The ‘corpuscle’ stereological problem—re‐evaluation using slab fragment volumes and application to the correction of DNA histograms from sections of spherical nuclei

SUMMARY A new category of stereological size distribution unfolding models is introduced. It is based on the use of the volumes of particle slab fragments, in addition to their profile dimensions. When spheres are cut by a slab of known (constant) thickness, an estimation of discrete sphere sizes from section data is then possible, as only one parent sphere solution exists for any slab fragment, given the latter's projection size and volume. The unfolding algorithm consists in sequentially testing a set of equations: only one of the solutions satisfies various constraints on bounds. A precise determination of the section thickness is required. Truncation parameters, instead of being troublesome inputs as in classical unfolding models, become valuable outputs. This model offers the first stereologically valid solution to the important problem of correcting DNA‐amount histograms obtained from sectioned spherical nuclei. Under the (biologically reasonable) assumption that the nuclear volume is proportional to the DNA amount, it is possible to estimate the DNA concentration and, subsequently, compute discrete slab fragment volumes from corresponding DNA values. An application to Feulgen‐stained rat liver sections is shown. Measurements of hepatocytic nuclear‐profile areas and integrated optical densities are obtained by automated image analysis (IBAS), and the model is used to unfold the section‐obtained DNA histogram. A maximum likelihood fitting of the final distribution with chi functions allows a parametric estimation of ploidy frequencies. This model can only be used for acceptably spherically shaped particles.