Simultaneous dose and dose rate optimization (SDDRO) of the FLASH effect for pencil-beam-scanning proton therapy

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.

Mixed-size spot scanning with a compact large momentum acceptance superconducting (LMA-SC) gantry beamline for proton therapy

Objective. Lowering treatment costs and improving treatment quality are two primary goals for next-generation proton therapy (PT) facilities. This work will design a compact large momentum acceptance superconducting (LMA-SC) gantry beamline to reduce the footprint and expense of the PT facilities, with a novel mixed-size spot scanning method to improve the sparing of organs at risk (OAR).Approach. For the LMA-SC gantry beamline, the movable energy slit is placed in the middle of the last achromatic bending section, and the beam momentum spread of delivered spots can be easily changed during the treatment. Simultaneously, changing the collimator size can provide spots with various lateral spot sizes. Based on the provided large-size and small-size spot models, the treatment planning with mixed spot scanning is optimized: the interior of the target is irradiated with large-size spots (to cover the uniform-dose interior efficiently), while the peripheral of the target is irradiated with small-size spots (to shape the sharp dose falloff at the peripheral accurately).Main results. The treatment plan with mixed-size spot scanning was evaluated and compared with small and large-size spot scanning for thirteen clinical prostate cases. The mixed-size spot plan had superior target dose homogeneities, better protection of OAR, and better plan robustness than the large-size spot plan. Compared to the small-size spot plan, the mixed-size spot plan had comparable plan quality, better plan robustness, and reduced plan delivery time from 65.9 to 40.0 s.Significance. The compact LMA-SC gantry beamline is proposed with mixed-size spot scanning, with demonstrated footprint reduction and improved plan quality compared to the conventional spot scanning method.

Development and benchmarking of a dose rate engine for raster-scanned FLASH helium ions

BACKGROUND

Radiotherapy with charged particles at high dose and ultra-high dose rate (uHDR) is a promising technique to further increase the therapeutic index of patient treatments. Dose rate is a key quantity to predict the so-called FLASH effect at uHDR settings. However, recent works introduced varying calculation models to report dose rate, which is susceptible to the delivery method, scanning path (in active beam delivery) and beam intensity.

PURPOSE

This work introduces an analytical dose rate calculation engine for raster scanned charged particle beams that is able to predict dose rate from the irradiation plan and recorded beam intensity. The importance of standardized dose rate calculation methods is explored here.

METHODS

Dose is obtained with an analytical pencil beam algorithm, using pre-calculated databases for integrated depth dose distributions and lateral penumbra. Dose rate is then calculated by combining dose information with the respective particle fluence (i.e., time information) using three dose-rate-calculation models (mean, instantaneous, and threshold-based). Dose rate predictions for all three models are compared to uHDR helium ion beam (145.7 MeV/u, range in water of approximatively 14.6 cm) measurements performed at the Heidelberg Ion Beam Therapy Center (HIT) with a diamond-detector prototype. Three scanning patterns (scanned or snake-like) and four field sizes are used to investigate the dose rate differences.

RESULTS

Dose rate measurements were in good agreement with in-silico generated distributions using the here introduced engine. Relative differences in dose rate were below 10% for varying depths in water, from 2.3 to 14.8 cm, as well as laterally in a near Bragg peak area. In the entrance channel of the helium ion beam, dose rates were predicted within 7% on average for varying irradiated field sizes and scanning patterns. Large differences in absolute dose rate values were observed for varying calculation methods. For raster-scanned irradiations, the deviation between mean and threshold-based dose rate at the investigated point was found to increase with the field size up to 63% for a 10 mm × 10 mm field, while no significant differences were observed for snake-like scanning paths.

CONCLUSIONS

This work introduces the first dose rate calculation engine benchmarked to instantaneous dose rate, enabling dose rate predictions for physical and biophysical experiments. Dose rate is greatly affected by varying particle fluence, scanning path, and calculation method, highlighting the need for a consensus among the FLASH community on how to calculate and report dose rate in the future. The here introduced engine could help provide the necessary details for the analysis of the sparing effect and uHDR conditions.

Feasibility study of multiple-energy Bragg peak proton FLASH on a superconducting gantry with large momentum acceptance

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.

PURPOSE

This study explores the feasibility of multiple-energy BP FLASH-RT on the LMA-SC gantry.

METHOD AND MATERIALS

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.

Pencil Beam Scanning Proton Bragg Peak Conformal FLASH in Prostate Cancer Stereotactic Body Radiotherapy

Bragg peak FLASH radiotherapy (RT) uses a distal tracking method to eliminate exit doses and can achieve superior OAR sparing. This study explores the application of this novel method in stereotactic body radiotherapy prostate FLASH-RT. An in-house platform was developed to enable intensity-modulated proton therapy (IMPT) planning using a single-energy Bragg peak distal tracking method. The patients involved in the study were previously treated with proton stereotactic body radiotherapy (SBRT) using the pencil beam scanning (PBS) technique to 40 Gy in five fractions. FLASH plans were optimized using a four-beam arrangement to generate a dose distribution similar to the conventional opposing beams. All of the beams had a small angle of two degrees from the lateral direction to increase the dosimetry quality. Dose metrics were compared between the conventional PBS and the Bragg peak FLASH plans. The dose rate histogram (DRVH) and FLASH metrics of 40 Gy/s coverage (V40Gy/s) were investigated for the Bragg peak plans. There was no significant difference between the clinical and Bragg peak plans in rectum, bladder, femur heads, large bowel, and penile bulb dose metrics, except for Dmax. For the CTV, the FLASH plans resulted in a higher Dmax than the clinical plans (116.9% vs. 103.3%). For the rectum, the V40Gy/s reached 94% and 93% for 1 Gy dose thresholds in composite and single-field evaluations, respectively. Additionally, the FLASH ratio reached close to 100% after the application of the 5 Gy threshold in composite dose rate assessment. In conclusion, the Bragg peak distal tracking method can yield comparable plan quality in most OARs while preserving sufficient FLASH dose rate coverage, demonstrating that the ultra-high dose technique can be applied in prostate FLASH SBRT.

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.

A Novel Ultrahigh-Dose-Rate Proton Therapy Technology: Spot-Scanning Proton Arc Therapy + FLASH (SPLASH)

PURPOSE

To take full advantage of FLASH dose rate (40 Gy/s) and high-dose conformity, we introduce a novel optimization and delivery technique, the spot-scanning proton arc therapy (SPArc) + FLASH (SPLASH).

METHODS AND MATERIALS

SPLASH framework was implemented in an open-source proton planning platform (MatRad, Department of Medical Physics in Radiation Oncology, German Cancer Research Center). It optimizes with the clinical dose-volume constraint based on dose distribution and the dose-average dose rate by minimizing the monitor unit constraint on spot weight and accelerator beam current sequentially, enabling the first dynamic arc therapy with voxel-based FLASH dose rate. This new optimization framework minimizes the overall cost function value combined with plan quality and voxel-based dose-rate constraints. Three representative cases (brain, liver, and prostate cancer) were used for testing purposes. Dose-volume histogram, dose-rate-volume histogram, and dose-rate map were compared among intensity modulated proton radiation therapy (IMPT), SPArc, and SPLASH.

RESULTS

SPLASH/SPArc could offer superior plan quality over IMPT in terms of dose conformity. The dose-rate-volume histogram results indicated SPLASH could significantly improve V40 Gy/s in the target and region of interest for all tested cases compared with SPArc and IMPT. The optimal beam current per spot is simultaneously generated, which is within the existing proton machine specifications in the research version (<200 nA).

CONCLUSIONS

SPLASH offers the first voxel-based ultradose-rate and high-dose conformity treatment using proton beam therapy. Such a technique has the potential to fit the needs of a broad range of disease sites and simplify clinical workflow without applying a patient-specific ridge filter, which has never before been demonstrated.

A FLASH model of radiolytic oxygen depletion and reactive oxygen species for differential tumor and normal-tissue response

Objective

FLASH-RT can potentially improve the sparing of normal tissues while preserving the tumoricidal efficiency, owing to the radiation with ultra-high dose rate. However, the FLASH mechanism remains to be solved. A popular FLASH model is based on radiolytic oxygen depletion (ROD), which explains for radiation protection of normal tissues under FLASH-RT. However, ROD does not explain the preservation of tumoricidal efficiency for tumors. This work will develop a ROS+ROD FLASH model that can explain the differential tumor and normal-tissue response.

Approach

The new FLASH model utilizes reactive oxygen species (ROS) in addition to ROD, and takes into account that ROS level decreases during FLASH-RT. Specifically, the differential-equation model takes into account that the basic ROS level is lower during FLASH-RT and the degeneration rates of ROS are different in tumor cells and healthy cells. Based on this ROS+ROD FLASH model, the surviving fractions of tumor and normal cells are respectively compared between conventional radiotherapy (CONV-RT) and FLASH-RT.

Main results

While ROD alone does not distinguish the response of tumors and normal tissues to FLASH-RT, the proposed new FLASH model based on ROD and ROS successfully explained the differential response of tumors and normal tissues to FLASH-RT, i.e., the preserved tumoricidal capability, which cannot be explained by ROD alone, and the extra normal-tissue protection owing to the ultra-high dose rate.

Significance

Since the ROS level decreases slower in tumors than in normal tissues, during FLASH-RT, ROS decreases more in normal tissue, thus can get more protection. By incorporating ROS in addition to ROD, the new FLASH model can not only recover all results by previous FLASH model with ROD alone, but also explain the differential response: preserved lethality of FLASH-RT to tumors and improved protection to normal tissues.

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.

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

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.

TVL1-IMPT: Optimization of Peak-to-Valley Dose Ratio Via Joint Total-Variation and L1 Dose Regularization for Spatially Fractionated Pencil-Beam-Scanning Proton Therapy

PURPOSE

Proton minibeam radiation therapy (pMBRT) is a novel proton modality of spatially fractionated RT. pMBRT can reduce the radiation damage to normal tissues via biological dose sparing of high peak-to-valley dose ratio (PVDR). This work will develop a new spatially fractionated IMPT treatment planning method for pMBRT that jointly optimizes the plan quality and maximizes the PVDR.

METHODS

The new optimization method simultaneously maximizes the normal-tissue PVDR and optimizes the dose distribution at tumor targets and organs at risk. The PVDR maximization is through the joint total variation (TV) and L1 regularization with respect to the normal-tissue dose. That is, the beam-eye view projects dose slices of several depths for each beam angle; the TV of dose is maximized, corresponding to the PVDR maximization; and the L1 of dose is minimized, corresponding to the minimization of the organs-at-risk dose and maximization of survival fraction (SF).

RESULTS

The new IMPT method with TV and L1 regularization was validated in comparison with the conventional IMPT method for pMBRT in several clinical cases. The results show that TVL1 provided larger PVDR and SF than the conventional IMPT method for biological sparing of normal tissues, with preserved plan quality in terms of physical dose distribution.

CONCLUSIONS

A new spatially fractionated IMPT treatment planning method was developed for pMBRT that can optimize and improve normal-tissue PVDR and SF by incorporating TV and L1 dose regularization with properly chosen regularization parameters into IMPT.

An iterative convex relaxation method for proton LET optimization

Objective:A constant relative biological effectiveness of 1.1 in current clinical practice of proton radiotherapy (RT) is a crude approximation and may severely underestimate the biological dose from proton RT to normal tissues, especially near the treatment target at the end of Bragg peaks that exhibits high linear energy transfer (LET). LET optimization can account for biological effectiveness of protons during treatment planning, for minimizing biological proton dose and hot spots to normal tissues. However, the LET optimization is usually nonlinear and nonconvex to solve, for which this work will develop an effective optimization method based on iterative convex relaxation (ICR).Approach: In contrast to the generic nonlinear optimization method, such as Quasi-Newton (QN) method, that does not account for specific characteristics of LET optimization, ICR is tailored to LET modeling and optimization in order to effectively and efficiently solve the LET problem. Specifically, nonlinear dose-averaged LET term is iteratively linearized and becomes convex during ICR, while nonconvex dose-volume constraint and minimum-monitor-unit constraint are also handled by ICR, so that the solution for LET optimization is obtained by solving a sequence of convex and linearized convex subproblems. Since the high LET mostly occurs near the target, a 1 cm normal-tissue expansion of clinical target volume (CTV) (excluding CTV), i.e. CTV1cm, is defined to as an auxiliary structure during treatment planning, where LET is minimized.Main results: ICR was validated in comparison with QN for abdomen, lung, and head-and-neck cases. ICR was effective for LET optimization, as ICR substantially reduced the LET and biological dose in CTV1cm the ring, with preserved dose conformality to CTV. Compared to QN, ICR had smaller LET, physical and biological dose in CTV1cm, and higher conformity index values; ICR was also computationally more efficient, which was about 3 times faster than QN.Significance: A LET-specific optimization method based on ICR has been developed for solving proton LET optimization, which has been shown to be more computationally efficient than generic nonlinear optimizer via QN, with better plan quality in terms of LET, biological and physical dose conformality.

Fraction optimization for hybrid proton-photon treatment planning

BACKGROUND

Hybrid proton-photon radiotherapy (RT) can provide better plan quality than proton or photon only RT, in terms of robustness of target coverage and sparing of organs-at-risk (OAR).

PURPOSE

This work develops a hybrid treatment planning method that can optimize the number of proton and photon fractions as well as proton and photon plan variables, so that the hybrid plans can be clinically delivered day-to-day using either proton or photon machine.

METHODS

In the new hybrid treatment planning method, the total dose distribution (sum of proton dose and photon dose) is optimized for robust target coverage and optimal OAR sparing, by jointly optimizing proton spots and photon fluences, while the target dose uniformity is also enforced individually on both proton dose and photon dose, so that the hybrid plans can be separately and robustly delivered on proton or photon machine. To ensure the target dose uniformity for proton and photon plans, the number of proton and photon fractions is explicitly modeled and optimized, so that the target dose for proton and photon dose components is constrained to be a constant fraction of the total prescription dose while the plan quality based on total dose is optimized. The feasibility of hybrid planning using the proposed method is validated with representative clinical cases including abdomen, lung, head-and-neck (HN), and brain.

RESULTS

For all cases, hybrid plans provided better overall plan quality and OAR sparing than proton-only or photon-only plans, better target dose uniformity and robustness than proton-only plans, quantified by treatment planning objectives and dosimetric parameters. Moreover, for HN and brain cases, hybrid plans also had better target coverage than photon-only plans.

CONCLUSIONS

We have developed a new hybrid treatment planning method that optimizes number of proton and photon fractions as well as proton spots and photon fluences, for generating hybrid plans that can be separately and robustly delivered on proton or photon machines. Preliminary results have demonstrated that hybrid plans generated by the new method have better plan quality than proton-only or photon-only plans.

An Integrated Physical Optimization Framework for Proton Stereotactic Body Radiation Therapy FLASH Treatment Planning Allows Dose, Dose Rate, and Linear Energy Transfer Optimization Using Patient-Specific Ridge Filters

PURPOSE

Patient-specific ridge filters provide a passive means to modulate proton energy to obtain a conformal dose. Here we describe a new framework for optimization of filter design and spot maps to meet the unique demands of ultrahigh-dose-rate (FLASH) radiation therapy. We demonstrate an integrated physical optimization Intensity-modulated proton therapy (IMPT) (IPO-IMPT) approach for optimization of dose, dose-averaged dose rate (DADR), and dose-averaged linear energy transfer (LET_d).

METHODS AND MATERIALS

We developed an inverse planning software to design patient-specific ridge filters that spread the Bragg peak from a fixed-energy, 250-MeV beam to a proximal beam-specific planning target volume. The software defines patient-specific ridge filter pin shapes and uses a Monte Carlo calculation engine, based on Geant4, to provide dose and LET influence matrices. Plan optimization, using matRAD, accommodates the IPO-IMPT objective function considering dose, dose rate, and LET simultaneously with minimum monitor unit constraints. The framework enables design of both regularly spaced and sparse-optimized ridge filters, from which some pins are omitted to allow faster delivery and selective LET optimization. To demonstrate the framework, we designed ridge filters for 3 example patients with lung cancer and optimized the plans using IPO-IMPT.

RESULTS

The IPO-IMPT framework selectively spared the organs at risk by reducing LET and increasing dose rate, relative to IMPT planning. Sparse-optimized ridge filters were superior to regularly spaced ridge filters in dose rate. Depending on which parameter is prioritized, volume distributions and histograms for dose, DADR, and LET_d, using evaluation structures specific to heart, lung, and esophagus, show high levels of FLASH dose-rate coverage and/or reduced LET_d, while maintaining dose coverage within the beam specific planning target volume.

CONCLUSIONS

This proof-of-concept study demonstrates the feasibility of using an IPO-IMPT framework to accomplish proton FLASH stereotactic body proton therapy, accounting for dose, DADR, and LET_d simultaneously.

Dose and dose rate objectives in Bragg peak and shoot-through beam orientation optimization for FLASH proton therapy

PURPOSE

The combined use of Bragg peak (BP) and shoot-through (ST) beams has previously been shown to increase the normal tissue volume receiving FLASH dose rates while maintaining dose conformality compared to conventional intensity-modulated proton therapy (IMPT) methods. However, the fixed beam optimization method has not considered the effects of beam orientation on the dose and dose rates. To maximize the proton FLASH effect, here, we incorporate dose rate objectives into our beam orientation optimization framework.

METHODS

From our previously developed group-sparsity dose objectives, we add upper and lower dose rate terms using a surrogate dose-averaged dose rate definition and solve using the fast-iterative shrinking threshold algorithm. We compare the dosimetry for three head-and-neck cases between four techniques: (1) spread-out BP IMPT (BP), (2) dose rate optimization using BP beams only (BP-DR), (3) dose rate optimization using ST beams only (ST-DR), and (4) dose rate optimization using combined BP and ST (BPST-DR), with the goal of sparing organs at risk without loss of tumor coverage and maintaining high dose rate within a 10 mm region of interest (ROI) surrounding the clinical target volume (CTV).

RESULTS

For BP, BP-DR, ST-DR, and BPST-DR, CTV homogeneity index and Dmax were found to be on average 0.886, 0.867, 0.687, and 0.936 and 107%, 109%, 135%, and 101% of prescription, respectively. Although ST-DR plans were not able to meet dosimetric standards, BPST-DR was able to match or improve either maximum or mean dose in the right submandibular gland, left and right parotids, constrictors, larynx, and spinal cord compared to BP plans. Volume of ROIs receiving greater than 40 Gy/s ( V γ 0 ) ${V_{\gamma 0}})$ was 51.0%, 91.4%, 95.5%, and 92.1% on average.

CONCLUSIONS

The dose rate techniques, particularly BPST-DR, were able to significantly increase dose rate without compromising physical dose compared with BP. Our algorithm efficiently selects beams that are optimal for both dose and dose rate.

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

PURPOSE

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 to 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 energy matrix that encourages desirable energy-layer map with minimal SU during SPArc, and then incorporate this energy matrix 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 to 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 ten-fold.

CONCLUSION

We have developed a new ELO method for SPArc using energy matrix regularization, and shown that this new method EM can improve both delivery efficiency and plan quality, with substantially reduced computational time, compared to ES. This article is protected by copyright. All rights reserved.

Normal tissue sparing by FLASH as a function of single fraction dose: A quantitative analysis

PURPOSE

The FLASH effect designates normal tissue sparing by ultra-high dose rate (UHDR) compared to conventional dose rate (CONV) irradiation without compromising tumor control. Understanding the magnitude of this effect and its dependency on dose are essential requirements for an optimized clinical translation of FLASH radiation therapy. In this context, we evaluated available experimental data on the magnitudes of normal tissue sparing provided by the FLASH effect as a function of dose, and followed a phenomenological data-driven approach for its parameterization.

METHODS

We gathered available in vivo data of the normal tissue sparing of CONV compared to UHDR single fraction doses and converted it to a common scale using isoeffect dose ratios, hereafter referred to as FLASH modifying factors (FMF). We then evaluated the suitability of a piecewise linear function with two pieces to parametrize FMF × D as a function of dose D.

RESULTS

We found that the magnitude of FMF generally decreases (i.e., sparing increases) as function of single fraction dose and that individual data series can be described by the piecewise linear function. The sparing magnitude appears organ specific. Pooled skin reaction data followed a consistent trend as a function of dose. Average FMF values and their standard deviations were 0.95±0.11 for all data below 10 Gy, 0.92±0.06 for mouse gut data between 10-25 Gy, and 0.96±0.07 and 0.71±0.06 for mammalian skin reaction data between 10-25 Gy and >25 Gy, respectively.

CONCLUSIONS

The magnitude of normal tissue sparing by FLASH is increasing with dose and is dependent on the irradiated tissue. A piecewise linear function can parameterize currently available individual data series.

Minimum-monitor-unit optimization via a stochastic coordinate descent method

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).

A quantitative FLASH effectiveness model to reveal potentials and pitfalls of high dose rate proton therapy

Purpose

In ultrahigh dose rate radiotherapy, the FLASH effect can lead to substantially reduced healthy tissue damage without affecting tumor control. Although many studies show promising results, the underlying biological mechanisms and the relevant delivery parameters are still largely unknown. It is unclear, particularly for scanned proton therapy, how treatment plans could be optimized to maximally exploit this protective FLASH effect.

Materials and Methods

To investigate the potential of pencil beam scanned proton therapy for FLASH treatments, we present a phenomenological model, which is purely based on experimentally observed phenomena such as potential dose rate and dose thresholds, and which estimates the biologically effective dose during FLASH radiotherapy based on several parameters. We applied this model to a wide variety of patient geometries and proton treatment planning scenarios, including transmission and Bragg peak plans as well as single‐ and multifield plans. Moreover, we performed a sensitivity analysis to estimate the importance of each model parameter.

Results

Our results showed an increased plan‐specific FLASH effect for transmission compared with Bragg peak plans (19.7% vs. 4.0%) and for single‐field compared with multifield plans (14.7% vs. 3.7%), typically at the cost of increased integral dose compared to the clinical reference plan. Similar FLASH magnitudes were found across the different treatment sites, whereas the clinical benefits with respect to the clinical reference plan varied strongly. The sensitivity analysis revealed that the threshold dose as well as the dose per fraction strongly impacted the FLASH effect, whereas the persistence time only marginally affected FLASH. An intermediate dependence of the FLASH effect on the dose rate threshold was found.

Conclusions

Our model provided a quantitative measure of the FLASH effect for various delivery and patient scenarios, supporting previous assumptions about potentially promising planning approaches for FLASH proton therapy. Positive clinical benefits compared to clinical plans were achieved using hypofractionated, single‐field transmission plans. The dose threshold was found to be an important factor, which may require more investigation.

An adaptive spot placement method on Cartesian grid for pencil beam scanning proton therapy

Pencil beam scanning proton radiotherapy (RT) offers flexible proton spot placement near treatment targets for delivering tumoricidal radiation dose to tumor targets while sparing organs-at-risk. Currently the spot placement is mostly based on a non-adaptive sampling (NS) strategy on a Cartesian grid. However, the spot density or spacing during NS is a constant for the Cartesian grid that is independent of the geometry of tumor targets, and thus can be suboptimal in terms of plan quality (e.g. target dose conformality) and delivery efficiency (e.g. number of spots). This work develops an adaptive sampling (AS) spot placement method on the Cartesian grid that fully accounts for the geometry of tumor targets. Compared with NS, AS places (1) a relatively fine grid of spots at the boundary of tumor targets to account for the geometry of tumor targets and treatment uncertainties (setup and range uncertainty) for improving dose conformality, and (2) a relatively coarse grid of spots in the interior of tumor targets to reduce the number of spots for improving delivery efficiency and robustness to the minimum-minitor-unit (MMU) constraint. The results demonstrate that (1) AS achieved comparable plan quality with NS for regular MMU and substantially improved plan quality from NS for large MMU, using merely about 10% of spots from NS, where AS was derived from the same Cartesian grid as NS; (2) on the other hand, with similar number of spots, AS had better plan quality than NS consistently for regular and large MMU.