A fully coupled binary biochemical reactive-diffusion model with analytic solution

Modeling and computer simulations of tumor growth and tumor response to radiotherapy

A model of tumor growth and tumor response to radiation is introduced in which each tumor cell is taken into account individually. Each cell is assigned a set of radiobiological parameters, and the status of each cell is checked in discrete intervals. Tumor proliferation is governed by the cell cycle times of tumor cells, the growth fraction, the apoptotic capacity of the tumor, and the degree of tumor angiogenesis. The response of tumor cells to radiation is determined by the radiosensitivities and the oxygenation status. Computer simulation is performed on a 3D rigid cubic lattice, starting out from a single tumor cell. Random processes are simulated by Monte Carlo methods. Short cell cycle time, high growth fraction, and tumor angiogenesis all increase tumor proliferation rates. Accelerated time-dose patterns result in lower total doses needed for tumor control, but the extent of dose reduction depends on the kinetics and the radiosensitivities of tumor cells. Tumor angiogenesis alters fully oxygenated and hypoxic fractions within the tumor and subsequently affects the radiation response. It is demonstrated for selected radiobiological parameters that the simulation tools are suitable to quantitatively assess the total doses needed for tumor control. Using the simulation tools, it is feasible to simulate time-dependent effects during fractionated radiotherapy and to compare different time-dose patterns in terms of their tumor control.