A novel energy layer optimization framework for spot-scanning proton arc therapy.

Spot-scanning proton arc therapy (SPAT) is an emerging modality to improve plan conformality and delivery efficiency. A greedy and heuristic method is proposed in the existing SPAT algorithm to select energy layers and sequence energy switching with gantry rotation, which does not promise optimality in either dosimetry or efficiency. We aim to develop a method to solve the energy layer switching and dosimetry optimization problems in an integrated framework for SPAT. In an integrated approach, energy layer optimization for spot-scanning proton arc therapy (ELO-SPAT) is formulated with a dose fidelity term, a group sparsity regularization, a log barrier regularization, and an energy sequencing (ES) penalty. The combination of L2,1/2-norm group sparsity regularization and log barrier function allows one energy layer being selected per control point. The ES regularization term sorts the delivery sequence from high energy to low energy to reduce the total energy layer switching time (ELST) and subsequently the total delivery time. Within the ES penalty, the gradient of layer weights between adjacent beams is first calculated along beam direction and then along energy direction. The gradients indicate energy switch patterns between two adjacent beams. The time-wise costly energy switch-up is more heavily penalized in the ES term. This ELO-SPAT method was tested on one frontal base-of-skull (BOS) patient, one chordoma (CHDM) patient with a simultaneous integrated boost, one bilateral head-and-neck (H&N) patient, and one lung (LNG) patient. We compared ELO-SPAT with intensity-modulated proton therapy (IMPT) using discrete beams and SPArc by Ding et al. For the two arc algorithms, both the plans with and without energy sequencing were created and compared. Energy layer optimization for spot-scanning proton arc therapy reduced the runtime of optimization by 84% on average compared with the greedy SPArc method. In both the ELO-SPAT plans with and without ES, one energy layer per control point was selected. Without ES regularization, the energy sequence was arbitrary, with around 40-60 switch-up for the tested cases. After adding ES regularization, the number of energy switch-up was reduced to less than 20. Compared with the energy sequenced SPArc plans, the ELO-SPAT plans with ES led to 24% less total ELST for synchrotron plans and 14% less for cyclotron plans. Both the ELO-SPAT and SPArc plans achieved better sparing compared with the IMPT plans for most Organs-at-risks (OARs), with or without ES. Without ES, the ELO-SPAT plans achieved further improvement of the OARs compared with the SPArc plans, with an averaged reduction of OAR [Dmean, Dmax] by [1.57, 3.34] GyRBE. Adding the ES regularization degraded the plan quality, but the ELO-SPAT plans still had comparable or slightly better sparing than the SPArc plans with ES, with an averaged reduction of OAR [Dmean, Dmax] by [1.42, 2.34] GyRBE. We developed a computationally efficient spot-scanning proton arc optimization method, which solved energy layer selection and sequencing in an integrated framework, generating plans with good dosimetry and high delivery efficiency.

Gu W ，Ruan D ，Lyu Q ，Zou W ，Dong L ，Sheng K ... -  《-》

Integrated beam orientation and scanning-spot optimization in intensity-modulated proton therapy for brain and unilateral head and neck tumors.

Intensity-Modulated Proton Therapy (IMPT) is the state-of-the-art method of delivering proton radiotherapy. Previous research has been mainly focused on optimization of scanning spots with manually selected beam angles. Due to the computational complexity, the potential benefit of simultaneously optimizing beam orientations and spot pattern could not be realized. In this study, we developed a novel integrated beam orientation optimization (BOO) and scanning-spot optimization algorithm for intensity-modulated proton therapy (IMPT). A brain chordoma and three unilateral head-and-neck patients with a maximal target size of 112.49 cm3 were included in this study. A total number of 1162 noncoplanar candidate beams evenly distributed across 4π steradians were included in the optimization. For each candidate beam, the pencil-beam doses of all scanning spots covering the PTV and a margin were calculated. The beam angle selection and spot intensity optimization problem was formulated to include three terms: a dose fidelity term to penalize the deviation of PTV and OAR doses from ideal dose distribution; an L1-norm sparsity term to reduce the number of active spots and improve delivery efficiency; a group sparsity term to control the number of active beams between 2 and 4. For the group sparsity term, convex L2,1-norm and nonconvex L2,1/2-norm were tested. For the dose fidelity term, both quadratic function and linearized equivalent uniform dose (LEUD) cost function were implemented. The optimization problem was solved using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The IMPT BOO method was tested on three head-and-neck patients and one skull base chordoma patient. The results were compared with IMPT plans created using column generation selected beams or manually selected beams. The L2,1-norm plan selected spatially aggregated beams, indicating potential degeneracy using this norm. L2,1/2-norm was able to select spatially separated beams and achieve smaller deviation from the ideal dose. In the L2,1/2-norm plans, the [mean dose, maximum dose] of OAR were reduced by an average of [2.38%, 4.24%] and[2.32%, 3.76%] of the prescription dose for the quadratic and LEUD cost function, respectively, compared with the IMPT plan using manual beam selection while maintaining the same PTV coverage. The L2,1/2 group sparsity plans were dosimetrically superior to the column generation plans as well. Besides beam orientation selection, spot sparsification was observed. Generally, with the quadratic cost function, 30%~60% spots in the selected beams remained active. With the LEUD cost function, the percentages of active spots were in the range of 35%~85%.The BOO-IMPT run time was approximately 20 min. This work shows the first IMPT approach integrating noncoplanar BOO and scanning-spot optimization in a single mathematical framework. This method is computationally efficient, dosimetrically superior and produces delivery-friendly IMPT plans.

Gu W ，O'Connor D ，Nguyen D ，Yu VY ，Ruan D ，Dong L ，Sheng K ... -  《-》

Energy layer optimization via energy matrix regularization for proton spot-scanning arc therapy.

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. 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). 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. 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.

Zhang G ，Shen H ，Lin Y ，Chen RC ，Long Y ，Gao H ... -  《-》

Robust optimization for intensity-modulated proton therapy with soft spot sensitivity regularization.

Proton dose distribution is sensitive to uncertainties in range estimation and patient positioning. Currently, the proton robustness is managed by worst-case scenario optimization methods, which are computationally inefficient. To overcome these challenges, we develop a novel intensity-modulated proton therapy (IMPT) optimization method that integrates dose fidelity with a sensitivity term that describes dose perturbation as the result of range and positioning uncertainties. In the integrated optimization framework, the optimization cost function is formulated to include two terms: a dose fidelity term and a robustness term penalizing the inner product of the scanning spot sensitivity and intensity. The sensitivity of an IMPT scanning spot to perturbations is defined as the dose distribution variation induced by range and positioning errors. To evaluate the sensitivity, the spatial gradient of the dose distribution of a specific spot is first calculated. The spot sensitivity is then determined by the total absolute value of the directional gradients of all affected voxels. The fast iterative shrinkage-thresholding algorithm is used to solve the optimization problem. This method was tested on three skull base tumor (SBT) patients and three bilateral head-and-neck (H&N) patients. The proposed sensitivity-regularized method (SenR) was implemented on both clinic target volume (CTV) and planning target volume (PTV). They were compared with conventional PTV-based optimization method (Conv) and CTV-based voxel-wise worst-case scenario optimization approach (WC). Under the nominal condition without uncertainties, the three methods achieved similar CTV dose coverage, while the CTV-based SenR approach better spared organs at risks (OARs) compared with the WC approach, with an average reduction of [Dmean, Dmax] of [4.72, 3.38]  GyRBE for the SBT cases and [2.54, 3.33] GyRBE for the H&N cases. The OAR sparing of the PTV-based SenR method was comparable with the WC method. The WC method, and SenR approaches all improved the plan robustness from the conventional PTV-based method. On average, under range uncertainties, the lowest [D95%, V95%, V100%] of CTV were increased from [93.75%, 88.47%, 47.37%] in the Conv method, to [99.28%, 99.51%, 86.64%] in the WC method, [97.71%, 97.85%, 81.65%] in the SenR-CTV method and [98.77%, 99.30%, 85.12%] in the SenR-PTV method, respectively. Under setup uncertainties, the average lowest [D95%, V95%, V100%] of CTV were increased from [95.35%, 94.92%, 65.12%] in the Conv method, to [99.43%, 99.63%, 87.12%] in the WC method, [96.97%, 97.13%, 77.86%] in the SenR-CTV method, and [98.21%, 98.34%, 83.88%] in the SenR-PTV method, respectively. The runtime of the SenR optimization is eight times shorter than that of the voxel-wise worst-case method. We developed a novel computationally efficient robust optimization method for IMPT. The robustness is calculated as the spot sensitivity to both range and shift perturbations. The dose fidelity term is then regularized by the sensitivity term for the flexibility and trade-off between the dosimetry and the robustness. In the stress test, SenR is more resilient to unexpected uncertainties. These advantages in combination with its fast computation time make it a viable candidate for clinical IMPT planning.

Gu W ，Ruan D ，O'Connor D ，Zou W ，Dong L ，Tsai MY ，Jia X ，Sheng K ... -  《-》

Spot-Scanning Proton Arc (SPArc) Therapy: The First Robust and Delivery-Efficient Spot-Scanning Proton Arc Therapy.

To present a novel robust and delivery-efficient spot-scanning proton arc (SPArc) therapy technique. A SPArc optimization algorithm was developed that integrates control point resampling, energy layer redistribution, energy layer filtration, and energy layer resampling. The feasibility of such a technique was evaluated using sample patients: 1 patient with locally advanced head and neck oropharyngeal cancer with bilateral lymph node coverage, and 1 with a nonmobile lung cancer. Plan quality, robustness, and total estimated delivery time were compared with the robust optimized multifield step-and-shoot arc plan without SPArc optimization (Arcmulti-field) and the standard robust optimized intensity modulated proton therapy (IMPT) plan. Dose-volume histograms of target and organs at risk were analyzed, taking into account the setup and range uncertainties. Total delivery time was calculated on the basis of a 360° gantry room with 1 revolutions per minute gantry rotation speed, 2-millisecond spot switching time, 1-nA beam current, 0.01 minimum spot monitor unit, and energy layer switching time of 0.5 to 4 seconds. The SPArc plan showed potential dosimetric advantages for both clinical sample cases. Compared with IMPT, SPArc delivered 8% and 14% less integral dose for oropharyngeal and lung cancer cases, respectively. Furthermore, evaluating the lung cancer plan compared with IMPT, it was evident that the maximum skin dose, the mean lung dose, and the maximum dose to ribs were reduced by 60%, 15%, and 35%, respectively, whereas the conformity index was improved from 7.6 (IMPT) to 4.0 (SPArc). The total treatment delivery time for lung and oropharyngeal cancer patients was reduced by 55% to 60% and 56% to 67%, respectively, when compared with Arcmulti-field plans. The SPArc plan is the first robust and delivery-efficient proton spot-scanning arc therapy technique, which could potentially be implemented into routine clinical practice.

Ding X ，Li X ，Zhang JM ，Kabolizadeh P ，Stevens C ，Yan D ... -  《-》