Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens.

In the first part of this paper we presented a tomographic method to reconstruct the refractive index profile of spherically symmetrical lenses. Here we perform the generalization to lenses that are rotationally symmetrical around the optical axis, as is the ideal human lens. Analysis of the accuracy and versatility of this method is carried out by performing numerical simulations in which different magnitudes of experimental errors and two extreme case scenarios for the likely shape of the refractive index distribution of the human lens are considered. Finally, experimental results for a porcine lens are shown. Conceptually simple and computationally swift, this method could prove to be a valuable tool for the accurate retrieval of the gradient index of a broad spectrum of rotationally symmetrical crystalline lenses.

The Nepal Longitudinal Study: biometric characteristics of developing eyes.

PURPOSE: To identify differences in potential biometric markers for predicting refractive error in school children. METHODS: Biometric data on 895 Tibetan children, aged 6 to 18 years, residing in Katmandu, Nepal, were collected biennially from 1992 to 2000. Measurements included cycloplegic autorefraction, A-scan ultrasonography, and video phakometry. Only those children who had been studied at least once at age 12 years or more were included in the analysis. Subjects were divided into two groups: a myopia group if the refractive error was myopic by more than -0.50 D and a nonmyopia group if the refractive error was maximally myopic by -0.50 D, expressed as a spherical equivalent error in the left eye. RESULTS: Biometric measures that differed significantly with increasing age between the two refractive groups included: anterior chamber depth + 0.012 mm/year (p = 0.014), anterior lens radius of curvature + 0.073 mm/year (p = 0.001), lens power -0.059 D/year (p = 0.082), lens thickness -0.005 mm/year (p = 0.02), and vitreous chamber depth + 0.084 mm/year (p < 0.001). Corneal radii of curvature of the myopic group were steeper at all ages by 0.09 mm (p < 0.001), but the rate of change with age was equivalent across the refractive groups. CONCLUSIONS: Compared with those who remained nonmyopic, children who developed myopia had a crystalline lens that was initially thicker and steeper, and a vitreous chamber that was initially shorter. With age, children who became myopic developed greater lens thinning, greater flattening of the anterior lens surface radius, and a greater increase in vitreous chamber depth than their nonmyopic counterparts.

Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens.

We present an iterative tomographic algorithm to reconstruct refractive-index profiles for meridional planes of the lens of the spherical fish eye from measurements of deflection angles of refracted rays. Numerical simulations show that the algorithm allows accuracy up to the fourth decimal place, provided that the refractive index can be regarded as an analytical function of the radial coordinate and the experimental errors are neglected. An experimental demonstration is given by applying the algorithm to retrieve the refractive-index profile of a spherical fish lens. The method is conceptually simple and does not require matching of the index of the surrounding medium to that of the surface of the lens, and the related iterative algorithm rapidly converges.

The relationship between the sagitta of the anterior corneal surface and refractive error of the eye.

Changes in the sagitta of the anterior corneal surface associated with a change in the corneal radius of curvature have been used to calculate the change in refractive error of the eye in two areas: the ablation depth for laser surgery, and the change in corneal thickness associated with orthokeratology lens wear. An approximate formula known as Munnerlyn's formula is commonly used to calculate the refractive error change from sagittal data. This article compares the change in refraction calculated using the approximate formulae with the change calculated from a formula based on an elliptical corneal section. The approximate formula underestimates the ablation depth for a given refractive change and overestimates the refractive change for a given change in corneal thickness, assuming a constant asphericity. When the corneal asphericity increases together with an increase in radius of curvature, a suggested mechanism in orthokeratology, the approximate formula underestimates the change in ocular refraction.

Posterior corneal changes with orthokeratology.

PURPOSE: To investigate changes in corneal thickness and the radius of curvature of the posterior corneal surface after orthokeratology (OK) rigid lens wear. METHODS: Nineteen young myopic subjects wore reverse-geometry OK lenses (BE/ABE, Ultravision Contact Lenses, Brisbane, Australia) every night for 1 month. Central and midperipheral corneal thickness (Allergan Humphrey ultrasound, Carl Zeiss Meditec, Dublin, CA), topography (EyeSys v.3.1, Houston, TX), subjective refraction, and posterior corneal radii (video photography of Purkinje images) were evaluated within 2 h of waking, prelens wear, and on four occasions postlens wear during a 1-month period. A mixed-models approach was used to analyze the data. We modeled the changes in posterior corneal radius of curvature and corneal thickness in terms of the sagittal height of the anterior and posterior cornea using an ellipsoidal model for the corneal surfaces. RESULTS: Refractive error reduced from -2.28 to -0.01 DS within 1 month. A significant thinning of the cornea was evident between 1 (p = 0.03) and 2 weeks (p = 0.0048) postlens wear. A significant increase in the anterior corneal radius of curvature was present at all time periods beyond 1 night (p < 0.001), and a significant posterior corneal flattening occurred centrally and midperipherally after 1 week (p = 0.04 and p = 0.013, respectively). CONCLUSIONS: These findings suggest that in addition to the significant topographic flattening of the anterior corneal surfaces, there is also a significant flattening of the posterior surface during the early adaptive stages of OK lens wear.

Can patients accurately read a visual analog pain scale?

The objective of this study was too determine if patients can accurately read a visual analog scale (VAS) for pain. A 100-mm visual analog pain scale designed for patient use was printed on the top page of carbonless copy paper with a perfectly aligned hatched scale on the second (bottom) page. Patients over the age of 18 in acute pain were enrolled in this prospective, descriptive study. Patients were asked demographic questions and to indicate their pain severity with a single mark through the 100-mm scale. Once scored, patients were asked to read the number from the hatched bottom scale. Two physician-raters, blinded to patients' and each other's readings, then scored the VAS. Analysis of physician interrater reliability and correlation of patient and physician readings was performed. One hundred forty-five patients were enrolled. Seventy-nine patients (54.5%) read the VAS exactly as physician-readers. One hundred thirty-eight (95.2%) read their VAS within +/-2 mm of physician readings. Ninety-five percent of patients are able to read a VAS within +/-2 mm of physician readings. The data suggests this instrument could be used by discharged patients in longitudinal pain studies or with help in management of chronic pain.

The relationship between the Stiles-Crawford effect of the first kind (SCE-I) and myopia.

The Stiles-Crawford effect of the first kind (SCE-I) was measured on both emmetropic and myopic subjects at six different retinal locations. The results revealed a number of significant discrepancies in receptor alignment between the groups of different refractive errors. In myopic subjects, the receptors in the nasal retina (i.e. between the fovea and the optic nerve head) were found to be aligned nasally towards the optic nerve head, whereas the receptors in the temporal retina were aligned towards the centre of the exit pupil. In emmetropic subjects, the receptors across the retina were finely tuned towards the centre of the exit pupil. The magnitude of the receptor displacement in myopic subjects was found to be directly associated with the length of the eyeball.

Stiles-Crawford effect of the first kind (SCE-I) in post-photorefractive keratectomy and anisometropic subjects.

The Stiles-Crawford effect of the first kind (SCE-I) was measured on both post-photorefractive keratectomy (PRK) and anisometropic subjects at six different locations of retina. The eye that underwent the PRK procedure showed results that were typical of myopic eyes, although the vision in that eye has been maintained at 6/5 (or 20/15) since the operation. The anisometropic subject had one eye that was emmetropic and the other eye was myopic with a refractive error of -3.00 DS. The emmetropic eye showed the normal well-centered SCE-I functions across the retina, whereas the myopic eye of the same subject showed the nasal tilting of receptors in the nasal retina, which has been the typical finding among myopic subjects.

Refractive index of the crystalline lens in young and aged eyes.

BACKGROUND: When the ageing crystalline lens is modelled on the basis of a constant equivalent lens, the changes in ocular dimensions would lead to an increase in power of the order of two dioptres. A comparable increase in myopia is usually not evident with increasing age and this inconsistency has been referred to as the lens paradox. It has been proposed that this paradox can be resolved if the refractive index is modelled as a gradient refractive index. The purpose of this paper was to study differences in the equivalent, gradient and surface refractive index of the crystalline lens between a young and old age group. METHODS: Biometric data was collected for 96 subjects: 48 young adults with an age range 19 to 31 years (mean 22.10 +/- 2.93 years) and 48 old adults with an age range 49 to 61 years (mean 53.88 +/- 3.88 years). The equivalent refractive index was determined for each subject by paraxial ray tracing and a merit function based on refractive error and Purkinje image height. The refractive index gradient was determined by modelling the crystalline lens as a bi-elliptical iso-indicial structure in a three-surface Gullstrand-Emsley schematic eye and a merit function based on the surface power, the gradient refractive index power and the equivalent power of the lens. The central refractive index of the lens was assumed to be 1.406. RESULTS: The differences between the groups included a decrease in the mean equivalent refractive index from 1.427 +/- 0.007 to 1.418 +/- 0.006, an increase in surface refractive index from 1.386 +/- 0.007 to 1.394 +/- 0.006 with a concurrent change in the gradient refractive index profile. The refractive index changes maintained a constant mean lens power in each group. CONCLUSIONS: The so-called 'lens paradox' whereby an increase in the power of the crystalline lens does not lead to an increase in myopia is resolved by a decrease in the equivalent refractive index of the lens or when modelled as a gradient refractive index structure, by an increase in the surface refractive index and an associated change in gradient for an assumed central refractive index of 1.406.

Age dependence of ocular biometric measurements under cycloplegia with tropicamide and cyclopentolate.

BACKGROUND: Cyclopentolate continues to be the cycloplegic of choice for refracting young children, although many studies of ocular biometry promote the use of tropicamide. METHODS: To clarify the role of drug type in biometric measurements, cycloplegia was induced in two disparate age groups using cyclopentolate and tropicamide on two separate occasions. Refraction, phakometry and A-scan ultrasonography measurements were made on two groups of Tibetan children resident in Nepal. RESULTS: Cyclopentolate produced significantly more cycloplegia in the younger group, which was supported by phakometry measurements. However, in clinical terms, the difference between the measurements was not significant. CONCLUSION: We conclude that although cyclopentolate is more effective than tropicamide in relaxing accommodation in young children, the use of a local anaesthetic prior to instillation of tropicamide produces refractive data virtually equivalent to that of cyclopentolate, regardless of the age group measured. However, biometric measurements may be susceptible to greater error when near fixation targets are used during phakometry procedures.