Dosimetric uncertainties as a result of temporal resolution in 4D dose calculations for PBS proton therapy

This work investigates the dosimetric impact on 4D dose distribution estimation for pencil beam scanned (PBS) proton therapy as function of the temporal resolution used for the time resolved dose calculation. For three liver patients (CTV volume: 403/122/264 cc), 10-phase 4DCT-MRI datasets with ~15 mm tumour motion were simulated for seven different motion periods (2-8 s). 4D dose distributions were calculated and compared by considering both coarser and finer temporal resolutions (200-800 ms and 20 ms). Single scanned 4D plans for seven fraction doses (0.7/2/4/6/8/10/12 Gy) were investigated, whose dose delivery timelines were simulated by assuming two types of PBS scanning modes: (1) layer-wise raster scanning with varying dose rate per layer and (2) fixed dose rate, discrete scanning. For both delivery scenarios, dosimetric assessments were performed by comparing corresponding dose distributions derived from the two 4D dose calculation (4DDC) results. Differences were quantified as the difference in D5-D95 of the CTV and by comparing total volume of the CTV receiving point-to-point absolute dose difference more than 5%. Our results show that varying temporal resolution in 4DDC has a direct influence on the final accumulated dose distribution. For all scenarios, patients, fraction doses and motion periods studied, pronounced dose differences can be observed between the two 4DDC results. However, the magnitude of differences varies depending on the selected PBS scanning model and prescribed dose per field. For fixed dose rate delivery, the average duration of the delivery of each spot increases for hypo-fractionated treatments, enhancing the benefit of using a finer temporal resolution for 4DDC. In particular, for fraction doses  >4 Gy and motion periods less than 4 s, warping the dose between discrete 4DCT phases can over predict the interplay effect (D5-D95 in CTV) by 3%-10% compared to the use of a finer temporal resolution, resulting in more than 20% of CTV voxels having absolute dose differences of over 5% between the two 4DDC approaches. These findings emphasize the importance for PBS 4DDC using finer temporal resolutions than provided by conventional 4D dose accumulation techniques. In particular, the observed differences in dosimetric effects using the fine temporal resolution provided by dose warping cannot be neglected for hypo-fractionation and short breathing periods, especially when using constant dose rates for dose delivery.