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.

Repair of superficial osteochondral defects with an autologous scaffold-free cartilage construct in a caprine model: implantation method and short-term results

OBJECTIVE: To compare four different implantation modalities for the repair of superficial osteochondral defects in a caprine model using autologous, scaffold-free, engineered cartilage constructs, and to describe the short-term outcome of successfully implanted constructs. METHODS: Scaffold-free, autologous cartilage constructs were implanted within superficial osteochondral defects created in the stifle joints of nine adult goats. The implants were distributed between four 6-mm-diameter superficial osteochondral defects created in the trochlea femoris and secured in the defect using a covering periosteal flap (PF) alone or in combination with adhesives (platelet-rich plasma (PRP) or fibrin), or using PRP alone. Eight weeks after implantation surgery, the animals were killed. The defect sites were excised and subjected to macroscopic and histopathologic analyses. RESULTS: At 8 weeks, implants that had been held in place exclusively with a PF were well integrated both laterally and basally. The repair tissue manifested an architecture similar to that of hyaline articular cartilage. However, most of the implants that had been glued in place in the absence of a PF were lost during the initial 4-week phase of restricted joint movement. The use of human fibrin glue (FG) led to massive cell infiltration of the subchondral bone. CONCLUSIONS: The implantation of autologous, scaffold-free, engineered cartilage constructs might best be performed beneath a PF without the use of tissue adhesives. Successfully implanted constructs showed hyaline-like characteristics in adult goats within 2 months. Long-term animal studies and pilot clinical trials are now needed to evaluate the efficacy of this treatment strategy.

An experimentally validated finite element method for augmented vertebral bodies

Background Finite element models of augmented vertebral bodies require a realistic modelling of the cement infiltrated region. Most methods published so far used idealized cement shapes or oversimplified material models for the augmented region. In this study, an improved, anatomy-specific, homogenized finite element method was developed and validated to predict the apparent as well as the local mechanical behavior of augmented vertebral bodies. Methods Forty-nine human vertebral body sections were prepared by removing the cortical endplates and scanned with high-resolution peripheral quantitative CT before and after injection of a standard and a low-modulus bone cement. Forty-one specimens were tested in compression to measure stiffness, strength and contact pressure distributions between specimens and loading-plates. From the remaining eight, fourteen cylindrical specimens were extracted from the augmented region and tested in compression to obtain material properties. Anatomy-specific finite element models were generated from the CT data. The models featured element-specific, density-fabric-based material properties, damage accumulation, real cement distributions and experimentally determined material properties for the augmented region. Apparent stiffness and strength as well as contact pressure distributions at the loading plates were compared between simulations and experiments. Findings The finite element models were able to predict apparent stiffness (R2 > 0.86) and apparent strength (R2 > 0.92) very well. Also, the numerically obtained pressure distributions were in reasonable quantitative (R2 > 0.48) and qualitative agreement with the experiments. Interpretation The proposed finite element models have proven to be an accurate tool for studying the apparent as well as the local mechanical behavior of augmented vertebral bodies.

Adsorption interaction of carrier-free thallium species with gold and quartz surfaces

The adsorption interactions of thallium and its compounds with gold and quartz surfaces were investigated. Carrier-free amounts of thallium were produced in nuclear fusion reactions of alpha particles with thick gold targets. The method chosen for the studies was gas thermochromatography and varying the redox potential of the carrier gases. It was observed that thallium is extremely sensitive to trace amounts of oxygen and water, and can even be oxidized by the hydroxyl groups located on the quartz surface. The experiments on a quartz surface with O2, He, H2 gas in addition with water revealed the formation and deposition of only one thallium species – TlOH. The adsorption enthalpy was determined to be Δ HSiO2ads(TlOH) = −134 ± 5 kJ mol−1. A series of experiments using gold as stationary surface and different carrier gases resulted in the detection of two thallium species – metallic Tl (H2 as carrier gas) and TlOH (O2, O2+H2O and H2+H2O as pure carrier gas or carrier gas mixture) with Δ HAuads(Tl) = −270 ± 10 kJ mol− and Δ HAuads(TlOH) = −146 ± 3 kJ mol−1. These data demonstrate a weak interaction of TlOH with both quartz and gold surfaces. The data represent important information for the design of future experiments with the heavier homologue of Tl in group 13 of the periodic table – element 113 (E113).