An objective function for radiation treatment optimization based on local biological measures

The implementation of biological optimization of radiation treatment plans is impeded by both computational and modelling problems. We derive an objective function from basic model assumptions which includes the normal tissue constraints as interior penalty functions. For organs that are composed of parallel subunits, a mean response model is proposed which leads to constraints similar to dose-volume constraints. This objective function is convex in the case when no parallel organs lie in the treatment volume. Otherwise, an argument is given to show that a number of local minima may exist which are near degenerate to the global minimum. Thus, together with the measure quality of the objective function, highly efficient gradient algorithms can be used. The number of essential biological model parameters could be reduced to a minimum. However, if the optimization constraints are given as TCP/NTCP values, Lagrange multiplier updates have to be performed by invoking comprehensive biological models.