Monte-Carlo-based 4D robust optimization using physical and temporal uncertainties for intensity-modulated proton therapy.

Purpose: Respiratory motion and the interplay effect cause the dose delivered to a patient with spot-scanned proton therapy to differ from the dose planned for during optimization. A new 4D robust optimization methodology was developed which incorporates patient breathing and the interplay effect, as well as their uncertainties, into the optimization process... Methods: The 4D robust optimizer used a 4DCT image set to obtain information regarding patient breathing and included a beam-delivery simulation to incorporate the interplay effect. The doses from potential spots were calculated on all breathing phases using Monte Carlo simulation, deformed to a reference phase using deformable image registration, and then added in a weighted sum. The weights for the different phases were based on the beam-delivery simulation. Robustness was added to the optimization by considering range and setup uncertainties as physical-uncertainty scenarios and uncertainties in the patient breathing and treatment delivery as temporal uncertainty scenarios... Results: The 4D robustly optimized plans exhibited improved target coverage with an average increase in the dose to 98% of the target volume of 4.9%, improved homogeneity with an average decrease in the homogeneity index of 6.0%, and improved robustness with decreased ranges in coverage and homogeneity amongst all uncertainty scenarios by averages of 35.0% and 52.5%, respectively... Conclusions: A 4D robust optimizer was developed which included the interplay effect and did not depend on the synchronization of breathing and delivery...