The efficiency of systematic sampling in stereology and its prediction*

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Abstract

The superior efficiency of systematic sampling at all levels in stereological studies is emphasized and various commonly used ways of implementing it are briefly described. Summarizing recent theoretical and experimental studies a set of very simple estimators of efficiency are presented and illustrated with a variety of biological examples. In particular, a nomogram for predicting the necessary number of points when performing point counting is provided. The very efficient and simple unbiased estimator of the volume of an arbitrary object based on Cavalieri's principle is dealt with in some detail. The efficiency of the systematic fractionating of an object is also illustrated.

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The unbiased estimation of number and sizes of arbitrary particles using the disector.

D Sterio (1984)

A three-dimensional counting rule and its integral test system, the disector, for obtaining unbiased estimates of the number of arbitrary particles in a specimen is presented. Used in combination with ordinary and recently developed stereological methods unbiased estimates of various mean particle sizes and the variance of particle volume are obtainable on sets of two parallel sections with a known separation. The same principle allows the unbiased estimation of the distribution of individual particle volumes in sets of serial sections.

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PRACTICAL STEREOLOGICAL METHODS FOR MORPHOMETRIC CYTOLOGY

Ewald Weibel, Gonzague S. Kistler, Walter Scherle (1966)

Stereological principles provide efficient and reliable tools for the determination of quantitative parameters of tissue structure on sections. Some principles which allow the estimation of volumetric ratios, surface areas, surface-to-volume ratios, thicknesses of tissue or cell sheets, and the number of structures are reviewed and presented in general form; means for their practical application in electron microscopy are outlined. The systematic and statistical errors involved in such measurements are discussed.

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Estimation of surface area from vertical sections.

H J Gundersen, A Baddeley, M Orive (1986)

'Vertical' sections are plane sections longitudinal to a fixed (but arbitrary) axial direction. Examples are sections of a cylinder parallel to the central axis; and sections of a flat slab normal to the plane of the slab. Vertical sections of any object can be generated by placing the object on a table and taking sections perpendicular to the plane of the table. The standard methods of stereology assume isotropic random sections, and are not applicable to this kind of biased sampling. However, by using specially designed test systems, one can obtain an unbiased estimate of surface area. General principles of stereology for vertical sections are outlined. No assumptions are necessary about the shape or orientation distribution of the structure. Vertical section stereology is valid on the same terms as standard stereological methods for isotropic random sections. The range of structural quantities that can be estimated from vertical sections includes VV, NV, SV and the volume-weighted mean particle volume vV, but not LV. There is complete freedom to choose the vertical axis direction, which makes the sampling procedure simple and 'natural'. Practical sampling procedures for implementation of the ideas are described, and illustrated by examples.