NUMERICAL-SIMULATION OF MASS-TRANSFER IN POROUS-MEDIA OF BLOOD-VESSELWALLS

The tunica media of a blood vessel wall is modeled as a heterogeneous medium composed of a periodic array of cylindrical smooth muscle cells and a continuous interstitial fluid phase of proteoglycan and collage n fibers. By applying Brinkman's model to describe the behavior of the interstitial flow we obtain an analytical solution for the transmural flow field through the periodic array of smooth muscle cells in the f orm of a power series, making it possible to compute the convection of solutes in the interstitial phase. With reaction of solutes at the su rface of smooth muscle cell membranes being treated as boundary condit ions and the diffusion of species being limited to the interstitial fl uid phase only, mass transfer in the media of blood vessel walls is si mulated numerically using Gray supercomputers. It is found that the Sh erwood number (the dimensionless mass-transfer coefficient) is not onl y constant for all interior smooth muscle cells but also minimally sen sitive to changes of parameters controlling the relative rates of diff usion and convection in the interstitial fluid phase and the reaction on the smooth muscle cell surface. In addition, the Sherwood number is not very sensitive to changes in the volume fraction of smooth muscle cells. A homogeneous, one-dimensional model (effective-medium model) is also developed to predict the built, concentration profile in the m edia, based on the equivalent properties of the effective medium deriv ed from the heterogeneous medium. A comparison of results from the one -dimensional model and two-dimensional simulation is quite satisfactor y for all practical ranges of parameters. It is also determined that, for a small molecule such as ATP, the mass transfer to the surface of smooth muscle cells is ''reaction limited'' as assumed previously in t he literature, whereas, for a large molecule such as low-density lipop rotein, the mass transfer might not be reaction limited.