A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density

Abstract

Most calculations of the biological effect of radiation on tumours assume that the clonogenic cell density is uniform even if account is taken of non-uniform dose distribution. In practice tumours will almost certainly have a non-uniform clonogenic cell density. This paper extends one particular model of tumour control probability (TCP) to incorporate a variable clonogenic cell density while at the same time assuming a constant 2 Gy fraction size and a uniform radiosensitivity throughout the treatment. Since there are virtually no in vivo data on the variation of density we consider some model situations. One clear conclusion is that a large reduction in clonogenic cell density at the edges of a tumour would permit only a very modest decrease in dose if the TCP is not to be reduced. In general the effect on TCP is a complicated function of the variation in both dose and clonogenic cell density. We give the equations which enable both to be included.

Local tumor control probability to evaluate an applicator‐guided volumetric‐modulated arc therapy solution as alternative of 3D brachytherapy for the treatment of the vaginal vault in patients affected by gynecological cancer

“…In practice, tumors will almost certainly have a nonuniform clonogenic cell density. Therefore we used the concept of LTCP, introduced by Webb and Nahum, ( 18 ) to take into account a possible spatial variation in tumor cell density ρ. Then, by means of LTCP curves, we evaluated the local reduction in TCP, depending on the spatial variation in tumor cell density and on the dose distributions from different techniques.…”

The impact of uncertainties associated with MammoSite brachytherapy on the dose distribution in the breast

“…The DVHs were then used to calculate the TCP using the following Poisson hypothesis: ( 23 ) $TCP=e^{-k\cdot S}$ …”

A dose‐volume‐based tool for evaluating and ranking IMRT treatment plans

“…The TCP model and parameters used in this study are based on the work of Webb and Nahum. ( 35 ) In the TCP model, a value of $0.35{\text{Gy}}^{-1}$ is used for the mean radiosensitivity of a cell population, ${\alpha }_{\text{mean}}$, and a value of $0.03{\text{Gy}}^{-2}$ is used for β. The standard deviation $\left({\sigma }_{\alpha }\right)$, or level of interpatient variability of radiosensitivity, is set to $0.08{\text{Gy}}^{-1}$.…”