Advection and diffusion in perivascular and extracellular spaces in the brain
Yisen Guo, Keelin Quirk, Douglas H. Kelley, John H. Thomas
Abstract
Knowledge of the relative importance of advection and diffusion in clearing waste from the brain has been elusive, especially concerning the extracellular space (ECS). With local and global computational models of the mouse brain, we explore how the presence or absence of advection in the ECS affects solute transport. Without advection in the ECS, clearance would occur by diffusion into flowing cerebrospinal fluid in perivascular spaces (PVSs) or elsewhere, but we find this process to be severely limited by build-up of solute in the PVSs. We simulate flow in the ECS driven by a pressure drop between arteriole and venule PVSs, which enhances clearance considerably. To assess the relative importance of advection and diffusion, we introduce a local Péclet number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="u1" overflow="scroll"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi class="mathcal" mathvariant="script">P</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mrow> <mml:mtext mathvariant="bold">x</mml:mtext> </mml:mrow> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:semantics> </mml:math> , a dimensionless scalar field. For our simulations, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="u2" overflow="scroll"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi class="mathcal" mathvariant="script">P</mml:mi> </mml:mrow> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> through much of the ECS but <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="u3" overflow="scroll"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi class="mathcal" mathvariant="script">P</mml:mi> </mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:semantics> </mml:math> near PVSs near the brain surface. This local dominance of advection in the ECS establishes a clearance mechanism markedly different from that produced by diffusion alone. In network simulations that explore different parameter values and efflux routes, the pressures needed to drive the PVS flows measured in vivo are unrealistically large for most cases lacking ECS flow. Collectively, our models indicate that a flow in the ECS is necessary to explain experimental measurements and maintain homeostasis.