SUMMARY 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.

Summary A series of three‐dimensional image analysis tools are used to measure the three‐dimensional orientation of nuclei of myocardial cells. Confocal scanning laser microscopy makes it possible to acquire series of sections up to 100 μm inside thick tissue sections. A mean orientation vector of unit length is calculated for each segmented nucleus. The global orientation statistics are obtained by calculating the vectorial sum of the nuclear unit vectors. The final orientation is expressed by a mean azimuth angle, an elevation angle and a measure of the angular homogeneity. The method is illustrated for two different regions of the myocardium (interventricular septum and papillary muscle) of a normal human fetal heart. This quantitative method will be used to assess and calibrate the information provided by polarized light microscopy.

The study of the topological organisation of myocardial cells is a basic requirement for the understanding of the mechanical design of the normal and pathological heart. We developed a technique based on multiparametric image analysis of transmitted polarized light to generate maps of the azimuth and the elevation angles of the myocardial cells. The properties of birefringence of the myocardium embedded in methylmetacrylate were measured in papillary muscles with monitored 3D orientation. This birefringence is positive uniaxial with a 0 degree extinction angle when the axis of the fiber is parallel to the axis of the polarizer or the analyzer. Thick sections were studied between crossed polars, and four images of each section were digitized for an angle of the polarizer with the section varying from 0-67.5 degrees in steps of 22.5 degrees. The amounts of transmitted light for each setup of the polarizer were combined in order to extract the values of the azimuth angle (modulo 90 degrees) and the elevation angle of the myocardial cells, according to the Johannsen equation. The respective maps of these angles were calculated and then assessed with confocal scanning laser microscopy. This method provides an efficient and accurate tool for the study of the histological architecture of the fetal and neonatal heart.

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