title: Mathematical models of radiation action on living cells: From the target theory to the modern approaches. A historical and critical review.
abstract: Cell survival is conventionally defined as the capability of irradiated cells to produce colonies. It is quantified by the clonogenic assays that consist in determining the number of colonies resulting from a known number of irradiated cells. Several mathematical models were proposed to describe the survival curves, notably from the target theory. The Linear-Quadratic (LQ) model, which is to date the most frequently used model in radiobiology and radiotherapy, dominates all the other models by its robustness and simplicity. Its usefulness is particularly important because the ratio of the values of the adjustable parameters, α and β, on which it is based, predicts the occurrence of post-irradiation tissue reactions. However, the biological interpretation of these parameters is still unknown. Throughout this review, we revisit and discuss historically, mathematically and biologically, the different models of the radiation action by providing clues for resolving the enigma of the LQ model.
authors.affiliation: Institut National de la Santé et de la Recherche Médicale (INSERM), UMR 1052, Radiobiology Group, Cancer Research Centre of Lyon, 69008 Lyon, France; Université Saint-Joseph, Faculté des sciences, 1107-2050 Beyrouth, Liban; Centre National de la Recherche Scientifique (CNRS), GDR 3536, Nuclear Architecture and Dynamics, Université Pierre et Marie Curie-Paris 6, 75252 Paris, France.
authors.forename: Larry
authors.initials: L
authors.lastname: Bodgi
authors.affiliation: Institut National de la Santé et de la Recherche Médicale (INSERM), UMR 1052, Radiobiology Group, Cancer Research Centre of Lyon, 69008 Lyon, France; Université Claude Bernard-Lyon 1, Institut Camille Jordan, 69622, Villeurbanne, France.
authors.forename: Aurélien
authors.initials: A
authors.lastname: Canet
authors.affiliation: Université Claude Bernard-Lyon 1, Institut Camille Jordan, 69622, Villeurbanne, France.
authors.forename: Laurent
authors.initials: L
authors.lastname: Pujo-Menjouet
authors.affiliation: Centre National de la Recherche Scientifique (CNRS), UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie-Paris 6, Sorbonne Universités, 75252 Paris, France; Centre National de la Recherche Scientifique (CNRS), UMR 5535, Institut de Génétique Moléculaire de Montpellier, Université de Montpellier, 34293 Montpellier, France; Centre National de la Recherche Scientifique (CNRS), GDR 3536, Nuclear Architecture and Dynamics, Université Pierre et Marie Curie-Paris 6, 75252 Paris, France.
authors.forename: Annick
authors.initials: A
authors.lastname: Lesne
authors.affiliation: Centre National de la Recherche Scientifique (CNRS), UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie-Paris 6, Sorbonne Universités, 75252 Paris, France; Centre National de la Recherche Scientifique (CNRS), UMR 5535, Institut de Génétique Moléculaire de Montpellier, Université de Montpellier, 34293 Montpellier, France; Centre National de la Recherche Scientifique (CNRS), GDR 3536, Nuclear Architecture and Dynamics, Université Pierre et Marie Curie-Paris 6, 75252 Paris, France.
authors.forename: Jean-Marc
authors.initials: JM
authors.lastname: Victor
authors.affiliation: Institut National de la Santé et de la Recherche Médicale (INSERM), UMR 1052, Radiobiology Group, Cancer Research Centre of Lyon, 69008 Lyon, France; Centre National de la Recherche Scientifique (CNRS), GDR 3536, Nuclear Architecture and Dynamics, Université Pierre et Marie Curie-Paris 6, 75252 Paris, France.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Foray
mesh_terms: D000818:Animals; D064007:Ataxia Telangiectasia Mutated Proteins / Q000378:metabolism; D002470:Cell Survival / Q000528:radiation effects; D002477:Cells / Q000528:radiation effects*; D002999:Clone Cells; D006801:Humans; D008322:Mammals; D008954:Models, Biological; D011827:Radiation; D011836:Radiation Tolerance / Q000528:radiation effects
chemical_list: D064007:Ataxia Telangiectasia Mutated Proteins
keywords: Cell survival; DSB repair; Ionising radiation; Models of radiation action; Radiosensitivity