title: New techniques for three-dimensional data analysis in histopathology.
abstract: This paper describes two three-dimensional (3D) analytical techniques based on 3D mathematical morphology that have been found useful in quantifying the 3D spatial distribution of S-phase cells in a tubular tumor of the human breast. One technique is based on determining the normalized radial distribution of the S-phase cells with respect to the central axis of the tumor. The other technique is a novel extension of the polyhedra of Voronoi to quantify the distribution. The Voronoi polyhedron of a given S-phase cell nucleus is that polyhedron of minimal volume defined by planes all of which are perpendicular bisectors of the vectors extending from the given cell to all other S-phase cells in the tumor. Methods are demonstrated for generating these polyhedra and for histogramming their volumes. An illustration is given of using the histogram to sort the S-phase cells according to their 3D positional relationships. Displays showing the sorted cells in 3D and their associated Voronoi polyhedra are provided.
authors.affiliation: Kensal Consulting, Tucson, Arizona 85711.
authors.forename: K
authors.initials: K
authors.lastname: Preston
authors.forename: R
authors.initials: R
authors.lastname: Siderits
mesh_terms: D000328:Adult; D001943:Breast Neoplasms / Q000473:pathology*; D004273:DNA, Neoplasm / Q000032:analysis*; D005260:Female; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008432:Mathematical Computing; D008954:Models, Biological; D010503:Periodic Acid-Schiff Reaction; D016196:S Phase; D012984:Software; D013194:Staining and Labeling
chemical_list: D004273:DNA, Neoplasm