  Directional fluid flow in perivascular spaces surrounding cerebral arteries
is hypothesized to play a key role in brain solute transport and clearance.
While various drivers for pulsatile flow, such as cardiac or respiratory
pulsations, are well quantified, the question remains as to which mechanisms
could induce directional flow within physiological regimes. To address this
question, we develop theoretical and numerical reduced-order models to quantify
the directional (net) flow induceable by peristaltic pumping in periarterial
networks. Each periarterial element is modeled as a slender annular space
bounded internally by a circular tube supporting a periodic traveling
(peristaltic) wave. Under the reasonable assumptions of small Reynolds number
flow, small radii, and small-amplitude peristaltic waves, we use lubrication
theory and regular perturbation methods to derive theoretical expressions for
the directional net flow and pressure distribution in the perivascular network.
The reduced model is used to derive closed-form analytical expressions for the
net flow for simple network configurations of interest, including single
elements, two elements in tandem, and a three element bifurcation, with results
compared with numerical predictions. In particular, we provide a computable
theoretical estimate of the net flow induced by peristaltic motion in
perivascular networks as a function of physiological parameters, notably wave
length, frequency, amplitude and perivascular dimensions. Quantifying the
maximal net flow for specific physiological regimes, we find that vasomotion
may induce net pial periarterial flow velocities on the order of a few to tens
of mum/s and that sleep-related changes in vasomotion pulsatility may drive a
threefold flow increase.
