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.

Scanning electron microscope study of the developing microvasculature in the postnatal rat lung.

During postnatal growth the parenchymal septa of rat lung undergo an impressive restructuring. While immature septa are thick and contain two capillary layers, mature septa are slender and contain a single microvascular network. Using the Mercox casting technique and scanning electron microscopy, we investigated the mode and the timing of the transformation of the pulmonary capillary bed. During the third postnatal week the parenchymal septa rapidly mature to match adult morphology. Even in adult lungs, however, remnants of the immature status are present: A capillary bilayer is regularly found at the base and the tip of the septa. Our observations support the concept that reduction of intervening tissue, partial fusion of the two capillary networks, and preferential growth lead to the mature vascular arrangement. The fact that true mature interalveolar septa show a denser capillary network than alveolar walls abutting onto pleura, bronchi, or larger vessels is consonant with the fusion theory. Towards the nonparenchyma, the capillary network surrounding every airspace had no counterpart to fuse with. From quantitative data it can be calculated that owing to lung growth, mesh size should increase more than four times between birth and adult age. The adult lung network, however, is denser than the one in young animals. This means that new meshes must be added during growth. We propose that small holes observed in sheet-like regions of the microvasculature enlarge to form new capillary meshes. With this mechanism of in-itself or intussusceptional growth, sprouting of individual capillary segments to increase network size is no longer needed.

Factors controlling decomposition rates of fine root litter in temperate forests and grasslands

Background and aims Fine root decomposition contributes significantly to element cycling in terrestrial ecosystems. However, studies on root decomposition rates and on the factors that potentially influence them are fewer than those on leaf litter decomposition. To study the effects of region and land use intensity on fine root decomposition, we established a large scale study in three German regions with different climate regimes and soil properties. Methods In 150 forest and 150 grassland sites we deployed litterbags (100 μm mesh size) with standardized litter consisting of fine roots from European beech in forests and from a lowland mesophilous hay meadow in grasslands. In the central study region, we compared decomposition rates of this standardized litter with root litter collected on-site to separate the effect of litter quality from environmental factors. Results Standardized herbaceous roots in grassland soils decomposed on average significantly faster (24 ± 6 % mass loss after 12 months, mean ± SD) than beech roots in forest soils (12 ± 4 %; p < 0.001). Fine root decomposition varied among the three study regions. Land use intensity, in particular N addition, decreased fine root decomposition in grasslands. The initial lignin:N ratio explained 15 % of the variance in grasslands and 11 % in forests. Soil moisture, soil temperature, and C:N ratios of soils together explained 34 % of the variance of the fine root mass loss in grasslands, and 24 % in forests. Conclusions Grasslands, which have higher fine root biomass and root turnover compared to forests, also have higher rates of root decomposition. Our results further show that at the regional scale fine root decomposition is influenced by environmental variables such as soil moisture, soil temperature and soil nutrient content. Additional variation is explained by root litter quality.

Mesh-based vs. Image-based Statistical Appearance Model of the Human Femur: a Preliminary Comparison Study for the Creation of Finite Element Meshes

Statistical models have been recently introduced in computational orthopaedics to investigate the bone mechanical properties across several populations. A fundamental aspect for the construction of statistical models concerns the establishment of accurate anatomical correspondences among the objects of the training dataset. Various methods have been proposed to solve this problem such as mesh morphing or image registration algorithms. The objective of this study is to compare a mesh-based and an image-based statistical appearance model approaches for the creation of nite element(FE) meshes. A computer tomography (CT) dataset of 157 human left femurs was used for the comparison. For each approach, 30 finite element meshes were generated with the models. The quality of the obtained FE meshes was evaluated in terms of volume, size and shape of the elements. Results showed that the quality of the meshes obtained with the image-based approach was higher than the quality of the mesh-based approach. Future studies are required to evaluate the impact of this finding on the final mechanical simulations.

Primary reconstruction of open depressed skull fractures with titanium mesh

Open skull fractures have been traditionally managed in 2 stages: urgent craniotomy and elevation of the fracture with removal of contaminated bone, debridement, and delayed cranioplasty. Primary, single-stage repair of these injures has been said to entail risks such as infections. Recent experience, however, disproved these concerns.We used a primary single-stage reconstruction for patients presenting with open depressed skull fractures. All patients received antibiotic prophylaxis. The patients underwent elevation of the compound fracture and craniotomy if necessary. Debridement was performed, followed by skull reconstruction using a 0.6-mm titanium mesh.We present 5 consecutive male patients (age, 32.2 +/- 15.6 years) who underwent primary reconstruction of open depressed skull fractures. Clinical and radiologic follow-up was performed 2 months after surgery. The duration of the surgery was 2 +/- 1.6 hours. The size of the implanted mesh was 13 +/- 13.1 cm. No infection was detected in our series, with a follow-up period of 22 +/- 6.5 months (range, 16-29 months). The cosmetic result was defined in 4 patients as "excellent" and in 1 patient as "good."Primary reconstruction of open skull fractures with titanium mesh is feasible, safe, and cosmetically preferable than the conventional staged approach. The introduction into clinical practice can be warranted.