Isotropy, iSectors, and vertical sections in stereology

Stereology provides meaningful quantitative descriptions of the geometry of three-dimensional (3D) structures from measurements that are made on two-dimensional (2D) images. One important consideration when designing such studies is that both length and surface features may have preferred orientations in 3D space; that is, they may not be isotropic. To fully understand the global estimators of length L and surface area S, it is essential that one understand the problems that the inherent anisotropy in the structure of most living organisms generates when designing unbiased sampling schemes for estimating length and surface. These same issues also apply to the use of local estimators of object volume v and surface s, in that they use line and surface probes. These problems and the various solutions to them, which involve sectioning and probing tissue in particular ways, are presented in this article.