Response of tumor spheroids to radiation: modeling and parameter estimation

We propose a spatially distributed continuous model for the spheroid responseto radiation, in which the oxygen distribution is represented by means of a diffusionconsumptionequation and the radiosensitivity parameters depend on the oxygen concentration.The induction of lethally damaged cells by a pulse of radiation, their death, andthe degradation of dead cells are included. The compartments of lethally damaged cellsand of dead cells are subdivided into different subcompartments to simulate the delaysthat occur in cell death and cell degradation, with a gain in model flexibility. It is shownthat, for a single irradiation and under the hypothesis of a sufficiently small spheroid radius,the model can be reformulated as a linear stationary ordinary differential equationsystem. For this system, the parameter identifiability has been investigated, showing thatthe set of unknown parameters can be univocally identified by exploiting the responseof the model to at least two different radiation doses. Experimental data from spheroidsoriginated from different cell lines are used to identify the unknown parameters and totest the predictive capability of the model with satisfactory results.Keywords Tumor spheroids · Radiotherapy · Linear quadratic model