Application of confocal laser microscopy and three-dimensional Voronoi diagrams for volume and surface estimates of...

This study demonstrates the use of Voronoi tessellation procedures to obtain quantitative morphological data for chromosome territories in the cell nucleus. As a model system, chromosomes 7 and X were visualized in human female amniotic fluid cell nuclei by chromosomal in situ suppression hybridization with chromosome-specific composite probes. Light optical serial sections of 18 nuclei were obtained with a confocal scanning laser fluorescence microscope. A three-dimensional (3-D) tessellation of the image volumes defined by the stack of serial sections was then performed. For this purpose a Voronoi diagram, which consists of convex polyhedra structured in a graph environment, was built for each nucleus. The chromosome territories were extracted by applying the Delaunay graph, the dual of the Voronoi diagram, which describes the neighbourhood in the Voronoi diagram. The chromosome territories were then described by three morphological parameters, i.e. volume, surface area and a roundness factor (shape factor). The complete evaluation of a nucleus, including the calculation of the Voronoi diagram, 3-D visualization of extracted territories using computer graphic methods and parameterization was carried out on a Silicon Graphics workstation and was generally completed within 5 min. The geometric information obtained by this procedure revealed that both X- and 7-chromosome territories were similar in volume. Roundness factors indicated a pronounced variability in interphase shape for both pairs of chromosomes. Surface estimates showed a significant difference between the two X-territories but not between chromosome 7-territories.