  Estimating the required dose in radiotherapy is of crucial importance since
the administrated dose should be sufficient to eradicate the tumor and at the
same time should inflict minimal damage on normal cells. The probability that a
given dose and schedule of ionizing radiation eradicates all the tumor cells in
a given tissue is called the tumor control probability (TCP), and is often used
to compare various treatment strategies used in radiation therapy. In this
paper, we aim to investigate the effects of including cell-cycle phase on the
TCP by analyzing a stochastic model of a tumor comprised of actively dividing
cells and quiescent cells with different radiation sensitivities. We derive an
exact phase-diagram for the steady-state TCP of the model and show that at
high, clinically-relevant doses of radiation, the distinction between active
and quiescent tumor cells (i.e. accounting for cell-cycle effects) becomes of
negligible importance in terms of its effect on the TCP curve. However, for
very low doses of radiation, these proportions become significant determinants
of the TCP. Moreover, we use a novel numerical approach based on the method of
characteristics for partial differential equations, validated by the Gillespie
algorithm, to compute the TCP as a function of time. We observe that our
results differ from the results in the literature using similar existing
models, even though similar parameters values are used, and the reasons for
this are discussed.
