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Crystalline lens and refractive development
Accepted Manuscript Crystalline lens and refractive development Rafael Iribarren, M.D PII:
S1350-9462(15)00008-7
DOI:
10.1016/j.preteyeres.2015.02.002
Reference:
JPRR 583
To appear in:
Progress in Retinal and Eye Research
Received Date: 1 November 2014 Revised Date:
30 January 2015
Accepted Date: 2 February 2015
Please cite this article as: Iribarren, R., Crystalline lens and refractive development, Progress in Retinal and Eye Research (2015), doi: 10.1016/j.preteyeres.2015.02.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Crystalline lens and refractive development.
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Rafael Iribarren
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Department of Ophthalmology, San Luis Medical Center, Buenos Aires, Argentina.
6 7 8 RUNNING TITLE: The lens in human refraction.
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WORDS: 15.806.
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FIGURES: 14; TABLES: 8; REFERENCES: 171.
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I declare no competing interests regarding the subject matter of this paper.
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CORRESPONDING AUTHOR:
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Rafael Iribarren, M.D., Department of Ophthalmology, Centro Medico San Luis, San
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Martin de Tours 2980, CABA 1428, Argentina;
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Tel.: 54-11-4393-1844; Fax: 54-11-4393-1844; Email: [email protected]
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Abstract Individual refractive errors usually change along lifespan. Most children are hyperopic in early life. This hyperopia is usually lost during growth years, leading to
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emmetropia in adults, but myopia also develops in children during school years or during
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early adult life. Those subjects who remain emmetropic are prone to have hyperopic shifts
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in middle life. And even later, at older ages, myopic shifts are developed with nuclear
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cataract.
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The eye grows from 15 mm in premature newborns to approximately 24 mm in early
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adult years, but, in most cases, refractions are maintained stable in a clustered distribution.
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This growth in axial length would represent a refractive change of more than 40 diopters,
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which is compensated by changes in corneal and lens powers. The process which maintains
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the balance between the ocular components of refraction during growth is still under study.
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As the lens power cannot be measured in vivo, but can only be calculated based on the
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other ocular components, there have not been many studies of lens power in humans. Yet,
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recent studies have confirmed that the lens loses power during growth in children, and that
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hyperopic and myopic shifts in adulthood may be also produced by changes in the lens.
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These studies in children and adults give a picture of the changing power of the lens along
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lifespan. Other recent studies about the growth of the lens and the complexity of its internal
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structure give clues about how these changes in lens power are produced along life.
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Key Words: lens power, refractive development, gradient refractive index.
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Contents.
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1. Introduction.
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2. The ocular biometric components.
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3. Calculation of crystalline lens power.
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4. Studies in preterm and full term infants.
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5. Nicholas Brown and the lens paradox.
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6. The lens during early growth in chickens.
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7. The shape and the power of the lens during childhood.
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8. The anterior segment growth.
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9. Change in lens shape during childhood.
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10. The anterior segment in premature children.
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11. The lens power in school years.
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12. Theories for lens thinning during childhood.
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13. Change in ocular components at myopia onset.
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14. The lens power loss during university study years.
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15. The lens in adulthood.
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16. Longer eyes of taller subjects have lower powered lenses.
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17. How can the lens change its power?
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18. Is the rate of lens power loss an actively regulated process?
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19. Conclusions and future directions.
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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
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distribution of refractions, and then move towards mild hyperopia with a narrower,
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leptokurtic distribution of refractions over the first year or two after birth. After this early
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stage, some children then progress in a myopic direction through an increased rate of axial
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elongation which is, at least in part, controlled by environmental exposures (Wallman &
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Winawer, 2004). This developmental phase may continue into the third decade after birth,
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when myopia prevalence reaches its maximum. During school years, many hyperopic
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children come to be emmetropic. After this, there is a slow shift in the hyperopic direction
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which may continue over several decades. This hyperopic shift with ageing can be disrupted
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by the formation of cataract which may lead to quite rapid and pronounced myopic shifts.
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Two early clinical cross-sectional studies which involved cycloplegia with atropine,
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characterized this change in refraction with age from birth to senescence (Brown, 1938;
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Slapater, 1950).
This pattern of change appears to be very general but has never been fully characterized
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with longitudinal data, because the study would inevitably last longer than the working life
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of most chief investigators and clinicians (except, perhaps, for the case of the 1958 British
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Cohort; Rahi et al., 2011). Another limitation of the existing literature is that much of the
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evidence is based on clinical samples, and has generally been measured without cycloplegia
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(except for the two early clinical studies mentioned above), even though it is generally
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recognized that the gold standard for measurement of refractive status requires cycloplegia,
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at least in children. This requirement may continue into adult life, since accommodation is
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powerful well until the ages of 40-50. As a result, some overestimation of myopia and
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major underestimation of hyperopia can occur (Fotouhi et al., 2012; Krantz et al., 2010).
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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
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cross-sectional study of refraction using cycloplegia over a wide age range, from 5 to over
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75 years of age. Three of the major developmental phases can be clearly seen. It should also
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be noted that while these data are cross-sectional, strong evidence of longitudinal change
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has been obtained for each of these phases (Fotedar et al., 2008; Gudmundsdottir et al.,
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2005; Wu et al., 2005; Lee et al., 2002; Saunders, 1986; Jones L.A. et al., 2005; Mutti et al.,
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2005).
Figure 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
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hyperopia at ±1 diopter (spherical equivalent) was chosen because most subjects with that
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amount of refractive error wear glasses on a permanent basis; a cut-off point of ±0.50
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diopters would make the prevalence of refractive error appear much higher in comparison
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with this more conservative cut-off point. Myopia is rare at age 5 and increases steadily up
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to age 25 when it reaches its maximum prevalence of 18% (in this study under this cut-off
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point). Then myopia prevalence remains stable along adulthood up to age 70, when it
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increases again. In the meantime hyperopia is very frequent (50%) at age 5 and decreases
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steadily reaching a minimum (10%) at age 25, the same age when myopia reaches its
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maximum prevalence (possibly the age at which axial elongation stops). From then on the
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prevalence of hyperopia increases slowly during adult life, reaching a value of 50% at age
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70, and from that age it decreases abruptly, by the same time as myopia prevalence
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increases.
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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
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from one category to the other. This is seen many times in the clinic. Hyperopic school
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children become emmetropic during adolescence. Emmetropic children develop myopia
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during school and university years. Emmetropic young adults develop hyperopia during
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their 40-50’s and cataract patients in their 70’s lose their hyperopia or develop myopia.
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(Duke-Elder & Abrams, 1970a; Saunders, 1984).
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2. The ocular biometric components.
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From a clinical perspective, refractive status is the key parameter, because clinical correction of refractive error, whether with glasses, contact lenses, refractive surgery, or
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intraocular lenses, is the key to ensuring good visual acuity. However, from a biological
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perspective, the ocular components of refraction, specifically corneal and lens power, as
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well as anterior chamber depth, lens thickness and vitreous chamber depth are optically
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more important, since it is the balance between these components which determines
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refractive status. For most of this period, refractive status appears to be a passive player, but
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early in development, refractive status does appear to act as a regulatory factor controlling
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the rate of axial elongation in particular. For example, infantile high hyperopic eyes tend to
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grow faster, such that this refractive error is compensated to some extent during the first
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years of life (Saunders et al., 1995; Mutti et al., 2005).
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Since the first classical studies (Tron, 1940; Stenstrom, 1948; Sorsby et al., 1957;
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Sorsby et al., 1961; van Alphen, 1961; Sorsby & Leary, 1969; Sorsby, 1971), many studies
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have examined the relationship between these biometric components and the refractive
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status. All studies showed that the major biometric correlate/determinant of refractive status
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was axial length, and that increased axial length was the major cause of myopia. Where the
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issue has been examined, the ratio of the axial length to the corneal radius of curvature was
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found to correlate even more strongly with refractive status than with the axial length itself.
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This is not hard to understand in principle, because while it is often stated that myopic eyes
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are longer (and it is known that in the emmetropic range longer eyes have flatter corneas,
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from Sorsby et al., 1957), strictly speaking, myopia results from an axial length that is
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longer than the image plane for distant objects, which is set by the optical power of the
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cornea and the lens. The axial length / corneal radius ratio correlates more strongly with
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refractive status because it partially adjusts for corneal power (Grosvenor & Scott, 1994).
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The changes in refractive error prevalence seen in Figure 1 should be associated
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with changes in the mentioned ocular components of refraction (mainly: corneal power,
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crystalline lens power and axial length). The cornea has been shown to develop small
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changes with ageing, mainly an against-the-rule change in astigmatism (Liu et al., 2001;
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Gudmundsdottir et al., 2005), but maintains constant power for most subjects along life
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(except for the uncommon progressive keratoconus cases). So the lens power and the axial
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length should be responsible for the observed changes. Mainly we can say that growth in
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axial length up to age 25-30 may be responsible for the development of myopia and for the
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decreasing prevalence of hyperopia. From that age on, the changes in prevalence of
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refractive error are surely driven by changes in the power of the lens (Iribarren et al., 2012b)
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3. Calculation of crystalline lens power. The crystalline lens power cannot be simply measured with a lensmeter since it is
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inside the eye. The same accounts for corneal power: usually only its anterior radius is
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measured, for example by a keratometer. The contribution of the posterior corneal power is
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assumed by an ideal index, which is calculated to obtain the power of the whole cornea only
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with the measured anterior radius and that ideal index (Olsen, 1986). Recently, using
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Scheimflug imaging it has been possible to measure the power of the whole cornea with the
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anterior and posterior radii, showing that the ideal index should be even lower than that
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calculated by Olsen (Dubbelman et al., 2005; Saad et al., 2013). Similarly, calculation of
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the power of the lens inside the eye is not straightforward: its power must be obtained from
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the other ocular components. Stenstrom’s formula based on refraction, keratometry, anterior
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chamber depth and axial length calculated lens power as if it were a thin lens placed at its
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anterior vertex. Later, intraocular lens power formulas were developed, but these also
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calculate the lens as if it were a thin lens placed at an estimated postoperative anterior
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chamber depth (effective lens position) (Olsen et al., 2007; Gordon & Donzis, 1985). By
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the end of the 80’s, Bennett and Rabbetts presented an in vivo crystalline lens power
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formula that, as Stenstrom’s, calculated lens power based on distance refraction, corneal
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power, anterior chamber depth and axial length (Bennett & Rabbetts, 1989). This formula,
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of which certain constants were recently revised (Rozema et al., 2011), can be used for
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calculating mean values of crystalline lens power in case of studies with biometry
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performed with the IOLMaster. When refraction, keratometry and A-Scan biometry or
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LENSTAR are available, then another Bennett’s formula including lens thickness can be
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used. (Bennett, 1988; Dunne et al., 1989; Rozema et al., 2011).
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Phakometric imaging of the crystalline lens in vivo has some problems (Mutti et al.,
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1992; Dubbelman & Van der Heijde, 2001; Rosales & Marcos, 2006). The Purkinje or
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Scheimpflug images of the anterior lens curvature are magnified and distorted because they
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are seen through the optics of the cornea. The posterior lens surface is distorted by both the
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optics of the cornea and the lens structure itself. The lens itself has a complex gradient of
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refractive index which makes the problem even more challenging. This gradient of
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refractive index is produced because the lens grows from the surface, sinking fibers in its
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deeper layers, and the newly laid fibers have greater water content and lower refractive
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index than the older ones. Thus a gradient of refractive index is produced, increasing from
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the cortex to the center of the lens. This complex structure is generally solved by modeling
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the lens as if it were a uniform thick lens, with an ―equivalent‖ or ―effective‖ index of
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refraction equal to that necessary to explain the whole power of the lens. This equivalent
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refractive index is greater than the peak index at the center of the lens, because the gradient
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refractive index, regardless of its profile, makes the rays bend incrementally as they go
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through the changing multilayer structure of the lens, thus giving what is called an internal
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power of the lens.
This gradient structure gives the lens another important property. Spherical lenses
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with uniform index have positive spherical aberration, produced as rays in the peripheral
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(equatorial) sections of the uniform lens bend more than those that go through the central
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part of the lens. But gradient spherical lenses can elegantly compensate this aberration
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because rays passing through the periphery are not bent as much because they pass through
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progressively lower refractive index sections. This was clearly shown bending laser rays
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through lenses in vitro for fish and mammals by Sivak in 1983 (Sivak & Kreuzer, 1983;
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Sivak, 1985) and later by Jagger & Sands (1996). Figure 2 shows that the spherical fish lens
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has no spherical aberration and that the laser rays are bent while passing through the lens
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structure because of the gradual index change.
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The phakometric measurements of the lens posterior curvature have to be iteratively
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corrected calculating an ideal equivalent index, in a recursive manner such that it agrees
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with the measured refraction. With these recalculated lens curvatures, its thickness and the
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calculated equivalent index, the lens power can be also calculated using Gullstrand’s well
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known thick lens formula to find the total lens power. This iterative method allows the
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accurate calculation of the lens curvatures and the equivalent refractive index. So, this
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phakometric method can be used when the objective is to calculate the equivalent index and
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the lens curvatures, as has been done in monkeys and humans (Jones LA et al., 2005; Mutti
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et al., 2005; Dubbelman & Van der Heijde, 2001; Qiao-Grider et al., 2007).
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When only biometric and refractive data are available, Bennett’s formula can be
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used to calculate the lens power alone. Two recent papers have shown that there is good
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agreement between phakometry and Bennett’s methods when the values of mean lens
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power are calculated in a given sample (Dunne et al., 1989; Rozema et al., 2011). In this
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review, we have calculated lens power with Bennett’s method when data available in the
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literature allowed this calculation and we have thus compared the data on lens power
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obtained in different biometric studies along the lifespan.
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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
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were homogeneous with the cortical index), and thus this surface power can be subtracted
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from the total lens power to find the gradient refractive index power contribution. In this
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way, the surface power was found to contribute to about half of total lens power (Borja et
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al., 2010). The rest was due to the internal or gradient power of the lens. The problem with
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this approach is that the cortex index has been measured in vitro and then calculated with
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magnetic resonance studies in vitro and in vivo, with different studies giving different
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results for this cortical index (Pierscionek & Chan, 1989; Moffat et al., 2002; Jones CE et
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al., 2005; Borja et al., 2010). So the calculation of the surface power is somewhat
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inaccurate, but taken prospectively or with successive measurements under different
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accommodative demands, this calculation can show differences in the contribution of the
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surface and internal powers of the lens both with age and accommodation (Borja et al.,
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2010; Maceo et al., 2011). Using these approaches we calculated the lens power for a number of published
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studies which included refraction and biometry, from preterm infants to adult years. We
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used 1.3315 as the ideal index for corneal power in all cases (Olsen, 1986), for consistency
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with our previous published data. These calculations give a picture of the change in lens
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power along life.
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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 retinopathy) from birth to 5 months of age,
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performing cycloplegic refractions. From the data in their published table (Cook et al.,
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2003), the crystalline lens power was calculated using Bennett’s formula (Bennett, 1985).
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Figure 3 shows how the lens power decreases steadily in premature infants from nearly 60
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diopters at birth to 45 diopters by 5 months. Mutti et al. (2005) prospectively studied full
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term infants at ages 3 and 9 months with cycloplegic refraction, biometry and phakometry,
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calculating the crystalline power, and they give decreasing lens power values of 41.01 D
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and 37.40 D for 3 and 9 months respectively (Figure 3). Figure 4 shows lens thickness in
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both studies (premature and full term). In premature children the lens becomes thicker
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during the first two months of life, and then begins to thin (Cook et al., 2003). In full term
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infants the lens thins from 3 to 9 months (Mutti et al. 2005). Besides, the lens has been
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reported to thin in schoolchildren from age 6 to 10 years (Larsen, 1971; Jones LA et al.,
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2005; Shih et al., 2009; Wong et al., 2010)
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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
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uniform index of refraction. While the lens thins and loses power, the Mutti et al. study of
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full term infants reported that the calculated equivalent refractive index of those lenses
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increased from 1.4526 to 1.4591 from 3 to 9 months (Mutti et al., 2005). Using similar
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methods, Jones et al. (Jones LA et al., 2005) showed that, on the contrary, the lens
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equivalent index decreased in school years (from age 6 to 14) while the lens consistently
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thins and loses power. They also showed prospectively that the curvatures of the lens flatten
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at these school ages, and they explained this loss of power by a scleral expansion theory in
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which the lens thins by the forces of zonular traction induced by eye growth in the anterior
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segment. This theory explained that as the lens thins, its curvatures flatten, and in
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consequence, the lens power decreases (Zadnik et al., 1995; Mutti et al., 1998). These
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authors also proposed, alternatively, that changing lens shape could modify the internal
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gradient index structure, but did not explore further this idea.
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However, what remained unclear was the decrease in the equivalent refractive index
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at a time when the actual peak index in the center of the lens is increasing (Augusteyn et al.,
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2008). Besides, that scleral expansion based theory cannot explain why the lens of
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premature children becomes thicker in the first months of life, while it is steadily losing
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power. Furthermore, why is the equivalent refractive index increasing in full term babies
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while the lens loses power? Interestingly, a longitudinal study of the change in the ocular
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components during growth in monkeys has also shown that the lens increases in thickness
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and equivalent index during the first months of life, then changing these growth patterns in
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the opposite direction with further growth, but consistently flattening curvatures and losing
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power during both periods (Qiao-Grider et al., 2007).
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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
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(Augusteyn, 2008, Review; Pierscionek & Regini, 2012, Review). As said, this is produced
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by the apposition of new cortical fibers with greater water content than those that are
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deeper, older, mature and full of protein content, or even deeper with less water, as they age
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and become compacted in the center of the lens. This gradient of index increases the power
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of the lens because rays going through the gradient are curved incrementally at each step.
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Thus the total power of the lens is composed of the surface power given by its curvatures,
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and an internal power given by its gradient index of refraction.
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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,
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developing a central plateau with ageing. As the profile of the peripheral gradient becomes
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more abrupt and the plateau develops, the gradient structure loses effective power. An in
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vivo magnetic imaging study has shown that the profile of the peripheral gradient becomes
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more abrupt with older age and smoother during accommodation in young subjects
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(Kasthurirangan et al., 2008). These changes in the gradient had been shown previously in
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in vitro studies and were related to the maintenance of emmetropia (Brown et al., 1999) or
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even before to the changes in lens power leading to presbyopia (Pierscionek, 1990).
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Changes in the gradient index have also been proposed as a cause of the hyperopic shifts
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leading to the development of hyperopic refractive errors in ageing adults (Brown et al.,
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1999; Moffat et al., 2002; Glasser & Campbell, 1988; Hashemi et al., 2010).
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One possible explanation for the loss of lens power during infant life is that the
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profile of the peripheral refractive index gradient is becoming more abrupt with age. As the
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peak index is becoming greater by fiber maturation and compaction, then the climbing
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index from the surface to the higher peak index in the center should have a more abrupt
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profile (with less power) even more so if the lens axial thickness is decreasing, as a thinner
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lens should also have a more abrupt profile to reach the same peak. Besides, the increase in
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peak index could drive the equivalent index up, as has been found in infants (Mutti et al.,
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2005), but the net change could be decreasing lens power produced both by flattening of
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curvatures and changing gradient profile.
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5. Nicholas Brown and the lens paradox.
The idea that changes in the internal power of the lens could have importance in
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refractive error began to gain acceptance in the 70’s when Nicholas Brown described the
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―lens paradox‖ consisting of an increment in lens thickness with a steepening of the surface
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and internal curvatures of the ageing lens that would produce systematic myopia at adult
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ages in which hyperopia and presbyopia are the norm (Brown, 1974; Koretz & Handelman,
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1988; Brown et al., 1999). He introduced Scheimpflug photography in Ophthalmology to
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study the lens, and soon discovered that the anterior lens surface was becoming steeper with
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ageing, just the opposite to current thinking of those days (Brown, 1974). He also studied
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eyes under accommodative effort and saw that older eyes at rest had steeper anterior lens
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surfaces compared to younger accommodated eyes (Brown, 1973). Then, Koretz &
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Handelman, studying his photographs with mathematical approaches, showed that the
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steepening of the lens curvatures with ageing should be accompanied by changes inside the
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lens. They suggested that the lens equivalent refractive index should be higher in younger
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subjects in order that the eye could be maintained in focus according to differences in lens
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shape (Koretz & Handelman, 1988).
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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
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(Dubbelman & Van der Heijde, 2001). A lens with decreasing equivalent index would
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maintain a constant power while its curvatures become steeper if both changes were
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matched in ageing subjects (Brown et al., 1999), but in subjects who develop hyperopia, the
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net change could be loss of power if the loss of gradient power is greater than the increase
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in curvatures (Brown et al., 1999; Hashemi et al., 2010; Iribarren et al., 2012b).
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Experimental studies on refractive development in animal models can provide information
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on the underlying mechanisms, as we will see in the next section.
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6. The lens during early growth in chickens.
Interestingly, the lens also loses power in growing chicken eyes. A recent re-analysis
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of the chick schematic eye model that was originally developed by Schaeffel & Howland in
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1988 showed that Bennett’s equation could be used for calculation of lens power in chick
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eyes (Iribarren et al., 2014a). As the original data included refraction, biometry and lens
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radii measurements, the lens power and equivalent index could be calculated for growing
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chicken eyes from age 10 to 90 days. While axial length increased in chicken eyes from 8 to
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14 mm in this period, the cornea and the lens lost power accordingly, such that refractions
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were maintained in the low hyperopic range. The lens thickness increased in chicken eyes
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during this period, and as the lens possibly grew in all directions (axially and equatorially),
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the curvatures flattened (Figure 5). In the meantime, the equivalent index decreased slowly
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with age. Thus, with all these changes, the lens lost 30 diopters of power in these 80 days of
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eye growth in chickens (Iribarren et al., 2014a)
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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
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the total lens power is calculated, based on Gullstrand’s thick lens equation, from its radii
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of curvature, thickness and equivalent refractive index, while for the surface power the
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cortical refractive index is used. The cortex index is lower than the equivalent index, as the
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cortex consists of new fibers with higher water content and a lower refractive index. The
7
cortical refractive index has been measured in vitro in chicken lenses by Sivak and
8
Mandelman (1982), giving a value of 1.374. Following Borja et al. (2008), we then derived
9
the gradient power as the total Gullstrand thick lens power (calculated with the equivalent
10
refractive index found for chick schematic eyes equal to 1.4502 for day 15 and 1.4409 for
11
day 90) minus the surface power (calculated using 1.374 as the cortical refractive index).
12
Table 1 shows the change in total lens power, surface lens power and gradient lens
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power in the period from 15 to 80 days. It can be seen that both surface and internal power
14
change with age in chicken eyes. As said, the total lens power decreases by some 30
15
diopters, of which 20 diopters are accounted for by changes in the internal power, so the
16
change in gradient power accounts for about 70% of the total change in power. Figure 5
17
shows the front and back curvatures of the 15 day old chick lens (inner lines) inside the 80
18
day old lens (outer lines). The increase in axial thickness and the flattening of the
19
curvatures can be seen as the lens expands in all directions by growth of new layers of
20
fibers. The equator was not drawn since lens surfaces are not spherical (and we only had
21
front and back surface lens radii for the schematic drawings).
22 23
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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.
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1 2
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 LA et al., 2005; Mutti et al., 2005; Shih et al., 2009;
4
Wong et al., 2010) the literature shows less data on lens equatorial diameter growth as the
5
lens equator is not visible in vivo by slit lamp observation because it is behind the iris, even
6
after pupil dilation. Augusteyn (2010) has recently reviewed the data of lens equatorial
7
growth. Duke-Elder (1961) gave values for in vitro measurements of 6.5mm for newborns,
8
7.5mm at the end of the first year, and 8.2 mm by 2-3 years. Similar in vitro values were
9
presented by Augusteyn et al. at the ARVO meeting (Augusteyn et al., 2012) showing that
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the main growth of lens equatorial diameter is achieved during the first two years of life
11
(see also Brown & Bron, 1996). Adult values are around 9 mm, increasing slightly and very
12
slowly with ageing (Augusteyn, 2010, Review). These in vitro data have the problem that
13
the lens is fully accommodated when free of zonular tension, especially in children’s lenses.
14
This would make the equatorial diameter in a 20-40 year lens about 0.6 mm shorter
15
according to in vivo data obtained by Strenk with magnetic resonance images (Strenk et al.,
16
1999, calculated from their data with lenses younger than 40). This difference between in
17
vivo and in vitro measurements could be more pronounced in infant lenses, which have
18
more spherical shape, capable of many diopters of accommodation. So these in vitro
19
measurements in infant lenses are possibly biased as if they were smaller. It is very possible
20
that the lens equatorial diameter increases in babies while the anterior segment is growing
21
steadily during the first months of life. A recent magnetic resonance image study (Ishii et
22
al., 2013) involving 26 children aged 1month to 6 years, showed that the lens equatorial
23
diameter in children under general anesthesia (tonic resting accommodation) increased
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1
steadily after birth reaching a value of 8 mm in by age 3. Thus, 90% of lens equatorial
2
diameter growth is achieved in the first 2-3 years of life.
3
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
5
growing as much in equatorial diameter as in axial thickness, as may be the case in the first
6
months of life in premature infants, then the decrease in curvature of the anterior surface
7
would be much less (the lens would maintain a constant shape while it thickens in the first
8
two months). But it is still steadily losing power as we have shown (Figure 3). This also
9
happens in growing chicken eyes, where the lens grows both in axial and equatorial
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10
diameter, flattens curvatures, and also loses power (Iribarren et al., 2014a, Figure 5). Then,
11
ellipsoidal lenses with flat front surfaces can flatten anterior curvature as they thin or as
12
they grow, depending on the change in lens shape.
The changes in the lens are rather complex, especially in infants who have very
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powerful lenses, with a more rounded shape, and possibly, with a newly developed very
15
smooth climbing gradient profile. The actual index of refraction is given by the
16
concentration of the crystalline proteins within the fibers’ cytoplasm, and this concentration
17
is a function of the amount of fiber differentiation and compaction. Fiber differentiation is
18
rapidly established in such a manner that even embryonic lenses have a gradient in a few
19
weeks (Peetermans et al., 1987). On the other hand, compaction, demonstrated originally by
20
Brown in adult lenses with cortical cataracts (Brown, 1976), is a process that takes years to
21
develop. It is well known that after birth there are changes in the synthesis of the different
22
crystalline proteins that compose the lens, such that the fetal nucleus (that part of the lens
23
formed prenatally) has no content of gamma crystallin (Augusteyn, 2007). It is possible that
24
the different types of crystallines have different time constants for losing water and
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compacting (Augusteyn et al., 2008). It is also known that the rate of synthesis of new
2
layers decreases drastically after birth (Augusteyn, 2007). Proof of this is the fact that the
3
lens develops approximately 4.0 mm axial thickness during prenatal life in only 8 months,
4
and then only 1.5 mm more from birth to senescence (Brown & Bron, 1996).
5
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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
7
nucleus during the following years after birth, probably beginning from the older fibers in
8
the center. But one has to consider that those fibers were laid in a few months during
9
gestation and they may be compacting at a relatively uniform rate during the first years after
10
birth. Evidence of this compaction is given in the Mutti et al. (2005) study in babies which
11
shows an increase in equivalent refractive index from 3 to 9 months of age. That would
12
increase the power of the lens, but as the lens at this time is losing much power, we propose
13
that both surface and internal powers are changing. Mutti et al. (2005) have demonstrated
14
that the anterior lens curvature flattens during development in babies. We propose that the
15
gradient index power is decreasing by compaction of the nucleus with a more abrupt
16
climbing gradient profile (before the adult index plateau is developed). Furthermore,
17
compaction inside the nucleus, with a slow rate of addition of new fibers in the newly
18
developed cortex after birth could also explain the lens thinning in the first 10 years of life
19
(Brown & Bron, 1996).
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The 6 year old lens studied in vitro in the Augusteyn et al. (2008) paper (Figure 6A
21
& B) has not yet achieved the peak index found in adult years, so it is probable that
22
compaction of the nuclear fibers is still not finished by age 6. As the cortex grows at a very
23
slow rate compared to the prenatal growth of the nucleus, one would expect lens thinning
24
until the rate of compaction in the nucleus equals the rate of growth in the newly developed
16
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cortex. The idea that lens cortical growth was balanced by nuclear compaction during
2
childhood was originally proposed by Nicholas Brown, who had studied prospectively the
3
lens in a few subjects with congenital lamellar cataracts, finding that children had
4
compaction in the nucleus, and that this compaction declined its rate with ageing (Brown et
5
al., 1988). He suggested that lens growth was due to a balance between epithelial growth
6
and fiber compaction, and that the nucleus became compacted up to age 30, and afterwards,
7
only the deep cortex became compacted for the rest of life. This was also discussed by other
8
members of his team (Cook et al., 1994) and during the presentation of Scheimpflug data in
9
normal growing children by Forbes et al. (1992).
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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
12
as can be seen in the Augusteyn in vitro lenses (Figures 6A & B, Augusteyn et al., 2008),
13
then the lens should lose internal power, explaining the loss of power that has been shown
14
in the different studies. In fact, the gradient index in Figures 6A & B is smoother in the
15
child lens compared to the abrupt climbing profile with a plateau of index developed in the
16
center of adult lenses. It is noted that the plateau section has no gradient (less power). The
17
schematic drawing of figure 6 C shows how a thinner lens has a more abrupt climbing
18
gradient index profile that reaches a higher peak index, as may be happening while the lens
19
thins and compacts from birth to school age, losing internal power (before the central
20
plateau is developed).
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8. Anterior segment growth.
23 24
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
17
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diameter (Ronneburger et al., 2006; Lagrèze & Zobor, 2007) and by the anterior segment
2
distance from the corneal apex to the posterior pole of the lens (anterior segment length)
3
(Larsen, 1971; Dubbelman et al., 2001; Koretz et al., 2004). It is well known that white to
4
white diameter reaches adult values during the first year of life and that the corneal power
5
also reaches adult values by age 1-2 (Gordon & Donzis, 1985; Ronneburger et al., 2006;
6
Inagaki, 1986). It looks like the cornea does not change much in diameter and power after
7
year 2.
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The anterior segment length up to the lens posterior pole has been calculated from
9
the data of Cook et al. (2003) and Mutti et al. (2005) (Figure 7) (adding anterior chamber
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depth + lens thickness). In full term and premature babies the anterior chamber grows
11
during the first months, while the lens thickness fluctuates, increasing in prematures during
12
months 1-3 and decreasing in full term babies from months 3-9. Yet the anterior segment
13
length increases steadily as shown in Figure 7, almost reaching adult values of 7-7.5 mm by
14
the end of year 1 (Koretz et al., 2004; Dubbelman et al., 2001; Larsen, 1971). In the follow
15
up of emmetropic children, Zadniks’s data (Zadnik et al., 2004) show little change in
16
anterior segment length at the time of lens thinning between ages 6 to 10 (Table 2), showing
17
that the anterior chamber deepening at these ages is a consequence of lens thinning and not
18
merely growth of the anterior segment. This was originally shown by Larsen (1971) who
19
stated that the anterior segment length growth ―stagnated by age 2-3 years‖.
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At ARVO 2013, Bailey et al. presented cross sectional data obtained with Visante
21
images showing that the ―anterior segment chord‖ located behind the iris, from sclera to
22
sclera, did not change with age in schoolchildren (Bailey et al., 2013). So we think that the
23
anterior segment growth is completed in the first year or two of life with no further change
24
in dimensions after this age, but with internal and external changes in the lens. It is also
18
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1
difficult to explain the scleral expansion theory (Zadnik et al., 1995; Mutti et al., 1998) if
2
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
4
in Figure 8, using the mean anterior and posterior curvatures and the mean lens thickness
5
for the lens at rest given in Mutti’s and Zadnik’s papers (Mutti et al., 1998, 2005). These
6
curvature radii were drawn spherical although it is known that the real lens has aspheric
7
curvatures and thus should have even greater equatorial diameter, so these data may be
8
negatively biased. The rounded edges at the equator were drawn following the
9
shadowgraphs of in vitro lenses (Borja et al., 2010). From these drawings the lens
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equatorial diameter was estimated to be 7.44 mm for the three month old babies’ lens, 7.99
11
mm for the 9 month old babies and 8.82 mm for the 14 year old lens in schoolchildren.
12
With the same data (Mutti et al., 2005) and the formula given by Rozema et al. (2012), the
13
lens diameter is estimated to be 7.38 mm in 9 month babies and 7.77 mm in 9 month
14
babies. These measurements may be biased by the method used, but they show that the lens
15
at rest (under cycloplegia) reaches equatorial diameter values similar to the 9 mm adult lens
16
very early in life. The same holds for the other described parameters of the anterior segment
17
of the eye.
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9. Change in lens shape during childhood. How can the lens change from a rounded ellipsoidal shape in babies to a flatter one
21
in adolescence? This change can be seen in Figure 9, comparing a 3 month lens with a 14
22
year old lens (based on Mutti’s and Zadnik’s published data of curvature and thickness,
23
Mutti et al., 1998, 2005; Zadnik et al., 1995). The internal structure and the growth of the
24
lens can give the clues for this change. As said, the nucleus of children has been shown to
19
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be compacted during school years according to Brown’s Scheimpflug images during the
2
follow up of children with lamellar cataracts (Brown et al., 1988) and by similar cross-
3
sectional measurement of nuclear thickness in a sample of 50 children aged 3 to 20 years
4
(Forbes, 1992).
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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
7
while their protein content is losing water. As the fibers in the embryonic and fetal nucleus
8
are oriented following the antero-posterior axis (Al-Ghoul et al., 2001), their folding and
9
compaction could possibly decrease the antero-posterior axis more than the equatorial
10
diameter (Augusteyn, 2010 review). The cortical fibers are progressively oriented in a
11
circular manner. These differences could make the lens thinner on its axis, and then its
12
ellipsoidal shape would become flatter by the antero-posterior poles. Notice that the profile
13
of the 6 year old lens (grey dots in Figure 6 B) has achieved a plateau in the axial view at
14
this early age, but has no plateau in the equatorial view (Figure 6 A). As the plateau is
15
developed when fibers reach a uniform compaction, it seems that this compaction is
16
developed earlier in the antero-posterior axis, along with lens axial thinning. But the
17
equatorial growth does not seem to be accompanied by similar rates of compaction. The
18
compaction of the older central fibers could shorten the axis if fiber shortening is relatively
19
greater than the decrease in fiber diameter.
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The other way in which the lens becomes more elliptical depends on the fact that the
21
equatorial growth of the lens epithelium develops fibers that elongate from the equator to
22
the anterior and posterior poles up to the sutures, becoming thinner as they migrate
23
elongating centripetally searching for the sutures (Al-Ghoul et al., 2003). In other words,
20
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elongating fibers are thicker at the equator than at the antero-posterior poles. This fact can
2
also make the lens grow more in the equatorial diameter than in its antero-posterior axis.
3
During adult years, from ages 20-80, the lens grows in another manner (Augusteyn, 2010). An in vitro study had shown that the lens increased both axial thickness and
5
equatorial diameter at similar rates (0.49 mm and 0.55 mm respectively) in 40 years of adult
6
life (Rosen et al., 2006) maintaining a constant aspect ratio (Augusteyn, 2010). More recent
7
very accurate in vitro measurements have shown that the aspect ratio (thickness / diameter)
8
increases with age (Mohamed et al., 2012). So in this new study the axial thickness
9
increased with age more than the equatorial diameter (0.75 vs. 0.51 slope, respectively).
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10
This would make sense if the anterior lens curvature is steepening with age (as was
11
described by Nicholas Brown in 1974), because if the lens grew equally in all directions, the
12
anterior curvature would flatten as happens in growing chicken eyes (Figure 5). This slow rate of equatorial growth contrasts with the 0.50 mm in 6 months taken
14
from the difference in our calculated equatorial diameter between 3 and 9 month babies’
15
lenses (Figure 8). There is no doubt that the lens has a high rate of equatorial growth during
16
the first year of life, at the same time in which corneal diameter and anterior segment length
17
have high rates of growth.
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The process of metamorphosis in amphibians like toads and frogs is a good example
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of the change in shape of the lens during early growth. In general, fish have spherical
20
lenses, and terrestrial animals have ellipsoidal lenses. During the metamorphosis of the
21
anuran Pelobates Syriacus the lenses of the aquatic form change from a spherical shape to a
22
flattened lens in the juvenile terrestrial form (Sivak et al., 1983). The same happens in
23
tadpoles when they become terrestrial toads (Mathis et al., 1988). In 1985 Sivak et al.
24
presented data about the change in shape during metamorphosis of different species of
21
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amphibians and their histological studies showed that the changes in lens shape were
2
brought about by a rapid increase of the mitotic activity of equatorial epithelial cells at
3
critical periods during metamorphosis. If a similar process occurs in the human lens, it may
4
be simple to explain that the lens changes shape between birth and adolescence by
5
differential growth and compaction of its internal structure (Figure 9). In fact, the human
6
lens during embryonic life is spherical as the fish lens, and it becomes more and more
7
ellipsoidal by growth of the equatorial fibers during late fetal life (Cook et al., 2006). So it
8
seems probable that this pattern of lens growth is also followed during the first years of
9
infant life in humans.
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10. The anterior segment in premature children.
The growth of the anterior chamber in premature children is interesting. These small
13
eyes of premature infants have shallower anterior chambers, thicker lenses, smaller anterior
14
segment lengths, more steeply curved corneas and more powerful lenses at 3 months than
15
do full-term infants of the same age (Cook et al., 2003, and Figures 3, 4 and 7). Some of the
16
eyes of premature infants develop retinopathy as was seen, for example, in the study of the
17
ocular components of a series of 108 premature children who were studied at age 7-9 in
18
Taiwan (Chen et al., 2010). In all, 44% of these premature children had developed some
19
form of retinopathy, 25% received laser treatment because of advanced retinopathy and
20
47% of these 108 children had myopia at ages 7-9 years. We have calculated the lens power
21
for these schoolchildren in Table 3, where it can be seen that prematures have a
22
combination of thicker and more powerful lenses at rest when compared to same age
23
normal term emmetropic children (Chen et al., 2010; Jones et al., 2005). While these
24
findings might be due to laser induced growth abnormalities at the peripheral retina (Chen
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et al., 2010), these could also be explained by visual or light induced control of anterior
2
segment growth. These eyes at birth are smaller than those of full term infants by about
3
2mm, and have smaller anterior segments, so exposure to light could delay anterior segment
4
growth and leave eyes with somehow immature anterior segments, with steep corneas, and
5
thicker and more powerful lenses by age 2-3 when the anterior segment growth reaches a
6
plateau. Myopia of prematurity looks different from common school myopia, in which axial
7
length is longer than usual, and the lens is thinner with lower power (just the opposite), as
8
will be seen in the next section.
10
11. The lens power in school years.
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Three recent prospective studies have reported on the loss of lens power in
12
schoolchildren. These are the Orinda Study (and its extension, the CLEERE study) (Jones
13
LA et al., 2005; Twelker et al., 2009), the SCORM Study (Wong et al., 2010; Iribarren et
14
al., 2012a) and a study involving Chinese myopic twins in Guangzhou (Xiang et al., 2012).
15
The Orinda and CLEERE studies included phakometry, so the lens equivalent refractive
16
index could be estimated and, as said, was shown to decrease with age in schoolchildren.
17
The power of the lens also decreased in all refractive groups in a similar manner from ages
18
6 to 14 in this study. As we have also said, decreasing effective index accompanied by a
19
decrease in power in lenses that must be compacting their fibers (thus increasing refractive
20
index by increasing protein concentration) can only be explained by changes in the
21
refractive index gradient profile.
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22
Myopic children had lower lens power and hyperopes had higher lens power than
23
emmetropes at follow up in the mentioned Orinda study (Jones LA et al., 2005). The lens
24
power loss prospectively matched the axial growth (still present at these school years) in the
23
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children who remained emmetropic (Jones LA et al., 2005; Zadnik et al., 2004). From the
2
figures of the Orinda paper (Jones LA et al., 2005) we can see that emmetropic eyes grew
3
about 1 mm after age 6 in the 10 years of follow up (approximately +0.10mm per year rate),
4
and that the power of the lens fell from 26 to 23 diopters in the same period (–0.30 diopters
5
per year rate), compensating for axial growth. In children who became myopic, the axial
6
growth was greater than that of emmetropes, about 2 mm on average in the same period
7
(+0.20mm per year rate), and as the lens lost power from 25.5 to 22 diopters (–0.35 diopters
8
per year rate), the net change in mean refraction was –3 diopters of myopic shift after the
9
follow up in the myopic group. We can also see in this paper that the lens thinned in all
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refractive groups up to age 10 and then slowly began to thicken again. Hyperopic eyes had
11
thicker lenses and myopic eyes began with the same lens thickness as the emmetropes but
12
ended with lower lens thickness at the follow up. It is noted that 76.1% of myopic subjects
13
in this study had their onset during the follow up, so most of them began the study being
14
emmetropes (Jones LA et al., 2005).
15
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If myopic eyes have lower lens power than emmetropes, and myopes come from previous emmetropes, emmetropic eyes developing myopia must have lost greater amounts
17
of lens power at some time point. The SCORM study in a Singaporean sample of
18
schoolchildren had a high prevalence of myopic children (Wong et al., 2010). So the study
19
could show a difference between persistent myopes (those already myopic at baseline) and
20
newly developed myopes (those developing myopia during the follow up, as most Orinda
21
myopic subjects). In this last study, persistent myopic eyes had lower lens power (and they
22
also had thinner lenses) than emmetropes. And here, newly developed myopes showed a
23
greater rate of decrease in lens power and in lens thickness than emmetropes or persistent
24
myopes (Iribarren et al., 2012a). This study then showed increased lens power loss at the
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time when the rate of axial elongation was also increased during myopia onset. When
2
Sorsby found negative correlations between axial length and the power of refractive
3
surfaces (cornea and lens) he postulated that the retina was an organizer of the coordinated
4
growth of the ocular components (Sorsby et al., 1957).
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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
7
consistent finding of lower lens thickness in myopic eyes could be due to a lower rate of
8
growth of the lens epithelial layer, mediated by humoral factors from the retina. Fibroblast
9
growth factor (FGF) is present in the retina and the vitreous adjacent to the lens, and is the
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principal factor inducing lens epithelial growth (Lovicu & McAvoy, 2005). As the lens
11
grows by apposition of new fibers with low index, and as the older deeper fibers mature and
12
are compacted gaining refractive index, the gradient refractive index (responsible for about
13
half of the lens power) may be maintained with a constant shape of its profile. But if the
14
growth rate slowly decreases with time and the compaction rate is maintained constant, then
15
the smoothness in the climbing gradient profile would be gradually lost according to that
16
decreasing rate of epithelial growth, and thus the lens power at rest would decrease
17
accordingly. So we postulate that a relative decrease in the rate of lens growth ends up in
18
myopic eyes with thinner and less powerful lenses than those of emmetropic eyes.
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A careful inspection of the data in Figure 4A of CLEERE study (see Mutti et al.,
20
2012) shows how the rate of lens power loss declines in myopes after myopia onset when
21
compared to emmetropes, and it also shows that before onset, myopes show an increased
22
rate of lens power loss compared to emmetropes (when looking at the unadjusted data).
23
This is concordant with a greater rate of power loss calculated for Orinda myopic subjects
24
when compared to emmetropic subjects in the previous paragraphs (-0.35 vs. -0.30 diopters
25
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per year, respectively). This is similar to what was found in SCORM newly developed
2
myopes, which showed a greater rate of lens power loss in children who developed myopia
3
during the study when compared to those who remained emmetropic (-0.36 vs. –0.29
4
diopters per years, respectively, Iribarren et al., 2012a).
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Myopia may then develop when the rate of axial growth is so rapid that it outgrows
6
the possibility of the lens to compensate that axial growth by further power loss. The study
7
of lens power change before and after myopia onset in CLEERE Study (Mutti et al., 2012)
8
found that myopia onset was ―characterized by an abrupt loss of compensatory changes in
9
the crystalline lens‖. Although this last finding should be confirmed in future studies, it is
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interesting that axial growth can increase the rate of the eye’s axial elongation by
11
myopigenic retinal signals during school years without any end point. But, on the other
12
hand, the lens might increase the rate of power loss until the shape of the gradient refractive
13
index profile approaches a relatively maximal abrupt climbing profile. The equatorial
14
growth and axial compaction that produces the described changes in lens shape during
15
childhood (with lens thinning and curvature flattening) might also have a relative end point
16
because nuclear compaction may also have a limit, showing another possible limitation for
17
the compensation of myopia acquired at the time of an increased rate of axial elongation.
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Recent studies with lenses in vitro have shown that the power of the refractive index
19
gradient changes with age and with accommodation (Borja et al., 2010; Maceo et al., 2011).
20
These studies could accurately measure the power of the isolated lens in vitro (an
21
impossible measurement with the lens inside the eye), and have calculated the relative
22
contributions of the internal and surface powers. This was done by calculating the surface
23
power with the in vitro measured curvatures, and by attributing an index to the first layers
24
of the cortex under the capsule, thus showing what the power of an homogeneous lens
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would be (without the gradient) with the given surface curvatures and the cortical index.
2
Then, subtracting the surface power from the total power, the gradient contribution could be
3
calculated. Using the well known Gullstrand’s equation for calculation of the power of a
4
thick lens (Mutti et al., 1998), and assuming an index for the cortex of 1.3709 (Jones CE et
5
al., 2005; Borja et al., 2008; Borja et al., 2010) we calculated the relative contributions of
6
the surface and internal powers for the data of Mutti et al. (2005) and Mutti et al. (1998) in
7
babies and schoolchildren respectively (Table 4). These studies showed that the anterior and
8
posterior lens curvatures flattened with age in babies and children as the lens thinned, but
9
from the data in Table 4 we can see that this change in curvature accounts for only half of
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the power loss. The relative contribution of the internal power given by the possible change
11
in the gradient is responsible for the other half of the lens power loss in growing children.
12
Then, it is possible that changes in the refractive index gradient profile within the lens are
13
an important cause of lens power loss during school years. And this internal power loss
14
could be responsible for the differences in lens power described among refractive groups in
15
schoolchildren. There is no doubt that a thicker or thinner lens can have different surface
16
curvatures and differences in the internal gradient index profile (Figures 6C and 9).
19
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12. Theories for lens thinning during childhood.
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Sorsby (Sorsby et al., 1957) proposed a coordinated growth of the components of
20
refraction (mainly axial length with corneal and lens powers) to explain the tendency to
21
produce emmetropic eyes in which differences in axial length were compensated by corneal
22
and lens power. He clearly showed that in the emmetropic range, longer eyes had flatter
23
corneas and less powerful lenses (and vice versa) (Sorsby et al., 1957). Then, van Alphen
24
(van Alphen, 1961) proposed a model for eye growth that comprised passive and active
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factors including a stretch factor. These ideas were further discussed by Hofstetter (1969)
2
(who showed passive mechanisms in emmetropization) and later by Dunne (1993) (who
3
proposed mathematical models of ocular growth). Weale (Weale, 1982) then proposed that
4
the lens changed shape during the first years of life because of a redistribution of volume
5
produced by zonular tension during eye growth. These ideas were further explored by Mutti
6
& Zadnik (Zadnik et al., 1995; Mutti et al., 1998) after their first longitudinal study of lens
7
thinning in children, when they proposed a theory for lens thinning based on zonular
8
traction mediated by ciliary muscle tension. In this last theory, lens thinning and lens power
9
loss were modified in myopic children by a restriction in scleral expansion during eye
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growth. By the same time, Brown & Bron (Brown & Bron, 1996) in their book called ―Lens
11
Disorders‖ made reference to Weale’s zonular traction theory when explaining lens shape
12
changes during school years. They argued that there was little anterior segment growth after
13
age 2 in children (from the available measurements of corneal diameter), and that slit
14
Scheimpflug images of children eyes showed that although lens axial thickness was
15
relatively stationary over childhood, there was vigorous cortical growth accompanied by a
16
reduction in the dimension of the nucleus (this last produced by compaction). In the present
17
review we follow this latter idea about the causes of lens thinning during childhood, further
18
proposing that the redistribution of the gradient index structure within the lens contributes
19
to the loss of lens power. A recent clinical trial designed to evaluate theories of myopia
20
progression concluded that the mechanical tension theory based on zonular traction was not
21
consistent with the findings of the study (Berntsen et al., 2012) so it is possible that
22
Brown’s observations about nuclear compaction in children lenses are the cause of lens
23
thinning.
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1 2
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
4
axial growth, and vice versa, images falling in front of the retina (myopic defocus) can
5
down-regulate the rate of axial growth (Wallman & Winawer, 2004). Low outdoor
6
exposure to natural ambient light probably produces an acceleration of axial growth by the
7
down-regulation of retinal dopamine activity (French et al., 2013). Myopic children have
8
been shown in CLEERE study to be exposed to significantly less time outdoors than their
9
emmetropic peers up to three years before myopia onset (Jones-Jordan et al., 2011). In three
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different studies, the rate of refractive change towards myopia and the rate of axial
11
elongation have been shown to be accelerated at the years around the onset (Thorn et al.,
12
2005; Mutti et al., 2007; Xiang et al., 2012). Then, one could argue that low outdoor
13
exposure seems to be accompanied by a higher rate of axial elongation in future myopic
14
children. Although the lens could compensate for this accelerated growth with an
15
accelerated rate of power loss (Iribarren et al., 2012a), myopia can be rapidly developed
16
once the lens reaches its described limit in power loss because of its internal structure. At
17
that time, any further axial elongation would be translated into a myopic shift. But once
18
myopia is established, the myopic eye is subject to myopic defocus for some periods each
19
day when spectacles are not used. Short periods of myopic defocus have been shown to
20
have a potent inhibitory effect on ocular growth in animal models (Wallman & Winawer,
21
2004). And it has been suggested that this myopic defocus could slow down the rate of axial
22
elongation once myopia is established (Xiang et al., 2012).
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More prospective studies about myopia onset following the changes in ocular
24
components during school years are needed to confirm these findings, and special attention
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should be paid to lens changes, because one mentioned study has shown that lens power
2
loss ―stops‖ around myopia onset (Mutti et al., 2012) and another has shown no change in
3
the rate of power loss at that time (Xiang et al., 2012). Further, it is difficult to understand
4
the ―stop‖ in lens power loss after myopia onset (Mutti et al., 2012) if Singaporean SCORM
5
persistent myopic children show consistently lens power loss after onset during the years of
6
progression (Iribarren et al., 2012a). As these studies in myopic children have been
7
performed at a mean age of onset around 10 years, the age at which the lens stops thinning
8
and reduces its rate of power loss, the finding of reduced power loss after myopia onset
9
could be an age effect. One alternative possibility is that after the lens increases its rate of
11
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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,
13
because the development of a refractive index plateau in the center of the lens further
14
changes the gradient profile and makes the lens lose power during adult years (Augusteyn et
15
al., 2008 and Figure 6A & B).
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14. The lens power loss during university study years. The mentioned SCORM study in Chinese Singaporean school children showed rates
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of axial length change of +0.10mm per year in emmetropes, and +0.28mm per year in
20
myopic eyes, with a change in lens power of –0.29 diopters per year in emmetropes, –0.36
21
diopters per year in newly developed myopes and –0.25 diopters per year in persistent
22
myopes (Iribarren et al., 2012a). A prospective study of engineering students in Norway
23
(Kinge et al., 1999) showed that during the three-year follow up, the group of 149 students
24
had a myopic shift in refraction from age 20 to 23 years. The lens power was calculated
30
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from the biometry and the cycloplegic refractions in that study (Iribarren et al., 2014b, in
2
press), showing that the initially emmetropic engineering students had a rate of axial length
3
growth of +0.39mm in three years, that is, +0.13mm per year, similar to that of emmetropic
4
children in SCORM or Orinda studies. And these engineering students had a rate of lens
5
power loss of –0.70 diopters in three years, that is, –0.23 diopters per year, similar to the
6
loss of lens power in Singaporean children. This compares well to the non-cycloplegic
7
calculations that gave a loss in lens power of –0.40 diopters in 3 years for emmetropic
8
young subjects followed by Grosvenor (–0.13 diopters per year) (Grosvenor & Scott, 1993).
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These few studies have then shown that the lens is still compensating, in part, for
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axial elongation during early adult years. This happens at a time when the lens is increasing
11
in axial thickness and possibly steepening curvatures (very different from the times of lens
12
thinning and flattening in schoolchildren up to age 10), so here again variations in the
13
gradient index structure may be driving the changes seen. It would be interesting to have
14
longitudinal cycloplegic studies with biometry in selected adult populations prone to
15
develop myopia (like engineering or law students) to confirm these findings about lens
16
power loss during early adulthood. If phacometry could be performed, then the equivalent
17
index could be calculated, perhaps showing a prospective decrease with age as was shown
18
in the Orinda and CLEERE studies.
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15. The lens in adulthood. We have seen that myopic children have lower lens power than emmetropic
22
children, and hyperopic children have higher lens power than their emmetropic peers. This
23
would produce a positive correlation between refraction and lens power, as higher spherical
24
equivalents have higher lens power and vice versa (Iribarren et al., 2012a). This would be in
31
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agreement with the fact that longer eyes, usually the myopic ones, have lower lens power,
2
and vice versa, shorter eyes have higher lens power. This can be seen in the negative
3
correlation between axial length and lens power, originally described by Sorsby and also
4
seen in the Sydney Myopia Study (Ip et al., 2007) or SCORM studies (Iribarren et al.,
5
2012a).
6
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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
8
reported a conflicting finding. In fact, lens power was negatively correlated with axial
9
length as it was known long ago (Sorsby et al., 1957) but lens power was also negatively
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correlated with refraction, assuming that myopic eyes had higher lens powers or vice versa,
11
hyperopic eyes lower lens power. Olsen et al. (2007) discussed these findings explaining
12
that refraction was in fact determined by a complex interplay between all the ocular
13
components. Indeed, the relations between the ocular components should be changing from
14
childhood to adulthood if the correlation between lens power and refraction is changing
15
from positive to negative.
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Figure 1 gives the clues for what is happening. From age 20 until age 75, the
17
prevalence of cycloplegic hyperopia greater than +1 diopter increases from 10% to 50%. At
18
these ages corneal power has been shown to be stable as is probably also the case for axial
19
length. In any way, eyes could not become shorter to explain this hyperopic shift in
20
refraction because in that case pseudophaquic eyes should have hyperopic shifts with
21
ageing in the clinic and that does not seem to happen (author’s clinical observation and
22
Brown et al., 1999). What indeed may be happening is that the lens is losing power in some
23
emmetropic subjects who develop hyperopic shifts and become hyperopes (Hashemi et al.,
24
2010). Then, by age 70, the 50% prevalence of hyperopes may be a mixture of 10% who
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were hyperopes since childhood (with high lens power) and of 40% of newly developed
2
hyperopes that may have come from the emmetropes who may have lost lens power. Then,
3
this number of hyperopes with low lens power would change the correlation between
4
refraction and lens power to a negative one (in adults aged 70) as has been found in
5
Reykjavik (Olsen et al., 2007) and later in the Los Angeles Latino Eye Study (Iribarren et
6
al., 2010) and the Central India Eye and Medical Study (CIEMS) (Iribarren et al., 2012b). In
7
these last two studies, in fact, adult hyperopes without cataract had significantly lower lens
8
power than the emmetropes, the opposite of what is found in school-aged children. This can
9
be seen in Figure 10 with data published in CIEMS Study (Iribarren et al., 2012b) where
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hyperopes with low amount of nuclear opacity have lower lens power than emmetropes or
11
myopes. This is probably produced by loss of lens power in many emmetropic eyes that turn
12
to be hyperopic with ageing. This last study also showed a significant negative correlation
13
between refractive error and lens power (Figure 11).
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The amount of lens power loss with age during adult years can be calculated
15
indirectly from a prospective population based study like the Beaver Dam Study (Lee et al.,
16
2002), which showed that subjects aged 43-59 at baseline had an hyperopic shift of +0.54
17
diopters in the 10 years follow up. If all the other ocular components are left unchanged, the
18
lens changes power by about –1.5 diopters per +1 diopter change in refraction (Wolfgang
19
Haigis, personal communication). Although those were not cycloplegic refractions and
20
could be biased, such hyperopic shift would represent –0.81 diopters of lens power change
21
in 10 years, or –0.081 diopters loss per year. This rate of lens power loss is lower (about
22
one third) than that calculated for young engineering students (–0.23 diopters per year)
23
(Iribarren et al., 2014b, in press) or that of Singaporean schoolchildren (–0.29 diopters per
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1
year) (Iribarren et al., 2012a) so the lens seems to lose power at a very slow rate during
2
adult years. As has been explained when speaking of children lenses, a lens which is increasing
4
in thickness and curvatures during adulthood can only lose power by changing its gradient
5
index profile. As we have also said, the maintenance of the refractive index gradient profile
6
could only be achieved if the rate of compaction equals the rate of apposition of new fibers.
7
An early study in rats has shown that the lens epithelial cells, with increasing age, show less
8
growth and differentiation under similar concentrations of FGF (Lovicu, 1992). It may be
9
true that, very slowly during adult life, the epithelial cells gradually lose the capacity to
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grow. And this would simply make the climbing gradient profile more abrupt. Besides, as
11
compaction probably reaches a relative end point after 10-20 years of human life, the
12
central gradient plateau is formed as nuclear fibers reach maximal compaction. As can be
13
seen in Figure 6A & B (Augusteyn et al., 2008), the adult lens develops a refractive index
14
plateau at the center of the lens, and this section of uniform index makes the lens resemble
15
an artificial homogeneous lens that has lost its gradient, with lower power (and greater
16
positive spherical aberration). Interestingly, several studies have shown that the internal
17
spherical aberrations of the human eye increase with ageing (Glasser & Campbell, 1998;
18
McLellan et al., 2001; Artal et al., 2002; Brunette et al., 2003). The lens has the gradient
19
index structure and aspheric curvatures such that the internal aberrations of the eye are
20
negative in youth compensating the positive spherical aberration of the cornea. The increase
21
in positive spherical aberration with age can be seen in Figure 12, where the juvenile clear
22
dog lens has negative spherical aberration while the human 70 year old lens has positive
23
spherical aberration (Sivak & Kreuzer, 1983; Sivak, 1985;). This older lens behaves as an
24
homogeneous lens, without a gradient index structure.
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1
During middle adulthood, myopia prevalence does not change much in Figure 1 (Hashemi et al., 2004). The myopic eyes are not as prone as emmetropic eyes to have
3
hyperopic shifts, as has been shown in a clinical retrospective study (Grosvenor & Skeates,
4
1999). Prospective population based studies of refractive error in adults could confirm this
5
last finding. In fact, hyperopic shifts in myopic subjects are uncommon in clinical practice.
6
Perhaps, only a few low myopes have small hyperopic shifts in their 40’s. Myopic eyes may
7
be less prone to have hyperopic shifts with ageing as they already have lower lens power
8
than emmetropes early in life in Orinda (Jones LA et al., 2005) and SCORM (Iribarren et
9
al., 2012a) studies. If the thinner lens of myopic eyes has lost gradient power to a greater
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extent than that of emmetropic eyes, it may thus have a limited capacity of possible further
11
power loss. Interestingly, a more abrupt climbing gradient profile would not compensate
12
accurately the spherical aberration of the lens, and myopes have been shown in some (but
13
not all studies) to have greater ocular aberrations than emmetropic eyes (He et al., 2002;
14
Marcos et al., 2002; Paquin et al., 2002; Kwan et al., 2009). It would be interesting to have
15
measurements of the gradient index profile in different refractive groups in young adults. At older ages, in Figure 1, new cases of myopia appear, this time produced by a
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different change in the lens associated with nuclear cataract. The lens in these cases should
18
be gaining power producing a myopic shift in refraction. Then the emmetropes who turn to
19
be myopic with cataract would have high powered lenses, the opposite of what is found in
20
myopic schoolchildren. So this would also turn the correlation of lens power and refraction
21
to the negative side, as myopic eyes would have higher lens power than their emmetropic
22
peers (Figure 10). This has been found in CIEMS study, which showed that the correlation
23
between lens power and spherical equivalent became more negative when cataract subjects
24
were included (Iribarren et al., 2012b, Figure 11). In Figure 1 of the present paper, the
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prevalence of myopia changes from 12% during adult years to 38% in aged subjects, and
2
this could be enough to change the correlation between lens power and refraction to the
3
negative side.
4 5
16. Longer eyes of taller subjects have lower powered lenses.
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The advent of ultrasound biometry in the 70’s produced two interesting studies. In
7
1979 Larsen (Larsen, 1979) showed that taller people had longer eyes (and vice versa) for
8
subjects in the emmetropic range. Since then, many population studies have found that
9
taller people have longer eyes with flatter corneas, irrespective of refractive error (Wong et
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al., 2001; Saw et al., 2002; Ojaimi et al., 2005; Eysteinsson et al., 2005; Wu et al., 2007;
11
Lee et al., 2009; Nangia et al., 2010). Also in 1979, Blomdhal showed that bigger newborns
12
had longer eyes with flatter corneas. A recent population based study with cycloplegia for
13
refractive error measurement showed that taller people had longer eyes with flatter corneas
14
and also, lower powered lenses, irrespective of refractive error (Iribarren et al., 2014c)
15
(Table 5). This study also calculated the lens power with published data of the ocular
16
components and refraction of two adult population studies (Wong et al., 2001; Wu et al.,
17
2007) and one study in schoolchildren (Saw et al., 2004), showing that this trend in taller
18
people, or children born bigger, having bigger eyes with less powerful lenses was also the
19
rule (Table 5).
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Interestingly, a recent study of stature growth trajectories in a longitudinal study of
21
British children showed that while refraction at age 15 was not related to height growth,
22
corneal radius at that age was related to growth in the first 2 years of life and axial length
23
was related to height growth in the first 10 years of life (Northstone et al., 2013). So, in the
24
first years of life, when the corneal radius and axial length are changing with eye growth,
36
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these changes may be then influenced by general growth patterns, and also coordinated by
2
the emmetropization mechanism that makes the axial length match the refractive surfaces
3
by defocus. Indeed, the lens should be part of this general pattern of co-regulation. Further
4
evidence of this is the finding of lower lens power in faster growing eyes which develop
5
myopia (Iribarren et al., 2012a). The finding of lower powered lenses in taller people with
6
longer eyes could be in concordance with some kind of regulation of lens power loss
7
according to axial length change during early growth (Iribarren et al., 2014c). Alternatively,
8
it could be possible that general somatic growth is linked to lens growth early in life such
9
that taller children could have lenses that grow thinner and less powerful; and then the axial
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length independently could match the optical power of the cornea and the lens by defocus
11
regulated eye growth. This would also produce longer axial lengths in eyes with lower
12
powered lenses or flatter corneas.
Since Sorsby (1957) it is known that, in the emmetropic range, longer eyes have
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flatter corneas. In Table 6 we have calculated the lens power for ideal emmetropic eyes with
15
a normal range of axial lengths and corneal powers such that they all have a normal axial
16
length / corneal radius ratio of 3.0 (Grosvenor & Scott, 1994). As was early recognized by
17
Grosvenor & Scott (1994), it can be clearly seen that not only the cornea and the axial
18
length adjust for eyes being emmetropic, as also longer eyes should have lower powered
19
lenses, and vice versa. This lead the former researchers to state that ―the lens had
20
emmetropized‖ in longer eyes.
22 23 24
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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?
37
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1
Can the lens adjust its power to the general growth of the eye? A theory that could explain
2
these changes can only be based on the understanding of both surface and internal structure
3
of the lens. As we said before, the lens has a gradient of refractive index because new fresh
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fibers mature and become compacted as they age and sink in the deeper layers of the lens.
6
As fibers mature and become compacted they gain index, so a gradient of refractive index is
7
established from the surface to the center of the lens. This gradient gives the lens an internal
8
power greater than the one due to its curvatures alone. This has been known since the time
9
of Thomas Young who even calculated the power given by a gradient lens (Young, 1801;
11
Atchison & Charman, 2011).
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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
13
(Dubbelman & Van der Heijde, 2001) showed that the lens effective index decreased with
14
age in adults in a similar manner as it was later described prospectively in schoolchildren
15
(Jones LA et al., 2005). If the lens effective index decreases while the lens is compacted
16
during childhood (and thus should gain index) the only possible explanation for this loss of
17
effective index is that the gradient profile is becoming less effective (its climbing profile is
18
becoming more abrupt and it is developing a central plateau). This fact was originally
19
discussed by Donders in 1864 when he was thinking how the eye could become hyperopic
20
with ageing (Donders, 1864). He wrote ―In advancing years the lens becomes externally
21
especially firmer, and thus the coefficient of refraction of the outer layers appears to
22
increase. If this actually takes place, and if the coefficient of the cortical layers thus
23
approaches more to that of the nucleus, the (lens) focal distance becomes greater. On this
24
the diminution in advanced life of the refractive condition of the eye appears really to
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depend.‖ (Donders, 1864, page 88). But then he erroneously thought that although this
2
could be possible, the main reason for hyperopia was a flatter lens surface with age. He
3
probably thought this because he imagined that a rounded lens would flatten curvatures
4
with growth. This idea of lens flattening with age lasted for more than 100 years, until
5
Nicholas Brown at Oxford in 1973, showed with Scheimpflug photography that the lens
6
curvatures became steeper with ageing. For example, Duke-Elder in 1970, when speaking
7
about hyperopic shifts during adulthood, still argued that the lens curvatures became flatter
8
with age (Duke-Elder & Abrams, 1970a), although he recognized that Parsons had thought
9
that ―hardening of the cortical material of the lens‖ could be responsible for hyperopic shifts
11
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with ageing (Parsons, 1906).
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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 (Figure 13).
13
Nicholas Brown began to talk about the lens paradox as he thought that greater curvature at
14
the lens surface (more power) was paradoxically accompanied by presbyopia and not
15
myopia with ageing. This paradox could only be explained by a decreasing gradient
16
refractive index power inside the lens. After Brown, the change in gradient refractive index
17
profile with age was shown in different studies (Pierscionek, 1990; Smith et al., 1992;
18
Hemenger, 1995; Smith & Pierscionek, 1998) and recently by magnetic resonance images
19
(Kasthurirangan et al., 2008). If the profile of the climbing gradient index becomes more
20
abrupt with age, then the rays passing through it do not bend so much as they did earlier
21
when the gradient was smoother. And the development of a central plateau with no gradient
22
power further makes the lens lose power and optical properties. The change in the
23
peripheral profile of the climbing gradient of refractive index is probably produced by
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compaction of the fibers inside the lens, especially in the deep layers of the cortex (Figure
2
6A & B, adult lens).
3
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).
5
And then the nuclear index should increase, changing again the profile of the gradient
6
structure, thus explaining the increase in power of the lens and the myopic shift in
7
refraction found in 40-80% of subjects with nuclear cataract in the clinic (Iribarren &
8
Iribarren, 2013; Diez Ajenjo et al., 2014; Pesudovs & Elliot, 2003). Further proof of this is
9
the finding of thinner lenses in cataract subjects in CIEMS Study (Iribarren et al., 2012b) as
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if the compaction produced with cataract formation could make the lens thinner. In that
11
sense, early observations of deeper anterior chambers in eyes with unilateral cataract made
12
Laursen & Fledelius think that with cataract the lens was becoming thinner (Laursen &
13
Fledelius, 1979)
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Although the lens does not seem to be responsible for changes in refraction in
15
animal studies of experimental refractive error (Sivak, 2008, Review), human studies show
16
that the lens somehow can compensate for the axial growth of the eye to some extent. This
17
compensation may have passive and active mechanisms. The lens seems to slowly lose
18
power from birth to senescence. Some of the changes in lens surface shape tend to cancel
19
each other: for example, during childhood, the lens thinning per se would increase the
20
power (optically speaking, a thinner homogeneous lens with constant curvatures should
21
have greater power) but the decrease in curvature that accompanies crystalline lens thinning
22
decreases its surface power, so lens thinning cancels to some extent lens flattening during
23
school years. Another possible active way that the lens has for changing its power is by the
24
regulation of the rate of growth and compaction of lens fibers, in such a way that it may
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alter the profile of its climbing gradient refractive index which is responsible for its internal
2
power. This may be a very slow mechanism in humans who have a very slow rate of lens
3
growth, but appears to be fast during metamorphosis in amphibians, which rapidly change
4
lens shape and refractive power of the eye when moving from water to aerial vision.
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Interestingly, the diameter of fibers decreases from the center to the periphery in
6
microscopic studies of adult human lenses (Taylor et al., 1996). For example, the mean
7
cross-sectional area of fibers decreases progressively from 80 square micrometers in the
8
embryonic center of the lens to only 7 square micrometers in the adult nucleus which is the
9
sector under the newly developed cortex. This newly developed cortex in the surface of the
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lens, in turn, has fibers with a greater area of 24 square micrometers. This pattern in an
11
adult lens that has laid and compacted fibers at different ages, and is still laying new fibers,
12
is certainly interesting. Although the fibers in the central refractive index plateau (formed in
13
the adult, juvenile and fetal nucleus) have similar protein concentration (and similar
14
refractive index) because a plateau of index is developed, the younger ones are
15
progressively smaller from the center to the periphery. It seems that the embryonic and fetal
16
fibers have been the biggest ones when laid, and that the ones laid during juvenile school
17
years are smaller when they achieve maximum compaction with a similar index as those at
18
the center of the lens. They were probably smaller than the embryonic when they were laid
19
and matured during postnatal life. And the ones laid in the adult years, which form the
20
outermost part near the cortex, are even smaller when compacted. The only exception in
21
this pattern of change in fiber diameter are the newly developed fibers in the surface cortex,
22
still not compacted, that are a little bigger than the ones near them in the adult nucleus,
23
which have been compacted. This pattern of change in fiber diameter probably shows that,
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as fibers are laid from embryo to adult, they are gradually growing smaller up to maturation,
2
this fact perhaps related to a slower rate of lens epithelial growth with ageing.
3
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
5
studies showed that the lens wet weight increased linearly with age in adult life (Augusteyn,
6
2007; Augusteyn, 2010). Such linear growth in wet weight during adult years, in principle,
7
tended to show that the human lens maintained a constant linear rate of growth throughout
8
the whole adult life. One study showed that the water content in the nucleus was constant
9
with age (Heys et al., 2004; Truscott, 2009), but as the lens becomes older, it becomes
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compacted (Al-Goul et al., 2001) with fibers more densely packed, probably with loss of
11
water as cataract develops (Heys et al., 2004). As proteins are heavier than water, older
12
lenses might maintain a constant increase in wet weight but not a similar increase in volume
13
of added fibers. Besides, if the increase in lens thickness and diameter were linear, the
14
volume should increase non-linearly by the third power (more added volume as the lens
15
becomes bigger). But the opposite seems to be true. In fact, a decreasing non-linear growth
16
in axial thickness, equatorial diameter and calculated lens volume has been preliminary
17
reported for in vitro human lenses (Mohamed et al., 2012), showing that the increase in
18
dimensions and volume slows down as the lens ages during adulthood. The increase in
19
volume for Mutti’s lenses in Figure 8 has been calculated in Table 7, where it can be seen
20
that during six months (in the first year of life) the lens volume increases by 13%, while in
21
the next fourteen years it only increases by 8%. Table 8 shows the decay in lens volume
22
growth during adulthood calculated from the data in Mohamed et al., 2012 for adult years.
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The increase in volume of the growing lens probably results from the balance
24
between new added fibers and compaction of older ones. If compaction is a time dependent
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process due to ageing of proteins which aggregate and lose water, then the decay in lens
2
volume growth means that less fiber volume is added as time passes by. If this in vitro
3
biometric preliminary finding is confirmed (Mohamed et al., 2012), and we consider that
4
individual fibers laid at older ages reach lower final volumes, then it is possible that the lens
5
may have a decreasing rate of lens epithelial growth with ageing. This pattern of decrease in
6
growth over time would undoubtedly make the climbing gradient profile more abrupt, as
7
the only way to maintain a constant climbing gradient profile that is being compacted in the
8
deeper layers would be to maintain a constant rate of growth of new fibers. This would also
9
produce a plateau of index in the center of the lens.
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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
12
compaction progressively increases its rate with ageing. This would also make the climbing
13
gradient profile more abrupt. But this is not likely as compaction seems to be an inherent
14
property of protein ageing. Most of the hyperopic changes analyzed are slow and take years
15
to develop. The only report of a rapid change in lens refractive properties is that related to a
16
myopic shift of about 2-3 diopters with nuclear cataract usually developed in few months.
17
The slit lamp observed changes are found in the nucleus that becomes more colored and
18
opalescent. So this compaction and probable loss of water that, also probably, changes the
19
nucleus index, seems very different to the slow change in the peripheral climbing gradient
20
index profile.
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Another important issue in this analysis it that in vitro and in vivo measurements of
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lens thickness may not be comparable in the sense that in vitro measurements are made with
23
the lens in maximally accommodated state and the lens power in the present study is
24
analyzed in vivo under cycloplegia at a resting position. The in vitro axial thickness would
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be overestimated in lenses of subjects younger than 40, (and equatorial diameter
2
underestimated, Strenk et al., 1999) when compared to lenses measured in vivo at rest under
3
cycloplegia because of the change in lens shape with accommodation. So the change with
4
age in the relation between axial thickness and equatorial diameter (aspect ratio) could be
5
even greater for lenses in vivo. To test for this hypothetical difference we have plotted in
6
Figure 14 the lens thickness measurements from five different in vivo population studies
7
with A-Scan biometry along with in vitro data from Mohamed et al, 2012. It can be clearly
8
seen that with the exception of the Chinese Singaporean who have thicker lenses, the
9
general pattern of lens axial growth is similar in all studies. And that axial growth decays
10
with age in both types of studies. So we think that our analysis is not biased by comparing
11
in vitro with in vivo studies of ocular biometry.
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18. Is the rate of lens power loss an actively regulated process?
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In the classical studies about the correlation of the ocular components with
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refraction performed by Tron (1940) and Stenstrom (1948) in younger adults, the lens was
16
found to have no correlation with refraction, and thus was not considered important in the
17
development of refractive error. But things might have looked different if those studies
18
would have been performed in children (who have a positive correlation between refraction
19
and lens power, Iribarren et al., 2012a) or in older adults (who have a negative correlation
20
between refraction and lens power, Figure 11, Iribarren et al., 2012b). Animal studies of
21
refractive error have concluded that the lens has a passive role in the development of
22
refractive error, as Sivak has extensively reviewed (Sivak, 2008). Indeed, those animal
23
experiments are performed during short periods of one or two weeks, so changes in the lens
24
may not have been shown, as these may take longer to develop.
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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
3
myopia development during the axial growth period in children. Once axial growth has
4
stopped in adulthood, the continuing loss of lens power produces hyperopic shifts in
5
refraction that seem to be an undesired passive process that impairs distance vision during
6
late adulthood. But, can the rate of lens power loss be modulated during childhood to
7
produce myopic eyes with consistently lower lens power at the end of childhood?
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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.
10
Fish lenses also grow continuously. The power of the fish lens has to decrease with age to
11
adapt for the increasing axial length as the fish grows. A defocus modulated axial growth
12
adapts the eye size to the lens focal length in fish eyes (Shen & Sivak, 2007). But an
13
interesting experiment with fish reared for 10 months under monochromatic light or under
14
light deprivation showed alterations both in longitudinal spherical aberrations and refractive
15
index profiles of those growing fish lenses (Kröger et al., 2001). These alterations are of
16
interest as they show that the gradient structure can be modified environmentally during
17
lens growth. A recent animal study of myopia development in chicks growing with
18
unrestricted vision under low light environments has shown that the lens power loss during
19
eye growth can be environmentally modulated, as the eyes of chicken developing myopia
20
growing under 500 lux ambient light, have thinner and less powerful lenses than the ones
21
which remain hyperopic growing under high ambient illumination. This environmental
22
change in the rate of lens power loss is slow as it takes 2-3 months to develop (Cohen et al.,
23
2011; Cohen et al., 2014).
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The lens has been shown to be also thinner in myopic children in several studies (Jones LA et al., 2005; Shih et al., 2009; Wong et al., 2010; Iribarren et al., 2012a). Myopic
3
eyes are generally longer. The lens is also thinner in taller subjects (who also have longer
4
eyes). A thinner lens is probably a lens with delayed growth. And human studies reviewed
5
here have shown that these thinner lenses have lower power. FGF is the principal molecule
6
involved in lens growth, and its concentration in the vitreous could be modified by genetic,
7
humoral or local factors. FGF could also be involved ocular growth signaling (Rhorer &
8
Stell, 1994; Gentle & McBrien, 2002; Wallman & Winawer, 2004). If the profile of the
9
gradient index structure is a function of lens growth, delayed growth could alter this
10
gradient and thus the internal power of the lens. So there is a possible mechanism for
11
regulating the lens power loss based on its rate of growth, which in turn may be a function
12
of FGF concentration.
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The findings reviewed herein, although they should be replicated, are possibly
14
showing that lens growth could be actively modulated in relation to axial or somatic growth
15
during early development in infants and also in myopic schoolchildren. FGF could be the
16
link of this regulation. It is possible that the emmetropization mechanism was adapted by
17
evolution to maintain a relative mild hyperopic refraction during growth as accommodation
18
can overcome this mild refractive error before presbyopic years (Morgan et al., 2010). This
19
would be protective from eyes being out of focus for distance viewing (myopia). Current
20
thinking about emmetropization suggests that a passive programmed loss of lens power is
21
counterbalanced by an actively regulated rate of axial length growth by retinal defocus. But
22
the growing eye could also have a slower feedback mechanism that regulates lens power
23
loss in relation to axial elongation, to protect from environmentally induced higher rates of
24
axial growth. In this sense, the chick model in which axial myopia is developed by growing
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under low ambient illumination during three months is interesting for studying lens power
2
loss in vivo (Cohen et al., 2011; Cohen et al., 2014).
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19. Conclusions and future directions.
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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
7
birth and during school years up to age 10-12. Lens thinning is accompanied by flattening
8
of lens curvatures because of changes in overall lens shape. These changes involve axial
9
thinning and equatorial growth from birth to puberty. The lens thinning per se, all other
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things the same, would increase the power of an homogeneous lens (optically speaking), but
11
flatter curvatures due to changing shape produce decreasing lens power while the lens thins.
12
Besides, the changing internal structure may be responsible for more than half of lens
13
power loss during childhood. Changes in the gradient index profile probably make the lens
14
lose power during this period. Myopic subjects have lower lens power than their
15
emmetropic peers, with thinner lenses, possibly because the gradient structure has become
16
less effective at a slower rate of growth. Thus, myopic subjects may be less prone to lose
17
lens power with ageing, maintaining stable refractions during adult years.
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The lens continues to lose power after ages 20-30 in many emmetropic subjects,
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explaining the development of hyperopic shifts with ageing. These hyperopic shifts may be
20
also produced by an age related change in the gradient refractive index inside the lens, the
21
only possible explanation after Nicholas Brown described increasing lens curvatures with
22
age (the Lens Paradox). This change of the gradient profile seems to be a consequence of
23
decreasing lens growth with ageing. As the lens grows slower, the systematic compaction of
24
the deeper layers possibly changes the profile of the gradient structure, because the later
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relies on growth of new fibers and can only be maintained unaltered if the rate of growth
2
were constant. The development of a refractive index plateau in the center of the lens
3
further reduces its internal power. After age 70, the lens gains power in many subjects that
4
have nuclear cataracts, producing myopic shifts in refraction. This last change is probably
5
due to increased index in the center of the cataractous lens due to further compaction and
6
water loss of the crystallin content.
Future prospective population based studies of cycloplegic refractive error,
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including keratometry and biometry, could calculate lens power. Then, the question of
9
whether the eye shrinks with ageing or the lens loses power during age related hyperopic
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shifts could be resolved. Besides, the loss of lens power with age could be studied
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prospectively in adults across refractive error groups, such that differences in lens power
12
loss could be studied further as has been done in school children.
Possible environmental influences on lens growth need replication of experimental
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studies. The profile of the gradient index could be indirectly studied prospectively in vivo
15
with new approaches such as Brillouin confocal microscopy, which has shown that the
16
profile of the elastic modulus changes with age in rat and human lenses (Scarcelli et al.,
17
2011; Scarcelli & Yun, 2012; Besner et al., 2013). The profile of the elastic modulus
18
resembles the profile of the gradient refractive index. This new non-destructive in vivo
19
approach could be useful to confirm suggested differences in the gradient index profile
20
across refractive groups. Besides, changes in the gradient profile could be studied
21
prospectively with this last method, which looks promising not only for the study of
22
hyperopic shifts with ageing, but also for the changes in the internal structure of the lens
23
during accommodation.
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Acknowledgements. This review was developed during long lasting discussions with Prof.
2
Ian G. Morgan (Australia), to whom I feel grateful. I wish to thank Prof. Akbar Fotouhi
3
(Iran) for the data in Figure 1 of Tehran Eye Study and for the data in Table 5. I also thank
4
Prof. Michiel Dubbelman (Netherlands) for his comments on the manuscript. I also wish to
5
thank Prof. Bob Augusteyn (Australia) for his permission to reproduce Figures 6A & B, and
6
for the friendly discussion about lens growth in his cited papers. Prof. Jake Sivak (Canada)
7
has been very kind in sending and discussing his interesting papers, and for letting me
8
reproduce Figure 12. Prof. Jos Rozema (Belgium) has helped me with Bennett’s formula
9
and Gullstrand’s equation. Profs. Peter Sands and Bill Jagger (Australia) have been very
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kind in letting me reproduce their fish lens Figure 2, and Prof. Jost Jonas in letting me
11
reproduce Figures 10 & 11. Finally, I wish to thank Vicente A. La Vitola (Argentina) and
12
Lautaro Gomez Alvarez (Argentina) for the AutoCad figures.
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Figure Legends.
2
Figure 1. Prevalence of refractive error along lifespan, with a +1/-1 diopter cut off point in
3
the Tehran Eye Study (Hashemi et al. 2004). Age 10 stands for 6-10 years, age 15 stands for
4
11-15 years and so on. (Reanalysis of data published in ―Hashemi, H., Fotouhi, A.,
5
Mohammad, K., 2004. The age- and gender-specific prevalences of refractive errors in
6
Tehran: the Tehran Eye Study. Ophthalmic Epidemiol. 11, 213-225,‖ and in ―Fotouhi, A.,
7
Morgan, I.G., Iribarren, R., Khabazkhoob, M., Hashemi, H., 2012. Validity of
8
noncycloplegic refraction in the assessment of refractive errors: the Tehran Eye Study. Acta
9
Ophthalmol. 90, 380-386.‖)
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Figure 2. Parallel laser beams seen from the side refracted by a trout lens. See the short
11
focal length of the fish lens and how the beams are bent inside the lens structure by the
12
gradient index, with no spherical aberration. Reprinted from ―Jagger, W.S., Sands, P.J.,
13
1996. A wide-angle gradient index optical model of the crystalline lens and eye of the
14
rainbow trout. Vision Res. 36, 2623-2639.‖ Copyright (1996), with permission from
15
Elsevier.
16
Figure 3. First, to the left, calculated lens power in premature infants from the data of Cook
17
et al. (2003) for premature infants form months 1 to 5 (white circles); second in the middle,
18
lens power data for full term infants from Mutti et al. (2005) aged 3 and 9 months (black
19
circles), and last to the right, lens power data for schoolchildren from Ip et al. (2007) (black
20
circles).
21
Figure 4. Lens thickness in premature infants from months 1 to 5 (Cook et al., 2003) (white
22
circles) and for full term infants aged 3 and 9 months (Mutti et al., 2005) (black circles).
23
The lens thickness increases in the first three months of life in premature infants, perhaps
24
following the high fetal rate of lens growth.
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Figure 5. Schematic drawing of the change in lens thickness and front and back curvatures
2
of the 15 day old chick lens (inner lines) inside the 80 day old lens (outer lines). It can be
3
seen that the lens becomes thicker with flatter curvatures as it grows. Reprinted from
4
―Iribarren, R., Rozema, J.J., Schaeffel, F., Morgan, I.G., 2014. Calculation of crystalline
5
lens power in chickens with a customized version of Bennett's equation. Vision. Res. 96,
6
33-38.‖ Copyright (2014), with permission from Elsevier.
7
Figure 6. Three gradient index profiles reconstructed from mri images of human lenses in
8
vitro. Figure 6 A equatorial axis, Figure 6 B saggital axis, (with permission from
9
―Augusteyn, R.C., 2008. Growth of the lens: in vitro observations. Clin. Exp. Optom. 91,
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226-239‖). In gray dots a 7 year old lens, with a smooth climbing gradient profile and a
11
lower peak index compared to the other adult lenses. In white dots a 27 year old lens with
12
adult peak index and more abrupt gradient that is developing a central plateau. In black dots
13
a 82 year old human lens with a very abrupt climbing gradient and an extended central
14
plateau. Figure 6 C. Schematic drawing of the gradient index profile of two lenses, one of
15
which is thinner and has a more abrupt climbing profile to reach a higher peak index.
16
Although the thinner lens may have a higher peak index, the change in gradient profile
17
could make it have lower power. The younger lens is 4.0mm thick and the older 3.6mm
18
thick, representing the compaction achieved since birth up to age 10.
19
Figure 7. Anterior Segment Length calculated from data in Cook et al. (2003) in premature
20
infants form months 1 to 5 (white circles), then for full term infants in Mutti et al. (2005)
21
aged 3 and 9 months (black circles), and for emmetropic schoolchildren at ages 6 and 12
22
years from Zadnik et al. (2004) (black circles).
23
Figure 8. Auto Cad drawings made with the data of curvatures and axial thickness given by
24
Mutti et al. in their studies for 3 months, 9 months and 14 year old children (Mutti et al.,
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2005 and 1998). Curvatures were assumed as spherical. The equatorial curvatures were
2
drawn following the equatorial shape of the shadowgraphs in Borja et al. (2008). From
3
these drawings, the equatorial diameter was estimated for the three ages, showing that the
4
lens grows up to adult values early in life.
5
Figure 9. The same figures as in Figure 8, this time superimposed for the 3 month old
6
(dotted line) and the 14 year old lens (full line), showing the change in shape achieved
7
during childhood. It can be seen that the lens thins from a more rounded shape at 3 months
8
and that the equatorial portion increases making the lens more ellipsoidal.
9
Figure 10. Significantly lower lens power in hyperopic subjects compared to emmetropic
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and myopic subjects (in the group with low nuclear opacity grades) of the Central India Eye
11
and Medical Study (Iribarren et al. 2012b).
12
Figure 11. Negative correlation between refractive error (spherical equivalent) and
13
crystalline lens power in participants in the Central India Eye and Medical Study. Subjects
14
with marked nuclear cataract (grades 6 and 7, crosses and dotted regression line), had a
15
greater negative correlation than those with less marked nuclear cataract (grades 2–5, full
16
regression line and circles). Reproduced from ―Iribarren, R., Morgan, I.G., Nangia, V.,
17
Jonas, J.B, 2012. Crystalline Lens Power and Refractive Error. Invest. Ophthalmol. Vis.
18
Sci. 53, 543-550.‖ Copyright (2012), with permission from Association for Research in
19
Vision and Ophthalmology.
20
Figure 12. In (A) a clear juvenile dog lens with negative spherical aberration and in (B) a
21
brown 70 year human old lens with positive spherical aberration. See how the laser beams
22
have different refraction through the peripheral or central sections of the lens. (Reproduced
23
with permission from: ―Sivak JG. The Glenn A. Fry Award Lecture: optics of the
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crystalline lens. Am J Optom Physiol Opt 1985;62:299-308.‖ ©The American Academy of
2
Optometry 1985).
3
Figure 13. Schematic drawings of growing lenses. In (A) an ellipsoidal lens that grows only
4
axially steepens front and back curvatures as it grows and in (B) same ellipsoidal lens that
5
grows in all directions flattening front and back curvatures.
6
Figure 14. Plot of the in vitro data for lens axial thickness growth with age from Mohamed
7
et al., 2012 along with the in vivo data from five population based studies with A-Scan
8
biometry (Singapore: Wong et al., 2001; Taiwan: Shih et al., 2007; Latino Eye Study:
9
Schufelt et al., 2005; Myanmar: Warrier et al., 2008; Mongolia: Wickremasinghe et al.,
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2004).
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Al-Ghoul, K.J., Kuszak, J.R., Lu, J.Y., Owens, M.J., 2003. Morphology and organization of
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cataractogenesis. Exp. Eye. Res. 72, 199-214.
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Augusteyn, R.C., 2010. On the growth and internal structure of the human lens. Exp. Eye.
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Augusteyn, R.C., Jones, C.E., Pope, J.M., 2008. Age-related development of a refractive
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Augusteyn, R.C., Maceo, B.M., Nankivil, D., Mohamed, A., Alawa, K., Parel, J-M., 2012.
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Bailey, M., Satiani, N., Sinnott, L., 2013. Longitudinal anterior globe width growth depends
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Bennett, A.G., 1988. A method of determining the equivalent powers of the eye and its
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Bennett, A.G., Rabbetts, R.B., 1989. Clinical Visual Optics, Butterworth-Heinemann Ltd,
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Berntsen, D., Sinnott, L.T., Mutti, D.O., Zadnik, K., 2012. A randomized trial using
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Besner, S., Scarcelli, G., Pineda, R., Yun, S.H., 2013. Age-related Stiffening of Human
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Abstract 4270.
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Blomdahl, S., 1979. Ultrasonic measurements of the eye in the newborn infant. Acta.
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E., Augusteyn, R.C., Parel, J.M., 2008. Optical power of the isolated human crystalline
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lens. Invest. Ophthalmol. Vis. Sci. 49, 2541-2548.
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Borja, D., Manns, F., Ho, A., Ziebarth, N.M., Acosta, A.C., Arrieta-Quintera, E.,
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Augusteyn, R.C., Parel, J.M., 2010. Refractive power and biometric properties of the
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nonhuman primate isolated crystalline lens. Invest. Ophthalmol. Vis. Sci. 51, 2118-2125.
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Brown, E.V.L., 1938. Net average yearly changes in refraction of atropinezed eyes from
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birth to beyond middle life. Arch. Ophthalmol. 19, 719-734.
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Brown, N., 1973. The change in shape and internal form of the lens of the eye on
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accommodation. Exp. Eye. Res. 15, 441-459.
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Brown, N., 1974. The change in lens curvature with age. Exp. Eye. Res. 19, 175-183.
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Table 1. Comparison of the surface and gradient contribution to the decrease in chicken lens power. 15 days old 80 days old difference % change Complete lens power (diopters) 79.9 50.7 -29.3 100.0% Surface lens power (diopters) 27.5 18.7 -8.8 30.0% Internal (gradient index) power (diopters) 52.4 32.0 -20.5 70.0%
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Table 2. Anterior Chamber (ACD), Lens Thicknees (LT) and Anterior Segment Length (ASL) in emmetropic children.* age (years) ACD (mm) LT (mm) ASL (mm) 6 3.62 3.53 7.15 7 3.68 3.5 7.18 8 3.71 3.45 7.16 9 3.73 3.43 7.16 10 3.75 3.43 7.18 11 3.76 3.41 7.17 12 3.75 3.43 7.18 * (calculated from Zadnik et al. 2004)
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Table 3. Refraction and ocular components at age 7-9 years in prematures compared with same age fullterm from Orinda Study. Chen et al. 2010. (prematures) Jones et al. 2005 Myopia Emmetropia Hyperopia Emmetropia Spherical equivalent (diopters) -3.22 +0,02 +2,15 0.54 Corneal Power (diopters) 43.79 42.94 43.68 43.61 Anterior Chamber Depth (mm) 3.29 3.46 3.44 3.69 Lens Thickness (mm) 3.76 3.62 3.61 3.47 Axial Length (mm) 23.39 22.98 21.93 22.93 Lens Power (diopters) 26.69 25.33 25.91 23.63 Anterior Segment length (mm) 7.05 7.08 7.05 7.16
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Table 4. Internal and surface lens power contributions, in diopters, for two prospective studies. (Mutti et al. IOVS 2005;46:3074-80.) Equivalent lens index Complete Gullstrand's lens power Surface Gullstrand's lens power Internal (gradient index) power
3 months 1.4526 40.00 12.19 27.81
9 months 1.4591 36.49 10.52 25.97
Difference
(Mutti et al. IOVS 1998;39:120-33.) Equivalent lens index Complete Gullstrand's lens power Surface Gullstrand's lens power Internal (gradient index) power
6 years old 1.431 24.52 9.09 15.43
14 years old 1.429 21.77 8.23 13.54
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LP D 22.93 22.71 22.43
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Table 5. Comparison of refraction and ocular components of the different studies by height and birthweight. Height and ocular components in adults (Iribarren et al., 2014 - Shahroud study. Invest Ophthamol Vis Sci. 55:1031-9.) HEIGHT SER CR ACD LT AL m D mm mm mm mm 1,31-1,57 -.04 7.58 2.60 4.27 22.99 1,57-1,65 .01 7.63 2.63 4.26 23.14 1,65-1,99 -.12 7.71 2.69 4.23 23.43
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Height and ocular components in adults (Wong et al., 2001 - Tanjong Pagar Survey. Invest Ophthalmol Vis Sci. 42:1237-42). HEIGHT SER CR ACD LT AL LP m D mm mm mm mm D 1,37-1,50 -0.24 7.55 2.7 4.92 22.74 25.68 1,51-1,55 -0.6 7.57 2.86 4.78 23.05 25.11 1,56-1,59 -0.49 7.66 2.83 4.78 23.19 25.01 1,60-1,65 -0.6 7.68 2.99 4.68 23.44 24.44 1,66-1,83 -0.52 7.79 3.1 4.63 23.78 23.94
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Height and ocular components in adults (Wu et al., 2007 - Rural Myanmar. Clin Exp Ophthalmol. 35:834-9). HEIGHT SER CR ACD LT AL m D mm mm mm mm 1,30-1,48 -1.53 7.53 2.7 4.47 22.36 1,49-1,54 -1.67 7.61 2.75 4.48 22.51 1,55-1,6 -1.12 7.68 2.87 4.44 22.76 1,61-1,80 -1.4 7.76 2.87 4.48 23.14
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Birthweight and ocular components - Singaporean Chinese children.(Saw et al., 2004 - Br J Ophthalmol 88:538-542). BIRTHWEIGHT SER CR ACD LT AL Kg D mm mm mm mm 2,5-2,9 -0.35 7.69 3.58 3.5 23.13 3,0-3,4 -0.52 7.76 3.61 3.48 23.44 3,5-3,9 -0.67 7.82 3.64 3.46 23.67 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).
AL/CR 3.03 3.03 3.04
AL/CR 3.01 3.04 3.03 3.05 3.05
LP D 28.35 28.67 27.56 26.96
AL/CR
LP D 25.04 24.54 24.30
AL/CR
2.97 2.96 2.96 2.98
3.01 3.02 3.03
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Table 6. Longer eyes with normal AL / CR ratio have lower powered lenses, and viceversa. Refraction Corneal Radius Keratometry ACD Lens Thickness Axial length (diopters) (mm) (diopters) (mm) (mm) (mm) 0 7 47.36 21,0 2.90 4.20 0 7.2 46.04 21.6 2.90 4.20 0 7.4 44.80 22.2 3.00 4.20 0 7.6 43.62 22.8 3.00 4.20 0 7.8 42.50 23.4 3.10 4.20 0 8 41.44 24,0 3.10 4.20 0 8.2 40.43 24.6 3.10 4.20 0 8.4 39.46 25.2 3.10 4.20
AL / CR 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
Lens Power (diopters) 28.08 26.83 25.95 24.87 24.11 23.18 22.31 21.50
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Table 7. Lens volume* calculated from the data in Figure 7 of Mutti's studies. Age Lens Volume (cubic mm) Volume change (%) 3 months 113.61 9 months 129.03 13.6% 14 years 139.71 8.3% * calculated from the volume of an ellipsoid (4/3*π*a*b*c)
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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 years 148.03 30 years 169.29 21.26 40 years 184.38 15.08 50 years 196.08 11.70 60 years 205.64 9.56 70 years 213.72 8.08 80 years 220.72 7.00
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S1350-9462(15)00008-7
DOI:
10.1016/j.preteyeres.2015.02.002
Reference:
JPRR 583
To appear in:
Progress in Retinal and Eye Research
Received Date: 1 November 2014 Revised Date:
30 January 2015
Accepted Date: 2 February 2015
Please cite this article as: Iribarren, R., Crystalline lens and refractive development, Progress in Retinal and Eye Research (2015), doi: 10.1016/j.preteyeres.2015.02.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Crystalline lens and refractive development.
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Rafael Iribarren
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Department of Ophthalmology, San Luis Medical Center, Buenos Aires, Argentina.
6 7 8 RUNNING TITLE: The lens in human refraction.
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WORDS: 15.806.
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FIGURES: 14; TABLES: 8; REFERENCES: 171.
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I declare no competing interests regarding the subject matter of this paper.
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CORRESPONDING AUTHOR:
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Rafael Iribarren, M.D., Department of Ophthalmology, Centro Medico San Luis, San
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Martin de Tours 2980, CABA 1428, Argentina;
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Tel.: 54-11-4393-1844; Fax: 54-11-4393-1844; Email: [email protected]
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Abstract Individual refractive errors usually change along lifespan. Most children are hyperopic in early life. This hyperopia is usually lost during growth years, leading to
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emmetropia in adults, but myopia also develops in children during school years or during
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early adult life. Those subjects who remain emmetropic are prone to have hyperopic shifts
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in middle life. And even later, at older ages, myopic shifts are developed with nuclear
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cataract.
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The eye grows from 15 mm in premature newborns to approximately 24 mm in early
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adult years, but, in most cases, refractions are maintained stable in a clustered distribution.
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This growth in axial length would represent a refractive change of more than 40 diopters,
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which is compensated by changes in corneal and lens powers. The process which maintains
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the balance between the ocular components of refraction during growth is still under study.
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As the lens power cannot be measured in vivo, but can only be calculated based on the
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other ocular components, there have not been many studies of lens power in humans. Yet,
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recent studies have confirmed that the lens loses power during growth in children, and that
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hyperopic and myopic shifts in adulthood may be also produced by changes in the lens.
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These studies in children and adults give a picture of the changing power of the lens along
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lifespan. Other recent studies about the growth of the lens and the complexity of its internal
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structure give clues about how these changes in lens power are produced along life.
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Key Words: lens power, refractive development, gradient refractive index.
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Contents.
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1. Introduction.
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2. The ocular biometric components.
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3. Calculation of crystalline lens power.
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4. Studies in preterm and full term infants.
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5. Nicholas Brown and the lens paradox.
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6. The lens during early growth in chickens.
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7. The shape and the power of the lens during childhood.
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8. The anterior segment growth.
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9. Change in lens shape during childhood.
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10. The anterior segment in premature children.
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11. The lens power in school years.
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12. Theories for lens thinning during childhood.
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13. Change in ocular components at myopia onset.
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14. The lens power loss during university study years.
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15. The lens in adulthood.
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16. Longer eyes of taller subjects have lower powered lenses.
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17. How can the lens change its power?
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18. Is the rate of lens power loss an actively regulated process?
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19. Conclusions and future directions.
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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
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distribution of refractions, and then move towards mild hyperopia with a narrower,
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leptokurtic distribution of refractions over the first year or two after birth. After this early
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stage, some children then progress in a myopic direction through an increased rate of axial
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elongation which is, at least in part, controlled by environmental exposures (Wallman &
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Winawer, 2004). This developmental phase may continue into the third decade after birth,
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when myopia prevalence reaches its maximum. During school years, many hyperopic
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children come to be emmetropic. After this, there is a slow shift in the hyperopic direction
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which may continue over several decades. This hyperopic shift with ageing can be disrupted
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by the formation of cataract which may lead to quite rapid and pronounced myopic shifts.
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Two early clinical cross-sectional studies which involved cycloplegia with atropine,
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characterized this change in refraction with age from birth to senescence (Brown, 1938;
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Slapater, 1950).
This pattern of change appears to be very general but has never been fully characterized
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with longitudinal data, because the study would inevitably last longer than the working life
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of most chief investigators and clinicians (except, perhaps, for the case of the 1958 British
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Cohort; Rahi et al., 2011). Another limitation of the existing literature is that much of the
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evidence is based on clinical samples, and has generally been measured without cycloplegia
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(except for the two early clinical studies mentioned above), even though it is generally
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recognized that the gold standard for measurement of refractive status requires cycloplegia,
23
at least in children. This requirement may continue into adult life, since accommodation is
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powerful well until the ages of 40-50. As a result, some overestimation of myopia and
2
major underestimation of hyperopia can occur (Fotouhi et al., 2012; Krantz et al., 2010).
3
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
5
cross-sectional study of refraction using cycloplegia over a wide age range, from 5 to over
6
75 years of age. Three of the major developmental phases can be clearly seen. It should also
7
be noted that while these data are cross-sectional, strong evidence of longitudinal change
8
has been obtained for each of these phases (Fotedar et al., 2008; Gudmundsdottir et al.,
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2005; Wu et al., 2005; Lee et al., 2002; Saunders, 1986; Jones L.A. et al., 2005; Mutti et al.,
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2005).
Figure 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
13
hyperopia at ±1 diopter (spherical equivalent) was chosen because most subjects with that
14
amount of refractive error wear glasses on a permanent basis; a cut-off point of ±0.50
15
diopters would make the prevalence of refractive error appear much higher in comparison
16
with this more conservative cut-off point. Myopia is rare at age 5 and increases steadily up
17
to age 25 when it reaches its maximum prevalence of 18% (in this study under this cut-off
18
point). Then myopia prevalence remains stable along adulthood up to age 70, when it
19
increases again. In the meantime hyperopia is very frequent (50%) at age 5 and decreases
20
steadily reaching a minimum (10%) at age 25, the same age when myopia reaches its
21
maximum prevalence (possibly the age at which axial elongation stops). From then on the
22
prevalence of hyperopia increases slowly during adult life, reaching a value of 50% at age
23
70, and from that age it decreases abruptly, by the same time as myopia prevalence
24
increases.
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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
3
from one category to the other. This is seen many times in the clinic. Hyperopic school
4
children become emmetropic during adolescence. Emmetropic children develop myopia
5
during school and university years. Emmetropic young adults develop hyperopia during
6
their 40-50’s and cataract patients in their 70’s lose their hyperopia or develop myopia.
7
(Duke-Elder & Abrams, 1970a; Saunders, 1984).
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2. The ocular biometric components.
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From a clinical perspective, refractive status is the key parameter, because clinical correction of refractive error, whether with glasses, contact lenses, refractive surgery, or
12
intraocular lenses, is the key to ensuring good visual acuity. However, from a biological
13
perspective, the ocular components of refraction, specifically corneal and lens power, as
14
well as anterior chamber depth, lens thickness and vitreous chamber depth are optically
15
more important, since it is the balance between these components which determines
16
refractive status. For most of this period, refractive status appears to be a passive player, but
17
early in development, refractive status does appear to act as a regulatory factor controlling
18
the rate of axial elongation in particular. For example, infantile high hyperopic eyes tend to
19
grow faster, such that this refractive error is compensated to some extent during the first
20
years of life (Saunders et al., 1995; Mutti et al., 2005).
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Since the first classical studies (Tron, 1940; Stenstrom, 1948; Sorsby et al., 1957;
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Sorsby et al., 1961; van Alphen, 1961; Sorsby & Leary, 1969; Sorsby, 1971), many studies
23
have examined the relationship between these biometric components and the refractive
24
status. All studies showed that the major biometric correlate/determinant of refractive status
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was axial length, and that increased axial length was the major cause of myopia. Where the
2
issue has been examined, the ratio of the axial length to the corneal radius of curvature was
3
found to correlate even more strongly with refractive status than with the axial length itself.
4
This is not hard to understand in principle, because while it is often stated that myopic eyes
5
are longer (and it is known that in the emmetropic range longer eyes have flatter corneas,
6
from Sorsby et al., 1957), strictly speaking, myopia results from an axial length that is
7
longer than the image plane for distant objects, which is set by the optical power of the
8
cornea and the lens. The axial length / corneal radius ratio correlates more strongly with
9
refractive status because it partially adjusts for corneal power (Grosvenor & Scott, 1994).
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The changes in refractive error prevalence seen in Figure 1 should be associated
11
with changes in the mentioned ocular components of refraction (mainly: corneal power,
12
crystalline lens power and axial length). The cornea has been shown to develop small
13
changes with ageing, mainly an against-the-rule change in astigmatism (Liu et al., 2001;
14
Gudmundsdottir et al., 2005), but maintains constant power for most subjects along life
15
(except for the uncommon progressive keratoconus cases). So the lens power and the axial
16
length should be responsible for the observed changes. Mainly we can say that growth in
17
axial length up to age 25-30 may be responsible for the development of myopia and for the
18
decreasing prevalence of hyperopia. From that age on, the changes in prevalence of
19
refractive error are surely driven by changes in the power of the lens (Iribarren et al., 2012b)
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3. Calculation of crystalline lens power. The crystalline lens power cannot be simply measured with a lensmeter since it is
23
inside the eye. The same accounts for corneal power: usually only its anterior radius is
24
measured, for example by a keratometer. The contribution of the posterior corneal power is
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assumed by an ideal index, which is calculated to obtain the power of the whole cornea only
2
with the measured anterior radius and that ideal index (Olsen, 1986). Recently, using
3
Scheimflug imaging it has been possible to measure the power of the whole cornea with the
4
anterior and posterior radii, showing that the ideal index should be even lower than that
5
calculated by Olsen (Dubbelman et al., 2005; Saad et al., 2013). Similarly, calculation of
6
the power of the lens inside the eye is not straightforward: its power must be obtained from
7
the other ocular components. Stenstrom’s formula based on refraction, keratometry, anterior
8
chamber depth and axial length calculated lens power as if it were a thin lens placed at its
9
anterior vertex. Later, intraocular lens power formulas were developed, but these also
10
calculate the lens as if it were a thin lens placed at an estimated postoperative anterior
11
chamber depth (effective lens position) (Olsen et al., 2007; Gordon & Donzis, 1985). By
12
the end of the 80’s, Bennett and Rabbetts presented an in vivo crystalline lens power
13
formula that, as Stenstrom’s, calculated lens power based on distance refraction, corneal
14
power, anterior chamber depth and axial length (Bennett & Rabbetts, 1989). This formula,
15
of which certain constants were recently revised (Rozema et al., 2011), can be used for
16
calculating mean values of crystalline lens power in case of studies with biometry
17
performed with the IOLMaster. When refraction, keratometry and A-Scan biometry or
18
LENSTAR are available, then another Bennett’s formula including lens thickness can be
19
used. (Bennett, 1988; Dunne et al., 1989; Rozema et al., 2011).
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Phakometric imaging of the crystalline lens in vivo has some problems (Mutti et al.,
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1992; Dubbelman & Van der Heijde, 2001; Rosales & Marcos, 2006). The Purkinje or
22
Scheimpflug images of the anterior lens curvature are magnified and distorted because they
23
are seen through the optics of the cornea. The posterior lens surface is distorted by both the
24
optics of the cornea and the lens structure itself. The lens itself has a complex gradient of
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refractive index which makes the problem even more challenging. This gradient of
2
refractive index is produced because the lens grows from the surface, sinking fibers in its
3
deeper layers, and the newly laid fibers have greater water content and lower refractive
4
index than the older ones. Thus a gradient of refractive index is produced, increasing from
5
the cortex to the center of the lens. This complex structure is generally solved by modeling
6
the lens as if it were a uniform thick lens, with an ―equivalent‖ or ―effective‖ index of
7
refraction equal to that necessary to explain the whole power of the lens. This equivalent
8
refractive index is greater than the peak index at the center of the lens, because the gradient
9
refractive index, regardless of its profile, makes the rays bend incrementally as they go
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through the changing multilayer structure of the lens, thus giving what is called an internal
11
power of the lens.
This gradient structure gives the lens another important property. Spherical lenses
13
with uniform index have positive spherical aberration, produced as rays in the peripheral
14
(equatorial) sections of the uniform lens bend more than those that go through the central
15
part of the lens. But gradient spherical lenses can elegantly compensate this aberration
16
because rays passing through the periphery are not bent as much because they pass through
17
progressively lower refractive index sections. This was clearly shown bending laser rays
18
through lenses in vitro for fish and mammals by Sivak in 1983 (Sivak & Kreuzer, 1983;
19
Sivak, 1985) and later by Jagger & Sands (1996). Figure 2 shows that the spherical fish lens
20
has no spherical aberration and that the laser rays are bent while passing through the lens
21
structure because of the gradual index change.
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The phakometric measurements of the lens posterior curvature have to be iteratively
23
corrected calculating an ideal equivalent index, in a recursive manner such that it agrees
24
with the measured refraction. With these recalculated lens curvatures, its thickness and the
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calculated equivalent index, the lens power can be also calculated using Gullstrand’s well
2
known thick lens formula to find the total lens power. This iterative method allows the
3
accurate calculation of the lens curvatures and the equivalent refractive index. So, this
4
phakometric method can be used when the objective is to calculate the equivalent index and
5
the lens curvatures, as has been done in monkeys and humans (Jones LA et al., 2005; Mutti
6
et al., 2005; Dubbelman & Van der Heijde, 2001; Qiao-Grider et al., 2007).
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When only biometric and refractive data are available, Bennett’s formula can be
8
used to calculate the lens power alone. Two recent papers have shown that there is good
9
agreement between phakometry and Bennett’s methods when the values of mean lens
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power are calculated in a given sample (Dunne et al., 1989; Rozema et al., 2011). In this
11
review, we have calculated lens power with Bennett’s method when data available in the
12
literature allowed this calculation and we have thus compared the data on lens power
13
obtained in different biometric studies along the lifespan.
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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
16
were homogeneous with the cortical index), and thus this surface power can be subtracted
17
from the total lens power to find the gradient refractive index power contribution. In this
18
way, the surface power was found to contribute to about half of total lens power (Borja et
19
al., 2010). The rest was due to the internal or gradient power of the lens. The problem with
20
this approach is that the cortex index has been measured in vitro and then calculated with
21
magnetic resonance studies in vitro and in vivo, with different studies giving different
22
results for this cortical index (Pierscionek & Chan, 1989; Moffat et al., 2002; Jones CE et
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al., 2005; Borja et al., 2010). So the calculation of the surface power is somewhat
24
inaccurate, but taken prospectively or with successive measurements under different
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accommodative demands, this calculation can show differences in the contribution of the
2
surface and internal powers of the lens both with age and accommodation (Borja et al.,
3
2010; Maceo et al., 2011). Using these approaches we calculated the lens power for a number of published
5
studies which included refraction and biometry, from preterm infants to adult years. We
6
used 1.3315 as the ideal index for corneal power in all cases (Olsen, 1986), for consistency
7
with our previous published data. These calculations give a picture of the change in lens
8
power along life.
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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 retinopathy) from birth to 5 months of age,
13
performing cycloplegic refractions. From the data in their published table (Cook et al.,
14
2003), the crystalline lens power was calculated using Bennett’s formula (Bennett, 1985).
15
Figure 3 shows how the lens power decreases steadily in premature infants from nearly 60
16
diopters at birth to 45 diopters by 5 months. Mutti et al. (2005) prospectively studied full
17
term infants at ages 3 and 9 months with cycloplegic refraction, biometry and phakometry,
18
calculating the crystalline power, and they give decreasing lens power values of 41.01 D
19
and 37.40 D for 3 and 9 months respectively (Figure 3). Figure 4 shows lens thickness in
20
both studies (premature and full term). In premature children the lens becomes thicker
21
during the first two months of life, and then begins to thin (Cook et al., 2003). In full term
22
infants the lens thins from 3 to 9 months (Mutti et al. 2005). Besides, the lens has been
23
reported to thin in schoolchildren from age 6 to 10 years (Larsen, 1971; Jones LA et al.,
24
2005; Shih et al., 2009; Wong et al., 2010)
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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
3
uniform index of refraction. While the lens thins and loses power, the Mutti et al. study of
4
full term infants reported that the calculated equivalent refractive index of those lenses
5
increased from 1.4526 to 1.4591 from 3 to 9 months (Mutti et al., 2005). Using similar
6
methods, Jones et al. (Jones LA et al., 2005) showed that, on the contrary, the lens
7
equivalent index decreased in school years (from age 6 to 14) while the lens consistently
8
thins and loses power. They also showed prospectively that the curvatures of the lens flatten
9
at these school ages, and they explained this loss of power by a scleral expansion theory in
10
which the lens thins by the forces of zonular traction induced by eye growth in the anterior
11
segment. This theory explained that as the lens thins, its curvatures flatten, and in
12
consequence, the lens power decreases (Zadnik et al., 1995; Mutti et al., 1998). These
13
authors also proposed, alternatively, that changing lens shape could modify the internal
14
gradient index structure, but did not explore further this idea.
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However, what remained unclear was the decrease in the equivalent refractive index
16
at a time when the actual peak index in the center of the lens is increasing (Augusteyn et al.,
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2008). Besides, that scleral expansion based theory cannot explain why the lens of
18
premature children becomes thicker in the first months of life, while it is steadily losing
19
power. Furthermore, why is the equivalent refractive index increasing in full term babies
20
while the lens loses power? Interestingly, a longitudinal study of the change in the ocular
21
components during growth in monkeys has also shown that the lens increases in thickness
22
and equivalent index during the first months of life, then changing these growth patterns in
23
the opposite direction with further growth, but consistently flattening curvatures and losing
24
power during both periods (Qiao-Grider et al., 2007).
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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
3
(Augusteyn, 2008, Review; Pierscionek & Regini, 2012, Review). As said, this is produced
4
by the apposition of new cortical fibers with greater water content than those that are
5
deeper, older, mature and full of protein content, or even deeper with less water, as they age
6
and become compacted in the center of the lens. This gradient of index increases the power
7
of the lens because rays going through the gradient are curved incrementally at each step.
8
Thus the total power of the lens is composed of the surface power given by its curvatures,
9
and an internal power given by its gradient index of refraction.
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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,
12
developing a central plateau with ageing. As the profile of the peripheral gradient becomes
13
more abrupt and the plateau develops, the gradient structure loses effective power. An in
14
vivo magnetic imaging study has shown that the profile of the peripheral gradient becomes
15
more abrupt with older age and smoother during accommodation in young subjects
16
(Kasthurirangan et al., 2008). These changes in the gradient had been shown previously in
17
in vitro studies and were related to the maintenance of emmetropia (Brown et al., 1999) or
18
even before to the changes in lens power leading to presbyopia (Pierscionek, 1990).
19
Changes in the gradient index have also been proposed as a cause of the hyperopic shifts
20
leading to the development of hyperopic refractive errors in ageing adults (Brown et al.,
21
1999; Moffat et al., 2002; Glasser & Campbell, 1988; Hashemi et al., 2010).
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One possible explanation for the loss of lens power during infant life is that the
23
profile of the peripheral refractive index gradient is becoming more abrupt with age. As the
24
peak index is becoming greater by fiber maturation and compaction, then the climbing
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index from the surface to the higher peak index in the center should have a more abrupt
2
profile (with less power) even more so if the lens axial thickness is decreasing, as a thinner
3
lens should also have a more abrupt profile to reach the same peak. Besides, the increase in
4
peak index could drive the equivalent index up, as has been found in infants (Mutti et al.,
5
2005), but the net change could be decreasing lens power produced both by flattening of
6
curvatures and changing gradient profile.
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5. Nicholas Brown and the lens paradox.
The idea that changes in the internal power of the lens could have importance in
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refractive error began to gain acceptance in the 70’s when Nicholas Brown described the
11
―lens paradox‖ consisting of an increment in lens thickness with a steepening of the surface
12
and internal curvatures of the ageing lens that would produce systematic myopia at adult
13
ages in which hyperopia and presbyopia are the norm (Brown, 1974; Koretz & Handelman,
14
1988; Brown et al., 1999). He introduced Scheimpflug photography in Ophthalmology to
15
study the lens, and soon discovered that the anterior lens surface was becoming steeper with
16
ageing, just the opposite to current thinking of those days (Brown, 1974). He also studied
17
eyes under accommodative effort and saw that older eyes at rest had steeper anterior lens
18
surfaces compared to younger accommodated eyes (Brown, 1973). Then, Koretz &
19
Handelman, studying his photographs with mathematical approaches, showed that the
20
steepening of the lens curvatures with ageing should be accompanied by changes inside the
21
lens. They suggested that the lens equivalent refractive index should be higher in younger
22
subjects in order that the eye could be maintained in focus according to differences in lens
23
shape (Koretz & Handelman, 1988).
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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
3
(Dubbelman & Van der Heijde, 2001). A lens with decreasing equivalent index would
4
maintain a constant power while its curvatures become steeper if both changes were
5
matched in ageing subjects (Brown et al., 1999), but in subjects who develop hyperopia, the
6
net change could be loss of power if the loss of gradient power is greater than the increase
7
in curvatures (Brown et al., 1999; Hashemi et al., 2010; Iribarren et al., 2012b).
8
Experimental studies on refractive development in animal models can provide information
9
on the underlying mechanisms, as we will see in the next section.
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6. The lens during early growth in chickens.
Interestingly, the lens also loses power in growing chicken eyes. A recent re-analysis
13
of the chick schematic eye model that was originally developed by Schaeffel & Howland in
14
1988 showed that Bennett’s equation could be used for calculation of lens power in chick
15
eyes (Iribarren et al., 2014a). As the original data included refraction, biometry and lens
16
radii measurements, the lens power and equivalent index could be calculated for growing
17
chicken eyes from age 10 to 90 days. While axial length increased in chicken eyes from 8 to
18
14 mm in this period, the cornea and the lens lost power accordingly, such that refractions
19
were maintained in the low hyperopic range. The lens thickness increased in chicken eyes
20
during this period, and as the lens possibly grew in all directions (axially and equatorially),
21
the curvatures flattened (Figure 5). In the meantime, the equivalent index decreased slowly
22
with age. Thus, with all these changes, the lens lost 30 diopters of power in these 80 days of
23
eye growth in chickens (Iribarren et al., 2014a)
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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
3
the total lens power is calculated, based on Gullstrand’s thick lens equation, from its radii
4
of curvature, thickness and equivalent refractive index, while for the surface power the
5
cortical refractive index is used. The cortex index is lower than the equivalent index, as the
6
cortex consists of new fibers with higher water content and a lower refractive index. The
7
cortical refractive index has been measured in vitro in chicken lenses by Sivak and
8
Mandelman (1982), giving a value of 1.374. Following Borja et al. (2008), we then derived
9
the gradient power as the total Gullstrand thick lens power (calculated with the equivalent
10
refractive index found for chick schematic eyes equal to 1.4502 for day 15 and 1.4409 for
11
day 90) minus the surface power (calculated using 1.374 as the cortical refractive index).
12
Table 1 shows the change in total lens power, surface lens power and gradient lens
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power in the period from 15 to 80 days. It can be seen that both surface and internal power
14
change with age in chicken eyes. As said, the total lens power decreases by some 30
15
diopters, of which 20 diopters are accounted for by changes in the internal power, so the
16
change in gradient power accounts for about 70% of the total change in power. Figure 5
17
shows the front and back curvatures of the 15 day old chick lens (inner lines) inside the 80
18
day old lens (outer lines). The increase in axial thickness and the flattening of the
19
curvatures can be seen as the lens expands in all directions by growth of new layers of
20
fibers. The equator was not drawn since lens surfaces are not spherical (and we only had
21
front and back surface lens radii for the schematic drawings).
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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.
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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 LA et al., 2005; Mutti et al., 2005; Shih et al., 2009;
4
Wong et al., 2010) the literature shows less data on lens equatorial diameter growth as the
5
lens equator is not visible in vivo by slit lamp observation because it is behind the iris, even
6
after pupil dilation. Augusteyn (2010) has recently reviewed the data of lens equatorial
7
growth. Duke-Elder (1961) gave values for in vitro measurements of 6.5mm for newborns,
8
7.5mm at the end of the first year, and 8.2 mm by 2-3 years. Similar in vitro values were
9
presented by Augusteyn et al. at the ARVO meeting (Augusteyn et al., 2012) showing that
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the main growth of lens equatorial diameter is achieved during the first two years of life
11
(see also Brown & Bron, 1996). Adult values are around 9 mm, increasing slightly and very
12
slowly with ageing (Augusteyn, 2010, Review). These in vitro data have the problem that
13
the lens is fully accommodated when free of zonular tension, especially in children’s lenses.
14
This would make the equatorial diameter in a 20-40 year lens about 0.6 mm shorter
15
according to in vivo data obtained by Strenk with magnetic resonance images (Strenk et al.,
16
1999, calculated from their data with lenses younger than 40). This difference between in
17
vivo and in vitro measurements could be more pronounced in infant lenses, which have
18
more spherical shape, capable of many diopters of accommodation. So these in vitro
19
measurements in infant lenses are possibly biased as if they were smaller. It is very possible
20
that the lens equatorial diameter increases in babies while the anterior segment is growing
21
steadily during the first months of life. A recent magnetic resonance image study (Ishii et
22
al., 2013) involving 26 children aged 1month to 6 years, showed that the lens equatorial
23
diameter in children under general anesthesia (tonic resting accommodation) increased
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steadily after birth reaching a value of 8 mm in by age 3. Thus, 90% of lens equatorial
2
diameter growth is achieved in the first 2-3 years of life.
3
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
5
growing as much in equatorial diameter as in axial thickness, as may be the case in the first
6
months of life in premature infants, then the decrease in curvature of the anterior surface
7
would be much less (the lens would maintain a constant shape while it thickens in the first
8
two months). But it is still steadily losing power as we have shown (Figure 3). This also
9
happens in growing chicken eyes, where the lens grows both in axial and equatorial
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diameter, flattens curvatures, and also loses power (Iribarren et al., 2014a, Figure 5). Then,
11
ellipsoidal lenses with flat front surfaces can flatten anterior curvature as they thin or as
12
they grow, depending on the change in lens shape.
The changes in the lens are rather complex, especially in infants who have very
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powerful lenses, with a more rounded shape, and possibly, with a newly developed very
15
smooth climbing gradient profile. The actual index of refraction is given by the
16
concentration of the crystalline proteins within the fibers’ cytoplasm, and this concentration
17
is a function of the amount of fiber differentiation and compaction. Fiber differentiation is
18
rapidly established in such a manner that even embryonic lenses have a gradient in a few
19
weeks (Peetermans et al., 1987). On the other hand, compaction, demonstrated originally by
20
Brown in adult lenses with cortical cataracts (Brown, 1976), is a process that takes years to
21
develop. It is well known that after birth there are changes in the synthesis of the different
22
crystalline proteins that compose the lens, such that the fetal nucleus (that part of the lens
23
formed prenatally) has no content of gamma crystallin (Augusteyn, 2007). It is possible that
24
the different types of crystallines have different time constants for losing water and
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compacting (Augusteyn et al., 2008). It is also known that the rate of synthesis of new
2
layers decreases drastically after birth (Augusteyn, 2007). Proof of this is the fact that the
3
lens develops approximately 4.0 mm axial thickness during prenatal life in only 8 months,
4
and then only 1.5 mm more from birth to senescence (Brown & Bron, 1996).
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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
7
nucleus during the following years after birth, probably beginning from the older fibers in
8
the center. But one has to consider that those fibers were laid in a few months during
9
gestation and they may be compacting at a relatively uniform rate during the first years after
10
birth. Evidence of this compaction is given in the Mutti et al. (2005) study in babies which
11
shows an increase in equivalent refractive index from 3 to 9 months of age. That would
12
increase the power of the lens, but as the lens at this time is losing much power, we propose
13
that both surface and internal powers are changing. Mutti et al. (2005) have demonstrated
14
that the anterior lens curvature flattens during development in babies. We propose that the
15
gradient index power is decreasing by compaction of the nucleus with a more abrupt
16
climbing gradient profile (before the adult index plateau is developed). Furthermore,
17
compaction inside the nucleus, with a slow rate of addition of new fibers in the newly
18
developed cortex after birth could also explain the lens thinning in the first 10 years of life
19
(Brown & Bron, 1996).
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The 6 year old lens studied in vitro in the Augusteyn et al. (2008) paper (Figure 6A
21
& B) has not yet achieved the peak index found in adult years, so it is probable that
22
compaction of the nuclear fibers is still not finished by age 6. As the cortex grows at a very
23
slow rate compared to the prenatal growth of the nucleus, one would expect lens thinning
24
until the rate of compaction in the nucleus equals the rate of growth in the newly developed
16
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cortex. The idea that lens cortical growth was balanced by nuclear compaction during
2
childhood was originally proposed by Nicholas Brown, who had studied prospectively the
3
lens in a few subjects with congenital lamellar cataracts, finding that children had
4
compaction in the nucleus, and that this compaction declined its rate with ageing (Brown et
5
al., 1988). He suggested that lens growth was due to a balance between epithelial growth
6
and fiber compaction, and that the nucleus became compacted up to age 30, and afterwards,
7
only the deep cortex became compacted for the rest of life. This was also discussed by other
8
members of his team (Cook et al., 1994) and during the presentation of Scheimpflug data in
9
normal growing children by Forbes et al. (1992).
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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
12
as can be seen in the Augusteyn in vitro lenses (Figures 6A & B, Augusteyn et al., 2008),
13
then the lens should lose internal power, explaining the loss of power that has been shown
14
in the different studies. In fact, the gradient index in Figures 6A & B is smoother in the
15
child lens compared to the abrupt climbing profile with a plateau of index developed in the
16
center of adult lenses. It is noted that the plateau section has no gradient (less power). The
17
schematic drawing of figure 6 C shows how a thinner lens has a more abrupt climbing
18
gradient index profile that reaches a higher peak index, as may be happening while the lens
19
thins and compacts from birth to school age, losing internal power (before the central
20
plateau is developed).
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8. Anterior segment growth.
23 24
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
17
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diameter (Ronneburger et al., 2006; Lagrèze & Zobor, 2007) and by the anterior segment
2
distance from the corneal apex to the posterior pole of the lens (anterior segment length)
3
(Larsen, 1971; Dubbelman et al., 2001; Koretz et al., 2004). It is well known that white to
4
white diameter reaches adult values during the first year of life and that the corneal power
5
also reaches adult values by age 1-2 (Gordon & Donzis, 1985; Ronneburger et al., 2006;
6
Inagaki, 1986). It looks like the cornea does not change much in diameter and power after
7
year 2.
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The anterior segment length up to the lens posterior pole has been calculated from
9
the data of Cook et al. (2003) and Mutti et al. (2005) (Figure 7) (adding anterior chamber
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depth + lens thickness). In full term and premature babies the anterior chamber grows
11
during the first months, while the lens thickness fluctuates, increasing in prematures during
12
months 1-3 and decreasing in full term babies from months 3-9. Yet the anterior segment
13
length increases steadily as shown in Figure 7, almost reaching adult values of 7-7.5 mm by
14
the end of year 1 (Koretz et al., 2004; Dubbelman et al., 2001; Larsen, 1971). In the follow
15
up of emmetropic children, Zadniks’s data (Zadnik et al., 2004) show little change in
16
anterior segment length at the time of lens thinning between ages 6 to 10 (Table 2), showing
17
that the anterior chamber deepening at these ages is a consequence of lens thinning and not
18
merely growth of the anterior segment. This was originally shown by Larsen (1971) who
19
stated that the anterior segment length growth ―stagnated by age 2-3 years‖.
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At ARVO 2013, Bailey et al. presented cross sectional data obtained with Visante
21
images showing that the ―anterior segment chord‖ located behind the iris, from sclera to
22
sclera, did not change with age in schoolchildren (Bailey et al., 2013). So we think that the
23
anterior segment growth is completed in the first year or two of life with no further change
24
in dimensions after this age, but with internal and external changes in the lens. It is also
18
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1
difficult to explain the scleral expansion theory (Zadnik et al., 1995; Mutti et al., 1998) if
2
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
4
in Figure 8, using the mean anterior and posterior curvatures and the mean lens thickness
5
for the lens at rest given in Mutti’s and Zadnik’s papers (Mutti et al., 1998, 2005). These
6
curvature radii were drawn spherical although it is known that the real lens has aspheric
7
curvatures and thus should have even greater equatorial diameter, so these data may be
8
negatively biased. The rounded edges at the equator were drawn following the
9
shadowgraphs of in vitro lenses (Borja et al., 2010). From these drawings the lens
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equatorial diameter was estimated to be 7.44 mm for the three month old babies’ lens, 7.99
11
mm for the 9 month old babies and 8.82 mm for the 14 year old lens in schoolchildren.
12
With the same data (Mutti et al., 2005) and the formula given by Rozema et al. (2012), the
13
lens diameter is estimated to be 7.38 mm in 9 month babies and 7.77 mm in 9 month
14
babies. These measurements may be biased by the method used, but they show that the lens
15
at rest (under cycloplegia) reaches equatorial diameter values similar to the 9 mm adult lens
16
very early in life. The same holds for the other described parameters of the anterior segment
17
of the eye.
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9. Change in lens shape during childhood. How can the lens change from a rounded ellipsoidal shape in babies to a flatter one
21
in adolescence? This change can be seen in Figure 9, comparing a 3 month lens with a 14
22
year old lens (based on Mutti’s and Zadnik’s published data of curvature and thickness,
23
Mutti et al., 1998, 2005; Zadnik et al., 1995). The internal structure and the growth of the
24
lens can give the clues for this change. As said, the nucleus of children has been shown to
19
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be compacted during school years according to Brown’s Scheimpflug images during the
2
follow up of children with lamellar cataracts (Brown et al., 1988) and by similar cross-
3
sectional measurement of nuclear thickness in a sample of 50 children aged 3 to 20 years
4
(Forbes, 1992).
5
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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
7
while their protein content is losing water. As the fibers in the embryonic and fetal nucleus
8
are oriented following the antero-posterior axis (Al-Ghoul et al., 2001), their folding and
9
compaction could possibly decrease the antero-posterior axis more than the equatorial
10
diameter (Augusteyn, 2010 review). The cortical fibers are progressively oriented in a
11
circular manner. These differences could make the lens thinner on its axis, and then its
12
ellipsoidal shape would become flatter by the antero-posterior poles. Notice that the profile
13
of the 6 year old lens (grey dots in Figure 6 B) has achieved a plateau in the axial view at
14
this early age, but has no plateau in the equatorial view (Figure 6 A). As the plateau is
15
developed when fibers reach a uniform compaction, it seems that this compaction is
16
developed earlier in the antero-posterior axis, along with lens axial thinning. But the
17
equatorial growth does not seem to be accompanied by similar rates of compaction. The
18
compaction of the older central fibers could shorten the axis if fiber shortening is relatively
19
greater than the decrease in fiber diameter.
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The other way in which the lens becomes more elliptical depends on the fact that the
21
equatorial growth of the lens epithelium develops fibers that elongate from the equator to
22
the anterior and posterior poles up to the sutures, becoming thinner as they migrate
23
elongating centripetally searching for the sutures (Al-Ghoul et al., 2003). In other words,
20
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1
elongating fibers are thicker at the equator than at the antero-posterior poles. This fact can
2
also make the lens grow more in the equatorial diameter than in its antero-posterior axis.
3
During adult years, from ages 20-80, the lens grows in another manner (Augusteyn, 2010). An in vitro study had shown that the lens increased both axial thickness and
5
equatorial diameter at similar rates (0.49 mm and 0.55 mm respectively) in 40 years of adult
6
life (Rosen et al., 2006) maintaining a constant aspect ratio (Augusteyn, 2010). More recent
7
very accurate in vitro measurements have shown that the aspect ratio (thickness / diameter)
8
increases with age (Mohamed et al., 2012). So in this new study the axial thickness
9
increased with age more than the equatorial diameter (0.75 vs. 0.51 slope, respectively).
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10
This would make sense if the anterior lens curvature is steepening with age (as was
11
described by Nicholas Brown in 1974), because if the lens grew equally in all directions, the
12
anterior curvature would flatten as happens in growing chicken eyes (Figure 5). This slow rate of equatorial growth contrasts with the 0.50 mm in 6 months taken
14
from the difference in our calculated equatorial diameter between 3 and 9 month babies’
15
lenses (Figure 8). There is no doubt that the lens has a high rate of equatorial growth during
16
the first year of life, at the same time in which corneal diameter and anterior segment length
17
have high rates of growth.
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The process of metamorphosis in amphibians like toads and frogs is a good example
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of the change in shape of the lens during early growth. In general, fish have spherical
20
lenses, and terrestrial animals have ellipsoidal lenses. During the metamorphosis of the
21
anuran Pelobates Syriacus the lenses of the aquatic form change from a spherical shape to a
22
flattened lens in the juvenile terrestrial form (Sivak et al., 1983). The same happens in
23
tadpoles when they become terrestrial toads (Mathis et al., 1988). In 1985 Sivak et al.
24
presented data about the change in shape during metamorphosis of different species of
21
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amphibians and their histological studies showed that the changes in lens shape were
2
brought about by a rapid increase of the mitotic activity of equatorial epithelial cells at
3
critical periods during metamorphosis. If a similar process occurs in the human lens, it may
4
be simple to explain that the lens changes shape between birth and adolescence by
5
differential growth and compaction of its internal structure (Figure 9). In fact, the human
6
lens during embryonic life is spherical as the fish lens, and it becomes more and more
7
ellipsoidal by growth of the equatorial fibers during late fetal life (Cook et al., 2006). So it
8
seems probable that this pattern of lens growth is also followed during the first years of
9
infant life in humans.
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10 11
10. The anterior segment in premature children.
The growth of the anterior chamber in premature children is interesting. These small
13
eyes of premature infants have shallower anterior chambers, thicker lenses, smaller anterior
14
segment lengths, more steeply curved corneas and more powerful lenses at 3 months than
15
do full-term infants of the same age (Cook et al., 2003, and Figures 3, 4 and 7). Some of the
16
eyes of premature infants develop retinopathy as was seen, for example, in the study of the
17
ocular components of a series of 108 premature children who were studied at age 7-9 in
18
Taiwan (Chen et al., 2010). In all, 44% of these premature children had developed some
19
form of retinopathy, 25% received laser treatment because of advanced retinopathy and
20
47% of these 108 children had myopia at ages 7-9 years. We have calculated the lens power
21
for these schoolchildren in Table 3, where it can be seen that prematures have a
22
combination of thicker and more powerful lenses at rest when compared to same age
23
normal term emmetropic children (Chen et al., 2010; Jones et al., 2005). While these
24
findings might be due to laser induced growth abnormalities at the peripheral retina (Chen
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et al., 2010), these could also be explained by visual or light induced control of anterior
2
segment growth. These eyes at birth are smaller than those of full term infants by about
3
2mm, and have smaller anterior segments, so exposure to light could delay anterior segment
4
growth and leave eyes with somehow immature anterior segments, with steep corneas, and
5
thicker and more powerful lenses by age 2-3 when the anterior segment growth reaches a
6
plateau. Myopia of prematurity looks different from common school myopia, in which axial
7
length is longer than usual, and the lens is thinner with lower power (just the opposite), as
8
will be seen in the next section.
10
11. The lens power in school years.
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Three recent prospective studies have reported on the loss of lens power in
12
schoolchildren. These are the Orinda Study (and its extension, the CLEERE study) (Jones
13
LA et al., 2005; Twelker et al., 2009), the SCORM Study (Wong et al., 2010; Iribarren et
14
al., 2012a) and a study involving Chinese myopic twins in Guangzhou (Xiang et al., 2012).
15
The Orinda and CLEERE studies included phakometry, so the lens equivalent refractive
16
index could be estimated and, as said, was shown to decrease with age in schoolchildren.
17
The power of the lens also decreased in all refractive groups in a similar manner from ages
18
6 to 14 in this study. As we have also said, decreasing effective index accompanied by a
19
decrease in power in lenses that must be compacting their fibers (thus increasing refractive
20
index by increasing protein concentration) can only be explained by changes in the
21
refractive index gradient profile.
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Myopic children had lower lens power and hyperopes had higher lens power than
23
emmetropes at follow up in the mentioned Orinda study (Jones LA et al., 2005). The lens
24
power loss prospectively matched the axial growth (still present at these school years) in the
23
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children who remained emmetropic (Jones LA et al., 2005; Zadnik et al., 2004). From the
2
figures of the Orinda paper (Jones LA et al., 2005) we can see that emmetropic eyes grew
3
about 1 mm after age 6 in the 10 years of follow up (approximately +0.10mm per year rate),
4
and that the power of the lens fell from 26 to 23 diopters in the same period (–0.30 diopters
5
per year rate), compensating for axial growth. In children who became myopic, the axial
6
growth was greater than that of emmetropes, about 2 mm on average in the same period
7
(+0.20mm per year rate), and as the lens lost power from 25.5 to 22 diopters (–0.35 diopters
8
per year rate), the net change in mean refraction was –3 diopters of myopic shift after the
9
follow up in the myopic group. We can also see in this paper that the lens thinned in all
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refractive groups up to age 10 and then slowly began to thicken again. Hyperopic eyes had
11
thicker lenses and myopic eyes began with the same lens thickness as the emmetropes but
12
ended with lower lens thickness at the follow up. It is noted that 76.1% of myopic subjects
13
in this study had their onset during the follow up, so most of them began the study being
14
emmetropes (Jones LA et al., 2005).
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If myopic eyes have lower lens power than emmetropes, and myopes come from previous emmetropes, emmetropic eyes developing myopia must have lost greater amounts
17
of lens power at some time point. The SCORM study in a Singaporean sample of
18
schoolchildren had a high prevalence of myopic children (Wong et al., 2010). So the study
19
could show a difference between persistent myopes (those already myopic at baseline) and
20
newly developed myopes (those developing myopia during the follow up, as most Orinda
21
myopic subjects). In this last study, persistent myopic eyes had lower lens power (and they
22
also had thinner lenses) than emmetropes. And here, newly developed myopes showed a
23
greater rate of decrease in lens power and in lens thickness than emmetropes or persistent
24
myopes (Iribarren et al., 2012a). This study then showed increased lens power loss at the
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time when the rate of axial elongation was also increased during myopia onset. When
2
Sorsby found negative correlations between axial length and the power of refractive
3
surfaces (cornea and lens) he postulated that the retina was an organizer of the coordinated
4
growth of the ocular components (Sorsby et al., 1957).
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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
7
consistent finding of lower lens thickness in myopic eyes could be due to a lower rate of
8
growth of the lens epithelial layer, mediated by humoral factors from the retina. Fibroblast
9
growth factor (FGF) is present in the retina and the vitreous adjacent to the lens, and is the
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principal factor inducing lens epithelial growth (Lovicu & McAvoy, 2005). As the lens
11
grows by apposition of new fibers with low index, and as the older deeper fibers mature and
12
are compacted gaining refractive index, the gradient refractive index (responsible for about
13
half of the lens power) may be maintained with a constant shape of its profile. But if the
14
growth rate slowly decreases with time and the compaction rate is maintained constant, then
15
the smoothness in the climbing gradient profile would be gradually lost according to that
16
decreasing rate of epithelial growth, and thus the lens power at rest would decrease
17
accordingly. So we postulate that a relative decrease in the rate of lens growth ends up in
18
myopic eyes with thinner and less powerful lenses than those of emmetropic eyes.
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A careful inspection of the data in Figure 4A of CLEERE study (see Mutti et al.,
20
2012) shows how the rate of lens power loss declines in myopes after myopia onset when
21
compared to emmetropes, and it also shows that before onset, myopes show an increased
22
rate of lens power loss compared to emmetropes (when looking at the unadjusted data).
23
This is concordant with a greater rate of power loss calculated for Orinda myopic subjects
24
when compared to emmetropic subjects in the previous paragraphs (-0.35 vs. -0.30 diopters
25
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per year, respectively). This is similar to what was found in SCORM newly developed
2
myopes, which showed a greater rate of lens power loss in children who developed myopia
3
during the study when compared to those who remained emmetropic (-0.36 vs. –0.29
4
diopters per years, respectively, Iribarren et al., 2012a).
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Myopia may then develop when the rate of axial growth is so rapid that it outgrows
6
the possibility of the lens to compensate that axial growth by further power loss. The study
7
of lens power change before and after myopia onset in CLEERE Study (Mutti et al., 2012)
8
found that myopia onset was ―characterized by an abrupt loss of compensatory changes in
9
the crystalline lens‖. Although this last finding should be confirmed in future studies, it is
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interesting that axial growth can increase the rate of the eye’s axial elongation by
11
myopigenic retinal signals during school years without any end point. But, on the other
12
hand, the lens might increase the rate of power loss until the shape of the gradient refractive
13
index profile approaches a relatively maximal abrupt climbing profile. The equatorial
14
growth and axial compaction that produces the described changes in lens shape during
15
childhood (with lens thinning and curvature flattening) might also have a relative end point
16
because nuclear compaction may also have a limit, showing another possible limitation for
17
the compensation of myopia acquired at the time of an increased rate of axial elongation.
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Recent studies with lenses in vitro have shown that the power of the refractive index
19
gradient changes with age and with accommodation (Borja et al., 2010; Maceo et al., 2011).
20
These studies could accurately measure the power of the isolated lens in vitro (an
21
impossible measurement with the lens inside the eye), and have calculated the relative
22
contributions of the internal and surface powers. This was done by calculating the surface
23
power with the in vitro measured curvatures, and by attributing an index to the first layers
24
of the cortex under the capsule, thus showing what the power of an homogeneous lens
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would be (without the gradient) with the given surface curvatures and the cortical index.
2
Then, subtracting the surface power from the total power, the gradient contribution could be
3
calculated. Using the well known Gullstrand’s equation for calculation of the power of a
4
thick lens (Mutti et al., 1998), and assuming an index for the cortex of 1.3709 (Jones CE et
5
al., 2005; Borja et al., 2008; Borja et al., 2010) we calculated the relative contributions of
6
the surface and internal powers for the data of Mutti et al. (2005) and Mutti et al. (1998) in
7
babies and schoolchildren respectively (Table 4). These studies showed that the anterior and
8
posterior lens curvatures flattened with age in babies and children as the lens thinned, but
9
from the data in Table 4 we can see that this change in curvature accounts for only half of
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the power loss. The relative contribution of the internal power given by the possible change
11
in the gradient is responsible for the other half of the lens power loss in growing children.
12
Then, it is possible that changes in the refractive index gradient profile within the lens are
13
an important cause of lens power loss during school years. And this internal power loss
14
could be responsible for the differences in lens power described among refractive groups in
15
schoolchildren. There is no doubt that a thicker or thinner lens can have different surface
16
curvatures and differences in the internal gradient index profile (Figures 6C and 9).
19
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12. Theories for lens thinning during childhood.
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Sorsby (Sorsby et al., 1957) proposed a coordinated growth of the components of
20
refraction (mainly axial length with corneal and lens powers) to explain the tendency to
21
produce emmetropic eyes in which differences in axial length were compensated by corneal
22
and lens power. He clearly showed that in the emmetropic range, longer eyes had flatter
23
corneas and less powerful lenses (and vice versa) (Sorsby et al., 1957). Then, van Alphen
24
(van Alphen, 1961) proposed a model for eye growth that comprised passive and active
27
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factors including a stretch factor. These ideas were further discussed by Hofstetter (1969)
2
(who showed passive mechanisms in emmetropization) and later by Dunne (1993) (who
3
proposed mathematical models of ocular growth). Weale (Weale, 1982) then proposed that
4
the lens changed shape during the first years of life because of a redistribution of volume
5
produced by zonular tension during eye growth. These ideas were further explored by Mutti
6
& Zadnik (Zadnik et al., 1995; Mutti et al., 1998) after their first longitudinal study of lens
7
thinning in children, when they proposed a theory for lens thinning based on zonular
8
traction mediated by ciliary muscle tension. In this last theory, lens thinning and lens power
9
loss were modified in myopic children by a restriction in scleral expansion during eye
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growth. By the same time, Brown & Bron (Brown & Bron, 1996) in their book called ―Lens
11
Disorders‖ made reference to Weale’s zonular traction theory when explaining lens shape
12
changes during school years. They argued that there was little anterior segment growth after
13
age 2 in children (from the available measurements of corneal diameter), and that slit
14
Scheimpflug images of children eyes showed that although lens axial thickness was
15
relatively stationary over childhood, there was vigorous cortical growth accompanied by a
16
reduction in the dimension of the nucleus (this last produced by compaction). In the present
17
review we follow this latter idea about the causes of lens thinning during childhood, further
18
proposing that the redistribution of the gradient index structure within the lens contributes
19
to the loss of lens power. A recent clinical trial designed to evaluate theories of myopia
20
progression concluded that the mechanical tension theory based on zonular traction was not
21
consistent with the findings of the study (Berntsen et al., 2012) so it is possible that
22
Brown’s observations about nuclear compaction in children lenses are the cause of lens
23
thinning.
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1 2
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
4
axial growth, and vice versa, images falling in front of the retina (myopic defocus) can
5
down-regulate the rate of axial growth (Wallman & Winawer, 2004). Low outdoor
6
exposure to natural ambient light probably produces an acceleration of axial growth by the
7
down-regulation of retinal dopamine activity (French et al., 2013). Myopic children have
8
been shown in CLEERE study to be exposed to significantly less time outdoors than their
9
emmetropic peers up to three years before myopia onset (Jones-Jordan et al., 2011). In three
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different studies, the rate of refractive change towards myopia and the rate of axial
11
elongation have been shown to be accelerated at the years around the onset (Thorn et al.,
12
2005; Mutti et al., 2007; Xiang et al., 2012). Then, one could argue that low outdoor
13
exposure seems to be accompanied by a higher rate of axial elongation in future myopic
14
children. Although the lens could compensate for this accelerated growth with an
15
accelerated rate of power loss (Iribarren et al., 2012a), myopia can be rapidly developed
16
once the lens reaches its described limit in power loss because of its internal structure. At
17
that time, any further axial elongation would be translated into a myopic shift. But once
18
myopia is established, the myopic eye is subject to myopic defocus for some periods each
19
day when spectacles are not used. Short periods of myopic defocus have been shown to
20
have a potent inhibitory effect on ocular growth in animal models (Wallman & Winawer,
21
2004). And it has been suggested that this myopic defocus could slow down the rate of axial
22
elongation once myopia is established (Xiang et al., 2012).
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More prospective studies about myopia onset following the changes in ocular
24
components during school years are needed to confirm these findings, and special attention
29
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should be paid to lens changes, because one mentioned study has shown that lens power
2
loss ―stops‖ around myopia onset (Mutti et al., 2012) and another has shown no change in
3
the rate of power loss at that time (Xiang et al., 2012). Further, it is difficult to understand
4
the ―stop‖ in lens power loss after myopia onset (Mutti et al., 2012) if Singaporean SCORM
5
persistent myopic children show consistently lens power loss after onset during the years of
6
progression (Iribarren et al., 2012a). As these studies in myopic children have been
7
performed at a mean age of onset around 10 years, the age at which the lens stops thinning
8
and reduces its rate of power loss, the finding of reduced power loss after myopia onset
9
could be an age effect. One alternative possibility is that after the lens increases its rate of
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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,
13
because the development of a refractive index plateau in the center of the lens further
14
changes the gradient profile and makes the lens lose power during adult years (Augusteyn et
15
al., 2008 and Figure 6A & B).
18
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14. The lens power loss during university study years. The mentioned SCORM study in Chinese Singaporean school children showed rates
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of axial length change of +0.10mm per year in emmetropes, and +0.28mm per year in
20
myopic eyes, with a change in lens power of –0.29 diopters per year in emmetropes, –0.36
21
diopters per year in newly developed myopes and –0.25 diopters per year in persistent
22
myopes (Iribarren et al., 2012a). A prospective study of engineering students in Norway
23
(Kinge et al., 1999) showed that during the three-year follow up, the group of 149 students
24
had a myopic shift in refraction from age 20 to 23 years. The lens power was calculated
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from the biometry and the cycloplegic refractions in that study (Iribarren et al., 2014b, in
2
press), showing that the initially emmetropic engineering students had a rate of axial length
3
growth of +0.39mm in three years, that is, +0.13mm per year, similar to that of emmetropic
4
children in SCORM or Orinda studies. And these engineering students had a rate of lens
5
power loss of –0.70 diopters in three years, that is, –0.23 diopters per year, similar to the
6
loss of lens power in Singaporean children. This compares well to the non-cycloplegic
7
calculations that gave a loss in lens power of –0.40 diopters in 3 years for emmetropic
8
young subjects followed by Grosvenor (–0.13 diopters per year) (Grosvenor & Scott, 1993).
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These few studies have then shown that the lens is still compensating, in part, for
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axial elongation during early adult years. This happens at a time when the lens is increasing
11
in axial thickness and possibly steepening curvatures (very different from the times of lens
12
thinning and flattening in schoolchildren up to age 10), so here again variations in the
13
gradient index structure may be driving the changes seen. It would be interesting to have
14
longitudinal cycloplegic studies with biometry in selected adult populations prone to
15
develop myopia (like engineering or law students) to confirm these findings about lens
16
power loss during early adulthood. If phacometry could be performed, then the equivalent
17
index could be calculated, perhaps showing a prospective decrease with age as was shown
18
in the Orinda and CLEERE studies.
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15. The lens in adulthood. We have seen that myopic children have lower lens power than emmetropic
22
children, and hyperopic children have higher lens power than their emmetropic peers. This
23
would produce a positive correlation between refraction and lens power, as higher spherical
24
equivalents have higher lens power and vice versa (Iribarren et al., 2012a). This would be in
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agreement with the fact that longer eyes, usually the myopic ones, have lower lens power,
2
and vice versa, shorter eyes have higher lens power. This can be seen in the negative
3
correlation between axial length and lens power, originally described by Sorsby and also
4
seen in the Sydney Myopia Study (Ip et al., 2007) or SCORM studies (Iribarren et al.,
5
2012a).
6
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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
8
reported a conflicting finding. In fact, lens power was negatively correlated with axial
9
length as it was known long ago (Sorsby et al., 1957) but lens power was also negatively
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correlated with refraction, assuming that myopic eyes had higher lens powers or vice versa,
11
hyperopic eyes lower lens power. Olsen et al. (2007) discussed these findings explaining
12
that refraction was in fact determined by a complex interplay between all the ocular
13
components. Indeed, the relations between the ocular components should be changing from
14
childhood to adulthood if the correlation between lens power and refraction is changing
15
from positive to negative.
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Figure 1 gives the clues for what is happening. From age 20 until age 75, the
17
prevalence of cycloplegic hyperopia greater than +1 diopter increases from 10% to 50%. At
18
these ages corneal power has been shown to be stable as is probably also the case for axial
19
length. In any way, eyes could not become shorter to explain this hyperopic shift in
20
refraction because in that case pseudophaquic eyes should have hyperopic shifts with
21
ageing in the clinic and that does not seem to happen (author’s clinical observation and
22
Brown et al., 1999). What indeed may be happening is that the lens is losing power in some
23
emmetropic subjects who develop hyperopic shifts and become hyperopes (Hashemi et al.,
24
2010). Then, by age 70, the 50% prevalence of hyperopes may be a mixture of 10% who
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were hyperopes since childhood (with high lens power) and of 40% of newly developed
2
hyperopes that may have come from the emmetropes who may have lost lens power. Then,
3
this number of hyperopes with low lens power would change the correlation between
4
refraction and lens power to a negative one (in adults aged 70) as has been found in
5
Reykjavik (Olsen et al., 2007) and later in the Los Angeles Latino Eye Study (Iribarren et
6
al., 2010) and the Central India Eye and Medical Study (CIEMS) (Iribarren et al., 2012b). In
7
these last two studies, in fact, adult hyperopes without cataract had significantly lower lens
8
power than the emmetropes, the opposite of what is found in school-aged children. This can
9
be seen in Figure 10 with data published in CIEMS Study (Iribarren et al., 2012b) where
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hyperopes with low amount of nuclear opacity have lower lens power than emmetropes or
11
myopes. This is probably produced by loss of lens power in many emmetropic eyes that turn
12
to be hyperopic with ageing. This last study also showed a significant negative correlation
13
between refractive error and lens power (Figure 11).
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The amount of lens power loss with age during adult years can be calculated
15
indirectly from a prospective population based study like the Beaver Dam Study (Lee et al.,
16
2002), which showed that subjects aged 43-59 at baseline had an hyperopic shift of +0.54
17
diopters in the 10 years follow up. If all the other ocular components are left unchanged, the
18
lens changes power by about –1.5 diopters per +1 diopter change in refraction (Wolfgang
19
Haigis, personal communication). Although those were not cycloplegic refractions and
20
could be biased, such hyperopic shift would represent –0.81 diopters of lens power change
21
in 10 years, or –0.081 diopters loss per year. This rate of lens power loss is lower (about
22
one third) than that calculated for young engineering students (–0.23 diopters per year)
23
(Iribarren et al., 2014b, in press) or that of Singaporean schoolchildren (–0.29 diopters per
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year) (Iribarren et al., 2012a) so the lens seems to lose power at a very slow rate during
2
adult years. As has been explained when speaking of children lenses, a lens which is increasing
4
in thickness and curvatures during adulthood can only lose power by changing its gradient
5
index profile. As we have also said, the maintenance of the refractive index gradient profile
6
could only be achieved if the rate of compaction equals the rate of apposition of new fibers.
7
An early study in rats has shown that the lens epithelial cells, with increasing age, show less
8
growth and differentiation under similar concentrations of FGF (Lovicu, 1992). It may be
9
true that, very slowly during adult life, the epithelial cells gradually lose the capacity to
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grow. And this would simply make the climbing gradient profile more abrupt. Besides, as
11
compaction probably reaches a relative end point after 10-20 years of human life, the
12
central gradient plateau is formed as nuclear fibers reach maximal compaction. As can be
13
seen in Figure 6A & B (Augusteyn et al., 2008), the adult lens develops a refractive index
14
plateau at the center of the lens, and this section of uniform index makes the lens resemble
15
an artificial homogeneous lens that has lost its gradient, with lower power (and greater
16
positive spherical aberration). Interestingly, several studies have shown that the internal
17
spherical aberrations of the human eye increase with ageing (Glasser & Campbell, 1998;
18
McLellan et al., 2001; Artal et al., 2002; Brunette et al., 2003). The lens has the gradient
19
index structure and aspheric curvatures such that the internal aberrations of the eye are
20
negative in youth compensating the positive spherical aberration of the cornea. The increase
21
in positive spherical aberration with age can be seen in Figure 12, where the juvenile clear
22
dog lens has negative spherical aberration while the human 70 year old lens has positive
23
spherical aberration (Sivak & Kreuzer, 1983; Sivak, 1985;). This older lens behaves as an
24
homogeneous lens, without a gradient index structure.
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During middle adulthood, myopia prevalence does not change much in Figure 1 (Hashemi et al., 2004). The myopic eyes are not as prone as emmetropic eyes to have
3
hyperopic shifts, as has been shown in a clinical retrospective study (Grosvenor & Skeates,
4
1999). Prospective population based studies of refractive error in adults could confirm this
5
last finding. In fact, hyperopic shifts in myopic subjects are uncommon in clinical practice.
6
Perhaps, only a few low myopes have small hyperopic shifts in their 40’s. Myopic eyes may
7
be less prone to have hyperopic shifts with ageing as they already have lower lens power
8
than emmetropes early in life in Orinda (Jones LA et al., 2005) and SCORM (Iribarren et
9
al., 2012a) studies. If the thinner lens of myopic eyes has lost gradient power to a greater
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extent than that of emmetropic eyes, it may thus have a limited capacity of possible further
11
power loss. Interestingly, a more abrupt climbing gradient profile would not compensate
12
accurately the spherical aberration of the lens, and myopes have been shown in some (but
13
not all studies) to have greater ocular aberrations than emmetropic eyes (He et al., 2002;
14
Marcos et al., 2002; Paquin et al., 2002; Kwan et al., 2009). It would be interesting to have
15
measurements of the gradient index profile in different refractive groups in young adults. At older ages, in Figure 1, new cases of myopia appear, this time produced by a
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different change in the lens associated with nuclear cataract. The lens in these cases should
18
be gaining power producing a myopic shift in refraction. Then the emmetropes who turn to
19
be myopic with cataract would have high powered lenses, the opposite of what is found in
20
myopic schoolchildren. So this would also turn the correlation of lens power and refraction
21
to the negative side, as myopic eyes would have higher lens power than their emmetropic
22
peers (Figure 10). This has been found in CIEMS study, which showed that the correlation
23
between lens power and spherical equivalent became more negative when cataract subjects
24
were included (Iribarren et al., 2012b, Figure 11). In Figure 1 of the present paper, the
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prevalence of myopia changes from 12% during adult years to 38% in aged subjects, and
2
this could be enough to change the correlation between lens power and refraction to the
3
negative side.
4 5
16. Longer eyes of taller subjects have lower powered lenses.
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The advent of ultrasound biometry in the 70’s produced two interesting studies. In
7
1979 Larsen (Larsen, 1979) showed that taller people had longer eyes (and vice versa) for
8
subjects in the emmetropic range. Since then, many population studies have found that
9
taller people have longer eyes with flatter corneas, irrespective of refractive error (Wong et
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al., 2001; Saw et al., 2002; Ojaimi et al., 2005; Eysteinsson et al., 2005; Wu et al., 2007;
11
Lee et al., 2009; Nangia et al., 2010). Also in 1979, Blomdhal showed that bigger newborns
12
had longer eyes with flatter corneas. A recent population based study with cycloplegia for
13
refractive error measurement showed that taller people had longer eyes with flatter corneas
14
and also, lower powered lenses, irrespective of refractive error (Iribarren et al., 2014c)
15
(Table 5). This study also calculated the lens power with published data of the ocular
16
components and refraction of two adult population studies (Wong et al., 2001; Wu et al.,
17
2007) and one study in schoolchildren (Saw et al., 2004), showing that this trend in taller
18
people, or children born bigger, having bigger eyes with less powerful lenses was also the
19
rule (Table 5).
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Interestingly, a recent study of stature growth trajectories in a longitudinal study of
21
British children showed that while refraction at age 15 was not related to height growth,
22
corneal radius at that age was related to growth in the first 2 years of life and axial length
23
was related to height growth in the first 10 years of life (Northstone et al., 2013). So, in the
24
first years of life, when the corneal radius and axial length are changing with eye growth,
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these changes may be then influenced by general growth patterns, and also coordinated by
2
the emmetropization mechanism that makes the axial length match the refractive surfaces
3
by defocus. Indeed, the lens should be part of this general pattern of co-regulation. Further
4
evidence of this is the finding of lower lens power in faster growing eyes which develop
5
myopia (Iribarren et al., 2012a). The finding of lower powered lenses in taller people with
6
longer eyes could be in concordance with some kind of regulation of lens power loss
7
according to axial length change during early growth (Iribarren et al., 2014c). Alternatively,
8
it could be possible that general somatic growth is linked to lens growth early in life such
9
that taller children could have lenses that grow thinner and less powerful; and then the axial
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length independently could match the optical power of the cornea and the lens by defocus
11
regulated eye growth. This would also produce longer axial lengths in eyes with lower
12
powered lenses or flatter corneas.
Since Sorsby (1957) it is known that, in the emmetropic range, longer eyes have
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flatter corneas. In Table 6 we have calculated the lens power for ideal emmetropic eyes with
15
a normal range of axial lengths and corneal powers such that they all have a normal axial
16
length / corneal radius ratio of 3.0 (Grosvenor & Scott, 1994). As was early recognized by
17
Grosvenor & Scott (1994), it can be clearly seen that not only the cornea and the axial
18
length adjust for eyes being emmetropic, as also longer eyes should have lower powered
19
lenses, and vice versa. This lead the former researchers to state that ―the lens had
20
emmetropized‖ in longer eyes.
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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?
37
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Can the lens adjust its power to the general growth of the eye? A theory that could explain
2
these changes can only be based on the understanding of both surface and internal structure
3
of the lens. As we said before, the lens has a gradient of refractive index because new fresh
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fibers mature and become compacted as they age and sink in the deeper layers of the lens.
6
As fibers mature and become compacted they gain index, so a gradient of refractive index is
7
established from the surface to the center of the lens. This gradient gives the lens an internal
8
power greater than the one due to its curvatures alone. This has been known since the time
9
of Thomas Young who even calculated the power given by a gradient lens (Young, 1801;
11
Atchison & Charman, 2011).
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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
13
(Dubbelman & Van der Heijde, 2001) showed that the lens effective index decreased with
14
age in adults in a similar manner as it was later described prospectively in schoolchildren
15
(Jones LA et al., 2005). If the lens effective index decreases while the lens is compacted
16
during childhood (and thus should gain index) the only possible explanation for this loss of
17
effective index is that the gradient profile is becoming less effective (its climbing profile is
18
becoming more abrupt and it is developing a central plateau). This fact was originally
19
discussed by Donders in 1864 when he was thinking how the eye could become hyperopic
20
with ageing (Donders, 1864). He wrote ―In advancing years the lens becomes externally
21
especially firmer, and thus the coefficient of refraction of the outer layers appears to
22
increase. If this actually takes place, and if the coefficient of the cortical layers thus
23
approaches more to that of the nucleus, the (lens) focal distance becomes greater. On this
24
the diminution in advanced life of the refractive condition of the eye appears really to
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depend.‖ (Donders, 1864, page 88). But then he erroneously thought that although this
2
could be possible, the main reason for hyperopia was a flatter lens surface with age. He
3
probably thought this because he imagined that a rounded lens would flatten curvatures
4
with growth. This idea of lens flattening with age lasted for more than 100 years, until
5
Nicholas Brown at Oxford in 1973, showed with Scheimpflug photography that the lens
6
curvatures became steeper with ageing. For example, Duke-Elder in 1970, when speaking
7
about hyperopic shifts during adulthood, still argued that the lens curvatures became flatter
8
with age (Duke-Elder & Abrams, 1970a), although he recognized that Parsons had thought
9
that ―hardening of the cortical material of the lens‖ could be responsible for hyperopic shifts
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with ageing (Parsons, 1906).
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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 (Figure 13).
13
Nicholas Brown began to talk about the lens paradox as he thought that greater curvature at
14
the lens surface (more power) was paradoxically accompanied by presbyopia and not
15
myopia with ageing. This paradox could only be explained by a decreasing gradient
16
refractive index power inside the lens. After Brown, the change in gradient refractive index
17
profile with age was shown in different studies (Pierscionek, 1990; Smith et al., 1992;
18
Hemenger, 1995; Smith & Pierscionek, 1998) and recently by magnetic resonance images
19
(Kasthurirangan et al., 2008). If the profile of the climbing gradient index becomes more
20
abrupt with age, then the rays passing through it do not bend so much as they did earlier
21
when the gradient was smoother. And the development of a central plateau with no gradient
22
power further makes the lens lose power and optical properties. The change in the
23
peripheral profile of the climbing gradient of refractive index is probably produced by
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compaction of the fibers inside the lens, especially in the deep layers of the cortex (Figure
2
6A & B, adult lens).
3
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).
5
And then the nuclear index should increase, changing again the profile of the gradient
6
structure, thus explaining the increase in power of the lens and the myopic shift in
7
refraction found in 40-80% of subjects with nuclear cataract in the clinic (Iribarren &
8
Iribarren, 2013; Diez Ajenjo et al., 2014; Pesudovs & Elliot, 2003). Further proof of this is
9
the finding of thinner lenses in cataract subjects in CIEMS Study (Iribarren et al., 2012b) as
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if the compaction produced with cataract formation could make the lens thinner. In that
11
sense, early observations of deeper anterior chambers in eyes with unilateral cataract made
12
Laursen & Fledelius think that with cataract the lens was becoming thinner (Laursen &
13
Fledelius, 1979)
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Although the lens does not seem to be responsible for changes in refraction in
15
animal studies of experimental refractive error (Sivak, 2008, Review), human studies show
16
that the lens somehow can compensate for the axial growth of the eye to some extent. This
17
compensation may have passive and active mechanisms. The lens seems to slowly lose
18
power from birth to senescence. Some of the changes in lens surface shape tend to cancel
19
each other: for example, during childhood, the lens thinning per se would increase the
20
power (optically speaking, a thinner homogeneous lens with constant curvatures should
21
have greater power) but the decrease in curvature that accompanies crystalline lens thinning
22
decreases its surface power, so lens thinning cancels to some extent lens flattening during
23
school years. Another possible active way that the lens has for changing its power is by the
24
regulation of the rate of growth and compaction of lens fibers, in such a way that it may
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alter the profile of its climbing gradient refractive index which is responsible for its internal
2
power. This may be a very slow mechanism in humans who have a very slow rate of lens
3
growth, but appears to be fast during metamorphosis in amphibians, which rapidly change
4
lens shape and refractive power of the eye when moving from water to aerial vision.
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Interestingly, the diameter of fibers decreases from the center to the periphery in
6
microscopic studies of adult human lenses (Taylor et al., 1996). For example, the mean
7
cross-sectional area of fibers decreases progressively from 80 square micrometers in the
8
embryonic center of the lens to only 7 square micrometers in the adult nucleus which is the
9
sector under the newly developed cortex. This newly developed cortex in the surface of the
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lens, in turn, has fibers with a greater area of 24 square micrometers. This pattern in an
11
adult lens that has laid and compacted fibers at different ages, and is still laying new fibers,
12
is certainly interesting. Although the fibers in the central refractive index plateau (formed in
13
the adult, juvenile and fetal nucleus) have similar protein concentration (and similar
14
refractive index) because a plateau of index is developed, the younger ones are
15
progressively smaller from the center to the periphery. It seems that the embryonic and fetal
16
fibers have been the biggest ones when laid, and that the ones laid during juvenile school
17
years are smaller when they achieve maximum compaction with a similar index as those at
18
the center of the lens. They were probably smaller than the embryonic when they were laid
19
and matured during postnatal life. And the ones laid in the adult years, which form the
20
outermost part near the cortex, are even smaller when compacted. The only exception in
21
this pattern of change in fiber diameter are the newly developed fibers in the surface cortex,
22
still not compacted, that are a little bigger than the ones near them in the adult nucleus,
23
which have been compacted. This pattern of change in fiber diameter probably shows that,
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as fibers are laid from embryo to adult, they are gradually growing smaller up to maturation,
2
this fact perhaps related to a slower rate of lens epithelial growth with ageing.
3
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
5
studies showed that the lens wet weight increased linearly with age in adult life (Augusteyn,
6
2007; Augusteyn, 2010). Such linear growth in wet weight during adult years, in principle,
7
tended to show that the human lens maintained a constant linear rate of growth throughout
8
the whole adult life. One study showed that the water content in the nucleus was constant
9
with age (Heys et al., 2004; Truscott, 2009), but as the lens becomes older, it becomes
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compacted (Al-Goul et al., 2001) with fibers more densely packed, probably with loss of
11
water as cataract develops (Heys et al., 2004). As proteins are heavier than water, older
12
lenses might maintain a constant increase in wet weight but not a similar increase in volume
13
of added fibers. Besides, if the increase in lens thickness and diameter were linear, the
14
volume should increase non-linearly by the third power (more added volume as the lens
15
becomes bigger). But the opposite seems to be true. In fact, a decreasing non-linear growth
16
in axial thickness, equatorial diameter and calculated lens volume has been preliminary
17
reported for in vitro human lenses (Mohamed et al., 2012), showing that the increase in
18
dimensions and volume slows down as the lens ages during adulthood. The increase in
19
volume for Mutti’s lenses in Figure 8 has been calculated in Table 7, where it can be seen
20
that during six months (in the first year of life) the lens volume increases by 13%, while in
21
the next fourteen years it only increases by 8%. Table 8 shows the decay in lens volume
22
growth during adulthood calculated from the data in Mohamed et al., 2012 for adult years.
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The increase in volume of the growing lens probably results from the balance
24
between new added fibers and compaction of older ones. If compaction is a time dependent
42
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process due to ageing of proteins which aggregate and lose water, then the decay in lens
2
volume growth means that less fiber volume is added as time passes by. If this in vitro
3
biometric preliminary finding is confirmed (Mohamed et al., 2012), and we consider that
4
individual fibers laid at older ages reach lower final volumes, then it is possible that the lens
5
may have a decreasing rate of lens epithelial growth with ageing. This pattern of decrease in
6
growth over time would undoubtedly make the climbing gradient profile more abrupt, as
7
the only way to maintain a constant climbing gradient profile that is being compacted in the
8
deeper layers would be to maintain a constant rate of growth of new fibers. This would also
9
produce a plateau of index in the center of the lens.
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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
12
compaction progressively increases its rate with ageing. This would also make the climbing
13
gradient profile more abrupt. But this is not likely as compaction seems to be an inherent
14
property of protein ageing. Most of the hyperopic changes analyzed are slow and take years
15
to develop. The only report of a rapid change in lens refractive properties is that related to a
16
myopic shift of about 2-3 diopters with nuclear cataract usually developed in few months.
17
The slit lamp observed changes are found in the nucleus that becomes more colored and
18
opalescent. So this compaction and probable loss of water that, also probably, changes the
19
nucleus index, seems very different to the slow change in the peripheral climbing gradient
20
index profile.
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Another important issue in this analysis it that in vitro and in vivo measurements of
22
lens thickness may not be comparable in the sense that in vitro measurements are made with
23
the lens in maximally accommodated state and the lens power in the present study is
24
analyzed in vivo under cycloplegia at a resting position. The in vitro axial thickness would
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be overestimated in lenses of subjects younger than 40, (and equatorial diameter
2
underestimated, Strenk et al., 1999) when compared to lenses measured in vivo at rest under
3
cycloplegia because of the change in lens shape with accommodation. So the change with
4
age in the relation between axial thickness and equatorial diameter (aspect ratio) could be
5
even greater for lenses in vivo. To test for this hypothetical difference we have plotted in
6
Figure 14 the lens thickness measurements from five different in vivo population studies
7
with A-Scan biometry along with in vitro data from Mohamed et al, 2012. It can be clearly
8
seen that with the exception of the Chinese Singaporean who have thicker lenses, the
9
general pattern of lens axial growth is similar in all studies. And that axial growth decays
10
with age in both types of studies. So we think that our analysis is not biased by comparing
11
in vitro with in vivo studies of ocular biometry.
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18. Is the rate of lens power loss an actively regulated process?
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In the classical studies about the correlation of the ocular components with
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refraction performed by Tron (1940) and Stenstrom (1948) in younger adults, the lens was
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found to have no correlation with refraction, and thus was not considered important in the
17
development of refractive error. But things might have looked different if those studies
18
would have been performed in children (who have a positive correlation between refraction
19
and lens power, Iribarren et al., 2012a) or in older adults (who have a negative correlation
20
between refraction and lens power, Figure 11, Iribarren et al., 2012b). Animal studies of
21
refractive error have concluded that the lens has a passive role in the development of
22
refractive error, as Sivak has extensively reviewed (Sivak, 2008). Indeed, those animal
23
experiments are performed during short periods of one or two weeks, so changes in the lens
24
may not have been shown, as these may take longer to develop.
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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
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myopia development during the axial growth period in children. Once axial growth has
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stopped in adulthood, the continuing loss of lens power produces hyperopic shifts in
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refraction that seem to be an undesired passive process that impairs distance vision during
6
late adulthood. But, can the rate of lens power loss be modulated during childhood to
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produce myopic eyes with consistently lower lens power at the end of childhood?
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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.
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Fish lenses also grow continuously. The power of the fish lens has to decrease with age to
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adapt for the increasing axial length as the fish grows. A defocus modulated axial growth
12
adapts the eye size to the lens focal length in fish eyes (Shen & Sivak, 2007). But an
13
interesting experiment with fish reared for 10 months under monochromatic light or under
14
light deprivation showed alterations both in longitudinal spherical aberrations and refractive
15
index profiles of those growing fish lenses (Kröger et al., 2001). These alterations are of
16
interest as they show that the gradient structure can be modified environmentally during
17
lens growth. A recent animal study of myopia development in chicks growing with
18
unrestricted vision under low light environments has shown that the lens power loss during
19
eye growth can be environmentally modulated, as the eyes of chicken developing myopia
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growing under 500 lux ambient light, have thinner and less powerful lenses than the ones
21
which remain hyperopic growing under high ambient illumination. This environmental
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change in the rate of lens power loss is slow as it takes 2-3 months to develop (Cohen et al.,
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2011; Cohen et al., 2014).
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The lens has been shown to be also thinner in myopic children in several studies (Jones LA et al., 2005; Shih et al., 2009; Wong et al., 2010; Iribarren et al., 2012a). Myopic
3
eyes are generally longer. The lens is also thinner in taller subjects (who also have longer
4
eyes). A thinner lens is probably a lens with delayed growth. And human studies reviewed
5
here have shown that these thinner lenses have lower power. FGF is the principal molecule
6
involved in lens growth, and its concentration in the vitreous could be modified by genetic,
7
humoral or local factors. FGF could also be involved ocular growth signaling (Rhorer &
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Stell, 1994; Gentle & McBrien, 2002; Wallman & Winawer, 2004). If the profile of the
9
gradient index structure is a function of lens growth, delayed growth could alter this
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gradient and thus the internal power of the lens. So there is a possible mechanism for
11
regulating the lens power loss based on its rate of growth, which in turn may be a function
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of FGF concentration.
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The findings reviewed herein, although they should be replicated, are possibly
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showing that lens growth could be actively modulated in relation to axial or somatic growth
15
during early development in infants and also in myopic schoolchildren. FGF could be the
16
link of this regulation. It is possible that the emmetropization mechanism was adapted by
17
evolution to maintain a relative mild hyperopic refraction during growth as accommodation
18
can overcome this mild refractive error before presbyopic years (Morgan et al., 2010). This
19
would be protective from eyes being out of focus for distance viewing (myopia). Current
20
thinking about emmetropization suggests that a passive programmed loss of lens power is
21
counterbalanced by an actively regulated rate of axial length growth by retinal defocus. But
22
the growing eye could also have a slower feedback mechanism that regulates lens power
23
loss in relation to axial elongation, to protect from environmentally induced higher rates of
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axial growth. In this sense, the chick model in which axial myopia is developed by growing
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under low ambient illumination during three months is interesting for studying lens power
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loss in vivo (Cohen et al., 2011; Cohen et al., 2014).
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19. Conclusions and future directions.
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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
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birth and during school years up to age 10-12. Lens thinning is accompanied by flattening
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of lens curvatures because of changes in overall lens shape. These changes involve axial
9
thinning and equatorial growth from birth to puberty. The lens thinning per se, all other
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things the same, would increase the power of an homogeneous lens (optically speaking), but
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flatter curvatures due to changing shape produce decreasing lens power while the lens thins.
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Besides, the changing internal structure may be responsible for more than half of lens
13
power loss during childhood. Changes in the gradient index profile probably make the lens
14
lose power during this period. Myopic subjects have lower lens power than their
15
emmetropic peers, with thinner lenses, possibly because the gradient structure has become
16
less effective at a slower rate of growth. Thus, myopic subjects may be less prone to lose
17
lens power with ageing, maintaining stable refractions during adult years.
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explaining the development of hyperopic shifts with ageing. These hyperopic shifts may be
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also produced by an age related change in the gradient refractive index inside the lens, the
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only possible explanation after Nicholas Brown described increasing lens curvatures with
22
age (the Lens Paradox). This change of the gradient profile seems to be a consequence of
23
decreasing lens growth with ageing. As the lens grows slower, the systematic compaction of
24
the deeper layers possibly changes the profile of the gradient structure, because the later
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relies on growth of new fibers and can only be maintained unaltered if the rate of growth
2
were constant. The development of a refractive index plateau in the center of the lens
3
further reduces its internal power. After age 70, the lens gains power in many subjects that
4
have nuclear cataracts, producing myopic shifts in refraction. This last change is probably
5
due to increased index in the center of the cataractous lens due to further compaction and
6
water loss of the crystallin content.
Future prospective population based studies of cycloplegic refractive error,
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including keratometry and biometry, could calculate lens power. Then, the question of
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whether the eye shrinks with ageing or the lens loses power during age related hyperopic
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shifts could be resolved. Besides, the loss of lens power with age could be studied
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prospectively in adults across refractive error groups, such that differences in lens power
12
loss could be studied further as has been done in school children.
Possible environmental influences on lens growth need replication of experimental
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studies. The profile of the gradient index could be indirectly studied prospectively in vivo
15
with new approaches such as Brillouin confocal microscopy, which has shown that the
16
profile of the elastic modulus changes with age in rat and human lenses (Scarcelli et al.,
17
2011; Scarcelli & Yun, 2012; Besner et al., 2013). The profile of the elastic modulus
18
resembles the profile of the gradient refractive index. This new non-destructive in vivo
19
approach could be useful to confirm suggested differences in the gradient index profile
20
across refractive groups. Besides, changes in the gradient profile could be studied
21
prospectively with this last method, which looks promising not only for the study of
22
hyperopic shifts with ageing, but also for the changes in the internal structure of the lens
23
during accommodation.
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Acknowledgements. This review was developed during long lasting discussions with Prof.
2
Ian G. Morgan (Australia), to whom I feel grateful. I wish to thank Prof. Akbar Fotouhi
3
(Iran) for the data in Figure 1 of Tehran Eye Study and for the data in Table 5. I also thank
4
Prof. Michiel Dubbelman (Netherlands) for his comments on the manuscript. I also wish to
5
thank Prof. Bob Augusteyn (Australia) for his permission to reproduce Figures 6A & B, and
6
for the friendly discussion about lens growth in his cited papers. Prof. Jake Sivak (Canada)
7
has been very kind in sending and discussing his interesting papers, and for letting me
8
reproduce Figure 12. Prof. Jos Rozema (Belgium) has helped me with Bennett’s formula
9
and Gullstrand’s equation. Profs. Peter Sands and Bill Jagger (Australia) have been very
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kind in letting me reproduce their fish lens Figure 2, and Prof. Jost Jonas in letting me
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reproduce Figures 10 & 11. Finally, I wish to thank Vicente A. La Vitola (Argentina) and
12
Lautaro Gomez Alvarez (Argentina) for the AutoCad figures.
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Figure Legends.
2
Figure 1. Prevalence of refractive error along lifespan, with a +1/-1 diopter cut off point in
3
the Tehran Eye Study (Hashemi et al. 2004). Age 10 stands for 6-10 years, age 15 stands for
4
11-15 years and so on. (Reanalysis of data published in ―Hashemi, H., Fotouhi, A.,
5
Mohammad, K., 2004. The age- and gender-specific prevalences of refractive errors in
6
Tehran: the Tehran Eye Study. Ophthalmic Epidemiol. 11, 213-225,‖ and in ―Fotouhi, A.,
7
Morgan, I.G., Iribarren, R., Khabazkhoob, M., Hashemi, H., 2012. Validity of
8
noncycloplegic refraction in the assessment of refractive errors: the Tehran Eye Study. Acta
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Ophthalmol. 90, 380-386.‖)
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Figure 2. Parallel laser beams seen from the side refracted by a trout lens. See the short
11
focal length of the fish lens and how the beams are bent inside the lens structure by the
12
gradient index, with no spherical aberration. Reprinted from ―Jagger, W.S., Sands, P.J.,
13
1996. A wide-angle gradient index optical model of the crystalline lens and eye of the
14
rainbow trout. Vision Res. 36, 2623-2639.‖ Copyright (1996), with permission from
15
Elsevier.
16
Figure 3. First, to the left, calculated lens power in premature infants from the data of Cook
17
et al. (2003) for premature infants form months 1 to 5 (white circles); second in the middle,
18
lens power data for full term infants from Mutti et al. (2005) aged 3 and 9 months (black
19
circles), and last to the right, lens power data for schoolchildren from Ip et al. (2007) (black
20
circles).
21
Figure 4. Lens thickness in premature infants from months 1 to 5 (Cook et al., 2003) (white
22
circles) and for full term infants aged 3 and 9 months (Mutti et al., 2005) (black circles).
23
The lens thickness increases in the first three months of life in premature infants, perhaps
24
following the high fetal rate of lens growth.
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Figure 5. Schematic drawing of the change in lens thickness and front and back curvatures
2
of the 15 day old chick lens (inner lines) inside the 80 day old lens (outer lines). It can be
3
seen that the lens becomes thicker with flatter curvatures as it grows. Reprinted from
4
―Iribarren, R., Rozema, J.J., Schaeffel, F., Morgan, I.G., 2014. Calculation of crystalline
5
lens power in chickens with a customized version of Bennett's equation. Vision. Res. 96,
6
33-38.‖ Copyright (2014), with permission from Elsevier.
7
Figure 6. Three gradient index profiles reconstructed from mri images of human lenses in
8
vitro. Figure 6 A equatorial axis, Figure 6 B saggital axis, (with permission from
9
―Augusteyn, R.C., 2008. Growth of the lens: in vitro observations. Clin. Exp. Optom. 91,
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226-239‖). In gray dots a 7 year old lens, with a smooth climbing gradient profile and a
11
lower peak index compared to the other adult lenses. In white dots a 27 year old lens with
12
adult peak index and more abrupt gradient that is developing a central plateau. In black dots
13
a 82 year old human lens with a very abrupt climbing gradient and an extended central
14
plateau. Figure 6 C. Schematic drawing of the gradient index profile of two lenses, one of
15
which is thinner and has a more abrupt climbing profile to reach a higher peak index.
16
Although the thinner lens may have a higher peak index, the change in gradient profile
17
could make it have lower power. The younger lens is 4.0mm thick and the older 3.6mm
18
thick, representing the compaction achieved since birth up to age 10.
19
Figure 7. Anterior Segment Length calculated from data in Cook et al. (2003) in premature
20
infants form months 1 to 5 (white circles), then for full term infants in Mutti et al. (2005)
21
aged 3 and 9 months (black circles), and for emmetropic schoolchildren at ages 6 and 12
22
years from Zadnik et al. (2004) (black circles).
23
Figure 8. Auto Cad drawings made with the data of curvatures and axial thickness given by
24
Mutti et al. in their studies for 3 months, 9 months and 14 year old children (Mutti et al.,
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2005 and 1998). Curvatures were assumed as spherical. The equatorial curvatures were
2
drawn following the equatorial shape of the shadowgraphs in Borja et al. (2008). From
3
these drawings, the equatorial diameter was estimated for the three ages, showing that the
4
lens grows up to adult values early in life.
5
Figure 9. The same figures as in Figure 8, this time superimposed for the 3 month old
6
(dotted line) and the 14 year old lens (full line), showing the change in shape achieved
7
during childhood. It can be seen that the lens thins from a more rounded shape at 3 months
8
and that the equatorial portion increases making the lens more ellipsoidal.
9
Figure 10. Significantly lower lens power in hyperopic subjects compared to emmetropic
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and myopic subjects (in the group with low nuclear opacity grades) of the Central India Eye
11
and Medical Study (Iribarren et al. 2012b).
12
Figure 11. Negative correlation between refractive error (spherical equivalent) and
13
crystalline lens power in participants in the Central India Eye and Medical Study. Subjects
14
with marked nuclear cataract (grades 6 and 7, crosses and dotted regression line), had a
15
greater negative correlation than those with less marked nuclear cataract (grades 2–5, full
16
regression line and circles). Reproduced from ―Iribarren, R., Morgan, I.G., Nangia, V.,
17
Jonas, J.B, 2012. Crystalline Lens Power and Refractive Error. Invest. Ophthalmol. Vis.
18
Sci. 53, 543-550.‖ Copyright (2012), with permission from Association for Research in
19
Vision and Ophthalmology.
20
Figure 12. In (A) a clear juvenile dog lens with negative spherical aberration and in (B) a
21
brown 70 year human old lens with positive spherical aberration. See how the laser beams
22
have different refraction through the peripheral or central sections of the lens. (Reproduced
23
with permission from: ―Sivak JG. The Glenn A. Fry Award Lecture: optics of the
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crystalline lens. Am J Optom Physiol Opt 1985;62:299-308.‖ ©The American Academy of
2
Optometry 1985).
3
Figure 13. Schematic drawings of growing lenses. In (A) an ellipsoidal lens that grows only
4
axially steepens front and back curvatures as it grows and in (B) same ellipsoidal lens that
5
grows in all directions flattening front and back curvatures.
6
Figure 14. Plot of the in vitro data for lens axial thickness growth with age from Mohamed
7
et al., 2012 along with the in vivo data from five population based studies with A-Scan
8
biometry (Singapore: Wong et al., 2001; Taiwan: Shih et al., 2007; Latino Eye Study:
9
Schufelt et al., 2005; Myanmar: Warrier et al., 2008; Mongolia: Wickremasinghe et al.,
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2004).
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1 Cook, C.A., Koretz, J.F., Pfahnl, A., Hyun, J., Kaufman, P.L., 1994. Aging of the human
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Eysteinsson, T., Jonasson, F., Arnarsson, A., Sasaki, H., Sasaki, K., 2005. Relationships
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1
Forbes, J., Holden, R., Harris, M., Brown, N.A., Bron, A., 1992. Growth of the human
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Table 1. Comparison of the surface and gradient contribution to the decrease in chicken lens power. 15 days old 80 days old difference % change Complete lens power (diopters) 79.9 50.7 -29.3 100.0% Surface lens power (diopters) 27.5 18.7 -8.8 30.0% Internal (gradient index) power (diopters) 52.4 32.0 -20.5 70.0%
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Table 2. Anterior Chamber (ACD), Lens Thicknees (LT) and Anterior Segment Length (ASL) in emmetropic children.* age (years) ACD (mm) LT (mm) ASL (mm) 6 3.62 3.53 7.15 7 3.68 3.5 7.18 8 3.71 3.45 7.16 9 3.73 3.43 7.16 10 3.75 3.43 7.18 11 3.76 3.41 7.17 12 3.75 3.43 7.18 * (calculated from Zadnik et al. 2004)
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Table 3. Refraction and ocular components at age 7-9 years in prematures compared with same age fullterm from Orinda Study. Chen et al. 2010. (prematures) Jones et al. 2005 Myopia Emmetropia Hyperopia Emmetropia Spherical equivalent (diopters) -3.22 +0,02 +2,15 0.54 Corneal Power (diopters) 43.79 42.94 43.68 43.61 Anterior Chamber Depth (mm) 3.29 3.46 3.44 3.69 Lens Thickness (mm) 3.76 3.62 3.61 3.47 Axial Length (mm) 23.39 22.98 21.93 22.93 Lens Power (diopters) 26.69 25.33 25.91 23.63 Anterior Segment length (mm) 7.05 7.08 7.05 7.16
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Table 4. Internal and surface lens power contributions, in diopters, for two prospective studies. (Mutti et al. IOVS 2005;46:3074-80.) Equivalent lens index Complete Gullstrand's lens power Surface Gullstrand's lens power Internal (gradient index) power
3 months 1.4526 40.00 12.19 27.81
9 months 1.4591 36.49 10.52 25.97
Difference
(Mutti et al. IOVS 1998;39:120-33.) Equivalent lens index Complete Gullstrand's lens power Surface Gullstrand's lens power Internal (gradient index) power
6 years old 1.431 24.52 9.09 15.43
14 years old 1.429 21.77 8.23 13.54
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Table 5. Comparison of refraction and ocular components of the different studies by height and birthweight. Height and ocular components in adults (Iribarren et al., 2014 - Shahroud study. Invest Ophthamol Vis Sci. 55:1031-9.) HEIGHT SER CR ACD LT AL m D mm mm mm mm 1,31-1,57 -.04 7.58 2.60 4.27 22.99 1,57-1,65 .01 7.63 2.63 4.26 23.14 1,65-1,99 -.12 7.71 2.69 4.23 23.43
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Height and ocular components in adults (Wong et al., 2001 - Tanjong Pagar Survey. Invest Ophthalmol Vis Sci. 42:1237-42). HEIGHT SER CR ACD LT AL LP m D mm mm mm mm D 1,37-1,50 -0.24 7.55 2.7 4.92 22.74 25.68 1,51-1,55 -0.6 7.57 2.86 4.78 23.05 25.11 1,56-1,59 -0.49 7.66 2.83 4.78 23.19 25.01 1,60-1,65 -0.6 7.68 2.99 4.68 23.44 24.44 1,66-1,83 -0.52 7.79 3.1 4.63 23.78 23.94
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Height and ocular components in adults (Wu et al., 2007 - Rural Myanmar. Clin Exp Ophthalmol. 35:834-9). HEIGHT SER CR ACD LT AL m D mm mm mm mm 1,30-1,48 -1.53 7.53 2.7 4.47 22.36 1,49-1,54 -1.67 7.61 2.75 4.48 22.51 1,55-1,6 -1.12 7.68 2.87 4.44 22.76 1,61-1,80 -1.4 7.76 2.87 4.48 23.14
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Birthweight and ocular components - Singaporean Chinese children.(Saw et al., 2004 - Br J Ophthalmol 88:538-542). BIRTHWEIGHT SER CR ACD LT AL Kg D mm mm mm mm 2,5-2,9 -0.35 7.69 3.58 3.5 23.13 3,0-3,4 -0.52 7.76 3.61 3.48 23.44 3,5-3,9 -0.67 7.82 3.64 3.46 23.67 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).
AL/CR 3.03 3.03 3.04
AL/CR 3.01 3.04 3.03 3.05 3.05
LP D 28.35 28.67 27.56 26.96
AL/CR
LP D 25.04 24.54 24.30
AL/CR
2.97 2.96 2.96 2.98
3.01 3.02 3.03
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Table 6. Longer eyes with normal AL / CR ratio have lower powered lenses, and viceversa. Refraction Corneal Radius Keratometry ACD Lens Thickness Axial length (diopters) (mm) (diopters) (mm) (mm) (mm) 0 7 47.36 21,0 2.90 4.20 0 7.2 46.04 21.6 2.90 4.20 0 7.4 44.80 22.2 3.00 4.20 0 7.6 43.62 22.8 3.00 4.20 0 7.8 42.50 23.4 3.10 4.20 0 8 41.44 24,0 3.10 4.20 0 8.2 40.43 24.6 3.10 4.20 0 8.4 39.46 25.2 3.10 4.20
AL / CR 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
Lens Power (diopters) 28.08 26.83 25.95 24.87 24.11 23.18 22.31 21.50
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Table 7. Lens volume* calculated from the data in Figure 7 of Mutti's studies. Age Lens Volume (cubic mm) Volume change (%) 3 months 113.61 9 months 129.03 13.6% 14 years 139.71 8.3% * calculated from the volume of an ellipsoid (4/3*π*a*b*c)
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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 years 148.03 30 years 169.29 21.26 40 years 184.38 15.08 50 years 196.08 11.70 60 years 205.64 9.56 70 years 213.72 8.08 80 years 220.72 7.00
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12 y
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emmetropia
hyperopia
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