Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations

The modelling of diffusive terms in particle methods is a delicate matter and several models were proposed in the literature to take such terms into account. The diffusion velocity method (DVM), originally designed for the diffusion of passive scalars, turns diffusive terms into convective ones by expressing them as a divergence involving a so-called diffusion velocity. In this paper, DVM is extended to the diffusion of vectorial quantities in the three-dimensional Navier–Stokes equations, in their incompressible, velocity–vorticity formulation. The integration of a large eddy simulation (LES) turbulence model is investigated and a DVM general formulation is proposed. Either with or without LES, a novel expression of the diffusion velocity is derived, which makes it easier to approximate and which highlights the analogy with the original formulation for scalar transport. From this statement, DVM is then analysed in one dimension, both analytically and numerically on test cases to point out its good behaviour.

Anti-Metastatic Properties of a Marine Bacterial Exopolysaccharide-Based Derivative Designed to Mimic Glycosaminoglycans

Osteosarcoma is the most frequent malignant primary bone tumor characterized by a high potency to form lung metastases. In this study, the effect of three oversulfated low molecular weight marine bacterial exopolysaccharides (OS-EPS) with different molecular weights (4, 8 and 15 kDa) were first evaluated in vitro on human and murine osteosarcoma cell lines. Different biological activities were studied: cell proliferation, cell adhesion and migration, matrix metalloproteinase expression. This in vitro study showed that only the OS-EPS 15 kDa derivative could inhibit the invasiveness of osteosarcoma cells with an inhibition rate close to 90%. Moreover, this derivative was potent to inhibit both migration and invasiveness of osteosarcoma cell lines; had no significant effect on their cell cycle; and increased slightly the expression of MMP-9, and more highly the expression of its physiological specific tissue inhibitor TIMP-1. Then, the in vivo experiments showed that the OS-EPS 15 kDa derivative had no effect on the primary osteosarcoma tumor induced by osteosarcoma cell lines but was very efficient to inhibit the establishment of lung metastases in vivo. These results can help to better understand the mechanisms of GAGs and GAG-like derivatives in the biology of the tumor cells and their interactions with the bone environment to develop new therapeutic strategies.