The applicability to a medium-term bioassay for liver carcinogens of mathematical formulae for the calculation of numbers of foci per volume was examined in F344 rats. Two weeks after initiation with diethylnitrosamine, animals were given test compounds for 6 weeks, partial hepatectomy being performed at week 3. At week 8, the rats were killed, the livers removed and stained immunohistochemically for assessment of glutathione S-transferase P form (GST-P)-positive foci development. Numbers and areas of lesions were measured two-dimensionally using a color image analyzer, and the Enzmann and Campbell formulae for estimation of number and volume per cm3 were applied to the results. In addition, three-dimensional reconstruction of individual foci was performed using up to 150 GST-P stained foci, with the aid of a computerized graphic system. Both two- and three-dimensionally expressed quantitative results were found to adequately demonstrate the modifying potential of test chemicals on hepatocarcinogenesis. The three-dimensional approach was only more accurate if most of the foci were small and the liver was enlarged by compound treatment. Stereological reconstruction revealed that the shape of GST-P-positive foci, especially if relatively large, is not always spherical but that many demonstrate irregular branching forms, so that the assumptions behind stereological estimation are not met. The results therefore show that care must be taken in applying mathematical formulae for the calculation of three-dimensional data.