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Prostate cancer (CaP) is evidenced by profound changes in the spatial distribution of cells. Spatial arrangement and architectural organization of nuclei, especially clustering of the cells, within CaP histopathology is known to be predictive of disease aggressiveness and potentially patient outcome. Quantitative histomorphometry is a relatively new field which attempt to develop and apply novel advanced computerized image analysis and feature extraction methods for the quantitative characterization of tumor morphology on digitized pathology slides. Recently, graph theory has been used to characterize the spatial arrangement of these cells by constructing a graph with cell/nuclei as the node. One disadvantage of several extant graph based algorithms (Voronoi, Delaunay, Minimum Spanning Tree) is that they do not allow for extraction of local spatial attributes from complex networks such as those that emerges from large histopathology images with potentially thousands of nuclei. In this paper, we define a cluster of cells as a node and construct a novel graph called Cell Cluster Graph (CCG) to characterize local spatial architecture. CCG is constructed by first identifying the cell clusters to use as nodes for the construction of the graph. Pairwise spatial relationship between nodes is translated into edges of the CCG, each of which are assigned certain probability, i.e. each edge between any pair of a nodes has a certain probability to exist. Spatial constraints are employed to deconstruct the entire graph into subgraphs and we then extract global and local graph based features from the CCG. We evaluated the ability of the CCG to predict 5 year biochemical failures in men with CaP and who had previously undergone radical prostatectomy. Extracted features from CCG constructed using nuclei as nodal centers on tissue microarray (TMA) images obtained from the surgical specimens of 80 patients allowed us to train a support vector machine classifier via a 3 fold randomized cross validation procedure which yielded a classification accuracy of 83:1±1:2%. By contrast the Voronoi, Delaunay, and Minimum spanning tree based graph classifiers yielded corresponding classification accuracies of 67:1±1:8% and 60:7±0:9% respectively.
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