RESUMO
The medial axis is an important shape representation that finds a wide range of applications in shape analysis. For large-scale shapes of high resolution, a progressive medial axis representation that starts with the lowest resolution and gradually adds more details is desired. In this paper, we propose a fast and robust geometric algorithm that computes progressive medial axes of a large-scale planar shape. The key ingredient of our method is a novel structural analysis of merging medial axes of two planar shapes along a shared boundary. Our method is robust by separating the analysis of topological structure from numerical computation. Our method is also fast and we show that the time complexity of merging two medial axes is O(n lognv) , where n is the number of total boundary generators, nv is strictly smaller than n and behaves as a small constant in all our experiments. Experiments on large-scale polygonal data and comparison with state-of-the-art methods show the efficiency and effectiveness of the proposed method.
RESUMO
BACKGROUND: To investigate the expression of cyclin-dependent kinase 8 (CDK8) and ß-catenin in colon cancer and evaluate the role of CDK8 in the proliferation, apoptosis and cell cycle progression of colon cancer cells, especially in HCT116 cell line. METHODS: Colon cancer cell line HCT116 was transfected with small interfering RNA (siRNA) targeting on CDK8. After CDK8-siRNA transfection, mRNA and protein expression levels of CDK8 and ß-catenin were determined by reverse transcriptase-polymerase chain reaction (RT-PCR) and Western blot assay in HCT116 cells. Cell proliferation was measured by 3-(4, 5-Dimethylthiazol-2-yl)-2, 5-diphenyltetrazolium bromide Methylthiazolyl tetrazolium (MTT) assay, and cell cycle distribution and apoptosis were analyzed by flow cytometry analysis (FACS). CDK8 and ß-catenin protein levels were also examined by real-time PCR and immunohistochemistry (IHC) in colon cancer tissues and adjacent normal tissues. RESULTS: After CDK8 specific siRNA transfection, mRNA and protein expression levels of CDK8 and ß-catenin in HCT116 cells were noticeably decreased (P < 0.05). CDK8 specific siRNA transfection inhibited HCT116 cells' proliferation and facilitated their apoptosis significantly (P < 0.05). In addition, the proportion of HCT116 cells in the G0/G1 phase was remarkably increased after CDK8-siRNA transfection (P < 0.05). The expression levels of CDK8 and ß-catenin in adjacent normal tissues were lower than in tumor tissues (P < 0.05). Moreover, the expression of CDK8 was correlated with the expression of ß-catenin in both tumor and adjacent normal tissues (P < 0.05). CONCLUSIONS: CDK8 and ß-catenin were expressed in colon cancer at a high frequency. CDK8 specific siRNA transfection down-regulated the expression of CDK8 in colon cancer cells, which was also associated with a decrease in the expression of ß-catenin Moreover, CDK8 specific siRNA inhibited the proliferation of colon cancer cells, promoted their apoptosis and arrested these cells in the G0/G1 phase. Interference of CDK8 might be an effective strategy through ß-catenin regulation of colon cancer.
