Models in radiotherapy: volume effects

A model for the dependence of normal tissue radiation dose response functions on volume variations and dose inhomogeneities is derived using probability theory. Power law volume correction factors and the complication probability factor are shown to be special cases arising from approximations applied to this model. Both require the assumption of small probabilities of complication. Power law volume corrections are shown to require a homogeneous dose distribution. The general model is tissue specific and can be used to calculate probabilities of complication for individual organs or isoprobability doses for radiation injury. The model is applicable to both homogeneous and inhomogeneous dose distributions and has been used in computer determination of optimal treatment parameters. Experimental data are presented which are consistent with the general model alone and which demonstrate the limits of applicability of previous models.