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

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.