Stereology. Definition and historic background.

Stereology is an applied science addressing the deduction of threedimensional structure from observations made on two of the three dimensions. Stereology deals with areas and volumes ofdefined bodies of solid geometry such as spheres, cubes and polyhedra. It is an interdisciplinary science with application of the methodology to biology and medicine as well as to materials sciences, minerology, forestry, and agriculture. Using quantitative methods, one attempts to answer the questions: 1 ) how large, by measuring circumference, length and diameter; 2) how many, by counting the number; 3) what the orientation in space is; 4) what the properties of the material are by equating shape, profile and tangent; 5) what are the relationships such as discreteness, contiguity, interdigitation, and branching. All of these questions can be expressed numerically by using stereologic methods. Initially the methodology of stereology (2) involved measuring the volume of fresh specimens by: 1) applying Archimedes’ principle, 2) ascertaining specific gravity, or 3) by making numerical counts after injecting supravital dyes. Later, indirect measurements were derived using tracings, camera lucida drawings, projections or photographs of cut surfaces or sections. More commonly, for light microscopy, scales or grids of either lines (linear analyses) or points (point sampling) are inserted into the eyepiece of a microscope for direct measurement of tissues on glass slides; a lattice or suitable template may be prepared (use turquoise ink, for contrast) on transparent plastic sheets as an overlay for electron micrographs. Most recently, coupling glass tablets or light pens with television viewing and interfacing with a computer has increased the rapidity of making measurements as well as the efficiency in obtaining statistical results; these methods are based on perimeter tracings, comparable to planimetry, that provide areal measurements. The mathematical basis for stereologic methodology is referrable to two theories or proofs established in the 1800’s. In 1847, Delesse (3), a French geologist, suggested an algebraic equation for using area to compute volume. He proved that the sum of the areas of components of rock, acquired by weighing paper tracings, was proportional to their volume in the rock provided the components were distributed uniformly. Later it was shown (1) that the theory is applicable when the distribution in tissue is not uniform. In 1898 Rosiwal (6), using scale and dividers, pointed out that volume could be computed from fractional lengths of components measured along intercepts or parallel lines. He proposed that the total traverse be 100 times the length of the smallest particle being measured and that the accuracy of the method is proportional to the length of traverse but inversely proportional to the size of the particle. The Cavalieri theorem is cited, too, as geometric evidence for the permissibility of using linear measurements in computing volume. Glagoleff (4), in 1934, showed that points could be substituted for lines. Although a few biologists have provided equations for establishing the accuracy of their technique, most investigators using stereologic methodology devise their experiments after accumulating empiric results from a pilot study. From the standard deviations obtained and the plotting of a progressive mean (7), an estimate of the number of samples required may be derived. In selecting a quantitative method, use the simplest, least timeconsuming method that will provide a standard deviation that is acceptable (usually 10%). The method should be reproducible to 1%. The data, at least among the controls, should represent a Gaussian distribution; when there are out-hers, one is dealing either with unacceptable obliquity, pathology or genetic differences. It is possible to draw the out-hers in, thus smoothing the distribution curve by using a reciprocal transformation (5). Factors that influence the accuracy of quantitative technics have been reported ( 1) as they relate to reproducibility of the methods, sampling, inhomogeneity of organs and comparison to other methods. These factors are pertinent regardless of the method of quantitation selected.