Method for decreasing the statistical variance of stereological estimates

Abstract

Three methods are described for decreasing the statistical variance of stereological estimates. Method 1 uses profile boundaries and surface densities of nuclear membranes, measured in thin sections, to estimate the mean diameter, surface area, and numerical density of spherical and nonspherical nuclei. For the guinea pig pancreas (number(m) = 4), the standard deviations (s.d.) as a percent of the mean for the estimates of the diameters of the exocrine, duct, and endothelial cell nuclei were 1.5%, 3.3% and 1.4%. The estimate for the mean diameter of exocrine nuclei (6.4 +/- 0.1 micron) was based on a spherical model, whereas the estimates for the diameters of the nonspherical (and nonconvex) nuclei of the duct (6.4 +/- 0.2 micron) and endothelial (6.7 +/- 0.1 micron) cells were calculated from the numerical density of the exocrine cells and the relative frequencies of the three cell types (determined from serial reconstructions). In an average cubic centimeter, there were 6.17 X 10(8) +/- 0.32 X 10(8) (s.d. 5.1% of mean) exocrine cells, 1.64 X 10(8) +/- 0.18 X 10(8) (10.9%) duct cells, and 0.803 X 10(8) +/- 0.13 X 10(8) (16.6%) endothelial cells. In contrast to method 1, conventional stereological approaches were found to have standard deviations two- to eightfold larger. Method 2 uses a mean nuclear surface area and a ratio of surface densities to estimate the surface area of a membrane compartment in an average cell. A s.d. equal to 6.5% of the mean was found for the surface area of the outer mitochondrial membrane in an average exocrine cell (672 +/- 43.6 micron 2), which represented an almost fourfold reduction in the s.d. compared with an earlier estimate (Bolender, 1974). Method 3 relates the surface area of a membrane compartment to a standard number of cells. Referenced to 10(6) cells, for example, the surface area of the inner nuclear membrane of endothelial cells had a s.d. equal to 2.9% of the mean, whereas the surface density of the same membrane compartment-referenced to a cm3 of cells-had a s.d. at 19.1% of the mean. In this case, method 3 produced almost a sevenfold reduction in the standard deviation. Similar results were found for exocrine and duct cells. The results of the study indicate that the standard deviation of a stereological estimate can be reduced to a minimum by using a mean nuclear profile boundary to generate an estimate for a nuclear numerical density, which, in turn, can be combined with a surface density to obtain average cell information.