Spatio-temporal cell dynamics in tumour spheroid irradiation

Multicellular tumour spheroids are realistic in vitro systems in radiation research that integrate cell-cell interaction and cell cycle control by factors in the medium. The dynamic reaction inside a tumour spheroid triggered by radiation is not well understood. Of special interest is the amount of cell cycle synchronisation which could be triggered by irradiation, since this would allow follow-up irradiations to exploit the increased sensitivity of certain cell cycle phases. In order to investigate these questions we need to support irradiation experiments with mathematical models. In this article a new model is introduced combining the dynamics of tumour growth and irradiation treatments. The tumour spheroid growth is modelled using an agent-based Delaunay/Voronoi hybrid model in which the cells are represented by weighted dynamic vertices. Cell properties like full cell cycle dynamics are included. In order to be able to distinguish between different cell reactions in response to irradiation quality we introduce a probabilistic model for damage dynamics. The overall cell survival from this model is in agreement with predictions from the linear-quadratic model. Our model can describe the growth of avascular tumour spheroids in agreement to experimental results. Using the probabilistic model for irradiation damage dynamics the classic 'four Rs' of radiotherapy can be studied in silico. We found a pronounced reactivation of the tumour spheroid in response to irradiation. A majority of the surviving cells is synchronized in their cell cycle progression after irradiation. The cell synchronisation could be actively triggered and should be exploited in an advanced fractionation scheme. Thus it has been demonstrated that our model could be used to understand the dynamics of tumour growth after irradiation and to propose optimized fractionation schemes in cooperation with experimental investigations.