Comparison of two methods for minimizing the effect of delayed charge on the dose delivered with a synchrotron based discrete spot scanning proton beam

Purpose: Delayed charge is a small amount of charge that is delivered to the patient after the planned irradiation is halted, which may degrade the quality of the treatment by delivering unwarranted dose to the patient. This study compares two methods for minimizing the effect of delayed charge on the dose delivered with a synchrotron based discrete spot scanning proton beam. Methods: The delivery of several treatment plans was simulated by applying a normally distributed value of delayed charge, with a mean of 0.001(SD 0.00025) MU, to each spot. Two correction methods were used to account for the delayed charge. Method one (CM1), which is in active clinical use, accounts for the delayed charge by adjusting the MU of the current spot based on the cumulative MU. Method two (CM2) in addition reduces the planned MU by a predicted value. Every fraction of a treatment was simulated using each method and then recomputed in the treatment planning system. The dose difference between the original plan and the sum of the simulated fractions was evaluated. Both methods were tested in a water phantom with a single beam and simple target geometry. Two separate phantom tests were performed. In one test the dose per fraction was varied from 0.5 to 2 Gy using 25 fractions per plan. In the other test the number fractions were varied from 1 to 25, using 2 Gy per fraction. Three patient plans were used to determine the effect of delayed charge on the delivered dose under realistic clinical conditions. The order of spot delivery using CM1 was investigated by randomly selecting the starting spot for each layer, and by alternating per layer the starting spot from first to last. Only discrete spot scanning was considered in this study. Results: Using the phantom setup and varying the dose per fraction, the maximum dose difference for each plan of 25 fractions was 0.37-0.39 Gy and 0.03-0.05 Gy for CM1 and CM2, respectively. While varying the total number of fractions, the maximum dose difference increased at a rate of 0.015 Gy and 0.0018 Gy per fraction for CM1 and CM2, respectively. For CM1, the largest dose difference was found at the location of the first spot in each energy layer, whereas for CM2 the difference in dose was small and showed no dependence on location. For CM1, all of the fields in the patient plans had an area where their excess dose overlapped. No such correlation was found when using CM2. Randomly selecting the starting spot reduces the maximum dose difference from 0.708 to 0.15 Gy. Alternating between first and last spot reduces the maximum dose difference from 0.708 to 0.37 Gy. In the patient plans the excess dose scaled linearly at 0.014 Gy per field per fraction for CM1 and standard delivery order. Conclusions: The predictive model CM2 is superior to a cumulative irradiation model CM1 for minimizing the effects of delayed charge, particularly when considering maximal dose discrepancies and the potential for unplanned hot-spots. This study shows that the dose discrepancy potentially scales at 0.014 Gy per field per fraction for CM1.