Stereological estimation of volume ratios by systematic sections

Abstract

Two related problems are explored. Firstly, a single opaque solid Ω₁ of arbitrary size and shape, containing an arbitrarily shaped phase Ω₂, is considered. The problem is to estimate the minimum number of systematic sections m, necessary to estimate the volume ratio v = V(Ω₂)/V(Ω₁) with a coefficient of error of at most _γ0 with a probability 1 - α. Secondly, we consider a population of such specimens. The second problem is to estimate the optimum number n of specimens to be sampled and the number m of systematic sections per specimen in order to estimate the mean volume ratio of the population with a relative error of at most ∍₀ with a probability 1 - α. General guidelines for solving the two problems are presented. Practical results applicable to two populations of mouse and guinea-pig lymph nodes, exhibiting a wide variation in size and shape, are obtained.