Mattfeldt T, Möbius H J, Mall G
J Microsc. 1985 Sep;139(Pt 3):279-89. doi: 10.1111/j.1365-2818.1985.tb02644.x.
If the axis of anisotropy of oriented, tubular or lamellar objects is unknown, the unbiased stereological estimation of length density and surface density (Lv and Sv) requires counts on sections with isotropic uniform random (IUR) orientation. It is shown theoretically that in homogeneous, anisotropic specimens the precision of Lv and Sv estimation is considerably augmented if IUR-oriented sets of three mutually perpendicular sections (orthogonal triplet probes = ortrips) are used instead of three directionally independent IUR sections. The mechanism of variance reduction results from a negative covariance between sections within 'ortrips' and corresponds to the antithetic variate principle of Monte Carlo work. Heterogeneity decreases the efficiency of the ortrip method, but this effect can often be counteracted by systematic sampling of ortrips within specimens. Practical estimation of length and surface area of the highly anisotropic, tubular myocardial capillaries per tissue volume in the left ventricles of eight normal, adult, male perfusion-fixed Wistar rats provided estimates of excellent precision with CEs of 3.3% (Lv) and 2.1% (Sv) of the group mean. The method will hopefully allow stereologists dealing with arbitrary anisotropic structures to apply the same simple, efficient, and unbiased sampling designs that have long been used in the study of liver, lung, and kidney tissue.
如果定向、管状或层状物体的各向异性轴未知，那么对长度密度和表面积密度（Lv和Sv）进行无偏倚的体视学估计就需要在具有各向同性均匀随机（IUR）取向的切片上进行计数。从理论上可以证明，在均匀的各向异性标本中，如果使用三个相互垂直的IUR取向切片集（正交三联体探针=ortrips）而不是三个方向独立的IUR切片，那么Lv和Sv估计的精度会显著提高。方差减小的机制源于“ortrips”内切片之间的负协方差，这与蒙特卡罗工作中的对偶变量原理相对应。异质性会降低ortrip方法的效率，但这种影响通常可以通过在标本内对ortrips进行系统抽样来抵消。对8只正常成年雄性灌注固定的Wistar大鼠左心室中每单位组织体积内高度各向异性的管状心肌毛细血管的长度和表面积进行实际估计，结果显示估计精度极高，组均值的CE分别为3.3%（Lv）和2.1%（Sv）。希望该方法能让处理任意各向异性结构的体视学家应用长期以来在肝脏、肺和肾脏组织研究中使用的同样简单、高效且无偏倚的抽样设计。
