Optimization algorithm for overlapping-field plans of scanned ion beam therapy with reduced sensitivity to range and setup uncertainties

A 'patch-field' strategy is often used for tumors with large volumes exceeding the available field size in passive irradiations with ion beams. Range and setup errors can cause hot and cold spots at the field junction within the target. Such errors will also displace the field to miss the target periphery. With scanned ion beams with fluence modulation, the two junctional fields can be overlapped rather than patched, which may potentially reduce the sensitivity to these uncertainties. In this study, we have developed such a robust optimization algorithm. This algorithm is composed of the following two steps: (1) expanding the target volume with margins against the uncertainties, and (2) solving the inverse problem where the terms suppressing the dose gradient of individual fields are added into the objective function. The validity of this algorithm is demonstrated through simulation studies for two extreme cases of two fields with unidirectional and opposing geometries and for a prostate-cancer case. With the proposed algorithm, we can obtain a more robust plan with minimized influence of range and setup uncertainties than the conventional plan. Compared to conventional optimization, the calculation time for the robust optimization increased by a factor of approximately 3.