Response of tumor spheroids to radiation: modeling and parameter estimation

Bulletin of Mathematical Biology
Alessandro BertuzziCarmela Sinisgalli

Abstract

We propose a spatially distributed continuous model for the spheroid response to radiation, in which the oxygen distribution is represented by means of a diffusion-consumption equation and the radiosensitivity parameters depend on the oxygen concentration. The induction of lethally damaged cells by a pulse of radiation, their death, and the degradation of dead cells are included. The compartments of lethally damaged cells and of dead cells are subdivided into different subcompartments to simulate the delays that occur in cell death and cell degradation, with a gain in model flexibility. It is shown that, 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 equation system. For this system, the parameter identifiability has been investigated, showing that the set of unknown parameters can be univocally identified by exploiting the response of the model to at least two different radiation doses. Experimental data from spheroids originated from different cell lines are used to identify the unknown parameters and to test the predictive capability of the model with satisfactory results.

References

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Feb 14, 2008·Bulletin of Mathematical Biology·A BertuzziC Sinisgalli
Jul 23, 2008·BMC Cancer·Paolo Ubezio, David Cameron

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Citations

Jun 3, 2011·Mathematical Biosciences and Engineering : MBE·Antonio FasanoAlberto Gandolfi
Feb 9, 2012·Journal of Mathematical Biology·A BertuzziC Sinisgalli
Mar 7, 2014·Bulletin of Mathematical Biology·J C L AlfonsoL Núñez
Mar 25, 2017·Mathematical Medicine and Biology : a Journal of the IMA·Ana Victoria Ponce BobadillaHelen Byrne
Jan 19, 2018·Mathematical Medicine and Biology : a Journal of the IMA·C BruniC Sinisgalli

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