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

Lyu

et al. 2020

Self Cite

Purpose: 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. Methods: 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. Results: 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. Conclusion: We developed a computationally efficient spot-scanning proton arc optimization method, which ...

Section: Discussionmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 99%

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

Lyu

et al. 2020

Self Cite

“…The optimal spot combinations are likely beam orientation dependent. We have previously developed a beam orientation optimization framework for IMPT . In this study, fixed beam orientations are used but both the SenR plan optimality and robustness can be conceivably improved by unifying the two optimization frameworks in future research.…”

Section: Discussionmentioning

confidence: 99%

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

O’Connor

et al. 2019

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Purpose 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. Methods 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). Results 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. Conclusion 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 b...

“…Assume

scriptB

is the set containing all the feasible candidate beams. As proposed in our previous work, the selection of a small number of beams from the set

scriptB

by group sparsity regularization is formulated as the following optimization problem:

\begin{matrix} \underset{x}{minimize} & normalΓ ()(, italicAx) + \sum_{b \in scriptB} α_{b} {| x_{b} |}_{2}^{1 / 2} \\ subjectto & x \geq 0 \end{matrix},

where x b is a vector representing the intensities of scanning spots from the candidate beam b , and x is the concatenation of all the vectors

x_{b} (b \in B)

. A is the dose calculation matrix including all candidate beams, with each column being the vectorized doses delivered to the patient from one unit intensity spot.…”

Section: Methodsmentioning

confidence: 99%

Robust beam orientation optimization for intensity‐modulated proton therapy

Neph

et al. 2019

Self Cite

Purpose Dose conformality and robustness are equally important in intensity modulated proton therapy (IMPT). Despite the obvious implication of beam orientation on both dosimetry and robustness, an automated, robust beam orientation optimization algorithm has not been incorporated due to the problem complexity and paramount computational challenge. In this study, we developed a novel IMPT framework that integrates robust beam orientation optimization (BOO) and robust fluence map optimization (FMO) in a unified framework. Methods The unified framework is formulated to include a dose fidelity term, a heterogeneity‐weighted group sparsity term, and a sensitivity regularization term. The L2, 1/2‐norm group sparsity is used to reduce the number of active beams from the initial 1162 evenly distributed noncoplanar candidate beams, to between two and four. A heterogeneity index, which evaluates the lateral tissue heterogeneity of a beam, is used to weigh the group sparsity term. With this index, beams more resilient to setup uncertainties are encouraged. There is a symbiotic relationship between the heterogeneity index and the sensitivity regularization; the integrated optimization framework further improves beam robustness against both range and setup uncertainties. This Sensitivity regularization and Heterogeneity weighting based BOO and FMO framework (SHBOO‐FMO) was tested on two skull‐base tumor (SBT) patients and two bilateral head‐and‐neck (H&N) patients. The conventional CTV‐based optimized plans (Conv) with SHBOO‐FMO beams (SHBOO‐Conv) and manual beams (MAN‐Conv) were compared to investigate the beam robustness of the proposed method. The dosimetry and robustness of SHBOO‐FMO plan were compared against the manual beam plan with CTV‐based voxel‐wise worst‐case scenario approach (MAN‐WC). Results With SHBOO‐FMO method, the beams with superior range robustness over manual beams were selected while the setup robustness was maintained or improved. On average, the lowest [D95%, V95%, V100%] of CTV were increased from [93.85%, 91.06%, 70.64%] in MAN‐Conv plans, to [98.62%, 98.61%, 96.17%] in SHBOO‐Conv plans with range uncertainties. With setup uncertainties, the average lowest [D98%, D95%, V95%, V100%] of CTV were increased from [92.06%, 94.83%, 94.31%, 78.93%] in MAN‐Conv plans, to [93.54%, 96.61%, 97.01%, 91.98%] in SHBOO‐Conv plans. Compared with the MAN‐WC plans, the final SHBOO‐FMO plans achieved comparable plan robustness and better OAR sparing, with an average reduction of [Dmean, Dmax] of [6.31, 6.55] GyRBE for the SBT cases and [1.89, 5.08] GyRBE for the H&N cases from the MAN‐WC plans. Conclusion We developed a novel method to integrate robust BOO and robust FMO into IMPT optimization for a unified solution of both BOO and FMO, generating plans with superior dosimetry and good robustness.