A 1-D Pulse Wave Model for Perivascular Flow

In vivo measurements of cerebrospinal fluid in the perivascular spaces (PVSs) indicate that flow is correlated with arterial wall motion. However, 3D simulations of the network are computationally expensive. To address this, we apply a one-dimensional modeling approach that couples the perivascular and arterial networks through vessel wall deformations that allow for wave reflections and transmission at vessel boundaries. We assume area waves from the arterial network are coupled to the PVS network’s area in a one-way interaction, a three-element Windkessel model represents the microvasculature, and pressure and volumetric flow are continuous at bifurcations. Our solver uses Richtmyer’s method, which is second-order accurate in time and space. This approach allows arterial deformations to be explicitly calculated for each segment in the entire network, rather than relying on isolated in vivo measurements of wall motion to drive perivascular flow.