BACKGROUND: While the Bragg peak proton beam (BP) is capable of superior target conformity and organs-at-risk sparing than the transmission proton beam (TB), its efficacy in FLASH-RT is hindered by both a slow energy switching process and the beam current. A universal range shifter (URS) can pull back the high-energy proton beam while preserving the beam current. Meanwhile, a superconducting gantry with large momentum acceptance (LMA-SC gantry) enables fast energy switching.
OBJECTIVE: This study explores the feasibility of multiple-energy BP FLASH-RT on the LMA-SC gantry.
METHODS: A simultaneous dose and spot map optimization algorithm was developed for BP FLASH-RT treatment planning to improve the dose delivery efficiency. The URS was designed to be 0-27 cm thick, with 1 cm per step. BP plans using the URS were optimized using single-field optimization (SFO) and multiple-field optimization (MFO) for ten prostate cancer patients and ten lung cancer patients. The plan delivery parameters, dose, and dose rate metrics of BP plans were compared to those of TB plans using the parameters of the LMA-SC gantry.
RESULTS: Compared to TB plans, BP plans significantly reduced MUs by 42.7% (P < 0.001) with SFO and 33.3% (P < 0.001) with MFO for prostate cases. For lung cases, the reduction in MUs was 56.8% (P < 0.001) with SFO and 36.4% (P < 0.001) with MFO. BP plans also outperformed TB plans by reducing mean normal tissue doses. BP-SFO plans achieved a reduction of 56.7% (P < 0.001) for prostate cases and 57.7% (P < 0.001) for lung cases, while BP-MFO plans achieved a reduction of 54.2% (P < 0.001) for the prostate case and 40.0% (P < 0.001) for lung cases. For both TB and BP plans, normal tissues in prostate and lung cases received 100.0% FLASH dose rate coverage (>40 Gy/s).
CONCLUSIONS: By utilizing the URS and the LMA-SC gantry, it is possible to perform multiple-energy BP FLASH-RT, resulting in better normal tissue sparing, as compared to TB plans.

BACKGROUND: The intensities (i.e., number of protons in monitor unit [MU]) of deliverable proton spots need to be either zero or meet a minimum-MU (MMU) threshold, which is a nonconvex problem. Since the dose rate is proportionally associated with the MMU threshold, higher-dose-rate proton radiation therapy (RT) (e.g., efficient intensity modulated proton therapy (IMPT) and ARC proton therapy, and high-dose-rate-induced FLASH effect needs to solve the MMU problem with larger MMU threshold, which however makes the nonconvex problem more difficult to solve.
OBJECTIVE: This work will develop a more effective optimization method based on orthogonal matching pursuit (OMP) for solving the MMU problem with large MMU thresholds, compared to state-of-the-art methods, such as alternating direction method of multipliers (ADMM), proximal gradient descent method (PGD), or stochastic coordinate descent method (SCD).
METHODS: The new method consists of two essential components. First, the iterative convex relaxation (ICR) method is used to determine the active sets for dose-volume planning constraints and decouple the MMU constraint from the rest. Second, a modified OMP optimization algorithm is used to handle the MMU constraint: the non-zero spots are greedily selected via OMP to form the solution set to be optimized, and then a convex constrained subproblem is formed and can be conveniently solved to optimize the spot weights restricted to this solution set via OMP. During this iterative process, the new non-zero spots localized via OMP will be adaptively added to or removed from the optimization objective.
RESULTS: The new method via OMP is validated in comparison with ADMM, PGD and SCD for high-dose-rate IMPT, ARC, and FLASH problems of large MMU thresholds, and the results suggest that OMP substantially improved the plan quality from PGD, ADMM and SCD in terms of both target dose conformality (e.g., quantified by max target dose and conformity index) and normal tissue sparing (e.g., mean and max dose). For example, in the brain case, the max target dose for IMPT/ARC/FLASH was 368.0%/358.3%/283.4% respectively for PGD, 154.4%/179.8%/150.0% for ADMM, 134.5%/130.4%/123.0% for SCD, while it was <120% in all scenarios for OMP; compared to PGD/ADMM/SCD, OMP improved the conformity index from 0.42/0.52/0.33 to 0.65 for IMPT and 0.46/0.60/0.61 to 0.83 for ARC.
CONCLUSIONS: A new OMP-based optimization algorithm is developed to solve the MMU problems with large MMU thresholds, and validated using examples of IMPT, ARC, and FLASH with substantially improved plan quality from ADMM, PGD, and SCD.

BACKGROUND: In treatment planning, beam angle optimization (BAO) refers to the selection of a subset with a given number of beam angles from all available angles that provides the best plan quality. BAO is a NP-hard combinatorial problem. Although exhaustive search (ES) can exactly solve BAO by exploring all possible combinations, ES is very time-consuming and practically infeasible.
OBJECTIVE: To the best of our knowledge, (1) no optimization method has been demonstrated that can provide the exact solution to BAO, and (2) no study has validated an optimization method for solving BAO by benchmarking with the optimal BAO solution (e.g., via ES), both of which will be addressed by this work.
METHODS: This work considers BAO for proton therapy, for example, the selection of 2-4 beam angles for IMPT. The optimal BAO solution is obtained via ES and serves as the ground truth. A new BAO algorithm, namely angle generation (AG) method, is proposed, and demonstrated to provide nearly-exact solutions for BAO in reference to the ES solution. AG iteratively optimizes the angular set via group-sparsity (GS) regularization, until the planning objective does not decrease further.
RESULTS: Since GS alone can also solve BAO, AG was validated and compared with GS for 2-angle brain, 3-angle lung, and 4-angle brain cases, in reference to the optimal BAO solutions obtained by ES: the AG solution had the rank (1/276, 1/2024, 4/10 626), while the GS solution had the rank (42/276, 279/2024, 4328/10 626).
CONCLUSIONS: A new BAO algorithm called AG is proposed and shown to provide substantially improved accuracy for BAO from current methods with nearly-exact solutions to BAO, in reference to the ground truth of optimal BAO solution via ES.

Objective. The optimization of energy layer distributions is crucial to 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 (NEJ) can substantially slow down the treatment delivery. This work will develop a new treatment plan optimization method with direct minimization of (NEJ), which will be shown to outperform state-of-the-art methods in both plan quality and delivery efficiency.Approach. The proposed method jointly optimizes the plan quality and minimizes the NEJ. To minimize NEJ, (1) the proton spotsxis summed per energy layer to form the energy vectory; (2)yis binarized via sigmoid transform intoy1; (3)y1is multiplied with a predefined energy order vector via dot product intoy2; (4)y2is filtered through the finite-differencing kernel intoy3in order to identify NEJ; (5) only the NEJ ofy3is penalized, whilexis optimized for plan quality. The solution algorithm to this new method is based on iterative convex relaxation.Main results. 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.Significance. 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.

UNASSIGNED: Previous studies show that dose escalation for gross tumor volume (GTV) improves local control of esophageal cancer (EC). However, optimal boosting remains uncertain. Recently, functional imaging guidance to achieve dose escalation in high-risk areas of tumors has been proposed.
UNASSIGNED: This study evaluated the feasibility of dose escalation in tumor regions with high fluorodeoxyglucose (FDG) uptake using intensity-modulated radiotherapy (IMRT) and intensity-modulated proton therapy (IMPT).
UNASSIGNED: GTVPET was defined as a high FDG uptake region with 50% SUVmax threshold for dose escalation. IMRT and IMPT plans were generated for three boosting modes: plan 50.4 (50.4 Gy in clinical target volume, CTV), plan 63 (50.4 Gy in CTV, 63 Gy in GTV), plan 70 (50.4 Gy in CTV, 63 Gy in GTV, and 70 Gy in GTVPET).
UNASSIGNED: Eleven patients with squamous cell carcinoma were evaluated. Dose parameters for heart, lung, and spinal cord were compared based on the dose-volume histogram (DVH).
UNASSIGNED: Paired t-test was performed on the doses to organs-at-risk (OARs) among plan 50.4, plan 63, and plan 70 for IMRT and IMPT.
UNASSIGNED: Dosimetric parameters for IMRT for heart, lung, and spinal cord increased significantly for plan 63 and some parameters even exceeded dose limits for OARs. Further dose escalation in GTV-PET did not increase dosimetric parameters significantly. Most dosimetric parameters of OARs in IMPT exhibited no statistical change compared with plan 50.4, and doses to OARs were far less than dose constraints.
UNASSIGNED: Dose escalation by IMRT may lead to increased risk of radiation-related injury. Further dose escalation in high FDG uptake regions did not increase doses to OARs. This dose escalation is ideal for achieving better outcomes for EC treatment.

OBJECTIVE: Spot-scanning arc therapy (SPArc) is an emerging proton modality that can potentially offer a combination of advantages in plan quality and delivery efficiency, compared with traditional IMPT of a few beam angles. Unlike IMPT, frequent low-to-high energy layer switching (so called switch-up (SU)) can degrade delivery efficiency for SPArc. However, it is a tradeoff between the minimization of SU times and the optimization of plan quality. This work will consider the energy layer optimization (ELO) problem for SPArc and develop a new ELO method via energy matrix (EM) regularization to improve plan quality and delivery efficiency.
METHODS: The major innovation of EM method for ELO is to design an EM that encourages desirable energy-layer map with minimal SU during SPArc, and then incorporate this EM into the SPArc treatment planning to simultaneously minimize the number of SU and optimize plan quality. The EM method is solved by the fast iterative shrinkage-thresholding algorithm and validated in comparison with a state-of-the-art method, so-called energy sequencing (ES).
RESULTS: EM is validated and compared with ES using representative clinical cases. In terms of delivery efficiency, EM had fewer SU than ES with an average of 35% reduction of SU. In terms of plan quality, compared with ES, EM had smaller optimization objective values and better target dose conformality, and generally lower dose to organs-at-risk and lower integral dose to body. In terms of computational efficiency, EM was substantially more efficient than ES by at least 10-fold.
CONCLUSIONS: We have developed a new ELO method for SPArc using EM regularization and shown that this new method EM can improve both delivery efficiency and plan quality, with substantially reduced computational time, compared with ES.

UNASSIGNED: To investigate the potential clinical benefit of utilizing intensity-modulated proton therapy (IMPT) to reduce acute hematologic toxicity for locally advanced non-small cell lung cancer (LA-NSCLC) patients and explore the feasibility of a model-based patient selection approach via the normal tissue complication probability (NTCP).
UNASSIGNED: Twenty patients with LA-NSCLC were retrospectively selected. Volumetric modulated arc photon therapy (VMAT) and IMPT plans were generated with a prescription dose of 60 Gy in 30 fractions. A wide range of cases with varied tumor size, location, stations of metastatic lymph nodes were selected to represent the general cancer group. Contouring and treatment planning followed RTOG-1308 protocol. Doses to thoracic vertebral bodies (TVB) and other organ at risks were compared. Risk of grade ≥ 3 acute hematologic toxicity (HT3+) were calculated based on the NTCP model, and patients with a reduction on NTCP of HT3+ from VMAT to IMPT (△NTCP_HT3+) ≥ 10% were considered to \'significantly benefit from proton therapy.\'
UNASSIGNED: Compared to VMAT, IMPT significantly reduced the dose to the TVB, the lung, the heart, the esophagus and the spinal cord. Tumor distance to TVB was significantly associated with △NTCP _HT3+ ≥ 10%. For the patients with tumor distance ≤ 0.7 cm to TVB, the absolute reduction of dose (mean, V30 and V40) to TVB was significantly lower than that in patients with tumor distance > 0.7 cm.
UNASSIGNED: IMPT decreased the probability of HT3+ compared to VMAT by reducing the dose to the TVB in LA-NSCLC patients. Patients with tumor distance to TVB less than 0.7 cm are likely to benefit most from proton over photon therapy.

OBJECTIVE: This paper focused on the design and optimization of ridge filter-based intensity-modulated proton therapy (IMPT), and its potential applications for FLASH. Differing from the standard pencil beam scanning (PBS) mode, no energy/layer switching is required and total treatment time can be shortened.
METHODS: Unique dose-influence matrices were generated as a proton beam traverses through slabs of different thicknesses (i.e., modulation by different layers). To establish the references for comparison, conventional IMPT plans (single field) were created using a large-scale nonlinear solver. The spot weights from the reference IMPT plans were used as inputs for optimizing the design of ridge filters. Two designs were evaluated: model A (static) and model B (dynamic). The ridge filter designs were first verified (by GEANT4 simulation) in a water phantom and then in an H&N case. A direct comparison was made between the GEANT4 simulation results of two models and their respective references, with regard to plan quality, dose-averaged dose rate, and total treatment time.
RESULTS: In both the water phantom and the H&N case, two models are able to modulate dose distributions with high conformity, showing no significant difference relative to the reference plans. Dose rate-volume histograms suggest that in order to achieve a dose rate of 40 Gy/s over 90% PTV, the beam intensity needs to be 2.5 × 1011 protons/s for both models. For a fraction dose of 10 Gy, the total treatment time (including both irradiation time and dead time) can be shortened by a factor of 4.9 (model A) and 6.5 (model B), relative to the reference plans.
CONCLUSIONS: Two proposed designs (both static and dynamic) can be used for PBS-IMPT requiring no layer switching. They are promising candidates for FLASH-IMPT capable of reducing treatment time and achieving high dose rates while maintaining dose conformity simultaneously.

Objective. Deliverable proton spots are subject to the minimum monitor-unit (MMU) constraint. The MMU optimization problem with relatively large MMU threshold remains mathematically challenging due to its strong nonconvexity. However, the MMU optimization is fundamental to proton radiotherapy (RT), including efficient IMPT and proton arc delivery (ARC). This work aims to develop a new optimization algorithm that is effective in solving the MMU problem.Approach.Our new algorithm is primarily based on stochastic coordinate decent (SCD) method. It involves three major steps: first to decouple the determination of active sets for dose-volume-histogram (DVH) planning constraints from the MMU problem via iterative convex relaxation method; second to handle the nonconvexity of the MMU constraint via SCD to localize the index set of nonzero spots; third to solve convex subproblems projected to this convex set of nonzero spots via projected gradient descent method.Main results.Our new method SCD is validated and compared with alternating direction method of multipliers (ADMM) for IMPT and ARC. The results suggest SCD had better plan quality than ADMM, e.g. the improvement of conformal index (CI) from 0.56 to 0.69 during IMPT, and from 0.28 to 0.80 during ARC for the lung case. Moreover, SCD successfully handled the nonconvexity from large MMU threshold that ADMM failed to handle, in the sense that (1) the plan quality from ARC was worse than IMPT (e.g. CI was 0.28 with IMPT and 0.56 with ARC for the lung case), when ADMM was used; (2) in contrast, with SCD, ARC achieved better plan quality than IMPT (e.g. CI was 0.69 with IMPT and 0.80 with ARC for the lung case), which is compatible with more optimization degrees of freedom from ARC compared to IMPT.Significance. To the best of our knowledge, our new MMU optimization method via SCD can effectively handle the nonconvexity from large MMU threshold that none of the current methods can solve. Therefore, we have developed a unique MMU optimization algorithm via SCD that can be used for efficient IMPT, proton ARC, and other particle RT applications where large MMU threshold is desirable (e.g. for the delivery of high dose rates or/and a large number of spots).

OBJECTIVE: Compared to CONV-RT (with conventional dose rate), FLASH-RT (with ultra-high dose rate) can provide biological dose sparing for organs-at-risk (OARs) via the so-called FLASH effect, in addition to physical dose sparing. However, the FLASH effect only occurs, when both dose and dose rate meet certain minimum thresholds. This work will develop a simultaneous dose and dose rate optimization (SDDRO) method accounting for both FLASH dose and dose rate constraints during treatment planning for pencil-beam-scanning proton therapy.
METHODS: SDDRO optimizes the FLASH effect (specific to FLASH-RT) as well as the dose distribution (similar to CONV-RT). The nonlinear dose rate constraint is linearized, and the reformulated optimization problem is efficiently solved via iterative convex relaxation powered by alternating direction method of multipliers. To resolve and quantify the generic tradeoff of FLASH-RT between FLASH and dose optimization, we propose the use of FLASH effective dose based on dose modifying factor (DMF) owing to the FLASH effect.
RESULTS: FLASH-RT via transmission beams (TB) (IMPT-TB or SDDRO) and CONV-RT via Bragg peaks (BP) (IMPT-BP) were evaluated for clinical prostate, lung, head-and-neck (HN), and brain cases. Despite the use of TB, which is generally suboptimal to BP for normal tissue sparing, FLASH-RT via SDDRO considerably reduced FLASH effective dose for high-dose OAR adjacent to the target. For example, in the lung SBRT case, the max esophageal dose constraint 27 Gy was only met by SDDRO (24.8 Gy), compared to IMPT-BP (35.3 Gy) or IMPT-TB (36.6 Gy); in the brain SRS case, the brain constraint V12Gy≤15cc was also only met by SDDRO (13.7cc), compared to IMPT-BP (43.9cc) or IMPT-TB (18.4cc). In addition, SDDRO substantially improved the FLASH coverage from IMPT-TB, e.g., an increase from 37.2% to 67.1% for lung, from 39.1% to 58.3% for prostate, from 65.4% to 82.1% for HN, from 50.8% to 73.3% for the brain.
CONCLUSIONS: Both FLASH dose and dose rate constraints are incorporated into SDDRO for FLASH-RT that jointly optimizes the FLASH effect and physical dose distribution. FLASH effective dose via FLASH DMF is introduced to reconcile the tradeoff between physical dose sparing and FLASH sparing, and quantify the net effective gain from CONV-RT to FLASH-RT.