Optimisation in stereotactic radiosurgery of AVMs: I. Mathematical considerations

One forward-planning method and five inverse-planning methods for optimisation of treatment in radiation therapy were compared in the particular case of radiosurgery with micro-multi-leaves collimator (MMLC) and arc therapy. The "manual" method, two matrix methods (singular value decomposition and non-negative least square fit), two gradient methods (quasi-Newton and conjugate gradient algorithms) and the "simulated annealing" stochastic method were investigated. The performance of these methods was assessed in terms of the speed of convergence to an optimum, the ability to account for the organs at risk, and probability of targeted success. The study employed an adapted version of the GRATIS treatment planning system. A group of 22 patients previously treated by arc therapy for arteriovenous malformations (AVMs) were studied to evaluate the performance of the various optimisation methods for MMLC and arc therapy. The conjugate gradient method proved to be the most appropriate for most cases.