Department of Pathology, Shonan Atugi Hospital, Nurumizu, Atsugi, Kanagawa 243-8551, Japan
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(Received October 15, 2011; Accepted March 15, 2012)
Abstract. 3D shapes of biological cells and their arrangement were discussed. The positional relationship between cell arrangement and blood vessels was studied, and it was found that the blood vessels go along some edges of the cells in the tissue. A quantitative topological analysis of the 3D microvascular network of the liver, i.e. hepatic sinusoids, was performed with the aid of a computer system for reconstruction from serial tissue sections. The pathologic change of the sinusoids (vascular channels between the liver cell plates) in cirrhosis (hard liver with nodular surface) and hepatocellular carcinoma (primary malignant epithelial tumor of the liver) was also studied. There was a statistically significant difference of the first Betti number, p1, of the sinusoids in the three groups, the two pathologic cases and normal one. A 2D index was proposed, based on the results from the reconstruction study and Alexander duality theorem in topology, to perform rapid structural analysis of the 3D sinusoidal network. It was concluded that the 2D index was useful for estimating the complexity degree of the 3D sinusoidal network.
Keywords: 3D Cell Arrangement, Topology, Alexander Duality Theorem, Hepatic Sinusoids, Pathologic Change