title: From cell population models to tumor control probability: including cell cycle effects.
abstract: BACKGROUND
  Classical expressions for the tumor control probability (TCP) are based on models for the survival fraction of cancer cells after radiation treatment. We focus on the derivation of expressions for TCP from dynamic cell population models. In particular, we derive a TCP formula for a generalized cell population model that includes the cell cycle by considering a compartment of actively proliferating cells and a compartment of quiescent cells, with the quiescent cells being less sensitive to radiation than the actively proliferating cells.
  
  
  METHODS
  We generalize previously derived TCP formulas of Zaider and Minerbo and of Dawson and Hillen to derive a TCP formula from our cell population model. We then use six prostate cancer treatment protocols as a case study to show how our TCP formula works and how the cell cycle affects the tumor treatment.
  
  
  RESULTS
  The TCP formulas of Zaider-Minerbo and of Dawson-Hillen are special cases of the TCP formula presented here. The former one represents the case with no quiescent cells while the latter one assumes that all newly born cells enter a quiescent cell phase before becoming active. From our case study, we observe that inclusion of the cell cycle lowers the TCP.
  
  
  CONCLUSIONS
  The cell cycle can be understood as the sequestration of cells in the quiescent compartment, where they are less sensitive to radiation. We suggest that our model can be used in combination with synchronization methods to optimize treatment timing.
authors.affiliation: Centre for Mathematical Biology, Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, AB, Canada. thillen@math.ualberta.ca
authors.forename: Thomas
authors.initials: T
authors.lastname: Hillen
authors.forename: Gerda
authors.initials: G
authors.lastname: de Vries
authors.forename: Jiafen
authors.initials: J
authors.lastname: Gong
authors.forename: Chris
authors.initials: C
authors.lastname: Finlay
mesh_terms: D002453:Cell Cycle / Q000528:radiation effects*; D045744:Cell Line, Tumor; D002470:Cell Survival / Q000528:radiation effects*; D004307:Dose-Response Relationship, Radiation; D006801:Humans; D008297:Male; D008432:Mathematical Computing; D015233:Models, Statistical; D014411:Neoplastic Stem Cells / Q000528:radiation effects*; D016012:Poisson Distribution; D011336:Probability; D011471:Prostatic Neoplasms / Q000532:radiotherapy; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted; D013269:Stochastic Processes