[Show abstract][Hide abstract] ABSTRACT: 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.
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.
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.
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.
Optometry and vision science: official publication of the American Academy of Optometry 03/2012; 89(5):E709-18. DOI:10.1097/OPX.0b013e3182508344 · 1.60 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: PURPOSE: To reconstruct the gradient index (GRIN) profile of human crystalline lenses ex-vivo using Optical Coherence Tomography (OCT) imaging with an optimization technique and to study the dependence of the GRIN profile with age. METHODS: Cross-sectional images of nine isolated human crystalline lenses with ages ranging from 6 to 72 (post mortem time 1 to 4 days) were obtained using a custom-made OCT system. Lenses were extracted from whole cadaver globes and placed in a measurement chamber filled with preservation medium (DMEM). Lenses were imaged with the anterior surface up and then flipped over and imaged again, to obtain posterior lens surface profiles both undistorted and distorted by the refraction through the anterior crystalline lens and GRIN. The GRIN distribution of the lens was described with three variables by means of power function, with variables being the nucleus and surface index, and a power coefficient that describes the decay of the refractive index from the nucleus to the surface. An optimization method was used to search for the parameters that produced the best match of the distorted posterior surface. RESULTS: The distorted surface was simulated with accuracy around the resolution of the OCT system (under 15 µm). The reconstructed refractive index values ranged from 1.356 to 1.388 for the surface, and from 1.396 to 1.434 for the nucleus. The power coefficient ranged between 3 and 18. The power coefficient increased significantly with age, at a rate of 0.24 per year. CONCLUSION: Optical Coherence Tomography allowed optical, non-invasive measurement of the 2-D gradient index profile of the isolated human crystalline lens ex vivo. The age-dependent variation of the changes is consistent with previous data using magnetic resonance imaging, and the progressive formation of a refractive index plateau.
Journal of Modern Optics 11/2011; 58(19-20):1781-1787. DOI:10.1080/09500340.2011.565888 · 1.01 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The purpose of this study was to determine the contribution of the gradient refractive index to the change in lens power in hamadryas baboon and cynomolgus monkey lenses during simulated accommodation in a lens stretcher. Thirty-six monkey lenses (1.4-14.1 years) and twenty-five baboon lenses (1.8-28.0 years) were stretched in discrete steps. At each stretching step, the lens back vertex power was measured and the lens cross-section was imaged with optical coherence tomography. The radii of curvature for the lens anterior and posterior surfaces were calculated for each step. The power of each lens surface was determined using refractive indices of 1.365 for the outer cortex and 1.336 for the aqueous. The gradient contribution was calculated by subtracting the power of the surfaces from the measured lens power. In all lenses, the contribution of the surfaces and gradient increased linearly with the amplitude of accommodation. The gradient contributes on average 65 ± 3% for monkeys and 66 ± 3% for baboons to the total power change during accommodation. When expressed in percent of the total power change, the relative contribution of the gradient remains constant with accommodation and age in both species. These findings are consistent with Gullstrand's intracapsular theory of accommodation.
Journal of Vision 11/2011; 11(13):23. DOI:10.1167/11.13.23 · 2.39 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Presbyopia is an age related, gradual loss of accommodation, mainly due to changes in the crystalline lens. As part of research efforts to understand and cure this condition, ex vivo, cross-sectional optical coherence tomography images of crystalline lenses were obtained by using the Ex-Vivo Accommodation Simulator (EVAS II) instrument and analyzed to extract their physical and optical properties. Various filters and edge detection methods were applied to isolate the edge contour. An ellipse is fitted to the lens outline to obtain central reference point for transforming the pixel data into the analysis coordinate system. This allows for the fitting of a high order equation to obtain a mathematical description of the edge contour, which obeys constraints of continuity as well as zero to infinite surface slopes from apex to equator. Geometrical parameters of the lens were determined for the lens images captured at different accommodative states. Various curve fitting functions were developed to mathematically describe the anterior and posterior surfaces of the lens. Their differences were evaluated and their suitability for extracting optical performance of the lens was assessed. The robustness of these algorithms was tested by analyzing the same images repeated times.
[Show abstract][Hide abstract] ABSTRACT: To characterize postnatal changes in eye size in glaucomatous DBA/2J (D2) mice and in nonglaucomatous C57BL/6J mice (B6) in vivo by means of whole-eye optical coherence tomography (OCT).
D2 (n = 32) and B6 (n = 36) mice were tested between 2 and 20 months of age in eight age bins. A custom time-domain OCT system with a center wavelength of 825 nm and an axial scan length of 7.1 mm produced axial A-scan interferograms at a rate of 20 A-lines/s with a resolution of 8 μm. Axial length (AL), corneal thickness (CT), anterior chamber depth (ACD), lens thickness (LT), vitreous chamber depth (VCD), and retinal thickness (RT) were measured in the optical axis and adjusted with corresponding refractive indices. Corneal curvature (CC) and IOP were also measured.
AL increased (P < 0.001) more in the D2 (21%) than in the B6 (9%) mice. There was an interaction effect (two-way ANOVA, P < 0.001) between age and strain for AL, CT, ACD, and VCD. In the D2 mice, the lens became dislocated posteriorly. Multiple regression analysis in the D2 mice revealed an independent effect of age and IOP (P ≤ 0.01) on axial length. CC steepened in the older D2 mice, whereas it flattened in the B6 mice.
In D2 mice, postnatal elongation of AL is larger than that in B6 mice and is associated with a greater increase in ACD and IOP, which seems to be a causal factor. The ease of use, short acquisition time, and noninvasiveness of whole-eye OCT make it suitable for routine use in longitudinal studies of mouse models.
[Show abstract][Hide abstract] ABSTRACT: We quantify the posterior surface distortions in optical coherence tomography (OCT) images of isolated crystalline lenses. The posterior radius of curvature and asphericity obtained from OCT images acquired with the beam incident first on the anterior, and then the posterior, surface were compared. The results were compared with predictions of a ray-tracing model which includes the index gradient. The results show that the error in the radius of curvature is within the measurement reproducibility and that it can be corrected by assuming a uniform refractive index. However, accurate asphericity values require a correction algorithm that takes into account the gradient.
[Show abstract][Hide abstract] ABSTRACT: Purpose. To characterize the age dependence of shape, refractive power, and refractive index of isolated lenses from nonhuman primates. Methods. Measurements were performed on ex vivo lenses from cynomolgus monkeys (cyno: n = 120; age, 2.7-14.3 years), rhesus monkeys (n = 61; age, 0.7-13.3 years), and hamadryas baboons (baboon: n = 16; age, 1.7-27.3 years). Lens thickness, diameter, and surface curvatures were measured with an optical comparator. Lens refractive power was measured with a custom optical system based on the Scheiner principle. The refractive contributions of the gradient, the surfaces, and the equivalent refractive index were calculated with optical ray-tracing software. The age dependence of the optical and biometric parameters was assessed. Results. Over the measured age range isolated lens thickness decreased (baboon: -0.04, cyno: -0.05, and rhesus: -0.06 mm/y) and equatorial diameter increased (logarithmically for the baboon and rhesus, and linearly for cyno: 0.07 mm/y). The isolated lens surfaces flattened and the corresponding refractive power from the surfaces decreased with age (-0.33, -0.48, and -0.68 D/y). The isolated lens equivalent refractive index decreased (only significant for the baboon, -0.001 D/y), and as a result the total isolated lens refractive power decreased with age (baboon: -1.26, cyno: -0.97, and rhesus: -1.76 D/y). Conclusions. The age-dependent trends in the optical and biometric properties, growth, and aging, of nonhuman primate lenses are similar to those of the pre-presbyopic human lens. As the lens ages, the decrease in refractive contributions from the gradient refractive index causes a rapid age-dependent decrease in maximally accommodated lens refractive power.
[Show abstract][Hide abstract] ABSTRACT: A custom-built OCT system was used to obtain images of the whole mouse
eye. We developed a semi-automated segmentation method to detect the
boundaries of the anterior and posterior corneal, lens and retinal
surfaces as well as the anterior surface of the iris. The radii of
curvature of the surfaces were calculated using a conic section fit of
each boundary. Image distortions due to refraction of the OCT beam at
the successive boundaries were corrected using a ray-tracing algorithm.
Corrected ocular distances, radii of curvature of the cornea and lens
surfaces, and anterior chamber angle were obtained on 3 C57BL/6J mice.
In vivo imaging of the whole eye, segmentation, conic function fits and
correction were successful in all three animals. The posterior lens
surface of one mouse could not be fit accurately with a conic section.
Biometric parameters of C57BL/6J mice compared well with previous
published data obtained from histological sections. The study
demonstrates the feasibility of quantitative in vivo biometry of mouse
Proceedings of SPIE - The International Society for Optical Engineering 02/2010; DOI:10.1117/12.846937 · 0.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: To quantify the role of anterior zonular tension on the optomechanical lens response during simulation of accommodation in primates.
Postmortem cynomolgus monkey eyes (n = 14; age range, 3.0-11.5 years) were dissected leaving intact the lens, zonules, ciliary body, hyaloid membrane, anterior vitreous, and a scleral rim. The lens was mounted in a lens-stretching system and stretched radially in step-wise fashion. The load, and the lens diameter and power were measured at each step and the diameter- and power-load relationships were quantified. The anterior zonular fibers were then transected, and the experiment was repeated. The equatorial lens diameter and lens optical power before and after zonular transection were compared.
Stretching increased the lens diameter by 0.25 +/- 0.09 mm (median +/- interquartile range) before and 0.25 +/- 0.19 mm after zonular transection. Stretching decreased the lens power by 13.0 +/- 6.5 D before and 10.6 +/- 8.0 D after zonular transection. The load required to change the diameter of the lens by 1 mm decreased from 18.8 +/- 10.7 g before to 15.0 +/- 7.8 g after zonular transection. The absolute change in power per gram of loading decreased from 2.5 +/- 1.1 before to 2.0 +/- 1.2 D after zonular transection.
The cynomolgus monkey lens retains a significant fraction of its accommodative ability after transection of the anterior zonules in simulated accommodation experiments.
[Show abstract][Hide abstract] ABSTRACT: Presbyopia is the age related, gradual loss of accommodation, mainly due to changes in the crystalline lens. As part of research efforts to understand and cure this condition, ex vivo, cross-sectional OCT images of crystalline lenses were obtained and analyzed to extract their physical and optical properties. The raw OCT images are distorted, as the probing beam passing through media of different refractive indices and refraction on curved surfaces. In a first step, various filters, edge detection and pattern matching methods are applied to isolate the edge contour. An ellipse is fitted to the lens outline to obtain central reference point for transforming the pixel data into the analysis coordinate system. This allows for the fitting of high order equation to obtain a mathematical description of the edge contour, which obeys constraints of continuity as well as zero to infinite surface slopes from apex to equator. Robustness of these algorithms are tested by analyzing the images at various contrast levels. Gradient refractive index of the lens is determined and the physical shape is reconstructed. In a further refinement, the refraction on the curved anterior surface is compensated to obtain the actual shape of the posterior surface. Once the physical shape is fully reconstructed, the optical properties are determined by fitting conic sections to both surfaces and calculating the power profile across the lens. The relative contribution of each of these refinement steps is investigated by comparing their influence on the effective power of the lens.
Proceedings of SPIE - The International Society for Optical Engineering 01/2009; DOI:10.1117/12.809986 · 0.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: To develop an age-dependent mathematical model of the isolated ex-vivo human crystalline lens shape to serve as basis for use in computational modeling.
Profiles of whole isolated human lenses (n=27) aged 6 to 82, were measured from shadow-photogrammetric images. Two methods were used to analyze the lenses. In the two curves method (TCM) the anterior and posterior surfaces of the lens were fit to 10th-order even polynomials and in the one curve method (OCM) the contour of one half-meridional section of the lens was fit to 10th-order polynomials. The age-dependence of the polynomial coefficients was assessed. The analysis was used to produce an age-dependent polynomial model of the whole lens shape.
The root mean squared errors for the fits ranged from 11 to 70 microm for the OCM, 9 to 27 microm for the posterior surface of the TCM and 8 to 134 microm for the anterior surface of the TCM. The coefficients of the OCM did not display a significant trend with age. The 2nd-, 6th- and 10th-order coefficients of the anterior surface of the TCM decreased with age while the 8th-order coefficient increased. For the posterior surface of the TCM, the 8th-order coefficient significantly decreased with age and the 10th-order coefficient increased. The age-dependent equations of both the models provide a reliable model from age 20 to 60. The OCM model can be used for lenses older than 60 as well.
The shape of the whole human crystalline lens can be accurately modeled with 10th-order polynomial functions. These models can serve to improve computational modeling, such as finite element (FE) modeling of crystalline lenses.
Vision research 11/2008; 49(1):74-83. DOI:10.1016/j.visres.2008.09.028 · 1.82 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An optical coherence tomography system has been developed that was designed specifically for imaging the isolated crystalline lens. Cross-sectional OCT images were recorded on 40 lenses from 32 human donors with an age range of 6-82 years. A method has been developed to measure the axial thickness and average refractive index of the lens from a single recorded image. The measured average group refractive index at the measurement wavelength of 825 nm was converted to the average phase refractive index at 589 nm using lens dispersion data from the literature. The average refractive index for all lenses measured was 1.408+/-0.005 which agrees well with recent MRI measurements of the lens index gradient. A linear regression of the data resulted in a statistically significant decrease in the average refractive index with age, but a simple linear model was insufficient to explain the age dependence. The results presented here suggest that the peak refractive index in the nucleus is closer to 1.420, rather than the previously accepted value of 1.406.
Vision research 10/2008; 48(27):2732-8. DOI:10.1016/j.visres.2008.09.010 · 1.82 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: To characterize the age dependence of isolated human crystalline lens power and quantify the contributions of the lens surfaces and refractive index gradient.
Experiments were performed on 100 eyes of 73 donors (average 2.8 +/- 1.6 days postmortem) with an age range of 6 to 94 years. Lens power was measured with a modified commercial lensmeter or with an optical system based on the Scheiner principle. The radius of curvature and asphericity of the isolated lens surfaces were measured by shadow photography. For each lens, the contributions of the surfaces and the refractive index gradient to the measured lens power were calculated by using optical ray-tracing software. The age dependency of these refractive powers was assessed.
The total refractive power and surface refractive power both showed a biphasic age dependency. The total power decreased at a rate of -0.41 D/y between ages 6 and 58.1, and increased at a rate of 0.33D/y between ages 58.1 and 82. The surface contribution decreased at a rate of -0.13 D/y between ages 6 and 55.2 and increased at a rate of 0.04 D/y between ages 55.2 and 94. The relative contribution of the surfaces increased by 0.17% per year. The equivalent refractive index also showed a biphasic age dependency with a decrease at a rate of -3.9 x 10(-4) per year from ages 6 to 60.4 followed by a plateau.
The lens power decreases with age, due mainly to a decrease in the contribution of the gradient. The use of a constant equivalent refractive index value to calculate lens power with the lens maker formula will underestimate the power of young lenses and overestimate the power of older lenses.
[Show abstract][Hide abstract] ABSTRACT: To determine whether changes in elastic properties of the lens capsule ex vivo with age contribute to the forces necessary for accommodation.
Postmortem human (n = 22; age average: 41 +/- 17 years; range: 6-7) and cynomolgus monkey (n = 19; age average: 7.7 +/- 1.8 years, range: 4.2-10) tissues including the lens, capsule, zonules, ciliary body, and sclera were mounted in an optomechanical lens-stretching system. Starting at 0 load, the sclera was symmetrically stretched to 2 mm in 0.25-mm steps at a speed of 0.1 mm x s(-1). The load and lens diameter were measured at each step. The lens contents were removed through a mini-capsulorhexis. The stretching cycles were repeated on the empty capsular bag. The forces necessary to stretch the natural lens and empty bag were quantified as a function of age and compared.
The force needed to stretch the empty lens capsule was independent of age (human, 2.6-34.9 g/mm [25.2-342.7 mN/mm]; monkey, 8.2-21.3 g/mm [80.3-208.6 mN/mm]). The ratio of the force necessary to stretch the empty lens capsule to the force necessary to stretch the natural lens decreased with age in the human and monkey lenses (P = 0.003, P = 0.72, respectively).
The mechanical properties of the empty lens capsule assessed ex vivo in a lens stretcher remain constant with age, suggesting that the changes in elasticity of the lens capsule do not play a significant role in presbyopia. In young eyes, the lens capsule determines the force necessary to stretch the whole lens. The age-related increase in force needed to stretch the lens is due to changes in the lens contents.
[Show abstract][Hide abstract] ABSTRACT: To quantify the forces necessary to change the shape and optical power of human and monkey lenses.
Cynomolgus monkey (n = 48; age: 3.8-11 years), rhesus monkey (n = 35; age: 0.7-17 years) and human (n = 20, age 8-70 years) eyes obtained postmortem, including the lens, capsule, zonules, ciliary body, and sclera were mounted in an optomechanical lens-stretching system. Starting at zero load, the lenses were symmetrically stretched in a stepwise fashion in 0.25- or 0.5-mm steps. The load, lens diameter, inner ciliary body diameter, and lens power were measured at each step and the diameter- and power-load responses were quantified.
The diameter- and power-load responses were found to be linear in the physiologically relevant range of stretching. The average change in cynomolgus, rhesus, and human lens diameter, respectively, was 0.094, 0.109, and 0.069 mm/g in young lenses, and 0.069, 0.067, and 0.036, mm/g in older lenses. For the same lenses, the average change in lens power was -3.73, -2.83, and -1.22 D/g in young lenses and -2.46, -2.16, and -0.49 D/g in older lenses.
The force necessary to change the lens diameter and lens power increases with age in human and monkey lenses. The results agree with the Helmholtz theory of accommodation and with presbyopia theories that predict that the force required to disaccommodate the lens increases with age.
[Show abstract][Hide abstract] ABSTRACT: 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.
Vision Research 04/2006; 46(6-7):1002-9. DOI:10.1016/j.visres.2005.10.019 · 1.82 Impact Factor