title: Stochastic model for tumor control probability: effects of cell cycle and (a)symmetric proliferation.
abstract: BACKGROUND
  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.
  
  
  METHODS
  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. 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.
  
  
  RESULTS
  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. We also present the results of TCP as a function of time for different values of asymmetric division factor.
  
  
  CONCLUSIONS
  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.
authors.forename: Andrew
authors.initials: A
authors.lastname: Dhawan
authors.forename: Kamran
authors.initials: K
authors.lastname: Kaveh
authors.affiliation: Department of Mathematics, University of Waterloo, N2L 3G1 Waterloo, ON, Canada. kohandel@uwaterloo.ca.
authors.forename: Mohammad
authors.initials: M
authors.lastname: Kohandel
authors.forename: Sivabal
authors.initials: S
authors.lastname: Sivaloganathan
mesh_terms: D002453:Cell Cycle; D049109:Cell Proliferation; D006801:Humans; D009369:Neoplasms / Q000473:pathology / Q000517:prevention & control*; D011336:Probability; D013269:Stochastic Processes