“…As in Malinen et al (2006) and Sovik et al (2007b), we ignore the effect of tumor proliferation for notational simplicity; it can, however, be incorporated without any changes to our methodology. This holds because, according to the standard tumor proliferation model based on tumor doubling times, the proliferation term does not depend on radiation dose (Williams et al 1985, Fowler 1990, 2001, Fowler 2007, 2008, Yang and Xing 2005a, Ho et al 2009, Qi et al 2012. Consequently, the proliferation term factors out of our objective function as a constant multiplier and does not affect the optimal fluence-maps.…”