Homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiotherapy

A few previous works of the authors derived and discussed the space–time mathematical description, the PhasTraM model, for oncogenic hyperplasia regarded as a genotoxically activated homeorhetic dysfunction. The model is based on the fluid-to-solid-and-back transitions and nonlinear reaction–diffusion equations relevant to a series of the key biomedical facts, and some distinguishing features of living systems. The first computer-simulation results have also been reported. The present work generalizes the PhasTraM model for the effect of radiation therapies (RTs), both external and internal. The resulting model also includes the autocrine mechanism promoting oncogenic hyperplasia and the suppression of this process by certain drugs. The autocrine signalling is implemented by the transforming-growth-factor-αα (TGF-αα) molecules released by the cells and bound to the epidermal-growth-factor receptors (EGFRs) at the cell surface. The suppression can be carried out by a drug deactivating the mentioned molecules. The work also presents and discusses examples of the computer-simulation results for four different settings of the applied RT. A few directions for future research, as well as prospective applications of the model and developed software, are also discussed.