Changes in lens dimensions and refractive index with age and accommodation

BCLA CLEAR presbyopia: Mechanism and optics

With over a billion adults worldwide currently affected, presbyopia remains a ubiquitous, global problem. Despite over a century of study, the precise mechanism of ocular accommodation and presbyopia progression remains a topic of debate. Accordingly, this narrative review outlines the lenticular and extralenticular components of accommodation together with the impact of age on the accommodative apparatus, neural control of accommodation, models of accommodation, the impact of presbyopia on retinal image quality, and both historic and contemporary theories of presbyopia.

Connexin 50 Influences the Physiological Optics of the In Vivo Mouse Lens

Purpose

The purpose of this study was to utilize multi-parametric magnetic resonance imaging (MRI) to investigate in vivo age-related changes in the physiology and optics of mouse lenses where Connexin 50 has been deleted (Cx50KO) or replaced by Connexin 46 (Cx50KI46).

Methods

The lenses of transgenic Cx50KO and Cx50KI46 mice were imaged between 3 weeks and 6 months of age using a 7T MRI. Measurements of lens geometry, the T2 (water-bound protein ratios), the refractive index (n), and T1 (free water content) values were calculated by processing the acquired images. The lens power was calculated from an optical model that combined the geometry and the n. All transgenic mice were compared with control mice at the same age.

Results

Cx50KO and Cx50KI46 mice developed smaller lenses compared with control mice. The lens thickness, volume, and surface radii of curvatures all increased with age but were limited to the size of the lenses. Cx50KO lenses exhibited higher lens power than Cx50KI46 lenses at all ages, and this was correlated with significantly lower water content in these lenses, which was probably modulated by the gap junction coupling. The refractive power tended to a steady state with age, similar to the control mice.

Conclusions

The modification of Cx50 gap junctions significantly impacted lens growth and physiological optics as the mouse aged. The lenses showed delayed development growth, and altered optics governed by different lens physiology. This research provides new insights into how gap junctions regulate the development of the lens's physiological optics.

Alterations in Lens Free Water Distribution Are Associated with Shape Deformation in Accommodation

Objective

To investigate whether a redistribution of water within the crystalline lens is associated with the shape deformation that occurs during accommodation.

Design

Observational, cross sectional study.

Subjects

Eleven young adults without presbyopia (aged 18-39 years) and 9 middle-aged adults with presbyopia (aged 40-55 years).

Methods

Magnetic resonance imaging (MRI) scans of the lens were acquired on a 3 Tesla clinical MRI scanner, without and with the presentation of a 3 Diopter accommodative stimulus. The MRIs were postprocessed using established methods to extract the geometric dimensions and spatial maps of water distribution of the lens.

Main Outcome Measures

Accommodative changes in the full 3-dimensional description of lens shape, the lens total-water distribution profile, and the lens free-water distribution profile.

Results

Viewing of an accommodative stimulus by young subjects elicited an elastic shape deformation of the lens consistent with accommodation that was associated with an elevated, smoother free-water distribution, primarily in the anterior region of the lens. In contrast, viewing of an accommodative stimulus by presbyopic subjects produced an atypical shape deformation of the lens that was instead associated with a lowered free-water distribution, primarily in the anterior region of the lens. No discernible changes to the lens total-water distribution were observed in response to the accommodative stimulus in either subject cohort.

Conclusions

The present study suggests that protein-mediated alterations in the free-water distribution of the anterior region of the lens influence the shape deformation in accommodation, presenting pharmacological modulation of free-water distribution as an attractive novel approach for treating presbyopia.

Financial Disclosures

The authors have no proprietary or commercial interest in any materials discussed in this article.

Refractive Index Measurement of the Crystalline Lens in Vivo

SIGNIFICANCE

This study provides a new method to measure the refractive index of crystalline lens in the human eye in vivo .

PURPOSE

Accessing the refractive index of crystalline lenses in the human eye in vivo has long been a challenge. This study aimed to measure the refractive index of a lens in vivo using an anterior segment optical coherence tomography (AS-OCT) system combined with a Scheimpflug imaging system.

METHOD

A ray-traceable Scheimpflug imaging was developed and integrated into an AS-OCT system. A theoretical study revealed that the combination of these two systems provides a unique solution for simultaneously measuring the refractive index and the thickness of the lens. The average lens refractive index along the ray pathway ( Nav ) and lens shape were measured for seven subjects.

RESULTS

The lens Nav along the central ray varies from 1.383 to 1.419 between subjects. The lens refractive index function across the lens diameter varies from subject to subject. The lens Nav increases for accommodated eyes. The thicknesses and profiles of the lenses are also determined.

CONCLUSIONS

The lens refractive index varies substantially from individual eye to individual eye, not only along the central ray pathway but also for the lens refractive index function across the lens diameter. Ray-traceable Scheimpflug imaging-equipped AS-OCT is useful for testing the refractive index of lenses in the human eye in vivo .

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.

Refractive development I: Biometric changes during emmetropisation

PURPOSE

Although there are many reports on ocular growth, these data are often fragmented into separate parameters or for limited age ranges. This work intends to create an overview of normal eye growth (i.e., in absence of myopisation) for the period before birth until 18 years of age.

METHODS

The data for this analysis were taken from a search of six literature databases using keywords such as "[Parameter] & [age group]", with [Parameter] the ocular parameter under study and [age group] an indication of age. This yielded 34,409 references that, after screening of title, abstract and text, left 294 references with usable data. Where possible, additional parameters were calculated, such as the Bennett crystalline lens power, whole eye power and axial power.

RESULTS

There were 3422 average values for 17 parameters, calculated over a combined total of 679,398 individually measured or calculated values. The age-related change in refractive error was best fitted by a sum of four exponentials (r²  = 0.58), while all other biometric parameters could be fitted well by a sum of two exponentials and a linear term ('bi-exponential function'; r² range: 0.64-0.99). The first exponential of the bi-exponential fits typically reached 95% of its end value before 18 months, suggesting that these reached genetically pre-programmed passive growth. The second exponentials reached this point between 4 years of age for the anterior curvature and well past adulthood for most lenticular dimensions, suggesting that this part represents the active control underlying emmetropisation. The ocular components each have different growth rates, but growth rate changes occur simultaneously at first and then act independently after birth.

CONCLUSIONS

Most biometric parameters grow according to a bi-exponential pattern associated with passive and actively modulated eye growth. This may form an interesting reference to understand myopisation.

Effect of age and cycloplegia on the morphology of the human crystalline lens: swept-source OCT study

PURPOSE

To evaluate the effect of age and cycloplegia on the morphology of the crystalline lens using a swept-source optical coherence tomography (SS-OCT) system.

SETTING

Hospital.

DESIGN

Prospective cross-sectional study.

METHODS

The parameters including anterior chamber depth (ACD), the radii of curvature of the anterior and posterior surface of the crystalline lens (ALR and PLR), lens thickness (LT), lens equatorial diameter (LED), and lens vault (LV) were quantified by the SS-OCT before and after cycloplegia. The paired t test was used to compare the parameters before and after cycloplegia. A multivariate linear regression model was built to analyze the association between the parameters/cycloplegia-induced changes and age, while adjusting for the effect of axial length, refractive status, and sex.

RESULTS

76 individuals (age range, 18 to 86 years) were recruited. The ALR and ACD were negatively correlated with age (P ≤ .002), and the LT, LV, and LED were positively correlated with age (P ≤ .004). In participants younger than 60 years, the ALR and ACD significantly increased, whereas the LV and LT significantly decreased after cycloplegia (all P < .001). With aging, cycloplegia-induced differences of ALR (P = .001) and ACD (P = .014) significantly decreased, and of LT (P < .001), LT (P < .001), and LV (P = .001) significantly increased.

CONCLUSIONS

The crystalline lens morphology measured by the SS-OCT revealed steepening anterior surface and increasing equatorial diameter with age. Cycloplegia caused a significant change of anterior surface morphology in participants younger than 60 years, and this effect diminished with age.

MR-EYE: High-Resolution MRI of the Human Eye and Orbit at Ultrahigh Field (7T)

Ultrahigh-field (7T) MRI provides improved contrast and a signal-to-noise gain compared with lower magnetic field strengths. Here, we demonstrate feasibility and optimization of anatomic imaging of the eye and orbit using a dedicated commercial multichannel transmit and receive eye coil. Optimization of participant setup techniques and MRI sequence parameters allowed for improvements in the image resolution and contrast, and the eye and orbit coverage with minimal susceptibility and motion artifacts in a clinically feasible protocol.

Age-Dependent Changes in Total and Free Water Content of In Vivo Human Lenses Measured by Magnetic Resonance Imaging

Purpose

To use magnetic resonance imaging (MRI) to measure age-dependent changes in total and free water in human lenses in vivo.

Methods

Sixty-four healthy adults aged 18 to 86 years were recruited, fitted with a 32-channel head receiver coil, and placed in a 3 Tesla clinical MR scanner. Scans of the crystalline lens were obtained using a volumetric interpolated breath-hold examination sequence with dual flip angles, which were corrected for field inhomogeneity post-acquisition using a B1-map obtained using a turbo-FLASH sequence. The spatial distribution and content of corrected total (ρlens) and free (T1) water along the lens optical axis were extracted using custom-written code.

Results

Lens total water distribution and content did not change with age (all P > 0.05). In contrast to total water, a gradient in free water content that was highest in the periphery relative to the center was present in lenses across all ages. However, this initially parabolic free water gradient gradually developed an enhanced central plateau, as indicated by increasing profile shape parameter values (anterior: 0.067/y, P = 0.004; posterior: 0.050/y, P = 0.020) and central free water content (1.932 ms/y, P = 0.022) with age.

Conclusions

MRI can obtain repeatable total and free water measurements of in vivo human lenses. The observation that the lens steady-state free, but not total, water gradient is abolished with age raises the possibility that alterations in protein-water interactions are an underlying cause of the degradation in lens optics and overall vision observed with aging.

Ultrahigh field MRI determination of water diffusion rates in ex vivo human lenses of different age

BACKGROUND

The development of presbyopia is correlated with increased lens stiffness. To reveal structural changes with age, ultrahigh field magnetic resonance imaging (UHF-MRI) was used to analyze water diffusion in differently aged human lenses ex vivo.

METHODS

After enucleation lens extractions were performed. Lenses were photographed, weighed, and embedded in 0.5% agarose dissolved in culture medium. UHF-MRI was conducted to analyze anatomical characteristics of the lens using T2-weighted Turbo-RARE imaging and to obtain apparent diffusion coefficients (ADC) measurements. A Gaussian fit routine was used to examine the ADC histograms.

RESULTS

An age-dependent increase in lens wet weight, lens thickness, and lens diameter was found (P<0.001). T2-weighted images revealed a hyperintense lens cortex and a gradually negative gradient in signal intensity towards the nucleus. ADC histograms of the lens showed bimodal distributions (lower ADC values mainly located in the nucleus and higher ADC values mainly located in the cortex), which did not change significantly with age [βPeak1=1.96E-7 (-20E-7, 10E-7), P=0.804 or βPeak2=15.4E-7 (-10E-7, 40E-7), P=0.276; respectively].

CONCLUSIONS

Clinically relevant age dependent lens hardening is probably not correlated with ADC changes within the nucleus, which could be confirmed by further measurements.

Correlation of Intraoperative Optical Coherence Tomography of Crystalline Lens Diameter, Thickness, and Volume with Biometry and Age

PURPOSE

To characterize crystalline lens dimensions derived from in vivo spectral-domain optical coherence tomography (SD-OCT) and identify associations among these parameters, ocular biometry, and age.

METHODS

In this retrospective study, lens thickness (LT), lens diameter (LD), and lens volume (LV) were measured intraoperatively using SD-OCT in 293 eyes undergoing lens surgery. Correlations among LT, LD, LV, age, axial length (AL), and anterior chamber depth (ACD) were analyzed. Multiple regression analysis was performed to determine whether a combination of biometric data could predict LD and LV.

RESULTS

Wide variations were observed in LT (3.6-5.7 mm), LD (7.5-11.9 mm), and LV (119.9-312.4 mm³) of aging eyes. Correlations among the 3 lens dimensions were statistically significant (LV-LT: r = 0.785; P < .001; LV-LD: r = 0.696; P < .001; and LT-LD: r = 0.121; P = .039). With age, the correlation coefficients of LT, LD, and LV were 0.526, 0.326, and 0.573, respectively (P < .001). Although there was significant correlation of AL with LT (r = -0.137; P = .002) and LD (r = 0.268; P < .001), it was not significant with LV (r = 0.084; P = .15). Subgroup analysis revealed that 19.8% of long eyes had LD >1 standard deviation (SD) above and that 5.2% had LD <1 SD below the mean LD.

CONCLUSIONS

Dimensions of the aging lens vary considerably and are most accurately characterized by direct measurement of LT, LD, and LV, rather than making assumptions based on AL. These findings challenge historically proposed relationships between LD and AL and represent a normative dataset of contemporary geometric features of the aging lens, possibly aiding in surgical decision making and future developments in lens surgery.

IMI Accommodation and Binocular Vision in Myopia Development and Progression

The role of accommodation in myopia development and progression has been debated for decades. More recently, the understanding of the mechanisms involved in accommodation and the consequent alterations in ocular parameters has expanded. This International Myopia Institute white paper reviews the variations in ocular parameters that occur with accommodation and the mechanisms involved in accommodation and myopia development and progression. Convergence is synergistically linked with accommodation and the impact of this on myopia has also been critiqued. Specific topics reviewed included accommodation and myopia, role of spatial frequency, and contrast of the task of objects in the near environment, color cues to accommodation, lag of accommodation, accommodative-convergence ratio, and near phoria status. Aspects of retinal blur from the lag of accommodation, the impact of spatial frequency at near and a short working distance may all be implicated in myopia development and progression. The response of the ciliary body and its links with changes in the choroid remain to be explored. Further research is critical to understanding the factors underlying accommodative and binocular mechanisms for myopia development and its progression and to guide recommendations for targeted interventions to slow myopia progression.

Etiologies and clinical characteristics of young patients with angle-closure glaucoma: a 15-year single-center retrospective study

Purpose

To investigate the etiologies and the clinical characteristics of angle-closure glaucoma (ACG) patients younger than 40 years old in Chinese.

Methods

Inpatients with diagnosis of ACG and diagnosed age younger than or equal to 40 years old, who were admitted in Eye, Ear, Nose, and Throat Hospital Fudan University from 2002 to 2017, were included in this retrospective non-comparative case series. The underlying causes and clinical features for all the patients were analyzed by comprehensive review of medical charts.

Results

A total of 298 patients (463 eyes) met the criteria, including 153 females (51.3%) and 145 males (48.7%); the mean age was 25.6 ± 13.0 years. Primary angle-closure glaucoma (PACG), uveitis, and anterior segment dysgenesis (ASD) were the top three etiologies in our patients, which accounted for 32.6%, 20.3%, and 15.1% of the total patients respectively. PACG mainly occurs after 30 years of age and ASD is the top reason of ACG in patients younger than 20 years old. Other known etiologies include iridocorneal endothelial syndrome, neovascular glaucoma, nanophthalmos, retinitis pigmentosa, spherophakia, bestrophinopathy, persistent fetal vasculature, iridociliary cysts, congenital retinoschisis, Marfan’s syndrome, retinopathy of prematurity, familial exudative vitreoretinopathy, congenital retinal folds, Coat’s disease, and neurofibromatosis.

Conclusions

We described the uncommon presentation of ACG in Chinese young patients. Although unusual, most of the etiologies could be identified. Therefore, more careful and comprehensive examinations are needed for early detection and timely treatment for young ACG patients.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00417-021-05172-6.

Age-Related Changes of the Human Crystalline Lens on High-Spatial Resolution Three-Dimensional T1-Weighted Brain Magnetic Resonance Images In Vivo

Purpose

To reveal age-related changes of the human crystalline lens by using high-spatial resolution T1-weighted brain magnetic resonance imaging of patients under general anesthesia.

Methods

We retrospectively identified 47 children (2–17 years) and 30 adults (18–70 years) without diabetes or eye disease, who required brain magnetic resonance imaging examinations under general anesthesia between 2012 and 2019. Normalized signal intensity of the crystalline lens and vitreous body, as well as equatorial diameter and axial thickness of the lens were assessed by using a three-dimensional T1-weighted magnetization prepared rapid acquisition gradient echo sequence of the brain with 0.9-mm spatial resolution. Patient dossiers were reviewed to record indication for magnetic resonance imaging examination and hypertension.

Results

Advancing age was significantly correlated with increasing equatorial diameter of the infantile lens (r = 0. 74; 95% confidence interval, 0.58–0.85; P < .0001) and increasing crystalline lens signal intensity of the adult lens (r = 0.38; 95% confidence interval, 0.02–0.65; P = .0382), which remained significant after accounting for potential confounding variables. There was no significant correlation between age and axial thickness or vitreous body signal intensity in the children and adult cohort.

Conclusions

The present study demonstrated that advancing age was significantly correlated with an increasing equatorial diameter of the infantile lens and with increasing crystalline lens signal intensity of the adult lens. These normative data can contribute to our understanding of age-related changes in eye health and function, especially in regard to the emmetropization process and should also be taken into account when investigating lens pathologies.

Real World Outcomes of Kahook Dual Blade Goniotomy in Black and Afro-Latinx Adult Patients with Glaucoma: A 6-Month Retrospective Study

INTRODUCTION

To determine the efficacy and safety of Kahook Dual Blade (KDB) goniotomy alone or combined with phacoemulsification cataract surgery to lower intraocular pressure and medication burden in Black and Afro-Latinx patients with open angle glaucoma (OAG).

MATERIALS AND METHOD

A retrospective, single center case series of patients with OAG who were managed with medications and underwent phacoemulsification combined with goniotomy (PE + KDB) using Kahook Dual Blade or goniotomy alone (KDB alone) in pseudophakic patients. Indications for glaucoma surgery included reduction of intraocular pressure (IOP) and reduction of medication burden. Our study parameters included pre- and postoperative information on IOP, the use of IOP-lowering medications, visual field, and adverse events through 6 months of follow-up.

RESULTS

Among all 63 eyes of 63 patients undergoing surgery, Kahook goniotomy with or without phacoemulsification, mean IOP was significantly reduced from 17.4 mmHg at baseline to 14.0 mmHg at month 6 (P = 0.0012), a 19.5% reduction (KDB alone -26.4%, PE + KDB -16.6%). The mean number of topical IOP-lowering medications was reduced from 2.6 at baseline to 1.6 ± 0.3 at month 6 (P = 0.0012), a 38.5% reduction (Kahook alone -10.7%, PE + Kahook -48.0%). Mean visual fields were stable in the PE + KDB group and progressed in the KDB alone group. Postoperative adverse events were mild and included transient hyphema, IOP spikes, posterior capsule opacification, tearing, glare and mild pain.

CONCLUSION

Phacoemulsification combined with Kahook dual blade goniotomy significantly lowers both IOP and medication burden in Black and Afro-Latinx patients with open angle glaucoma. In pseudophakic patients with advanced glaucoma medication burden is not significantly reduced and visual field progression occurred. Adverse events were not sight-threatening and self limited.

Morphometric analysis of in vitro human crystalline lenses using digital shadow photogrammetry

There is a great need for accurate biometric data on human lenses. To meet this, a compact tabletop optical comparator, the minishadowgraph, was built for measuring isolated eye lens shape and dimensions while the lens was fully immersed in supporting medium. The instrument was based around a specially designed cell and an illumination system which permitted image recording in both sagittal and equatorial (coronal) directions. Data were acquired with a digital camera and analyzed using a specially written MATLAB program as well as by manual measurements in image analysis software. The possible effect of lens orientation and gravity on the dimensions was examined by measuring dimensions with anterior or posterior surfaces up and by measuring lenses with calipers after removal from the minishadowgraph cell. Dimensions, curvatures and shape factors were obtained for 134 fully accommodated lenses ranging in age from birth to 88 years postnatal. Of these, 41 were from donors aged under 20 years, ages which are generally of limited availability. Thickness and diameter showed the same age-related trends described in previous studies but, for the lenses measured in air, age-dependent differences were observed in thickness (-5 to 0%) and diameter (+5 to 0%), consistent with gravitational sag. Anterior and posterior radii of curvature of the central 3 or 6 mm, depending on lens diameter, increase with age, with the anterior increase greater than the posterior. The anterior surface shape of the neonatal lens is that of a prolate ellipse and the posterior, an oblate ellipse. Both surfaces become hyperbolic after age 20. The data presented here on dimensions, shape and sagging will be of great value in assessing age-related changes in the optical and mechanical performance of the lens. In particular, the comprehensive data set from donors aged under 20 years provides a unique and valuable insight to the changes in size and shape during the early dynamic growth period of the lens.

Physiology-like crystalline lens modelling for children

Understanding the age-dependent properties of the crystalline lenses of children is fundamental in studying the mechanism of myopic development and progression. A more realistic lens structure has more power for predicting the optical properties of the crystalline lenses. In this manuscript, a new lens model is proposed to predict the age-dependent change in the crystalline lens for children aged 6 to 15 years old. The lens model has the capability of involving most parameters measurable on the in vivo human lens. Moreover, the discrepancy of refractive indices at the equatorial edge and anterior and posterior vertices of the external lens surface is explained systematically. The analysis shows that this discrepancy has a significant role on the optical performance of the lens. The age-dependent properties are modelled based on available experimental data. The relationship between structural and optical performance is investigated with three-dimensional ray-tracing. The contributions of each parameter to the optical power and spherical aberration are revealed. The study has highlighted the importance of building physiology-like crystalline lens structure since some parameters ignored by previous studies can have a great optical impact.

Using the Lens Paradox to Optimize an In Vivo MRI-Based Optical Model of the Aging Human Crystalline Lens

Purpose

To optimize our in vivo magnetic resonance imaging (MRI)-based optical model of the human crystalline lens, developed with a small group of young adults, for a larger cohort spanning a wider age range.

Methods

Subjective refraction and ocular biometry were measured in 57 healthy adults ages 18 to 86 years who were then scanned using 3T clinical magnetic resonance imaging (MRI) to obtain lens gradient of refractive index (GRIN) and geometry measurements. These parameters were combined with ocular biometric measurements to construct individualized Zemax eye models from which ocular refractive errors and lens powers were determined. Models were optimized by adding an age-dependent factor to the transverse relaxation time (T₂)-refractive index (n) calibration to match model-calculated refractive errors with subjective refractions.

Results

In our subject cohort, subjective refraction shifted toward hyperopia by 0.029 diopter/year as the lens grew larger and developed flatter GRINs with advancing age. Without model optimization, lens powers did not reproduce this clinically observed decrease, the so-called lens paradox, instead increasing by 0.055 diopter/year. However, modifying the T₂-n calibration by including an age-dependent factor reproduced the decrease in lens power associated with the lens paradox.

Conclusions

After accounting for age-related changes in lens physiology in the T₂-n calibration, our model was capable of accurately measuring in vivo lens power across a wide age range. This study highlights the need for a better understanding of how age-dependent changes to the GRIN impact the refractive properties of the lens.

Translational Relevance

MRI is applied clinically to calculate the effect of age-related refractive index changes in the lens paradox.

A Modeling Approach for Investigating Opto-Mechanical Relationships in the Human Eye Lens

OBJECTIVE

The human visual system alters its focus by a shape change of the eye lens. The extent to which the lens can adjust ocular refractive power is dependent to a significant extent on its material properties. Yet, this fundamental link between the optics and mechanics of the lens has been relatively under-investigated. This study aims to investigate this opto-mechanical link within the eye lens to gain insight into the processes of shape alteration and their respective decline with age.

METHODS

Finite Element models based on biological lenses were developed for five ages: 16, 35, 40, 57, and 62 years by correlating in vivo measurements of the longitudinal modulus using Brillouin scattering with in vitro X-ray interferometric measurements of refractive index and taking into account various directions of zonular force.

RESULTS

A model with radial cortical Young's moduli provides the same amount of refractive power with less change in thickness than a model with uniform cortical Young's modulus with a uniform stress distribution and no discontinuities along the cortico-nuclear boundary. The direction of zonular angles can significantly influence curvature change regardless of the modulus distribution.

CONCLUSIONS

The present paper proposes a modelling approach for the human lens, coupling optical and mechanical properties, which shows the effect of parameter choice on model response.

SIGNIFICANCE

This advanced modelling approach, considering the important interplay between optical and mechanical properties, has potential for use in design of accommodating implant lenses and for investigating non-biological causes of pathological processes in the lens (e.g., cataract).

Off-axis optical coherence tomography imaging of the crystalline lens to reconstruct the gradient refractive index using optical methods

Earlier studies have shown that the gradient index of refraction (GRIN) of the crystalline lens can be reconstructed in vitro using Optical Coherence Tomography (OCT) images. However, the methodology cannot be extended in vivo because it requires accurate measurements of the external geometry of the lens. Specifically, the posterior surface is measured by flipping the lens so that the posterior lens surface faces the OCT beam, a method that cannot be implemented in vivo. When the posterior surface is imaged through the lens in its natural position, it appears distorted by the unknown GRIN. In this study, we demonstrate a method to reconstruct both the GRIN and the posterior surface shape without the need to flip the lens by applying optimization routines using both on-axis and off-axis OCT images of cynomolgous monkey crystalline lenses, obtained by rotating the OCT delivery probe from -45 to +45 degrees in 5 degree steps. We found that the GRIN profile parameters can be reconstructed with precisions up to 0.009, 0.004, 1.7 and 1.1 (nucleus and surface refractive indices, and axial and meridional power law, respectively), the radius of curvature within 0.089 mm and the conic constant within 0.3. While the method was applied on isolated crystalline lenses, it paves the way to in vivo lens GRIN and posterior lens surface reconstruction.

Accommodation and age-dependent eye model based on in vivo measurements

PURPOSE

To develop a flexible model of the average eye that incorporates changes with age and accommodation in all optical parameters, including entrance pupil diameter, under photopic, natural, environmental conditions.

METHODS

We collated retrospective in vivo measurements of all optical parameters, including entrance pupil diameter. Ray-tracing was used to calculate the wavefront aberrations of the eye model as a function of age, stimulus vergence and pupil diameter. These aberrations were used to calculate objective refraction using paraxial curvature matching. This was also done for several stimulus positions to calculate the accommodation response/stimulus curve.

RESULTS

The model predicts a hyperopic change in distance refraction as the eye ages (+0.22D every 10 years) between 20 and 65 years. The slope of the accommodation response/stimulus curve was 0.72 for a 25 years-old subject, with little change between 20 and 45 years. A trend to a more negative value of primary spherical aberration as the eye accommodates is predicted for all ages (20-50 years). When accommodation is relaxed, a slight increase in primary spherical aberration (0.008μm every 10 years) between 20 and 65 years is predicted, for an age-dependent entrance pupil diameter ranging between 3.58mm (20 years) and 3.05mm (65 years). Results match reasonably well with studies performed in real eyes, except that spherical aberration is systematically slightly negative as compared with the practical data.

CONCLUSIONS

The proposed eye model is able to predict changes in objective refraction and accommodation response. It has the potential to be a useful design and testing tool for devices (e.g. intraocular lenses or contact lenses) designed to correct the eye's optical errors.

Optical Coherence Tomography Reveals Sigmoidal Crystalline Lens Changes during Accommodation

This study aimed to quantify biometric modifications of the anterior segment (AS) during accommodation and to compare them against changes in both accommodative demand and response. Thirty adults, aged 18–25 years were rendered functionally emmetropic with contact lenses. AS optical coherence tomography (AS-OCT) images were captured along the 180° meridian (Visante, Zeiss Meditec, Jena, Germany) under stimulated accommodative demands (0–4 D). Images were analysed and lens thickness (LT) was measured, applying a refractive index correction of 1.00. Accommodative responses were also measured sequentially through a Badal optical system fitted to an autorefractor (Shin Nippon NVision-K 5001, Rexxam, Japan). Data were compared with Dubbelman schematic eye calculations. Significant changes occurred in LT, anterior chamber depth (ACD), lens centroid (i.e., ACD + LT/2), and AS length (ASL = ACD + LT) with accommodation (all p < 0.01). There was no significant change in CT with accommodation (p = 0.81). Measured CT, ACD, and lens centroid values were similar to Dubbelman modelled parameters, however AS-OCT overestimated LT and ASL. As expected, the accommodative response was less than the demand. Interestingly, up until approximately 1.5 D of response (2.0 D demand), the anterior crystalline lens surface appears to be the primary correlate. Beyond this point, the posterior lens surface moves posteriorly resulting in an over-all sigmoidal trajectory. he posterior crystalline lens surface demonstrates a sigmoidal response with increasing accommodative effort.

Change in human lens dimensions, lens refractive index distribution and ciliary body ring diameter with accommodation

We investigated changes in ciliary body ring diameter, lens dimensions and lens refractive index distributions with accommodation in young adults. A 3T clinical magnetic resonance imaging scanner imaged right eyes of 38 18-29 year old participants using a multiple spin echo sequence to determine accommodation-induced changes along lens axial and equatorial directions. Accommodation stimuli were approximately 1 D and 5 D. With accommodation, ciliary body ring diameter, and equatorial lens diameter decreased (-0.43 ± 0.31 mm and -0.30 ± 0.23 mm, respectively), and axial lens thickness increased ( + 0.34 ± 0.16 mm). Lens shape changes cause redistribution of the lens internal structure, leading to change in refractive index distribution profiles. With accommodation, in the axial direction refractive index profiles became flatter in the center and steeper near the periphery of the lens, while in the equatorial direction they became steeper in the center and flatter in the periphery. The results suggest that the anatomical accuracy of lens optical models can be improved by accounting for changes in the refractive index profile during accommodation.

Axial elongation measured by long scan depth optical coherence tomography during pilocarpine-induced accommodation in intraocular lens-implanted eyes

We used an ultra-long scan depth optical coherence tomography (UL-OCT) system to investigate changes in axial biometry of pseudophakic eyes during pilocarpine- induced accommodation. The right eyes from 25 healthy subjects (age range 49 to 84 years) with an intraocular lens (IOL) were imaged twice in the non-accommodative and the accommodative states. A custom-built UL-OCT instrument imaged the whole eye. Then accommodation was induced by two drops of 0.5% pilocarpine hydrochloride separated by a 5-minute interval. Following the same protocol, images were acquired again 30 minutes after the first drop. The central corneal thickness (CCT), anterior chamber depth (ACD), IOL thickness (IOLT), and vitreous length (VL) were obtained using custom automated software. The axial length (AL) was calculated by summing the CCT, ACD, IOLT, and VL. With accommodation, ACD increased by +0.08 ± 0.09 mm, while the VL decreased by −0.04 ± 0.09 mm (paired t-test each, P<0.05). CCT and IOLT remained constant during accommodation (P > 0.05). The non-accommodative AL was 23.47 ± 0.93 mm, and it increased by +0.04 ± 0.04 mm after accommodation (P<0.01). The AL increased and the IOL moved backward during pilocarpine-induced accommodation in pseudophakic eyes.

The importance of parameter choice in modelling dynamics of the eye lens

The lens provides refractive power to the eye and is capable of altering ocular focus in response to visual demand. This capacity diminishes with age. Current biomedical technologies, which seek to design an implant lens capable of replicating the function of the biological lens, are unable as yet to provide such an implant with the requisite optical quality or ability to change the focussing power of the eye. This is because the mechanism of altering focus, termed accommodation, is not fully understood and seemingly conflicting theories require experimental support which is difficult to obtain from the living eye. This investigation presents finite element models of the eye lens based on data from human lenses aged 16 and 35 years that consider the influence of various modelling parameters, including material properties, a wide range of angles of force application and capsular thickness. Results from axisymmetric models show that the anterior and posterior zonules may have a greater impact on shape change than the equatorial zonule and that choice of capsular thickness values can influence the results from modelled simulations.

Mechanism of accommodation assessed by change in precisely registered ocular images associated with concurrent change in auto-refraction

PURPOSE

Our purpose was to determine the changes in anterior chamber depth (ACD) and central lens thickness (CLT) during pharmacologically induced accommodation.

METHODS

Following pupillary dilation with phenylephrine 10%, baseline auto-refractions and swept-source optical coherence tomographic biometric images (Zeiss IOLMaster 700) were obtained from the right eyes of 25 subjects aged 19 to 24 years. Pilocarpine 4% and phenylephrine 10% were then instilled into these right eyes. One hour later, auto-refractions and biometric imaging were repeated. Only data from eight of 25 subjects met the following stringent criteria to be included in the study analysis: pre and post-pilocarpine biometric foveal images were registerable, the images of the corneal centers were shifted by ≤100 μm, pupils >5 mm and the pharmacologically induced refractive change was ≥ -7 diopters.

RESULTS

The mean auto-refractive accommodative change for the eight included subjects was -12.45 diopters (± 3.45 diopters). The mean change in CLT was 81 μm (± 54 μm) and the mean change in ACD was -145 μm (± 86 μm). Superimposition of the registered pre and post-pilocarpine biometric images of the sagittal sections of the whole eye from each subject demonstrated that the position of the whole lens did not shift either anteriorly, posteriorly or vertically during pharmacologically induced accommodation.

CONCLUSIONS

A small increase in lens thickness was associated with a large change in accommodative amplitude and no significant change in lens position as predicted by the Schachar theory.

Repeatability assessment of anterior segment biometric measurements under accommodative and nonaccommodative conditions using an anterior segment OCT

PURPOSE

As accommodation is a dynamic process changing anterior ocular structures, we aim to compare the repeatability between the biometric measurements taken with and without accommodation.

METHODS

Thirty healthy right eyes were measured in a baseline and an accommodative state using Visante-OCT. Three repeated measurements were taken to obtain central corneal thickness (CCT), anterior chamber depth (ACD), angle-to-angle distance (ATA), iridocorneal angles (IA), and crystalline lens thickness (LT). Repeatability was evaluated by the calculation of coefficient of repeatability (CoR), coefficient of variation (CoV), and intraclass correlation coefficient (ICC). In addition, the Passing-Bablok regression method was applied.

RESULTS

For the nonaccommodative state, the CoR for CCT, ACD, ATA, and LT was 20.02 μm, 0.09 mm, 0.25 mm, and 0.12 mm respectively. The CoR for CCT, ACD, ATA, and LT in the 6D-accommodative state was 20.85 μm, 0.08 mm, 0.26 mm, and 0.14 mm respectively. IA had similar results for both states; the CoR ranged between 3 and 4°, CoV was less than 4%, and the ICC was between 0.984-0.988. There were no significant differences between the three repeated measurements for any measurement.

CONCLUSIONS

Visante-OCT provides good repeatability for anterior segment measurements for both accommodative and nonaccommodative states.

Image registration reveals central lens thickness minimally increases during accommodation

Purpose

To evaluate anterior chamber depth, central crystalline lens thickness and lens curvature during accommodation.

Setting

California Retina Associates, El Centro, CA, USA.

Design

Healthy volunteer, prospective, clinical research swept-source optical coherence biometric image registration study of accommodation.

Methods

Ten subjects (4 females and 6 males) with an average age of 22.5 years (range: 20–26 years) participated in the study. A 45° beam splitter attached to a Zeiss IOLMaster 700 (Carl Zeiss Meditec Inc., Jena, Germany) biometer enabled simultaneous imaging of the cornea, anterior chamber, entire central crystalline lens and fovea in the dilated right eyes of subjects before, and during focus on a target 11 cm from the cornea. Images with superimposable foveal images, obtained before and during accommodation, that met all of the predetermined alignment criteria were selected for comparison. This registration requirement assured that changes in anterior chamber depth and central lens thickness could be accurately and reliably measured. The lens radii of curvatures were measured with a pixel stick circle.

Results

Images from only 3 of 10 subjects met the predetermined criteria for registration. Mean anterior chamber depth decreased, −67 μm (range: −0.40 to −110 μm), and mean central lens thickness increased, 117 μm (range: 100–130 μm). The lens surfaces steepened, anterior greater than posterior, while the lens, itself, did not move or shift its position as appeared from the lack of movement of the lens nucleus, during 7.8 diopters of accommodation, (range: 6.6–9.7 diopters).

Conclusion

Image registration, with stable invariant references for image correspondence, reveals that during accommodation a large increase in lens surface curvatures is associated with only a small increase in central lens thickness and no change in lens position.

The effect of topical administration of cyclopentolate on ocular biometry: An analysis for mouse and human models

Mydriasis with muscarinic antagonists have been used routinely prior to retinal examination and sometimes prior to refractive measurements of the mouse eye. However, biometric changes during topical administration of muscarinic antagonists have not been fully investigated in mice and humans. We found that the mouse eyes treated with cyclopentolate developed a hyperopia with a reduction in both the vitreous chamber depth and axial length. In humans, prior to the cyclopentolate treatment, a 6D accommodative stimulus produced a myopic shift with a reduced anterior chamber depth, choroidal thickness and anterior lens radius of curvature and an increase in lens thickness. After the cyclopentolate treatment, human eyes developed a hyperopic shift with an increased anterior chamber depth and anterior lens radius of curvature and a reduced lens thickness. Therefore, the biometric changes associated with this hyperopic shift were mainly located in the posterior segment of the eye in mice. However, it is the anterior segment of the eye that plays a main role in the hyperopic shift in human subjects. These results further indicate that mouse eyes do not have accommodation which needs to be taken into account when they are used for the study of human refractive errors.

Predicting Accommodative Response Using Paraxial Schematic Eye Models

PURPOSE

Previous ultrasound biomicroscopy (UBM) studies showed that accommodative optical response (AOR) can be predicted from accommodative biometric changes in a young and a pre-presbyopic population from linear relationships between accommodative optical and biometric changes, with a standard deviation of less than 0.55D. Here, paraxial schematic eyes (SE) were constructed from measured accommodative ocular biometry parameters to see if predictions are improved.

METHODS

Measured ocular biometry (OCT, A-scan, and UBM) parameters from 24 young and 24 pre-presbyopic subjects were used to construct paraxial SEs for each individual subject (individual SEs) for three different lens equivalent refractive index methods. Refraction and AOR calculated from the individual SEs were compared with Grand Seiko (GS) autorefractor measured refraction and AOR. Refraction and AOR were also calculated from individual SEs constructed using the average population accommodative change in UBM measured parameters (average SEs).

RESULTS

Schematic eye calculated and GS measured AOR were linearly related (young subjects: slope = 0.77, r = 0.86; pre-presbyopic subjects: slope = 0.64, r = 0.55). The mean difference in AOR (GS - individual SEs) for the young subjects was -0.27D and for the pre-presbyopic subjects was 0.33D. For individual SEs, the mean ± SD of the absolute differences in AOR between the GS and SEs was 0.50 ± 0.39D for the young subjects and 0.50 ± 0.37D for the pre-presbyopic subjects. For average SEs, the mean ± SD of the absolute differences in AOR between the GS and the SEs was 0.77 ± 0.88D for the young subjects and 0.51 ± 0.49D for the pre-presbyopic subjects.

CONCLUSIONS

Individual paraxial SEs predict AOR, on average, with a standard deviation of 0.50D in young and pre-presbyopic subject populations. Although this prediction is only marginally better than from individual linear regressions, it does consider all the ocular biometric parameters.

Does transient increase in axial length during accommodation attenuate with age?

Background

The aim was to profile transient accommodative axial length changes from early adulthood to advanced presbyopia and to determine whether any differences exist between the responses of myopic and emmetropic individuals.

Methods

Ocular biometry was measured by the LenStar biometer (Haag‐Streit, Switzerland) in response to zero, 3.00 and 4.50 D accommodative stimuli in 35 emmetropes and 37 myopes, aged 18 to 60 years. All results were corrected to reduce errors arising from the increase in crystalline lens thickness with accommodation. Accommodative responses were measured sequentially by the WAM 5500 Auto Ref/Keratometer (Grand Seiko, Hiroshima, Japan).

Results

Axial length increased significantly with accommodation (p < 0.001), with a mean corrected increase in axial length of 2 ± 18 µm and 8 ± 16 µm observed at 3.00 and 4.50 D, respectively. The magnitude of accommodative change in axial length was not dependent on refractive error classification (p = 0.959); however, a significant reduction in the magnitude and variance of axial length change was evident after 43 to 44 years of age (p < 0.002).

Conclusion

The negative association between transient increase in axial length and age, in combination with reduced variance of data after age 43 to 44 years, is consistent with a significant increase in posterior ocular rigidity, which may be influential in the development of presbyopia.

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.

The Effect of Age, Accommodation, and Refractive Error on the Adult Human Eye

PURPOSE

To quantify changes in ocular dimensions associated with age, refractive error, and accommodative response, in vivo, in 30- to 50-year-old human subjects.

METHODS

The right eyes of 91 adults were examined using ultrasonography, phakometry, keratometry, pachymetry, interferometry, anterior segment optical coherence tomography, and high-resolution magnetic resonance imaging. Accommodation was measured subjectively with a push-up test and objectively using open-field autorefraction. Regression analyses were used to assess differences in ocular parameters with age, refractive error, and accommodation.

RESULTS

With age, crystalline lens thickness increased (0.03 mm/yr), anterior lens curvature steepened (0.11 mm/yr), anterior chamber depth decreased (0.02 mm/yr), and lens equivalent refractive index decreased (0.001/yr) (all p < 0.01). With increasing myopia, there were significant increases in axial length (0.37 mm/D), vitreous chamber depth (0.34 mm/D), vitreous chamber height (0.09 mm/D), and ciliary muscle ring diameter (0.10 mm/D) (all p < 0.05). Increasing myopia was also associated with steepening of both the cornea (0.16 mm/D) and anterior lens surface (0.011 mm/D) (both p < 0.04). With accommodation, the ciliary muscle ring diameter decreased (0.08 mm/D) and the muscle thinned posteriorly (0.008 mm/D), allowing the lens to shorten equatorially (0.07 mm/D) and thicken axially (0.06 mm/D) (all p < 0.03).

CONCLUSIONS

Refractive error is significantly correlated with not only the axial dimensions but also the anterior equatorial dimension of the adult eye. Further testing and development of accommodating intraocular lenses should account for differences in patients' preoperative refractive error.

Calculation of crystalline lens power using a modification of the Bennett method

We present a method for measuring lens power from extended depth OCT biometry, corneal topography, and refraction using an improvement on the Bennett method. A reduced eye model was used to derive a formula for lens power in terms of ocular distances, corneal power, and objective spherical equivalent refraction. An error analysis shows that the formula predicts relaxed lens power with a theoretical accuracy of ± 0.5 D for refractive error ranging from -10 D to + 10 D. The formula was used to calculate lens power in 16 eyes of 8 human subjects. Mean lens power was 24.3 D ± 1.7 D.

Objective measurement of accommodative biometric changes using ultrasound biomicroscopy

PURPOSE

To demonstrate that ultrasound biomicroscopy (UBM) can be used for objective quantitative measurements of anterior segment accommodative changes.

SETTING

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

DESIGN

Prospective cross-sectional study.

METHODS

Anterior segment biometric changes in response to 0 to 6.0 diopters (D) of accommodative stimuli in 1.0 D steps were measured in eyes of human subjects aged 21 to 36 years. Imaging was performed in the left eye using a 35 MHz UBM (Vumax) and an A-scan ultrasound (A-5500) while the right eye viewed the accommodative stimuli. An automated Matlab image-analysis program was developed to measure the biometry parameters from the UBM images.

RESULTS

The UBM-measured accommodative changes in anterior chamber depth (ACD), lens thickness, anterior lens radius of curvature, posterior lens radius of curvature, and anterior segment length were statistically significantly linearly correlated with accommodative stimulus demands. Standard deviations of the UBM-measured parameters were independent of the accommodative stimulus demands (ACD: 0.0176 mm; lens thickness: 0.0294 mm; anterior lens radius of curvature: 0.3350 mm; posterior lens radius of curvature: 0.1580 mm; and anterior segment length: 0.0340 mm). The mean difference between the A-scan and UBM measurements was -0.070 mm for ACD and 0.166 mm for lens thickness.

CONCLUSIONS

Accommodating phakic eyes imaged using UBM allowed visualization of the accommodative response, and automated image analysis of the UBM images allowed reliable, objective, quantitative measurements of the accommodative intraocular biometric changes.

FINANCIAL DISCLOSURE

Neither author has a financial or proprietary interest in any material or method mentioned.

Mechanism of accommodation: A review of theoretical propositions

Accommodation is the process by which the human eye changes its focus to see objects at varying distances from the eye. For nearly 300 years, scientists have investigated and presented various views on the mechanism of accommodation. The purpose of this review is to present both the historical and contemporary theories that underpin the process of accommodation. Keywords such as ocular accommodation, mechanism of accommodation and accommodative mechanism were used to retrieve published material on the subject. Classical propositions by Thomas Young and Hermann von Helmholtz, amongst others, are presented.

Refractive index measurement of the mouse crystalline lens using optical coherence tomography

In recent years, there has been a growing interest for using mouse models in refractive development and myopia research. The crystalline lens is a critical optical component of the mouse eye that occupies greater than 50% of the ocular space, and significant increases in thickness with age. However, changes in refractive index of the mouse crystalline lens are less known. In this study, we examined the changes in thickness and refractive index of the mouse crystalline lens for two different strains, wild-type (WT) and a nyx mutant (nob) over the course of normal visual development or after form deprivation. Refractive index and lens thickness measurements were made on ex vivo lenses using spectral domain optical coherence tomography (SD-OCT). Comparison of refractive index measurements on 5 standard ball lenses using the SD-OCT and their known refractive indices (manufacturer provided) indicated good precision (intra-class correlation coefficient, 0.998 and Bland-Altman coefficient of repeatability, 0.116) of the SD-OCT to calculate mouse lens refractive index ex vivo. During normal visual development, lens thickness increased significantly with age for three different cohorts of mice, aged 4 (average thickness from both eyes; WT: 1.78 ± 0.03, nob: 1.79 ± 0.08 mm), 10 (WT: 2.02 ± 0.05, nob: 2.01 ± 0.04 mm) and 16 weeks (WT: 2.12 ± 0.06, nob: 2.09 ± 0.06 mm, p < 0.001). Lens thickness was not significantly different between the two strains at any age (p = 0.557). For mice with normal vision, refractive index for isolated crystalline lenses in nob mice was significantly greater than WT mice (mean for all ages; WT: 1.42 ± 0.01, nob: 1.44 ± 0.001, p < 0.001). After 4 weeks of form deprivation to the right eye using a skull-mounted goggling apparatus, a thinning of the crystalline lens was observed in both right and left eyes of goggled animals compared to their naïve controls (average from both the right and the left eye) for both strains (p = 0.052). In form deprived mice, lens refractive index was significantly different between the goggled animals and non-goggled naïve controls in nob mice, but not in WT mice (p = 0.009). Both eyes of goggled nob mice had significantly greater lens refractive index (goggled, 1.49 ± 0.01; opposite, 1.47 ± 0.03) compared to their naïve controls (1.45 ± 0.02, p < 0.05). The results presented here suggest that there are genetic differences in the crystalline lens refractive index of the mouse eye, and that the lens refractive index in mice significantly increase with form deprivation. Research applications requiring precise optical measurements of the mouse eye should take these lens refractive indices into account when interpreting SD-OCT data.

An analytical method for predicting the geometrical and optical properties of the human lens under accommodation

We present an analytical method to describe the accommodative changes in the human crystalline lens. The method is based on the geometry-invariant lens model, in which the gradient-index (GRIN) iso-indicial contours are coupled to the external shape. This feature ensures that any given number of iso-indicial contours does not change with accommodation, which preserves the optical integrity of the GRIN structure. The coupling also enables us to define the GRIN structure if the radii and asphericities of the external lens surfaces are known. As an example, the accommodative changes in lenticular radii and central thickness were taken from the literature, while the asphericities of the external surfaces were derived analytically by adhering to the basic physical conditions of constant lens volume and its axial position. The resulting changes in lens geometry are consistent with experimental data, and the optical properties are in line with expected values for optical power and spherical aberration. The aim of the paper is to provide an anatomically and optically accurate lens model that is valid for 3 mm pupils and can be used as a new tool for better understanding of accommodation.

Repeatability of OCT lens thickness measures with age and accommodation

PURPOSE

To investigate crystalline lens thickness (LT) across a range of ages and accommodative demands and to evaluate the repeatability of LT measurements using the Visante Anterior Segment Optical Coherence Tomographer (AS-OCT) (Zeiss Meditec, Germany) under non-cycloplegic conditions.

METHODS

Participants were 98 visually normal adults aged 18-75 years, stratified into age groups of 18-29, 30-39, 40-49, 50-59, and 60-75 years of age. Images of the crystalline lens were taken using the Visante AS-OCT during stimulation of accommodation at demands of 0, 1, 2, 3, 4, 5, and 8 D with accommodative response measured in a subgroup of participants. Images were analyzed and LT measured assuming a refractive index of 1.42. Repeat measures were taken from 86 participants for each accommodative demand at a second visit.

RESULTS

The mean unaccommodated LT for all participants was 4.07 ± 0.40 mm. An average increase in LT of 20 μm per year was calculated (linear regression, R² = 0.61, F(1,89) = 143.92, p < 0.00001). Increase in LT with accommodation was shown to be significant in the 18- to 29-year-olds (repeated measures ANOVA, F(6,105) = 96.31, p < 0.00001), 30- to 39-year-olds (F(6,93) = 71.25, p < 0.00001), and 40- to 49-year-olds (F(6,90) = 12.60, p < 0.01) with little or no measureable change in the older age groups. Eighty-six participants returned for a second visit. The mean difference in LT in the unaccommodated state for all participants between visit 1 and visit 2 was 0.0006 mm (95% limits of agreement of -0.07 to 0.07 mm). The 95% limits of agreement were widest for youngest age groups and narrowest for the oldest participants.

CONCLUSIONS

This study is the first to report the repeatability of LT measures using the Visante AS-OCT in the non-cyclopleged eye. It has also demonstrated the ability of the Visante AS-OCT to detect small changes in lens thickness with accommodation.

Age-dependence of the average and equivalent refractive indices of the crystalline lens

Lens average and equivalent refractive indices are required for purposes such as lens thickness estimation and optical modeling. We modeled the refractive index gradient as a power function of the normalized distance from lens center. Average index along the lens axis was estimated by integration. Equivalent index was estimated by raytracing through a model eye to establish ocular refraction, and then backward raytracing to determine the constant refractive index yielding the same refraction. Assuming center and edge indices remained constant with age, at 1.415 and 1.37 respectively, average axial refractive index increased (1.408 to 1.411) and equivalent index decreased (1.425 to 1.420) with age increase from 20 to 70 years. These values agree well with experimental estimates based on different techniques, although the latter show considerable scatter. The simple model of index gradient gives reasonable estimates of average and equivalent lens indices, although refinements in modeling and measurements are required.

Anterior segment changes produced in response to long-term overnight orthokeratology

PURPOSE

To evaluate the effect of overnight orthokeratology (OK) on anterior chamber depth (ACD), posterior radius of corneal curvature (PRCC) and axial length (AL) over one year.

METHODS

In this prospective longitudinal study, measurements were made in 34 right eyes of 34 subjects at baseline, 15 days, 1 and 12 months after starting OK treatment. ACD and PRCC measurements were obtained using a Pentacam system and AL was measured using an IOL-Master. ACD and PRCC were measured along the horizontal and vertical meridians at 1 mm intervals. These measurements were expressed as the distance from the center in the nasal (N), temporal (T), superior (S) and inferior (I) directions.

RESULTS

A significant reduction in ACD was observed in both meridians during treatment. PRCC flattened significantly in the (T) direction after 15 d (1 mm, p < 0.05), at the corneal center after 15 d (p < 0.01), in the (T) direction after 1 month (1 mm, p < 0.05), in the (S) direction after 12 months (1 mm p < 0.05), in the (N) direction after 12 months (1 mm p < 0.05), in the (N) and (T) directions after 12 months (3 mm, p < 0.05) and in the (T) direction after 12 months (4 mm p < 0.05), at the corneal center after 12 months (p < 0.01). AL was significantly reduced during treatment (p < 0.05).

CONCLUSIONS

A long period of OK reduces ACD and AL and changes PRCC.

Quantification of age-related and per diopter accommodative changes of the lens and ciliary muscle in the emmetropic human eye

PURPOSE

To calculate age-related and per diopter (D) accommodative changes in crystalline lens and ciliary muscle dimensions in vivo in a single cohort of emmetropic human adults ages 30 to 50 years.

METHODS

The right eyes of 26 emmetropic adults were examined using ultrasonography, phakometry, anterior segment optical coherence tomography, and high resolution magnetic resonance imaging. Accommodation was measured both subjectively and objectively.

RESULTS

In agreement with previous research, older age was linearly correlated with a thicker lens, steeper anterior lens curvature, shallower anterior chamber, and lower lens equivalent refractive index (all P < 0.01). Age was not related to ciliary muscle ring diameter (CMRD) or lens equatorial diameter (LED). With accommodation, lens thickness increased (+0.064 mm/D, P < 0.001), LED decreased (-0.075 mm/D, P < 0.001), CMRD decreased (-0.105 mm/D, P < 0.001), and the ciliary muscle thickened anteriorly (+0.013 to +0.026 mm/D, P < 0.001) and thinned posteriorly (-0.011 to -0.015, P < 0.01). The changes per diopter of accommodation in LED, CMRD, and ciliary muscle thickness were not related to subject age.

CONCLUSIONS

The per diopter ciliary muscle contraction is age independent, even as total accommodative amplitude declines. Quantifying normal biometric dimensions of the accommodative structures and changes with age and accommodative effort will further the development of new IOLs designed to harness ciliary muscle forces.

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.

Distortion correction of OCT images of the crystalline lens: gradient index approach

PURPOSE

To propose a method to correct optical coherence tomography (OCT) images of posterior surface of the crystalline lens incorporating its gradient index (GRIN) distribution and explore its possibilities for posterior surface shape reconstruction in comparison to existing methods of correction.

METHODS

Two-dimensional images of nine human lenses were obtained with a time-domain OCT system. The shape of the posterior lens surface was corrected using the proposed iterative correction method. The parameters defining the GRIN distribution used for the correction were taken from a previous publication. The results of correction were evaluated relative to the nominal surface shape (accessible in vitro) and compared with the performance of two other existing methods (simple division, refraction correction: assuming a homogeneous index). Comparisons were made in terms of posterior surface radius, conic constant, root mean square, peak to valley, and lens thickness shifts from the nominal data.

RESULTS

Differences in the retrieved radius and conic constant were not statistically significant across methods. However, GRIN distortion correction with optimal shape GRIN parameters provided more accurate estimates of the posterior lens surface in terms of root mean square and peak values, with errors <6 and 13 μm, respectively, on average. Thickness was also more accurately estimated with the new method, with a mean discrepancy of 8 μm.

CONCLUSIONS

The posterior surface of the crystalline lens and lens thickness can be accurately reconstructed from OCT images, with the accuracy improving with an accurate model of the GRIN distribution. The algorithm can be used to improve quantitative knowledge of the crystalline lens from OCT imaging in vivo. Although the improvements over other methods are modest in two dimension, it is expected that three-dimensional imaging will fully exploit the potential of the technique. The method will also benefit from increasing experimental data of GRIN distribution in the lens of larger populations.

Optical modelling of the possible origins of transient refractive changes in diabetic patients

PURPOSE

To explore theoretically the ocular components that might be responsible for the transient refractive changes observed in the eyes of diabetic patients, particularly during intensive glycaemic control.

METHODS

Paraxial ray tracing with a model eye having a lens with a single equivalent refractive index was used to determine the sensitivity of refraction to change in the values of each biometric component. The changes required to produce a refractive change of 0.50 D were compared with the reliability of current instrumentation to measure each parameter.

RESULTS

If transient shifts of 0.50 D or more were caused by changes in surface curvatures or separations, the latter would easily be detectable by available measurement techniques. The fact that such parameter changes have not been reliably detected in clinical studies supports the concept that changes in refractive index cause the refractive changes. The most probable site of such index changes is the lens, a change of about 0.003 in equivalent index being required to produce a 0.50 change in refractive error.

CONCLUSION

This analysis supports the concept that transient changes in refraction in diabetics are due to changes in the lens. It is likely that changes in the gradients of refractive index lens within the lens, and in their associated contribution to the overall power of the lens, play the key role, rather than changes in surface powers.