title: On the estimation of particle number.
abstract: Two methods are proposed for estimating the number of separated particles within a solid structure per unit volume of structure, Nv. Apart from being arranged with independence of any size parameter, no special assumptions upon the size, shape and orientation of the particles are made. The first method is based on the identity NV = (NA)u . microunits-1, where (NA)u is the mean number of particle sections per unit area of a plane probe Tu which is uniform random within the structure and perpendicular to a given direction u, whereas microunits is the mean particle caliper length along u. The second method uses NV - AA . v-1, where AA is the mean areal fraction of the particles per unit area of section, whereas v is the mean particle volume. The estimation of (NA)u, microunits and v requires the examination of parallel serial sections above and below Tu. Particle model reconstructions are not needed, however. Previous approaches to the problem are discussed.
mesh_terms: D000715:Anatomy / Q000379:methods*; D008433:Mathematics