Ocular residual astigmatism and topographic disparity vector indexes in normal healthy eyes

Purpose: To define a range of normality for the vectorial parameters Ocular Residual Astigmatism (ORA) and topography disparity (TD) and to evaluate their relationship with visual, refractive, anterior and posterior corneal curvature, pachymetric and corneal volume data in normal healthy eyes. Methods: This study comprised a total of 101 consecutive normal healthy eyes of 101 patients ranging in age from 15 to 64 years old. In all cases, a complete corneal analysis was performed using a Scheimpflug photography-based topography system (Pentacam system Oculus Optikgeräte GmbH). Anterior corneal topographic data were imported from the Pentacam system to the iASSORT software (ASSORT Pty. Ltd.), which allowed the calculation of the ocular residual astigmatism (ORA) and topography disparity (TD). Linear regression analysis was used for obtaining a linear expression relating ORA and posterior corneal astigmatism (PCA). Results: Mean magnitude of ORA was 0.79 D (SD: 0.43), with a normality range from 0 to 1.63 D. 90 eyes (89.1%) showed against-the-rule ORA. A weak although statistically significant correlation was found between the magnitudes of posterior corneal astigmatism and ORA (r = 0.34, p < 0.01). Regression analysis showed the presence of a linear relationship between these two variables, although with a very limited predictability (R2: 0.08). Mean magnitude of TD was 0.89 D (SD: 0.50), with a normality range from 0 to 1.87 D. Conclusion: The magnitude of the vector parameters ORA and TD is lower than 1.9 D in the healthy human eye.

Constraint qualifications in linear vector semi-infinite optimization

Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.

Clinical utility of ocular residual astigmatism and topographic disparity vector indexes in subclinical and clinical keratoconus

Purpose. We aimed to characterize the distribution of the vector parameters ocular residual astigmatism (ORA) and topography disparity (TD) in a sample of clinical and subclinical keratoconus eyes, and to evaluate their diagnostic value to discriminate between these conditions and healthy corneas. Methods. This study comprised a total of 43 keratoconic eyes (27 patients, 17–73 years) (keratoconus group), 11 subclinical keratoconus eyes (eight patients, 11–54 years) (subclinical keratoconus group) and 101 healthy eyes (101 patients, 15–64 years) (control group). In all cases, a complete corneal analysis was performed using a Scheimpflug photography-based topography system. Anterior corneal topographic data was imported from it to the iASSORT software (ASSORT Pty. Ltd), which allowed the calculation of ORA and TD. Results. Mean magnitude of the ORA was 3.23 ± 2.38, 1.16 ± 0.50 and 0.79 ± 0.43 D in the keratoconus, subclinical keratoconus and control groups, respectively (p < 0.001). Mean magnitude of the TD was 9.04 ± 8.08, 2.69 ± 2.42 and 0.89 ± 0.50 D in the keratoconus, subclinical keratoconus and control groups, respectively (p < 0.001). Good diagnostic performance of ORA (cutoff point: 1.21 D, sensitivity 83.7 %, specificity 87.1 %) and TD (cutoff point: 1.64 D, sensitivity 93.3 %, specificity 92.1 %) was found for the detection of keratoconus. The diagnostic ability of these parameters for the detection of subclinical keratoconus was more limited (ORA: cutoff 1.17 D, sensitivity 60.0 %, specificity 84.2 %; TD: cutoff 1.29 D, sensitivity 80.0 %, specificity 80.2 %). Conclusion. The vector parameters ORA and TD are able to discriminate with good levels of precision between keratoconus and healthy corneas. For the detection of subclinical keratoconus, only TD seems to be valid.

Constraint qualifications in convex vector semi-infinite optimization

Convex vector (or multi-objective) semi-infinite optimization deals with the simultaneous minimization of finitely many convex scalar functions subject to infinitely many convex constraints. This paper provides characterizations of the weakly efficient, efficient and properly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The results in this paper generalize those obtained by the same authors on linear vector semi-infinite optimization problems.