Department of Mathematics, Statistics and Computation, Faculty of Sciences, University of Cantabria, Avda. Los Castros s/n, E-39005 Santander, Spain.
J Microsc. 2010 Nov;240(2):94-110. doi: 10.1111/j.1365-2818.2010.03387.x.
The invariator is a new stereological design to generate motion invariant test lines in three dimensions on an isotropic plane through a fixed point. The theory has been published recently. The purpose of this paper is to illustrate the application of the invariator on a group of rat brains to estimate brain volume and external surface area. Each brain was first split into its two hemispheres and then embedded into a ball filled with agar following a configuration named the antithetic isector, with the idea of reducing the error variance. After rolling the ball at random it was scanned by magnetic resonance imaging into a stack of parallel systematic sections: this is the isotropic Cavalieri design which, combined with the antithetic isector idea, proves to be very accurate. The invariator used only an equatorial section of the ball, and in the present case the coefficient of error of the volume and surface area estimators of an individual brain was about 30%. As it is design unbiased, the invariator may prove its strength mainly to estimate population means.
变等器是一种新的体视学设计，用于在各向同性平面上通过固定点生成三维运动不变测试线。该理论最近已经发表。本文的目的是说明变等器在一组大鼠脑上的应用，以估计脑容量和外表面面积。每个脑首先被分为两个半球，然后嵌入一个充满琼脂的球中，采用一种名为对偶等分器的配置，其目的是减少误差方差。在随机滚动球之后，通过磁共振成像将其扫描成一组平行的系统切片：这就是各向同性 Cavalieri 设计，它与对偶等分器的思想结合起来，被证明非常准确。变等器仅使用球的一个赤道部分，在目前的情况下，单个脑的体积和表面积估计量的误差系数约为 30%。由于它是无偏设计，变等器可能主要通过估计总体均值来证明其优势。
