Particle number can be estimated using a disector of unknown thickness: the selector

A new stereological method is presented whereby the number of particles in a material can be estimated unbiasedly using a few parallel sections from a block of the material, without having to know either section thickness or the distance between sections, and irrespective of particle size, shape and orientation. All that is needed is the final magnification. The method consists of three steps. Firstly, a few particles are sampled with identical probabilities using a disector (Sterio, 1984) of unknown thickness, namely a selector. Secondly, the volume of each sampled particle is unbiasedly estimated by means of point-sampled intercepts (Gundersen & Jensen, 1985) on a few particle transects. Thus, the mean individual particle volume vN in the population is estimated directly without having to refer to any containing volume. Finally, the particle volume fraction VV is estimated on a random section (by point-counting, say) and the numerical density of particles is estimated via the identity NV = VV/vN. Multiplying the estimate of NV with the reference volume we get an estimate of the total number of particles. The selector may be used not only for counting but also for choosing particles with identical probabilities in order to make, say, serial reconstructions of them. The practical details of the counting method are explained with the aid of a worked synthetic example and a real one involving hepatocytic nuclei. The mathematical proofs are given in two appendices.