Hybrid Simulation of tumor growth combining Cellular Automata with continuous state dynamics

Cellular Automaton theory has proved to be an innovative and reliable tool in describing complex processes such as tumor growth. The concept is extended with special interest on the extrusion of tissue with regard to angiogenesis. The model is divided into different components where the discrete states of the cellular automaton interact with the continuous states from the description of the nutrient supply. Computation of such models can be compared with clinical data from oncology and can provide a deeper understanding of tumor dynamics. The model under observation bases on an inhomogeneous nutrient supply and is able to simulate different supply scenarios. Therefore an arterial tree serves as input for the nutrient distribution. The supply is described by a diffusion process. The nutrient supply on the other hand serves as input for the cellular automaton which governs the growth of the simulated tumor. Angiogenesis is introduced by subsequent modification of the vascular network. The parameters are tuned to attain exponential growth with fixed growth factors in homogeneous environments. The model can be used to simulate tumor growth with a special focus on the effects of angiogenesis.