IMRT optimization: variability of solutions and its radiobiological impact.

We aim at (1) defining and measuring a "complexity" index for the optimization process of an intensity modulated radiation therapy treatment plan (IMRT TP), (2) devising an efficient approximate optimization strategy, and (3) evaluating the impact of the complexity of the optimization process on the radiobiological quality of the treatment. In this work, for a prostate therapy case, the IMRT TP optimization problem has been formulated in terms of dose-volume constraints. The cost function has been minimized in order to achieve the optimal solution, by means of an iterative procedure, which is repeated for many initial modulation profiles, and for each of them the final optimal solution is recorded. To explore the complexity of the space of such solutions we have chosen to minimize the cost function with an algorithm that is unable to avoid local minima. The size of the (sub)optimal solutions distribution is taken as an indicator of the complexity of the optimization problem. The impact of the estimated complexity on the probability of success of the therapy is evaluated using radiobiological indicators (Poissonian TCP model [S. Webb and A. E. Nahum, Phys. Med. Biol. 38(6), 653-666 (1993)] and NTCP relative seriality model [Kallman et al., Int. J. Radiat. Biol. 62(2), 249-262 (1992)]). We find in the examined prostate case a nontrivial distribution of local minima, which has symmetry properties allowing a good estimate of near-optimal solutions with a moderate computational load. We finally demonstrate that reducing the a priori uncertainty in the optimal solution results in a significant improvement of the probability of success of the TP, based on TCP and NTCP estimates.