A dual-field strategy is often used for tumors with highly complex shapes and/or with large volumes exceeding available field-size in both passive and scanning irradiations with ion beams. Range and setup uncertainties can cause hot and cold doses at
the field junction within the target. Such uncertainties will also cause cold doses in the peripheral region of the target. We have developed an algorithm to reduce the sensitivity of the dual-field plan to these uncertainties in scanning irradiations. This algorithm is composed of the following two steps: 1) generating the expanded target volume, 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 the simulation studies for three extreme cases of two fields with unidirectional, opposing and orthogonal geometries. With the proposed algorithm, we can obtain a more robust plan to minimize the effects of range and setup uncertainties than the conventional plan. Compared to that for the conventional plan, the optimization time for the robust plan increased by a factor of approximately three.
