Monte Carlo as a four-dimensional radiotherapy treatment-planning tool to account for respiratory motion

Four-dimensional (4D) radiotherapy is the explicit inclusion of the temporal changes in anatomy during the imaging, planning and delivery of radiotherapy. Temporal anatomic changes can occur for many reasons, though the focus of the current investigation was respiration motion for lung tumours. The aims of the current research were first to develop a 4D Monte Carlo methodology and second to apply this technique to an existing 4D treatment plan. A 4D CT scan consisting of a series of 3D CT image sets acquired at different respiratory phases was used. Deformable image registration was performed to map each CT set from the end-inhale respiration phase to the CT image sets corresponding with subsequent respiration phases. This deformable registration allowed the contours drawn on the end-inhale CT to be automatically drawn on the other respiratory phase CT image sets. A treatment plan was created on the end-inhale CT image set and then automatically created on each of the 3D CT image sets corresponding with subsequent respiration phases, based on the beam arrangement and dose prescription in the end-inhale plan. Dose calculation using Monte Carlo was simultaneously performed on each of the N (=8) 3D image sets with 1/N fewer particles per calculation than for a 3D plan. The dose distribution from each respiratory phase CT image set was mapped back to the end-inhale CT image set for analysis. This use of deformable image registration to merge all the statistically noisy dose distributions back onto one CT image set effectively yielded a 4D Monte Carlo calculation with a statistical uncertainty equivalent to a 3D calculation, with a similar calculation time for the 3D and 4D methods. Monte Carlo as a dose calculation tool for 4D radiotherapy planning has two advantages: (1) higher accuracy for calculation in electronic disequilibrium conditions, such as those encountered during lung radiotherapy, and (2) if deformable image registration is used, the calculation time for Monte Carlo is independent of the number of 3D CT image sets constituting a 4D CT, unlike other algorithms for which the calculation time scales linearly with the number of 3D CT image sets constituting a 4D CT.