D. Borja

In vitro dimensions and curvatures of human lenses

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

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

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.

Optical Power of the Isolated Human Crystalline Lens

PURPOSE To characterize the age dependence of isolated human crystalline lens power and quantify the contributions of the lens surfaces and refractive index gradient. METHODS 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. RESULTS 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. CONCLUSIONS 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.

Distortions of the posterior surface in optical coherence tomography images of the isolated crystalline lens: effect of the lens index gradient

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.

Postnatal Elongation of Eye Size in DBA/2J Mice Compared with C57BL/6J Mice: In Vivo Analysis with Whole-Eye OCT

PURPOSE 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). METHODS 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. RESULTS 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. CONCLUSIONS 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.

Age-dependent variation of the Gradient Index profile in human crystalline lenses.

An investigation was carried out with the aim of reconstructing 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. 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. 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. Optical coherence tomography allowed optical, non-invasive measurement of the 2D 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.

Contribution of the crystalline lens gradient refractive index to the accommodation amplitude in non-human primates: in vitro studies.

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 Gullstrands intracapsular theory of accommodation.

Semianalytical thermal model for subablative laser heating of homogeneous nonperfused biological tissue: application to laser thermokeratoplasty

We present a semianalytical technique to calculate the temperature in homogeneous nonperfused tissue during subablative laser heating. Analytical expressions of the temperature distribution in time and space are provided for collimated beams with Gaussian and top-hat intensity distributions perpendicularly incident on a finite tissue slab. The temperature distribution produced with a collimated Gaussian beam is the triple sum of the product of four functions of separate variables. The semianalytical technique can be used to rapidly calculate the temperature in laser-irradiated tissue at any point in time and space. The model was used to estimate the corneal temperature during pulsed holmium:YAG laser thermokeratoplasty with various boundary conditions at the anterior and posterior corneal surface. The model demonstrates that the corneal temperature during laser thermokeratoplasty (LTK) with a pulsed Ho:YAG laser may be sufficient to induce superficial vaporization of epithelial cells and local thermal damage to the endothelium. The calculations show that convection at the anterior corneal surface does not have a significant effect on the corneal temperature distribution, but that a better knowledge of the cooling effect of the aqueous is required to better estimate the corneal temperature distribution during LTK.

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 &mgr;m, respectively, on average. Thickness was also more accurately estimated with the new method, with a mean discrepancy of 8 &mgr;m. 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.

Preparation and hydration control of corneal tissue strips for experimental use.

Purpose The purpose of this study was to develop an experimental protocol to maintain corneal tissue strips at normal hydration and avoid swelling or dehydration during experimental studies on corneal biomechanics and thermal stability. Methods The corneal thickness of 9 whole Eye-Bank eyes was brought back to normal values by immersion in a 25% dextran solution for 24 hours. Corneal buttons were then removed and cut into 2 × 6 mm strips. The 9 strips were immersed successively in Dextran solutions at 25%, 22.5%, and 20% concentration at 35°C. The thickness of the immersed strip in solution was measured every 5 minutes for 1 hour using a modified optical comparator. Results The mean final thickness for the nine corneal strips after one hour in 25%, 22.5%, and 20% dextran solution was 508 ± 38, 563 ± 56, and 592 ± 33 &mgr;m, respectively. Average swelling in 25%, 22.5%, and 20% dextran solutions was 1.06 ± 0.03, 1.20 ± 0.07, and 1.24 ± 0.07 times the initial thickness, respectively. Conclusion The hydration of corneal tissue strips is maintained at normal values when the strips are immersed in 25% Dextran solution. Corneal strips swell to thicknesses above normal values in solutions with lower molecular weights.