A review of the surgical options for the correction of presbyopia

Presbyopia is an age-related eye condition where one of the signs is the reduction in the amplitude of accommodation, resulting in the loss of ability to change the eye's focus from far to near. It is the most common age-related ailments affecting everyone around their mid-40s. Methods for the correction of presbyopia include contact lens and spectacle options but the surgical correction of presbyopia still remains a significant challenge for refractive surgeons. Surgical strategies for dealing with presbyopia may be extraocular (corneal or scleral) or intraocular (removal and replacement of the crystalline lens or some type of treatment on the crystalline lens itself). There are however a number of limitations and considerations that have limited the widespread acceptance of surgical correction of presbyopia. Each surgical strategy presents its own unique set of advantages and disadvantages. For example, lens removal and replacement with an intraocular lens may not be preferable in a young patient with presbyopia without a refractive error. Similarly treatment on the crystalline lens may not be a suitable choice for a patient with early signs of cataract. This article is a review of the options available and those that are in development stages and are likely to be available in the near future for the surgical correction of presbyopia.

Data methods in optometry. Part 6: fitting a regression line to data

1. Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, r squared estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. 2. Always check whether the data collected fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary. 3. If the regression line is to be used for prediction, it is important to determine whether the prediction involves an individual y value or a mean. Care should be taken if predictions are made close to the extremities of the data and are subject to considerable error if x falls beyond the range of the data. Multiple predictions require correction of the P values. 3. If several individual regression lines have been calculated from a number of similar sets of data, consider whether they should be combined to form a single regression line. 4. If the data exhibit a degree of curvature, then fitting a higher-order polynomial curve may provide a better fit than a straight line. In this case, a test of whether the data depart significantly from a linear regression should be carried out.

When to use the Bonferroni correction

PURPOSE: The Bonferroni correction adjusts probability (p) values because of the increased risk of a type I error when making multiple statistical tests. The routine use of this test has been criticised as deleterious to sound statistical judgment, testing the wrong hypothesis, and reducing the chance of a type I error but at the expense of a type II error; yet it remains popular in ophthalmic research. The purpose of this article was to survey the use of the Bonferroni correction in research articles published in three optometric journals, viz. Ophthalmic & Physiological Optics, Optometry & Vision Science, and Clinical & Experimental Optometry, and to provide advice to authors contemplating multiple testing. RECENT FINDINGS: Some authors ignored the problem of multiple testing while others used the method uncritically with no rationale or discussion. A variety of methods of correcting p values were employed, the Bonferroni method being the single most popular. Bonferroni was used in a variety of circumstances, most commonly to correct the experiment-wise error rate when using multiple 't' tests or as a post-hoc procedure to correct the family-wise error rate following analysis of variance (anova). Some studies quoted adjusted p values incorrectly or gave an erroneous rationale. SUMMARY: Whether or not to use the Bonferroni correction depends on the circumstances of the study. It should not be used routinely and should be considered if: (1) a single test of the 'universal null hypothesis' (Ho ) that all tests are not significant is required, (2) it is imperative to avoid a type I error, and (3) a large number of tests are carried out without preplanned hypotheses.

Comparison of bit error rate estimation methods for QPSK CO-OFDM transmission

In this letter, we experimentally study the statistical properties of a received QPSK modulated signal and compare various bit error rate (BER) estimation methods for coherent optical orthogonal frequency division multiplexing transmission. We show that the statistical BER estimation method based on the probability density function of the received QPSK symbols offers the most accurate estimate of the system performance.

Bit error rate estimation methods for QPSK CO-OFDM transmission

Coherent optical orthogonal frequency division multiplexing (CO-OFDM) is an attractive transmission technique to virtually eliminate intersymbol interference caused by chromatic dispersion and polarization-mode dispersion. Design, development, and operation of CO-OFDM systems require simple, efficient, and reliable methods of their performance evaluation. In this paper, we demonstrate an accurate bit error rate estimation method for QPSK CO-OFDM transmission based on the probability density function of the received QPSK symbols. By comparing with other known approaches, including data-aided and nondata-aided error vector magnitude, we show that the proposed method offers the most accurate estimate of the system performance for both single channel and wavelength division multiplexing QPSK CO-OFDM transmission systems. © 2014 IEEE.

Is pupil diameter influenced by refractive error?

Purpose: To investigate the relationship between pupil diameter and refractive error and how refractive correction, target luminance, and accommodation modulate this relationship. Methods: Sixty emmetropic, myopic, and hyperopic subjects (age range, 18 to 35 years) viewed an illuminated target (luminance: 10, 100, 200, 400, 1000, 2000, and 4100 cd/m2) within a Badal optical system, at 0 diopters (D) and −3 D vergence, with and without refractive correction. Refractive error was corrected using daily disposable contact lenses. Pupil diameter and accommodation were recorded continuously using a commercially available photorefractor. Results: No significant difference in pupil diameter was found between the refractive groups at 0 D or −3 D target vergence, in the corrected or uncorrected conditions. As expected, pupil diameter decreased with increasing luminance. Target vergence had no significant influence on pupil diameter. In the corrected condition, at 0 D target vergence, the accommodation response was similar in all refractive groups. At −3 D target vergence, the emmetropic and myopic groups accommodated significantly more than the hyperopic group at all luminance levels. There was no correlation between accommodation response and pupil diameter or refractive error in any refractive group. In the uncorrected condition, the accommodation response was significantly greater in the hyperopic group than in the myopic group at all luminance levels, particularly for near viewing. In the hyperopic group, the accommodation response was significantly correlated with refractive error but not pupil diameter. In the myopic group, accommodation response level was not correlated with refractive error or pupil diameter. Conclusions: Refractive error has no influence on pupil diameter, irrespective of refractive correction or accommodative demand. This suggests that the pupil is controlled by the pupillary light reflex and is not driven by retinal blur.

Comparison of numerical bit error rate estimation methods in 112Gbs QPSK CO-OFDM transmission

We demonstrate an accurate BER estimation method for QPSK CO-OFDM transmission based on the probability density function of the received QPSK symbols. Using a 112Gbs QPSK CO-OFDM transmission as an example, we show that this method offers the most accurate estimate of the system's performance in comparison with other known approaches.

Evaluation of the evidential value of the elemental composition of glass, ink and paper by laser-based microspectrochemical methods

Elemental analysis can become an important piece of evidence to assist the solution of a case. The work presented in this dissertation aims to evaluate the evidential value of the elemental composition of three particular matrices: ink, paper and glass. In the first part of this study, the analytical performance of LIBS and LA-ICP-MS methods was evaluated for paper, writing inks and printing inks. A total of 350 ink specimens were examined including black and blue gel inks, ballpoint inks, inkjets and toners originating from several manufacturing sources and/or batches. The paper collection set consisted of over 200 paper specimens originating from 20 different paper sources produced by 10 different plants. Micro-homogeneity studies show smaller variation of elemental compositions within a single source (i.e., sheet, pen or cartridge) than the observed variation between different sources (i.e., brands, types, batches). Significant and detectable differences in the elemental profile of the inks and paper were observed between samples originating from different sources (discrimination of 87–100% of samples, depending on the sample set under investigation and the method applied). These results support the use of elemental analysis, using LA-ICP-MS and LIBS, for the examination of documents and provide additional discrimination to the currently used techniques in document examination. In the second part of this study, a direct comparison between four analytical methods (µ-XRF, solution-ICP-MS, LA-ICP-MS and LIBS) was conducted for glass analyses using interlaboratory studies. The data provided by 21 participants were used to assess the performance of the analytical methods in associating glass samples from the same source and differentiating different sources, as well as the use of different match criteria (confidence interval (±6s, ±5s, ±4s, ±3s, ±2s), modified confidence interval, t-test (sequential univariate, p=0.05 and p=0.01), t-test with Bonferroni correction (for multivariate comparisons), range overlap, and Hotelling's T2 tests. Error rates (Type 1 and Type 2) are reported for the use of each of these match criteria and depend on the heterogeneity of the glass sources, the repeatability between analytical measurements, and the number of elements that were measured. The study provided recommendations for analytical performance-based parameters for µ-XRF and LA-ICP-MS as well as the best performing match criteria for both analytical techniques, which can be applied now by forensic glass examiners.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation

In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier--Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I a posteriori bounds are derived for the estimation of the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated. This general approach leads to the design of economical finite element meshes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed approach will be presented.

A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity

We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement and isotropic and anisotropic polynomial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp-isotropic mesh refinement algorithms and an h-anisotropic/p-isotropic adaptive procedure is illustrated by a series of numerical experiments.

Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.

Evaluation of the Evidential Value of the Elemental Composition of Glass, Ink and Paper by Laser-Based Micro-Spectrochemical Methods

Elemental analysis can become an important piece of evidence to assist the solution of a case. The work presented in this dissertation aims to evaluate the evidential value of the elemental composition of three particular matrices: ink, paper and glass. In the first part of this study, the analytical performance of LIBS and LA-ICP-MS methods was evaluated for paper, writing inks and printing inks. A total of 350 ink specimens were examined including black and blue gel inks, ballpoint inks, inkjets and toners originating from several manufacturing sources and/or batches. The paper collection set consisted of over 200 paper specimens originating from 20 different paper sources produced by 10 different plants. Micro-homogeneity studies show smaller variation of elemental compositions within a single source (i.e., sheet, pen or cartridge) than the observed variation between different sources (i.e., brands, types, batches). Significant and detectable differences in the elemental profile of the inks and paper were observed between samples originating from different sources (discrimination of 87 – 100% of samples, depending on the sample set under investigation and the method applied). These results support the use of elemental analysis, using LA-ICP-MS and LIBS, for the examination of documents and provide additional discrimination to the currently used techniques in document examination. In the second part of this study, a direct comparison between four analytical methods (µ-XRF, solution-ICP-MS, LA-ICP-MS and LIBS) was conducted for glass analyses using interlaboratory studies. The data provided by 21 participants were used to assess the performance of the analytical methods in associating glass samples from the same source and differentiating different sources, as well as the use of different match criteria (confidence interval (±6s, ±5s, ±4s, ±3s, ±2s), modified confidence interval, t-test (sequential univariate, p=0.05 and p=0.01), t-test with Bonferroni correction (for multivariate comparisons), range overlap, and Hotelling’s T2 tests. Error rates (Type 1 and Type 2) are reported for the use of each of these match criteria and depend on the heterogeneity of the glass sources, the repeatability between analytical measurements, and the number of elements that were measured. The study provided recommendations for analytical performance-based parameters for µ-XRF and LA-ICP-MS as well as the best performing match criteria for both analytical techniques, which can be applied now by forensic glass examiners.