Stochastic model for predicting the temporal structure of the plan delivery in a synchrotron-based pencil beam scanning proton therapy system

Accurately predicting dose delivery is crucial for achieving fully personalized treatments in external beam radiation therapy. However, this task remains challenging in some current technologies. In the case of Proton Therapy, for example, current systems employ complex strategies where a pencil beam is scanned in the tumor for treatment delivery. Some parameters in these treatments fluctuate and cannot be fully controlled. Therefore, a stochastic model that accounts for temporal uncertainties can be the best approach to describe these behaviors, particularly when the time-dependent beam interacts with other processes such as moving tumors or organs at risk. This paper aims to provide medical physicists with a tool for accurately predicting the temporal structure of beam delivery. To achieve this, we followed a two-step process. First, we characterized the probability distributions for all relevant times in dose delivery. Second, we developed a model based on the measured data. This model serves as a starting point to improve treatment planning performance by providing a range of expected times for dose delivery. While the process was carried out using a compact synchrotron at our university, it can be easily adapted to other technologies.