Coordinate transformations for BEAM/EGSnrc Monte Carlo dose calculations of non-coplanar fields received from a...

The Monte Carlo (MC) method provides the most accurate to-date dose calculations in heterogeneous media and complex geometries, and this spawns increasing interest in incorporating MC calculations in the treatment planning quality assurance process. This process involves MC dose calculations for the treatment plans produced clinically. Commonly used in radiotherapy, MC codes are BEAMnrc and DOSXYZnrc, which transport particles in a coordinate system (c.s.) that has been established historically and does not correspond to the c.s. of treatment planning systems (TPSs). Relative rotations of these c.s. are not straightforward, especially for non-coplanar treatments. Transformation equations are therefore required to re-calculate a treatment plan using BEAM/DOSXYZnrc codes. This paper presents such transformations for beam angles defined in a DICOM-compliant treatment planning coordinate system. Verification of the derived transformations with two three-field plans simulated on a phantom using TPS as well as MC codes has been performed demonstrating exact geometrical agreement of the MC treatment fields' placement.