A treatment plan optimization method with direct minimization of number of energy jumps for proton arc therapy

TEAM: Triangular-mEsh Adaptive and Multiscale proton spot generation method

BACKGROUND

Proton therapy is preferred for its dose conformality to spare normal tissues and organs-at-risk (OAR) via Bragg peaks with negligible exit dose. However, proton dose conformality can be further optimized: (1) the spot placement is based on the structured (e.g., Cartesian) grid, which may not offer conformal shaping to complex tumor targets; (2) the spot sampling pattern is uniform, which may be insufficient at the tumor boundary to provide the sharp dose falloff, and at the same time may be redundant at the tumor interior to provide the uniform dose coverage, for example, due to multiple Coulomb scattering (MCS); and (3) the lateral spot penumbra increases with respect to the depth due to MCS, which blurs the lateral dose falloff. On the other hand, while (1) the deliverable spots are subject to the minimum-monitor-unit (MMU) constraint, and (2) the dose rate is proportional to the MMU threshold, the current spot sampling method is sensitive to the MMU threshold and can fail to provide satisfactory plan quality for a large MMU threshold (i.e., high-dose-rate delivery).

PURPOSE

This work will develop a novel Triangular-mEsh-based Adaptive and Multiscale (TEAM) proton spot generation method to address these issues for optimizing proton dose conformality and plan delivery efficiency.

METHODS

Compared to the standard clinically-used spot placement method, three key elements of TEAM are as follows: (1) a triangular mesh instead of a structured grid: the triangular mesh is geometrically more conformal to complex target shapes and therefore more efficient and accurate for dose shaping inside and around the target; (2) adaptive sampling instead of uniform sampling: the adaptive sampling consists of relatively dense sampling at the tumor boundary to create the sharp dose falloff, which is more accurate, and coarse sampling at the tumor interior to uniformly cover the target, which is more efficient; and (3) depth-dependent sampling instead of depth-independent sampling: the depth-dependent sampling is used to compensate for MCS, that is, with increasingly dense sampling at the tumor boundary to improve dose shaping accuracy, and increasingly coarse sampling at the tumor interior to improve dose shaping efficiency, as the depth increases. In the TEAM method the spot locations are generated for each energy layer and layer-by-layer in the multiscale fashion; and then the spot weights are derived by solving the IMPT problem of dose-volume planning objectives, MMU constraints, and robustness optimization with respect to range and setup uncertainties.

RESULTS

Compared to the standard clinically-used spot placement method UNIFORM, TEAM achieved (1) better plan quality using <60% number of spots of UNIFORM; (2) better robustness to the number of spots; (3) better robustness to a large MMU threshold. Furthermore, TEAM provided better plan quality with fewer spots than other adaptive methods (Cartesian-grid or triangular-mesh).

CONCLUSIONS

A novel triangular-mesh-based proton spot placement method called TEAM is proposed, and it is demonstrated to improve plan quality, robustness to the number of spots, and robustness to the MMU threshold, compared to the clinically-used spot placement method and other adaptive methods.

Simultaneous dose and dose rate optimization via dose modifying factor modeling for FLASH effective dose

BACKGROUND

Although the FLASH radiotherapy (FLASH) can improve the sparing of organs-at-risk (OAR) via the FLASH effect, it is generally a tradeoff between the physical dose coverage and the biological FLASH coverage, for which the concept of FLASH effective dose (FED) is needed to quantify the net improvement of FLASH, compared to the conventional radiotherapy (CONV).

PURPOSE

This work will develop the first-of-its-kind treatment planning method called simultaneous dose and dose rate optimization via dose modifying factor modeling (SDDRO-DMF) for proton FLASH that directly optimizes FED.

METHODS

SDDRO-DMF models and optimizes FED using FLASH dose modifying factor (DMF) models, which can be classified into two categories: (1) the phenomenological model of the FLASH effect, such as the FLASH effectiveness model (FEM); (2) the mechanistic model of the FLASH radiobiology, such as the radiolytic oxygen depletion (ROD) model. The general framework of SDDRO-DMF will be developed, with specific DMF models using FEM and ROD, as a demonstration of general applicability of SDDRO-DMF for proton FLASH via transmission beams (TB) or Bragg peaks (BP) with single-field or multi-field irradiation. The FLASH dose rate is modeled as pencil beam scanning dose rate. The solution algorithm for solving the inverse optimization problem of SDDRO-DMF is based on iterative convex relaxation method.

RESULTS

SDDRO-DMF is validated in comparison with IMPT and a state-of-the-art method called SDDRO, with demonstrated efficacy and improvement for reducing the high dose and the high-dose volume for OAR in terms of FED. For example, in a SBRT lung case of the dose-limiting factor that the max dose of brachial plexus should be no more than 26 Gy, only SDDRO-DMF met this max dose constraint; moreover, SDDRO-DMF completely eliminated the high-dose (V70%) volume to zero for CTV10mm (a high-dose region as a 10 mm ring expansion of CTV).

CONCLUSION

We have proposed a new proton FLASH optimization method called SDDRO-DMF that directly optimizes FED using phenomenological or mechanistic models of DMF, and have demonstrated the efficacy of SDDO-DMF in reducing the high-dose volume or/and the high-dose value for OAR, compared to IMPT and a state-of-the-art method SDDRO.

A novel treatment planning method via scissor beams for uniform-target-dose proton GRID with peak-valley-dose-ratio optimization

BACKGROUND

Proton spatially fractionated RT (SFRT) can potentially synergize the unique advantages of using proton Bragg peak and SFRT peak-valley dose ratio (PVDR) to reduce the radiation-induced damage for normal tissues. Uniform-target-dose (UTD) proton GRID is a proton SFRT modality that can be clinically desirable and conveniently adopted since its UTD resembles target dose distribution in conventional proton RT (CONV). However, UTD proton GRID is not used clinically, which is likely due to the lack of an effective treatment planning method.

PURPOSE

This work will develop a novel treatment planning method using scissor beams (SB) for UTD proton GRID, with the joint optimization of PVDR and dose objectives.

METHODS

The SB method for spatial dose modulation in normal tissues with UTD has two steps: (1) a primary beam (PB) is halved with interleaved beamlets, to generate spatial dose modulation in normal tissues; (2) a complementary beam (CB) is added to fill in previously valley-dose positions in the target to generate UTD, while the CB is angled slightly from the PB, to maintain spatial dose modulation in normal tissues. A treatment planning method with PVDR optimization via the joint total variation and L1 (TVL1) regularization is developed to jointly optimize PVDR and dose objectives. The plan optimization solution is obtained using an iterative convex relaxation algorithm.

RESULTS

The new methods SB and SB-TVL1 were validated in comparison with CONV. Compared to CONV of relatively homogeneous dose distribution, SB had modulated spatial dose pattern in normal tissues with UTD and comparable plan quality. Compared to SB, SB-TVL1 further maximized PVDR, with comparable dose-volume parameters.

CONCLUSIONS

A novel SB method is proposed that can generate modulated spatial dose pattern in normal tissues to achieve UTD proton GRID. A treatment planning method with PVDR optimization capability via TVL1 regularization is developed that can jointly optimize PVDR and dose objectives for proton GRID.

A novel fast robust optimization algorithm for intensity-modulated proton therapy with minimum monitor unit constraint

BACKGROUND

Intensity-modulated proton therapy (IMPT) optimizes spot intensities and position, providing better conformability. However, the successful application of IMPT is dependent upon addressing the challenges posed by range and setup uncertainties. In order to address the uncertainties in IMPT, robust optimization is essential.

PURPOSE

This study aims to develop a novel fast algorithm for robust optimization of IMPT with minimum monitor unit (MU) constraint.

METHODS AND MATERIALS

The study formulates a robust optimization problem and proposes a novel, fast algorithm based on the alternating direction method of multipliers (ADMM) framework. This algorithm enables distributed computation and parallel processing. Ten clinical cases were used as test scenarios to evaluate the performance of the proposed approach. The robust optimization method (RBO-NEW) was compared with plans that only consider nominal optimization using CTV (NMO-CTV) without handling uncertainties and PTV (NMO-PTV) to handle the uncertainties, as well as with conventional robust-optimized plans (RBO-CONV). Dosimetric metrics, including D95, homogeneity index, and Dmean, were used to evaluate the dose distribution quality. The area under the root-mean-square dose (RMSD)-volume histogram curves (AUC) and dose-volume histogram (DVH) bands were used to evaluate the robustness of the treatment plan. Optimization time cost was also assessed to measure computational efficiency.

RESULTS

The results demonstrated that the RBO plans exhibited better plan quality and robustness than the NMO plans, with RBO-NEW showing superior computational efficiency and plan quality compared to RBO-CONV. Specifically, statistical analysis results indicated that RBO-NEW was able to reduce the computational time from389.70 ± 207.40 $389.70\pm 207.40$ to228.60 ± 123.67 $228.60\pm 123.67$ s (p < 0.01 $p<0.01$ ) and reduce the mean organ-at-risk (OAR) dose from9.38 ± 12.80 $9.38\pm 12.80$ % of the prescription dose to9.07 ± 12.39 $9.07\pm 12.39$ % of the prescription dose (p < 0.05 $p<0.05$ ) compared to RBO-CONV.

CONCLUSION

This study introduces a novel fast robust optimization algorithm for IMPT treatment planning with minimum MU constraint. Such an algorithm is not only able to enhance the plan's robustness and computational efficiency without compromising OAR sparing but also able to improve treatment plan quality and reliability.

Efficient proton arc optimization and delivery through energy layer pre-selection and post-filtering

BACKGROUND

Proton arc therapy (PAT) has emerged as a promising approach for improving dose distribution, but also enabling simpler and faster treatment delivery in comparison to conventional proton treatments. However, the delivery speed achievable in proton arc relies on dedicated algorithms, which currently do not generate plans with a clear speed-up and sometimes even result in increased delivery time.

PURPOSE

This study aims to address the challenge of minimizing delivery time through a hybrid method combining a fast geometry-based energy layer (EL) pre-selection with a dose-based EL filtering, and comparing its performance to a baseline approach without filtering.

METHODS

Three methods of EL filtering were developed: unrestricted, switch-up (SU), and switch-up gap (SU gap) filtering. The unrestricted method filters the lowest weighted EL while the SU gap filtering removes the EL around a new SU to minimize the gantry rotation braking. The SU filtering removes the lowest weighted group of EL that includes a SU. These filters were combined with the RayStation dynamic proton arc optimization framework energy layer selection and spot assignment (ELSA). Four bilateral oropharyngeal and four lung cancer patients' data were used for evaluation. Objective function values, target coverage robustness, organ-at-risk doses and normal tissue complication probability evaluations, as well as comparisons to intensity-modulated proton therapy (IMPT) plans, were used to assess plan quality.

RESULTS

The SU gap filtering algorithm performed best in five out of the eight cases, maintaining plan quality within tolerance while reducing beam delivery time, in particular for the oropharyngeal cohort. It achieved up to approximately 22% and 15% reduction in delivery time for oropharyngeal and lung treatment sites, respectively. The unrestricted filtering algorithm followed closely. In contrast, the SU filtering showed limited improvement, suppressing one or two SU without substantial delivery time shortening. Robust target coverage was kept within 1% of variation compared to the PAT baseline plan while organs-at-risk doses slightly decreased or kept about the same for all patients.

CONCLUSIONS

This study provides insights to accelerate PAT delivery without compromising plan quality. These advancements could enhance treatment efficiency and patient throughput.

Biological optimization for hybrid proton-photon radiotherapy

Objective.Hybrid proton-photon radiotherapy (RT) is a cancer treatment option to broaden access to proton RT. Additionally, with a refined treatment planning method, hybrid RT has the potential to offer superior plan quality compared to proton-only or photon-only RT, particularly in terms of target coverage and sparing organs-at-risk (OARs), when considering robustness to setup and range uncertainties. However, there is a concern regarding the underestimation of the biological effect of protons on OARs, especially those in close proximity to targets. This study seeks to develop a hybrid treatment planning method with biological dose optimization, suitable for clinical implementation on existing proton and photon machines, with each photon or proton treatment fraction delivering a uniform target dose.Approach.The proposed hybrid biological dose optimization method optimized proton and photon plan variables, along with the number of fractions for each modality, minimizing biological dose to the OARs and surrounding normal tissues. To mitigate underestimation of hot biological dose spots, proton biological dose was minimized within a ring structure surrounding the target. Hybrid plans were designed to be deliverable separately and robustly on existing proton and photon machines, with enforced uniform target dose constraints for the proton and photon fraction doses. A probabilistic formulation was utilized for robust optimization of setup and range uncertainties for protons and photons. The nonconvex optimization problem, arising from minimum monitor unit constraint and dose-volume histogram constraints, was solved using an iterative convex relaxation method.Main results.Hybrid planning with biological dose optimization effectively eliminated hot spots of biological dose, particularly in normal tissues surrounding the target, outperforming proton-only planning. It also provided superior overall plan quality and OAR sparing compared to proton-only or photon-only planning strategies.Significance.This study presents a novel hybrid biological treatment planning method capable of generating plans with reduced biological hot spots, superior plan quality to proton-only or photon-only plans, and clinical deliverability on existing proton and photon machines, separately and robustly.

The proton arc therapy treatment planning problem is NP-Hard

Proton arc therapy (PAT) is an advanced radiotherapy technique using charged particles in which the radiation device rotates continuously around the patient while irradiating the tumor. Compared to conventional, fixed-angle beam delivery mode, proton arc therapy has the potential to further improve the quality of cancer treatment by delivering accurate radiation dose to tumors while minimizing damage to surrounding healthy tissues. However, the computational complexity of treatment planning in PAT raises challenges as to its effective implementation. In this paper, we demonstrate that designing a PAT plan through algorithmic methods is a NP-hard problem (in fact, NP-complete), where the problem size is determined by the number of discrete irradiation angles from which the radiation can be delivered. This finding highlights the inherent complexity of PAT treatment planning and emphasizes the need for efficient algorithms and heuristics to address the challenges associated with optimizing the delivery of radiation doses in this context.

Lattice position optimization for LATTICE therapy

BACKGROUND

LATTICE radiation therapy delivers 3D heterogenous dose of high peak-to-valley dose ratio (PVDR) to the tumor target, with peak dose at lattice vertices inside the target and valley dose for the rest of the target. Although the lattice vertex positions can impact PVDR inside the target and sparing of organs-at-risk (OAR), they are fixed as constants and not optimized during treatment planning in current clinical practice.

PURPOSE

This work proposes a new LATTICE plan optimization method that can optimize lattice vertex positions during LATTICE treatment planning, which is the first lattice position optimization study to the best of our knowledge.

METHODS

The new LATTICE treatment planning method optimizes lattice vertex positions as well as other plan variables (e.g., photon fluences or proton spot weights), with optimization objectives for target PVDR and OAR sparing. To satisfy mathematical differentiability, the lattice vertices are approximated in sigmoid functions. For geometric feasibility, proper geometry constraints are enforced onto lattice vertex positions. The lattice position optimization problem is solved by iterative convex relaxation (ICR) method and alternating direction method of multipliers (ADMM), and lattice vertex positions and photon/proton plan variables are jointly updated via the Quasi-Newton method.

RESULTS

Both photon and proton LATTICE RT were considered, and the optimal lattice vertex positions in terms of plan objectives were found by solving all possible combinations on given discrete positions via exhaustive searching based on standard IMRT/IMPT, which served as the ground truth for validating the new LATTICE method. The results show that the new method indeed provided the optimal lattice vertex positions with the smallest optimization objective, the largest target PVDR, and the best OAR sparing.

CONCLUSIONS

A new LATTICE treatment planning method is proposed and validated that can optimize lattice vertex positions as well as other photon or proton plan variables for improving target PVDR and OAR sparing.

An orthogonal matching pursuit optimization method for solving minimum-monitor-unit problems: Applications to proton IMPT, ARC and FLASH

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.

PURPOSE

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.