A dose error evaluation study for 4D dose calculations

Previous studies have shown that respiration induced motion is not negligible for Stereotactic Body Radiation Therapy. The intrafractional breathing induced motion influences the delivered dose distribution on the underlying patient geometry such as the lung or the abdomen. If a static geometry is used, a planning process for these indications does not represent the entire dynamic process. The quality of a full 4D dose calculation approach depends on the dose coordinate transformation process between deformable geometries. This article provides an evaluation study that introduces an advanced method to verify the quality of numerical dose transformation generated by four different algorithms. The used transformation metric value is based on the deviation of the dose mass histogram (DMH) and the mean dose throughout dose transformation. The study compares the results of four algorithms. In general, two elementary approaches are used: dose mapping and energy transformation. Dose interpolation (DIM) and an advanced concept, so called divergent dose mapping model (dDMM), are used for dose mapping. The algorithms are compared to the basic energy transformation model (bETM) and the energy mass congruent mapping (EMCM). For evaluation 900 small sample regions of interest (ROI) are generated inside an exemplary lung geometry (4DCT). A homogeneous fluence distribution is assumed for dose calculation inside the ROIs. The dose transformations are performed with the four different algorithms. The study investigates the DMH-metric and the mean dose metric for different scenarios (voxel sizes: 8 mm, 4 mm, 2 mm, 1 mm; 9 different breathing phases). dDMM achieves the best transformation accuracy in all measured test cases with 3-5% lower errors than the other models. The results of dDMM are reasonable and most efficient in this study, although the model is simple and easy to implement. The EMCM model also achieved suitable results, but the approach requires a more complex programming structure. The study discloses disadvantages for the bETM and for the DIM. DIM yielded insufficient results for large voxel sizes, while bETM is prone to errors for small voxel sizes.