Monte Carlo calculation of VMAT and helical tomotherapy dose distributions for lung stereotactic treatments with intra-fraction motion

The aim of this study is to calculate realistic dose distributions that include the continuous deformation of organs and continuous motion of machine using 4D Monte Carlo methods for both volumetric modulated arc therapy and helical tomotherapy treatments. As part of a previous study, we presented a method to perform position-probability-sampled Monte Carlo dose calculations in the BEAMnrc and DOSXZYnrc user codes of EGSnrc. In this study, the DOSXYZnrc user code was further modified to account for the continuous intra-fraction deformation of the patient geometry. We implemented in the user code a method to update the transport grid densities as a function of time and map the energy deposited in the time dependent transport grid back to a reference grid. We provide information on the measurements performed to validate the implementation of this method and present an example of the application of the method for lung stereotactic treatments with intra-fraction motion. The results show that breathing motion is properly addressed with the internal target volume method for the cases studied.