  Background: Proton arc therapy is an emerging radiation therapy technique
where either the gantry or the patient continuously rotates during the
irradiation treatment. One of the perceived advantages of proton arc therapy is
the reduced treatment time, but it is still unclear exactly how long these
treatment times will be, given that no machine capable of its delivery is
available at the market at the time of writing. Purpose: We introduce the
algorithm Arc Trajectory Optimization Method (ATOM), which aims to determine an
efficient velocity profile for the gantry for rapid delivery of a given proton
arc treatment plan. Methods: ATOM computes the trajectory with the shortest
delivery time while ensuring there is enough time to deliver all spots in each
energy layer and switch energy between layers. The feasibility of the dynamic
gantry movement was assured by enforcing maximum and minimum limits for
velocity, acceleration, and jerk. This was achieved by discretizing the gantry
velocity and combining the A* algorithm with the open-source motion generation
library Ruckig. The algorithm was tested on a synthetic data set as well as a
liver case, a prostate case and a head and neck case. Results: Arc trajectories
for plans with 360 energy layers were calculated in under a second using 256
discrete velocities. Conclusions: ATOM is an open-source C++ library with a
Python interface that rapidly generates velocity profiles, making it a highly
efficient tool for determining proton arc delivery times, which could be
integrated into the treatment planning process.
