title: 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.
authors.affiliation: Joint Department of Physics, Institute of Cancer Research and Royal Marsden Hospital, Sutton, Surrey, UK.
authors.forename: S
authors.initials: S
authors.lastname: Webb
authors.forename: A E
authors.initials: AE
authors.lastname: Nahum
mesh_terms: D002452:Cell Count; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D009364:Neoplasm Recurrence, Local / Q000453:epidemiology*; D009369:Neoplasms / Q000473:pathology / Q000532:radiotherapy*; D011879:Radiotherapy Dosage; D011882:Radiotherapy, High-Energy; D014410:Tumor Stem Cell Assay