Probability of radiation-induced complications for normal tissues with parallel architecture subject to non-uniform irradiation.

A biologically based model is developed to predict radiation-induced normal tissue complication probability (NTCP) in inhomogeneously irradiated organs such as the lung or the kidney. The organ is assumed to be composed of independent functional subunits (FSUs) organized with a parallel architecture and it is assumed that the complication is produced only if a sufficiently large number of FSUs (the "functional reserve") are destroyed. A general expression for NTCP is derived, as well as simple expressions for the mean and standard deviation of the radiation damage to the FSUs. It is demonstrated that these results for inhomogeneous irradiation reproduce those of the serial and tumor control models when the functional reserve consists of one or all of the FSUs, respectively. When the number of FSUs is large, the dose response for organs with identical characteristics is very steep. Since clinical dose-response curves may arise from populations with varying functional reserves and radiosensitivities, we derive expressions for the NTCP for inhomogeneously irradiated organs that incorporate such variations.