An improved stereologic method for three-dimensional estimation of particle size distribution from observations in two dimensions and its application.

Single enzyme-altered hepatocytes; altered hepatic foci (AHF); and nodular lesions have been implicated, respectively in the processes of initiation, promotion, and progression in rodent hepatocarcinogenesis. Qualitative and quantitative analyses of such lesions have been utilized both to identify and to determine the potency of initiating, promoting, and progressor agents in rodent liver. Of a number of possible parameters determined in the study of such lesions, estimation of the number of foci or nodules in the liver is very important. The method of Saltykov has been used for estimating the number of AHF in rat liver. However, in practice, the Saltykov calculation has at least two weak points: (a) the size class range is limited to 12, which in many instances is too narrow to cover the range of AHF data obtained; and (b) under some conditions, the Saltykov equation generates negative values in several size classes, an obvious impossibility in the real world. In order to overcome these limitations in the Saltykov calculations, a study of the particle size distribution in a wide-range, polydispersed sphere system was performed. A stereologic method, termed the 25F Association method, was developed from this study. This method offers 25 association factors that are derived from the frequency of different-sized transections obtained from transecting a spherical particle, thus expanding the size class range to be analyzed up to 25, which is sufficiently wide to encompass all rat AHF found in most cases. This method exhibits greater flexibility, which allows adjustments to be made within the calculation process when NA((k,k)), the net number of transections from the same size spheres, was found to be a negative value, which is not possible in real situations. The reliability of the 25F Association method was tested thoroughly by computer simulation in both monodispersed and polydispersed sphere systems. The test results were compared with the original Saltykov method. We found that the 25F Association method yielded a better estimate of the total number of spheres in the three-dimensional tissue sample as well as the detailed size distribution information. Although the 25F Association method was derived from the study of a polydispersed sphere system, it can be used for continuous size distribution sphere systems. Application of this method to the estimation of parameters of preneoplastic foci in rodent liver is presented as an example of its utility. An application software program, 3D_estimation.exe, which uses the 25F Association method to estimate the number of AHF in rodent liver, has been developed and is now available at the website of this laboratory.