Limitations of phase-sorting based pencil beam scanned 4D proton dose calculations under irregular motion

Objective. 4D dose calculation (4DDC) for pencil beam scanned (PBS) proton therapy is typically based on phase-sorting of individual pencil beams onto phases of a single breathing cycle 4DCT. Understanding the dosimetric limitations and uncertainties of this approach is essential, especially for the realistic treatment scenario with irregular free breathing motion. Approach. For three liver and three lung cancer patient CTs, the deformable multi-cycle motion from 4DMRIs was used to generate six synthetic 4DCT(MRI)s, providing irregular motion (11/15 cycles for liver/lung; tumor amplitudes similar to 4-18 mm). 4DDCs for two-field plans were performed, with the temporal resolution of the pencil beam delivery (4-200 ms) or with 8 phases per breathing cycle (500-1000 ms). For the phase-sorting approach, the tumor center motion was used to determine the phase assignment of each spot. The dose was calculated either using the full free breathing motion or individually repeating each single cycle. Additionally, the use of an irregular surrogate signal prior to 4DDC on a repeated cycle was simulated. The CTV volume with absolute dose differences >5% (V (dosediff>5%)) and differences in CTV V (95%) and D (5%)-D (95%) compared to the free breathing scenario were evaluated. Main results. Compared to 4DDC considering the full free breathing motion with finer spot-wise temporal resolution, 4DDC based on a repeated single 4DCT resulted in V (dosediff>5%) of on average 34%, which resulted in an overestimation of V (95%) up to 24%. However, surrogate based phase-sorting prior to 4DDC on a single cycle 4DCT, reduced the average V (dosediff>5%) to 16% (overestimation V (95%) up to 19%). The 4DDC results were greatly influenced by the choice of reference cycle (V (dosediff>5%) up to 55%) and differences due to temporal resolution were much smaller (V (dosediff>5%) up to 10%). Significance. It is important to properly consider motion irregularity in 4D dosimetric evaluations of PBS proton treatments, as 4DDC based on a single 4DCT can lead to an underestimation of motion effects.