Derivation of the Tumour Control Probability (TCP) from a Cell Cycle Model. Issue 2 (2006)

• Record Type: Journal Article
• Authors: Dawson Dawson, A. A.; Hillen Hillen, T. T.
• Is Part Of: Computational and mathematical methods in medicine. Volume 7:Issue 2/3(2006)
• Page Start: 121
• Page End: 141
• Publication Date: 2006
• Subjects: Radiation treatment -- Cell cycle -- Tumor control probability -- Birth–death process; Medicine -- Computer simulation -- Periodicals; Medicine -- Mathematical models -- Periodicals; 610.11
• DOI: 10.1080/10273660600968937
• Languages: English
• ISSNs: 1748-670X

Abstract

Abstract : 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 G 0 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.