Incorporation of relative biological effectiveness uncertainties into proton plan robustness evaluation

Adaptive intensity modulated proton therapy using 4D robust planning: a proof-of-concept for the application of dose mimicking approach

Objective.A four-dimensional robust optimisation (4DRO) is usually employed when the tumour respiratory motion needs to be addressed. However, it is computationally demanding, and an automated method is preferable for adaptive planning to avoid manual trial-and-error. This study proposes a 4DRO technique based on dose mimicking for automated adaptive planning.Approach.Initial plans for 4DRO intensity modulated proton therapy were created on an average CT for four patients with clinical target volume (CTV) in the lung, oesophagus, or pancreas, respectively. These plans were robustly optimised using three phases of four-dimensional computed tomography (4DCT) and accounting for setup and density uncertainties. Weekly 4DCTs were used for adaptive replanning, using a constant relative biological effectiveness (cRBE) of 1.1. Two methods were used: (1) template-based adaptive (TA) planning and (2) dose-mimicking-based adaptive (MA) planning. The plans were evaluated using variable RBE (vRBE) weighted doses and biologically consistent dose accumulation (BCDA).Main results.MA and TA plans had comparable CTV coverage except for one patient where the MA plan had a higher D98 and lower D2 but with an increased D2 in few organs at risk (OARs). CTV D98 deviations in non-adaptive plans from the initial plans were up to -7.2 percentage points (p.p.) in individual cases and -1.8 p.p. when using BCDA. For the OARs, MA plans showed a reduced mean dose and D2 compared to the TA plans, with few exceptions. The vRBE-weighted accumulated doses had a mean dose and D2 difference of up to 0.3 Gy and 0.5 Gy, respectively, in the OARs with respect to cRBE-weighted doses.Significance.MA plans indicate better performance in target coverage and OAR dose sparing compared to the TA plans in 4DRO adaptive planning. Moreover, MA method is capable of handling both forms of anatomical variation, namely, changes in density and relative shifts in the position of OARs.

Robustness evaluation of pencil beam scanning proton therapy treatment planning: A systematic review

Compared to conventional radiotherapy using X-rays, proton therapy, in principle, allows better conformity of the dose distribution to target volumes, at the cost of greater sensitivity to physical, anatomical, and positioning uncertainties. Robust planning, both in terms of plan optimization and evaluation, has gained high visibility in publications on the subject and is part of clinical practice in many centers. However, there is currently no consensus on the methods and parameters to be used for robust optimization or robustness evaluation. We propose to overcome this deficiency by following the modified Delphi consensus method. This method first requires a systematic review of the literature. We performed this review using the PubMed and Web Of Science databases, via two different experts. Potential conflicts were resolved by a third expert. We then explored the different methods before focusing on clinical studies that evaluate robustness on a significant number of patients. Many robustness assessment methods are proposed in the literature. Some are more successful than others and their implementation varies between centers. Moreover, they are not all statistically or mathematically equivalent. The most sophisticated and rigorous methods have seen more limited application due to the difficulty of their implementation and their lack of widespread availability.

A Novel Framework for Thermoradiotherapy Treatment Planning

PURPOSE

Thermoradiotherapy combines radiation therapy with hyperthermia to increase therapeutic effectiveness. Currently, both modalities are optimized separately and in state-of-the-art research the enhanced therapeutic effect is evaluated using equivalent radiation dose in 2-Gy fractions (EQD2). This study proposes a novel thermoradiotherapy treatment planning framework with voxelwise EQD2 radiation therapy optimizing including thermal radiosensitization and direct thermal cytotoxicity.

METHODS AND MATERIALS

To demonstrate proof-of-concept of the planning framework, 3 strategies consisting of 20 radiation therapy fractions were planned for 4 prostate cancer cases with substantially different temperature distributions: (1) Conventional radiation therapy plan of 60 Gy combined with 4 hyperthermia sessions (RT60 + HT), (2) standalone uniform dose escalation to 68 Gy without hyperthermia (RT68), and (3) uniform target EQD2 that maximizes the tumor control probability (TCP) accounting for voxelwise thermal effects of 4 hyperthermia sessions without increasing normal tissue doses (RTHT + HT). Assessment included dose, EQD2, TCP, and rectal normal tissue complication probability (NTCP), alongside robustness analyses for TCP and NTCP against parameter uncertainties.

RESULTS

The estimated TCP of around 76% for RT60 without hyperthermia was increased to an average of 85.9% (range, 81.3%-90.5%) for RT60 + HT, 92.5% (92.4%-92.5%) for RT68, and 94.4% (91.7%-96.6%) for RTHT + HT. The corresponding averaged rectal NTCPs were 8.7% (7.9%-10.0%), 14.9% (13.8%-17.1%), and 8.4% (7.5%-9.7%), respectively. RT68 and RTHT + HT exhibited slightly enhanced TCP robustness against parameter uncertainties compared with RT60 + HT, and RT68 presented higher and less robust rectal NTCP values compared with the other planning strategies.

CONCLUSIONS

This study introduces an innovative thermoradiotherapy planning approach, integrating thermal effects into EQD2-based radiation therapy optimization. Results demonstrate an ability to achieve enhanced and uniform target EQD2 and TCP across various temperature distributions without elevating normal tissue EQD2 or NTCP compared with conventional methods. Although promising for improving clinical outcomes, realizable enhancements depend on accurate tumor- and tissue-specific data and precise quantification of hyperthermic effects, which are seamlessly integrable in the planning framework as they emerge.

Quantifying the Dosimetric Impact of Proton Range Uncertainties on RBE-Weighted Dose Distributions in Intensity-Modulated Proton Therapy for Bilateral Head and Neck Cancer

BACKGROUND

In current clinical practice, intensity-modulated proton therapy (IMPT) head and neck cancer (HNC) plans are generated using a constant relative biological effectiveness (cRBE) of 1.1. The primary goal of this study was to explore the dosimetric impact of proton range uncertainties on RBE-weighted dose (RWD) distributions using a variable RBE (vRBE) model in the context of bilateral HNC IMPT plans.

METHODS

The current study included the computed tomography (CT) datasets of ten bilateral HNC patients who had undergone photon therapy. Each patient's plan was generated using three IMPT beams to deliver doses to the CTV_High and CTV_Low for doses of 70 Gy(RBE) and 54 Gy(RBE), respectively, in 35 fractions through a simultaneous integrated boost (SIB) technique. Each nominal plan calculated with a cRBE of 1.1 was subjected to the range uncertainties of ±3%. The McNamara vRBE model was used for RWD calculations. For each patient, the differences in dosimetric metrices between the RWD and nominal dose distributions were compared.

RESULTS

The constrictor muscles, oral cavity, parotids, larynx, thyroid, and esophagus showed average differences in mean dose (Dmean) values up to 6.91 Gy(RBE), indicating the impact of proton range uncertainties on RWD distributions. Similarly, the brachial plexus, brain, brainstem, spinal cord, and mandible showed varying degrees of the average differences in maximum dose (Dmax) values (2.78-10.75 Gy(RBE)). The Dmean and Dmax to the CTV from RWD distributions were within ±2% of the dosimetric results in nominal plans.

CONCLUSION

The consistent trend of higher mean and maximum doses to the OARs with the McNamara vRBE model compared to cRBE model highlighted the need for consideration of proton range uncertainties while evaluating OAR doses in bilateral HNC IMPT plans.

Plan robustness and RBE influence for proton dose painting by numbers for head and neck cancers

PURPOSE

To investigate the feasibility of dose painting by numbers (DPBN) with respect to robustness for proton therapy for head and neck cancers (HNC), and to study the influence of variable RBE on the TCP and OAR dose burden.

METHODS AND MATERIALS

Data for 19 patients who have been scanned pretreatment with PET-FDG and subsequently treated with photon therapy were used in the study. A dose response model developed for photon therapy was implemented in a TPS, allowing DPBN plans to be created. Conventional homogeneous dose and DPBN plans were created for each patient, optimized with either fixed RBE = 1.1 or a variable RBE model. Robust optimization was used to create clinically acceptable plans. To estimate the maximum potential loss in TCP due to actual SUV variations from the pre-treatment imaging, we applied a test case with randomized SUV distribution.

RESULTS

Regardless of the use of variable RBE for optimization or evaluation, a statistically significant increase (p < 0.001) in TCP was found for DPBN plans as compared to homogeneous dose plans. Randomizing the SUV distribution decreased the TCP for all plans. A correlation between TCP increase and variance of the SUV distribution and target volume was also found.

CONCLUSION

DPBN for protons and HNC is feasible and could lead to a TCP gain. Risks associated with the temporal variation of SUV distributions could be mitigated by imposing minimum doses to targets. The correlation found between TCP increase and SUV variance and target volume may be used for patient selection.

Hyperfractionated intensity-modulated proton therapy for pharyngeal cancer with variable relative biological effectiveness: A simulation study

BACKGROUND

The relative biological effectiveness (RBE) of proton is considered to be dependent on biological parameters and fractional dose. While hyperfractionated photon therapy was effective in the treatment of patients with head and neck cancers, its effect in intensity-modulated proton therapy (IMPT) under the variable RBE has not been investigated in detail.

PURPOSE

To study the effect of variable RBE on hyperfractionated IMPT for the treatment of pharyngeal cancer. We investigated the biologically effective dose (BED) to determine the theoretical effective hyperfractionated schedule.

METHODS

The treatment plans of three pharyngeal cancer patients were used to define the ΔBED for the clinical target volume (CTV) and soft tissue (acute and late reaction) as the difference between the BED for the altered schedule with variable RBE and conventional schedule with constant RBE. The ΔBED with several combinations of parameters (treatment days, number of fractions, and prescribed dose) was comprehensively calculated. Of the candidate schedules, the one that commonly gave a higher ΔBED for CTV was selected as the resultant schedule. The BED volume histogram was used to compare the influence of variable RBE and fractionation.

RESULTS

In the conventional schedule, compared with the constant RBE, the variable RBE resulted in a mean 2.6 and 2.7 Gy reduction of BED_mean for the CTV and soft tissue (acute reaction) of the three plans, respectively. Moreover, the BED_mean for soft tissue (late reaction) increased by 7.4 Gy, indicating a potential risk of increased RBE. Comprehensive calculation of the ΔBED resulted in the hyperfractionated schedule of 80.52 Gy (RBE = 1.1)/66 fractions in 6.5 weeks. When variable RBE was used, compared with the conventional schedule, the hyperfractionated schedule increased the BED_mean for CTV by 7.6 Gy; however, this was associated with a 7.8 Gy increase for soft tissue (acute reaction). The BED_mean for soft tissue (late reaction) decreased by 2.4 Gy.

CONCLUSION

The results indicated a potential effect of the variable RBE on IMPT for pharyngeal cancer but with the possibility that hyperfractionation could outweigh this effect. Although biological uncertainties require conservative use of the resultant schedule, hyperfractionation is expected to be an effective strategy in IMPT for pharyngeal cancer.

Reformulated McNamara RBE-weighted beam orientation optimization for intensity modulated proton therapy

PURPOSE

Empirical relative biological effectiveness (RBE) models have been used to estimate the biological dose in proton therapy but do not adequately capture the factors influencing RBE values for treatment planning. We reformulate the McNamara RBE model such that it can be added as a linear biological dose fidelity term within our previously developed sensitivity-regularized and heterogeneity-weighted beam orientation optimization (SHBOO) framework.

METHODS

Based on our SHBOO framework, we formulated the biological optimization problem to minimize total McNamara RBE dose to OARs. We solve this problem using two optimization algorithms: FISTA (McNam-FISTA) and Chambolle-Pock (McNam-CP). We compare their performances with a physical dose optimizer assuming RBE = 1.1 in all structures (PHYS-FISTA) and an LET-weighted dose model (LET-FISTA). Three head and neck patients were planned with the four techniques and compared on dosimetry and robustness.

RESULTS

Compared to Phys-FISTA, McNam-CP was able to match CTV [HI, Dmax, D95%, D98%] by [0.00, 0.05%, 1.4%, 0.8%]. McNam-FISTA and McNam-CP were able to significantly improve overall OAR [Dmean, Dmax] by an average of [36.1%,26.4%] and [29.6%, 20.3%], respectively. Regarding CTV robustness, worst [Dmax, V95%, D95%, D98%] improvement of [-6.6%, 6.2%, 6.0%, 4.8%] was reported for McNam-FISTA and [2.7%, 2.7%, 5.3%, -4.3%] for McNam-CP under combinations of range and setup uncertainties. For OARs, worst [Dmax, Dmean] were improved by McNam-FISTA and McNam-CP by an average of [25.0%, 19.2%] and [29.5%, 36.5%], respectively. McNam-FISTA considerably improved dosimetry and CTV robustness compared to LET-FISTA, which achieved better worst-case OAR doses.

CONCLUSION

The four optimization techniques deliver comparable biological doses for the head and neck cases. Besides modest CTV coverage and robustness improvement, OAR biological dose and robustness were substantially improved with both McNam-FISTA and McNam-CP, showing potential benefit for directly incorporating McNamara RBE in proton treatment planning.

RBE-weighted dose and its impact on the risk of acute coronary event for breast cancer patients treated with intensity modulated proton therapy

PURPOSE

To evaluate the relative biological effectiveness (RBE)-weighted dose to the heart and to estimate RBE uncertainties when assuming a constant RBE of 1.1, for breast cancer patients receiving intensity-modulated proton therapy (IMPT). Further, to study the impact of RBE uncertainties on the risk of an acute coronary event (ACE).

MATERIAL AND METHODS

We analyzed 20 patients who received IMPT to either the left breast (n = 10) or left chest wall (n = 10) and regional lymph nodes. The Monte Carlo simulation engine, MCsquare, was used to simulate the dose-averaged linear energy transfer (LETd) map. The RBE-weighted dose to the heart and its substructures was calculated using three different RBE models. The risk of ACE was estimated per its linear relationship with mean heart dose (MHD) as established by Darby et al.

RESULTS

The median MHD increased from 1.33 GyRBE assuming an RBE of 1.1 to 1.64, 1.87, and 1.99 GyRBE when using the RBE-weighted dose models. The median values (and ranges) of the excess absolute risk of ACE were 0.4% (0.1%-0.8%) when assuming an RBE of 1.1, and 0.6% (0.2%-1.0%), 0.6% (0.2%-1.1%), and 0.7% (0.2%-1.1%) with the RBE-weighted models. For our patient cohort, the maximum excess absolute risk of ACE increased by 0.3% with the RBE-weighted doses compared to the constant RBE of 1.1, reaching an excess absolute ACE risk of 1.1%. The interpatient LETd variation was small for the relevant high-dose regions of the heart.

CONCLUSION

All three RBE models predicted a higher biological dose compared to the clinical standard dose assuming a constant RBE of 1.1. An underestimation of the biological dose results in underestimation of the ACE risk. Analyzing the voxel-by-voxel biological dose and the LET map alongside clinical outcomes is warranted in the development of a more accurate normal-tissue complication probability model.

Towards harmonizing clinical linear energy transfer (LET) reporting in proton radiotherapy: a European multi-centric study

BACKGROUND

Clinical data suggest that the relative biological effectiveness (RBE) in proton therapy (PT) varies with linear energy transfer (LET). However, LET calculations are neither standardized nor available in clinical routine. Here, the status of LET calculations among European PT institutions and their comparability are assessed.

MATERIALS AND METHODS

Eight European PT institutions used suitable treatment planning systems with their center-specific beam model to create treatment plans in a water phantom covering different field arrangements and fulfilling commonly agreed dose objectives. They employed their locally established LET simulation environments and procedures to determine the corresponding LET distributions. Dose distributions D1.1 and DRBE assuming constant and variable RBE, respectively, and LET were compared among the institutions. Inter-center variability was assessed based on dose- and LET-volume-histogram parameters.

RESULTS

Treatment plans from six institutions fulfilled all clinical goals and were eligible for common analysis. D1.1 distributions in the target volume were comparable among PT institutions. However, corresponding LET values varied substantially between institutions for all field arrangements, primarily due to differences in LET averaging technique and considered secondary particle spectra. Consequently, DRBE using non-harmonized LET calculations increased inter-center dose variations substantially compared to D1.1 and significantly in mean dose to the target volume of perpendicular and opposing field arrangements (p < 0.05). Harmonizing LET reporting (dose-averaging, all protons, LET to water or to unit density tissue) reduced the inter-center variability in LET to the order of 10-15% within and outside the target volume for all beam arrangements. Consequentially, inter-institutional variability in DRBE decreased to that observed for D1.1.

CONCLUSION

Harmonizing the reported LET among PT centers is feasible and allows for consistent multi-centric analysis and reporting of tumor control and toxicity in view of a variable RBE. It may serve as basis for harmonized variable RBE dose prescription in PT.

Impact of RBE variations on risk estimates of temporal lobe necrosis in patients treated with intensity-modulated proton therapy for head and neck cancer

BACKGROUND

Temporal lobe necrosis (TLN) is a potential late effect after radiotherapy for skull base head and neck cancer (HNC). Several photon-derived dose constraints and normal tissue complication probability (NTCP) models have been proposed, however variation in relative biological effectiveness (RBE) may challenge the applicability of these dose constraints and models in proton therapy. The purpose of this study was therefore to investigate the influence of RBE variations on risk estimates of TLN after Intensity-Modulated Proton Therapy for HNC.

MATERIAL AND METHODS

Seventy-five temporal lobes from 45 previously treated patients were included in the analysis. Sixteen temporal lobes had radiation associated Magnetic Resonance image changes (TLIC) suspected to be early signs of TLN. Fixed (RWD_Fix) and variable RBE-weighed doses (RWD_Var) were calculated using RBE = 1.1 and two RBE models, respectively. RWD_Fix and RWD_Var for temporal lobes were compared using Friedman's test. Based on RWD_Fix, six NTCP models were fitted and internally validated through bootstrapping. Estimated probabilities from RWD_Fix and RWD_Var were compared using paired Wilcoxon test. Seven dose constraints were evaluated separately for RWD_Fix and RWD_Var by calculating the observed proportion of TLIC in temporal lobes meeting the specific dose constraints.

RESULTS

RWD_Var were significantly higher than RWD_Fix (p < 0.01). NTCP model performance was good (AUC:0.79-0.84). The median difference in estimated probability between RWD_Fix and RWD_Var ranged between 5.3% and 20.0% points (p < 0.01), with V_60GyRBE and D_Max at the smallest and largest differences, respectively. The proportion of TLIC was higher for RWD_Fix (4.0%-13.1%) versus RWD_Var (1.3%-5.3%). For V_65GyRBE ≤ 0.03 cc the proportion of TLIC was less than 5% for both RWD_Fix and RWD_Var.

CONCLUSION

NTCP estimates were significantly influenced by RBE variations. D_max as model predictor resulted in the largest deviations in risk estimates between RWD_Fix and RWD_Var. V_65GyRBE ≤ 0.03 cc was the most consistent dose constraint for RWD_Fix and RWD_Var.

A Critical Review of LET-Based Intensity-Modulated Proton Therapy Plan Evaluation and Optimization for Head and Neck Cancer Management

In this review article, we review the 3 important aspects of linear-energy-transfer (LET) in intensity-modulated proton therapy (IMPT) for head and neck (H&N) cancer management. Accurate LET calculation methods are essential for LET-guided plan evaluation and optimization, which can be calculated either by analytical methods or by Monte Carlo (MC) simulations. Recently, some new 3D analytical approaches to calculate LET accurately and efficiently have been proposed. On the other hand, several fast MC codes have also been developed to speed up the MC simulation by simplifying nonessential physics models and/or using the graphics processor unit (GPU)–acceleration approach. Some concepts related to LET are also briefly summarized including (1) dose-weighted versus fluence-weighted LET; (2) restricted versus unrestricted LET; and (3) microdosimetry versus macrodosimetry. LET-guided plan evaluation has been clinically done in some proton centers. Recently, more and more studies using patient outcomes as the biological endpoint have shown a positive correlation between high LET and adverse events sites, indicating the importance of LET-guided plan evaluation in proton clinics. Various LET-guided plan optimization methods have been proposed to generate proton plans to achieve biologically optimized IMPT plans. Different optimization frameworks were used, including 2-step optimization, 1-step optimization, and worst-case robust optimization. They either indirectly or directly optimize the LET distribution in patients while trying to maintain the same dose distribution and plan robustness. It is important to consider the impact of uncertainties in LET-guided optimization (ie, LET-guided robust optimization) in IMPT, since IMPT is sensitive to uncertainties including both the dose and LET distributions. We believe that the advancement of the LET-guided plan evaluation and optimization will help us exploit the unique biological characteristics of proton beams to improve the therapeutic ratio of IMPT to treat H&N and other cancers.

Development of robustness evaluation strategies for enabling statistically consistent reporting

Robustness evaluation of proton therapy treatment plans is essential for ensuring safe treatment delivery. However, available evaluation procedures feature a limited exploration of the actual robustness of the plan and generally do not provide confidence levels. This study compared established and more sophisticated robustness evaluation procedures, with quantified confidence levels. We have evaluated several robustness evaluation methods for 5 bilateral head-and-neck patients optimized considering spot scanning delivery and with a conventional CTV-to-PTV margin of 4 mm. Method (1) good practice scenario selection (GPSS) (e.g. +/- 4 mm setup error 3% range uncertainty); (2) statistically sound scenario selection (SSSS) either only on or both on and inside isoprobability hypersurface encompassing 90% of the possible errors; (3) statistically sound dosimetric selection (SSDS). In the last method, the 90% best plans were selected according to either target coverage quantified by D 95 (SSDS_D 95) or to an approximation of the final objective function (OF) used during treatment optimization (SSDS_OF). For all methods, we have considered systematic setup and systematic range errors. A mix of systematic and random setup errors were also simulated for SSDS, but keeping the same conventional margin of 4 mm. All robustness evaluations have been performed using the fast Monte Carlo dose engine MCsquare. Both SSSS strategies yielded on average very similar results. SSSS and GPSS yield comparable values for target coverage (within 0.5 Gy). The most noticeable differences were found for the CTV between GPSS, on the one hand, and SSDS_D 95 and SSDS_OF, on the other hand (average worst-case D 98 were 2.8 and 2.0 Gy larger than for GPSS, respectively). Simulating explicitly random errors in SSDS improved almost all DVH metrics. We have observed that the width of DVH-bands and the confidence levels depend on the method chosen to sample the scenarios. Statistically sound estimation of the robustness of the plan in the dosimetric space may provide an improved insight on the actual robustness of the plan for a given confidence level.

Incorporation of the LETd-weighted biological dose in the evaluation of breast intensity-modulated proton therapy plans

PURPOSE

To evaluate the LETd-weighted biological dose to OARs in proton therapy for breast cancer and to study the relationship of the LETd-weighted biological dose relative to the standard dose (RBE = 1.1) and thereby to provide estimations of the biological dose uncertainties with the standard dose calculations (RBE = 1.1) commonly used in clinical practice.

METHOD

This study included 20 patients who received IMPT treatment to the whole breast/chest wall and regional lymph nodes. The LETd distributions were calculated along with the physical dose using an open-source Monte Carlo simulation package, MCsquare. Using the McMahon linear model, the LETd-weighted biological dose was computed from the physical dose and LETd. OAR doses were compared between the Dose (RBE = 1.1) and the LETd-weighted biological dose, on brachial plexus, rib, heart, esophagus, and Ipsilateral lung.

RESULTS

On average, the LETd-weighted biological dose compared to the Dose (RBE = 1.1) was higher by 8% for the brachial plexus D0.1 cc, 13% for the ribs D0.5 cc, 24% for mean heart dose, and 10% for the esophagus D0.1 cc, respectively. The LETd-weighted doses to the Ipsilateral lung V5, V10, and V20 were comparable to the Dose (RBE = 1.1). No statistically significant difference in biological dose enhancement to OARs was observed between the intact breast group and the CW group, with the exception of the ribs: the CW group experienced slightly greater biological dose enhancement (13% vs. 12%, p = 0.04) to the ribs than the intact breast group.

CONCLUSION

Enhanced biological dose was observed compared to standard dose with assumed RBE of 1.1 for the heart, ribs, esophagus, and brachial plexus in breast/CW and regional nodal IMPT plans. Variable RBE models should be considered in the evaluation of the IMPT breast plans, especially for OARs located near the end of range of a proton beam. Clinical outcome studies are needed to validate model predictions for clinical toxicities.

The impact of variable relative biological effectiveness in proton therapy for left-sided breast cancer when estimating normal tissue complications in the heart and lung

The aim of this study was to evaluate the clinical impact of relative biological effectiveness (RBE) variations in proton beam scanning treatment (PBS) for left-sided breast cancer versus the assumption of a fixed RBE of 1.1, particularly in the context of comparisons with photon-based three-dimensional conformal radiotherapy (3DCRT) and volumetric modulated arc therapy (VMAT). Ten patients receiving radiation treatment to the whole breast/chest wall and regional lymph nodes were selected for each modality. For PBS, the dose distributions were re-calculated with both a fixed RBE and a variable RBE using an empirical RBE model. Dosimetric indices based on dose-volume histogram analysis were calculated for the entire heart wall, left anterior descending artery (LAD) and left lung. Furthermore, normal tissue toxicity probabilities for different endpoints were evaluated. The results show that applying a variable RBE significantly increases the RBE-weighted dose and consequently the calculated dosimetric indices increases for all organs compared to a fixed RBE. The mean dose to the heart and the maximum dose to the LAD and the left lung are significantly lower for PBS assuming a fixed RBE compared to 3DCRT. However, no statistically significant difference is seen when a variable RBE is applied. For a fixed RBE, lung toxicities are significantly lower compared to 3DCRT but when applying a variable RBE, no statistically significant differences are noted. A disadvantage is seen for VMAT over both PBS and 3DCRT. One-to-one plan comparison on 8 patients between PBS and 3DCRT shows similar results. We conclude that dosimetric analysis for all organs and toxicity estimation for the left lung might be underestimated when applying a fixed RBE for protons. Potential RBE variations should therefore be considered as uncertainty bands in outcome analysis.

Spatial Agreement of Brainstem Dose Distributions Depending on Biological Model in Proton Therapy for Pediatric Brain Tumors

Purpose

During radiation therapy for pediatric brain tumors, the brainstem is a critical organ at risk, possibly with different radio-sensitivity across its substructures. In proton therapy, treatment planning is currently performed using a constant relative biological effectiveness (RBE) of 1.1 (RBE_1.1), whereas preclinical studies point toward spatial variability of this factor. To shed light on this biological uncertainty, we investigated the spatial agreement between isodose maps produced by different RBE models, with emphasis on (smaller) substructures of the brainstem.

Methods and Materials

Proton plans were recalculated using Monte Carlo simulations in 3 anonymized pediatric patients with brain tumors (a craniopharyngioma, a low-grade glioma, and a posterior fossa ependymoma) to obtain dose and linear energy transfer distributions. Doses and volume metrics for the brainstem and its substructures were calculated using a constant RBE_1.1, 4 phenomenological RBE models with varying (α/β)_x parameters, and with a simpler linear energy transfer-dependent model. The spatial agreement between the dose distributions of constant RBE_1.1 versus the variable RBE models was compared using the Dice similarity coefficient.

Results

The spatial agreement between the variable RBE dose distributions and RBE_1.1 decreased with increasing isodose levels in all patient cases. The patient with ependymoma showed the greatest variation in dose and dose volumes, where V_50Gy(RBE) in the brainstem increased from 32% (RBE_1.1) to 35% to 49% depending on the applied model, corresponding to a spatial agreement (Dice similarity coefficient) between 0.79 and 0.95. The remaining patients showed similar trends, however, with lower absolute values due to lower brainstem doses.

Conclusions

All phenomenological RBE models fully enclosed the isodose volumes of the constant RBE_1.1, and the volumes based on variable RBE spatially agreed. The spatial agreement was dependent on the isodose level, where higher isodose levels showed larger expansions and less agreement between the variable RBE models and RBE_1.1.

Silicon 3D Microdetectors for Microdosimetry in Hadron Therapy

The present overview describes the evolution of new microdosimeters developed in the National Microelectronics Center in Spain (IMB-CNM, CSIC), ranging from the first ultra-thin 3D diodes (U3DTHINs) to the advanced 3D-cylindrical microdetectors, which have been developed over the last 10 years. In this work, we summarize the design, main manufacture processes, and electrical characterization of these devices. These sensors were specifically customized for use in particle therapy and overcame some of the technological challenges in this domain, namely the low noise capability, well-defined sensitive volume, high spatial resolution, and pile-up robustness. Likewise, both architectures reduce the loss of charge carriers due to trapping effects, the charge collection time, and the voltage required for full depletion compared to planar silicon detectors. In particular, a 3D‒cylindrical architecture with electrodes inserted into the silicon bulk and with a very well‒delimited sensitive volume (SV) mimicked a cell array with shapes and sizes similar to those of mammalian cells for the first time. Experimental tests of the carbon beamlines at the Grand Accélérateur National d’Lourds (GANIL, France) and Centro Nazionale Adroterapia Oncologica (CNAO, Italy) showed the feasibility of the U3DTHINs in hadron therapy beams and the good performance of the 3D‒cylindrical microdetectors for assessing linear energy distributions of clinical beams, with clinical fluence rates of 5 × 10⁷ s⁻¹cm⁻² without saturation. The dose-averaged lineal energies showed a generally good agreement with Monte Carlo simulations. The results indicated that these devices can be used to characterize the microdosimetric properties in hadron therapy, even though the charge collection efficiency (CCE) and electronic noise may pose limitations on their performance, which is studied and discussed herein. In the last 3D‒cylindrical microdetector generation, we considerably improved the CCE due to the microfabrication enhancements, which have led to shallower and steeper dopant profiles. We also summarize the successive microdosimetric characterizations performed with both devices in proton and carbon beamlines.

Impact of range uncertainty on clinical distributions of linear energy transfer and biological effectiveness in proton therapy

PURPOSE

Increased radiation response after proton irradiation, such as late radiation-induced toxicity, is determined by high dose and elevated linear energy transfer (LET). Steep dose-averaged LET (LET_d ) gradients and elevated LET_d occur at the end of proton range and might be particularly sensitive to uncertainties in range prediction. Therefore, this study quantified LET_d distributions and the impact of range uncertainty in robust dose-optimized proton treatment plans and assessed the biological effect in normal tissues and tumors of patients.

METHODS

For each of six cancer patients (two brain, head-and-neck, and prostate), two nominal treatment plans were robustly dose optimized using single- and multi-field optimization, respectively. For each plan, two additional scenarios with ±3.5% range deviation relative to the nominal plan were derived by global rescaling of stopping-power ratios. Dose and LET_d distributions were calculated for each scenario using the beam parameters of the corresponding nominal plan. The variability in relative biological effectiveness (RBE) and probability of late radiation-induced brain toxicity (P_IC ) was assessed.

RESULTS

The optimization technique (single- vs multi-field) had a negligible impact on the LET_d distributions in the clinical target volume (CTV) and in most organs at risk (OARs). LET_d distributions in the CTV were rather homogeneous with arithmetic mean of LET_d below 3.2 keV/µm and robust against range deviations. The RBE variability within the CTV induced by range uncertainty was small (≤0.05, 95% confidence interval). In OARs, LET_d hotspots (>7 keV/µm) occurred and LET_d distributions were inhomogeneous and sensitive to range deviations. LET_d hotspots and the impact of range deviations were most prominent in OARs of brain tumor patients which translated in RBE values exceeding 1.1 in all brain OARs. The near-maximum predicted P_IC in healthy brain tissue of brain tumor patients was smaller than 5% and occurred adjacent to the CTV. Range deviations induced absolute differences in P_IC up to 1.2%.

CONCLUSIONS

Robust dose optimization generates LET_d distributions in the target volume robust against range deviations. The current findings support using a constant RBE within the CTV. The impact of range deviations on the considered probability of late radiation-induced toxicity in brain tissue was limited for robust dose-optimized treatment plans. Incorporation of LET_d in robust optimization frameworks may further reduce uncertainty related to the RBE-weighted dose estimation in normal tissues.

RBE for proton radiation therapy - a Nordic view in the international perspective

BACKGROUND

This paper presents an insight into the critical discussions and the current strategies of the Nordic countries for handling the variable proton relative biological effectiveness (RBE) as presented at The Nordic Collaborative Workshop for Particle Therapy that took place at the Skandion Clinic on 14th and 15th of November 2019.

MATERIAL AND METHODS

In the current clinical practice at the two proton centres in operation at the date, Skandion Clinic, and the Danish Centre for Particle Therapy, a constant proton RBE of 1.1 is applied. The potentially increased effectiveness at the end of the particle range is however considered at the stage of treatment planning at both places based on empirical observations and knowledge. More elaborated strategies to evaluate the plans and mitigate the problem are intensely investigated internationally as well at the two centres. They involve the calculation of the dose-averaged linear energy transfer (LET_d) values and the assessment of their distributions corroborated with the distribution of the dose and the location of the critical clinical structures.

RESULTS

Methods and tools for LET_d calculations are under different stages of development as well as models to account for the variation of the RBE with LET_d, dose per fraction, and type of tissue. The way they are currently used for evaluation and optimisation of the plans and their robustness are summarised. A critical but not exhaustive discussion of their potential future implementation in the clinical practice is also presented.

CONCLUSIONS

The need for collaboration between the clinical proton centres in establishing common platforms and perspectives for treatment planning evaluation and optimisation is highlighted as well as the need of close interaction with the research academic groups that could offer a complementary perspective and actively help developing methods and tools for clinical implementation of the more complex metrics for considering the variable effectiveness of the proton beams.

Inter-patient variations in relative biological effectiveness for cranio-spinal irradiation with protons

Cranio-spinal irradiation (CSI) using protons has dosimetric advantages compared to photons and is expected to reduce risk of adverse effects. The proton relative biological effectiveness (RBE) varies with linear energy transfer (LET), tissue type and dose, but a variable RBE has not replaced the constant RBE of 1.1 in clinical treatment planning. We examined inter-patient variations in RBE for ten proton CSI patients. Variable RBE models were used to obtain RBE and RBE-weighted doses. RBE was quantified in terms of dose weighted organ-mean RBE ([Formula: see text] = mean RBE-weighted dose/mean physical dose) and effective RBE of the near maximum dose (D2%), i.e. RBED2% = [Formula: see text], where subscripts RBE and phys indicate that the D2% is calculated based on an RBE model and the physical dose, respectively. Compared to the median [Formula: see text] of the patient population, differences up to 15% were observed for the individual [Formula: see text] values found for the thyroid, while more modest variations were seen for the heart (6%), lungs (2%) and brainstem (<1%). Large inter-patient variation in RBE could be correlated to large spread in LET and dose for these organs at risk (OARs). For OARs with small inter-patient variations, the results show that applying a population based RBE in treatment planning may be a step forward compared to using RBE of 1.1. OARs with large inter-patient RBE variations should ideally be selected for patient-specific biological or RBE robustness analysis if the physical doses are close to known dose thresholds.

Proton therapy for head and neck squamous cell carcinomas: A review of the physical and clinical challenges

The quality of radiation therapy has been shown to significantly influence the outcomes for head and neck squamous cell carcinoma (HNSCC) patients. The results of dosimetric studies suggest that intensity-modulated proton therapy (IMPT) could be of added value for HNSCC by being more effective than intensity-modulated (photon) radiation therapy (IMRT) for reducing side effects of radiation therapy. However, the physical properties of protons make IMPT more sensitive than photons to planning uncertainties. This could potentially have a negative effect on the quality of IMPT planning and delivery. For this review, the three French proton therapy centers collaborated to evaluate the differences between IMRT and IMPT. The review explored the effects of these uncertainties and their management for developing a robust and optimized IMPT treatment delivery plan to achieve clinical outcomes that are superior to those for IMRT. We also provide practical suggestions for the management of HNSCC carcinoma with IMPT. Because metallic dental implants can increase range uncertainties (3-10%), patient preparation for IMPT may require more systematic removal of in-field alien material than is done for IMRT. Multi-energy CT may be an alternative to calculate more accurately the dose distribution. The practical aspects that we describe are essential to guarantee optimal quality in radiation therapy in both model-based and randomized clinical trials.

The impact of proton LET/RBE modeling and robustness analysis on base-of-skull and pediatric craniopharyngioma proton plans relative to VMAT

Purpose: Pediatric craniopharyngioma, adult base-of-skull sarcoma and chordoma cases are all regarded as priority candidates for proton therapy. In this study, a dosimetric comparison between volumetric modulated arc therapy (VMAT) and intensity modulated proton therapy (IMPT) was first performed. We then investigated the impact of physical and biological uncertainties. We assessed whether IMPT plans remained dosimetrically superior when such uncertainty estimates were considered, especially with regards to sparing organs at risk (OARs).Methodology: We studied 10 cases: four chondrosarcoma, two chordoma and four pediatric craniopharyngioma. VMAT and IMPT plans were created according to modality-specific protocols. For IMPT, we considered (i) variable RBE modeling using the McNamara model for different values of (α/β)x, and (ii) robustness analysis with ±3 mm set-up and 3.5% range uncertainties.Results: When comparing the VMAT and IMPT plans, the dosimetric advantages of IMPT were clear: IMPT led to reduced integral dose and, typically, improved CTV coverage given our OAR constraints. When physical robustness analysis was performed for IMPT, some uncertainty scenarios worsened the CTV coverage but not usually beyond that achieved by VMAT. Certain scenarios caused OAR constraints to be exceeded, particularly for the brainstem and optical chiasm. However, variable RBE modeling predicted even more substantial hotspots, especially for low values of (α/β)x. Variable RBE modeling often prompted dose constraints to be exceeded for critical structures.Conclusion: For base-of-skull and pediatric craniopharyngioma cases, both physical and biological robustness analyses should be considered for IMPT: these analyses can substantially affect the sparing of OARs and comparisons against VMAT. All proton RBE modeling is subject to high levels of uncertainty, but the clinical community should remain cognizant possible RBE effects. Careful clinical and imaging follow-up, plus further research on end-of-range RBE mitigation strategies such as LET optimization, should be prioritized for these cohorts of proton patients.

Robustness Analysis for External Beam Radiation Therapy Treatment Plans: Describing Uncertainty Scenarios and Reporting Their Dosimetric Consequences

PURPOSE

With external beam radiation therapy, uncertainties in treatment planning and delivery can result in an undesirable dose distribution delivered to the patient that can compromise the benefit of treatment. Techniques including geometric margins and probabilistic optimization have been used effectively to mitigate the effects of uncertainties. However, their broad application is inconsistent and can compromise the conclusions derived from cross-technique and cross-modality comparisons.

METHODS AND MATERIALS

Conventional methods to deal with treatment planning and delivery uncertainties are described, and robustness analysis is presented as a framework that is applicable across treatment techniques and modalities.

RESULTS

This report identifies elements that are imperative to include when conducting a robustness analysis and describing uncertainties and their dosimetric effects.

CONCLUSION

The robustness analysis approach described here is presented to promote reliable plan evaluation and dose reporting, particularly during clinical trials conducted across institutions and treatment modalities.

Fixed- versus Variable-RBE Computations for Intensity Modulated Proton Therapy

Purpose

To evaluate how using models of proton therapy that incorporate variable relative biological effectiveness (RBE) versus the current practice of using a fixed RBE of 1.1 affects dosimetric indices on treatment plans for large cohorts of patients treated with intensity modulated proton therapy (IMPT).

Methods and Materials

Treatment plans for 4 groups of patients who received IMPT for brain, head-and-neck, thoracic, or prostate cancer were selected. Dose distributions were recalculated in 4 ways: 1 with a fast-dose Monte Carlo calculator with fixed RBE and 3 with RBE calculated to 3 different models—McNamara, Wedenberg, and repair-misrepair-fixation. Differences among dosimetric indices (D02, D50, D98, and mean dose) for target volumes and organs at risk (OARs) on each plan were compared between the fixed-RBE and variable-RBE calculations.

Results

In analyses of all target volumes, for which the main concern is underprediction or RBE less than 1.1, none of the models predicted an RBE less than 1.05 for any of the cohorts. For OARs, the 2 models based on linear energy transfer, McNamara and Wedenberg, systematically predicted RBE >1.1 for most structures. For the mean dose of 25% of the plans for 2 OARs, they predict RBE equal to or larger than 1.4, 1.3, 1.3, and 1.2 for brain, head-and-neck, thorax, and prostate, respectively. Systematically lower increases in RBE are predicted by repair-misrepair-fixation, with a few cases (eg, femur) in which the RBE is less than 1.1 for all plans.

Conclusions

The variable-RBE models predict increased doses to various OARs, suggesting that strategies to reduce high-dose linear energy transfer in critical structures should be developed to minimize possible toxicity associated with IMPT.

Introducing Proton Track-End Objectives in Intensity Modulated Proton Therapy Optimization to Reduce Linear Energy Transfer and Relative Biological Effectiveness in Critical Structures

PURPOSE

We propose the use of proton track-end objectives in intensity modulated proton therapy (IMPT) optimization to reduce the linear energy transfer (LET) and the relative biological effectiveness (RBE) in critical structures.

METHODS AND MATERIALS

IMPT plans were generated for 3 intracranial patient cases (1.8 Gy (RBE) in 30 fractions) and 3 head-and-neck patient cases (2 Gy (RBE) in 35 fractions), assuming a constant RBE of 1.1. Two plans were generated for each patient: (1) physical dose objectives only (DOSEopt) and (2) same dose objectives as the DOSEopt plan, with additional proton track-end objectives (TEopt). The track-end objectives penalized protons stopping in the risk volume of choice. Dose evaluations were made using a RBE of 1.1 and the LET-dependent Wedenberg RBE model, together with estimates of normal tissue complication probabilities (NTCPs). In addition, the distributions of proton track-ends and dose-average LET (LET_d) were analyzed.

RESULTS

The TEopt plans reduced the mean LET_d in the critical structures studied by an average of 37% and increased the mean LET_d in the primary clinical target volume (CTV) by an average of 23%. This was achieved through a redistribution of the proton track-ends, concurrently keeping the physical dose distribution virtually unchanged compared to the DOSEopt plans. This resulted in substantial RBE-weighted dose (D_RBE) reductions, allowing the TEopt plans to meet all clinical goals for both RBE models and reduce the NTCPs by 0 to 19 percentage points compared to the DOSEopt plans, assuming the Wedenberg RBE model. The DOSEopt plans met all clinical goals assuming a RBE of 1.1 but failed 10 of 19 normal tissue goals assuming the Wedenberg RBE model.

CONCLUSIONS

Proton track-end objectives allow for LET_d reductions in critical structures without compromising the physical target dose. This approach permits the lowering of D_RBE and NTCP in critical structures, independent of the variable RBE model used, and it could be introduced in clinical practice without changing current protocols based on the constant RBE of 1.1.

Exploration and application of phenomenological RBE models for proton therapy

The relative biological effectiveness (RBE) of protons varies with multiple physical and biological factors. Phenomenological RBE models have been developed to include such factors in the estimation of a variable RBE, in contrast to the clinically applied constant RBE of 1.1. In this study, eleven published phenomenological RBE models and two plan-based models were explored and applied to simulated patient cases. All models were analysed with respect to the distribution and range of linear energy transfer (LET) and reference radiation fractionation sensitivity ((α/β) _x ) of their respective experimental databases. Proton therapy plans for a spread-out Bragg peak in water and three patient cases (prostate adenocarcinoma, pituitary adenoma and thoracic sarcoma) were optimised using an RBE of 1.1 in the Eclipse^™ treatment planning system prior to recalculation and modelling in the FLUKA Monte Carlo code. Model estimated dose-volume parameters for the planning target volumes (PTVs) and organs at risk (OAR) were compared. The experimental in vitro databases for the various models differed greatly in the range of (α/β) _x values and dose-averaged LET (LET_d). There were significant variations between the model estimations, which arose from fundamental differences in the database definitions and model assumptions. The greatest variations appeared in organs with low (α/β) _x and high LET_d, e.g. biological doses given to late responding OARs located distal to the target in the treatment field. In general, the variation in maximum dose (D_2%) was larger than the variation in mean dose and other dose metrics, with D_2% of the left optic nerve ((α/β) _x   =  2.1 Gy) in the pituitary adenoma case showing the greatest discrepancies between models: 28-52 Gy(RBE), while D_2% for RBE_1.1 was 30 Gy(RBE). For all patient cases, the estimated mean RBE to the PTV was in the range 1.09-1.29 ((α/β) _x   =  1.5/3.1/10.6 Gy). There were considerable variations between the estimations of RBE and RBE-weighted doses from the different models. These variations were a consequence of fundamental differences in experimental databases, model assumptions and regression techniques. The results from the implementation of RBE models in dose planning studies should be evaluated in light of these deviations.

Normal tissue sparing potential of scanned proton beams with and without respiratory gating for the treatment of internal mammary nodes in breast cancer radiotherapy

Proton therapy has shown potential for reducing doses to normal tissues in breast cancer radiotherapy. However data on the impact of protons when including internal mammary nodes (IMN) in the target for breast radiotherapy is comparatively scarce. This study aimed to evaluate normal tissue doses when including the IMN in regional RT with scanned proton beams, with and without respiratory gating. The study cohort was composed of ten left-sided breast patients CT-scanned during enhanced inspiration gating (EIG) and free-breathing (FB). Proton plans were designed for the target including or excluding the IMN. Targets and organs-at-risk were delineated according to RTOG guidelines. Comparison was performed between dosimetric parameters characterizing target coverage and OAR radiation burden. Statistical significance of differences was tested using a paired, two-tailed Student's t-test. Inclusion of the IMN in the target volume led to a small increase of the cardiopulmonary burden. The largest differences were seen for the ipsilateral lung where the mean dose increased from 6.1 to 6.6 Gy (RBE) (P < 0.0001) in FB plans and from 6.9 to 7.4 Gy (RBE) (P = 0.003) in EIG plans. Target coverage parameters were very little affected by the inclusion of IMN into the treatment target. Radiotherapy with scanned proton beams has the potential of maintaining low cardiovascular burden when including the IMN into the target, irrespective of whether respiratory gating is used or not.

The influence of breathing motion and a variable relative biological effectiveness in proton therapy of left-sided breast cancer

BACKGROUND

Proton breast radiotherapy has been suggested to improve target coverage as well as reduce cardiopulmonary and integral dose compared with photon therapy. This study aims to assess this potential when accounting for breathing motion and a variable relative biological effectiveness (RBE).

METHODS

Photon and robustly optimized proton plans were generated to deliver 50 Gy (RBE) in 25 fractions (RBE = 1.1) to the CTV (whole left breast) for 12 patients. The plan evaluation was performed using the constant RBE and a variable RBE model. Robustness against breathing motion, setup, range and RBE uncertainties was analyzed using CT data obtained at free-breathing, breath-hold-at-inhalation and breath-hold-at-exhalation.

RESULTS

All photon and proton plans (RBE = 1.1) met the clinical goals. The variable RBE model predicted an average RBE of 1.18 for the CTVs (range 1.14-1.21) and even higher RBEs in organs at risk (OARs). However, the dosimetric impact of this latter aspect was minor due to low OAR doses. The normal tissue complication probability (NTCP) for the lungs was low for all patients (<1%), and similar for photons and protons. The proton plans were generally considered robust for all patients. However, in the most extreme scenarios, the lowest dose received by 98% of the CTV dropped from 96 to 99% of the prescribed dose to around 92-94% for both protons and photons. Including RBE uncertainties in the robustness analysis resulted in substantially higher worst-case OAR doses.

CONCLUSIONS

Breathing motion seems to have a minor effect on the plan quality for breast cancer. The variable RBE might impact the potential benefit of protons, but could probably be neglected in most cases where the physical OAR doses are low. However, to be able to identify outlier cases at risk for high OAR doses, the biological evaluation of proton plans taking into account the variable RBE is recommended.

Modeling in vivo relative biological effectiveness in particle therapy for clinically relevant endpoints

BACKGROUND

The relative biological effectiveness (RBE) of particle therapy compared to photon radiotherapy is known to be variable but the exact dependencies are still subject to debate. In vitro data suggested that RBE is to a large extend independent of ion type if parametrized by the beam quality Q. This study analyzed the RBE dependence of pre-clinical data on late toxicity with an emphasis on the beam quality.

MATERIAL AND METHODS

Published pre-clinical RBE dose-response data of the spinal cord following one and two fractions of photon and carbon ion irradiation were compiled. The beam quality for each treatment condition was obtained from Monte Carlo simulations. The α_p and β_p parameters of the linear-quadratic (LQ) model for particle irradiation were determined from the pre-clinical data and was provided as a function of Q. An introduced model proposed α_p to increase linearly with Q and β_p to remain constant. RBE values predicted by the model were compared to the published data.

RESULTS

The α_p parameter was highly correlated with Q (R² = 0.96) with a linear slope of 0.019 Gy^-1. No significant variation of β_p with Q was found. RBE and Q were also highly correlated (R² = 0.98) for one and two fractions. The (extrapolated) RBE at Q = 0 (theoretical photon limit) for one and two fractions was 1.22 and significantly larger than 1 (p = .004). The model reproduced the dependence of RBE on fractionation well.

CONCLUSIONS

Fraction dose and beam quality Q were sufficient to describe the RBE variability for a late toxicity model within a carbon ion treatment field. Assuming the independence of the identified RBE parameters on the ion type might suggest the translation of variable (pre-) clinical RBE data from carbon ion to proton therapy.

Impact of respiratory motion on variable relative biological effectiveness in 4D-dose distributions of proton therapy

BACKGROUND

Organ motion during radiation therapy with scanned protons leads to deviations between the planned and the delivered physical dose. Using a constant relative biological effectiveness (RBE) of 1.1 linearly maps these deviations into RBE-weighted dose. However, a constant value cannot account for potential nonlinear variations in RBE suggested by variable RBE models. Here, we study the impact of motion on recalculations of RBE-weighted dose distributions using a phenomenological variable RBE model.

MATERIAL AND METHODS

4D-dose calculation including variable RBE was implemented in the open source treatment planning toolkit matRad. Four scenarios were compared for one field and two field proton treatments for a liver cancer patient assuming (α∕β)_x = 2 Gy and (α∕β)_x = 10 Gy: (A) the optimized static dose distribution with constant RBE, (B) a static recalculation with variable RBE, (C) a 4D-dose recalculation with constant RBE and (D) a 4D-dose recalculation with variable RBE. For (B) and (D), the variable RBE was calculated by the model proposed by McNamara. For (C), the physical dose was accumulated with direct dose mapping; for (D), dose-weighted radio-sensitivity parameters of the linear quadratic model were accumulated to model synergistic irradiation effects on RBE.

RESULTS

Dose recalculation with variable RBE led to an elevated biological dose at the end of the proton field, while 4D-dose recalculation exhibited random deviations everywhere in the radiation field depending on the interplay of beam delivery and organ motion. For a single beam treatment assuming (α∕β)_x = 2 Gy, D_95% was 1.98 Gy (RBE) (A), 2.15 Gy (RBE) (B), 1.81 Gy (RBE) (C) and 1.98 Gy (RBE) (D). The homogeneity index was 1.04 (A), 1.08 (B), 1.23 (C) and 1.25 (D).

CONCLUSION

For the studied liver case, intrafractional motion did not reduce the modulation of the RBE-weighted dose postulated by variable RBE models for proton treatments.