title: On the surviving fraction in irradiated multicellular tumour spheroids: calculation of overall radiosensitivity parameters, influence of hypoxia and volume effects.
abstract: We model the heterogeneous response to radiation of multicellular tumour spheroids assuming position- and volume-dependent radiosensitivity. We propose a method to calculate the overall radiosensitivity parameters to obtain the surviving fraction of tumours. A mathematical model of a spherical tumour with a hypoxic core and a viable rim which is a caricature of a real tumour is constructed. The model is embedded in a two-compartment linear-quadratic (LQ) model, assuming a mixed bivariated Gaussian distribution to attain the radiosensitivity parameters. Ergodicity, i.e., the equivalence between ensemble and volumetric averages is used to obtain the overall radiosensitivities for the two compartments. We obtain expressions for the overall radiosensitivity parameters resulting from the use of both a linear and a nonlinear dependence of the local radiosensitivity with position. The model's results are compared with experimental data of surviving fraction (SF) for multicellular spheroids of different sizes. We make one fit using only the smallest spheroid data and we are able to predict the SF for the larger spheroids. These predictions are acceptable particularly using bounded sensitivities. We conclude with the importance of taking into account the contribution of clonogenic hypoxic cells to radiosensitivity and with the convenience of using bounded local sensitivities to predict overall radiosensitivity parameters.
authors.affiliation: Department of Physics, Facultad de Ciencias Fisico Matematicas y Naturales, Instituto de Matematica Aplicada San Luis (CONICET), Universidad Nacional de San Luis, Argentina. jhoras@unsl.edu.ar
authors.forename: Jorge A
authors.initials: JA
authors.lastname: Horas
authors.forename: Osvaldo R
authors.initials: OR
authors.lastname: Olguin
authors.forename: Marcos G
authors.initials: MG
authors.lastname: Rizzotto
mesh_terms: D000818:Animals; D015687:Cell Hypoxia / Q000502:physiology* / Q000528:radiation effects; D048429:Cell Size / Q000528:radiation effects; D002470:Cell Survival / Q000528:radiation effects*; D003198:Computer Simulation; D004247:DNA / Q000528:radiation effects; D004249:DNA Damage; D004307:Dose-Response Relationship, Radiation; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology* / Q000503:physiopathology*; D011829:Radiation Dosage; D011836:Radiation Tolerance / Q000502:physiology*; D018874:Spheroids, Cellular / Q000473:pathology* / Q000528:radiation effects*; D014407:Tumor Cells, Cultured
chemical_list: D004247:DNA