GLOBAL SPATIAL SAMPLING WITH ISOTROPIC VIRTUAL PLANES - ESTIMATORS OFLENGTH DENSITY AND TOTAL LENGTH IN THICK, ARBITRARILY ORIENTATED SECTIONS

Existing design-based direct length estimators require random rotation around at least one axis of the tissue specimen prior to sectioning t o ensure isotropy of test probes. Ln some tissue it is, however, diffi cult or even impossible to define the region of interest, unless the t issue is sectioned in a specific, nonrandom orientation. Spatial unifo rm sampling with isotropic virtual planes circumvents the use of physi cally isotropic or vertical sections, The structure that is contained in a thick physical section is investigated with software-randomized i sotropic virtual planes in volume probes in systematically sampled mic roscope fields using computer-assisted stereological analysis, A fixed volume of 3D space in each uniformly sampled field is probed with sys tematic random, isotropic virtual planes by a line that moves across t he computer screen showing live video images of the microscope field w hen the test volume is scanned with a focal plane. The intersections b etween the linear structure and the virtual probes are counted with co lumns of two dimensional disectors. Global spatial sampling with sets of isotropic uniform random virtual planes provides a basis for length density estimates from a set of parallel physical sections of any ori entation preferred by the investigator i,e. the simplest sampling sche me in stereology, additional virtues include optimal conditions for re ducing the estimator variance, the possibility to estimate total lengt h directly using a fractionator design and the potential to estimate e fficiently the distribution of directions from a set of parallel physi cal sections with arbitrary orientation. Other implementations of the basic idea, systematic uniform sampling using probes that have total 3 Dx4 pi freedom inside the section, and therefore independent of the po sition and the orientation of the physical section, are briefly discus sed.