Misalignment limited the repeatability of TMS-5 and Pentacam HR, but had little influence on the repeatability of CASIA SS-1000.

SUMMARYLack of conservation has been the biggest drawback in meshfree generalized finite difference methods (GFDMs). In this paper, we present a novel modification of classical meshfree GFDMs to include local balances which produce an approximate conservation of numerical fluxes. This numerical flux conservation is done within the usual moving least squares framework. Unlike Finite Volume Methods, it is based on locally defined control cells, rather than a globally defined mesh. We present the application of this method to an advection diffusion equation and the incompressible Navier-Stokes equations. Our simulations show that the introduction of flux conservation significantly reduces the errors in conservation in meshfree GFDMs.

The capabilities of a weighted least squares approach for the optimization of the intraocular lens (IOL) constants for the Haigis formula are studied in comparison to an ordinary least squares approach. The weights are set to the inverse variances of the effective optical anterior chamber depth. The effect of random measurement noise is simulated 100000 times using data from N = 69 cataract patients and the measurement uncertainty of two different biometers. A second, independent data set (N = 33) is used to show the differences that can be expected between both methods. The weighted least squares formalism reduces the effect of measurement error on the final constants. In more than 64% it will result in a better approximation, if the measurement errors are estimated correctly. The IOL constants can be calculated with higher precision using the weighted least squares method.

Purpose: To present strategies for optimization of lens power formula constants and to show options how to present the results adequately. Methods: A dataset of N=1601 preoperative biometric values, lens power data and postoperative refraction data was split into a training set and a test set using a random sequence. Based on the training set we calculated the formula constants for established lens calculation formulae with different methods. Based on the test set we derived the formula prediction error as difference of the achieved refraction from the formula predicted refraction. Results: For formulae with 1 constant it is possible to back-calculate the individual constant for each case using formula inversion. However, this is not possible for formulae with more than 1 constant. In these cases, more advanced concepts such as nonlinear optimization strategies are necessary to derive the formula constants. During cross-validation, measures such as the mean absolute or the root mean squared prediction error or the ratio of cases within mean absolute prediction error limits could be used as quality measures. Conclusions: Different constant optimization concepts yield different results. To test the performance of optimized formula constants a cross-validation strategy is mandatory. We recommend performance curves, where the ratio of cases within absolute prediction error limits is plotted against the mean absolute prediction error.

PurposeTo compare corneal tomography measurements (elevation and pachymetry) as made by two corneal tomographers: Pentacam AXL and CASIA 2.Material and methodsThe devices were used in a standard measuring mode. 77 normal eyes were measured five times with both devices. The data maps for anterior and posterior corneal elevation and pachymetry were exported and analyzed. Repeatability and average values were calculated for each valid data point on the exported data maps. We also calculated a corrected repeatability of the elevation data maps by removing rotation, tilt, and decentration through realignment of the elevation measurement of each eye prior to analyzing the variations in the measurement usingthe same method as for the repeatability.ResultsPentacam AXL offered the better (corrected) repeatability for anterior corneal elevation measurements. CASIA 2 offered better repeatability for the pachymetry measurements. The tomographers could not be used interchangeably. The central corneal thickness was measured 9 μm ± 3 μm larger when measured with Pentacam AXL compared to CASIA 2.