A Greedy reassignment algorithm for the PBS minimum monitor unit constraint

Proton pencil beam scanning (PBS) treatment plans are made of numerous unique spots of different weights. These weights are optimized by the treatment planning systems, and sometimes fall below the deliverable threshold set by the treatment delivery system. The purpose of this work is to investigate a Greedy reassignment algorithm to mitigate the effects of these low weight pencil beams. The algorithm is applied during post-processing to the optimized plan to generate deliverable plans for the treatment delivery system. The Greedy reassignment method developed in this work deletes the smallest weight spot in the entire field and reassigns its weight to its nearest neighbor(s) and repeats until all spots are above the minimum monitor unit (MU) constraint. Its performance was evaluated using plans collected from 190 patients (496 fields) treated at our facility. The Greedy reassignment method was compared against two other post-processing methods. The evaluation criteria was the gamma-index pass rate that compares the pre-processed and post-processed dose distributions. A planning metric was developed to predict the impact of post-processing on treatment plans for various treatment planning, machine, and dose tolerance parameters. For fields with a pass rate of 90 +/- 1% the planning metric has a standard deviation equal to 18% of the centroid value showing that the planning metric and gamma-index pass rate are correlated for the Greedy reassignment algorithm. Using a 3rd order polynomial fit to the data, the Greedy reassignment method has 1.8 times better planning metric at 90% pass rate compared to other post-processing methods. As the planning metric and pass rate are correlated, the planning metric could provide an aid for implementing parameters during treatment planning, or even during facility design, in order to yield acceptable pass rates. More facilities are starting to implement PBS and some have spot sizes (one standard deviation) smaller than 5 mm, hence would require small spot spacing. While this is not the only parameter that affects the optimized plan, the perturbation due to the minimum MU constraint increases with decreasing spot spacing. This work could help to design the minimum MU threshold with the goal to keep the gamma-index pass rate above an acceptable value.