  This paper addresses the pulsating motion of cerebrospinal fluid in the
aqueduct of Sylvius, a slender canal connecting the third and fourth ventricles
of the brain. Specific attention is given to the relation between the
instantaneous values of the flow rate and the interventricular pressure
difference, needed in clinical applications to enable indirect evaluations of
the latter from direct magnetic-resonance measurements of the former. An
order-of-magnitude analysis accounting for the slenderness of the canal is used
in simplifying the flow description. The boundary-layer approximation is found
to be applicable in the slender canal, where the oscillating flow is
characterized by stroke lengths comparable to the canal length and periods
comparable to the transverse diffusion time. By way of contrast, the flow in
the non-slender opening regions connecting the aqueduct with the two ventricles
is found to be inviscid and quasi-steady in the first approximation. The
resulting simplified description is validated by comparison with results of
direct numerical simulations. The model is used to investigate the relation
between the interventricular pressure and the stroke length, in parametric
ranges of interest in clinical applications.
