the equatorial shape of the shadowgraphs in Borja et al. (2008).
From these drawings, the equatorial diameter was estimated for the three ages,
showing that the lens grows up to adult values early in life.
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R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
9. Change in lens shape during childhood
How can the lens change from a rounded ellipsoidal shape in
babies to a flatter one in adolescence? This change can be seen in
Fig. 9, comparing a 3 month lens with a 14 year old lens (based on
Mutti's and Zadnik's published data of curvature and thickness,
Mutti et al., 1998, 2005; Zadnik et al., 1995). The internal structure
and the growth of the lens can give the clues for this change. As
said, the nucleus of children has been shown to be compacted
during school years according to Brown's Scheimpflug images
during the follow up of children with lamellar cataracts (Brown
et al., 1988) and by similar cross-sectional measurement of nuclear thickness in a sample of 50 children aged 3e20 years (Forbes
et al., 1992).
Lens fibers decrease both in length and diameter during
compaction (Augusteyn, 2010). It is possible that the lens fibers
shorten and decrease diameter at different rates while their protein
content is losing water. As the fibers in the embryonic and fetal
nucleus are oriented following the antero-posterior axis (Al-Ghoul
et al., 2001), their folding and compaction could possibly decrease
the antero-posterior axis more than the equatorial diameter
(Augusteyn, 2010 review). The cortical fibers are progressively
oriented in a circular manner. These differences could make the
lens thinner on its axis, and then its ellipsoidal shape would
become flatter by the antero-posterior poles. Notice that the profile
of the 6 year old lens (gray dots in Fig. 6B) has achieved a plateau in
the axial view at this early age, but has no plateau in the equatorial
view (Fig. 6A). As the plateau is developed when fibers reach a
uniform compaction, it seems that this compaction is developed
earlier in the antero-posterior axis, along with lens axial thinning.
But the equatorial growth does not seem to be accompanied by
similar rates of compaction. The compaction of the older central
fibers could shorten the axis if fiber shortening is relatively greater
than the decrease in fiber diameter.
The other way in which the lens becomes more elliptical depends on the fact that the equatorial growth of the lens epithelium
develops fibers that elongate from the equator to the anterior and
posterior poles up to the sutures, becoming thinner as they migrate
elongating centripetally searching for the sutures (Al-Ghoul et al.,
2003). In other words, elongating fibers are thicker at the equator
than at the antero-posterior poles. This fact can also make the lens
grow more in the equatorial diameter than in its antero-posterior
axis.
During adult years, from ages 20 to 80, the lens grows in another
manner (Augusteyn, 2010). An in vitro study had shown that the
lens increased both axial thickness and equatorial diameter at
similar rates (0.49 mm and 0.55 mm respectively) in 40 years of
adult life (Rosen et al., 2006) maintaining a constant aspect ratio
(Augusteyn, 2010). More recent very accurate in vitro measurements have shown that the aspect ratio (thickness/diameter) increases with age (Mohamed et al., 2012). So in this new study the
axial thickness increased with age more than the equatorial
diameter (0.75 vs. 0.51 slope, respectively). This would make sense
if the anterior lens curvature is steepening with age (as was
described by Nicholas Brown in 1974), because if the lens grew
equally in all directions, the anterior curvature would flatten as
happens in growing chicken eyes (Fig. 5).
This slow rate of equatorial growth contrasts with the 0.50 mm
in 6 months taken from the difference in our calculated equatorial
diameter between 3 and 9 month babies' lenses (Fig. 8). There is no
doubt that the lens has a high rate of equatorial growth during the
first year of life, at the same time in which corneal diameter and
anterior segment length have high rates of growth.
The process of metamorphosis in amphibians like toads and
frogs is a good example of the change in shape of the lens during
early growth. In general, fish have spherical lenses, and terrestrial
animals have ellipsoidal lenses. During the metamorphosis of the
anuran Pelobates Syriacus the lenses of the aquatic form change
from a spherical shape to a flattened lens in the juvenile terrestrial
form (Sivak and Kreuzer, 1983). The same happens in tadpoles
when they become terrestrial toads (Mathis et al., 1988). In 1985
Sivak et al. presented data about the change in shape during
metamorphosis of different species of amphibians and their histological studies showed that the changes in lens shape were
brought about by a rapid increase of the mitotic activity of equatorial epithelial cells at critical periods during metamorphosis. If a
similar process occurs in the human lens, it may be simple to
explain that the lens changes shape between birth and adolescence
by differential growth and compaction of its internal structure
(Fig. 9). In fact, the human lens during embryonic life is spherical as
the fish lens, and it becomes more and more ellipsoidal by growth
of the equatorial fibers during late fetal life (Cook et al., 2006). So it
seems probable that this pattern of lens growth is also followed
during the first years of infant life in humans.
10. The anterior segment in premature children
The growth of the anterior chamber in premature children is
interesting. These small eyes of premature infants have shallower
anterior chambers, thicker lenses, smaller anterior segment
lengths, more steeply curved corneas and more powerful lenses at
3 months than do full-term infants of the same age (Cook et al.,
2003, and Figs. 3, 4 and 7). Some of the eyes of premature infants
develop retinopathy as was seen, for example, in the study of the
ocular components of a series of 108 premature children who were
studied at age 7e9 in Taiwan (Chen et al., 2010). In all, 44% of these
premature children had developed some form of retinopathy, 25%
received laser treatment because of advanced retinopathy and 47%
of these 108 children had myopia at ages 7e9 years. We have
calculated the lens power for these schoolchildren in Table 3, where
it can be seen that prematures have a combination of thicker and
more powerful lenses at rest when compared to same age normal
term emmetropic children (Chen et al., 2010; Jones et al., 2005b).
While these findings might be due to laser induced growth abnormalities at the peripheral retina (Chen et al., 2010), these could
also be explained by visual or light induced control of anterior
segment growth. These eyes at birth are smaller than those of full
term infants by about 2 mm, and have smaller anterior segments, so
exposure to light could delay anterior segment growth and leave
eyes with somehow immature anterior segments, with steep corneas, and thicker and more powerful lenses by age 2e3 when the
anterior segment growth reaches a plateau. Myopia of prematurity
looks different from common school myopia, in which axial length
is longer than usual, and the lens is thinner with lower power (just
the opposite), as will be seen in the next section.
11. The lens power in school years
Three recent prospective studies have reported on the loss of
lens power in schoolchildren. These are the Orinda Study (and its
extension, the CLEERE study) (Jones et al., 2005b; Twelker et al.,
2009), the SCORM Study (Wong et al., 2010; Iribarren et al.,
2012a) and a study involving Chinese myopic twins in Guangzhou (Xiang et al., 2012). The Orinda and CLEERE studies included
phakometry, so the lens equivalent refractive index could be estimated and, as said, was shown to decrease with age in schoolchildren. The power of the lens also decreased in all refractive
groups in a similar manner from ages 6 to 14 in this study. As we
have also said, decreasing effective index accompanied by a
decrease in power in lenses that must be compacting their fibers
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
95
et al., 2005b) we can see that emmetropic eyes grew about 1 mm
after age 6 in the 10 years of follow up (approximately þ0.10 mm
per year rate), and that the power of the lens fell from 26 to 23
diopters in the same period (0.30 diopters per year rate),
compensating for axial growth. In children who became myopic,
the axial growth was greater than that of emmetropes, about 2 mm
on average in the same period (þ0.20 mm per year rate), and as the
lens lost power from 25.5 to 22 diopters (0.35 diopters per year
rate), the net change in mean refraction was 3 diopters of myopic
shift after the follow up in the myopic group. We can also see in this
paper that the lens thinned in all refractive groups up to age 10 and
then slowly began to thicken again. Hyperopic eyes had thicker
lenses and myopic eyes began with the same lens thickness as the
emmetropes but ended with lower lens thickness at the follow up.
It is noted that 76.1% of myopic subjects in this study had their
onset during the follow up, so most of them began the study being
emmetropes (Jones et al., 2005b).
If myopic eyes have lower lens power than emmetropes, and
myopes come from previous emmetropes, emmetropic eyes
developing myopia must have lost greater amounts of lens power at
some time point. The SCORM study in a Singaporean sample of
schoolchildren had a high prevalence of myopic children (Wong
et al., 2010). So the study could show a difference between
persistent myopes (those already myopic at baseline) and newly
developed myopes (those developing myopia during the follow up,
as most Orinda myopic subjects). In this last study, persistent
myopic eyes had lower lens power (and they also had thinner
lenses) than emmetropes. And here, newly developed myopes
showed a greater rate of decrease in lens power and in lens thickness than emmetropes or persistent myopes (Iribarren et al.,
2012a). This study then showed increased lens power loss at the
time when the rate of axial elongation was also increased during
myopia onset. Interestingly, when Sorsby found negative correlations between axial length and the power of refractive surfaces
(cornea and lens) he postulated that the retina was an organizer of
the coordinated growth of the ocular components (Sorsby et al.,
1957).
A cross-sectional study of school children in Taiwan (Shih et al.,
2009) also found significantly thinner lenses in myopic children
when compared to emmetropes. The consistent finding of lower
lens thickness in myopic eyes could be due to a lower rate of growth
of the lens epithelial layer, mediated by humoral factors from the
retina. Fibroblast growth factor (FGF) is present in the retina and
the vitreous adjacent to the lens, and is the principal factor
inducing lens epithelial growth (Lovicu and McAvoy, 2005). As the
lens grows by apposition of new fibers with low index, and as the
older deeper fibers mature and are compacted gaining refractive
index, the gradient refractive index (responsible for about half of
the lens power) may be maintained with a constant shape of its
profile. But if the growth rate slowly decreases with time and the
compaction rate is maintained constant, then the smoothness in
the climbing gradient profile would be gradually lost according to
Fig. 9. The same figures as in Fig. 8, this time superimposed for the 3 month old
(dotted line) and the 14 year old lens (full line), showing the change in shape achieved
during childhood. It can be seen that the lens thins from a more rounded shape at 3
months and that the equatorial portion increases making the lens more ellipsoidal.
(thus increasing refractive index by increasing protein concentration) can only be explained by changes in the refractive index
gradient profile.
Myopic children had lower lens power and hyperopes had
higher lens power than emmetropes at follow up in the mentioned
Orinda study (Jones et al., 2005b). The lens power loss prospectively matched the axial growth (still present at these school years)
in the children who remained emmetropic (Jones et al., 2005b;
Zadnik et al., 2004). From the figures of the Orinda paper (Jones
Table 3
Refraction and ocular components at age 7e9 years in prematures compared with same age fullterm from Orinda Study.
Chen et al. (2010) (Prematures)
Spherical equivalent (diopters)
Corneal power (diopters)
Anterior chamber depth (mm)
Lens thickness (mm)
Axial length (mm)
Lens power (diopters)
Anterior segment length (mm)
Jones et al. (2005b)
Myopia
Emmetropia
Hyperopia
Emmetropia
3.22
43.79
3.29
3.76
23.39
26.69
7.05
þ0.02
42.94
3.46
3.62
22.98
25.33
7.08
þ2.15
43.68
3.44
3.61
21.93
25.91
7.05
0.54
43.61
3.69
3.47
22.93
23.63
7.16
96
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
that decreasing rate of epithelial growth, and thus the lens power at
rest would decrease accordingly. So we postulate that a relative
decrease in the rate of lens growth ends up in myopic eyes with
thinner and less powerful lenses than those of emmetropic eyes.
A careful inspection of the data in Fig. 4A of CLEERE study (see
Mutti et al., 2012) shows how the rate of lens power loss declines in
myopes after myopia onset when compared to emmetropes, and it
also shows that before onset, myopes show an increased rate of lens
power loss compared to emmetropes (when looking at the unadjusted data). This is concordant with a greater rate of power loss
calculated for Orinda myopic subjects when compared to emmetropic subjects in the previous paragraphs (0.35 vs. 0.30 diopters per year, respectively). This is similar to what was found in
SCORM newly developed myopes, which showed a greater rate of
lens power loss in children who developed myopia during the study
when compared to those who remained emmetropic (0.36 vs.
e0.29 diopters per year, respectively, Iribarren et al., 2012a).
Myopia may then develop when the rate of axial growth is so
rapid that it outgrows the possibility of the lens to compensate that
axial growth by further power loss. The study of lens power change
before and after myopia onset in CLEERE Study (Mutti et al., 2012)
found that myopia onset was “characterized by an abrupt loss of
compensatory changes in the crystalline lens”. Although this last
finding should be confirmed in future studies, it is interesting that
axial growth can increase the rate of the eye's axial elongation by
myopigenic retinal signals during school years without any end
point. But, on the other hand, the lens might increase the rate of
power loss until the shape of the gradient refractive index profile
approaches a relatively maximal abrupt climbing profile. The
equatorial growth and axial compaction that produces the
described changes in lens shape during childhood (with lens
thinning and curvature flattening) might also have a relative end
point because nuclear compaction may also have a limit, showing
another possible limitation for the compensation of myopia acquired at the time of an increased rate of axial elongation.
Recent studies with lenses in vitro have shown that the power of
the refractive index gradient changes with age and with accommodation (Borja et al., 2010; Maceo et al., 2011). These studies could
accurately measure the power of the isolated lens in vitro (an
impossible measurement with the lens inside the eye), and have
calculated the relative contributions of the internal and surface
powers. This was done by calculating the surface power with the
in vitro measured curvatures, and by attributing an index to the first
layers of the cortex under the capsule, thus showing what the power
of a homogeneous lens would be (without the gradient) with the
given surface curvatures and the cortical index. Then, subtracting
the surface power from the total power, the gradient contribution
could be calculated. Using the well known Gullstrand's equation for
calculation of the power of a thick lens (Mutti et al., 1998), and
assuming an index for the cortex of 1.3709 (Jones et al., 2005a; Borja
et al., 2008, 2010) we calculated the relative contributions of the
surface and internal powers for the data of Mutti et al. (2005, 1998)
in babies and schoolchildren respectively (Table 4). These studies
showed that the anterior and posterior lens curvatures flattened
with age in babies and children as the lens thinned, but from the
data in Table 4 we can see that this change in curvature accounts for
only half of the power loss. The relative contribution of the internal
power given by the possible change in the gradient is responsible for
the other half of the lens power loss in growing children. Then, it is
possible that changes in the refractive index gradient profile within
the lens are an important cause of lens power loss during school
years. And this internal power loss could be responsible for the
differences in lens power described among refractive groups in
schoolchildren. There is no doubt that a thicker or thinner lens can
have different surface curvatures and differences in the internal
gradient index profile (Figs. 6C and 9).
12. Theories for lens thinning during childhood
Sorsby et al. (1957) proposed a coordinated growth of the
components of refraction (mainly axial length with corneal and
lens powers) to explain the tendency to produce emmetropic eyes
in which differences in axial length were compensated by corneal
and lens power. He clearly showed that in the emmetropic range,
longer eyes had flatter corneas and less powerful lenses (and vice
versa) (Sorsby et al., 1957). Then, van Alphen (1961) proposed a
model for eye growth that comprised passive and active factors
including a stretch factor. These ideas were further discussed by
Hofstetter (1969) (who showed passive mechanisms in emmetropization) and later by Dunne (1993) (who proposed mathematical models of ocular growth). Weale (1982) then proposed that
the lens changed shape during the first years of life because of a
redistribution of volume produced by zonular tension during eye
growth. These ideas were further explored by Mutti & Zadnik
(Zadnik et al., 1995; Mutti et al., 1998) after their first longitudinal
study of lens thinning in children, when they proposed a theory for
lens thinning based on zonular traction mediated by ciliary muscle
tension. In this last theory, lens thinning and lens power loss were
modified in myopic children by a restriction in scleral expansion
during eye growth. By the same time, Brown and Bron (1996) in
their book called “Lens Disorders” made reference to Weale's
zonular traction theory when explaining lens shape changes during
school years. They argued that there was little anterior segment
growth after age 2 in children (from the available measurements of
corneal diameter), and that slit Scheimpflug images of children
eyes showed that although lens axial thickness was relatively stationary over childhood, there was vigorous cortical growth
accompanied by a reduction in the dimension of the nucleus (this
last produced by compaction). In the present review we follow this
latter idea about the causes of lens thinning during childhood,
further proposing that the redistribution of the gradient index
structure within the lens contributes to the loss of lens power.
Table 4
Internal and surface lens power contributions, in diopters, for two prospective studies.
(Mutti et al. IOVS 2005; 46: 3074e3080.)
3 months
9 months
Difference
% change
Equivalent lens index
Complete Gullstrand's lens power
Surface Gullstrand's lens power
Internal (gradient index) power
1.4526
40.00
12.19
27.81
1.4591
36.49
10.52
25.97
3.51
1.68
1.83
100.0%
47.8%
52.2%
(Mutti et al. IOVS 1998; 39: 120e133.)
6 years old
14 years old
Difference
% change
Equivalent lens index
Complete Gullstrand's lens power
Surface Gullstrand's lens power
Internal (gradient index) power
1.431
24.52
9.09
15.43
1.429
21.77
8.23
13.54
2.75
0.86
1.89
100.0%
31.2%
68.8%
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
A recent clinical trial designed to evaluate theories of myopia
progression concluded that the mechanical tension theory based
on zonular traction was not consistent with the findings of the
study (Berntsen et al., 2012) so it is possible that Brown's observations about nuclear compaction in children lenses are the cause
of lens thinning.
13. Change in ocular components at myopia onset
In experimental models of refractive error, during early eye
growth, images falling behind the retina in hyperopic eyes (hyperopic defocus) can induce an accelerated rate of axial growth, and
vice versa, images falling in front of the retina (myopic defocus) can
down-regulate the rate of axial growth (Wallman and Winawer,
2004). Low outdoor exposure to natural ambient light probably
produces an acceleration of axial growth by the down-regulation of
retinal dopamine activity (French et al., 2013). Myopic children
have been shown in CLEERE study to be exposed to significantly
less time outdoors than their emmetropic peers up to three years
before myopia onset (Jones-Jordan et al., 2011). In three different
studies, the rate of refractive change towards myopia and the rate of
axial elongation have been shown to be accelerated at the years
around the onset (Thorn et al., 2005; Mutti et al., 2007; Xiang et al.,
2012). Then, one could argue that low outdoor exposure seems to
be accompanied by a higher rate of axial elongation in future
myopic children. Although the lens could compensate for this
accelerated growth with an accelerated rate of power loss
(Iribarren et al., 2012a), myopia can be rapidly developed once the
lens reaches its described limit in power loss because of its internal
structure. At that time, any further axial elongation would be
translated into a myopic shift. But once myopia is established, the
myopic eye is subject to myopic defocus for some periods each day
when spectacles are not used. Short periods of myopic defocus have
been shown to have a potent inhibitory effect on ocular growth in
animal models (Wallman and Winawer, 2004). And it has been
suggested that this myopic defocus could slow down the rate of
axial elongation once myopia is established (Xiang et al., 2012).
More prospective studies about myopia onset following the
changes in ocular components during school years are needed to
confirm these findings, and special attention should be paid to lens
changes, because one mentioned study has shown that lens power
loss “stops” around myopia onset (Mutti et al., 2012) and another
has shown no change in the rate of power loss at that time (Xiang
et al., 2012). Further, it is difficult to understand the “stop” in lens
power loss after myopia onset (Mutti et al., 2012) if Singaporean
SCORM persistent myopic children show consistently lens power
loss after onset during the years of progression (Iribarren et al.,
2012a). As these studies in myopic children have been performed
at a mean age of onset around 10 years, the age at which the lens
stops thinning and reduces its rate of power loss, the finding of
reduced power loss after myopia onset could be an age effect. One
alternative possibility is that after the lens increases its rate of power loss at myopia onset, it returns to baseline age related rate of
power loss.
As will be seen in the following section, adult myopes also show
lens power loss during myopic progression. In fact, the lens does
not stop losing power with ageing, because the development of a
refractive index plateau in the center of the lens further changes the
gradient profile and makes the lens lose power during adult years
(Augusteyn et al., 2008 and Fig. 6A & B).
14. The lens power loss during university study years
The mentioned SCORM study in Chinese Singaporean school
children showed rates of axial length change of þ0.10 mm per year
97
in emmetropes, and þ0.28 mm per year in myopic eyes, with a
change in lens power of 0.29 diopters per year in emmetropes,
e0.36 diopters per year in newly developed myopes and 0.25
diopters per year in persistent myopes (Iribarren et al., 2012a). A
prospective study of engineering students in Norway (Kinge et al.,
1999) showed that during the three-year follow up, the group of
149 students had a myopic shift in refraction from age 20 to 23
years. The lens power was calculated from the biometry and the
cycloplegic refractions in that study (Iribarren et al., 2014b),
showing that the initially emmetropic engineering students had a
rate of axial length growth of þ0.39 mm in three years, that
is, þ0.13 mm per year, similar to that of emmetropic children in
SCORM or Orinda studies. And these engineering students had a
rate of lens power loss of 0.70 diopters in three years, that is,
e0.23 diopters per year, similar to the loss of lens power in Singaporean children. This compares well to the non-cycloplegic calculations that gave a loss in lens power of 0.40 diopters in 3 years
for emmetropic young subjects followed by Grosvenor (0.13 diopters per year) (Grosvenor and Scott, 1993).
These few studies have then shown that the lens is still
compensating, in part, for axial elongation during early adult years.
This happens at a time when the lens is increasing in axial thickness
and possibly steepening curvatures (very different from the times
of lens thinning and flattening in schoolchildren up to age 10), so
here again variations in the gradient index structure may be driving
the changes seen. It would be interesting to have longitudinal
cycloplegic studies with biometry in selected adult populations
prone to develop myopia (like engineering or law students) to
confirm these findings about lens power loss during early adulthood. If phacometry could be performed, then the equivalent index
could be calculated, perhaps showing a prospective decrease with
age as was shown in the Orinda and CLEERE studies.
15. The lens in adulthood
We have seen that myopic children have lower lens power than
emmetropic children, and hyperopic children have higher lens
power than their emmetropic peers. This would produce a positive
correlation between refraction and lens power, as higher spherical
equivalents have higher lens power and vice versa (Iribarren et al.,
2012a). This would be in agreement with the fact that longer eyes,
usually the myopic ones, have lower lens power, and vice versa,
shorter eyes have higher lens power. This can be seen in the
negative correlation between axial length and lens power, originally described by Sorsby and also seen in the Sydney Myopia Study
(Ip et al., 2007) or SCORM studies (Iribarren et al., 2012a).
But a recent population study with adults living in Reykjavik
(Olsen et al., 2007), which reported on lens power correlations with
both refraction and axial length, also reported a conflicting finding.
In fact, lens power was negatively correlated with axial length as it
was known long ago (Sorsby et al., 1957) but lens power was also
negatively correlated with refraction, assuming that myopic eyes
had higher lens powers or vice versa, hyperopic eyes lower lens
power. Olsen et al. (2007) discussed these findings explaining that
refraction was in fact determined by a complex interplay between
all the ocular components. Indeed, the relations between the ocular
components should be changing from childhood to adulthood if the
correlation between lens power and refraction is changing from
positive to negative.
Fig. 1 gives the clues for what is happening. From age 20 until
age 75, the prevalence of cycloplegic hyperopia greater than þ1
diopter increases from 10% to 50%. At these ages corneal power has
been shown to be stable as is probably also the case for axial length.
In any way, eyes could not become shorter to explain this hyperopic
shift in refraction because in that case pseudophaquic eyes should
98
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
Fig. 10. Significantly lower lens power in hyperopic subjects compared to emmetropic
and myopic subjects (in the group with low nuclear opacity grades) of the Central India
Eye and Medical Study (Iribarren et al., 2012b).
have hyperopic shifts with ageing in the clinic and that does not
seem to happen (author's clinical observation and Brown et al.,
1999). What indeed may be happening is that the lens is losing
power in some emmetropic subjects who develop hyperopic shifts
and become hyperopes (Hashemi et al., 2010). Then, by age 70, the
50% prevalence of hyperopes may be a mixture of 10% who were
hyperopes since childhood (with high lens power) and of 40% of
newly developed hyperopes that may have come from the
emmetropes who may have lost lens power. Then, this number of
hyperopes with low lens power would change the correlation between refraction and lens power to a negative one (in adults aged
70) as has been found in Reykjavik (Olsen et al., 2007) and later in
the Los Angeles Latino Eye Study (Iribarren et al., 2010) and the
Central India Eye and Medical Study (CIEMS) (Iribarren et al.,
2012b). In these last two studies, in fact, adult hyperopes without
cataract had significantly lower lens power than the emmetropes,
the opposite of what is found in school-aged children. This can be
seen in Fig. 10 with data published in CIEMS Study (Iribarren et al.,
2012b) where hyperopes with low amount of nuclear opacity have
lower lens power than emmetropes or myopes. This is probably
produced by loss of lens power in many emmetropic eyes that turn
to be hyperopic with ageing. This last study also showed a significant negative correlation between refractive error and lens power
(Fig. 11).
The amount of lens power loss with age during adult years can
be calculated indirectly from a prospective population based study
like the Beaver Dam Study (Lee et al., 2002), which showed that
subjects aged 43e59 at baseline had a hyperopic shift of þ0.54
diopters in the 10 years follow up. If all the other ocular components are left unchanged, the lens changes power by about 1.5
diopters per þ1 diopter change in refraction (Wolfgang Haigis,
personal communication). Although those were not cycloplegic
refractions and could be biased, such hyperopic shift would
represent 0.81 diopters of lens power change in 10 years,
or 0.081 diopters loss per year. This rate of lens power loss is
lower (about one third) than that calculated for young engineering
students (0.23 diopters per year) (Iribarren et al., 2014b) or that of
Singaporean schoolchildren (0.29 diopters per year) (Iribarren
et al., 2012a) so the lens seems to lose power at a very slow rate
during adult years.
As has been explained when speaking of children lenses, a lens
which is increasing in thickness and curvatures during adulthood
can only lose power by changing its gradient index profile. As we
have also said, the maintenance of the refractive index gradient
profile could only be achieved if the rate of compaction equals the
rate of apposition of new fibers. An early study in rats has shown
that the lens epithelial cells, with increasing age, show less growth
and differentiation under similar concentrations of FGF (Lovicu and
Fig. 11. Negative correlation between refractive error (spherical equivalent) and crystalline lens power in participants in the Central India Eye and Medical Study. Subjects with
marked nuclear cataract (grades 6 and 7, crosses and dotted regression line), had a greater negative correlation than those with less marked nuclear cataract (grades 2e5, full
regression line and circles). Reproduced from Iribarren et al. (2012b). Copyright (2012), with permission from Association for Research in Vision and Ophthalmology.
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
McAvoy, 1992). It may be true that, very slowly during adult life, the
epithelial cells gradually lose the capacity to grow. And this would
simply make the climbing gradient profile more abrupt. Besides, as
compaction probably reaches a relative end point after 10e20 years
of human life, the central gradient plateau is formed as nuclear
fibers reach maximal compaction. As can be seen in Fig. 6A & B
(Augusteyn et al., 2008), the adult lens develops a refractive index
plateau at the center of the lens, and this section of uniform index
makes the lens resemble an artificial homogeneous lens that has
lost its gradient, with lower power (and greater positive spherical
aberration). Interestingly, several studies have shown that the internal spherical aberrations of the human eye increase with ageing
(Glasser and Campbell, 1998; McLellan et al., 2001; Artal et al.,
2002; Brunette et al., 2003). The lens has the gradient index
structure and aspheric curvatures such that the internal aberrations
of the eye are negative in youth compensating the positive spherical aberration of the cornea. The increase in positive spherical
aberration with age can be seen in Fig. 12, where the juvenile clear
dog lens has negative spherical aberration while the human 70 year
old lens has positive spherical aberration (Sivak and Kreuzer, 1983;
Sivak, 1985). This older lens behaves as a homogeneous lens,
without a gradient index structure.
During middle adulthood, myopia prevalence does not change
much in Fig. 1 (Hashemi et al., 2004). The myopic eyes are not as
prone as emmetropic eyes to have hyperopic shifts, as has been
shown in a clinical retrospective study (Grosvenor and Skeates,
1999). Prospective population based studies of refractive error in
adults could confirm this last finding. In fact, hyperopic shifts in
myopic subjects are uncommon in clinical practice. Perhaps, only a
few low myopes have small hyperopic shifts in their 40's. Myopic
eyes may be less prone to have hyperopic shifts with ageing as they
already have lower lens power than emmetropes early in life in
Orinda (Jones et al., 2005b) and SCORM (Iribarren et al., 2012a)
studies. If the thinner lens of myopic eyes has lost gradient power to
a greater extent than that of emmetropic eyes, it may thus have a
limited capacity of possible further power loss. Interestingly, a
more abrupt climbing gradient profile would not compensate
accurately the spherical aberration of the lens, and myopes have
been shown in some (but not all studies) to have greater ocular
aberrations than emmetropic eyes (He et al., 2002; Marcos et al.,
2002; Paquin et al., 2002; Kwan et al., 2009). It would be interesting to have measurements of the gradient index profile in
different refractive groups in young adults.
Fig. 12. In (A) a clear juvenile dog lens with negative spherical aberration and in (B) a
brown 70 year human old lens with positive spherical aberration. See how the laser
beams have different refraction through the peripheral or central sections of the lens
(Reproduced with permission from: Sivak (1985). ©The American Academy of
Optometry 1985).
99
At older ages, in Fig. 1, new cases of myopia appear, this time
produced by a different change in the lens associated with nuclear
cataract. The lens in these cases should be gaining power producing
a myopic shift in refraction. Then the emmetropes who turn to be
myopic with cataract would have high powered lenses, the opposite
of what is found in myopic schoolchildren. So this would also turn
the correlation of lens power and refraction to the negative side, as
myopic eyes would have higher lens power than their emmetropic
peers (Fig. 10). This has been found in CIEMS study, which showed
that the correlation between lens power and spherical equivalent
became more negative when cataract subjects were included
(Iribarren et al., 2012b, Fig. 11). In Fig. 1 of the present paper, the
prevalence of myopia changes from 12% during adult years to 38% in
aged subjects, and this could be enough to change the correlation
between lens power and refraction to the negative side.
16. Longer eyes of taller subjects have lower powered lenses
The advent of ultrasound biometry in the 70's produced two
interesting studies. In 1979 Larsen (Larsen, 1979) showed that taller
people had longer eyes (and vice versa) for subjects in the emmetropic range. Since then, many population studies have found that
taller people have longer eyes with flatter corneas, irrespective of
refractive error (Wong et al., 2001a; Saw et al., 2002; Ojaimi et al.,
2005; Eysteinsson et al., 2005; Wu et al., 2007; Lee et al., 2009;
Nangia et al., 2010). Also in 1979, Blomdhal showed that bigger
newborns had longer eyes with flatter corneas. A recent population
based study with cycloplegia for refractive error measurement
showed that taller people had longer eyes with flatter corneas and
also, lower powered lenses, irrespective of refractive error
(Iribarren et al., 2014c) (Table 5). This study also calculated the lens
power with published data of the ocular components and refraction
of two adult population studies (Wong et al., 2001a; Wu et al.,
2007) and one study in schoolchildren (Saw et al., 2004),
showing that this trend in taller people, or children born bigger,
having bigger eyes with less powerful lenses was also the rule
(Table 5).
Interestingly, a recent study of stature growth trajectories in a
longitudinal study of British children showed that while refraction
at age 15 was not related to height growth, corneal radius at that
age was related to growth in the first 2 years of life and axial length
was related to height growth in the first 10 years of life (Northstone
et al., 2013). So, in the first years of life, when the corneal radius and
axial length are changing with eye growth, these changes may be
then influenced by general growth patterns, and also coordinated
by the emmetropization mechanism that makes the axial length
match the refractive surfaces by defocus. Indeed, the lens should be
part of this general pattern of co-regulation. Further evidence of
this is the finding of lower lens power in faster growing eyes which
develop myopia (Iribarren et al., 2012a). The finding of lower
powered lenses in taller people with longer eyes could be in
concordance with some kind of regulation of lens power loss according to axial length change during early growth (Iribarren et al.,
2014c). Alternatively, it could be possible that general somatic
growth is linked to lens growth early in life such that taller children
could have lenses that grow thinner and less powerful; and then
the axial length independently could match the optical power of
the cornea and the lens by defocus regulated eye growth. This
would also produce longer axial lengths in eyes with lower powered lenses or flatter corneas.
Since Sorsby et al. (1957) it is known that, in the emmetropic
range, longer eyes have flatter corneas. In Table 6 we have calculated the lens power for ideal emmetropic eyes with a normal range
of axial lengths and corneal powers such that they all have a normal
axial length/corneal radius ratio of 3.0 (Grosvenor and Scott, 1994).
100
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
Table 5
Comparison of refraction and ocular components of the different studies by height and birthweight.
Height
m
SER
D
CR
mm
Height and ocular components in adults (Iribarren et al., 2014c)
1.31e1.57
0.04
7.58
1.57e1.65
0.01
7.63
1.65e1.99
0.12
7.71
Height and ocular components in adults (Wong et al., 2001a)
1.37e1.50
0.24
7.55
1.51e1.55
0.6
7.57
1.56e1.59
0.49
7.66
1.60e1.65
0.6
7.68
1.66e1.83
0.52
7.79
Height and ocular components in adults (Wu et al., 2007)
1.30e1.48
1.53
7.53
1.49e1.54
1.67
7.61
1.55e1.6
1.12
7.68
1.61e1.80
1.4
7.76
Birthweight
m
SER
D
CR
mm
ACD
mm
LT
mm
AL
mm
LP
D
AL/CR
2.60
2.63
2.69
4.27
4.26
4.23
22.99
23.14
23.43
22.93
22.71
22.43
3.03
3.03
3.04
2.7
2.86
2.83
2.99
3.1
4.92
4.78
4.78
4.68
4.63
22.74
23.05
23.19
23.44
23.78
25.68
25.11
25.01
24.44
23.94
3.01
3.04
3.03
3.05
3.05
2.7
2.75
2.87
2.87
4.47
4.48
4.44
4.48
22.36
22.51
22.76
23.14
28.35
28.67
27.56
26.96
2.97
2.96
2.96
2.98
ACD
mm
LT
mm
AL
mm
LP
D
AL/CR
3.5
3.48
3.46
23.13
23.44
23.67
25.04
24.54
24.30
3.01
3.02
3.03
Birthweight and ocular components e Singaporean Chinese children (Saw et al., 2004)
2.5e2.9
0.35
7.69
3.58
3.0e3.4
0.52
7.76
3.61
3.5e3.9
0.67
7.82
3.64
SER (Spherical Equivalent Refraction) CR (Corneal Radius) ACD (Anterior Chamber Depth) LT (lens thickness).
AL (Axial length) LP (Lens Power) AL/CR (Axial Length/Corneal Radius ratio).
As was early recognized by Grosvenor and Scott (1994), it can be
clearly seen that not only the cornea and the axial length adjust for
eyes being emmetropic, as also longer eyes should have lower
powered lenses, and vice versa. This lead the former researchers to
state that “the lens had emmetropized” in longer eyes.
17. How can the lens change its power?
How is it possible that the lens changes its power in opposite
directions with ageing, first losing power from birth up to age 70
and then gaining power with cataract formation? Can the lens
adjust its power to the general growth of the eye? A theory that
could explain these changes can only be based on the understanding of both surface and internal structure of the lens.
As we said before, the lens has a gradient of refractive index
because new fresh fibers mature and become compacted as they
age and sink in the deeper layers of the lens. As fibers mature and
become compacted they gain index, so a gradient of refractive index is established from the surface to the center of the lens. This
gradient gives the lens an internal power greater than the one due
to its curvatures alone. This has been known since the time of
Thomas Young who even calculated the power given by a gradient
lens (Young, 1801; Atchison and Charman, 2011).
The “effective” or “equivalent” index is the index the lens would
have if it were a uniform media explaining both surface and internal powers. As we said, Dubbelman (Dubbelman and Van der
Heijde, 2001) showed that the lens effective index decreased
with age in adults in a similar manner as it was later described
prospectively in schoolchildren (Jones et al., 2005b). If the lens
effective index decreases while the lens is compacted during
childhood (and thus should gain index) the only possible explanation for this loss of effective index is that the gradient profile is
becoming less effective (its climbing profile is becoming more
abrupt and it is developing a central plateau). This fact was originally discussed by Donders in 1864 when he was thinking how the
eye could become hyperopic with ageing (Donders, 1864). He wrote
“In advancing years the lens becomes externally especially firmer,
and thus the coefficient of refraction of the outer layers appears to
increase. If this actually takes place, and if the coefficient of the
cortical layers thus approaches more to that of the nucleus, the
(lens) focal distance becomes greater. On this the diminution in
advanced life of the refractive condition of the eye appears really to
depend.” (Donders, 1864, page 88). But then he erroneously
thought that although this could be possible, the main reason for
hyperopia was a flatter lens surface with age. He probably thought
this because he imagined that a rounded lens would flatten curvatures with growth. This idea of lens flattening with age lasted for
more than 100 years, until Nicholas Brown at Oxford in 1973,
showed with Scheimpflug photography that the lens curvatures
became steeper with ageing. For example, Duke-Elder in 1970,
when speaking about hyperopic shifts during adulthood, still
argued that the lens curvatures became flatter with age (Duke-
Table 6
Longer eyes with normal AL/CR ratio have lower powered lenses, and viceversa.
Refraction
(diopters)
Corneal radius
(mm)
Keratometry
(diopters)
ACD
(mm)
Lens thickness
(mm)
Axial length
(mm)
AL/CR
e
Lens power
(diopters)
0
0
0
0
0
0
0
0
7
7.2
7.4
7.6
7.8
8
8.2
8.4
47.36
46.04
44.80
43.62
42.50
41.44
40.43
39.46
2.90
2.90
3.00
3.00
3.10
3.10
3.10
3.10
4.20
4.20
4.20
4.20
4.20
4.20
4.20
4.20
21.0
21.6
22.2
22.8
23.4
24.0
24.6
25.2
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
28.08
26.83
25.95
24.87
24.11
23.18
22.31
21.50
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
Elder and Abrams, 1970b), although he recognized that Parsons had
thought that “hardening of the cortical material of the lens” could
be responsible for hyperopic shifts with ageing (Parsons, 1906).
An ellipsoidal lens which has a flatter anterior pole steepens its
front curvature if it only increases axial thickness without changing
much its equatorial diameter (Fig. 13). Nicholas Brown began to talk
about the lens paradox as he thought that greater curvature at the
lens surface (more power) was paradoxically accompanied by
presbyopia and not myopia with ageing. This paradox could only be
explained by a decreasing gradient refractive index power inside
the lens. After Brown, the change in gradient refractive index
profile with age was shown in different studies (Pierscionek, 1990;
Smith et al., 1992; Hemenger, 1995; Smith and Pierscionek, 1998)
and recently by magnetic resonance images (Kasthurirangan et al.,
2008). If the profile of the climbing gradient index becomes more
abrupt with age, then the rays passing through it do not bend so
much as they did earlier when the gradient was smoother. And the
development of a central plateau with no gradient power further
makes the lens lose power and optical properties. The change in the
peripheral profile of the climbing gradient of refractive index is
probably produced by compaction of the fibers inside the lens,
especially in the deep layers of the cortex (Fig. 6A & B, adult lens).
On the other hand, nuclear cataract develops in the center of the
lens. With this type of cataract the lens could be even more compacted in the center (Al-Ghoul et al., 2001). And then the nuclear
index should increase, changing again the profile of the gradient
structure, thus explaining the increase in power of the lens and the
myopic shift in refraction found in 40e80% of subjects with nuclear
cataract in the clinic (Iribarren and Iribarren, 2013; Díez Ajenjo
et al., 2014; Pesudovs and Elliot, 2003). Further proof of this is
the finding of thinner lenses in cataract subjects in CIEMS Study
(Iribarren et al., 2012b) as if the compaction produced with cataract
formation could make the lens thinner. In that sense, early observations of deeper anterior chambers in eyes with unilateral cataract
made Laursen & Fledelius think that with cataract the lens was
becoming thinner (Laursen and Fledelius, 1979).
Although the lens does not seem to be responsible for changes
in refraction in animal studies of experimental refractive error
(Sivak, 2008, Review), human studies show that the lens somehow
can compensate for the axial growth of the eye to some extent. This
compensation may have passive and active mechanisms. The lens
seems to slowly lose power from birth to senescence. Some of the
changes in lens surface shape tend to cancel each other: for
example, during childhood, the lens thinning per se would increase
the power (optically speaking, a thinner homogeneous lens with
constant curvatures should have greater power) but the decrease in
Fig. 13. Schematic drawings of growing lenses. In (A) an ellipsoidal lens that grows
only axially steepens front and back curvatures as it grows and in (B) same ellipsoidal
lens that grows in all directions flattening front and back curvatures.
101
curvature that accompanies crystalline lens thinning decreases its
surface power, so lens thinning cancels to some extent lens flattening during school years. Another possible active way that the
lens has for changing its power is by the regulation of the rate of
growth and compaction of lens fibers, in such a way that it may
alter the profile of its climbing gradient refractive index which is
responsible for its internal power. This may be a very slow mechanism in humans who have a very slow rate of lens growth, but
appears to be fast during metamorphosis in amphibians, which
rapidly change lens shape and refractive power of the eye when
moving from water to aerial vision.
Interestingly, the diameter of fibers decreases from the center to
the periphery in microscopic studies of adult human lenses (Taylor
et al., 1996). For example, the mean cross-sectional area of fibers
decreases progressively from 80 square micrometers in the embryonic center of the lens to only 7 square micrometers in the adult
nucleus which is the sector under the newly developed cortex. This
newly developed cortex in the surface of the lens, in turn, has fibers
with a greater area of 24 square micrometers. This pattern in an
adult lens that has laid and compacted fibers at different ages, and
is still laying new fibers, is certainly interesting. Although the fibers
in the central refractive index plateau (formed in the adult, juvenile
and fetal nucleus) have similar protein concentration (and similar
refractive index) because a plateau of index is developed, the
younger ones are progressively smaller from the center to the periphery. It seems that the embryonic and fetal fibers have been the
biggest ones when laid, and that the ones laid during juvenile
school years are smaller when they achieve maximum compaction
with a similar index as those at the center of the lens. They were
probably smaller than the embryonic when they were laid and
matured during postnatal life. And the ones laid in the adult years,
which form the outermost part near the cortex, are even smaller
when compacted. The only exception in this pattern of change in
fiber diameter are the newly developed fibers in the surface cortex,
still not compacted, that are a little bigger than the ones near them
in the adult nucleus, which have been compacted. This pattern of
change in fiber diameter probably shows that, as fibers are laid
from embryo to adult, they are gradually growing smaller up to
maturation, this fact perhaps related to a slower rate of lens
epithelial growth with ageing. Besides, older fibers could have
smaller cross-sectional area because they are circumferentially
longer as they grow far apart from the center.
Further proof that the lens can decrease its rate of growth with
age comes from Augusteyn studies measuring in vitro wet weight of
postmortem donor eyes. Augusteyn studies showed that the lens
wet weight increased linearly with age in adult life (Augusteyn,
2007; Augusteyn, 2010). Such linear growth in wet weight during
adult years, in principle, tended to show that the human lens
maintained a constant linear rate of growth throughout the whole
adult life. One study showed that the water content in the nucleus
was constant with age (Heys et al., 2004; Truscott, 2009), but as the
lens becomes older, it becomes compacted (Al-Ghoul et al., 2001)
with fibers more densely packed, probably with loss of water as
cataract develops (Heys et al., 2004). As proteins are heavier than
water, older lenses might maintain a constant increase in wet
weight but not a similar increase in volume of added fibers. Besides,
if the increase in lens thickness and diameter were linear, the
volume should increase non-linearly by the third power (more
added volume as the lens becomes bigger). But the opposite seems
to be true. In fact, a decreasing non-linear growth in axial thickness,
equatorial diameter and calculated lens volume has been preliminary reported for in vitro human lenses (Mohamed et al., 2012),
showing that the increase in dimensions and volume slows down
as the lens ages during adulthood. The increase in volume for
Mutti's lenses in Fig. 8 has been calculated in Table 7, where it can
102
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
Table 7
Lens volumea calculated from the data in Figure 7 of Mutti's studies.
Age
Lens volume (cubic mm)
Volume change (%)
3 months
9 months
14 years
113.61
129.03
139.71
13.6%
8.3%
a
Calculated from the volume of an ellipsoid (4/3*p*a*b*c).
be seen that during six months (in the first year of life) the lens
volume increases by 13%, while in the next fourteen years it only
increases by 8%. Table 8 shows the decay in lens volume growth
during adulthood calculated from the data in Mohamed et al., 2012
for adult years.
The increase in volume of the growing lens probably results
from the balance between new added fibers and compaction of
older ones. If compaction is a time dependent process due to ageing
of proteins which aggregate and lose water, then the decay in lens
volume growth means that less fiber volume is added as time
passes by. If this in vitro biometric preliminary finding is confirmed
(Mohamed et al., 2012), and we consider that individual fibers laid
at older ages reach lower final volumes, then it is possible that the
lens may have a decreasing rate of lens epithelial growth with
ageing. This pattern of decrease in growth over time would undoubtedly make the climbing gradient profile more abrupt, as the
only way to maintain a constant climbing gradient profile that is
being compacted in the deeper layers would be to maintain a
constant rate of growth of new fibers. This would also produce a
plateau of index in the center of the lens.
If this decreasing lens growth with age is not confirmed in
future studies, one alternative possibility for the change in the
climbing gradient profile would be that compaction progressively
increases its rate with ageing. This would also make the climbing
gradient profile more abrupt. But this is not likely as compaction
seems to be an inherent property of protein ageing. Most of the
hyperopic changes analyzed are slow and take years to develop. The
only report of a rapid change in lens refractive properties is that
related to a myopic shift of about 2e3 diopters with nuclear cataract usually developed in few months. The slit lamp observed
changes are found in the nucleus that becomes more colored and
opalescent. So this compaction and probable loss of water that, also
probably, changes the nucleus index, seems very different to the
slow change in the peripheral climbing gradient index profile.
Another important issue in this analysis it that in vitro and
in vivo measurements of lens thickness may not be comparable in
the sense that in vitro measurements are made with the lens in
maximally accommodated state and the lens power in the present
study is analyzed in vivo under cycloplegia at a resting position. The
in vitro axial thickness would be overestimated in lenses of subjects
younger than 40, (and equatorial diameter underestimated, Strenk
et al., 1999) when compared to lenses measured in vivo at rest
under cycloplegia because of the change in lens shape with accommodation. So the change with age in the relation between axial
thickness and equatorial diameter (aspect ratio) could be even
greater for lenses in vivo. To test for this hypothetical difference we
Table 8
Decreasing growth in lens volume taken from Figure 5 in Mohamed et al. (2012).
Age
Lens volume (cubic mm)
Absolute change (cubic mm)
20
30
40
50
60
70
80
148.03
169.29
184.38
196.08
205.64
213.72
220.72
e
21.26
15.08
11.70
9.56
8.08
7.00
years
years
years
years
years
years
years
Fig. 14. Plot of the in vitro data for lens axial thickness growth with age from Mohamed
et al., 2012 along with the in vivo data from five population based studies with A-Scan
biometry (Singapore: Wong et al., 2001b; Taiwan: Shih et al., 2007; Latino Eye Study:
Shufelt et al., 2005; Myanmar: Warrier et al., 2008; Mongolia: Wickremasinghe et al.,
2004).
have plotted in Fig. 14 the lens thickness measurements from five
different in vivo population studies with A-Scan biometry along
with in vitro data from Mohamed et al., 2012. It can be clearly seen
that with the exception of the Chinese Singaporean who have
thicker lenses, the general pattern of lens axial growth is similar in
all studies. And that axial growth decays with age in both types of
studies. So we think that our analysis is not biased by comparing
in vitro with in vivo studies of ocular biometry.
18. Is the rate of lens power loss an actively regulated
process?
In the classical studies about the correlation of the ocular
components with refraction performed by Tron (1940) and
Stenstrom (1948) in younger adults, the lens was found to have no
correlation with refraction, and thus was not considered important
in the development of refractive error. But things might have
looked different if those studies would have been performed in
children (who have a positive correlation between refraction and
lens power, Iribarren et al., 2012a) or in older adults (who have a
negative correlation between refraction and lens power, Fig. 11,
Iribarren et al., 2012b). Animal studies of refractive error have
concluded that the lens has a passive role in the development of
refractive error, as Sivak has extensively reviewed (Sivak, 2008).
Indeed, those animal experiments are performed during short periods of one or two weeks, so changes in the lens may not have been
shown, as these may take longer to develop.
The consistent age related loss of lens power during life seems to
be an inherent consequence of lens growth, passive in nature. This
loss of lens power protects from myopia development during the
axial growth period in children. Once axial growth has stopped in
adulthood, the continuing loss of lens power produces hyperopic
shifts in refraction that seem to be an undesired passive process that
impairs distance vision during late adulthood. But, can the rate of
lens power loss be modulated during childhood to produce myopic
eyes with consistently lower lens power at the end of childhood?
The optical power of the fish eye is mainly given by the lens (the
flat fish cornea does not have much power under water). The fish
eye grows continuously throughout life. Fish lenses also grow
continuously. The power of the fish lens has to decrease with age to
adapt for the increasing axial length as the fish grows. A defocus
modulated axial growth adapts the eye size to the lens focal length
in fish eyes (Shen and Sivak, 2007). But an interesting experiment
with fish reared for 10 months under monochromatic light or under
light deprivation showed alterations both in longitudinal spherical
R. Iribarren / Progress in Retinal and Eye Research 47 (2015) 86e106
aberrations and refractive index profiles of those growing fish
€ ger et al., 2001). These alterations are of interest as they
lenses (Kro
show that the gradient structure can be modified environmentally
during lens growth. A recent animal study of myopia development
in chicks growing with unrestricted vision under low light environments has shown that the lens power loss during eye growth
can be environmentally modulated, as the eyes of chicken developing myopia growing under 500 lux ambient light, have thinner
and less powerful lenses than the ones which remain hyperopic
growing under high ambient illumination. This environmental
change in the rate of lens power loss is slow as it takes 2e3 months
to develop (Cohen et al., 2011, 2014).
The lens has been shown to be also thinner in myopic children in
several studies (Jones et al., 2005b; Shih et al., 2009; Wong et al.,
2010; Iribarren et al., 2012a). Myopic eyes are generally longer. The
lens is also thinner in taller subjects (who also have longer eyes). A
thinner lens is probably a lens with delayed growth. And human
studies reviewed here have shown that these thinner lenses have
lower power. FGF is the principal molecule involved in lens growth,
and its concentration in the vitreous could be modified by genetic,
humoral or local factors. FGF could also be involved ocular growth
signaling (Rhorer and Stell, 1994; Gentle and McBrien, 2002;
Wallman and Winawer, 2004). If the profile of the gradient index
structure is a function of lens growth, delayed growth could alter this
gradient and thus the internal power of the lens. So there is a
possible mechanism for regulating the lens power loss based on its
rate of growth, which in turn may be a function of FGF concentration.
The findings reviewed herein, although they should be replicated, are possibly showing that lens growth could be actively
modulated in relation to axial or somatic growth during early
development in infants and also in myopic schoolchildren. FGF
could be the link of this regulation. It is possible that the emmetropization mechanism was adapted by evolution to maintain a
relative mild hyperopic refraction during growth as accommodation can overcome this mild refractive error before presbyopic years
(Morgan et al., 2010). This would be protective from eyes being out
of focus for distance viewing (myopia). Current thinking about
emmetropization suggests that a passive programmed loss of lens
power is counterbalanced by an actively regulated rate of axial
length growth by retinal defocus. But the growing eye could also
have a slower feedback mechanism that regulates lens power loss
in relation to axial elongation, to protect from environmentally
induced higher rates of axial growth. In this sense, the chick model
in which axial myopia is developed by growing under low ambient
illumination during three months is interesting for studying lens
power loss in vivo (Cohen et al., 2011, 2014).
19. Conclusions and future directions
A decreased rate of lens growth after birth, accompanied by
compaction of the nuclear lens fibers in the first decade of life is
probably responsible for lens thinning after birth and during school
years up to age 10e12. Lens thinning is accompanied by flattening of
lens curvatures because of changes in overall lens shape. These
changes involve axial thinning and equatorial growth from birth to
puberty. The lens thinning per se, all other things the same, would
increase the power of a homogeneous lens (optically speaking), but
flatter curvatures due to changing shape produce decreasing lens
power while the lens thins. Besides, the changing internal structure
may be responsible for more than half of lens power loss during
childhood. Changes in the gradient index profile probably make the
lens lose power during this period. Myopic subjects have lower lens
power than their emmetropic peers, with thinner lenses, possibly
because the gradient structure has become less effective at a slower
103
rate of growth. Thus, myopic subjects may be less prone to lose lens
power with ageing, maintaining stable refractions during adult years.
The lens continues to lose power after ages 20e30 in many
emmetropic subjects, explaining the development of hyperopic
shifts with ageing. These hyperopic shifts may be also produced by
an age related change in the gradient refractive index inside the
lens, the only possible explanation after Nicholas Brown described
increasing lens curvatures with age (the Lens Paradox). This change
of the gradient profile seems to be a consequence of decreasing lens
growth with ageing. As the lens grows slower, the systematic
compaction of the deeper layers possibly changes the profile of the
gradient structure, because the later relies on growth of new fibers
and can only be maintained unaltered if the rate of growth were
constant. The development of a refractive index plateau in the
center of the lens further reduces its internal power. After age 70,
the lens gains power in many subjects that have nuclear cataracts,
producing myopic shifts in refraction. This last change is probably
due to increased index in the center of the cataractous lens due to
further compaction and water loss of the crystallin content.
Future prospective population based studies of cycloplegic
refractive error, including keratometry and biometry, could calculate lens power. Then, the question of whether the eye shrinks with
ageing or the lens loses power during age related hyperopic shifts
could be resolved. Besides, the loss of lens power with age could be
studied prospectively in adults across refractive error groups, such
that differences in lens power loss could be studied further as has
been done in school children.
Possible environmental influences on lens growth need replication of experimental studies. The profile of the gradient index
could be indirectly studied prospectively in vivo with new approaches such as Brillouin confocal microscopy, which has shown
that the profile of the elastic modulus changes with age in rat and
human lenses (Scarcelli et al., 2011; Scarcelli and Yun, 2012; Besner
et al., 2013). The profile of the elastic modulus resembles the profile
of the gradient refractive index. This new non-destructive in vivo
approach could be useful to confirm suggested differences in the
gradient index profile across refractive groups. Besides, changes in
the gradient profile could be studied prospectively with this last
method, which looks promising not only for the study of hyperopic
shifts with ageing, but also for the changes in the internal structure
of the lens during accommodation.
Acknowledgments
This review was developed during long lasting discussions with
Prof. Ian G. Morgan (Australia), to whom I feel grateful. I wish to
thank Prof. Akbar Fotouhi (Iran) for the data in Figure 1 of Tehran
Eye Study and for the data in Table 5. I also thank Prof. Michiel
Dubbelman (Netherlands) for his comments on the manuscript. I
also wish to thank Prof. Bob Augusteyn (Australia) for his permission to reproduce Figures 6A & B, and for the friendly discussion
about lens growth in his cited papers. Prof. Jake Sivak (Canada) has
been very kind in sending and discussing his interesting papers,
and for letting me reproduce Figure 12. Prof. Jos Rozema (Belgium)
has helped me with Bennett's formula and Gullstrand's equation.
Profs. Peter Sands and Bill Jagger (Australia) have been very kind in
letting me reproduce their fish lens Figure 2, and Prof. Jost Jonas
(Germany) in letting me reproduce Figures 10 & 11. Finally, I wish to
thank Vicente A. La Vitola (Argentina) and Lautaro Gomez Alvarez
(Argentina) for the AutoCad figures.
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