A quantitative theoretical model for the development of malignancy in ductal carcinoma in situ

Mathematical models and clinical observations have demonstrated that microenvironmental hypoxia and acidosis are important selection factors during the later stages of the somatic evolution of breast cancer. The consequent promotion of constitutive upregulation of glycolysis and resistance to acid-induced cellular toxicity is hypothesized to be critical for the ability of cancer cells to invade host tissue. In this work we developed a 3D fixed lattice cellular automata model to study the role of these two phenotypes in determining morphology and the potential for invasion of ductal carcinoma in situ (DCIS), which in this work is defined as the erosion of a healthy epithelial cell layer and direct contact with the basement membrane. The model was conceived as a 40-cell wide epithelial duct surrounded by blood vessels and composed of a basement membrane and one internal layer of epithelial cells. Our results show that an increment in the order of 8-fold in glucose metabolism and an increase in acid resistance corresponding to pH thresholds of approximately 6.8 and 6.45 for quiescence and death, respectively, are required for the tumor to breach through the layer of healthy epithelial cells and reach the basement membrane as a first step for invasion. Our model also suggests correlations between classic morphologies and different values of hyperglycolytic and acid-resistant phenotypes, indicating that immunohistochemistry studies targeting these genes may improve the predictive power of morphological analyses of biopsies.