Modeling interstitial flow in an artery wall allows estimation of wall shear stress on smooth muscle cells

The arterial media is modeled as a periodic array of cylindrical smooth muscle cells residing in a matrix comprised of proteoglycan and collagen fibers. Using Brinkman's model to describe transmural flow through such a fibrous media, we calculate the effective hydraulic permeability of the media and the wall shear stress on smooth muscle cells. Two interesting results are obtained: first, the wall shear stress on smooth muscle cells is on the order of 1 dyne/cm2, which is the range known to affect endothelial cells in vitro; second, the flow resistance due to smooth muscle cells is not negligible compared to the resistance due to the fiber matrix.