The influence of posterior corneal surface astigmatism on residual astigmatism

It has often been found that corneal astigmatism exceeds the amount exhibited by the eye as a whole. This difference is usually referred to as residual astigmatism. Scrutiny of the studies of corneal astigmatismreveal that what has actually been measured is the astigmatic contributionof the anterior corneal surface alone. This anterior surface is easily measured whereas measurement of the posterior corneal surface is much more difficult. A method was therefore developed to measure the radius and toricity of the posterior corneal surface. The method relies upon photography of the first and second Purkinje images in three fixed meridians. Keratometry, comparison of anterior and posterior corneal Purkinje images and pachometricdata were applied to three meridional analysis equations, allowing the posterior corneal surface to be described in sphero-cylindrical form. Measurements were taken from 80 healthy subjects from two distinct age groups. The first consisted of 60 young subjects, mean age 22.04 years and the second consisted of 20 old subjects, mean age 74.64 years. The young group consisted of 28 myopes, 24 emmetropes and 8 hyperopes. The old group consisted of 6 myopes and 14 hyperopes. There was an equal number of males and females in each group. These groupings allowed the study of the effects of age, ametropia and gender on the posterior corneal toricity. The effect of the posterior corneal surface on residual astigmatism was assessed and was found to cause an overall reduction. This reduction was due primarily to the posterior corneal surface being consistently steeper relative to the anterior surface in the vertical meridian compared to the horizontal meridian.

The relationship between measurement method and corneal structure on apparent intraocular pressure in glaucoma and ocular hypertension

Purpose: To analyse the relationship between measured intraocular pressure (IOP) and central corneal thickness (CCT), corneal hysteresis (CH) and corneal resistance factor (CRF) in ocular hypertension (OHT), primary open-angle (POAG) and normal tension glaucoma (NTG) eyes using multiple tonometry devices. Methods: Right eyes of patients diagnosed with OHT (n=47), normal tension glaucoma (n=17) and POAG (n=50) were assessed, IOP was measured in random order with four devices: Goldmann applanation tonometry (GAT); Pascal(R) dynamic contour tonometer (DCT); Reichert(R) ocular response analyser (ORA); and Tono-Pen(R) XL. CCT was then measured using a hand-held ultrasonic pachymeter. CH and CRF were derived from the air pressure to corneal reflectance relationship of the ORA data. Results: Compared to the GAT, the Tonopen and ORA Goldmann equivalent (IOPg) and corneal compensated (IOPcc) measured higher IOP readings (F=19.351, p<0.001), particularly in NTG (F=12.604, p<0.001). DCT was closest to Goldmann IOP and had the lowest variance. CCT was significantly different (F=8.305, p<0.001) between the 3 conditions as was CH (F=6.854, p=0.002) and CRF (F=19.653, p<0.001). IOPcc measures were not affected by CCT. The DCT was generally not affected by corneal biomechanical factors. Conclusion: This study suggests that as the true pressure of the eye cannot be determined non-invasively, measurements from any tonometer should be interpreted with care, particularly when alterations in the corneal tissue are suspected.

Coherence imaging by use of a Newton rings sampling function

We show that, with suitable optics in the arm of a Michelson interferometer, orthogonal galvo-scanning mirrors build a sampling function in the form of Newton rings when the two interferometer arms are matched. Using a low-coherence source, one can obtain transversal depth-resolved images. A fast display procedure using a storage oscilloscope was devised based on this method.

Corneal pachymetry in normal and keratoconic eyes:Orbscan II versus ultrasound

Purpose: To compare corneal thickness measurements using Orbscan II (OII) and ultrasonic (US) pachymetry in normal and in keratoconic eyes. Setting: Eye Department, Heartlands and Solihull NHS Trust, Birmingham, United Kingdom. Methods: Central corneal thickness (CCT) was measured by means of OII and US pachymetry in 1 eye of 72 normal subjects and 36 keratoconus patients. The apical corneal thickness (ACT) in keratoconus patients was also evaluated using each method. The mean of the difference, standard deviation (SD), and 95% limits of agreement (LoA = mean ± 2 SD), with and without applying the default linear correction factor (LCF), were determined for each sample. The Student t test was used to identify significant differences between methods, and the correlation between methods was determined using the Pearson bivariate correlation. Bland-Altman analysis was performed to confirm that the results of the 2 instruments were clinically comparable. Results: In normal eyes, the mean difference (± 95% LoA) in CCT was 1.04 μm ± 68.52 (SD) (P>.05; r = 0.71) when the LCF was used and 46.73 ± 75.40 μm (P = .0001; r = 0.71) without the LCF. In keratoconus patients, the mean difference (± 95% LoA) in CCT between methods was 42.46 ± 66.56 μm (P<.0001: r = 0.85) with the LCF, and 2.51 ± 73.00 μm (P>.05: r = 0.85) without the LCF. The mean difference (± 95% LoA) in ACT for this group was 49.24 ± 60.88 μm (P<.0001: r = 0.89) with the LCF and 12.71 ± 68.14 μm (P = .0077; r = 0.89) when the LCF was not used. Conclusions: This study suggests that OII and US pachymetry provide similar readings for CCT in normal subjects when an LCF is used. In keratoconus patients, OII provides a valid clinical tool for the noninvasive assessment of CCT when the LCF is not applied. © 2004 ASCRS and ESCRS.

Numerical simulation of corneal transport processes

This paper presents a numerical study on the transport of ions and ionic solution in human corneas and the corresponding influences on corneal hydration. The transport equations for each ionic species and ionic solution within the corneal stroma are derived based on the transport processes developed for electrolytic solutions, whereas the transport across epithelial and endothelial membranes is modelled by using phenomenological equations derived from the thermodynamics of irreversible processes. Numerical examples are provided for both human and rabbit corneas, from which some important features are highlighted.

Grading of corneal transparency

Aim: To examine the academic literature on the grading of corneal transparency and to assess the potential use of objective image analysis. Method: Reference databases of academic literature were searched and relevant manuscripts reviewed. Annunziato, Efron (Millennium Edition) and Vistakon-Synoptik corneal oedema grading scale images were analysed objectively for relative intensity, edges detected, variation in intensity and maximum intensity. In addition, corneal oedema was induced in one subject using a low oxygen transmissibility (Dk/t) hydrogel contact lens worn for 3 hours under a light eye patch. Recovery from oedema was monitored over time using ultrasound pachymetry, high and low contrast visual acuity measures, bulbar hyperaemia grading and transparency image analysis of the test and control eyes. Results: Several methods for assessing corneal transparency are described in the academic literature, but none have gained widespread in clinical practice. The change in objective image analysis with printed scale grade was best described by quadratic parametric or sigmoid 3-parameter functions. ‘Pupil image scales’ (Annunziato and Vistakon-Synoptik) were best correlated to average intensity; however, the corneal section scale (Efron) was strongly correlated to variations in intensity. As expected, patching an eye wearing a low Dk/t hydrogel contact lens caused a significant (F=119.2, P<0.001) 14.3% increase in corneal thickness, which gradually recovered under open eye conditions. Corneal section image analysis was the most affected parameter and intensity variation across the slit width, in isolation, was the strongest correlate, accounting for 85.8% of the variance with time following patching, and 88.7% of the variance with corneal thickness. Conclusion: Corneal oedema is best determined objectively by the intensity variation across the width of a corneal section. This can be easily measured using a slit-lamp camera connected to a computer. Oedema due to soft contact lens wear is not easily determined over the pupil area by sclerotic scatter illumination techniques.

Boolean Rings that are Baire Spaces

∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.

Presbyopic LASIK using hybrid bi-aspheric micro-monovision ablation profile for presbyopic corneal treatments

Purpose: To evaluate distance and near image quality after hybrid bi-aspheric multifocal central presbyLASIK treatments. Design: Consecutive case series. Methods: Sixty-four eyes of 32 patients consecutively treated with central presbyLASIK were assessed. The mean age of the patients was 51 ± 3 years with a mean spherical equivalent refraction of-1.08 ± 2.62 diopters (D) and mean astigmatism of 0.52 ± 0.42 D. Monocular corrected distance visual acuity (CDVA), corrected near visual acuity (CNVA), and distance corrected near visual acuity (DCNVA) of nondominant eyes; binocular uncorrected distance visual acuity (UDVA); uncorrected intermediate visual acuity (UIVA); distance corrected intermediate visual acuity (DCIVA); and uncorrected near visual acuity (UNVA) were assessed pre- and postoperatively. Subjective quality of vision and near vision was assessed using the 10-item Rasch-scaled Quality of Vision and Near Activity Visual Questionnaire, respectively. Results: At 1 year postoperatively, 93% of patients achieved 20/20 or better binocular UDVA; 90% and 97% of patients had J2 or better UNVA and UIVA, respectively; 7% lost 2 Snellen lines of CDVA; Strehl ratio reduced by ~-4% ± 14%. Defocus curves revealed a loss of half a Snellen line at best focus, with no change for intermediate vergence (-1.25 D) and a mean gain of 2 lines for near vergence (-3 D). Conclusions: Presbyopic treatment using a hybrid bi-aspheric micro-monovision ablation profile is safe and efficacious. The postoperative outcomes indicate improvements in binocular vision at far, intermediate, and near distances with improved contrast sensitivity. A 19% retreatment rate should be considered to increase satisfaction levels, besides a 3% reversal rate.

Algorithms for Generating Near-Rings on Finite Cyclic Groups

In the present work are described the algorithms that generate all near-rings on finite cyclic groups of order 16 to 29.

Group Rings – A Brief History and some their Generalizations

We give a brief exposition of the history of the group rings and some their generalizations. Also we indicate some information of certain problems and results.

Sylow P-Subgroups of Abelian Group Rings

2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.

Zero-Dimensionality and Serre Rings

2000 Mathematics Subject Classification: Primary 13A99; Secondary 13A15, 13B02, 13E05.

Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation

2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.