... For any single radiation modality, the optimal number of fractions and the corresponding dose in each fraction depend on (i) the relative difference between the tumour's and the healthy tissue's biological response to that modality, (ii) the dose deposition profile of that modality with respect to the anatomy of the irradiated area and (iii) the tumour proliferation rate. The trade-offs in determining an optimal number of fractions and doses have been studied over the past several decades mainly for photon therapy (Rockwell, 1988;Fowler, 1990Fowler, , 2001Fowler, , 2007Fowler, , 2008Fowler & Ritter, 1995;Jones et al., 1995;Horiot et al., 1997Horiot et al., , 1992Fu et al., 2000;Garden, 2001;Armpilia et al., 2004;Ahamad et al., 2005;Trotti et al., 2005;Yang & Xing, 2005;Ho et al., 2009;Marzi et al., 2009;Arcangeli et al., 2010;Kader et al., 2011;Keller et al., 2012;Mizuta et al., 2012;Bertuzzi et al., 2013;Unkelbach et al., 2013a, b;Bortfeld et al., 2015;Saberian et al., 2015Saberian et al., , 2016Saberian et al., , 2017Badri et al., 2016). 364 S. NOUROLLAHI ET AL. ...