Estimating Particle Number and Size

Summary

This paper is mainly concerned with the stereology of particles. It has been written bearing the interests of quantitative synaptology in mind, but the results can be applied elsewhere.

The first section deals with the assumption-free estimation of geometric particle properties from serial sections, notably particle number. A ready-to-use version of an earlier method (Cruz-Orive, 1980a) is given which is now valid under arbitrary overprojection (due to section thickness) and truncation (namely unobservability of grazing particle fragments). The recent method of Sterio (1984) is also worth considering, especially for not too complex and not too small particles. In addition, relevant considerations on the proper use of quantitative information from serial sections are brought forward (section 1.4). It is shown that serial sectioning does not always guarantee the unbiased estimation of particle properties.

In general, an optimal combination of serial section and random section measurements should be sought. This is the aim of sections 1 and 2 taken together. The models in section 2 have to be rather restrictive, however, because satisfactory corrections of random section measurements affected by overprojection and truncation are known only for spheres and disks.

Finally, section 3 contains two models for ‘platelets with dark spots’ with the purpose of estimating the mean number of dense projections sitting on a presynaptic grid of arbitrary shape and connectivity.

Most of the methods described here were tried on extensive data kindly supplied by Didima M.G. De Groot (TNO Rijswijk, NL). Related results have been reported (De Groot & Bierman, 1983, De Groot, 1984). For reasons of the time and space the present paper does not contain any numerical comparisons or cross-checks, however. This was planned for a future joint paper.

The skillful assistance of Mr K. Babl, Ms R. Fankhauser and Ms M. Schweizer in preparing the typescript is gratefully acknowleged.

Research supported by the Swiss National Science Foundation grants 3.762.80 and 3.524.83