A new unsteady three-dimensional convective-diffusive mathematical model for the transportation of macromolecules and water across the arterial wall was proposed . After the formation of leaky junctions due to the mit...A new unsteady three-dimensional convective-diffusive mathematical model for the transportation of macromolecules and water across the arterial wall was proposed . After the formation of leaky junctions due to the mitosis of endothelial cell of the arterial wall, the macromolecular transport happens surrounding the leaky cells. The arterial wall was divided into four layers: the endothelial layer, the subendothelial intima, the internal elastic lamina and the media for the convenience of research. The time-dependent concentration growth, the effect of the shape of endothelial cell and the effect of physiological parameters were analyzed. The analytical solution of velocity field and pressure field of water flow across the arterial wall were obtained; and concentration distribution of three macromolecules; LDL, HRP and Albumin, were calculated with numerical simulation method. The new theory predicts, the maximum and distribution areas of time dependent concentration with round-shape endothelial cell are both larger than that with ellipse-shape endothelial cell. The model also predicts the concentration growth is much alike that of a two-dimensional model and it shows that the concentration reaches its peak at the leaky junction where atherosclerotic formation frequently occurs and falls down rapidly in a limited area beginning from its earlier-time growth to the state when macromolecular transfer approaches steadily. These predictions of the new model are in agreement with the experimental observation for the growth and concentration distribution of LDL and Albumin.展开更多
The comparative study between unsteady flow models in alluvial streams shows a chaotic residue as for the choices of a forecasting model. The difficulty resides in the choice of the expressions of friction resistance ...The comparative study between unsteady flow models in alluvial streams shows a chaotic residue as for the choices of a forecasting model. The difficulty resides in the choice of the expressions of friction resistance and sediment transport. Three types of mathematical models were selected. Models of type one and two are fairly general, but require a considerable number of boundary conditions, which related to each size range of sediments. It can be a handicap during rivers studies which are not very well followed in terms of experimental measurements. Also, the use of complex models is not always founded. But then, the model of type three requires a limited number of boundary conditions and solves only a system of three equations at each time step. It allows a considerable saving in calculating times.展开更多
文摘A new unsteady three-dimensional convective-diffusive mathematical model for the transportation of macromolecules and water across the arterial wall was proposed . After the formation of leaky junctions due to the mitosis of endothelial cell of the arterial wall, the macromolecular transport happens surrounding the leaky cells. The arterial wall was divided into four layers: the endothelial layer, the subendothelial intima, the internal elastic lamina and the media for the convenience of research. The time-dependent concentration growth, the effect of the shape of endothelial cell and the effect of physiological parameters were analyzed. The analytical solution of velocity field and pressure field of water flow across the arterial wall were obtained; and concentration distribution of three macromolecules; LDL, HRP and Albumin, were calculated with numerical simulation method. The new theory predicts, the maximum and distribution areas of time dependent concentration with round-shape endothelial cell are both larger than that with ellipse-shape endothelial cell. The model also predicts the concentration growth is much alike that of a two-dimensional model and it shows that the concentration reaches its peak at the leaky junction where atherosclerotic formation frequently occurs and falls down rapidly in a limited area beginning from its earlier-time growth to the state when macromolecular transfer approaches steadily. These predictions of the new model are in agreement with the experimental observation for the growth and concentration distribution of LDL and Albumin.
文摘The comparative study between unsteady flow models in alluvial streams shows a chaotic residue as for the choices of a forecasting model. The difficulty resides in the choice of the expressions of friction resistance and sediment transport. Three types of mathematical models were selected. Models of type one and two are fairly general, but require a considerable number of boundary conditions, which related to each size range of sediments. It can be a handicap during rivers studies which are not very well followed in terms of experimental measurements. Also, the use of complex models is not always founded. But then, the model of type three requires a limited number of boundary conditions and solves only a system of three equations at each time step. It allows a considerable saving in calculating times.
