Determining the effective Taylor dispersion in an annulus with a pulsatile inner boundary

We develop analytical expressions for the spread of concentration of a solute in an annular channel with a spatiotemporally pulsating inner boundary. The problem is motivated by perivascular spaces (PVSs; annular channels surrounding the arteries in the brain) that provide a medium for cerebrospinal fluid (CSF) to flow and transport metabolic waste products and solutes from the brain interstitium. We study the dispersion dynamics in an annular channel where the inner wall corresponds to the pulsatile arterial lumen, and the outer wall is constant, corresponding to the astrocytic end feet and the brain parenchyma. Using the invariant manifold theory, we derive a second-order asymptotic expression to determine the effective Taylor dispersion equation and dispersion parameters in the annulus for various wavelengths and frequencies of pulsations expected in the brain. The research introduces a generalized framework to quantify solute dispersion in spatiotemporally varying annular channels, and provides important insights on controlling CSF flow and solute transport in the PVSs.