Iordache B E, Remuzzi A
Biomedical Engineering Laboratory, Mario Negri Institute for Pharmacological Research, Bergamo, Italy.
Microvasc Res. 1995 Jan;49(1):1-11. doi: 10.1006/mvre.1995.1001.
Poiseuille's formula is conventionally used to calculate hydraulic resistance of blood capillaries. This law, however, applies to tubes with constant diameter and straight axis. Since blood capillaries, especially in the glomerular microcirculation, are far from having these features, we wanted to estimate the effect of the shape of glomerular capillary segments on the calculation of their hydraulic resistance in comparison to the values obtained with Poiseuille's formula. We studied blood flow through capillary segments of a reconstructed glomerular network from a normal Munich-Wistar rat. Geometrical parameters of capillary segments derived from serial section reconstruction of the glomerulus were used to perform numerical analysis of blood flow. Non-Newtonian properties of blood were simulated by calculating apparent blood viscosity as a function of local rheological parameters for each capillary segment. The numerically calculated hydraulic resistances were always higher than those given by the Poiseuille equation (from 22 to 99%), and this was attributed to the geometrical complexity of the reconstructed vessels. We also performed simulations of the blood flow and filtration along the glomerular network using a previously developed theoretical model that considers the topographical organization of the network structure and dimensions of individual capillary segments. Considering higher hydraulic resistances (as estimated with the numerical analysis) we found that the calculated ultrafiltration coefficient did not change appreciably, but the total network pressure drop and the fraction of filtering surface area at filtration equilibrium were higher than previously estimated.
泊肃叶公式通常用于计算毛细血管的水力阻力。然而，该定律适用于直径恒定且轴为直线的管道。由于毛细血管，尤其是肾小球微循环中的毛细血管，远不具备这些特征，我们想评估肾小球毛细血管段的形状对其水力阻力计算的影响，并与用泊肃叶公式得到的值进行比较。我们研究了来自正常慕尼黑-维斯塔尔大鼠的重建肾小球网络中毛细血管段的血流情况。通过肾小球的连续切片重建得出的毛细血管段几何参数被用于进行血流的数值分析。通过计算每个毛细血管段的表观血液粘度作为局部流变学参数的函数来模拟血液的非牛顿特性。数值计算得到的水力阻力总是高于泊肃叶方程给出的阻力（从22%到99%），这归因于重建血管的几何复杂性。我们还使用一个先前开发的理论模型对沿肾小球网络的血流和滤过进行了模拟，该模型考虑了网络结构的地形组织和各个毛细血管段的尺寸。考虑到更高的水力阻力（如通过数值分析估计的），我们发现计算得到的超滤系数没有明显变化，但总网络压降和滤过平衡时的滤过表面积分数高于先前的估计值。
