Determining nucleolar multiplicity and cell number from sectional data

The occurrence of more than one nucleolus within the cellular nucleus (polynucleolarity) is a well-known phenomenon during the proliferative cell cycle, both under normal and pathological conditions (e.g. neoplasia). It can also be observed in neuronal nuclei at early stages of their maturation. Polynucleolarity merits investigation for cytological reasons. In an histological section, the observed number of nucleoli in a nucleus may be smaller than the actual number. In order to estimate the true distribution of the number of nucleoli per nucleus from the observed distribution, the mathematical relation between these distributions is derived on the basis of rather restrictive stereological assumptions. It is indicated how these distributions can be estimated from the data available and how the statistical uncertainties involved can be expressed. This paper arose from making cell counts. Two methods may be applied: all visible nuclear profiles are counted, nuclear profiles are only included if at least one nucleolus is visible in the section. We recommended a combination of these two methods. An advantage of our theory for determining cell number is that one can often manage without the rather restrictive stereological assumptions needed hitherto. The advantage of expressing statistical uncertainties in estimated nucleolar multiplicity probabilities and cell numbers is indicated.