Estimating mean particle volume and number from random sections by sampling profile boundaries

We describe some new shape-independent stereological estimates of particle mean volume and surface area. Finding volumes or surface areas of cell nuclei, from electron micrographs of random thin sections, is a central problem of biological stereology. The well-known point-sampled intercept (PSI) method samples profile interiors to find the volume-weighted mean volume. This can be used in place of the true mean volume, but to do so introduces bias when volumes vary a great deal, as they do in fixed specimens. Jensen and Gundersen quite recently extended the PSI estimator to provide particle surface area, with no bias in the case of uniform surface areas. Here we extend the PSI volume estimator in a different way, sampling profile boundaries rather than their interiors. We obtain a boundary-sampled intercept (BSI) volume estimator, simpler than the PSI surface area estimator, but also unbiased for uniform surface areas. Both of these estimators are attractive, for example, in measuring and counting cell nuclei, where membrane surface area varies less than volume. Furthermore, they have no shape bias whatsoever. This paper also examines the general relationship between boundary- and area-sampled estimates, and we clarify the formal connection between our volume estimator and the PSI surface area estimator. We also calculate and compare their theoretical efficiencies.