Coherence of oscillations in the weak-noise limit.

In a noisy environment, oscillations lose their coherence, which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional potential analytically in the weak-noise limit. With this expression, we can prove for this continuum model the analog of an upper bound that has been conjectured for the coherence of oscillations in discrete Markov network models. We show that our approach can also be adapted to motion along a noisy two-dimensional limit cycle. Specifically, we apply our scheme to the noisy Stuart-Landau oscillator and the thermodynamically consistent Brusselator as a simple model for a chemical clock. Our approach thus complements the fairly sophisticated extant general framework based on techniques from Hamilton-Jacobi theory with which we compare our results numerically.

Influence of Synthetic Bone Substitutes on the Anchorage Behavior of Open-Porous Acetabular Cup.

BACKGROUND: The development in implants such as acetabular cups using additive manufacturing techniques is playing an increasingly important role in the healthcare industry. METHOD: This study compared the primary stability of four selectively laser-melted press-fit cups (Ti6Al4V) with open-porous, load-bearing structural elements on the surface. The aim was to assess whether the material of the artificial bone stock affects the primary stability of the acetabular cup. The surface structures consist of repeated open-porous, load-bearing elements orthogonal to the acetabular surface. Experimental pull-out and lever-out tests were performed on exact-fit and press-fit cups to evaluate the primary stability of the cups in different synthetic bone substitutes. The acetabular components were placed in three different commercially available synthetic materials (ROHACELL-IGF 110, SikaBlock M330, Sawbones Solid Rigid). Results & conclusions: Within the scope of the study, it was possible to show the differences in fixation strength between the tested acetabular cups depending on their design, the structural elements used, and the different bone substitute material. In addition, functional correlations could be found which provide a qualitative reference to the material density of the bone stock and the press-fit volume of the acetabular cups.

Effects of Build Orientation on Surface Morphology and Bone Cell Activity of Additively Manufactured Ti6Al4V Specimens.

Additive manufacturing of lightweight or functional structures by selective laser beam (SLM) or electron beam melting (EBM) is widespread, especially in the field of medical applications. SLM and EBM processes were applied to prepare Ti6Al4V test specimens with different surface orientations (0°, 45° and 90°). Roughness measurements of the surfaces were conducted and cell behavior on these surfaces was analyzed. Hence, human osteoblasts were seeded on test specimens to determine cell viability (metabolic activity, live-dead staining) and gene expression of collagen type 1 (Col1A1), matrix metalloprotease (MMP) 1 and its natural inhibitor, TIMP1, after 3 and 7 days. The surface orientation of specimens during the manufacturing process significantly influenced the roughness. Surface roughness showed significant impact on cellular viability, whereas differences between the time points day 3 and 7 were not found. Collagen type 1 mRNA synthesis rates in human osteoblasts were enhanced with increasing roughness. Both manufacturing techniques further influenced the induction of bone formation process in the cell culture. Moreover, the relationship between osteoblastic collagen type 1 mRNA synthesis rates and specimen orientation during the building process could be characterized by functional formulas. These findings are useful in the designing of biomedical applications and medical devices.

A novel approach to determine primary stability of acetabular press-fit cups.

Today hip cups are used in a large variety of design variants and in increasing numbers of units. Their development is steadily progressing. In addition to conventional manufacturing methods for hip cups, additive methods, in particular, play an increasingly important role as development progresses. The present paper describes a modified cup model developed based on a commercially available press-fit cup (Allofit 54/JJ). The press-fit cup was designed in two variants and manufactured using selective laser melting (SLM). Variant 1 (Ti) was modeled on the Allofit cup using an adapted process technology. Variant 2 (Ti-S) was provided with a porous load bearing structure on its surface. In addition to the typical (complete) geometry, both variants were also manufactured and tested in a reduced shape where only the press-fit area was formed. To assess the primary stability of the press-fit cups in the artificial bone cavity, pull-out and lever-out tests were carried out. Exact fit conditions and two-millimeter press-fit were investigated. The closed-cell PU foam used as an artificial bone cavity was mechanically characterized to exclude any influence on the results of the investigation. The pull-out forces of the Ti-variant (complete-526 N, reduced-468 N) and the Ti-S variant (complete-548 N, reduced-526 N) as well as the lever-out moments of the Ti-variant (complete-10 Nm, reduced-9.8 Nm) and the Ti-S variant (complete-9 Nm, reduced-7.9 N) show no significant differences in the results between complete and reduced cups. The results show that the use of reduced cups in a press-fit design is possible within the scope of development work.

Continuous cellularization of calcium phosphate hybrid scaffolds induced by plasma polymer activation.

The generation of hybrid materials based on ß-tricalcium phosphate (TCP) and various biodegradable polymers like poly(l-lactide-co-d,l-lactide) (PLA) represents a common approach to overcoming the disadvantages of pure TCP devices. These disadvantages lie in TCP's mechanical properties, such as brittleness. The positive characteristic of PLA - improvement of compressive strength of calcium phosphate scaffolds - is diametrically opposed to its cell attractiveness. Therefore, the objective of this work was to optimize osteoblast migration and cellularization inside a three-dimensionally (3D) printed, PLA polymer stabilized TCP hybrid scaffold by a plasma polymer process depositing amino groups via allylamine. MG-63 osteoblastic cells inside the 10mm hybrid scaffold were dynamically cultivated for 14days in a 3D model system integrated in a perfusion reactor. The whole TCP/PLA hybrid scaffold was continuously colonized due to plasma polymerized allylamine activation inducing the migration potential of osteoblasts.

Cellular Nutrition in Complex Three-Dimensional Scaffolds: A Comparison between Experiments and Computer Simulations.

Studies on bone cell ingrowth into synthetic, porous three-dimensional (3D) implants showed difficulties arising from impaired cellular proliferation and differentiation in the core region of these scaffolds with increasing scaffold volume in vitro. Therefore, we developed an in vitro perfusion cell culture module, which allows the analysis of cells in the interior of scaffolds under different medium flow rates. For each flow rate the cell viability was measured and compared with results from computer simulations that predict the local oxygen supply and shear stress inside the scaffold based on the finite element method. We found that the local cell viability correlates with the local oxygen concentration and the local shear stress. On the one hand the oxygen supply of the cells in the core becomes optimal with a higher perfusion flow. On the other hand shear stress caused by high flow rates impedes cell vitality, especially at the surface of the scaffold. Our results demonstrate that both parameters must be considered to derive an optimal nutrient flow rate.

Influence of Different Three-Dimensional Open Porous Titanium Scaffold Designs on Human Osteoblasts Behavior in Static and Dynamic Cell Investigations.

In the treatment of osseous defects micro-structured three-dimensional materials for bone replacement serve as leading structure for cell migration, proliferation and bone formation. The scaffold design and culture conditions are crucial for the limited diffusion distance of nutrients and oxygen. In static culture, decreased cell activity and irregular distribution occur within the scaffold. Dynamic conditions entail physical stimulation and constant medium perfusion imitating physiological nutrient supply and metabolite disposal. Therefore, we investigated the influence of different scaffold configurations and cultivation methods on human osteoblasts. Cells were seeded on three-dimensional porous Ti-6Al-4V scaffolds manufactured with selective laser melting (SLM) or electron beam melting (EBM) varying in porosity, pore size and basic structure (cubic, diagonal, pyramidal) and cultured under static and dynamic conditions. Cell viability, migration and matrix production were examined via mitochondrial activity assay, fluorescence staining and ELISA. All scaffolds showed an increasing cell activity and matrix production under static conditions over time. Expectations about the dynamic culture were only partially fulfilled, since it enabled proliferation alike the static one and enhanced cell migration. Overall, the SLM manufactured scaffold with the highest porosity, small pore size and pyramidal basic structure proved to be the most suitable structure for cell proliferation and migration.