Adaptive Enrichment Research Articles

Bilateral Hypochondrial Pain

An 85-year-old hypertensive woman was started on amoxicillin for a dental abscess. Two days later she developed nausea and vomiting with dull pain over the left upper abdomen, later involving the right side as well. On examination she was febrile with severe tenderness over both hypochondria with no palpable hepatosplenomegaly.Her laboratory investigations showed a leukocyte count of 15.5 × 109/L/mm3 (normal range, 3.5–10.5 × 109/L). Liver function tests showed normal bilirubin levels with aspartate aminotransferase levels of 2001 U/L (normal range, 8–43), alanine aminotransferase levels of 2333 U/L (normal range, 9–29), and alkaline phosphatase levels of 157 U/L (normal range, 55–142). Hepatitis serologies were negative. An axial image from a computerized tomography scan (Figure A) in the portal venous phase (long arrow) shows thrombus in the splenic vein, the 2 short arrows show thrombus in the segmental branches of the right portal vein. There is extensive splenic infarction. In the coronal image (Figure B), a portal venous phase scan shows extensive splenic vein thrombus (long arrows), thrombus in the segmental branch of the right portal vein (short arrow), extensive splenic infarct, and a large area of low attenuation in the superior portion of the right hepatic lobe that could represent perfusion abnormality, fatty infiltration, or evolving infarct. An axial view of a computerized tomography scan of the liver 5 months later showed a small wedge-shaped area of low attenuation in the right hepatic lobe with volume loss and overlying capsular retraction, consistent with infarct (Figure C).A thrombophilia screen was negative. A work-up for intra-abdominal malignancy also was negative. Common causes for hepatic infarction are post–liver transplant, hepatic artery embolization, vasculitis, and thrombophilia. She developed mesenteric ischemia 14 months after the initial episode, which required emergency laparotomy. Her international normalized ratio was subtherapeutic at this time. An 85-year-old hypertensive woman was started on amoxicillin for a dental abscess. Two days later she developed nausea and vomiting with dull pain over the left upper abdomen, later involving the right side as well. On examination she was febrile with severe tenderness over both hypochondria with no palpable hepatosplenomegaly. Her laboratory investigations showed a leukocyte count of 15.5 × 109/L/mm3 (normal range, 3.5–10.5 × 109/L). Liver function tests showed normal bilirubin levels with aspartate aminotransferase levels of 2001 U/L (normal range, 8–43), alanine aminotransferase levels of 2333 U/L (normal range, 9–29), and alkaline phosphatase levels of 157 U/L (normal range, 55–142). Hepatitis serologies were negative. An axial image from a computerized tomography scan (Figure A) in the portal venous phase (long arrow) shows thrombus in the splenic vein, the 2 short arrows show thrombus in the segmental branches of the right portal vein. There is extensive splenic infarction. In the coronal image (Figure B), a portal venous phase scan shows extensive splenic vein thrombus (long arrows), thrombus in the segmental branch of the right portal vein (short arrow), extensive splenic infarct, and a large area of low attenuation in the superior portion of the right hepatic lobe that could represent perfusion abnormality, fatty infiltration, or evolving infarct. An axial view of a computerized tomography scan of the liver 5 months later showed a small wedge-shaped area of low attenuation in the right hepatic lobe with volume loss and overlying capsular retraction, consistent with infarct (Figure C). A thrombophilia screen was negative. A work-up for intra-abdominal malignancy also was negative. Common causes for hepatic infarction are post–liver transplant, hepatic artery embolization, vasculitis, and thrombophilia. She developed mesenteric ischemia 14 months after the initial episode, which required emergency laparotomy. Her international normalized ratio was subtherapeutic at this time. Improving Clinical Trial Efficiency in GastroenterologyGastroenterologyVol. 157Issue 3PreviewWe read with interest the recent article by Harris and Howden, “Innovative Trial Designs in GI Drug Development: Why Trials Succeed and Fail,”1 Given the rich pipeline of next-generation therapies across multiple disciplines of gastroenterology, we are pleased to see this dialogue on critical, although often neglected topics, in clinical trial design. Many agents that seem to be promising in preclinical studies fail to show efficacy in human trials, and Harris and Howden discuss several concepts that may improve trial success rates, including integrated phase and adaptive enrichment designs, early assessment of pharmacodynamic effects with biomarker and target engagement, objective disease evaluation by endoscopy and histology, and prospective, randomized, open-label blinded end point studies. Full-Text PDF

Adaptive enrichment meshfree simulation and experiment on buckling and post-buckling analysis in sheet metal forming

Sheet buckling, a form of instability, is one of the major considerations in the design of part shape, die geometry and processing parameters of sheet metal forming. In this study, an adaptive enrichment meshfree method is developed to capture wrinkling and post-buckling behavior in sheet metal forming. A three-dimensional meshfree continuum approach is applied to the large deformation of plate/shell structures. A stress-based wrinkling predictor is used to predict the onset of buckling within effective compressive regions. Enrichment particles with a proper enrichment function are inserted/deleted in those regions to capture the buckling mode and therefore post-buckling behavior. For verification of the simulation results, a high-resolution wedge strip test is designed to study the onset and post-buckling behavior of a sheet under different boundary conditions.

Main nutrient compounds in food bodies of Mexican Acacia ant-plants

Myrmecophytic plants use obligate ant mutualists as a constitutive indirect defence mechanism. These plants often produce cellular food bodies (FBs) to nourish their resident ants. Lipids, proteins, and even highly specialised compounds such as glycogen have been reported from FBs, but detailed chemical analyses of FB composition have so far been presented only for Southeast Asian Macaranga and Central American Piper myrmecophytes. Here we report the chemical composition of FBs of five myrmecophytic Acacia (Fabaceae) species from Mexico using HPLC (carbohydrates and proteins) and GC-MS (lipids). Feeding experiments revealed no hints on any use of external food sources by the inhabiting Pseudomyrmex ants. These ants obviously rely completely on FBs and extrafloral nectar provided by their hosts. The total content of nutrients in Acacia FBs was 15-25% of FB dry mass, being much lower than in Macaranga or Piper FBs. Proteins were dominating (8-14 % dm) in Acacia FBs and thus were present in higher amounts than in Macaranga FBs, yet in lower amounts than in Piper. Lipids contributed 1-9 % of dry mass, showing a lower proportion than in FBs of Macaranga or Piper. Carbohydrates made up 3-11 % dm, reaching in most Acacia species the same range as observed in Macaranga and in Piper FBs. Water content was 18-24 % of FB fresh mass, and structural tissue obviously made up a much higher proportion in Acacia FBs than in Macaranga or Piper FBs. Both characters might represent an adaptation to producing FBs unprotected at the leaf tips under dry conditions. Acacia FBs contain all amino acids and all fatty acids that are considered essential for insects, and their contents of lipids and proteins are higher than in the leaves from which they are ontogenetically derived. This indicates a putatively adaptive enrichment of nutritionally valuable compounds in structures functioning as ant-food.

Process zone resolution by extended finite elements

A new numerical technique for the computational resolution of highly localized strains in narrow damage process zones of quasibrittle materials is proposed. Objective description of localization due to softening is provided by a nonlocal damage model. The extended finite element method is exploited for an adaptive enrichment of the standard displacement approximation by regularized Heaviside functions that are close to the exact localization mode. An accurate closed-form expression for the width of the enriched zone is derived by localization analysis under uniaxial stress. Numerical examples show that satisfactory results can be obtained even on coarse basic meshes with only a few added degrees of freedom.

Problems and Techniques

This installment of Problems and Techniques features articles on extremal properties of the Schur complement of a matrix and the computation of superconvergent functionals from approximate solutions of partial differential equations. In the first article, Chi-Kwong Li and Roy Mathias describe extremal properties of the generalized Schur complement of a positive semidefinite matrix. The generalization refers to the use of a pseudoinverse when the matrix is not invertible. Using the extremal properties, the authors derive several operator and eigenvalue inequalities involving generalized Schur complements. While some of these results were known, the extremal principles simplify their analysis and also provide a technology for generating several new inequalities. The authors also provide an interesting historical perspective of the development and use of Schur complements. The use of the adjoint solutions has been suggested by several investigators as a means of constructing a posteriori error bounds for finite element solutions and their integral functionals. Niles Pierce and Michael Giles use this approach more generally, without reliance on the finite element method, to correct the leading order error term in integral functional estimates. This is a very powerful technique that can be used to construct superconvergent approximations of the integral functionals or to control an adaptive enrichment process. The authors indicate several problems where accuracy of an integral functional is of primary concern. In optimal design, for example, the adjoint solution is often needed as part of the optimization. The importance of this work was recognized when Niles Pierce received the Fox Prize in Numerical Analysis last June. I hope that you enjoy these articles as much as I did. Please join me in thanking our authors for their very interesting contributions.

Parallel structures and dynamic load balancing for adaptive finite element computation

An adaptive technique for a partial differential system automatically adjusts a computational mesh or varies the order of a numerical procedure to obtain a solution satisfying prescribed accuracy criteria in an optimal fashion. We describe data structures for distributed storage of finite element mesh data as well as software for mesh adaptation, load balancing, and solving compressible flow problems. Processor load imbalances are introduced at adaptive enrichment steps during the course of a parallel computation. To correct this, we have developed three dynamic load balancing procedures based, respectively, on load imbalance trees, moment of inertia, and octree traversal. Computational results on an IBM SP2 computer are presented for steady and transient solutions of the three-dimensional Euler equations of compressible flow.

Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws

Conservation laws are solved by a local Galerkin finite element procedure with adaptive space-time mesh refinement and explicit time integration. The Courant stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to methods having a single global time step. Processor load imbalances, introduced at adaptive enrichment steps, are corrected by using traversals of an octree representing a spatial decomposition of the domain. To accommodate the variable time steps, octree partitioning is extended to use weights derived from element size. Partition boundary smoothing reduces the communications volume of partitioning procedures for a modest cost. Computational results comparing parallel octree and inertial partitioning procedures are presented for the three-dimensional Euler equations of compressible flow solved on an IBM SP2 computer.

Load balancing for the parallel adaptive solution of partial differential equations

An adaptive technique for a partial differential system automatically adjusts a computational mesh or varies the order of a numerical procedure with a goal of obtaining a solution satisfying prescribed accuracy criteria in an optimal fashion. Processor load imbalances will, therefore, be introduced at adaptive enrichment steps during the course of a parallel computation. We develop and describe three procedures for retaining and restoring load balance that have low unit cost and are appropriate for use in an adaptive solution environment. Tiling balances load by using local optimality criteria within overlapping processor neighborhoods. Elemental data are migrated between processors within the same neighborhoods to restore balance. Tiling is restricted to uniform two-dimensional meshes and provides limited control of communications volume by priority-based element selection criteria. These shortcomings can potentially be overcome by creating a dynamic partition graph connecting processors and their neighboring regions. After coloring the edges of the graph, elemental data are iteratively transferred between processors by pairwise exchange to permit a more global migration. Octree decomposition of a spatial domain is a successful three-dimensional mesh generation strategy. The octree structure facilities a rapid load balancing procedure by performing tree traversals that (i) appraise subtree costs and (ii) partition spatial regions accordingly. Computational results are reported for two- and three-dimensional problems using nCUBE/2 hypercube, MasPar MP-2, and Thinking Machines CM-5 computers.

High-order adaptive methods for parabolic systems

We consider the adaptive solution of parabolic partial differential systems in one and two space dimensions by finite element procedures that automatically refine and coarsen computational meshes, vary the degree of the piecewise polynomial basis and, in one dimension, move the computational mesh. Two-dimensional meshes of triangular, quadrilateral, or a mixture of triangular and quadrilateral elements are generated using a finite quadtree procedure that is also used for data management. A posteriori estimates, used to control adaptive enrichment, are generated from the hierarchical polynomial basis. Temporal integration, within a method-of-lines framework, uses either backward difference methods or a variant of the singly implicit Runge-Kutta (SIRK) methods. A high-level user interface facilitates use of the adaptive software.