Hydraulic resistance of periarterial spaces in the brain

Jeffrey Tithof, Douglas H. Kelley, Humberto Mestre, Maiken Nedergaard, John H. Thomas

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


Background: Periarterial spaces (PASs) are annular channels that surround arteries in the brain and contain cerebrospinal fluid (CSF): a flow of CSF in these channels is thought to be an important part of the brain's system for clearing metabolic wastes. In vivo observations reveal that they are not concentric, circular annuli, however: the outer boundaries are often oblate, and the arteries that form the inner boundaries are often offset from the central axis. Methods: We model PAS cross-sections as circles surrounded by ellipses and vary the radii of the circles, major and minor axes of the ellipses, and two-dimensional eccentricities of the circles with respect to the ellipses. For each shape, we solve the governing Navier-Stokes equation to determine the velocity profile for steady laminar flow and then compute the corresponding hydraulic resistance. Results: We find that the observed shapes of PASs have lower hydraulic resistance than concentric, circular annuli of the same size, and therefore allow faster, more efficient flow of cerebrospinal fluid. We find that the minimum hydraulic resistance (and therefore maximum flow rate) for a given PAS cross-sectional area occurs when the ellipse is elongated and intersects the circle, dividing the PAS into two lobes, as is common around pial arteries. We also find that if both the inner and outer boundaries are nearly circular, the minimum hydraulic resistance occurs when the eccentricity is large, as is common around penetrating arteries. Conclusions: The concentric circular annulus assumed in recent studies is not a good model of the shape of actual PASs observed in vivo, and it greatly overestimates the hydraulic resistance of the PAS. Our parameterization can be used to incorporate more realistic resistances into hydraulic network models of flow of cerebrospinal fluid in the brain. Our results demonstrate that actual shapes observed in vivo are nearly optimal, in the sense of offering the least hydraulic resistance. This optimization may well represent an evolutionary adaptation that maximizes clearance of metabolic waste from the brain.

Original languageEnglish (US)
Article number19
JournalFluids and Barriers of the CNS
Issue number1
StatePublished - Jun 20 2019
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported by a grant from the NIH/National Institute of Aging (RF1 AG057575-01 to MN, JHT, and DHK) and a grant from the Army Research Office (MURI W911NF1910280 to MN, DHK, and JHT).

Publisher Copyright:
© 2019 The Author(s).


  • Bulk flow
  • Cerebrospinal fluid
  • Fluid mechanics
  • Glymphatic system
  • Hydraulic resistance
  • Perivascular flow


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