Langmuir-Maxwell and Langmuir-Smoluchowski boundary conditions for thermal gas flow simulations in hypersonic aerodynamics

The simulation of nonequilibrium thermal gas flow is important for the aerothermodynamic design of re-entry and other high-altitude vehicles. In computational fluid dynamics, the accuracy of the solution to the Navier–Stokes–Fourier (N–S–F) equations depends on the accuracy of the surface boundary conditions. We propose new boundary conditions (called the Langmuir–Maxwell and the Langmuir–Smoluchowski conditions), for use with the N–S–F equations, which combine the Langmuir surface adsorption isotherm with the Maxwell/Smoluchowski slip/jump conditions in order to capture some of the physical processes involved in gas flow over a surface. These new conditions are validated for flat plate flow, circular cylinder in cross-flow, and the flow over a sharp wedge for Mach numbers ranging from 6 to 24, and for argon and nitrogen as the working gases. Our simulation results show that the new boundary conditions give better predictions for the surface pressures, compared with published experimental and DSMC data

Chondrogenic differentiation and functional maturation of bovine mesenchymal stem cells in long-term agarose culture

SummaryBackgroundThe developmental history of the chondrocyte results in a cell whose biosynthetic activities are optimized to maintain the concentration and organization of a mechanically functional cartilaginous extracellular matrix. While useful for cartilage tissue engineering studies, the limited supply of healthy autologous chondrocytes may preclude their clinical use. Consequently, multipotential mesenchymal stem cells (MSCs) have been proposed as an alternative cell source.ObjectiveWhile MSCs undergo chondrogenesis, few studies have assessed the mechanical integrity of their forming matrix. Furthermore, efficiency of matrix formation must be determined in comparison to healthy chondrocytes from the same donor. Given the scarcity of healthy human tissue, this study determined the feasibility of isolating bovine chondrocytes and MSCs, and examined their long-term maturation in three-dimensional agarose culture.Experimental designBovine MSCs were seeded in agarose and induced to undergo chondrogenesis. Mechanical and biochemical properties of MSC-laden constructs were monitored over a 10-week period and compared to those of chondrocytes derived from the same group of animals maintained similarly.ResultsOur results show that while chondrogenesis does occur in MSC-laden hydrogels, the amount of the forming matrix and measures of its mechanical properties are lower than that produced by chondrocytes under the same conditions. Furthermore, some important properties, particularly glycosaminoglycan content and equilibrium modulus, plateau with time in MSC-laden constructs, suggesting that diminished capacity is not the result of delayed differentiation.ConclusionsThese findings suggest that while MSCs do generate constructs with substantial cartilaginous properties, further optimization must be done to achieve levels similar to those produced by chondrocytes

Aveiro discretization method in mathematics: a new discretization principle

We found a very general discretization method for solving wide classes of mathematical problems by applying the theory of reproducing kernels. An illustration of the generality of the method is here performed by considering several distinct classes of problems to which the method is applied. In fact, one of the advantages of the present method -- in comparison to other well-known and well established methods -- is its global nature and no need of special or very particular data conditions. Numerical experiments have been made, and consequent results are here exhibited. Due to the powerful results which arise from the application of the present method, we consider that this method has everything to become one of the next generation methods of solving general analytical problems by using computers. In particular, we would like to point out that we will be able to solve very global linear partial differential equations satisfying very general boundary conditions or initial values (and in a somehow independent way of the boundary and domain). Furthermore, we will be able to give an ultimate sampling theory and an ultimate realization of the consequent general reproducing kernel Hilbert spaces. The general theory is here presented in a constructive way, and containing some related historical and concrete examples

Genetic Sharing with Cardiovascular Disease Risk Factors and Diabetes Reveals Novel Bone Mineral Density Loci.

Bone Mineral Density (BMD) is a highly heritable trait, but genome-wide association studies have identified few genetic risk factors. Epidemiological studies suggest associations between BMD and several traits and diseases, but the nature of the suggestive comorbidity is still unknown. We used a novel genetic pleiotropy-informed conditional False Discovery Rate (FDR) method to identify single nucleotide polymorphisms (SNPs) associated with BMD by leveraging cardiovascular disease (CVD) associated disorders and metabolic traits. By conditioning on SNPs associated with the CVD-related phenotypes, type 1 diabetes, type 2 diabetes, systolic blood pressure, diastolic blood pressure, high density lipoprotein, low density lipoprotein, triglycerides and waist hip ratio, we identified 65 novel independent BMD loci (26 with femoral neck BMD and 47 with lumbar spine BMD) at conditional FDR < 0.01. Many of the loci were confirmed in genetic expression studies. Genes validated at the mRNA levels were characteristic for the osteoblast/osteocyte lineage, Wnt signaling pathway and bone metabolism. The results provide new insight into genetic mechanisms of variability in BMD, and a better understanding of the genetic underpinnings of clinical comorbidity

Cellular interactions and signaling in cartilage development

AbstractThe long bones of the developing skeleton, such as those of the limb, arise from the process of endochondral ossification, where cartilage serves as the initial anlage element and is later replaced by bone. One of the earliest events of embryonic limb development is cellular condensation, whereby pre-cartilage mesenchymal cells aggregate as a result of specific cell–cell interactions, a requisite step in the chondrogenic pathway. In this review an extensive examination of historical and recent literature pertaining to limb development and mesenchymal condensation has been undertaken. Topics reviewed include limb initiation and axial induction, mesenchymal condensation and its regulation by various adhesion molecules, and regulation of chondrocyte differentiation and limb patterning. The complexity of limb development is exemplified by the involvement of multiple growth factors and morphogens such as Wnts, transforming growth factor-beta and fibroblast growth factors, as well as condensation events mediated by both cell-cell (neural cadherin and neural cell adhesion molecule) and cell–matrix adhesion (fibronectin, proteoglycans and collagens), as well as numerous intracellular signaling pathways transduced by integrins, mitogen activated protein kinases, protein kinase C, lipid metabolites and cyclic adenosine monophosphate. Furthermore, information pertaining to limb patterning and the functional importance of Hox genes and various other signaling molecules such as radical fringe, engrailed, Sox-9, and the Hedgehog family is reviewed. The exquisite three-dimensional structure of the vertebrate limb represents the culmination of these highly orchestrated and strictly regulated events. Understanding the development of cartilage should provide insights into mechanisms underlying the biology of both normal and pathologic (e.g. osteoarthritis) adult cartilage

Long-term in vitro analysis of limb cartilage development: involvement of Wnt signaling

Endochondral skeletal development involves the condensation of mesenchymal cells, their differentiation into chondrocytes, followed by chondrocyte maturation, hypertrophy, and matrix mineralization, and replacement by osteoblasts. The Wnt family of secreted proteins have been shown to play important roles in vertebrate limb formation. To examine the role(s) of Wnt members and their transmembrane-spanning receptor(s), Frizzled (fz), we retrovirally misexpressed Wnt-5a, Wnt-7a, chicken frizzled-1 (Chfz-1), and frizzled-7 (Chfz-7) in long-term (21 day) high density, micromass cultures of stage 23/24 chick embryonic limb mesenchyme. This culture system recapitulates in vitro the entire differentiation (days 1-10), growth (days 5-12), and maturation and hypertrophy (from day 12 on) program of cartilage development. Wnt-7a misexpression severely inhibited chondrogenesis from day 7 onward. Wnt-5a misexpression resulted in a poor hypertrophic phenotype by day 14. Chfz-7 misexpression caused a slight delay of chondrocyte maturation based on histology, whereas Chfz-1 misexpression did not affect the chondrogenic phenotype. Misexpression of all Wnt members decreased collagen type X expression and alkaline phosphatase activity at day 21. Our findings implicate functional role(s) for Wnt signaling throughout embryonic cartilage development, and show the utility of the long-term in vitro limb mesenchyme culture system for such studies