A Monte Carlo simulation of the determination of mean particle volume using the Cavalieri estimator.

Abstract

A common morphometric problem is the determination of an estimate of the size of biological particles obtained from measurements made on a sample of profiles observed in sections. Results are reported typically in terms of mean caliper diameter or mean volume of the particle. We have investigated the use of the Cavalieri estimator for obtaining estimates of mean particle volume using a Monte Carlo simulation. Samples of spherical and ellipsoidal particles were generated by computer and serially sectioned at a fixed mean thickness with a small, imposed random variation. The area of each profile was determined and the volume of the particle was calculated according to the Cavalieri estimator. The influence on the estimate of the mean particle volume and its 95% confidence interval was evaluated for several variables: the shape of the particles, the standard deviation of the particle volume in the population, the section thickness, and the standard deviation of the section thickness. The results obtained with the Cavalieri estimator correspond favorably with those obtained with previously reported alternative methods. This leads to a recommendation for the strong consideration for the use of the Cavalieri estimator in cases in which it is technically feasible to obtain at least three sections through the individual particles. Graphs are provided, which relate the confidence interval for the mean volume to the number of particles measured.