{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:09:33Z","timestamp":1792786173479,"version":"4.5.0"},"reference-count":63,"publisher":"The Royal Society","issue":"243","license":[{"start":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Royal Society International Exchanges","award":["IES\\R3\\233\u2009021"],"award-info":[{"award-number":["IES\\R3\\233\u2009021"]}],"id":[{"id":"https:\/\/ror.org\/03wnrjx87","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,10,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>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\u2013drainage 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\u00a0in which advection is governed by the Lagrangian mean velocity, incorporating steady streaming, production\u2013drainage 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.<\/jats:p>","DOI":"10.1098\/rsif.2026.0196","type":"journal-article","created":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:22:00Z","timestamp":1791332520000},"source":"Crossref","is-referenced-by-count":0,"title":["How brain pulsations drive solute transport in the cranial subarachnoid space: insights from a toy model"],"prefix":"10.1098","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4668-6867","authenticated-orcid":false,"given":"Alannah","family":"Neff","sequence":"first","affiliation":[{"name":"School of Mathematics and Maxwell Institute, University of Edinburgh 1 , Edinburgh, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4772-8512","authenticated-orcid":false,"given":"Alexandra","family":"Vallet","sequence":"additional","affiliation":[{"name":"SAINBIOSE INSERM U 1059, \u00c9cole nationale sup\u00e9rieure des Mines de Saint-\u00c9tienne 2 , Saint-\u00c9tienne, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6057-1919","authenticated-orcid":false,"given":"Mariia","family":"Dvoriashyna","sequence":"additional","affiliation":[{"name":"School of Mathematics and Maxwell Institute, University of Edinburgh 1 , Edinburgh, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2026,10,7]]},"reference":[{"key":"2026100620215470100_RSIF20260196C1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1146\/annurev-fluid-120720-011638","article-title":"Cerebrospinal fluid flow","volume":"55","author":"Kelley","year":"2022","journal-title":"Annu. 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