Impact of limited temporal resolution on 4D Monte Carlo dose calculation for intensity modulated proton therapy

Abstract

The interplay between the beam delivery time structure and the patient motion makes 4D dose calculation (4DDC) important when treating moving tumors with intensity modulated proton therapy. 4DDC based on phase sorting of a 4DCT suffers from approximation errors in the assignment of spots to phases, since the temporal image resolution of the 4DCT is much lower than that of the delivery time structure. In this study we investigate and address this limitation by a method which applies registration-based interpolation between phase images to increase the temporal resolution of the 4DCT. First, each phase image is deformed toward its neighbor using the deformation vector field that aligns them, scaled by the desired time step. Then Monte Carlo-based 4DDC is performed on both the original 4DCT (10 phases), and extended 4DCTs at increasingly fine temporal resolutions. The method was evaluated on seven lung cancer patients treated with three robustly optimized beams, with simulated delivery time structures. Errors resulting from limited temporal resolution were measured by comparisons of doses computed using extended 4DCTs of various resolutions. The dose differences were quantified by gamma pass rates and volumes of the CTV that had dose differences above certain thresholds. The ground truth was taken as the dose computed using 100 phase images, and was justified by considering the diminishing effects of adding more images. The effect on dose-averaged linear energy transfer was also included in the analysis. A resolution of 20 (30) phase images per breathing cycle was sufficient to bring mean CTV $\gamma$-pass rates for $3\%/3$mm ($2\%/2$mm) above 99$\%$. For the patients with well behaved image data, mean CTV $\gamma$-pass rates for $1\%/1$mm surpassed 99$\%$ at a resolution of 50 images.