Abstract
BackgroundEstimating 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.MethodIn 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. 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.ResultsWe 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. We also present the results of TCP as a function of time for different values of asymmetric division factor.ConclusionWe 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.
Highlights
External beam radiotherapy remains one of the most common treatment options for various cancers
We derive an exact phase-diagram for the steady-state tumor control probability (TCP) of the model and show that at high, clinically-relevant doses of radiation, the distinction between active and quiescent tumor cells becomes of negligible importance in terms of its effect on the TCP curve
We present the results of TCP as a function of time for different values of asymmetric division factor
Summary
External beam radiotherapy remains one of the most common treatment options for various cancers. A widely used model for radiation treatment is the linear-quadratic (LQ) model [1,2] This model estimates the surviving fraction of cancer cells after each treatment based on the total dose, and has the form: S(D) = e−αD−βD2 , (1). A model for the TCP accounting for cell proliferation dynamics was suggested by [6] Their model is a birth-death process for the probability distribution function of the tumor cells, pn(t), and the corresponding master equation of such a birth-death model is: dpn(t) dt. 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
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