Aging of the human lens: changes in lens shape at zero-diopter accommodation

The significance of growth shells in development of symmetry, transparency, and refraction of the human lens

Human visual function depends on the biological lens, a biconvex optical element formed by coordinated, synchronous generation of growth shells produced from ordered cells at the lens equator, the distal edge of the epithelium. Growth shells are comprised of straight (St) and S-shaped (SSh) lens fibers organized in highly symmetric, sinusoidal pattern which optimizes both the refractile, transparent structure and the unique microcirculation that regulates hydration and nutrition over the lifetime of an individual. The fiber cells are characterized by diversity in composition and age. All fiber cells remain interconnected in their growth shells throughout the life of the adult lens. As an optical element, cellular differentiation is constrained by the physical properties of light and its special development accounts for its characteristic symmetry, gradient of refractive index (GRIN), short range transparent order (SRO), and functional longevity. The complex sinusoidal structure is the basis for the lens microcirculation required for the establishment and maintenance of image formation.

Intracapsular accommodation mechanism in terms of lens curvature gradient

The intracapsular accommodation mechanism (IAM) may be understood as an increase in the lens equivalent refractive index as the eye accommodates. Our goal was to evaluate the existence of an IAM by analysing observed changes in the inner curvature gradient of the lens. To this end, we fitted a gradient index and curvature lens model to published experimental data on external and nucleus geometry changes during accommodation. For each case analysed, we computed the refractive power and equivalent index for each accommodative state using a ray transfer matrix. All data sets showed an increase in the effective refractive index, indicating a positive IAM, which was stronger for older lenses. These results suggest a strong dependence of the lens equivalent refractive index on the inner curvature gradient.

Estimation of the full shape of the crystalline lens from OCT: validation using stretched donor lenses

Quantifying human crystalline lens geometry as a function of age and accommodation is important for improved cataract and presbyopia treatments. In previous works we presented eigenlenses as a basis of 3-D functions to represent the full shape of the crystalline lens ex vivo. Also, we presented the application of eigenlenses to estimate the full shape of the lens in vivo from 3-D optical coherence tomography (OCT) images, where only the central part of the lens -visible through the pupil- is available. The current work presents a validation of the use of eigenlenses to estimate in vivo the full shape of dis-accommodated lenses. We used 14 ex vivo crystalline lenses from donor eyes (11-54 y/o) mounted in a lens stretcher, and measured the geometry and the power of the lenses using a combined OCT and ray tracing aberrometry system. Ex vivo, the full extent of the lens is accessible from OCT because the incident light is not blocked by the iris. We measured in non-stretched (fully accommodated) and stretched (mimicking in vivo dis-accommodated lenses) conditions. Then, we simulated computationally in vivo conditions on the obtained ex vivo lenses geometry (assuming that just the portion of the lens within a given pupil is available), and estimated the full shape using eigenlenses. The mean absolute error (MAE) between estimated and measured lens' diameters and volumes were MAE = 0.26 ± 0.18 mm and MAE = 7.0 ± 4.5 mm3, respectively. Furthermore, we concluded that the estimation error between measured and estimated lenses did not depend on the accommodative state (change in power due to stretching), and thus eigenlenses are also useful for the full shape estimation of in vivo dis-accommodated lenses.

Estimation of the full shape of the crystalline lens in-vivo from OCT images using eigenlenses

Quantifying the full 3-D shape of the human crystalline lens is important for improving intraocular lens power or sizing calculations in treatments of cataract and presbyopia. In a previous work we described a novel method for the representation of the full shape of the ex vivo crystalline lens called eigenlenses, which proved more compact and accurate than compared state-of-the art methods of crystalline lens shape quantification. Here we demonstrate the use of eigenlenses to estimate the full shape of the crystalline lens in vivo from optical coherence tomography images, where only the information visible through the pupil is available. We compare the performance of eigenlenses with previous methods of full crystalline lens shape estimation, and demonstrate an improvement in repeatability, robustness and use of computational resources. We found that eigenlenses can be used to describe efficiently the crystalline lens full shape changes with accommodation and refractive error.

Paraxial equivalent of the gradient-index lens of the human eye

The lens of the eye has a refractive index gradient that changes as the lens grows throughout life. These changes play a key role in the optics of the eye. Yet, the lens is generally simulated using a homogeneous model with an equivalent index that does not accurately represent the gradient. We present an analytical paraxial model of the gradient lens of the eye that gives the direct relation between refractive index distribution and paraxial characteristics. The model accurately simulates the changes in lens power with age and accommodation. It predicts that a decrease in equivalent index with age is associated with a flattening of the axial refractive index profile and that changes in lens power with accommodation are due primarily to changes in the axial variation of the iso-indicial curvature, consistent with Gullstrand's intracapsular theory of accommodation. The iso-indicial curvature gradient causes a shift of the principal planes compared to the homogeneous equivalent model. This shift introduces a clinically significant error in eye models that implement a homogenous lens. Our gradient lens model can be used in eye models to better predict the optics of the eye and the changes with age and accommodation.

Prediction of Subjective Refraction From Anterior Corneal Surface, Eye Lengths, and Age Using Machine Learning Algorithms

Purpose

To develop a machine learning regression model of subjective refractive prescription from minimum ocular biometry and corneal topography features.

Methods

Anterior corneal surface parameters (Zernike coefficients and keratometry), axial length, anterior chamber depth, and age were posed as features to predict subjective refractions. Measurements from 355 eyes were split into training (75%) and test (25%) sets. Different machine learning regression algorithms were trained by 10-fold cross-validation, optimized, and tested. A neighborhood component analysis provided features’ normalized weights in predictions.

Results

Gaussian process regression algorithms provided the best models with mean absolute errors of around 1.00 diopters (D) in the spherical component and 0.15 D in the astigmatic components.

Conclusions

The normalized weights showed that subjective refraction can be predicted by only keratometry, age, and axial length. Increasing the topographic description detail of the anterior corneal surface implied by a high-order Zernike decomposition versus adjustment to a spherocylindrical surface is not reflected as improved subjective refraction prediction, which is poor, mainly in the spherical component. However, the highest achievable accuracy differs by only 0.75 D from that of other works with a more exhaustive eye refractive elements description. Although the chosen parameters may have not been the most efficient, applying machine learning and big data to predict subjective refraction can be risky and impractical when evaluating a particular subject at statistical extremes.

Translational Relevance

This work evaluates subjective refraction prediction by machine learning from the anterior corneal surface and ocular biometry. It shows the minimum biometric information required and the highest achievable accuracy.

RESUMEN

Objetivo

El desarrollo de un modelo de regresión de aprendizaje automático prescripción refractiva subjetiva a partir de las características mínimas de la biometría ocular y la superficie corneal.

Métodos

Los parámetros de la superficie corneal anterior (coeficientes de Zernike y queratometría), además de longitudes axiales y de cámara anterior, edades y las refracciones subjetivas no ciclopléjicas de 355 ojos se dividieron en un conjunto de entrenamiento (75%) y otro de test (25%) y se entrenaron diferentes algoritmos de regresión de aprendizaje automático mediante validación cruzada 10 veces, se optimizaron y se probaron sobre el conjunto test.

Resultados

Los algoritmos de regresión del proceso gaussiano proporcionaron los mejores modelos con un error absoluto medio fue de alrededor de 1.00 D en el componente esférico y de 0.25 D en los componentes astigmáticos.

Conclusiones

Los pesos normalizados mostraron que la refracción subjetiva puede predecirse utilizando únicamente la queratometría, la edad y la longitud axial como características. El aumento del detalle de la descripción topográfica de la superficie corneal anterior que supone una descomposición de Zernike de alto orden frente al ajuste a una superficie esferocilíndrica realizado por queratometría no se refleja en una mejora de la predicción de la refracción subjetiva, que es pobre, en cualquier caso, principalmente en el componente esférico. Sin embargo, la máxima precisión alcanzada difiere en sólo 0,75 D de la de otros trabajos con una descripción más exhaustiva de los elementos refractivos del ojo. De todos modos, el aprendizaje automático y los datos masivos aplicados a la predicción de la refracción subjetiva pueden ser arriesgados y poco prácticos cuando se evalúa a un sujeto concreto en los extremos estadísticos, aunque los parámetros elegidos puedan no haber sido los más ineficaces.

Relevancia Traslativa

El trabajo evalúa la predicción de la refracción subjetiva mediante aprendizaje automático a partir de la superficie corneal anterior y la biometría ocular, mostrando la mínima información biométrica requerida y la máxima precisión alcanzable.

Eigenlenses: a new model for full crystalline lens shape representation and its applications

The crystalline lens is an important optical element in the eye, responsible for focusing, and which experiences significant changes throughout life. The shape of the lens is usually studied only in the optical area (central 4 to 6 mm). However, for a great number of applications, a description of the full shape of the crystalline lens is required. We propose a new method for the representation of the full shape of the crystalline lens, constructed from 3-dimensional optical coherence tomography images of 133 isolated crystalline lenses (0-71 y/o), which we have called eigenlenses. The method is shown to be compact and accurate to describe not only the full shape of the crystalline lens, but also the optical zone in comparison with other methods. We also demonstrate its application to the extrapolation of the full shape of the crystalline lens from in-vivo optical images of the anterior segment of the eye, where only the central part of the lens visible through the pupil is available, and in the generation (synthesis) of realistic full lenses of a given age. The method has critical applications, among others, in improving and evaluating myopia and presbyopia treatments.

Age-Related Changes to the Three-Dimensional Full Shape of the Isolated Human Crystalline Lens

Purpose

Studying the full shape crystalline lens geometry is important to understand the changes undergone by the crystalline lens leading to presbyopia, cataract, or failure of emmetropization, and to aid in the design and selection of intraocular lenses and new strategies for correction. We used custom-developed three-dimensional (3-D) quantitative optical coherence tomography (OCT) to study age-related changes in the full shape of the isolated human crystalline lens.

Methods

A total of 103 ex vivo human isolated lenses from 87 subjects (age range, 0–56 years) were imaged using a 3-D spectral-domain OCT system. Lens models, constructed after segmentation of the surfaces and distortion correction, were used to automatically quantify central geometric parameters (lens thickness, radii of curvatures, and asphericities of anterior and posterior surfaces) and full shape parameters (lens volume, surface area, diameter, and equatorial plane position). Age-dependencies of these parameters were studied.

Results

Most of the measured parameters showed a biphasic behavior, statistically significantly increasing (radii of curvature, lens volume, surface area, diameter) or decreasing (asphericities, lens thickness) very fast in the first two decades of life, followed by a slow but significant increase after age 20 years (for all the parameters except for the posterior surface asphericity and the equatorial plane position, that remained constant).

Conclusions

Three-dimensional quantitative OCT allowed us to study the age-dependency of geometric parameters of the full isolated human crystalline lens. We found that most of the lens geometric parameters showed a biphasic behavior, changing rapidly before age 20 years and with a slower linear growth thereafter.

System for on- and off-axis volumetric OCT imaging and ray tracing aberrometry of the crystalline lens

We present a new in vitro instrument for measuring shape and wavefront aberrations of the primate crystalline lens, both on- and off-axis, while simulating accommodation with a motorized lens stretching system. The instrument merges spectral domain optical coherence tomography (SD-OCT) imaging and ray tracing aberrometry using an approach that senses wavefront aberrations of the lens with the OCT probing beam. Accuracy and repeatability of aberration measurements were quantified. Preliminary experiments on two human and four cynomolgus monkey lenses demonstrate the ability of the system to measure the lens shape, spherical aberration and peripheral defocus, and their changes during simulated accommodation.

In Vivo Brillouin Analysis of the Aging Crystalline Lens

Purpose

To analyze the age dependence of the longitudinal modulus of the crystalline lens in vivo using Brillouin scattering data in healthy subjects.

Methods

Brillouin scans were performed along the crystalline lens in 56 eyes from 30 healthy subjects aged from 19 to 63 years. Longitudinal elastic modulus was acquired along the sagittal axis of the lens with a transverse and axial resolution of 4 and 60 μm, respectively. The relative lens stiffness was computed, and correlations with age were analyzed.

Results

Brillouin axial profiles revealed nonuniform longitudinal modulus within the lens, increasing from a softer periphery toward a stiffer central plateau at all ages. The longitudinal modulus at the central plateau showed no age dependence in a range of 19 to 45 years and a slight decrease with age from 45 to 63 years. A significant intersubject variability was observed in an age-matched analysis. Importantly, the extent of the central stiff plateau region increased steadily over age from 19 to 63 years. The slope of change in Brillouin modulus in the peripheral regions were nearly age-invariant.

Conclusions

The adult human lens showed no measurable age-related increase in the peak longitudinal modulus. The expansion of the stiff central region of the lens is likely to be the major contributing factor to age-related lens stiffening. Brillouin microscopy may be useful in characterizing the crystalline lens for the optimization of surgical or pharmacological treatments aimed at restoring accommodative power.

OCT-based full crystalline lens shape change during accommodation in vivo

The full shape of the accommodating crystalline lens was estimated using custom three-dimensional (3-D) spectral OCT and image processing algorithms. Automatic segmentation and distortion correction were used to construct 3-D models of the lens region visible through the pupil. The lens peripheral region was estimated with a trained and validated parametric model. Nineteen young eyes were measured at 0-6 D accommodative demands in 1.5 D steps. Lens volume, surface area, diameter, and equatorial plane position were automatically quantified. Lens diameter & surface area correlated negatively and equatorial plane position positively with accommodation response. Lens volume remained constant and surface area decreased with accommodation, indicating that the lens material is incompressible and the capsular bag elastic.

Comparison of anterior segment parameters in juvenile diabetes mellitus and healthy eyes

PURPOSE

To compare the anterior segment parameters of patients with juvenile diabetes mellitus (DM) and healthy children by optical biometry.

METHODS

This prospective controlled clinical trial included 47 patients with juvenile type 1 DM and 50 age- and sex-matched healthy children. Central corneal thickness (CCT), aqueous depth (AD), lens thickness (LT), axial length, pupillary diameter (PD), K1 and K2 keratometry, and white to white distance (WTW) measurements were performed with optical biometry. The glycosylated hemoglobin (HbA1c) levels of the DM cases were obtained. Kolmogorov-Smirnov test, t test, χ2 test, and Pearson correlation test were used for statistical analysis.

RESULTS

The mean age of the 20 boys and 27 girls with DM was 10.91 ± 3.24 years and the mean age of the 29 healthy boys and 21 girls was 11.61 ± 3.6 years (age p = 0.42; sex p = 0.09). The mean LT was thicker (p = 0.001), the mean AD was lower (p = 0.001), and the mean PD was smaller (p = 0.001) in the DM cases and all were statistically significant. There was no significant difference between the groups for AU, CCT, WTW, or K1 and K2 (p = 0.12; p = 0.83; p = 0.54; p = 0.97; p = 0.21, respectively). We also found a significant negative correlation between HbA1c levels and PD (r = -0.37 p = 0.01).

CONCLUSIONS

Juvenile DM may affect anterior segment parameters and cause thicker LT, smaller PD, and lower AD. These effects may change the refractive status and should be considered during the examination of these children.

Prediction of accommodative optical response in prepresbyopic subjects using ultrasound biomicroscopy

PURPOSE

To determine whether relatively low-resolution ultrasound biomicroscopy (UBM) can be used to predict the accommodative optical response in prepresbyopic eyes as well as in a previous study of young phakic subjects, despite lower accommodative amplitudes.

SETTING

College of Optometry, University of Houston, Houston, USA.

DESIGN

Observational cross-sectional study.

METHODS

Static accommodative optical response was measured with infrared photorefraction and an autorefractor (WR-5100K) in subjects aged 36 to 46 years. A 35 MHz UBM device (Vumax, Sonomed Escalon) was used to image the left eye, while the right eye viewed accommodative stimuli. Custom-developed Matlab image-analysis software was used to perform automated analysis of UBM images to measure the ocular biometry parameters. The accommodative optical response was predicted from biometry parameters using linear regression, 95% confidence intervals (CIs), and 95% prediction intervals.

RESULTS

The study evaluated 25 subjects. Per-diopter (D) accommodative changes in anterior chamber depth (ACD), lens thickness, anterior and posterior lens radii of curvature, and anterior segment length were similar to previous values from young subjects. The standard deviations (SDs) of accommodative optical response predicted from linear regressions for UBM-measured biometry parameters were ACD, 0.15 D; lens thickness, 0.25 D; anterior lens radii of curvature, 0.09 D; posterior lens radii of curvature, 0.37 D; and anterior segment length, 0.42 D.

CONCLUSIONS

Ultrasound biomicroscopy parameters can, on average, predict accommodative optical responses with SDs of less than 0.55 D using linear regressions and 95% CIs. Ultrasound biomicroscopy can be used to visualize and quantify accommodative biometric changes and predict accommodative optical response in prepresbyopic eyes.

Ocular biometry in the adult population in rural central China: a population-based, cross-sectional study

AIM

To describe the distribution and determinants of ocular biometric parameters and to ascertain the relative importance of these determinants in a large population of adults in rural central China.

METHODS

A population-based, cross-sectional study performed in rural central China included 1721 participants aged 40 or more years. Ocular biometrical parameters including axial length (AL), anterior chamber depth (ACD), radius of corneal curvature (K) and horizontal corneal diameter [white-to-white (WTW) distance] were measured using non-contact partial coherence interferometry [intraocular lens (IOL)-Master].

RESULTS

Ocular biometric data on 1721 participants with a average age of 57.0±8.7y were analyzed at last. The general mean AL, ACD, mean corneal curvature radius (MCR), WTW were 22.80±1.12, 2.96±0.36, 7.56±0.26 and 11.75±0.40 mm, respectively. The mean values of each parameter in 40 to 49, 50 to 59, 60 to 69, and 70 to 91 years age groups were as follows: AL, 22.77±0.87, 22.76±1.06, 22.89±1.41, 22.92±0.80 mm; ACD, 3.10±0.32, 2.98±0.34, 2.86±0.36, 2.77±0.35 mm; MCR, 7.58±0.25, 7.54±0.26, 7.55±0.26, 7.49±0.28 mm; WTW, 11.79±0.38, 11.75±0.40, 11.72±0.41, 11.67±0.41 mm. The AL, ACD, MCR and WTW were correlated with age and the AL was correlated with height and weight.

CONCLUSION

Our findings can serve as an important normative reference for multiple purposes and may help to improve the quality of rural eye care.

Intra-session repeatability of iridocorneal angle measurements provided by a Scheimpflug photography-based system in healthy eyes

PURPOSE

The purpose of this study was to evaluate intra-session repeatability of measurements of the iridocorneal angle at different meridians in the nasal and temporal areas in healthy eyes using the Sirius Scheimpflug photography-based system in glaucoma analysis mode.

METHODS

A total of 43 eyes of 43 patients ranging in age from 36 to 79 years were enrolled in the study. All eyes received a comprehensive ophthalmologic examination including a complete anterior segment analysis with the Costruzione Strumenti Oftalmici [CSO] Sirius system. Three consecutive measurements of nasal and temporal angles at 0°, ±10°, ±20°, and ±30° meridians were obtained in order to assess the intra-session repeatability of iridocorneal angle measurements provided by the device using the glaucoma analysis mode. Within-subject standard deviation (Sw), coefficient of variation (CV), and intraclass correlation coefficient (ICC) values were calculated.

RESULTS

The mean Sw was 1.07 ± 1.09°, 1.22 ± 1.53°, 0.66 ± 0.51°, 0.86 ± 0.57°, 0.68 ± 0.65°, 0.84 ± 0.68°, and 0.91 ± 0.70° at the temporal 30°, 20°, 10°, 0°, -10°, -20°, and -30° positions, respectively. Mean Sw was 3.13 ± 3.15°, 3.43 ± 3.63°, 2.75 ± 2.29°, 2.19 ± 1.55°, 1.90 ± 1.49°, 2.14 ± 1.74°, and 2.24 ± 2.06° at the temporal -30°, -20°, -10°, 0°, 10°, 20°, and 30° positions, respectively. Mean CV ranged from 1.36 ± 1.05 % (nasal 0° position) to 10.92 ± 13.95 % (nasal -20° position). ICC values ranged from 0.778 to 0.972.

CONCLUSIONS

The glaucoma analysis mode of the Sirius system provides consistent measurements of the iridocorneal angle at different meridians in healthy eyes, with slightly less consistency for nasal measurements. It may be considered a clinically useful non-invasive technique for the detection of potentially occludable angles.

Extralenticular and lenticular aspects of accommodation and presbyopia in human versus monkey eyes

PURPOSE

To determine if the accommodative forward movements of the vitreous zonule and lens equator occur in the human eye, as they do in the rhesus monkey eye; to investigate the connection between the vitreous zonule posterior insertion zone and the posterior lens equator; and to determine which components-muscle apex width, lens thickness, lens equator position, vitreous zonule, circumlental space, and/or other intraocular dimensions, including those stated in the objectives above-are most important in predicting accommodative amplitude and presbyopia.

METHODS

Accommodation was induced pharmacologically in 12 visually normal human subjects (ages 19-65 years) and by midbrain electrical stimulation in 11 rhesus monkeys (ages 6-27 years). Ultrasound biomicroscopy imaged the entire ciliary body, anterior and posterior lens surfaces, and the zonule. Relevant distances were measured in the resting and accommodated eyes. Stepwise regression analysis determined which variables were the most important predictors.

RESULTS

The human vitreous zonule and lens equator move forward (anteriorly) during accommodation, and their movements decline with age, as in the monkey. Over all ages studied, age could explain accommodative amplitude, but not as well as accommodative lens thickening and resting muscle apex thickness did together. Accommodative change in distances between the vitreous zonule insertion zone and the posterior lens equator or muscle apex were important for predicting accommodative lens thickening.

CONCLUSIONS

Our findings quantify the movements of the zonule and ciliary muscle during accommodation, and identify their age-related changes that could impact the optical change that occurs during accommodation and IOL function.

The effect of phenylephrine on the ciliary muscle and accommodation

PURPOSE

To objectively measure changes in the human ciliary muscle dimensions in vivo after instillation of topical phenylephrine, a mydriatic and vasodilating agent.

METHODS

A cross-sectional study of 25 healthy young adults was conducted. Measurements of pupil size, accommodation, and ciliary muscle thickness were made both before and 30 min after instillation of 1% proparacaine and 2.5% phenylephrine. Accommodation was measured in three ways: subjectively using a push-up technique and Royal Air Force (RAF) rule, and objectively using both the Grand Seiko autorefractor and PowerRefractor. Images of the temporal ciliary muscle were acquired using the Visante Anterior Segment Optical Coherence Tomographer (OCT). Ciliary muscle images were objectively analyzed using a computer-based segmentation technique.

RESULTS

Amplitude of accommodation using the push-up test was reduced by about 1 D with phenylephrine (p < 0.001). Phenylephrine did not change the accommodative response to a 4 D Badal target as measured by either autorefraction or photorefraction (p > 0.30). There was statistically significant thickening of the anterior region and thinning of the posterior region of the ciliary muscle with accommodation (p < 0.001, all locations). Phenylephrine did not affect either baseline ciliary muscle thickness or the accommodative contraction of the muscle (p > 0.09).

CONCLUSIONS

Low-dose phenylephrine does not affect ciliary muscle dimensions, ciliary muscle contractility, or accommodative response to a 4 D near target.

Effect of age on components of peripheral ocular aberrations

PURPOSE

To investigate the effect of age on the contributions of the anterior cornea and internal components to ocular aberrations in the peripheral visual field.

METHODS

Ocular aberrations were measured in 10 young emmetropes and 7 older emmetropes using a modified commercial Hartmann-Shack aberrometer across 42° × 32° of central visual field. Anterior corneal aberrations were estimated from anterior corneal topography using theoretical ray-tracing. Internal aberrations were calculated by subtracting anterior corneal aberrations from ocular aberrations.

RESULTS

Anterior corneal aberrations of young subjects were reasonably compensated by the internal aberrations, except for astigmatism for which the internal contribution was small out to the 21° field limit. The internal coma and spherical aberration of the older subjects were considerably smaller in magnitude than those of the young subjects such that the compensation for anterior corneal aberrations was poorer. This can be explained by age-related changes in the lens shape and refractive index distribution.

CONCLUSIONS

Loss of balance between anterior cornea and internal components of higher order aberrations with increasing age, found previously for on-axis vision, applies also to the peripheral visual field.

Ex vivo measurement of postmortem tissue changes in the crystalline lens by Brillouin spectroscopy and confocal reflectance microscopy

Use of Brillouin spectroscopy in ophthalmology enables noninvasive, spatially resolved determination of the rheological properties of crystalline lens tissue. Furthermore, the Brillouin shift correlates with the protein concentration inside the lens. In vitro measurements on extracted porcine lenses demonstrate that results obtained with Brillouin spectroscopy depend strongly on time after death. The intensity of the Brillouin signal decreases significantly as early as 5 h postmortem. Moreover, the fluctuation of the Brillouin frequency shift inside the lens increases with postmortem time. Images of lens tissue taken with a confocal reflectance microscope between measurements reveal a degenerative aging process. These tissue changes correlate with our results from Brillouin spectroscopy. It is concluded that only in vivo measurements appropriately reflect the rheological properties of the eye lens and its protein concentration.

Accuracy and resolution of in vitro imaging based porcine lens volumetric measurements

There is considerable interest in determining lens volume in the living eye. Lens volume is of interest to understand accommodative changes in the lens and to size accommodative IOLs (A-IOLs) to fit the capsular bag. Some studies have suggested lens volume change during accommodation. Magnetic Resonance Imaging (MRI) is the only method available to determine lens volume in vivo. MRI is, by its nature, relatively low in temporal and spatial resolution. Therefore analysis often requires determining lens volume from single image slices with relatively low resolution on which only simple image analysis methods can be used and without repeated measures. In this study, 7 T MRI scans encompassing the full lens volume were performed on 19 enucleated pig eyes. The eyes were then dissected to isolate and photograph the lens in profile and the lens volumes were measured empirically using a fluid displacement method. Lens volumes were calculated from two- and three-dimensional (2D and 3D) MR and 2D photographic profile images of the isolated lenses using several different analysis methods. Image based and actual measured lens volumes were compared. The average image-based volume of all lenses varied from the average measured volume of all lenses by 0.6%-6.4% depending on the image analysis method. Image analysis methods that use gradient based edge detection showed higher precision with actual volumes (r(2): 0.957-0.990), while threshold based segmentation had poorer correlations (r(2): 0.759-0.828). The root-mean-square (RMS) difference between image analysis based volumes and fluid displacement measured volumes ranged from 8.51 μl to 25.79 μl. This provides an estimate of the error of previously published methods used to calculate lens volume. Immobilized, enucleated porcine eyes permit improved MR image resolution relative to living eyes and therefore improved image analysis methods to calculate lens volume. The results show that some of the accommodative changes in lens volume reported in the literature are likely below the resolution limits of imaging methods used. MRI, even with detailed image analysis methods used here, is unlikely to achieve the resolution required to accurately size an A-IOL to the capsular bag.

Light-scattering study of the normal human eye lens: elastic properties and age dependence

The human ocular lens is a tissue capable of changing its shape to dynamically adjust the optical power of the eye, a function known as accommodation, which gradually declines with age. This capability is the response of the lens tissue to external forces, which, in turn, is modulated by the biomechanical characteristics of lens tissues. In order to investigate the contributions of lens sclerosis to loss of accommodation, we report on in vitro confocal Brillouin light scattering studies of human ocular lenses spanning over a 30-70 year age range. Using this nondestructive measurement method, we determined that the longitudinal bulk modulus (average ± SD) of the lens nucleus (2.79 ± 0.14 GPa) was consistently greater than the bulk modulus of the lens cortex (2.36 ± 0.09 GPa). Moreover, our results showed that these differences were not age dependent over the 40 year age range that we evaluated using healthy lens tissues. Our results are consistent with the hypothesis that an age-dependent change in the bulk modulus of lens tissues does not fully account for the natural decline of accommodation.

Exploring ocular aberrations with a schematic human eye model

PURPOSE

Advances in ophthalmic technologies now offer both the measurement and reduction of ocular aberrations by surgically or otherwise honing refraction in the anterior eye. Ocular aberrations, however, are known to change with a multitude of factors, including field position, accommodation level, and age. Thus, although static correction of aberrations provides some vision improvement, this may be less than expected.

METHODS

In this article, we use an aspheric, variable-focus, age-dependent, gradient index schematic eye to investigate where ocular aberrations arise in the eye and how these change with field position, accommodation, and age. Optical ray tracing was carried out using optical design software ZEMAX, and Seidel aberration analysis was performed with custom written software in MATLAB.

RESULTS AND CONCLUSIONS

Our modeling is consistent with clinical findings that certain corneal aberrations almost balance those arising from the lens. Our calculations also support the general notion that, by optical sculpting, corneal aberrations can be adjusted to completely balance out those of the lens. This can effectively eliminate the eye's total monochromatic aberrations, but for only one retinal image point at a time. Centered on this point of minimal aberration is a region (the isoplanatic patch) within which the aberrations produce a point spread smaller than some tolerable limit. Also, using available evidence in the literature concerning changes in critical ocular parameters with age and accommodation, our modeling results parallel established clinical findings, and additionally indicate that the major source of aberration change can be attributed to the gradient index distribution in the lens.

Lens diameter and thickness as a function of age and pharmacologically stimulated accommodation in rhesus monkeys

Uncertainty exists regarding accommodative and age changes in lens diameter and thickness in humans and monkeys. In this study, unaccommodated and accommodated refraction, lens diameter, and lens thickness were measured in rhesus monkeys across a range of ages. Iridectomized eyes were studied in 33 anesthetized monkeys aged 4-23 years. Refraction was measured using a Hartinger coincidence refractometer and lens thickness was measured with A-scan ultrasound. Lens diameters were measured with image analysis from slit-lamp images captured via a video camera while a saline filled, plano perfusion lens was placed on the cornea. Accommodation was pharmacologically stimulated with 2% pilocarpine via the perfusion lens in 21 of the monkeys and lens diameters were measured until a stable minimum was achieved. Refraction and lens thickness were measured again after the eye was accommodated. Unaccommodated lens thickness increased linearly with age by 0.029 mm/year while unaccommodated lens diameter showed no systematic change with age. Accommodative amplitude decreased by 0.462 D/year in response to pilocarpine. The accommodative increase in lens thickness decreased with age by 0.022 mm/year. The accommodative decrease in lens diameter declined linearly with age by 0.021 mm/year. Rhesus monkeys undergo the expected presbyopic changes including increasing lens thickness and a decreasing ability of the lens to undergo changes in thickness and diameter with accommodation, however without an age-related change in unaccommodated lens diameter. As in humans, the age-related decrease in accommodative amplitude in rhesus monkeys cannot be attributed to an age-related increase in lens diameter.

Change in the accommodative force on the lens of the human eye with age

The aim of the study was to determine the age-dependence of the accommodative force on the lens in order to make it clear whether the causes of presbyopia are due to lenticular or extralenticular changes. A finite element model of the lens of an 11-, 29- and 45-year-old human eye was constructed to represent the fully accommodated state. Subsequently, the force that was needed to mould the lens into its unaccommodated state was calculated. The force on the lens appeared to be preserved with age, with only a slight increase to a value of approximately 0.06N. In conclusion, the preservation of the net force delivered by the extralenticular ciliary body indicates that the causes of presbyopia must be ascribed to lenticular changes.

[Measurement of accommodation using optical biometry]

BACKGROUND

Making accommodation possible for all age groups is a topic of great interest. We applied optical biometry in order to study the physiological mechanisms in detail. Longitudinal relations in the optical axis were measured during accommodation in volunteers of different ages and lens states.

METHODS

A total of 60 subjects (children, adolescents, adults, and pseudophakes) were examined using the IOL Master. We measured anterior chamber depth (ACD), axial length (AL), and changes in these two measurements during accommodation.

RESULTS

Near accommodation (NA) in adolescents caused the largest ACD decrease (0.14+/-0.03 mm). ACD decreased in adults during NA but not in pseudophakic patients of comparable age. AL increased during NA in all groups by 0.01+/-0.01 mm.

CONCLUSIONS

ACD decreased with age. Using a physiological stimulus, no change in ACD was measured during NA in pseudophakic patients. The documented increase in AL needs to be evaluated further.

Wide-field schematic eye models with gradient-index lens

We propose a wide-field schematic eye model, which provides a more realistic description of the optical system of the eye in relation to its anatomical structure. The wide-field model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarro's model for off-axis aberrations and Thibos's chromatic on-axis model (the Indiana eye). These two models are based on extensive experimental data, which makes the derived wide-field eye model also consistent with that data. A mathematical method to construct a GRIN lens with its iso-indicial contours following the optical surfaces of given asphericity is presented. The efficiency of the method is demonstrated with three variants related to different age groups. The role of the GRIN structure in relation to the lens paradox is analyzed. The wide-field model with a GRIN lens can be used as a starting design for the eye inverse problem, i.e., reconstructing the optical structure of the eye from off-axis wavefront measurements. Anatomically more accurate age-dependent optical models of the eye could ultimately help an optical designer to improve wide-field retinal imaging.

Adaptive model of the gradient index of the human lens. I. Formulation and model of aging ex vivo lenses

A simple, parametric adaptive model of the refractive index distribution of the ex vivo crystalline lens is presented. It assumes conicoid (or nonrevolution quadric in 3D) iso-indical surfaces, concentric with the external surfaces of the lens. The model uses a minimum number of internal structural parameters, while the shape of the iso-indical surfaces adapts automatically to the external geometry. In this way, it is able to adapt and fit individual distributions as well as adapt to the changes of the lens shape and structure with age and accommodation. The model is fit to experimental data for individual eyes spanning ages 7 to 82 years, where for each eye the crystalline lens dimensions and iso-indical index data are known. The analysis demonstrates that only one age-dependent structural parameter is needed to replicate the internal iso-indical index structure, given age-dependent models for the external surfaces. An age-dependent-parameter global model is derived and is shown to predict age-dependent changes in the ex vivo lens power and longitudinal spherical aberration with age.

Aspects of eye accommodation evaluated by finite elements

Axisymmetric nonlinear finite models of accommodation incorporating the posteriorly sloped force and vitreous effects have been studied by means of their effectiveness in mechanical and optical performances. All materials were assumed to be linearly elastic, vitreous and lens matrices were incompressible. The present model is subjected to certain indicated shortcomings, however, the behavior of the model is predictable, reasonable and favourably consistent with different published data, supporting the Helmholtz theory of accommodation.

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.

In vitro dimensions and curvatures of human lenses

The purpose of this study was to determine dimensions and curvatures of excised human lenses using the technique of shadowphotogrammetry. A modified optical comparator and digital camera were used to photograph magnified sagittal and coronal lens profiles. Equatorial diameter, anterior and posterior sagittal thickness, anterior and posterior curvatures, and shape factors were obtained from these images. The data were used to calculate lens volumes, which were compared with the lens weights. Measurements were made on 37 human lenses ranging in age from 20 to 99 years. These showed that lens dimensions and the anterior radius of curvature increase linearly throughout adult life while posterior curvature remains constant. The relative shape (or aspect ratio) of the posterior lens is unchanged through adult life since both equatorial diameter and posterior thickness increase at the same rate. The ratio of anterior thickness to posterior thickness is constant at 0.70. It is suggested that in vivo forces alter the apparent location of the lens equator, that the in vitro lens shape corresponds to the maximally accommodated shape in vivo and that the shapes of the accommodated and unaccommodated lens progressively converge toward each other due to lens growth with age, with a convergence point located near the age of total loss of accommodation (55-60 years). Together, these observations provide additional support for the Helmholtz theory of accommodation.

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.

On the prediction of optical aberrations by personalized eye models

PURPOSE

The purpose of this study is to develop and analyze a method to obtain optical schematic models of individual eyes. Each model should be able to reproduce the measured monochromatic wave aberration with high fidelity.

METHODS

First, we choose a generic eye model as the input guess and then apply a two-stage customization procedure. Stage 1 consists of replacing, in the initial generic model, those anatomic and optical parameters with experimental data measured on the eye under analysis. The set of experimental data was that provided by a standard clinical preoperative examination, namely lens topography, ultrasound biometry, and total wave aberration. Then, the second stage is to find the unknown lens structure that would reproduce the measured wave aberration through optical optimization. Two totally different initial eye models have been compared; one considers a simpler constant refractive index for the lens, whereas the second model has a gradient-index (GRIN) lens.

RESULTS

This automatic customization method has been applied to 19 eyes with different degrees of spherical ametropia (from +0.4 D to -8 D). Two models have been obtained for each eye (constant and gradient index lens). The results were highly satisfactory, with 100% convergence, and with average RMS prediction errors approximately lambda/100. This is one order of magnitude lower than typical measurement errors. The models with a constant refractive index lens tended to overestimate surface curvatures, whereas for the GRIN model, lens surfaces were too flat.

CONCLUSIONS

The proposed method is highly efficient and robust giving a high-fidelity reproduction of the wavefront in all cases attempted so far. Limitations found in reproducing the geometry of the lens seem to be associated with the use of inaccurate models of its refractive index.

Estimating the external force acting on the human eye lens during accommodation by finite element modelling

Using new geometric information on the shape of the lens that has recently become available, a finite element model has been developed in order to estimate the forces that act on the lens during accommodation for a typical 29-year-old human eye. To investigate the influence of the anterior, posterior and central zonular fibres insertion regions, three models with different configurations were built. All three configurations appeared to be capable of inducing the required accommodative changes in the lens. Based on material properties from the literature, the estimated summed net force for each of the three models was approximately 0.08 N.

Comment on "Scheimpflug and high-resolution magnetic resonance imaging of the anterior segment: a comparative study"

In a recent paper, Koretz et al. [J. Opt. Soc. Am. A 21, 346 (2004)] conclude that the results of the "corrected Scheimpflug technique" to obtain the shape of the human lens differ significantly from their magnetic resonance imaging (MRI) data. We demonstrate that the conclusions are based on incorrect statistical methods. A straightforward statistical comparison shows that there is no significant difference between the corrected Scheimpflug results and the MRI data.

The mechanism of presbyopia

Accommodation in humans refers to the ability of the lens to change shape in order to bring near objects into focus. Accommodative loss begins during childhood, with symptomatic presbyopia, or presbyopia that affects one's day to day activities, striking during midlife. While symptomatic presbyopia has traditionally been treated with reading glasses or contact lenses, a number of surgical interventions and devices are being actively developed in an attempt to restore at least some level of accommodation. This is occurring at a time when the underlying cause of presbyopia remains unknown, and even the mechanism of accommodation is occasionally debated. While Helmholtz' theory regarding the mechanism of accommodation is generally accepted with regard to broad issues, additional details continue to emerge. Age-related changes in anterior segment structures associated with accommodation have been documented, often through in vitro and/or rhesus monkey studies. A review of these findings suggests that presbyopia develops very differently in humans compared to non-human primates. Focusing on non-invasive in vivo human imaging technologies, including Scheimpflug photography and high-resolution magnetic resonance imaging (MRI), the data suggest that the human uveal tract acts as a unit in response to age-related increasing lens thickness and strongly implicates lifelong lens growth as the causal factor in the development of presbyopia.

Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)

Using a non-invasive MRI technique for measuring the refractive index distribution through the crystalline lens, refractive index maps were obtained through 20 intact isolated human lenses (7-82years). Focal length measurements, obtained by simulated light ray propagation through each index map were found to be in agreement with direct measurements performed on a scanning laser apparatus. With increasing age, the refractive index profiles became flatter in the central region, accompanied by steepening of the profile in the periphery. This appears to be an important mechanism underlying the observed changes in power and longitudinal aberration of the human lens.

Central surface curvatures of postmortem- extracted intact human crystalline lenses: implications for understanding the mechanism of accommodation

PURPOSE

To measure the radii of curvature of postmortem, whole, encapsulated human crystalline lenses, free of all zonular attachments, and to calculate their corresponding optical powers.

DESIGN

Experimental study.

PARTICIPANTS

Thirty human crystalline lenses from donors with a mean age of 33.6+/-14.4 years.

METHODS

Intact clear human crystalline lenses were obtained within an average of 21 hours of death. The lenses were removed from the eye by the contributing eye bank and shipped in Optisol-GS, a physiologic preservative storage medium. These lenses, with intact capsules, were freed of all zonular attachments. The lenses were stored at 7 degrees C and were maintained in the same storage medium during the period that they were held for evaluation. Using a portable Keratron Scout corneal topographer (Eyequip, Ponte Vedra Beach, FL) fixed to an optical bench, the radii of curvatures of the anterior and posterior surfaces of the crystalline lens were measured daily for 10 days after receipt of the tissue. The capsules of the crystalline lenses remained intact, and the lenses were clear throughout the study. Measurements were made at room temperature after removing the lens from storage. Eight repetitions of the topography were made from each surface on each day to determine the accuracy and stability of the measurement. Profile photographs were taken daily to establish the central crystalline lens thickness. The corresponding optical power of each physiologically maintained crystalline lens was calculated.

MAIN OUTCOME MEASURES

The main outcome measures were the central anterior radius of curvature, the central posterior radius of curvature, the central thickness of each crystalline lens, and the amount of change in these parameters over 10 days.

RESULTS

The means +/- standard deviations of the central anterior and posterior radii of curvatures of the 30 adult lenses were 10.5+/-0.6 mm and 7.1+/-1.0 mm, respectively. The mean +/- standard deviation of the central thickness, as measured from profile photographs, was 3.9+/-0.5 mm. These mean measurements remained stable for up to 5 days after receipt of the tissue. The mean and standard deviation of the calculated optical power of these postmortem, physiologically maintained, intact human crystalline lenses from donors with a mean age of 33.6 years was 19.8+/-1.7 diopters.

CONCLUSIONS

Lenses free of zonular tension are at an optical power that would be associated with optimal distance acuity.

Scheimpflug and high-resolution magnetic resonance imaging of the anterior segment: a comparative study

High-resolution imaging with a camera system built on the Scheimpflug principle has been used to characterize the geometry of the anterior segment of the adult human eye as a function of aging and accommodative state but is critically dependent on algorithms for correction of distortion. High-resolution magnetic resonance imaging (MRI), in contrast, provides lower-resolution information about the adult eye but is undistorted. To test the accuracy of the Scheimpflug correction methods used by Cook and Koretz [J. Opt. Soc. Am. A 15, 1473 (1998)]; [Appl. Opt. 30, 2088 (1991)], data on anterior chamber and segment lengths, as well as lens thickness and anterior and posterior curvatures, were compared with corresponding MRI data for adults aged 18-50 at 0 diopter accommodation. Excellent statistical agreement was found between the MRI and the Scheimpflug data sets with the exception of the posterior lens radius of curvature, which is less well defined than the other measurements in the Scheimpflug images. The considerable agreement between data obtained with MR and Scheimpflug imaging, two different yet complementary in vivo imaging techniques, validates the Scheimpflug correction algorithms of Cook and Koretz and suggests the capability of directly integrating information from both. A third, equivalent, data set obtained with a Scheimpflug-style camera system differs considerably from both Scheimpflug and MRI results in magnitude and age dependence, with negative implications for this alternative method and its correction procedures.

Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses

The purpose of this study was to measure the shape of the anterior and posterior surface of human cadaver lenses in situ using a corneal topography system. Measurements were performed on 13 pairs of eyes using the PAR Corneal Topography System (PAR-CTS). The age of the donors ranged from 46 to 93 years, with an average age of 76.4 years. Anterior lens topography was measured after excision of the cornea and iris. Posterior lens topography was measured after sectioning the posterior segment and adherent vitreous. The PAR-CTS files providing raw surface height were exported for analysis. In each surface, 18 meridians separated by 10 degrees were fitted using conic sections to obtain values of the apical radius of curvature (R) and shape factor (p). The average apical radius of curvature and asphericity were R=10.15+/-1.39mm and p=4.27+/-1.39 for the anterior surface and R=-6.25+/-0.79mm and p=-0.64+/-1.85 for the posterior surface. A significant variation of the radius of curvature and shape factor as a function of the meridian angle (lens astigmatism) was found in some lenses. Contrary to previous findings, the anterior lens surface was found to steepen toward the periphery.

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.

Modelling the mechanics of accommodation and presbyopia

Finite element methods have been used to compute the expected relationship between changes in ciliary body diameter and the change in refractive power implied by the change in geometry of the human ocular lens, using values for the material properties and initial geometry taken from the literature (notably the slit lamp photography of Brown (1973) and the studies by Fisher (1969) of the lens material properties). The results show that if the non-linearity associated with the changing geometry is taken into account the lens does not respond to ciliary body stretch by an increase in power [as recently claimed by Schachar et al. (1993), but in the conventional way with a decrease in power. The models show a decrease in the amplitude of accommodation between the age of 29 and 45 years (using Brown's data, 1973), but using Brown's data for the 11-year-old eye leads to the paradoxical conclusion that accommodation amplitude in this eye would have been small. In the process of carrying out the modelling, we have examined the consistency of the published measurements and also the validity of the mathematical methods used in interpreting them, and this analysis suggests that further work is needed before one can be confident that the assumptions about geometry and material properties on which the modelling is based are sound.

Aging of the human lens: changes in lens shape upon accommodation and with accommodative loss

Accommodation in the human eye occurs through controlled changes in crystalline lens shape, thickness, and refractive surface placement relative to the cornea. The changes in lens curvatures, whether surface or internal, have been characterized as a function of accommodation and subject age by use of quantitative analysis of Scheimpflug slit-lamp photographic images. Radii of curvature of the major lens refractive surfaces--the external and nuclear boundaries--decrease linearly with increasing accommodation in all eyes that are capable of accommodation. The rates at which they change with accommodation are age dependent, decreasing steadily toward zero with increased age. For the curves visible in each lens half, arising from boundaries between adjacent zones of discontinuity, radius of curvature and location are linearly related over the entire accommodative range for a given lens and over the age range for the population. The slope of this relationship changes with both accommodation and age, decreasing linearly in both cases. The relationship between these geometric changes and the loss of accommodative amplitude is discussed.

Aging of the optics of the human eye: lens refraction models and principal plane locations

Biometric data describing the geometry and spacings of emmetropic human eyes were combined with lens shape and placement within the globe to generate paraxial models of image formation as a function of age. Three different representations of the shape of the internal refractive index gradient of the lens were evaluated--a Gullstrand-type model consisting of cortical and nuclear regions with different refractive indices, a power series model, and a linear-gradient model. All three refractive models satisfy the requirements for focus for all the data sets, indicating that lenticular refractive index gradient shape is essentially underdetermined in the paraxial limit. Lens refractive power decreases by almost 2 D during a 50-year period, and the concomitant decrease in system refractive power is due almost entirely to this effect. The reduction in spacing between the lens principal planes is a function of this, as is their anterior movement with age, and suggests that the compensatory processes maintaining far focus at the expense of near are not exactly balanced. Despite these changes in the lens contribution and their effect on the location of the system principal planes, which also move anteriorly, the spacing between the system principal planes remains constant. However, the trend toward reduced overall system power with age indicates the primary role of the lens in mediating image formation onto the retina over time.