Quality assurance in current 4D radiotherapy workflows is of great importance to assure a positive treatment outcome, i.e. total tumor eradication. Especially for the treatment of lung and liver tumors, which are subject to high motion magnitudes due to patient breathing, it is crucial to verify the applied dose to the target volume. In this study, we present a new 4D Monte Carlo dose accumulation approach that accounts for internal patient motion during treatment and is therefore able to predict the actual 3D dose distribution delivered to the patient for quality assurance purposes. Monte Carlo simulations are conducted using the EGSnrc software toolkit, which models the propagation of photons, electrons and positrons. However, to consider dynamic beam parameters and the movement of internal patient geometry, we developed a method to compute the dose for each control point of the actual VMAT patient treatment plan to account for breathing induced internal patient motion. The internal motion during treatment is predicted using correspondence modeling, which correlates patient-specific DIR-based internal motion information and external breathing signals and is trained on 4D CT data of the patient. For each VMAT control point, a corresponding motion vector field is predicted and applied to the original patient CT to allow for dose computation on the patient geometry as it was irradiated during treatment. Thus, density changes while treatment due to patient breathing motion are taken into account during computation of the resulting dose distribution.