Computational and Mathematical Methods in Medicine
Volume 7 (2006), Issue 2-3, Pages 121-141

Derivation of the Tumour Control Probability (TCP) from a Cell Cycle Model

University of Alberta, Edmonton, Alta., T6G 2G1, Canada

Received 3 May 2006; Revised 22 June 2006; Accepted 22 August 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, a model for the radiation treatment of cancer which includes the effects of the cell cycle is derived from first principles. A malignant cell population is divided into two compartments based on radiation sensitivities. The active compartment includes the four phases of the cell cycle, while the quiescent compartment consists of the G0 state. Analysis of this active-quiescent radiation model confirms the classical interpretation of the linear quadratic (LQ) model, which is that a larger α/β ratio corresponds to a fast cell cycle, while a smaller ratio corresponds to a slow cell cycle. Additionally, we find that a large α/β ratio indicates the existence of a significant quiescent phase. The active-quiescent model is extended as a nonlinear birth–death process in order to derive an explicit time dependent expression for the tumour control probability (TCP). This work extends the TCP formula from Zaider and Minerbo and it enables the TCP to be calculated for general time dependent treatment schedules.