Nyengaard J R, Marcussen N
Stereological Research Laboratory, University of Aarhus, Denmark.
J Microsc. 1993 Jul;171(Pt 1):27-37. doi: 10.1111/j.1365-2818.1993.tb03356.x.
A method for unbiased capillary number estimation based on the estimation of the Euler-Poincaré characteristic or Euler number with the disector is evaluated. The generation of a new capillary creates a new loop in the capillary network corresponding to a change of exactly one unit in the Euler number of the network. In this way the Euler number has a one-to-one relationship to the number of capillaries in a network. In this report rat glomerular capillaries are counted. Three tissue blocks from each of 14 perfusion-fixed rat kidneys, aged between 5 days and 18 months, were uniformly sampled and embedded in Epon. Two complete glomerular profiles were sampled per block. Three consecutive sections were studied per glomerulus using the middle one to evaluate the topological events of the capillaries in the sampled glomerulus. The use of complete glomerular profiles eliminated problems with the edges, whereas the disector ensured unbiased sampling in the third dimension. Estimates per animal were weighted averages over blocks, the weights being half the number of glomerular profiles in a section from a block. The number of capillaries in a glomerulus is the mean Euler number per disector volume multiplied by the mean volume of glomeruli obtained by the fractionator. The observed coefficient of variation between animals was 18.3% for the estimated number of capillaries per glomerulus, and the observed coefficient of error at the level of blocks within animals was 14.7%. The exact capillary number from the node-branch network of two reconstructed glomeruli equalled the capillary number obtained by the total Euler number from the same glomeruli. This shows in an applied example, as would be expected, that the estimation of capillary number using the Euler number is unbiased and independent of the direction of sectioning.
评估了一种基于使用分割器估计欧拉 - 庞加莱特征或欧拉数来进行无偏毛细血管数量估计的方法。新毛细血管的生成会在毛细血管网络中产生一个新环，这对应于网络欧拉数恰好一个单位的变化。通过这种方式，欧拉数与网络中毛细血管的数量具有一一对应关系。在本报告中，对大鼠肾小球毛细血管进行了计数。从14只年龄在5天至18个月之间的灌注固定大鼠肾脏中，每个肾脏取三个组织块进行均匀采样，并包埋在环氧树脂中。每个组织块取两个完整的肾小球轮廓进行采样。每个肾小球使用中间的连续三个切片来研究，以评估采样肾小球中毛细血管的拓扑事件。使用完整的肾小球轮廓消除了边缘问题，而分割器确保了在三维空间中的无偏采样。每只动物的估计值是各组织块的加权平均值，权重为来自一个组织块的切片中肾小球轮廓数量的一半。肾小球中毛细血管的数量是每个分割器体积的平均欧拉数乘以通过分数法获得的肾小球平均体积。每只动物肾小球毛细血管估计数量的观察变异系数为18.3%，动物体内组织块水平的观察误差系数为14.7%。两个重建肾小球的节点 - 分支网络中的精确毛细血管数量等于相同肾小球的总欧拉数所得到的毛细血管数量。正如预期的那样，这在一个应用实例中表明，使用欧拉数估计毛细血管数量是无偏的，并且与切片方向无关。
