Improving one-dimensional simulations of glymphatic flow using Windkessel boundary conditions

Cerebrospinal fluid (CSF) flow through perivascular spaces (PVSs) plays a critical role in clearing metabolic waste from the brain via the glymphatic system. Accumulation of metabolic wastes such as amyloid-β is connected to various neurological disorders such as Alzheimer’s disease. We derive a one-dimensional (1D) finite volume model (FVM) to simulate CSF flow in PVSs driven by propagating waves of arterial pulsations. We perform simulations using a domain with realistic dimensions comparable to that of the middle cerebral artery of a mouse. To better characterize the impact of the complex downstream CSF pathway, we implement a three-element Windkessel model as the outlet boundary condition. The Windkessel model is a simplified lumped parameter model that captures the relationship between pressure and volumetric flow rate using hydraulic resistance and capacitance, and therefore provides a more realistic pressure variation at the domain outlet. We quantify how variations in Windkessel parameters influence mean and peak CSF flow velocities, and we compare our results to in vivo experimental measurements from our lab. These simulations provide an important step toward understanding mechanisms propelling CSF flow through the brain. In turn, such modeling may help predict the efficacy of various interventions that seek to enhance glymphatic flow and prevent diseases like Alzheimer’s.