Series model volume effects in a population of non-identical patients: howlow is low?

Working with several mechanisms of critical local tissue damage, formulae a re analytically derived that describe normal tissue complication probabilit ies (ntcps) for series-type radiotherapy complications arising in heterogen eous patient populations. Using the formulae, values are calculated for Del taD(5010)-the increase in dose leading to a 50% series-type complication ra te (D-50) when irradiated organ volume is reduced tenfold. From the structu re of the mcp formulae derived, it follows that dose-levels leading to clin ically relevant serious complication rates (less than 5%) will change less with it-radiated volume than will D-50. Calculated values of DeltaD(5010) for the heterogeneous series model are lo w-generally less than 6 Gy; such values are much lower than those calculate d 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 stu died in this work. then even very substantial improvements in technique-lea ding to large reductions in highly dosed normal tissue volumes-would be unl ikely to allow a useful degree of escalation of the dose delivered to the t umour, unless highly dosed normal tissue volumes can be reduced below the l ength-scale of a functional subunit.