Perivascular spaces (PVSs) carry cerebrospinal fluid (CSF) around the brain, facilitating healthy waste clearance. Measuring those flows in vivo is difficult, and often impossible, because PVSs are small, so accurate modeling is essential for understanding brain clearance. The most important parameter for modeling flow in a PVS is its hydraulic resistance, defined as the ratio of pressure drop to volume flow rate, which depends on its size and shape. In particular, the local resistance per unit length varies along a PVS and depends on variations in the local cross section. Using segmented, three-dimensional images of pial PVSs in mice, we performed fluid dynamical simulations to calculate the resistance per unit length. We applied extended lubrication theory to elucidate the difference between the calculated resistance and the expected resistance assuming a uniform flow. We tested four different approximation methods, and a novel correction factor to determine how to accurately estimate resistance per unit length with low computational cost. To assess the impact of assuming unidirectional flow, we also considered a circular duct whose cross-sectional area varied sinusoidally along its length. We found that modeling a PVS as a series of short ducts with uniform flow, and numerically solving for the flow in each, yields good resistance estimates at low cost. If the second derivative of area with respect to axial location is less than 2, error is typically less than 15%, and can be reduced further with our correction factor. To make estimates with even lower cost, we found that instead of solving for the resistance numerically, the well-known resistance of a circular duct could be scaled by a shape factor. As long as the aspect ratio of the cross section was less than 0.7, the additional error was less than 10%. Neglecting off-axis velocity components underestimates the average resistance, but the error can be reduced with a simple correction factor. These results could increase the accuracy of future models of brain-wide and local CSF flow, enabling better prediction of clearance, for example, as it varies with age, brain state, and pathological conditions.

中文翻译：

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大脑三维软脑膜血管周围空间的液压阻力

血管周围空间 (PVS) 在大脑周围携带脑脊液 (CSF)，促进健康的废物清除。在体内测量这些流量很困难，而且通常是不可能的，因为 PVS 很小，因此准确的建模对于了解大脑清除率至关重要。PVS 中的流量建模最重要的参数是其水力阻力，定义为压降与体积流量之比，这取决于其尺寸和形状。特别地，每单位长度的局部电阻沿着PVS变化并且取决于局部横截面的变化。使用小鼠软脑膜 PVS 的分段三维图像，我们进行流体动力学模拟来计算每单位长度的阻力。我们应用扩展润滑理论来阐明计算阻力与假设均匀流动的预期阻力之间的差异。我们测试了四种不同的近似方法和一种新颖的校正因子，以确定如何以较低的计算成本准确估计每单位长度的电阻。为了评估假设单向流的影响，我们还考虑了横截面积沿其长度呈正弦变化的圆形管道。我们发现，将 PVS 建模为一系列具有均匀流动的短管道，并对每个管道中的流动进行数值求解，可以以较低的成本产生良好的阻力估计。如果面积相对于轴向位置的二阶导数小于 2，则误差通常小于 15%，并且可以通过我们的校正因子进一步减小。为了以更低的成本进行估计，我们发现不必以数值方式求解阻力，而是可以通过形状因子来缩放圆形管道的众所周知的阻力。只要横截面的长宽比小于0.7，附加误差就小于10%。忽略离轴速度分量会低估平均阻力，但可以通过简单的校正因子来减少误差。这些结果可以提高未来全脑和局部脑脊液流动模型的准确性，从而更好地预测清除率，例如，因为清除率随年龄、大脑状态和病理状况而变化。