Enhanced optimization of volumetric modulated arc therapy plans using Monte Carlo generated beamlets

A treatment planning system (TPS) produces volumetric modulated arc therapy (VMAT) plans by applying an optimization process to an objective function, followed by an accurate calculation of the final, deliverable dose. However, during the optimization step, a rapid dose calculation algorithm is required, which reduces its accuracy and its representation of the objective function space. Monte Carlo (MC) routines, considered the gold standard in accuracy, are currently too slow for practical comprehensive VMAT optimization. Therefore, we propose a novel approach called enhanced optimization (EO), which employs the TPS VMAT plan as a starting point, and applies small perturbations to nudge the solution closer to a true objective minimum. The perturbations consist of beamlet dose matrices, calculated using MC routines on a distributed-computing framework.

DICOM files for clinical VMAT plans files are exported from the TPS and used to generate input files for the EGSnrc MC toolkit. Beamlet doses are calculated using the MC routines, each corresponding to a single multileaf collimator leaf from a single control point traveling 0.5 cm in or out of the field. A typical VMAT plan requires 5000 to 10 000 beamlets, which may be calculated overnight. This results in a ternary-valued objective function, which may use the same clinical objectives as the original VMAT plan. A simple greedy search algorithm is applied to minimize this function and determine the optimal set of ternary variables. The resulting modified control point parameters are imported into the TPS to calculate the final, deliverable dose, and to compare the EO plan with the original. EO was evaluated retrospectively on seven VMAT plans (two adult brain, one pediatric brain, two head and neck, and two prostate). Additionally, the use of stricter objectives was investigated for two of the cases: the left cochlea planning organ at risk (OAR) volume objective for the pediatric brain case, and the rectum objective for a prostate case.

EO produced improved objective scores (by 6% to 60%) and dose-volume histograms (DVH) for the brain plans and the head and neck plans. For each of these plans, the target dose minimum and homogeneity were preserved, while one or more of the OAR DVH's was reduced. Although EO also reduced the objective scores for the prostate plans (by 46% and 79%), their absolute score and DVH improvements were not substantial. The stricter objective on the pediatric brain case resulted in lower dose to the OAR without compromising the target dose. However, the rectum dose in the prostate case could not be improved without reducing dose homogeneity to the planning target volume, suggesting that VMAT prostate cases may already be highly optimized by the TPS.

We have developed a novel approach to improving the dose distribution of VMAT plans, which relies on MC calculations to provide small modifications to the control points. This method may be particularly useful for complex treatments in which a certain OAR is of concern and it is difficult for the treatment planner to obtain an acceptable solution with the TPS. Further development will reduce the beamlet computation time and result in more sophisticated EO treatment planning methods.