Advanced treatment planning using direct 4D optimisation for pencil-beam scanned particle therapy.

We report on development of a new four-dimensional (4D) optimisation approach for scanned proton beams, which incorporates both irregular motion patterns and the delivery dynamics of the treatment machine into the plan optimiser. Furthermore, we assess the effectiveness of this technique to reduce dose to critical structures in proximity to moving targets, while maintaining effective target dose homogeneity and coverage. The proposed approach has been tested using both a simulated phantom and a clinical liver cancer case, and allows for realistic 4D calculations and optimisation using irregular breathing patterns extracted from e.g. 4DCT-MRI (4D computed tomography-magnetic resonance imaging). 4D dose distributions resulting from our 4D optimisation can achieve almost the same quality as static plans, independent of the studied geometry/anatomy or selected motion (regular and irregular). Additionally, current implementation of the 4D optimisation approach requires less than 3 min to find the solution for a single field planned on 4DCT of a liver cancer patient. Although 4D optimisation allows for realistic calculations using irregular breathing patterns, it is very sensitive to variations from the planned motion. Based on a sensitivity analysis, target dose homogeneity comparable to static plans (D5-D95  <5%) has been found only for differences in amplitude of up to 1 mm, for changes in respiratory phase  <200 ms and for changes in the breathing period of  <20 ms in comparison to the motions used during optimisation. As such, methods to robustly deliver 4D optimised plans employing 4D intensity-modulated delivery are discussed.