Continuously Deforming 4D Voxel Phantom for Realistic Representation of Respiratory Motion in Monte Carlo Dose Calculation

We propose a new type of computational phantom, the “4D voxel phantom,” for realistic modeling of continuous respiratory motion in Monte Carlo dose calculation. In this phantom, continuous respiratory motion is realized by linear interpolation of the deformation vector fields (DVFs) between the neighboring original phases in the 4D CT data of a patient and by subsequent application of the DVFs to the phase images or to the reference image to produce multiple inter-phase images between the neighboring original phase images. A 4D voxel phantom is a combination of high-temporal-resolution voxel phantoms and on-the-fly dose registration to the reference phase image. In the course of particle transport simulation, the dose or deposited energy is directly registered to the reference phase image on-the-fly (i.e., after each event) using a DVF for dose registration. In the present study, we investigated two methods - DRP (DIR [deformable image registration] with respect to Reference Phase image) and DNP (DIR with respect to Neighboring original Phase image) - for production of multiple inter-phase images or high-temporal-resolution voxel phantoms. Utilizing these two methods, two 4D voxel phantoms each with 100 phases were produced from the original 10-phase images of the 4D CT data of a real patient in order to compare the two methods and to test the feasibility of the 4D voxel phantom methodology in general. We found that it is possible to produce a 4D voxel phantom very rapidly (i.e., <;40 min on a 4-core personal computer for a 100-phase phantom) in a fully automated process. The dose calculation results showed that the constructed 100-phase 4D voxel phantoms provide cumulative-dose distributions very similar to those of the conventional 10-phase approach for stationary proton-beam irradiation. The passing rates of the dose distributions of the 4D voxel phantoms were higher than 99.9% according to the 3% and 3 mm gamma criteria, which results validate the 4D voxel phantom methodology. The point-and dose-tracking analysis data showed that the DRP method, which uses the minimal number of DIR operations but uses inverse DVFs, provides significantly better results than those of the DNP method, which uses only DIR to generate the DVFs for inter-phase image generation and dose registration. The present study also showed that the computation time does not significantly increase when the number of phases in the 4D voxel phantom is increased for more realistic representation of continuous respiratory motion; the only significant increase is in the memory occupancy, which grows almost linearly with the number of phases.