Due to the impact of range uncertainties, Proton Beam Therapy is more subject to systematic error than photon radiotherapy. Conventional intensity modulated proton therapy optimization algorithms determine spot weights based the ideal expected dose. Robust optimization differs in that potential errors are also incorporated into the objective function, yielding plans that are less subject to dramatic dose fluctuations when errors occur.  However, quantifying the “robustness” of a plan remains a challenge, leaving clinicians without much guidance regarding the likelihood of exceeding constraints or under-dosing targets. 

We describe a novel method of quantifying robustness that allows for probabilistic approximation of dose coverage. Rather than creating a Dij matrix that is limited to those beam spots intended for use in radiation delivery, we propose creating a “dense” Dij matrix with finer spot spacing and wider margins.  Following optimization, the “dense” Dij matrix is utilized to quickly calculate a number of error scenarios (i.e. 100).  Each scenario is created by translating the treatment plan with a normal random shift in the X, Y, and Energy axes, corresponding to the known uncertainty distributions in these respective directions.  Each shifted plan will also align with spots on the dense grid, thus dose calculation of that error scenario can be completed with minimal computation.  Review of a composite DVH comprise of all simulated error plans will allow the one to quickly determine the fraction of possible error scenarios fail to meet a given constraint.  The Dense Dij matrix is further applied to the robust optimization itself, allowing for consideration of uncertainties is both range and translation of the isocenter. Such information will allow clinicians to provide safer and more effective treatments.