A biophysical model of cell evolution after cytotoxic treatments: damage, repair and cell response

Abstract

We present a theoretical agent-based model of cell evolution under the action of cytotoxic treatments, such as radioteraphy or chemoteraphy. The major features of cell cycle and proliferation, cell damage and repair, and chemical diffusion are included. Cell evolution is based on a discrete Markov chain, with cells stepping along a sequence of discrete internal states from 'normal' to 'inactive'. Probabilistic laws are introduced for each type of event a cell can undergo during its life cycle: duplication, arrest, apoptosis, senescence, damage, healing. We adjust the model parameters on a series of cell irradiation experiments, carried out in a clinical LINAC at 20 MV, in which the damage and repair kinetics of single- and double-strand breaks are followed. Two showcase applications of the model are then presented. In the first one, we reconstruct the cell survival curves from a number of published low- and high-dose irradiation experiments. We reobtain a very good description of the data without assuming the well-known linear-quadratic model, but instead including a variable DSB repair probability, which is found to spontaneously saturate with an exponential decay at increasingly high doses. As a second test, we attempt to simulate the two extreme possibilities of the so-called 'bystander' effect in radiotherapy: the 'local' effect versus a 'global' effect, respectively activated by the short-range or long-range diffusion of some factor, presumably secreted by the irradiated cells. Even with an oversimplified simulation, we could demonstrate a sizeable difference in the proliferation rate of non-irradiated cells, the proliferation acceleration being much larger for the global than the local effect, for relatively small fractions of irradiated cells in the colony.