How brain pulsations drive solute transport in the cranial subarachnoid space: insights from a toy model

Overview

Authors: Alannah Neff¹, Alexandra Vallet², Mariia Dvoriashyna¹

ORCID iDs: Alannah Neff, Alexandra Vallet, Mariia Dvoriashyna

School of Mathematics and Maxwell Institute, University of Edinburgh, Edinburgh, UK
SAINBIOSE INSERM U 1059, École nationale supérieure des Mines de Saint-Étienne, Saint-Étienne, France

Journal: Journal of the Royal Society, Interface, volume 23, issue 243, article 20260196

Dates: received 19 February 2026; accepted 16 July 2026; published online 7 October 2026

Type: Research article · Language: English

License: CC BY

Identifiers: DOI · PMCID PMC13641946

Status: code found, still to be checked (how the code is found and verified)

Categories: computational (subfield)

Keywords: cerebrospinal fluid, glymphatic system, transport in oscillatory flows, steady streaming, lubrication theory

Journal subjects: Biomathematics, Biophysics, Life Sciences–Mathematics interface

Funding: Royal Society International Exchanges (IES\R3\233 021)

Citations: not cited yet (Europe PMC); 63 references in the paper

Abstract

Cerebrospinal fluid (CSF) circulates around and through the brain, supporting neural homeostasis by regulating the extracellular chemical environment. Yet, the physical mechanisms governing CSF-driven solute transport remain poorly understood, limiting the design of diagnostic and therapeutic strategies targeting brain clearance and drug delivery. Pulsatile CSF flow in the cranial subarachnoid space (cSAS) is driven by cardiac, respiratory and sleep-related vasomotion. Over longer timescales, weaker steady flows, such as inertial steady streaming, Stokes drift and production–drainage flow, may contribute to solute transport, but their role and relative importance remain unclear. Here, we develop a simplified two-dimensional model of CSF flow and solute transport in the cSAS using lubrication theory. Through multiple-timescale and asymptotic analyses, we derive a reduced long-time transport equation in which advection is governed by the Lagrangian mean velocity, incorporating steady streaming, production–drainage flow and Stokes drift. Analysing three physiologically relevant case studies, we show that steady flows can substantially reshape concentration profiles, enhance dispersion and alter clearance efficiency. Our results clarify the mechanisms underlying CSF-mediated transport, predict distinct regimes in humans and mice and highlight the importance of subject-specific physiological parameters when interpreting contrast-agent and intrathecal drug-delivery studies.

Reproduced under the paper's license (CC BY), from the paper cited above.

Code

No file of the authors' code could be read here: it is described below, and read at its source.

doi:10.6084/m9.figshare.c.8636084

License: none: the authors keep all their rights

State: unreachable at the last attempt, verified on 8 October 2026

Evidence: found in the paper

Software Heritage: not checked

Found in: the references

Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation

Availability: 1 check, the latest on 8 October 2026: unreachable at the last attempt (HTTP 202)

8 October 2026: unreachable at the last attempt (HTTP 202)

At the source: doi.org/10.6084/m9.figshare.c.8636084

The paper's code and data availability statement is in the Data section.

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Data

No dataset and no data link were found in the paper.

Data accessibility

All codes have been published on Zenodo [62]. The supplementary material contains detailed derivations of the model and choice of model parameters.

Supplementary material is available online [63].

Reproduced under the paper's license (CC BY), from the paper cited above.

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Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 5 keywords, 1 funder, 61 references.

Cite

This paper

Neff, A., Vallet, A., & Dvoriashyna, M. (2026). How brain pulsations drive solute transport in the cranial subarachnoid space: insights from a toy model. Journal of the Royal Society, Interface, 23(243), 20260196.

BibTeX

@article{neff2026how, author = {Neff, Alannah and Vallet, Alexandra and Dvoriashyna, Mariia}, title = {{How brain pulsations drive solute transport in the cranial subarachnoid space: insights from a toy model}}, journal = {Journal of the Royal Society, Interface}, year = {2026}, month = oct, volume = {23}, number = {243}, pages = {20260196}, publisher = {The Royal Society}, issn = {1742-5689}, pmcid = {PMC13641946} }

RIS

TY - JOUR AU - Neff, Alannah AU - Vallet, Alexandra AU - Dvoriashyna, Mariia TI - How brain pulsations drive solute transport in the cranial subarachnoid space: insights from a toy model T2 - Journal of the Royal Society, Interface J2 - J R Soc Interface PY - 2026 DA - 2026/10/08 VL - 23 IS - 243 SP - 20260196 SN - 1742-5689 PB - The Royal Society LA - en ER -

CSL-JSON

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