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).

Hermitian curve interpolation for CT-data re-sampling

Purpose: Development of an interpolation algorithm for re‐sampling spatially distributed CT‐data with the following features: global and local integral conservation, avoidance of negative interpolation values for positively defined datasets and the ability to control re‐sampling artifacts. Method and Materials: The interpolation can be separated into two steps: first, the discrete CT‐data has to be continuously distributed by an analytic function considering the boundary conditions. Generally, this function is determined by piecewise interpolation. Instead of using linear or high order polynomialinterpolations, which do not fulfill all the above mentioned features, a special form of Hermitian curve interpolation is used to solve the interpolation problem with respect to the required boundary conditions. A single parameter is determined, by which the behavior of the interpolation function is controlled. Second, the interpolated data have to be re‐distributed with respect to the requested grid. Results: The new algorithm was compared with commonly used interpolation functions based on linear and second order polynomial. It is demonstrated that these interpolation functions may over‐ or underestimate the source data by about 10%–20% while the parameter of the new algorithm can be adjusted in order to significantly reduce these interpolation errors. Finally, the performance and accuracy of the algorithm was tested by re‐gridding a series of X‐ray CT‐images. Conclusion: Inaccurate sampling values may occur due to the lack of integral conservation. Re‐sampling algorithms using high order polynomialinterpolation functions may result in significant artifacts of the re‐sampled data. Such artifacts can be avoided by using the new algorithm based on Hermitian curve interpolation

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

An Isopach Map and Discussion of the Marine Jurassic of Western United Sates and Canada

Recent demands for petroleum to carry on the war effort have resulted in widespread prospecting in the northern Great Plains. Nearly all oil wells now drilled are of a depth to penetrate the marine Jurassic formations. It is known that these strata differ in thickness from place to place, but information of distribution, thickness, and lithology has not yet been compiled.

A Discussion of the Geology and an Isopach Map of the Pennsylvanian System in Wyoming and Adjacent Areas

Pennsylvanian strata in Wyoming and adjacent areas have been the subject of much work and discussion. Most of the work has been due to the economic importance of the system as an oil producer in this region. Oil production from strata of Pennsylvanian age is rather recent history; and therefore, much of the available information is local­ized and incomplete.

An Isopach Map and a Discussion of the Permian in Wyoming and Adjacent Areas

The accelerated post-war demand for petroleum products with resultant high prices and dwindling reserves has spurred producers to an extensive search for new fields and for ad­ditional production in known fields. Exploration and discov­ery is dependent on the collection and correlation of vast amounts of data both in the field and that found in liter­ature.

An Isopach Map and a Discussion of the Cambrian Strata in the Central Cordilleran Area

In the past few years intensive studies have been going on concerning Cambrian formations as a locale for orebodies. Many of the dolomites and limestones of southwestern Montana are susceptible to replacement by mineralizing solutions, especially when overlain by a rather impervious layer of shale, as is the Pilgrim limestone of Upper Cambrian time.

An Isopach Map and Discussion of Triassic Strata in Southern Montana and Wyoming

Oil and gas have been found in the Triassic strata of Wyoming. Although the Triassic has not as yet proven to be a large producing horizon it is very probable that ad­ditional oil will be found in Triassic strata in the future, and it is one of the goals at which oil well drillers aim their tools.

Dextran sulfate modulates MAP kinase signaling and reduces endothelial injury in a rat aortic clamping model

OBJECTIVE: Mitogen-activated protein kinases (MAPKs), including JNK, p38, and ERK1/2, noticeably influence ischemia/reperfusion injury (IRI). The complement inhibitor dextran sulfate (DXS) associates with damaged endothelium denudated of its heparan sulfate proteoglycan (HSPG) layer. Other glycosaminoglycan analogs are known to influence MAPK signaling. Hypothetically therefore, targeted intravascular cytoprotection by DXS may function in part through influencing MAPK activation to reduce IRI-induced damage of the vasculature. METHODS: IRI of the infrarenal aorta of male Wistar rats was induced by 90 minutes clamping followed by 120 minutes reperfusion. DXS (5 mg/mL) or physiologic saline (NaCl controls) was infused locally into the ischemic aortic segment immediately prior to reperfusion. Ninety minutes ischemia-only and heparinase infusion (maximal damage) experiments, as well as native rat aorta, served as controls. Aortas were excised following termination of the experiments for further analysis. RESULTS: DXS significantly inhibited IRI-induced JNK and ERK1/2 activation (P = .043; P =.005) without influencing the p38 pathway (P =.110). Reduced aortic injury, with significant inhibition of apoptosis (P = .032 for DXS vs NaCl), correlated with decreased nuclear factor kappaB translocation within the aortic wall. DXS treatment clearly reduced C1q, C4b/c, C3b/c, and C9 complement deposition, whilst preserving endothelial cell integrity and reducing reperfusion-induced HSPG shedding. Protection was associated with binding of fluorescein labeled DXS to ischemically damaged tissue. CONCLUSIONS: Local application of DXS into ischemic vasculature immediately prior to reperfusion reduces complement deposition and preserves endothelial integrity, partially through modulating activation of MAPKs and may offer a new approach to tackle IRI in vascular surgical procedures. CLINICAL RELEVANCE: The purpose of the present study was to determine the role of dextran sulfate (DXS), a glycosaminoglycan analog and complement inhibitor, in modulating intracellular MAPK signaling pathways, reducing complement activation and ultimately attenuating ischemia/reperfusion injury (IRI) in a rat aortic-clamping model, in part a surrogate model to study the microvasculature. The study shows a role for DXS in ameliorating endothelial injury by reducing IRI-mediated damage and intravascular, local inflammation in the affected aortic segment. DXS may be envisaged as an endothelial protectant in vascular injury, such as occurs during vascular surgical procedures.