Mathematical modelling of cerebrospinal and interstitial fluid dynamics associated with perivascular spaces surrounding penetrating arteries

Two studies examine the flow of neurofluids in human perivascular spaces (PVSs) surrounding brain penetrating arteries. Brain pulsations are included, a physiological feature previously overlooked in research into brain waste clearance. The first study models cerebrospinal fluid (CSF) flow in PVSs surrounding brain penetrating arteries. Arterial wall motion is driven by a blood pressure wave, while the outer PVS boundary oscillates due to brain pulsations. Lubrication theory is employed to derive a mathematical model for the flow, which is solved numerically. An analysis is undertaken to investigate the effect of key cardiovascular parameters and brain pulsations, with the latter found to magnify the net axial CSF flows created by the arterial wall motion. The findings suggest that these CSF flows are almost always antegrade and highly dependent on PVS-penetrating artery configurations. Clinical implications are discussed in the light of the glymphatic hypothesis, such as arterial wall stiffening and thickening impairing flow and dilated PVSs acting as indicators of an increased likelihood of neurodegenerative conditions. The second study examines the ability of the CSF flows in PVSs to generate net bulk interstitial fluid (ISF) flows in the surrounding brain parenchyma. By treating the parenchyma as a porous medium and incorporating time-dependent parenchymal porosity into Darcy’s fluid flow law, a number of findings emerge. First, in the presence of brain pulsations, oscillatory ISF flows are rectified into net bulk flows, raising flow rates by up to four orders of magnitude. Second, a power-law relationship between net mean axial CSF flows and net bulk ISF flows is established across all the cardiovascular parameters, raising the future prospect of assessing brain waste clearance efficiency from CSF flow measurements in PVSs. Finally, while brain pulsations uplift net bulk ISF flow rates, the Péclet number remains below unity and diffusion continues to dominate waste clearance.