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

Computed tomography (CT) virtual autopsy and classical autopsy discrepancies: radiologist's error or a demonstration of post-mortem multi-detector computed tomography (MDCT) limitation?

Modern imaging technologies, such as computed tomography (CT) techniques, represent a great challenge in forensic pathology. The field of forensics has experienced a rapid increase in the use of these new techniques to support investigations on critical cases, as indicated by the implementation of CT scanning by different forensic institutions worldwide. Advances in CT imaging techniques over the past few decades have finally led some authors to propose that virtual autopsy, a radiological method applied to post-mortem analysis, is a reliable alternative to traditional autopsy, at least in certain cases. The authors investigate the occurrence and the causes of errors and mistakes in diagnostic imaging applied to virtual autopsy. A case of suicide by a gunshot wound was submitted to full-body CT scanning before autopsy. We compared the first examination of sectional images with the autopsy findings and found a preliminary misdiagnosis in detecting a peritoneal lesion by gunshot wound that was due to radiologist's error. Then we discuss a new emerging issue related to the risk of diagnostic failure in virtual autopsy due to radiologist's error that is similar to what occurs in clinical radiology practice.

Au@Hg nanoalloy formation through direct amalgamation: Structural, spectroscopic, and computational evidence for slow nanoscale diffusion

Dynamic core-shell nanoparticles have received increasing attention in recent years. This paper presents a detailed study of Au-Hg nanoalloys, whose composing elements show a large difference in cohesive energy. A simple method to prepare Au@Hg particles with precise control over the composition up to 15 atom% mercury is introduced, based on reacting a citrate stabilized gold sol with elemental mercury. Transmission electron microscopy shows an increase of particle size with increasing mercury content and, together with X-ray powder diffraction, points towards the presence of a core-shell structure with a gold core surrounded by an Au-Hg solid solution layer. The amalgamation process is described by pseudo-zero-order reaction kinetics, which indicates slow dissolution of mercury in water as the rate determining step, followed by fast scavenging by nanoparticles in solution. Once adsorbed at the surface, slow diffusion of Hg into the particle lattice occurs, to a depth of ca. 3 nm, independent of Hg concentration. Discrete dipole approximation calculations relate the UV-vis spectra to the microscopic details of the nanoalloy structure. Segregation energies and metal distribution in the nanoalloys were modeled by density functional theory calculations. The results indicate slow metal interdiffusion at the nanoscale, which has important implications for synthetic methods aimed at core-shell particles.

Three-dimensional surface reconstruction within noncontact diffuse optical tomography using structured light

A main field in biomedical optics research is diffuse optical tomography, where intensity variations of the transmitted light traversing through tissue are detected. Mathematical models and reconstruction algorithms based on finite element methods and Monte Carlo simulations describe the light transport inside the tissue and determine differences in absorption and scattering coefficients. Precise knowledge of the sample's surface shape and orientation is required to provide boundary conditions for these techniques. We propose an integrated method based on structured light three-dimensional (3-D) scanning that provides detailed surface information of the object, which is usable for volume mesh creation and allows the normalization of the intensity dispersion between surface and camera. The experimental setup is complemented by polarization difference imaging to avoid overlaying byproducts caused by inter-reflections and multiple scattering in semitransparent tissue.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

On the comparison of VR-responses, as performance measures in prospective memory, with auditory P300 responses in MCI detection

Patients with amnestic mild cognitive impairment are at high risk for developing Alzheimer's disease. Besides episodic memory dysfunction they show deficits in accessing contextual knowledge that further specifies a general spatial navigation task or an executive function (EF) virtual action planning. There has been only one previous work with virtual reality and the use of a virtual action planning supermarket for the diagnosis of mild cognitive impairment. The authors of that study examined the feasibility and the validity of the virtual action planning supermarket (VAP-S) for the diagnosis of patients with mild cognitive impairment (MCI) and found that the VAP-S is a viable tool to assess EF deficits. In our study we employed the in-house platform of virtual action planning museum (VAP-M) and a sample of 25 MCI and 25 controls, in order to investigate deficits in spatial navigation, prospective memory and executive function. In addition, we used the morphology of late components in event-related potential (ERP) responses, as a marker for cognitive dysfunction. The related measurements were fed to a common classification scheme facilitating the direct comparison of both approaches. Our results indicate that both the VAP-M and ERP averages were able to differentiate between healthy elders and patients with amnestic mild cognitive impairment and agree with the findings of the virtual action planning supermarket (VAP-S). The sensitivity (specificity) was 100% (98%) for the VAP-M data and 87%(90%) for the ERP responses. Considering that ERPs have proven to advance the early detection and diagnosis of "presymptomatic AD", the suggested VAP-M platform appears as an appealing alternative.

On the comparison of a novel serious game and electroencephalography biomarkers for early dementia screening

Patients with amnestic mild cognitive impairment are at high risk for developing Alzheimer's disease. Besides episodic memory dysfunction they show deficits in accessing contextual knowledge that further specifies a general spatial navigation task or an executive function (EF) virtual action planning. Virtual reality (VR) environments have already been successfully used in cognitive rehabilitation and show increased potential for use in neuropsychological evaluation allowing for greater ecological validity while being more engaging and user friendly. In our study we employed the in-house platform of virtual action planning museum (VAP-M) and a sample of 25 MCI and 25 controls, in order to investigate deficits in spatial navigation, prospective memory, and executive function. In addition, we used the morphology of late components in event-related potential (ERP) responses, as a marker for cognitive dysfunction. The related measurements were fed to a common classification scheme facilitating the direct comparison of both approaches. Our results indicate that both the VAP-M and ERP averages were able to differentiate between healthy elders and patients with amnestic mild cognitive impairment and agree with the findings of the virtual action planning supermarket (VAP-S). The sensitivity (specificity) was 100% (98%) for the VAP-M data and 87% (90%) for the ERP responses. Considering that ERPs have proven to advance the early detection and diagnosis of "presymptomatic AD," the suggested VAP-M platform appears as an appealing alternative.