Calculation of normal tissue complication probability and dose-volume histogram reduction schemes for tissues with a critical element architecture.

We investigate a model of normal tissue complication probability for tissues that may be represented by a critical element architecture. We derive formulas for complication probability that apply to both a partial volume irradiation and to an arbitrary inhomogeneous dose distribution. The dose-volume isoeffect relationship which is a consequence of a critical element architecture is discussed and compared to the empirical power law relationship. A dose-volume histogram reduction scheme for a "pure" critical element model is derived. In addition, a point-based algorithm which does not require precomputation of a dose-volume histogram is derived. The existing published dose-volume histogram reduction algorithms are analyzed. We show that the existing algorithms, developed empirically without an explicit biophysical model, have a close relationship to the critical element model at low levels of complication probability. However, we also show that they have aspects which are not compatible with a critical element model and we propose a modification to one of them to circumvent its restriction to low complication probabilities.