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.

翻译：摘要：大脑动脉周围血管外膜间隙中的定向流体流动被认为在大脑溶质运输与清除中起关键作用。尽管心脏或呼吸搏动等驱动脉动流的多种因素已被充分量化，但生理条件下何种机制能诱导定向流动的问题仍悬而未决。为解决此问题，我们发展了理论与数值降阶模型，以量化动脉周围网络内蠕动泵送可诱导的定向（净）流动。每个动脉周围单元被建模为细长环形间隙，其内边界由支撑周期性行波（蠕动波）的圆形管道构成。在低雷诺数流动、小半径和小振幅蠕动波的合理假设下，我们利用润滑理论与正则摄动方法推导出血管周围网络中定向净流与压力分布的理论表达式。该降阶模型用于导出简单网络构型（包括单单元、串联双单元及三单元分叉结构）净流的闭式解析表达式，并与数值预测结果进行对比。特别地，我们提供了可计算的生理参数依赖理论估计值，用以描述蠕动运动在血管周围网络中诱导的净流，关键参数包括波长、频率、振幅及血管外膜间隙尺寸。通过量化特定生理条件下的最大净流，我们发现血管舒缩可诱导软脑膜动脉周围净流速达到数至数十微米/秒量级，而与睡眠相关的血管舒缩搏动变化可能驱动三倍量的流量增加。