An evolutionary optimization algorithm for proton arc therapy

Objective. Proton arc plan normally contains thousands of spot numbers and hundreds of energy layers. A recent study reported that the beam delivery time (BDT) is proportional to the spot numbers. Thus, it is critical to find an optimal plan with a fast delivery speed while maintaining a good plan quality. Thus, we developed a novel evolutionary algorithm to directly search for the optimal spot sparsity solution to balance plan quality and BDT.Approach. The planning platform included a plan quality objective, a generator, and a selector. The generator is based on trust-region-reflective solver. A selector was designed to filter or add the spot according to the expected spot number, based on the user's input of BDT. The generator and selector are used alternatively to optimize a spot sparsity solution. Three clinical cases' CT and structure datasets, e.g. brain, lung, and liver cancer, were used for testing purposes. A series of user-defined BDTs from 15 to 250 s were used as direct inputs. The relationship between the plan's cost function value and BDT was evaluated in these three cases.Main results. The evolutionary algorithm could optimize a proton arc plan based on clinical user input BDT directly. The plan quality remains optimal in the brain, lung, and liver cases until the BDT was shorter than 25 s, 50 s and 100 s, respectively. The plan quality degraded as the input delivery time became too short, indicating that the plan lacked enough spot or degree of freedom.Significance. This is the first proton arc planning framework to directly optimize plan quality with the BDT as an input for the new generation of proton therapy systems. This work paved the roadmap for implementing such new technology in a routine clinic and provided a planning platform to explore the trade-off between the BDT and plan quality.