An integral conservative gridding--algorithm using Hermitian curve interpolation

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Virtual Cilicia Project. How to use Google Earth as a visualization environment in an archaeological context

Over the past few years, archaeology has experienced a rapid development in geophysical prospection and remote sensing techniques. At the same time, the focus of archaeological research has shifted to landscape evelopment and human interaction. To impart the results, new methods and techniques are necessary. Virtual globes such as Google Earth offer fascinating methods of giving interested amateurs the possibility to interactively explore ancient cities and landscapes. Thanks to the increasing usage of GIS in cultural heritage, the implementation of interactive three dimensional learning opportunities becomes less and less tedious, but the non-linear narrative story telling medium demands for a special adaption of the content. This paper summarizes the experience gained during the realization of the “Virtual Cilicia Project” and outlines the future potential of virtual globes in the field of cultural heritage.

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

Minimized extracorporeal circulation does not impair cognitive brain function after coronary artery bypass grafting

OBJECTIVES Objective evaluation of the impact of minimized extracorporeal circulation (MECC) on perioperative cognitive brain function in coronary artery bypass grafting (CABG) by electroencephalogram P300 wave event-related potentials and number connection test (NCT) as metrics of cognitive function. METHODS Cognitive brain function was assessed in 31 patients in 2013 with a mean age of 65 years [standard deviation (SD) 10] undergoing CABG by the use of MECC with P300 auditory evoked potentials (peak latencies in milliseconds) directly prior to intervention, 7 days after and 3 months later. Number connection test, serving as method of control, was performed simultaneously in all patients. RESULTS Seven days following CABG, cognitive P300 evoked potentials were comparable with preoperative baseline values [vertex (Cz) 376 (SD 11) ms vs 378 (18) ms, P = 0.39; frontal (Fz) 377 (11) vs 379 (21) ms, P = 0.53]. Cognitive brain function at 3 months was compared with baseline values [(Cz) 376 (11) ms vs 371 (14 ms) P = 0.09; (Fz) 377 (11) ms vs 371 (15) ms, P = 0.04]. Between the first postoperative measurement and 3 months later, significant improvement was observed [(Cz) 378 (18) ms vs 371 (14) ms, P = 0.03; (Fz) 379 (21) vs 371 (15) ms, P = 0.02]. Similar clearly corresponding patterns could be obtained via the number connection test. Results could be confirmed in repeated measures analysis of variance for Cz (P = 0.05) and (Fz) results (P = 0.04). CONCLUSIONS MECC does not adversely affect cognitive brain function after CABG. Additionally, these patients experience a substantial significant cognitive improvement after 3 months, evidentiary proving that the concept of MECC ensures safety and outcome in terms of brain function.

Minimized Extracorporeal Circulation does not impair cognitive brain function after coronary artery bypass grafting

Gebiet: Chirurgie Abstract: Minimized Extracorporeal Circulation does not impair cognitive brain function after coronary artery bypass grafting – – Objectives – Objective evaluation of the impact of minimized extracorporeal circulation (MECC) on perioperative cognitive brain function in coronary bypass grafting (CABG) by Electroencephalogram (EEG) P 300 wave event related potentials (ERP) and number connection test ( NCT) as metrics of cognitive function. – – Methods – Cognitive brain function was assessed in 31 patients with a mean age of 65y (Standard Deviation/SD 10) undergoing coronary artery bypass grafting (CABG) by the use of MECC with P300 auditory evoked potentials (peak latencies in milliseconds [ms]) directly prior to intervention, 7 days after and 3 month later. Number connection test (NCT), serving as method of control, was performed simultaneously in all patients. – – Results – Seven days following CABG, cognitive P300 evoked potentials were comparable to preoperative baseline values (vertex [Cz] 376 (SD 11) ms vs. 378 (18) ms, p=0.39, frontal [Fz] 377 (11) vs. 379 (21) ms, p=0.53). Cognitive brain function showed at 3 months compared to baseline values ([Cz] 376 (11) ms vs. 371 (14 ms) p=0.09, [Fz] 377 (11) ms vs. 371 (15) ms, p=0.04. Between the first postoperative measurement and 3 months later, significant improvement was observed ([Cz] 378 (18) ms vs. 371 (14) ms, p=0.03, [Fz] 379 (21) vs. 371 (15) ms, p=0.02). Similar clearly corresponding patterns could be obtained via number connection test. Results could be confirmed in repeated measures analysis of variance for Cz (p = 0.05) and (Fz) results (p = 0.04). – – Conclusions