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• Cerebrospinal fluid in brain surface perivascular spaces flows and pulses. • Prior experiments show close links to wall motion, suggesting perivascular pumping. • Prior theory and simulations predict different pulsatility and phase than observed. • We add resistance and compliance as boundary conditions, using measured values. • Then, theory and simulations match observations much more closely. Cerebrospinal fluid (CSF) flows through the perivascular spaces (PVSs) surrounding cerebral arteries. Revealing the mechanisms driving that flow could bring improved understanding of brain waste transport and insights for disorders including Alzheimer's disease and stroke. In vivo velocity measurements of CSF in surface PVSs in mice have been used to argue that flow is driven primarily by the pulsatile motion of artery walls — perivascular pumping. However, fluid dynamics theory and simulation have predicted that perivascular pumping produces flows differing from in vivo observations starkly, particularly in the phase and relative amplitude of flow oscillation. We show that coupling theoretical and simulated flows to more realistic end boundary conditions, using resistance and compliance values measured in mice instead of using periodic boundaries, results in velocities that match observations more closely in phase and relative amplitude of oscillation, while preserving the existing agreement in mean flow speed. This quantitative agreement among theory, simulation, and in vivo measurement further supports the idea that perivascular pumping is an important CSF driver in physiological conditions. [ABSTRACT FROM AUTHOR]