title: A proof that uniform dose gives the greatest TCP for fixed integral dose in the planning target volume.
abstract: In this note it is shown that for a fixed integral dose to the planning target volume, the highest tumour control probability (TCP) arises when the dose is spatially uniform. This 'uniform dose theorem' is proved both for (i) a specific TCP model based on Poisson/independent voxel statistics, and (ii) any model for voxel control probability having a specific shape with respect to increasing dose.
authors.affiliation: Joint Department of Physics, Institute of Cancer Research and Royal Marsden Hospital, Sutton, UK.
authors.forename: S
authors.initials: S
authors.lastname: Webb
authors.forename: P M
authors.initials: PM
authors.lastname: Evans
authors.forename: W
authors.initials: W
authors.lastname: Swindell
authors.forename: J O
authors.initials: JO
authors.lastname: Deasy
mesh_terms: D004307:Dose-Response Relationship, Radiation; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D009369:Neoplasms / Q000532:radiotherapy*; D016012:Poisson Distribution; D011879:Radiotherapy Dosage; D020266:Radiotherapy, Conformal