Flow in porous media as a model for transport of interstitial fluid in the brain.

There is emerging evidence that the vasculatue of the brain dictates the drainage of beta-amyloid proteins and interstitial fluid. One of the pathways to clear these proteins out of the brain is along arterial walls. This flow occurs along the tunica media of the arteries and arterioles that consists mainly of smooth muscle cells and extracellular matrix. Recent studies suggest that ultraslow frequency oscillations resulting from contractile activity of smooth muscle cells in the tunica media play an important role in the drainage of fluids and solutes. These oscillations in the microvasculature are independent of the neuronal activity. In our earlier work, deformations of the arterial wall boundaries due to heart pulses were theorized to drive the interstitial fluid flow. In our current work, we investigate the role of forward propagating arterial pulsations and reverse low-frequency smooth muscle contraction waves on the flow transport along the arterial walls. We created a mathematical model that accounts for the porosity dynamics of the periarterial basement membrane space. We report phase diagrams that identify combinations of the parameters of these waves that induce either forward or reverse flows in these periarterial channels.