An optimisation algorithm for determination of treatment margins around moving and deformable targets.

PURPOSE Determining treatment margins for inter-fractional motion of moving and deformable clinical target volumes (CTVs) remains a major challenge. This paper describes and applies an optimisation algorithm designed to derive such margins. MATERIAL AND METHODS The algorithm works by expanding the CTV, as determined from a pre-treatment or planning scan, to enclose the CTV positions observed during treatment. CTV positions during treatment may be obtained using, for example, repeat CT scanning and/or repeat electronic portal imaging (EPI). The algorithm can be applied to both individual patients and to a set of patients. The margins derived will minimise the excess volume outside the envelope that encloses all observed CTV positions (the CTV envelope). Initially, margins are set such that the envelope is more than adequately covered when the planning CTV is expanded. The algorithm uses an iterative method where the margins are sampled randomly and are then either increased or decreased randomly. The algorithm is tested on a set of 19 bladder cancer patients that underwent weekly repeat CT scanning and EPI throughout their treatment course. RESULTS From repeated runs on individual patients, the algorithm produces margins within a range of +/-2 mm that lie among the best results found with an exhaustive search approach, and that agree within 3mm with margins determined by a manual approach on the same data. The algorithm could be used to determine margins to cover any specified geometrical uncertainty, and allows for the determination of reduced margins by relaxing the coverage criteria, for example disregarding extreme CTV positions, or an arbitrarily selected volume fraction of the CTV envelope, and/or patients with extreme geometrical uncertainties. CONCLUSION An optimisation approach to margin determination is found to give reproducible results within the accuracy required. The major advantage with this algorithm is that it is completely empirical, and it is therefore particularly useful for CTVs where the geometrical uncertainties are difficult to model, such as the bladder.