Vascular calcifications (VCs) are actively regulated biological processes associated with crystallization of hydroxyapatite in the extracellular matrix and in cells of the media (VCm) or intima (VCi) of the arterial wall. Both patterns of VC often coincide and occur in patients with type II diabetes, chronic kidney disease, and other less frequent disorders; VCs are also typical in senile degeneration. In this article, we review the current state of knowledge about the pathology, molecular biology, and nosology of VCm, expand on potential mechanisms responsible for poor prognosis, and expose some of the directions for future research in this area.

Computational fluid dynamics (CFD) and magnetic resonance (MR) gas velocimetry were concurrently performed to study airflow in the same model of human proximal airways. Realistic in vivo-based human airway geometry was segmented from thoracic computed tomography. The three-dimensional numerical description of the airways was used for both generation of a physical airway model using rapid prototyping and mesh generation for CFD simulations. Steady laminar inspiratory experiments (Reynolds number Re = 770) were performed and velocity maps down to the fourth airway generation were extracted from a new velocity mapping technique based on MR velocimetry using hyperpolarized (3)He gas. Full two-dimensional maps of the velocity vector were measured within a few seconds. Numerical simulations were carried out with the experimental flow conditions, and the two sets of data were compared between the two modalities. Flow distributions agreed within 3%. Main and secondary flow velocity intensities were similar, as were velocity convective patterns. This work demonstrates that experimental and numerical gas velocity data can be obtained and compared in the same complex airway geometry. Experiments validated the simulation platform that integrates patient-specific airway reconstruction process from in vivo thoracic scans and velocity field calculation with CFD, hence allowing the results of this numerical tool to be used with confidence in potential clinical applications for lung characterization. Finally, this combined numerical and experimental approach of flow assessment in realistic in vivo-based human airway geometries confirmed the strong dependence of airway flow patterns on local and global geometrical factors, which could contribute to gas mixing.

SUMMARYBoundary value problems for Stokes and Navier-Stokes equations with non-standard boundary conditions are studied. Included is the case where the pressure or its normal derivative is given on some part of the boundary or the pressure is given up to a constant but given velocity flux. First, a variational formulation is introduced which is shown to be equivalent to the Stokes equations with the non-standard boundary conditions under consideration. The existence and uniqueness of the solution of the variational problem are studied. Secondly, most of the results obtained for the Stokes equations are extended to the case of the Navier-Stokes equations. The final section is devoted to numerical experiments, flows in pipes and physiological flows.KEY WORDS velocity-pressure formulation; pressure boundary condition; single and branched pipes; steady and periodic flows NTRODUCTIONThis paper is concerned with the stationary Stokes and Navier-Stokes equations with non-standard boundary conditions. Specifically, the case where the pressure is given on some part of the boundary will be considered.To be precise, the flow of a viscous incompressible fluid which occupies a bounded domain R of R3 is studied. The velocity u and pressure p are assumed to satisfy in this domain R either the stationary Stokes equationsor the stationary Navier-Stokes equations

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