M. Dubbelman

The shape of the anterior and posterior surface of the aging human cornea

PURPOSE To determine the shape and astigmatism of the posterior corneal surface in a healthy population with age, using Scheimpflug photography corrected for distortion due to the geometry of the Scheimpflug imaging system and the refraction of the anterior corneal surface. METHODS Scheimpflug imaging was used to measure in six meridians the cornea of the right eye of 114 subjects, ranging in age from 18 to 65 years. RESULTS The average radius of the anterior corneal surface was 7.79+/-0.27 (SD) mm and the average radius of the posterior corneal surface was 6.53+/-0.25 (SD) mm. Both surfaces were found to be flatter horizontally than vertically. The cylindrical component of the posterior surface of 0.33 mm is twice that of the anterior surface (0.16 mm). The asphericity of both the anterior and the posterior surface was independent of the radius of curvature at the vertex, refractive error and gender. In contrast with that of the anterior corneal surface, the asphericity of the posterior corneal surface varied significantly between meridians. With age, the asphericity of both the anterior and the posterior corneal surface changes significantly, which results in a slight peripheral thinning of the cornea. CONCLUSION On average, the astigmatism of the posterior corneal surface (-0.305 D) compensates the astigmatism of the anterior corneal surface (0.99 D) with 31%. The results show that the effective refractive index is 1.329, which is lower than values commonly used. There is no correlation between the asphericity of the anterior and the posterior corneal surface. As a result, the shape of the anterior corneal surface provides no definitive basis for knowing the asphericity of the posterior surface.

Change in shape of the aging human crystalline lens with accommodation

The objective was to measure the change in shape of the aging human crystalline eye lens in vivo during accommodation. Scheimpflug images were made of 65 subjects between 16 and 51 years of age, who were able to accommodate at least 1D. The Scheimpflug images were corrected for distortion due to the geometry of the camera and the refraction of the cornea and anterior lens surface, which is necessary to determine the real shape of the lens. To ensure accurate correction for the refraction of the anterior lens surface, the refractive index of the crystalline lens must be determined. Therefore, axial length was also measured, which made it possible to calculate the equivalent refractive index of the lens and possible changes in this index during accommodation. The results show that during accommodation there is a decrease in both the anterior and the posterior radius of the lens, although the change in mm per diopter of the latter is much smaller. The increase in lens thickness with accommodation is higher than the decrease in the anterior chamber depth, indicating that the posterior lens surface moves backwards with accommodation. During accommodation the anterior lens surface becomes more hyperbolic. Furthermore, an increase in the equivalent refractive index during accommodation was determined.

Changes in the internal structure of the human crystalline lens with age and accommodation.

Scheimpflug images were made of the unaccommodated and accommodated right eye of 102 subjects ranging in age between 16 and 65 years. In contrast with earlier Scheimpflug studies, the images were corrected for distortion due to the geometry of the Scheimpflug camera and the refraction of the cornea and the lens itself. The different nuclear and cortical layers of the human crystalline lens were determined using densitometry and it was investigated how the thickness of these layers change with age and accommodation. The results show that, with age, the increase in thickness of the cortex is approximately 7 times greater than that of the nucleus. The increase in thickness of the anterior cortex was found to be 1.5 times greater than that of the posterior cortex. It was also found that specific parts of the cortex, known as C1 and C3, showed no significant change in thickness with age, and that the thickening of the cortex is entirely due to the increase in thickness of the C2 zone. With age, the distance between the sulcus (centre of the nucleus) and the cornea does not change. With accommodation, the nucleus becomes thicker, but the thickness of the cortex remains constant.

Crystalline lens radii of curvature from Purkinje and Scheimpflug imaging

We present a comparison between measurements of the radius of the anterior and posterior lens surface, which was performed using corrected Scheimpflug imaging and Purkinje imaging in the same group of participants (46 for the anterior lens, and 34 for the posterior lens). Comparisons were also made as a function of accommodation (0 to 7 D) in a subset of 11 eyes. Data were captured and processed using laboratory prototypes and custom processing algorithms [for optical and geometrical distortion correction in the Scheimpflug system and using either equivalent mirror (EM) or merit function (MF) methods for Purkinje]. We found statistically significant differences in 4 of 46 eyes for the anterior lens radius, and 10 of 34 eyes for the posterior radius (using the MF and individual biometric data to process the Purkinje images). For the anterior lens, the agreement increases using individual biometry as opposed to biometric data from a model eye. For the posterior lens, the agreement increases using the MF as opposed to the EM method. For the changes during accommodation, no significant difference between the two techniques was found. In conclusion, the results of the cross-validation using the Scheimpflug and Purkinje imaging technique show that both techniques provide comparable lens radii and similar changes with accommodation. Purkinje tends to overestimate posterior lens radius, whereas pupil size limits the acquisition of posterior lens data with the Scheimpflug camera. Computer simulations using the Scheimpflug data as input show that the consistent slight overestimation of the posterior lens radius using Purkinje imaging can be partly attributed to the asphericity of the lens surface.

Constant volume of the human lens and decrease in surface area of the capsular bag during accommodation: an MRI and Scheimpflug Study.

PURPOSE A change in surface area of the capsular bag and a change in volume of the lens can indicate whether a change in the shape of the lens during accommodation is due to the compressibility or the elasticity of the lens material. METHODS 3D magnetic resonance imaging (MRI) was used to image the complete shape of the lens in a group of five healthy subjects between 18 and 35 years of age. A parametric representation of the cross-sectional shape was fitted to the edges of the lens, which were determined with a Canny edge filter. Based on a partition of the lens into eight parts, the parametric shape makes it possible to calculate the mean cross-sectional area, the volume, and the surface area as a function of accommodation. Corrected Scheimpflug imaging was used to validate the results obtained with MRI. RESULTS No significant difference in central anterior and posterior radius of curvature and thickness was found between the MRI and Scheimpflug measurements. In accordance with the Helmholtz accommodation theory, a decrease in the anterior and posterior radius of curvature and equatorial diameter and an increase in lens thickness occurred with accommodation. During accommodation, the mean cross-sectional area increased and the surface area decreased. However, no significant change in lens volume was found. CONCLUSIONS The preservation of lens volume implies that the internal human lens material can be assumed to be incompressible and is undergoing elastic deformation. Furthermore, the change in surface area indicates that the capsular bag also undergoes elastic deformation.

Spherical aberration of the anterior and posterior surfaces of the human cornea

A ray-tracing procedure was applied to corrected Scheimpflug photography measurements to determine the spherical aberration of the anterior and posterior surfaces of the cornea. It was found that the total spherical aberration of the cornea increases slightly with age. The spherical aberration of the posterior corneal surface is negative at a young age and becomes positive at an older age. To make an accurate description of the spherical aberration for the whole eye, the posterior surface must also be measured.

The shape of the human lens nucleus with accommodation

Knowledge about geometric properties such as shape and volume and Poissons ratio of the nucleus can be used in the mechanical and optical modeling of the accommodation process. Therefore, Scheimpflug imaging was used to determine the shape of the human lens nucleus during accommodation in five subjects. To describe the shape of the nucleus, we fitted a parametric model of the cross-sectional geometry to the gradient of the Scheimpflug images using the Hough transform. The geometric model made it possible to estimate the anterior and the posterior central radius, central thickness, equatorial diameter, and cross-sectional area of the nucleus. Assuming that the nucleus is rotationally symmetric, the volume of the nucleus can be estimated by integrating around the circumference. For all five subjects, the results show that during accommodation the nucleus became more convex and that the central thickness increased whereas the equatorial diameter decreased. This decrease in equatorial diameter of the nucleus with accommodation is in accordance with the Helmholtz accommodation theory. Finally, the volume of the nucleus (on average 35 mm(3)) showed no significant change during accommodation in any of the subjects, presumably due to the fact that the human nucleus consists of incompressible material with a Poissons ratio that is near .5.

The contribution of the posterior surface to the coma aberration of the human cornea.

Scheimpflug imaging was used to measure in six meridians the shape of the anterior and posterior cornea of the right eye of 114 subjects, ranging in age from 18 to 65 years. Subsequently, a three-dimensional model of the shape of the whole cornea was reconstructed, from which the coma aberration of the anterior and whole cornea could be calculated. This made it possible to investigate the compensatory role of the posterior surface to the coma aberration of the anterior corneal surface with age. Results show that, on average, the posterior surface compensates approximately 3.5% of the coma of the anterior surface. The compensation tends to be larger for young subjects (6%) than for older subjects (0%). This small effect of the posterior cornea on the coma aberration makes it clear that for the coma aberration of the whole eye, only the anterior corneal surface and the crystalline lens play a role. Consequently, for the design of an intraocular lens that is able to correct for coma aberration, it would be sufficient to only take the anterior corneal surface into account.

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

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

Microfluctuations of steady-state accommodation measured with ultrasonography

Over the past 30 years investigators have noted fluctuations in accommodation when the eye views a stationary target. These microfluctuations have been studied mainly with the use of infrared optometers. Two dominant components have been found: a low frequency component (LFC; 0.05-0.5 Hz) and a high frequency component (HFC; 1.0-2.2 Hz). The LFC probably has a neurological origin. The HFC is supposed to be related to the arterial pulse. The aim of this study was to investigate accommodative fluctuations and gain more information about their origin by using a non-optical method. We used continuous ultrasonographic biometry to measure changes in anterior chamber (AC) depth, lens thickness and vitreous length during steady-state accommodation. Simultaneously, the electrocardiogram (ECG) was recorded. Changes in axial length were calculated offline by taking the sum of the changes in the three intraocular distances. Results show that fluctuations with an LFC were present in all three intraocular distances but not in the axial length, proving that only the lens was involved. In contrast with the findings of investigators using optical methods, no HFC was present in fluctuations of AC depth and lens thickness. However, a small HFC was found in registrations of the vitreous and axial length, which appeared to correspond with the heart rate.