A stochastic model of cancer growth with immune response

A cellular automaton model for the growth of an avascular tumor on a two-dimensional square lattice is presented. The pattern formation and the growth of the cell population are investigated by using a Monte Carlo simulation. A microscopic description of the immune system response, including cell proliferation, cell death, and cell degradation, is used to simulate the growth. In particular, the escape rate for cancer from immune surveillance is included for consistency with experimental observations. The simulation results give rise to a growth curve with an explanation on a microscopic scale that is shown to agree well with experimental animal tumor growth and relevant biological implications. Our model clearly shows that an increase in the lysis rate leads to a decrease in the proliferation rate of cancer cells. The spatial distribution of proliferated cell and the fractal dimension of the boundary are also measured.