A Novel Inverse Algorithm To Solve the Integrated Optimization of Dose, Dose Rate, and Linear Energy Transfer of Proton FLASH Therapy With Sparse Filters

Embracing the Future of Clinical Trials in Radiation Therapy: An NRG Oncology CIRO Technology Retreat Whitepaper on Pioneering Technologies and AI-Driven Solutions

This white paper examines the potential of pioneering technologies and artificial intelligence-driven solutions in advancing clinical trials involving radiation therapy. As the field of radiation therapy evolves, the integration of cutting-edge approaches such as radiopharmaceutical dosimetry, FLASH radiation therapy, image guided radiation therapy, and artificial intelligence promises to improve treatment planning, patient care, and outcomes. Additionally, recent advancements in quantum science, linear energy transfer/relative biological effect, and the combination of radiation therapy and immunotherapy create new avenues for innovation in clinical trials. The paper aims to provide an overview of these emerging technologies and discuss their challenges and opportunities in shaping the future of radiation oncology clinical trials. By synthesizing knowledge from experts across various disciplines, this white paper aims to present a foundation for the successful integration of these innovations into radiation therapy research and practice, ultimately enhancing patient outcomes and revolutionizing cancer care.

Experimental validation of LET in intensity-modulated proton therapy with a miniaturized pixel detector

Objective.Given the increased interest in incorporating linear energy transfer (LET) as an optimization parameter in intensity-modulated proton therapy (IMPT), a solution for experimental validation of simulations and patient-specific quality assurance (PSQA) in terms of proton LET is needed. Here, we present the methodology and results of LET spectra measurements for spread-out Bragg peak (SOBP) and IMPT plans using a miniaturized pixel detector Timepix3.Approach.We used a MiniPIX Timepix3 detector that provides single-particle tracking, type-resolving power, and spectral information while allowing measurement in quasi-continuous mode. We performed measurements for SOBP and IMPT plans in homogeneous RW3 and heterogeneous CIRS head phantoms with reduced beam current. An artificial intelligence-based model was applied for proton identification and a GPU-accelerated FRED Monte Carlo (MC) code was applied for corresponding MC simulations.Main results.We compared the deposited energy and LET spectra obtained in mixed radiation fields from measurements and MC simulations. The peak positions of deposited energy and LET spectra for the SOBP and IMPT plans agree within the error bars. Discrepancies exceeding the error bars are only visible in the logarithmic scale in high-energy deposition and high-LET tails of the distributions. The mean relative difference of dose-averaged LET values between measurements and MC simulations for individual energy layers is about 5.1%.Significance.This study presents a methodology for assessing radiation quality in proton therapy through energy deposition and LET spectra measurements in uniform and clinical IMPT fields. Findings show an agreement between experimental data and MC simulations, validating our approach. The presented results demonstrate the feasibility of a commercially available Timepix3 detector to validate LET computations in IMPT fields and perform PSQA in terms of LET. This will support the implementation of LET in treatment planning, which will ultimately increase the effectiveness of the treatment.

Medical physics dataset article: A database of FLASH murine in vivo studies

PURPOSE

The FLASH effect refers to a lower normal tissue damage for an equivalent tumor response, potentially widening the therapeutic window for radiotherapy. Although this effect has been demonstrated in various experiments using different types of particles and irradiation parameters, the underlying mechanism is not yet clearly understood. Uncertainties surround the conducted experiments, the explored parameter space, and the variability of reported results. To gain a better overview, we have created a dataset that includes in vivo FLASH experiments. This dataset documents all machine and biological dosimetric parameters, and for determined endpoints, it includes the outcome of the experiment. Our goal with this database is to increase awareness of the results and their variability and provide a useful research and analysis tool for the community.

ACQUISITION AND VALIDATION METHODS

The database contains peer-reviewed papers published until March 2024 on the FLASH in vivo (murine) experiments. From each paper, previously defined parameters have been manually extracted and/or recalculated to ensure compatibility within the database entries.

DATA FORMAT AND USAGE NOTES

We provide two types of datasets: a user-friendly web-based Notion database and spreadsheets on a Zenodo repository. The database contains all the reviewed papers with extracted information in text or numeric form. Users can duplicate the database or view, search, filter, and reorganize online entries. The spreadsheets contain the data for the most analyzed endpoints (skin toxicity, survival rate, and crypt cells), allowing a comparative analysis.

POTENTIAL APPLICATIONS

The study has two main applications. The web-based database will allow for a user-friendly search of information and metadata of all published FLASH murine data. This will facilitate future research efforts to better understand the FLASH effect. The spreadsheets are a simple and useful tool for the community to conduct statistical analysis and determine the parameters associated with the FLASH effect.

Photon mini-GRID therapy for preoperative breast cancer tumor treatment: A treatment plan study

BACKGROUND

Breast cancer is the leading cause of female cancer mortality worldwide, accounting for 1 in 6 cancer deaths. Surgery, radiation, and systemic therapy are the three pillars of breast cancer treatment, with several strategies developed to combine them. The association of preoperative radiotherapy with immunotherapy may improve breast cancer tumor control by exploiting the tumor radio-induced immune priming. However, this requires the use of hypofractionated radiotherapy (3 × 8 Gy), increasing the risk of toxicity. Mini-GRID therapy (mini-GRT) is an innovative form of spatially fractionated radiation therapy (SFRT) characterized by narrow beam widths between 1 to 2 mm that promises a significant increase in normal tissue dose tolerances and could thereby represent a new alternative for preoperative breast cancer treatment. Mini-GRT has been successfully implemented at the Hospital de Santiago de Compostela (Spain) with a flattening filter-free LINAC (megavoltage x-rays).

PURPOSE

In this dosimetry proof-of-concept study, we evaluate the feasibility of photon mini-GRT for preoperative breast cancer treatment. We also assess the clinical potential of mini-GRT and compare it with the current treatment standard of intensity-modulated radiotherapy (IMRT).

METHODS

Seven unbiased breast cancer dosimetries of patients treated with stereotactic body radiotherapy (SBRT) (3 × 8 Gy, IMRT) were selected for the study. Photon mini-GRT was compared with SBRT using three main criteria: (i) the dose to organs at risk (OARs), (ii) the dose constraints dictated by normal tissue tolerance, and (iii) the lateral penumbra in OARs. Tumor coverage was evaluated in terms of normalized total dose at 8 Gy-fractions. The optimized SBRT by IMRT was realized at the Institut Curie, Paris, France. The dose in mini-GRT was calculated by means of Monte Carlo simulations based on the mini-GRT implementation realized at the University Hospital in Santiago de Compostela.

RESULTS

Compared to SBRT plans, mini-GRT resulted in a reduction of the mean dose to the lungs, heart, chest wall, and lymph nodes in the studied cases by a factor ranging from 50% to 100%. Additionally, valley, mean, and peak doses to normal tissues meet the dose tolerance limits for the considered OARs, the most challenging of all being the skin. The mean dose to the skin was reduced (20%-60% less) for most of the studied cases. Mini-GRT also yielded sharper lateral penumbras in the skin and lungs (size reduced by at least 50%). Similar tumor integral doses were obtained for the two treatment modalities.

CONCLUSION

Mini-GRT with megavoltage x-rays is an innovative treatment approach already implemented in a clinical context. In this proof-of-concept study, we evaluated mini-GRT for partial breast cancer irradiation, demonstrating its potential for preoperative treatment thanks to the high skin and normal tissue-sparing capabilities. These initial results represent a first step towards clinical use and encourage further prospective clinical studies.

Requirements and Study Design for the Next Proton FLASH Clinical Trials: an International Multidisciplinary Delphi Consensus

PURPOSE

The FLASH effect, defined as normal tissue sparing while maintaining tumor control with ultra-high dose-rate irradiation, has been demonstrated preclinically in different tumors and tissues. Although the biological mechanisms are unclear, there is a need for clinical trials investigating the value of proton FLASH irradiation (pFLASH). The purpose of this study was to establish an expert consensus regarding prerequisites, study design, and endpoints for the next clinical trials exploring the clinical potentials of pFLASH.

METHODS AND MATERIALS

Delphi methodology was used to develop a systematic expert consensus. An international expert panel was composed of 21 clinicians, physicists, and biologists, well-balanced in expertise and geography, using predefined inclusion criteria. Statements were scored on a 5-point Likert scale in 2 rounds of online questionnaire voting. The definition of consensus was set a priori.

RESULTS

The response rate was 100% in both rounds. Preclinical in vivo demonstration of the FLASH effect in normal tissue while maintaining tumor response was deemed essential before starting a clinical trial in a specific tumor site. The next clinical pFLASH trials are advised to include adult patients only, with a minimal expected overall survival of 1 year for palliative settings or, preferably, oligometastatic disease in the ablative setting. The pFLASH effect should be studied in a single treatment modality setting with toxicity reduction as the primary endpoint. Recommendations were formulated on the use of clinical targets and organs at risk constraints, requirements for evaluation and reporting, and accuracy levels and pretreatment verification of dose rates. No consensus was reached on the use of multiple beams, multiple fractions, and fraction dose.

CONCLUSIONS

There is a need for additional data regarding the influence of fractionation and multiple beam planning. The results of this study can be used to develop roadmaps to guide future clinical trial design.

Enabling clinical use of linear energy transfer in proton therapy for head and neck cancer - A review of implications for treatment planning and adverse events study

Proton therapy offers significant advantages due to its unique physical and biological properties, particularly the Bragg peak, enabling precise dose delivery to tumors while sparing healthy tissues. However, the clinical implementation is challenged by the oversimplification of the relative biological effectiveness (RBE) as a fixed value of 1.1, which does not account for the complex interplay between dose, linear energy transfer (LET), and biological endpoints. Lack of heterogeneity control or the understanding of the complex interplay may result in unexpected adverse events and suboptimal patient outcomes. On the other hand, expanding our knowledge of variable tumor RBE and LET optimization may provide a better management strategy for radioresistant tumors. This review examines recent advancements in LET calculation methods, including analytical models and Monte Carlo simulations. The integration of LET into plan evaluation is assessed to enhance plan quality control. LET-guided robust optimization demonstrates promise in minimizing high-LET exposure to organs at risk, thereby reducing the risk of adverse events. Dosimetric seed spot analysis is discussed to show its importance in revealing the true LET-related effect upon the adverse event initialization by finding the lesion origins and eliminating the confounding factors from the biological processes. Dose-LET volume histograms (DLVH) are discussed as effective tools for correlating physical dose and LET with clinical outcomes, enabling the derivation of clinically relevant dose-LET volume constraints without reliance on uncertain RBE models. Based on DLVH, the dose-LET volume constraints (DLVC)-guided robust optimization is introduced to upgrade conventional dose-volume constraints-based robust optimization, which optimizes the joint distribution of dose and LET simultaneously. In conclusion, translating the advances in LET-related research into clinical practice necessitates a better understanding of the LET-related biological mechanisms and the development of clinically relevant LET-related volume constraints directly derived from the clinical outcomes. Future research is needed to refine these models and conduct prospective trials to assess the clinical benefits of LET-guided optimization on patient outcomes.

Biological dose-based fractional dose optimization of Bragg peak FLASH-RT for lung cancer treatment

BACKGROUND

The FLASH effect is dose-dependent, and fractional dose optimization may enhance it, improving normal tissue sparing.

PURPOSE

This study investigates the performance of fractional dose optimization in enhancing normal tissue sparing for Bragg peak FLASH radiotherapy (FLASH-RT).

METHODS

15 lung cancer patients, including eight with peripherally located tumors and seven with centrally located tumors, were retrospectively analyzed. A uniform fractionation prescription of 50 Gy in five fractions was utilized, corresponding to a biological equivalent dose (BED) of 100 Gy, calculated using an α/β value of 10 Gy. For each patient, uniform (UFD) and nonuniform fractional dose (non-UFD) plans were designed. In UFD FLASH plans, five multi-energy Bragg peak beams were optimized using single-field optimization, each delivering 10 Gy to the target. In non-UFD FLASH plans, fractional doses were optimized to enhance sparing effects while ensuring the target received a BED comparable to UFD plans. A dose-dependent FLASH enhancement ratio (FER) was integrated with the BED to form the FER-BED metric to compare the UFD and non-UFD plans. An α/β value of 3 Gy was applied for normal tissues in the calculations.

RESULTS

Bragg peak FLASH plans showed high dose conformality for both peripheral and central tumors, with all plans achieving a conformality index (the ratio of the volume receiving the prescribed dose to the CTV volume) below 1.2. In non-UFD plans, fractional doses ranged from 5.0 Gy to 20.0 Gy. Compared to UFD plans, non-UFD plans achieved similar BED coverage (BED98%: 96.6 Gy vs. 97.1 Gy, p = 0.256), while offering improved organ-at-risk sparing. Specifically, the FER-BED15cc for the heart reduced by 10.5% (9.4 Gy vs. 10.5 Gy, p = 0.017) and the V6.7GyFER-BED for the ipsilateral lung decreased by 4.3% (29 .1% vs. 30.4%, p = 0.008). No significant difference was observed in FER-BED0.25cc of spinal cord (UFD: 7.1 Gy, non-UFD: 6.9 Gy, p = 0.626) and FER-BED5cc in esophagus (UFD: 0.4 Gy, non-UFD: 0.4 Gy, p = 0.831).

CONCLUSIONS

Bragg peak FLASH-RT achieved high dose conformality for both peripheral and central tumors. Fractional dose optimization, using a single beam per fraction delivery mode, enhanced normal tissue sparing by leveraging both fractionation and FLASH effects.

Characterizing devices for validation of dose, dose rate, and LET in ultra high dose rate proton irradiations

BACKGROUND

Ultra high dose rate (UHDR) radiotherapy using ridge filter is a new treatment modality known as conformal FLASH that, when optimized for dose, dose rate (DR), and linear energy transfer (LET), has the potential to reduce damage to healthy tissue without sacrificing tumor killing efficacy via the FLASH effect.

PURPOSE

Clinical implementation of conformal FLASH proton therapy has been limited by quality assurance (QA) challenges, which include direct measurement of UHDR and LET. Voxel DR distributions and LET spectra at planning target margins are paramount to the DR/LET-related sparing of organs at risk. We hereby present a methodology to achieve experimental validation of these parameters.

METHODS

Dose, DR, and LET were measured for a conformal FLASH treatment plan involving a 250-MeV proton beam and a 3D-printed ridge filter designed to uniformly irradiate a spherical target. We measured dose and DR simultaneously using a 4D multi-layer strip ionization chamber (MLSIC) under UHDR conditions. Additionally, we developed an "under-sample and recover (USRe)" technique for a high-resolution pixelated semiconductor detector, Timepix3, to avoid event pile-up and to correct measured LET at high-proton-flux locations without undesirable beam modifications. Confirmation of these measurements was done using a MatriXX PT detector and by Monte Carlo (MC) simulations.

RESULTS

MC conformal FLASH computed doses had gamma passing rates of >95% (3 mm/3% criteria) when compared to MatriXX PT and MLSIC data. At the lateral margin, DR showed average agreement values within 0.3% of simulation at 100 Gy/s and fluctuations ∼10% at 15 Gy/s. LET spectra in the proximal, lateral, and distal margins had Bhattacharyya distances of <1.3%.

CONCLUSION

Our measurements with the MLSIC and Timepix3 detectors shown that the DR distributions for UHDR scenarios and LET spectra using USRe are in agreement with simulations. These results demonstrate that the methodology presented here can be used effectively for the experimental validation and QA of FLASH treatment plans.

A Fast 3D Range-Modulator Delivery Approach: Validation of the FLUKA Model on a Varian ProBeam System Including a Robustness Analysis

A 3D range-modulator (RM), optimized for a single energy and a specific target shape, is a promising and viable solution for the ultra-fast dose delivery in particle therapy. The aim of this work was to investigate the impact of potential beam and modulator misalignments on the dose distribution. Moreover, the FLUKA Monte Carlo model, capable of simulating 3D RMs, was adjusted and validated for the 250 MeV single-energy proton irradiation from a Varian ProBeam system. A 3D RM was designed for a cube target shape rotated 45° around two axes using a Varian-internal research version of the Eclipse treatment planning software, and the resulting dose distribution was simulated in a water phantom. Deviations from the ideal alignment were introduced, and the dose distributions from the modified simulations were compared to the original unmodified one. Finally, the FLUKA model and the workflow were validated with base-line data measurements and dose measurements of the manufactured modulator prototype at the HollandPTC facility in Delft. The adjusted FLUKA model, optimized particularly in the scope of a single-energy FLASH irradiation with a PMMA pre-absorber, demonstrated very good agreement with the measured dose distribution resulting from the 3D RM. Dose deviations resulting from modulator-beam axis misalignments depend on the specific 3D RM and its shape, pin aspect ratio, rotation angle, rotation point, etc. A minor modulator shift was found to be more relevant for the distal dose distribution than for the spread-out Bragg Peak (SOBP) homogeneity. On the other hand, a modulator tilt (rotation away from the beam axis) substantially affected not only the depth dose profile, transforming a flat SOBP into a broad, Gaussian-like distribution with increasing rotation angle, but also shifted the lateral dose distribution considerably. This work strives to increase awareness and highlight potential pitfalls as the 3D RM method progresses from a purely research concept to pre-clinical studies and human trials. Ensuring that gantry rotation and the combined weight of RM, PMMA, and aperture do not introduce alignment issues is critical. Given all the other range and positioning uncertainties, etc., not related to the modulator, the RM must be aligned with an accuracy below 1° in order to preserve a clinically acceptable total uncertainty budget. Careful consideration of critical parameters like the pin aspect ratio and possibly a novel robust modulator geometry optimization are potential additional strategies to mitigate the impact of positioning on the resulting dose. Finally, even the rotated cube 3D modulator with high aspect ratio pin structures (~80 mm height to 3 mm pin base width) was found to be relatively robust against a slight misalignment of 0.5° rotation or a 1.5 mm shift in one dimension perpendicular to the beam axis. Given a reliable positioning and QA concept, the additional uncertainties introduced by the 3D RM can be successfully managed adopting the concept into the clinical routine.

Fractionation dose optimization facilities the implementation of transmission proton FLASH-RT

Objective.The beam switching time and fractional dose influence the FLASH effect. A single-beam-per-fraction (SBPF) scheme using uniform fractional dose (UFD) has been proposed for FLASH- radiotherapy (FLASH-RT) to eliminate the beam switching time. Based on SBPF schemes, a fractionation dose optimization algorithm is proposed to optimize non-UFD plans to maximize the fractionation effect and dose-dependent FLASH effect.Approach.The UFD plan, containing five 236 MeV transmission proton beams, was optimized for 11 patients with peripheral lung cancer, with each beam delivering a uniform dose of 11 Gy to the target. Meanwhile, the non-UFD plan was optimized using fractionation dose optimization. To compare the two plans, the equivalent dose to 2 Gy (EQD2) for the target and normal tissues was calculated with anα/βratio of 10 and 3, respectively. Both UFD and non-UFD plans ensured that the target received an EQD2 of 96.3 Gy. To investigate the overall improvement in normal tissue sparing with the non-UFD plan, the FLASH-enhanced EQD2 was calculated.Main results.The fractional doses in non-UFD plans ranged between 5.0 Gy and 24.2 Gy. No significant differences were found in EQD22%and EQD298%of targets between UFD and non-UFD plans. However, theD95%of the target in non-UFD plans was significantly reduced by 15.1%. The sparing effect in non-UFD plans was significantly improved. The FLASH-enhanced EQD2meanin normal tissue and ipsilateral lung was significantly reduced by 3.5% and 10.4%, respectively, in non-UFD plans. The overall improvement is attributed to both the FLASH and fractionation effects.Significance.The fractionation dose optimization can address the limitation of multiple-beam FLASH-RT and utilize the relationship between fractional dose and FLASH effect. Consequently, the non-UFD scheme results in further improvements in normal tissue sparing compared to the UFD scheme, attributed to enhanced fractionation and FLASH effects.

Biological-equivalent-dose-based integrated optimization framework for fast-energy-switching Bragg peak FLASH-RT using single-beam-per-fraction

BACKGROUNDS

When comparing the delivery of all beams per fraction (ABPF) to single beam per fraction (SBPF), it is observed that SBPF not only helps meet the FLASH dose threshold but also mitigates the uncertainty with beam switching in the FLASH effect. However, SBPF might lead to a higher biological equivalent dose in 2 Gy (EQD2) for normal tissues.

PURPOSE

This study aims to develop an EQD2-based integrated optimization framework (EQD2-IOF), encompassing robust dose, delivery efficiency, and beam orientation optimization (BOO) for Bragg peak FLASH plans using the SBPF treatment schedule. The EQD2-IOF aims to enhance both dose sparing and the FLASH effect.

METHODS

A superconducting gantry was employed for fast energy switching within 27 ms, while universal range shifters were utilized to improve beam current in the implementation of FLASH plans with five Bragg peak beams. To enhance dose delivery efficiency while maintaining plan quality, a simultaneous dose and spot map optimization (SDSMO) algorithm for single field optimization was incorporated into a Bayesian optimization-based auto-planning algorithm. Subsequently, a BOO algorithm based on Tabu search was developed to select beam angle combinations (BACs) for 10 lung cases. To simultaneously consider dose sparing and FLASH effect, a quantitative model based on dose-dependent dose modification factor (DMF) was used to calculate FLASH-enhanced dose distribution. The EQD2-IOF plan was compared to the plan optimized without SDSMO using BAC selected by a medical physicist (Manual plan) in the SBPF treatment schedule. Meanwhile, the mean EQD2 in the normal tissue was evaluated for the EQD2-IOF plan in both SBPF and ABPF treatment schedules.

RESULTS

No significant difference was found in D2% and D98% of the target between EQD2-IOF plans and Manual Plans. When using a minimum DMF of 0.67 and a dose threshold of 4 Gy, EQD2-IOF plans showed a significant reduction in FLASH-enhanced EQD2mean of the ipsilateral lung and normal tissue by 10.5% and 11.5%, respectively, compared to Manual plans. For normal tissues that received a dose greater than 70% of the prescription dose, using a minimum DMF of 0.7 for FLASH sparing compensated for the increase in EQD2mean resulting from replacing ABPF with SBPF schedules.

CONCLUSIONS

The EQD2-IOF can automatically optimize SBPF FLASH-RT plans to achieve optimal sparing of normal tissues. With an energy switching time of 27 ms, the loss of fractionate repairing using SBPF schedules in high-dose regions can be compensated for by the FLASH effect. However, when an energy switching time of 500 ms is utilized, the SBPF schedule needs careful consideration, as the FLASH effect diminishes with longer irradiation time.

Time structures of proton pencil beam scanning delivery on a microsecond scale measured with a pixelated semiconductor detector Timepix3

PURPOSE

The time structures of proton spot delivery in proton pencil beam scanning (PBS) radiation therapy are essential in many clinical applications. This study aims to characterize the time structures of proton PBS delivered by both synchrotron and synchrocyclotron accelerators using a non-invasive technique based on scattered particle tracking.

METHODS

A pixelated semiconductor detector, AdvaPIX-Timepix3, with a temporal resolution of 1.56 ns, was employed to measure time of arrival of secondary particles generated by a proton beam. The detector was placed laterally to the high-flux area of the beam in order to allow for single particle detection and not interfere with the treatment. The detector recorded counts of radiation events, their deposited energy and the timestamp associated with the single events. Individual recorded events and their temporal characteristics were used to analyze beam time structures, including energy layer switch time, magnet switch time, spot switch time, and the scanning speeds in the x and y directions. All the measurements were repeated 30 times on three dates, reducing statistical uncertainty.

RESULTS

The uncertainty of the measured energy layer switch times, magnet switch time, and the spot switch time were all within 1% of average values. The scanning speeds uncertainties were within 1.5% and are more precise than previously reported results. The measurements also revealed continuous sub-milliseconds proton spills at a low dose rate for the synchrotron accelerator and radiofrequency pulses at 7 µs and 1 ms repetition time for the synchrocyclotron accelerator.

CONCLUSION

The AdvaPIX-Timepix3 detector can be used to directly measure and monitor time structures on microseconds scale of the PBS proton beam delivery. This method yielded results with high precision and is completely independent of the machine log files.

Creating uniform cluster dose spread-out Bragg peaks for proton and carbon beams

BACKGROUND

Preliminary data have shown a close association of the generalized ionization cluster size dose (in short, cluster dose) with cell survival, independent of particle type, and energy, when cluster dose is derived from an ionization detail parameter preferred for its association with cell survival. Such results suggest cluster dose has the potential to replace RBE-weighted dose in proton and ion beam radiotherapy treatment plan optimization, should a uniform cluster dose lead to comparable biological effects. However, further preclinical investigations are warranted to confirm this premise.

PURPOSE

To present an analytical approach to create uniform cluster dose spread-out Bragg peaks (SOBP) for evaluation of the potential of cluster dose to result in uniform biological effect.

METHODS

We modified the coefficients of the Bortfeld and Schlegel weight formula, an analytical method typically used for the creation of radiation dose SOBP in particle therapy, to produce uniform cluster dose SOBP of different widths (1-5 cm) at relevant clinical proton and carbon beam energies. Optimum parameters were found by minimization of the ratio between the maximum and minimum cluster dose in the SOBP region using the Nelder-Mead method.

RESULTS

The coefficients of the Bortfeld and Schlegel weight formula leading to uniform cluster dose SOBPs were determined for each combination of beam energy and SOBP width studied. The uniformity of the resulting cluster dose SOBPs, calculated as the relative difference between the maximum and minimum cluster dose within the SOBP, was within 0.3%-3.5% for the evaluated proton beams and 1.3%-3.4% for the evaluated carbon beams.

CONCLUSIONS

The modifications to the analytical approach to create radiation dose SOBPs resulted in uniform cluster dose proton and carbon SOBPs over a wide range of beam energies and SOBP widths. Such SOBPs should prove valuable in preclinical investigations for the selection of nanodosimetric quantities to be used in proton and ion therapy treatment planning.