A New Treatment Planning Method for Efficient Proton ARC Therapy with Direct Minimization of Number of Energy Jumps

Abstract

The optimization of energy layer distributions is crucial for efficient proton ARC therapy: on one hand, a sufficient number of energy layers is needed to ensure the plan quality; on the other hand, an excess number of energy jumps can substantially slow down the treatment delivery. This work will develop a new treatment plan optimization method with direct minimization of number of energy jumps (NEJ), which will be shown to outperform state-of-the-art methods in both plan quality and delivery efficiency. The proposed method jointly optimizes the plan quality and minimizes the NEJ. To minimize NEJ, (1) the proton spots x is summed per energy layer to form the energy vector y; (2) y is binarized via sigmoid transform into y1; (3) y1 is multiplied with a predefined energy order vector via dot product into y2; (4) y2 is filtered through the finite-differencing kernel into y3 in order to identify NEJ; (5) only the NEJ of y3 is penalized, while x is optimized for plan quality. The solution algorithm to this new method is based on iterative convex relaxation. The new method is validated in comparison with state-of-the-art methods called energy sequencing (ES) method and energy matrix (EM) method. In terms of delivery efficiency, the new method had fewer NEJ, less energy switching time, and generally less total delivery time. In terms of plan quality, the new method had smaller optimization objective values, lower normal tissue dose, and generally better target coverage. A head-and-neck case is provided in the table with the following dosimetric parameters: planning objective value F; conformity index CI; homogeneity index HI; mean dose of larynx DOAR; mean body dose Dbody; the unit of dose is Gy. We have developed a new treatment plan optimization method with direct minimization of NEJ, and demonstrated that this new method outperformed state-of-the-art methods (ES and EM) in both plan quality and delivery efficiency.