Tumour control probability: a formulation applicable to any temporal protocol of dose delivery

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Abstract
An analytic expression for the tumour control probability (TCP), valid for any temporal distribution of dose, is discussed. The TCP model, derived using the theory of birth-and-death stochastic processes, generalizes several results previously obtained. The TCP equation is where S (t ) is the survival probability at time t of the n clonogenic tumour cells initially present (at t = 0), and b and d are, respectively, the birth and death rates of these cells. Equivalently, b = 0.693/T pot and d /b is the cell loss factor of the tumour. In this expression t refers to any time during or after the treatment; typically, one would take for t the end of the treatment period or the expected remaining life span of the patient. This model, which provides a comprehensive framework for predicting TCP, can be used predictively, or - when clinical data are available for one particular treatment modality (e.g. fractionated radiotherapy) - to obtain TCP-equivalent regimens for other modalities (e.g. low dose-rate treatments).