Hybrid cellular Potts model for solid tumor growth

We present a hybrid computational framework whose aim is to reproduce and analyze the early growth of a solid tumor. The model couples an extended version of the discrete Cellular Potts Model, used to represent the phenomenological behavior of malignant cells, with a continuous approach of reaction-diffusion equations, employed to describe the evolution of microscopic variables, as the growth factors and the matrix proteins present in the host tissue and the proteolytic enzymes secreted by the tumor. The behavior of each cancer cell is determined by a balance of interaction forces, such as homotypic (cell-cell) and heterotypic (cell-matrix) adhesions and haptotaxis, and is mediated by its molecular state, which regulates the motility and proliferation rate. The resulting model captures the different phases of the development of the tumor mass, i.e. its exponential growth and the subsequent stabilization in a steady-state due to limitations in vital molecules. The proposed approach also predicts the influence on the cancer morphology of changes in specific intercellular adhesive mechanisms.