We consider the drainage of blood plasma across the capillary wall, focusing on the flow through the endothelial glycocalyx layer that coats the luminal surface of vascular endothelial cells. We investigate how the presence of a sub-glycocalyx space between the porous glycocalyx and the impermeable endothelial cells affects the flow, using the Darcy and Stokes equations to model the flow in the glycocalyx and sub-glycocalyx space, respectively. Using an asymptotic analysis, we exploit the disparity of lengthscales to reduce the problem complexity to reveal the existence of several asymptotic regions in space. We provide a detailed characterisation of the flow through the glycocalyx layer in terms of the microscale system parameters, and we derive analytic macroscale results, such as for the flux through and hydraulic conductivity of the glycocalyx layer. We show that the presence of a sub-glycocalyx space results in a higher flux of blood plasma through the glycocalyx layer, and we use our theoretical predictions to suggest experiments that could be carried out to shed light on the extent of the layer.

中文翻译：

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确定次糖萼空间影响的数学模型

我们考虑血浆通过毛细血管壁的引流，重点是流经覆盖在血管内皮细胞腔表面的内皮糖萼层的流量。我们使用Darcy和Stokes方程分别对糖萼和亚糖萼空间中的流动进行建模，研究了多孔糖萼和不可渗透的内皮细胞之间亚糖萼空间的存在如何影响流量。使用渐近分析，我们利用长度尺度的差异来减少问题的复杂性，以揭示空间中存在几个渐近区域。我们根据微观系统参数对糖萼层中的流动进行了详细描述，并得出了宏观分析结果，例如对于糖萼层的通量和水力传导率。我们表明存在一个糖基下层空间会导致较高的血浆通过糖层层的通量，并且我们使用理论上的预测来建议进行一些实验，以阐明该层的范围。