Error induced by the estimation of the corneal power and the effective lens position with a rotationally asymmetric refractive multifocal intraocular lens

AIM: To evaluate the prediction error in intraocular lens (IOL) power calculation for a rotationally asymmetric refractive multifocal IOL and the impact on this error of the optimization of the keratometric estimation of the corneal power and the prediction of the effective lens position (ELP). METHODS: Retrospective study including a total of 25 eyes of 13 patients (age, 50 to 83y) with previous cataract surgery with implantation of the Lentis Mplus LS-312 IOL (Oculentis GmbH, Germany). In all cases, an adjusted IOL power (PIOLadj) was calculated based on Gaussian optics using a variable keratometric index value (nkadj) for the estimation of the corneal power (Pkadj) and on a new value for ELP (ELPadj) obtained by multiple regression analysis. This PIOLadj was compared with the IOL power implanted (PIOLReal) and the value proposed by three conventional formulas (Haigis, Hoffer Q and Holladay). RESULTS: PIOLReal was not significantly different than PIOLadj and Holladay IOL power (P>0.05). In the Bland and Altman analysis, PIOLadj showed lower mean difference (-0.07 D) and limits of agreement (of 1.47 and -1.61 D) when compared to PIOLReal than the IOL power value obtained with the Holladay formula. Furthermore, ELPadj was significantly lower than ELP calculated with other conventional formulas (P<0.01) and was found to be dependent on axial length, anterior chamber depth and Pkadj. CONCLUSION: Refractive outcomes after cataract surgery with implantation of the multifocal IOL Lentis Mplus LS-312 can be optimized by minimizing the keratometric error and by estimating ELP using a mathematical expression dependent on anatomical factors.

Positional accommodative intraocular lens power error induced by the estimation of the corneal power and the effective lens position

Purpose: To evaluate the predictability of the refractive correction achieved with a positional accommodating intraocular lenses (IOL) and to develop a potential optimization of it by minimizing the error associated with the keratometric estimation of the corneal power and by developing a predictive formula for the effective lens position (ELP). Materials and Methods: Clinical data from 25 eyes of 14 patients (age range, 52–77 years) and undergoing cataract surgery with implantation of the accommodating IOL Crystalens HD (Bausch and Lomb) were retrospectively reviewed. In all cases, the calculation of an adjusted IOL power (PIOLadj) based on Gaussian optics considering the residual refractive error was done using a variable keratometric index value (nkadj) for corneal power estimation with and without using an estimation algorithm for ELP obtained by multiple regression analysis (ELPadj). PIOLadj was compared to the real IOL power implanted (PIOLReal, calculated with the SRK-T formula) and also to the values estimated by the Haigis, HofferQ, and Holladay I formulas. Results: No statistically significant differences were found between PIOLReal and PIOLadj when ELPadj was used (P = 0.10), with a range of agreement between calculations of 1.23 D. In contrast, PIOLReal was significantly higher when compared to PIOLadj without using ELPadj and also compared to the values estimated by the other formulas. Conclusions: Predictable refractive outcomes can be obtained with the accommodating IOL Crystalens HD using a variable keratometric index for corneal power estimation and by estimating ELP with an algorithm dependent on anatomical factors and age.

Democracy Promotion and the EU, US Formulas: Photo Opportunities or Potential. Jean Monnet/Robert Schuman Paper Series Vol. 14 No. 5, May 2014

Why do we think more of the United States (US) than the European Union (EU) in discussing Afghani or Iraqi democratization, and EU more than US when it is East European? Should not democratization be the same? A comparative study asks what democracy has historically meant in the two regions, how democratization has been spelled out, why instruments utilized differ, and democracy within global leadership contexts. Neither treats democracy as a vital interest, but differences abound: (a) While the US shifted from relative bottom-up to top-down democracy, the EU added bottom-up to its top-down approach; (b) the US interprets democracy as the ends of other policy interests, the EU treats it as the means to other goals; and (c) flexible US instruments contrast with rigid EU counterparts. Among the implications: (a) the 4-stage US approach reaches globally wider than EU’s multi-dimensional counterpart, but EU’s regional approach sinks deeper than the US’s; (b) human rights find better EU than US anchors; (c) whereas the US approach makes intergovernmental actions the sine qua non of democratization, EU’s intergovernmental, transnational, and supranational admixture promotes quid pro quo dynamics and incremental growth; and (d) competitive democratization patterns creates lock-ins for both recipient and supplier countries.

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

The coal and metal miners' pocketbook of principles : rules, formulas, and tables.

"Specially compiled and prepared for the convenient use of mine officials, mining engineers, and students preparing themselves for certificates of competency as mine inspectors or mine foremen."

Numerical quadrature over a rectangular domain in two or more dimensions /

"This work was supported in part by the Office of Naval Research under Contract Nonr-1834(27)."

Algorithms for sparse Gaussian elimination with partial pivoting /

Bibliography: p. 17.

Gaussian elimination and numerical instability /

"UILU-ENG 77 1714."

Selected problems of minimization of variable-valued logic formulas /

"UIUCDCS-R-75-726"

Equivalent forms of multistep formulas /

"UIUL-ENG 78 1730."

Unified modified divided difference implementation of Adams and BDF formulas /

"March 1980."

Determination of symmetric VL1 formulas : algorithm and program SYM4 /

Mode of access: Internet.

Deposition and washout computations based on the generalized Gaussian plume model /

"September 30, 1963."

Brewing formulas practically considered,

Advertising matter: p. 56-59.

A system of mineralogy, comprising the most recent discoveries: including full descriptions of species and their localities, chemical analyses and formulas, tables for the determination of minerals, with a treatise on mathematical crystallography and the drawing of figures of crystals.

Mode of access: Internet.