Refractive changes after descemet stripping endothelial keratoplasty: a simplified mathematical model.

PURPOSE: To develop a mathematical model that can predict refractive changes after Descemet stripping endothelial keratoplasty (DSEK). METHODS: A mathematical formula based on the Gullstrand eye model was generated to estimate the change in refractive power of the eye after DSEK. This model was applied to four DSEK cases retrospectively, to compare measured and predicted refractive changes after DSEK. RESULTS: The refractive change after DSEK is determined by calculating the difference in the power of the eye before and after DSEK surgery. The power of the eye post-DSEK surgery can be calculated with modified Gullstrand eye model equations that incorporate the change in the posterior radius of curvature and change in the distance between the principal planes of the cornea and lens after DSEK. Analysis of this model suggests that the ratio of central to peripheral graft thickness (CP ratio) and central thickness can have significant effect on refractive change where smaller CP ratios and larger graft thicknesses result in larger hyperopic shifts. This model was applied to four patients, and the average predicted hyperopic shift in the overall power of the eye was calculated to be 0.83 D. This change reflected in a mean of 93% (range, 75%-110%) of patients' measured refractive shifts. CONCLUSIONS: This simplified DSEK mathematical model can be used as a first step for estimating the hyperopic shift after DSEK. Further studies are necessary to refine the validity of this model.

Optical-CT 3D Dosimetry Using Fresnel Lenses with Minimal Refractive-Index Matching Fluid.

Telecentric optical computed tomography (optical-CT) is a state-of-the-art method for visualizing and quantifying 3-dimensional dose distributions in radiochromic dosimeters. In this work a prototype telecentric system (DFOS-Duke Fresnel Optical-CT Scanner) is evaluated which incorporates two substantial design changes: the use of Fresnel lenses (reducing lens costs from $10-30K t0 $1-3K) and the use of a 'solid tank' (which reduces noise, and the volume of refractively matched fluid from 1 ltr to 10 cc). The efficacy of DFOS was evaluated by direct comparison against commissioned scanners in our lab. Measured dose distributions from all systems were compared against the predicted dose distributions from a commissioned treatment planning system (TPS). Three treatment plans were investigated including a simple four-field box treatment, a multiple small field delivery, and a complex IMRT treatment. Dosimeters were imaged within 2 h post irradiation, using consistent scanning techniques (360 projections acquired at 1 degree intervals, reconstruction at 2mm). DFOS efficacy was evaluated through inspection of dose line-profiles, and 2D and 3D dose and gamma maps. DFOS/TPS gamma pass rates with 3%/3mm dose difference/distance-to-agreement criteria ranged from 89.3% to 92.2%, compared to from 95.6% to 99.0% obtained with the commissioned system. The 3D gamma pass rate between the commissioned system and DFOS was 98.2%. The typical noise rates in DFOS reconstructions were up to 3%, compared to under 2% for the commissioned system. In conclusion, while the introduction of a solid tank proved advantageous with regards to cost and convenience, further work is required to improve the image quality and dose reconstruction accuracy of the new DFOS optical-CT system.

Difficulties and errors in number reasoning development

The detailed study of difficulties and errors in young learner comprehension is a relevant and productive research field in Mathematics Education. Studies in the field are numerous although somewhat too varied. The present paper is suggesting methodological perspectives and principles applying to the field of research; we also show an example with school work. The use of figurate numbers as a representation system gives richer conceptual values, boosts visual reasoning and facilitates learner understanding.

Predicting physical properties of ionic liquids

A simple method to predict the densities of a range of ionic liquids from their surface tensions, and vice versa, using a surface-tension-weighted molar volume, the parachor, is reported. The parachors of ionic liquids containing 1-alkyl-3-methylimidazolium cations were determined experimentally, but were also calculated directly from their structural compositions using existing parachor contribution data for neutral compounds. The calculated and experimentally determined parachors were remarkably similar, and the latter data were subsequently employed to predict the densities and surface tensions of the investigated ionic liquids. Using a similar approach, the molar refractions of ionic liquids were determined experimentally, as well as calculated using existing molar refraction contribution data for uncharged compounds. The calculated molar refraction data were employed to predict the refractive indices of the ionic liquids from their surface tensions. The errors involved in the refractive index predictions were much higher than the analogous predictions employing the parachor, but nevertheless demonstrated the potential for developing parachor and molar refraction contribution data for ions as tools to predict ionic liquid physical properties.

Error sensitive historical GIS: Identifying areal interpolation errors in time series data

Historical GIS has the potential to re-invigorate our use of statistics from historical censuses and related sources. In particular, areal interpolation can be used to create long-run time-series of spatially detailed data that will enable us to enhance significantly our understanding of geographical change over periods of a century or more. The difficulty with areal interpolation, however, is that the data that it generates are estimates which will inevitably contain some error. This paper describes a technique that allows the automated identification of possible errors at the level of the individual data values.

Single-Mode Fiber Refractive Index Sensor Based on Core-Offset Attenuators

Mach-Zehnder and Michelson interferometers using core-offset attenuators were demonstrated. As the relative offset direction of the two attenuators in the Mach-Zehnder interferometer can significantly affect the extinction ratio of the interference pattern, single core-offset attenuator-based sensors appear more robust and repeatable. A novel fiber Michelson interferometer refractive index (RI) sensor was subsequently realized by a single core-offset attenuator and a layer of ~ 500-nm gold coating. The device had a minimum insertion loss of 0.01 dB and maximum extinction ratio over 9 dB. The sensitivity (0.333 nm) of the new sensor to its surrounding RI change (0.01) was found to be comparable to that (0.252 nm) of an identical long period gratings pair Mach-Zehnder interferometric sensor, and its ease of fabrication makes it a low-cost alternative to existing sensing applications.

Densities, speeds of sound, isentropic compressibilities, refractive indices and viscosities of binary mixtures of tetrahydrofuran with hydrocarbons at 303.15 K

Isentropic compressibilities, Rao's molar sound functions, molar refractions, excess isentropic compressibilities, excess molar volumes, viscosity deviations and excess Gibbs energies of activation of viscous flow for seven binary mixtures of tetrahydrofuran (THF) with cyclohexane, methylcyclohexane, n-hexane, benzene, toluene, p-xylene and propylbenzene over the entire range of composition at 303.15 K have been derived from experimental densities, speeds of sound, refractive indices and viscosities. The excess partial molar volumes of THF in different solvents have been estimated. The experimental results have been analyzed in terms of the Prigogine–Flory–Patterson theory.

Densities, speeds of sound, isentropic compressibilities, refractive indexes, and viscosities of tetrahydrofuran with haloalkane or alkyl ethanoate at T = 303.15 K

Isentropic compressibilities ?S, excess isentropic compressibilities image, excess molar volumes VE, viscosity deviations ??, and excess Gibbs energy of activation of viscous flow ?G*E for nine binary mixtures of C4H8O with CCl4, CHCl3, CHCl2CHCl2, 1-C6H13Cl, 1-C6H13Br, CH3CO2CH3, CH3CO2C2H5, CH3CO2C4H9, and CH3CO2C5H11 at 303.15 K have been derived from experimental densities ?, speeds of sound u, refractive indexes nD and viscosities ?. The limiting values of excess partial molar volumes of C4H8O at infinite dilution image in different solvents have been estimated. The results obtained for dynamic viscosity of binary mixtures were used to test the semi-empirical relations of Grunberg–Nissan, Tamura–Kurata, Hind–McLaughlin–Ubbelohde, Katti–Chaudhri, McAllister, Heric, and Auslaender. Finally, the experimental refractive indexes were compared with the predicted results for Lorentz–Lorenz, Dale–Gladstone, Eykman, Arago–Boit, Newton, Oster, Heller, and Wiener equations.

Non-ideal behaviour of a room temperature ionic liquid in an alkoxyethanol or poly ethers at T = (298.15 to 318.15) K

Non-ideal behaviour of 1-butyl-3-methylimidazolium hexafluorophosphate [bmim][PF6] in ethylene glycol monomethyl ether; CH3OCH2CH2OH (EGMME), ethylene glycol dimethyl ether; CH3OCH2CH2OCH3 (EGDME) and diethylene glycol dimethyl ether; CH3(OCH2CH2)2OCH3 (DEGDME) have been investigated over the whole composition range at T = (298.15 to 318.15) K. To gain insight into the mixing behaviour, results of density measurements were used to estimate excess molar volumes, image, apparent molar volumes, Vphi,i, partial molar volumes, image, excess partial molar volumes, image, and their limiting values at infinite dilution, image, image, and image, respectively. Volumetric results have been analyzed in the light of Prigogine–Flory–Patterson (PFP) statistical mechanical theory. Measurements of refractive indices n were also performed for all the binary mixtures over whole composition range at T = 298.15 K. Deviations in refractive indices ?phin and the deviation of molar refraction ?xR have been calculated from experimental data. Refractive indices results have been correlated with volumetric results and have been interpreted in terms of molecular interactions. Excess properties are fitted to the Redlich–Kister polynomial equation to obtain the binary coefficients and the standard errors.

Neoteric optical media for refractive index determination of gems and minerals

Refractive index determination of minerals and gems often requires their immersion in fluids with the same refractive index. However, these natural materials frequently have refractive indices above the ranges of common organic solvents. Most available high refractive index immersion materials are solid at room temperature, toxic, noxious, corrosive, carcinogenic, or any combination thereof. Since the physical properties of ionic liquids can be tuned by varying the cation and/or anion, we have developed immersion fluids for mineralogical studies which are relatively benign. We report here the syntheses of a range of ionic liquids ( many novel) based on the 1-alkyl-3-methylimidazolium cation, which all have refractive indices greater than 1.4, and can be used as immersion fluids for optical mineralogy studies. We further show that for a series of ionic liquids with the same anion, the refractive indices can be adjusted by systematic changes in the cation.