Caveats: Numerical requirements in graph theory based quantitation of tissue architecture

Graph theory based methods represent one approach to an objective and repro ducible structural analysis of tissue architecture. By these methods, neigh borhood relations between a number of objects (e.g., cells) are explored an d inherent to these methods are therefore certain requirements as to the nu mber of objects to be included in the analysis. However, the question of ho w many objects are required to achieve reproducible values in repeated comp utations of proposed structural features, has previously not been adressed specifically. After digitising HE stained slides and storing them as grey level images, c ell nuclei were segmented and their geometrical centre of gravity were comp uted, serving as the basis for construction of the Voronoi diagram (VD) and its subgraphs. Variations in repeated computations of structural features derived from these graphs were related to the number of cell nuclei include d in the analysis. We demonstrate a large variation in the values of the structural features f rom one computation to another in one and the same section when only a limi ted number of cells (100-500) are included in the analysis. This variation decreased with increasing number of cells analyzed. The exact number of cel ls required to achieve reproducible values differ significantly between tis sues, but not between separate cases of similar lesions. There are no signi ficant differences between normal and malignantly changed tissues in oral m ucosa with respect to how many cells must be included. For graph theory based analysis of tissue architecture, care must be taken to include an adequate number of objects; for some of the structural featur es we have tested, more than 3000 cells.