Presbyopia — a maverick of human aging

Design of an Automatically Controlled Multi-Axis Stretching Device for Mechanical Evaluations of the Anterior Eye Segment

The young eye has an accommodative ability involving lens shape changes to focus over different distances. This function gradually decreases with age, resulting in presbyopia. Greater insights into the mechanical properties of anterior eye structures can improve understanding of the causes of presbyopia. The present study aims to develop a multi-axis stretching device for evaluating the mechanical properties of the intact eye lens. A stretching device integrating the mechanical stretcher, motor, torque sensor and data transmission mechanism was designed and developed by 3D printing. The mechanical stretcher can convert rotation into radial movement, both at constant speeds, according to the spiral of Archimedes. The loading unit equipped with eight jaws can hold the eye sample tightly. The developed device was validated with a spring of known constant and was further tested with anterior porcine eye segments. The validation experiment using the spring resulted in stiffness values close to the theoretical spring constant. Findings from measurements with porcine eye samples indicated that the measured forces are within the ranges reported in the literature. The developed multi-axis stretching device has good repeatability during experiments with similar settings and can be reliably used for mechanical evaluations of the intact eye lens.

The eye lens: age-related trends and individual variations in refractive index and shape parameters

The eye lens grows throughout life by cell accrual on its surface and can change shape to adjust the focussing power of the eye. Varying concentrations of proteins in successive cell layers create a refractive index gradient. The continued growth of the lens and age-related changes in proteins render it less able to alter shape with loss of capacity by the end of the sixth decade of life. Growth and protein ageing alter the refractive index but as accurate measurement of this parameter is difficult, the nature of such alterations remains uncertain. The most accurate method to date for measuring refractive index in intact lenses has been developed at the SPring-8 synchrotron. The technique, based on Talbot interferometry, has an X-ray source and was used to measure refractive index in sixty-six human lenses, aged from 16 to 91 years. Height and width were measured for forty-five lenses. Refractive index contours show decentration in some older lenses but individual variations mask age-related trends. Refractive index profiles along the optic axis have relatively flat central sections with distinct micro-fluctuations and a steep gradient in the cortex but do not exhibit an age-related trend. The refractive index profiles in the equatorial aspect show statistical significance with age, particularly for lenses below the age of sixty that had capacity to alter shape in vivo. The maximum refractive index in the lens centre decreases slightly with age with considerable scatter in the data and there are age-related variations in sagittal thickness and equatorial height.

Model of accommodation: contributions of lens geometry and mechanical properties to the development of presbyopia

PURPOSE

To determine the relative importance of lens geometry and mechanical properties for the mechanics of accommodation and the role of these elements in the causes and potential correction of presbyopia.

SETTING

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey, USA.

DESIGN

Experimental study.

METHODS

Finite element methods and ray-tracing algorithms were used to model the deformation and optical power of the human crystalline lens during accommodation. The mechanical model treats the lens as an axisymmetric object, and the optical model incorporates a gradient refractive index. Using these models, the accommodation of a broad range of lenses with different geometries and mechanical properties were investigated.

RESULTS

The most significant result was that reshaping the 45-year-old lens to the geometry of the 29-year-old lens, while retaining the mechanical properties, restored the former's accommodation amplitude to 72% to 94% of that of the 29-year-old lens, depending on ciliary body displacement. That is, reshaping can add 1.8 to 3.7 diopters of accommodation. A sensitivity analysis showed that this result was robust over a wide range of mechanical and geometrical properties.

CONCLUSION

The study results suggest that a significant amount of the loss of accommodation is due to changes in lens geometry.

Lens thickness with age and accommodation by optical coherence tomography

PURPOSE

To utilize time-domain optical coherence tomography (OCT) to measure changes in the crystalline lens with age and accommodation.

METHODS

A cross-sectional study of pre-presbyopic and presbyopic subjects was conducted. Amplitude of accommodation was measured with the push-up test. Objective accommodation was measured with the Grand Seiko auto-refractor and a Badal lens system. Lens thickness was measured with the Zeiss Visante OCT and an internal optometer. The data were analysed using correlation coefficients, linear regression, and by calculating the average change in lens thickness per diopter change in objective accommodation.

RESULTS

Twenty-two subjects between the ages of 36 and 50 years completed the study. Subjective amplitude of accommodation ranged from 2.17 to 6.38 D. Objective accommodation ranged from 0.22 to 4.56 D. The mean lens thickness was 4.05+/-0.20 mm. The mean change in lens thickness for up to a 5-D accommodative stimulus ranged from 0.01 to 0.26 mm. The correlation coefficients were: age and subjective accommodation, r= -0.74; age and objective accommodation, r= -0.84; change in lens thickness and age, r= -0.65; change in lens thickness and subjective accommodation, r=0.74; change in lens thickness and objective accommodation, r=0.64; objective and subjective accommodation, r=0.82 (all p<0.01). An increase in lens thickness of 21 microm per year of age was determined by linear regression. For the subjects who showed at least 1 D of accommodative response on the Grand Seiko auto-refractor, there was an increase of 51+/-19 microm per dioptre of accommodation.

CONCLUSIONS

Optical coherence tomography is a non-invasive technique that can be used to quantify changes in the thickness of the crystalline lens. Subjective and objective measurements of accommodation, as well as age, were robustly correlated with the measured changes in lens thickness. Lens thickness changes with age and accommodation as measured with the Visante OCT compare well with previous findings using Scheimpflug photography and ultrasound.

Topographical changes of biconvex objects during equatorial traction: an analogy for accommodation of the human lens

AIM

To assess and compare the changes in shape of encapsulated biconvex structures undergoing equatorial traction with those changes reported in the human lens during accommodation.

METHODS

Equatorial traction was applied to several different biconvex structures: air, water, and gel filled mylar and rubber balloons and spherical vesicles. In the vesicles, traction was applied externally, using optical tweezers, or from within, by the assembly of encapsulated microtubules. The shape changes were recorded photographically and the change in central radius of curvature of water filled mylar balloons was quantified.

RESULTS

Whenever an outward equatorial force was applied to the long axis of long oval biconvex objects, where the minor to major axis ratio was

CONCLUSIONS

All biconvex structures that have been studied demonstrate similar shape changes in response to equatorial traction. This effect is independent of capsular thickness. The consistent observation of this physical change in the configuration of biconvex structures in response to outward equatorial force suggests that this may be a universal response of biconvex structures, also applicable to the human lens undergoing accommodation.

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Key Words

• lens shape
• equatorial traction
• accommodation

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MESH Headings

• Accommodation, Ocular/physiology
• Humans
• Lens Capsule, Crystalline/anatomy & histology
• Lens, Crystalline/physiology
• Models, Biological
• Stress, Mechanical

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Affiliation(s)

R A Schachar Department of Physics, University of Texas at Arlington, Arlington, Texas, USA.
D K Fygenson

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Age-related changes in static accommodation and accommodative miosis

An attempt was made to explore the validity of the Hess-Gullstrand and Duane-Fincham models of presbyopia development, on the assumption that accommodative miosis could be used as an indicator of ciliary muscle effort. Monocular accommodation response and pupil size were measured as a function of accommodation demand over the range 0-4 D, in 48 normal subjects with ages between 17 and 56 years. The slope of the response/stimulus curve was found to decrease only slowly with age up to about 35 years and then to decline more rapidly. Accommodative miosis per dioptre of accommodation response did not change systematically with age up to about 35 years, this being apparently more in accord with the Hess-Gullstrand model. However, accommodative miosis varied very widely between younger subjects of similar age and accommodative amplitude (from zero to around 1 mm per dioptre of accommodation response for subjects in their twenties). It is concluded that miosis does not necessarily accompany accommodation and that its magnitude is not related in any simple general way to ciliary muscle contraction. Hence it cannot be used to support or refute particular theories of presbyopia.

Sensitivity study of human crystalline lens accommodation

A nonlinear axisymmetric finite element method (FEM) analysis was employed to determine the critical geometric and material properties that affect human accommodation. In this model, commencing at zero, zonular traction on all lens profiles resulted in central lenticular surface steepening and peripheral surface flattening, with a simultaneous increase in central lens thickness and central optical power. An age-related decline in maximum zonular tension appears to be the most likely etiology for the decrease in accommodative amplitude with age.

Insights into the age-related decline in the amplitude of accommodation of the human lens using a non-linear finite-element model

AIM

To understand the effect of the geometric and material properties of the lens on the age-related decline in accommodative amplitude.

METHODS

Using a non-linear finite-element model, a parametric assessment was carried out to determine the effect of stiffness of the cortex, nucleus, capsule and zonules, and that of thickness of the capsule and lens, on the change in central optical power (COP) associated with zonular traction. Convergence was required for all solutions.

RESULTS

Increasing either capsular stiffness or capsular thickness was associated with an increase in the change in COP for any specific amount of zonular traction. Weakening the attachment between the capsule and its underlying cortex increased the magnitude of the change in COP. When the hardness of the total lens stroma, cortex or nucleus was increased, there was a reduction in the amount of change in COP associated with a fixed amount of zonular traction.

CONCLUSIONS

Increasing lens hardness reduces accommodative amplitude; however, as hardness of the lens does not occur until after the fourth decade of life, the age-related decline in accommodative amplitude must be due to another mechanism. One explanation is a progressive decline in the magnitude of the maximum force exerted by the zonules with ageing.

Accommodation as a function of age and the linearity of the response dynamics

The changes with age in the accommodation responses to dynamic stimuli can reveal useful information on the factors underlying presbyopia development. Analysis of the monocular accommodation responses of 19 normal observers (ages 18-49 years) to stimuli whose vergence varied sinusoidally with time at different temporal frequencies (peak-to-peak stimulus 1.33-2.38 D, at 0.05-1.00 Hz) showed that at all ages both the gain and phase of the response were essentially linear functions of the temporal frequency. Extrapolation of least-squares, regression line fits to the gain data for each subject gave the gain at zero frequency, G0, and the cut-off frequency, fc, at which the gain fell to zero. G0 reduced with age but fc remained essentially constant at about 1.7 Hz, up to at least the age of about 40. The magnitude of the response to step stimuli covering the same stimulus range was well correlated with the value of G0. The linear changes in phase lag with temporal frequency corresponded to simple time delays td. The time lag varied from close to zero for the youngest subjects to about 0.5 s for the subjects in their late forties. There was substantial variation between the responses of subjects of similar age: those subjects with high values of G0 also tended to have low values of td, both effects probably being due to the superior ability of some individuals to predict the sinusoidal changes in the accommodation stimulus. Comparison of theoretical step responses, derived by applying linear theory to the parameters obtained from the results for the sinusoidal stimuli, with the actual responses to unpredictable steps for the same subjects supports the view that prediction effects and other possible factors make linear theory inapplicable to this type of data. The results are discussed in the context of current ideas on the development of presbyopia: it is suggested that the constancy of fc with age is the result of the ciliary body maintaining its efficiency, whereas the fall in G0 and increase in td result from increases in lens rigidity.

Epidemiology of refractive errors and presbyopia

Limitations in existing studies of the epidemiological aspects of refraction are attributed to both technical and statistical procedures. Early influences of ocular parameters on refraction are identified accordingly as prematurity and may or may not be involved. Attention is paid to familial and genetic influences, and infants and toddlers are examined as a group separate from schoolchildren and teenagers, who are likely to have experienced significant periods of near work. The effects of sex and geographical distribution are considered both for younger and older age ranges. Special attention is paid to anisometropia, which is shown-apparently for the first time-to increase appreciably among presbyopes. The connection between refractive errors and ocular pathologies is reviewed, and possible means of preventing early onset myopia are examined. Presbyopia is addressed with reference to its geographical distribution and hypothetical links to accommodation insufficiency.

Why we need reading-glasses before a zimmer-frame

Accommodative loss represents the fastest human biological decrement. Why? To examine this, the shape of the eye-lens during accommodation or its relaxation is analysed with special reference to age-related changes. The capsule is viewed as a force transmitter: the distribution of forces along centripetal capsular arcs and the resulting stresses and strains are calculated. The effect of zonular 'shifts' is considered. Age-related accommodative loss can be modelled successfully if changes in mechanical properties are linked to those in lenticular and capsular shape.

Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia

The biometric, optical and physical properties of 19 pairs of isolated human eye-bank lenses ranging in age from 5 to 96 years were compared. Lens focal length and spherical aberration were measured using a scanning laser apparatus, lens thickness and the lens surface curvatures were measured by digitizing the lens profiles and equivalent refractive indices were calculated for each lens using this data. The second lens from each donor was used to measure resistance to physical deformation by providing a compressive force to the lens. The lens capsule was then removed from each lens and each measurement was repeated to ascertain what role the capsule plays in determining these optical and physical characteristics. Age dependent changes in lens focal length, lens surface curvatures and lens resistance to physical deformation are described. Isolated lens focal length was found to be significantly linearly correlated with both the anterior and posterior surface curvatures. No age dependent change in equivalent refractive index of the isolated lens was found. Although decapsulating human lenses causes similar changes in focal length to that which we have shown to occur when human lenses are mechanically stretched into an unaccommodated state, the effects are due to nonsystematic changes in lens curvatures. These studies reinforce the conclusion that lens hardening must be considered as an important factor in the development of presbyopia, that age changes in the human lens are not limited to the loss of accommodation that characterizes presbyopia but that the lens optical and physical properties change substantially with age in a complex manner.

Accommodation dynamics in aging rhesus monkeys

Accommodation, the mechanism by which the eye focuses on near objects, is lost with increasing age in humans and monkeys. This pathophysiology, called presbyopia, is poorly understood. We studied aging-related changes in the dynamics of accommodation in rhesus monkeys aged 4-24 yr after total iridectomy and midbrain implantation of an electrode to permit visualization and stimulation, respectively, of the eye's accommodative apparatus. Real-time video techniques were used to capture and quantify images of the ciliary body and lens. During accommodation in youth, ciliary body movement was biphasic, lens movement was monophasic, and both slowed as the structures approached their new steady-state positions. Disaccommodation occurred more rapidly for both ciliary body and lens, but with longer latent period, and slowed near the end point. With increasing age, the amplitude of lens and ciliary body movement during accommodation declined, as did their velocities. The latent period of lens and ciliary body movements increased, and ciliary body movement became monophasic. The latent period of lens and ciliary body movement during disaccommodation was not significantly correlated with age, but their velocity declined significantly. The age-dependent decline in amplitude and velocity of ciliary body movements during accommodation suggests that ciliary body dysfunction plays a role in presbyopia. The age changes in lens movement could be a consequence of increasing inelasticity or hardening of the lens, or of age changes in ciliary body motility.

Static aspects of accommodation: age and presbyopia

Although the progressive reduction in accommodative amplitude with increased age is well documented, little is known about several other aspects of static or steady-state accommodation to provide a comprehensive assessment of changes related to age and presbyopia. Static components of accommodation (tonic accommodation, depth-of-focus, slope of the stimulus/response function, and accommodative controller gain) were assessed objectively using an infrared (IR) optometer in 30 human subjects aged 21-50 years; depth-of-focus was also determined psychophysically as was accommodative amplitude. Tonic accommodation and the amplitude of accommodation decreased with increased age, whereas the subjective depth-of-focus increased; the other parameters remained unchanged. The decrease in tonic accommodation and amplitude of accommodation was attributed to biomechanical factors, whereas the increase in subjective depth-of-focus was believed to result from increased tolerance to defocus related to the gradual onset of presbyopia. Constancy of the objective depth-of-focus suggested absence of age effects on the neurologic control of reflex accommodation, whereas the lack of systematic change in slope and controller gain provided support for the Hess-Gullstrand theory of accommodation and presbyopia.

Presbyopia and the optical changes in the human crystalline lens with age

Lenses from 27 human eyes ranging in age from 10 to 87 years were used to determine how accommodation and age affect the optical properties of the lens. A scanning laser technique was used to measure focal length and spherical aberration of the lenses, while the lenses were subjected to stretching forces applied through the ciliary body/zonular complex. The focal length of all unstretched lenses increased linearly with increasing age. Younger lenses were able to undergo significant changes in focal length with stretching, whereas lenses older than 60 years of age showed no changes in focal length with stretching. These data provide additional evidence for predominantly lens-based theories of presbyopia. Further, these results show that there are substantial optical changes in the human lens with increasing age and during accommodation, since both the magnitude and the sign of the spherical aberration change with age and stretching. These results show that the optical properties of the older presbyopic lens are quite different from the younger, accommodated lens.

Human biological decline and mortality rates

Intercepts on the x (age)-axis of 107 normalized declining human biological functions were determined and assembled in 3 histograms, being placed in increasing order within each decade (10 year period). The histograms were classed accordingly as they contained properties associated with dividing cells, sensory properties and non-dividing cells respectively. Their cumulants were determined, multiple regressions calculated and compared with current death-rates for women and men respectively, for 10 amongst the longest living populations in the World. An alternative verification based on risk theory led to an estimate of an optimal life expectancy of 96 years. The survival curve turns out to be of the form (See text: Formula) where the inner integral represents the cumulant dimension (t') and the outer one age (t"). The premises underlying this study are compatible with the notion of a probable life-span, rather than a fixed one.

Refractive index contours in the human lens

The refractive index values along the equatorial and sagittal planes of lenses of varying ages were measured using a reflectometric fibre optic sensor. In younger lenses (from the third decade) and in one older lens, the index profiles from the two planes did not concur when plotted on a normalized scale refuting, in these lenses, the assumption of concentric, isoindicial contours which follow the shape of the lens. Agreement between the normalized profiles did occur with all other lenses investigated (aged 47 and older).

The optics of the eye-lens and lenticular senescence. A review

Although the lens of the eye is structurally a biological tissue, it functions as an optical element providing one third of the refracting power of the human eye, and a variable focus in younger years. Throughout a life-time the optical properties of the eye-lens alter, resulting in changes in function: there is a gradual depletion of the focussing amplitude from infancy to middle age, and a loss of transmittance in the later decades of life. The optical properties of the lens depend on its power, which in turn is determined by its physical dimensions (curvatures and thickness) and its refractive index as well as transmissivity and the organization of its internal components. The power of the functional lens is, however, modifiable by virtue of the lens being attached via the zonule to the ciliary muscle. The contraction and relaxation of the latter respectively increases and decreases lens power in accordance with innervations determined by the physical distance of external objects to be imaged on the retina. This review will consider many of these features and how alterations in any of them may lead to changes in lenticular function. However, as we have recently devoted a detailed study to presbyopia [1] its mechanism will not be considered here.

Age-related response of human lenses to stretching forces

Five human lenses of varying ages were subjected to radial stretching forces which mimic the action of the ciliary muscle in vivo. Although the number of lenses was small, it was found that the human lens becomes more resistant, with age, to radial stretching forces and that lenses over the age of 50 years showed very little response to stretch. In prepresbyopic lenses, stretching has a greater effect on the shape of the anterior surface than it does on the shape of the posterior surface. The five lenses studied showed individual variations in lens size and shape and a trend to increased curvature with age, particularly marked for the anterior surface.