A new unsteady three dimensional model for macromolecular transport and water filtration across the arterial wall

A new unsteady three-dimensional convective-diffusive mathematical model fo r the transportation of macromolecules and water across the arterial wall w as proposed. After the formation of leaky junctions due to the mitosis of e ndothelial cell of the arterial wall, the macromolecular transport happens surrounding the leaky, cells. The arterial wall was divided into four layer s: the endothelial layer, the subendothelial intima, the internal elastic l amina and the media for the convenience of research. The time-dependent con centration growth, the effect of the shape of endothelial cell and the effe ct of physiological parameters were analyzed. The analytical solution of ve locity 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 the ory predicts, the maximum and distribution areas of time dependent concentr ation with round-shape endothelial cell are both larger than that with elli pse-shape endothelial cell. The model also predicts the concentration growt h is much alike that of a two-dimensional model and it shows that the conce ntration reaches its peak at the leaky junction where atherosclerotic forma tion frequently occurs and falls down rapidly in a limited area beginning f rom its earlier time growth to the state when macromolecular transfer appro aches steadily. These predictions of the new model are in agreement with th e experimental observation for the growth and concentration distribution of LDL and Albumin.