  The linear-quadratic (LQ) model to describe the survival of irradiated cells
may be the most frequently used biomathematical model in radiotherapy. There
has been an intense debate on the mechanistic origin of the LQ model. An
interesting approach is that of obtaining LQ-like behavior from kinetic models,
systems of differential equations that model the induction and repair of
damage. Development of such kinetic models is particularly interesting for
application to continuous dose rate therapies, such as molecular radiotherapy
or brachytherapy. In this work, we present a simple kinetic model that
describes the kinetics of populations of tumor cells, rather than
lethal/sub-lethal lesions, which may be especially useful for application to
continuous dose rate therapies, as in molecular radiotherapy. The
multi-compartment model consists of a set of three differential equations. The
model incorporates in an easy way different cross-interacting compartments of
cells forming a tumor, and may be of especial interest for studying dynamics of
treated tumors. In the fast dose delivery limit, the model can be analytically
solved, obtaining a simple closed-form expression. Fitting of several surviving
curves with both this solution and the LQ model shows that they produce similar
fits, despite being functionally different. We have also investigated the
operation of the model in the continuous dose rate scenario, firstly by fitting
pre-clinical data of tumor response to 131I-CLR1404 therapy, and secondly by
showing how damage repair and proliferation rates can cause a treatment to
achieve control or not. Kinetic models like the one presented in this work may
be of special interest when modeling response to molecular radiotherapy.
