Perturbation of water-equivalent thickness as a surrogate for respiratory motion in proton therapy

Respiratory motion is traditionally assessed using tumor motion magnitude. In proton therapy, respiratory motion causes density variations along the beam path that result in uncertainties of proton range. This work has investigated the use of water-equivalent thickness (WET) to quantitatively assess the effects of respiratory motion on calculated dose in passively scattered proton therapy (PSPT). A cohort of 29 locally advanced non-small cell lung cancer patients treated with 87 PSPT treatment fields were selected for analysis. The variation in WET (ΔWET) along each field was calculated between exhale and inhale phases of the simulation four-dimensional computed tomography. The change in calculated dose (ΔDose) between full-inhale and full-exhale phase was quantified for each field using dose differences, 3D gamma analysis, and differential area under the curve (ΔAUC) analysis. Pearson correlation coefficients were calculated between ΔDose and ΔWET. Three PSPT plans were redesigned using field angles to minimize variations in ΔWET and compared to the original plans. The median ΔWET over 87 treatment fields ranged from 1-9 mm, while the ΔWET 95th percentile value ranged up to 42 mm. The ΔWET was significantly correlated (p < 0.001) to the ΔDose for all metrics analyzed. The patient plans that were redesigned using ΔWET analysis to select field angles were more robust to the effects of respiratory motion, as ΔAUC values were reduced by more than 60% in all three cases. The tumor motion magnitude alone does not capture the potential dosimetric error due to respiratory motion because the proton range is sensitive to the motion of all patient anatomy. The use of ΔWET has been demonstrated to identify situations where respiratory motion can impact the calculated dose. Angular analysis of ΔWET may be capable of designing radiotherapy plans that are more robust to the effects of respiratory motion.