血管周围网络中蠕动产生的定向流动——理论与数值降阶描述
The directional flow generated by peristalsis in perivascular networks -- theoretical and numerical reduced-order descriptions
AI总结：
该研究构建理论与数值降阶模型，分析血管周围网络中蠕动泵送的定向净流动，推导不同网络构型下的解析表达式，量化生理参数对流速的影响，揭示血管运动及睡眠相关脉动变化对脑周血流的调控作用。
摘要：
围绕脑动脉的血管周围间隙中的定向流体流动，被假设在脑溶质转运和清除中发挥关键作用。虽然脉动流的多种驱动因素（如心脏或呼吸搏动）已得到充分量化，但在生理状态下哪些机制能够诱导定向流动的问题仍未得到解答。为解决这一问题，我们开发了理论与数值降阶模型，以量化动脉周围网络中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空间，其内部边界为承载周期性行进（蠕动）波的圆管。在小雷诺数流动、小半径、小振幅蠕动波的合理假设下，我们利用润滑理论和正则摄动方法，推导出血管周围网络中定向净流动和压力分布的理论表达式。利用该降阶模型，我们推导出了感兴趣的简单网络构型（包括单个单元、两个串联单元、三单元分叉结构）下净流动的解析闭式表达式，并将结果与数值预测进行了对比。我们特别给出了血管周围网络中蠕动运动诱导的净流动的可计算理论估计值，该估计值是生理参数的函数，尤其是波长、频率、振幅和血管周围尺寸。通过量化特定生理状态下的最大净流动，我们发现血管运动可诱导的软脑膜动脉周围净流速约为几到几十微米每秒，而与睡眠相关的血管运动脉动性变化可使流动增加三倍。
英文摘要：
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.
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