title: Series model volume effects in a population of non-identical patients: how low is low?
abstract: Working with several mechanisms of critical local tissue damage, formulae are analytically derived that describe normal tissue complication probabilities (ntcps) for series-type radiotherapy complications arising in heterogeneous patient populations. Using the formulae, values are calculated for deltaD50(10)-the increase in dose leading to a 50% series-type complication rate (D50) when irradiated organ volume is reduced tenfold. From the structure of the ntcp formulae derived, it follows that dose-levels leading to clinically relevant serious complication rates (less than 5%) will change less with irradiated volume than will D50. Calculated values of deltaD50(10) for the heterogeneous series model are low-generally less than 6 Gy; such values are much lower than those calculated for the non-heterogeneous series model (27-37 Gy). These results suggest that if the dose-limiting toxicity of a radiotherapy treatment is a series-type complication with a local damage mechanism similar to any of those studied in this work, then even very substantial improvements in technique-leading to large reductions in highly dosed normal tissue volumes-would be unlikely to allow a useful degree of escalation of the dose delivered to the tumour, unless highly dosed normal tissue volumes can be reduced below the length-scale of a functional subunit.
authors.affiliation: Joint Department of Physics, Institute of Cancer Research and the Royal Marsden NHS Trust, Sutton, Surrey, UK. johnf@ccotrust.co.uk
authors.forename: J D
authors.initials: JD
authors.lastname: Fenwick
authors.forename: A E
authors.initials: AE
authors.lastname: Nahum
mesh_terms: D015331:Cohort Studies; D016207:Cytokines / Q000378:metabolism; D004307:Dose-Response Relationship, Radiation; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical; D011832:Radiation Injuries; D011878:Radiotherapy / Q000009:adverse effects*
chemical_list: D016207:Cytokines