Variable Relative Biological Effectiveness Models Research Articles

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, D95% 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.

Inclusion of a variable RBE into proton and photon plan comparison for various fractionation schedules in prostate radiation therapy.

A constant relative biological effectiveness (RBE) of 1.1 is currently used in proton radiation therapy to account for the increased biological effectiveness compared to photon therapy. However, there is increasing evidence that proton RBE vary with the linear energy transfer (LET), the dose per fraction, and the type of the tissue. Therefore, this study aims to evaluate the impact of disregarding variations in RBE when comparing proton and photon dose plans for prostate treatments for various fractionation schedules using published RBE models and several α/β assumptions. Photon and proton dose plans were created for three generic prostate cancer cases. Three BED3Gy equivalent schedules were studied, 78, 57.2, and 42.8Gy in 39, 15, and 7 fractions, respectively. The proton plans were optimized assuming a constant RBE of 1.1. By using the Monte Carlo calculated dose-averaged LET (LETd ) distribution and assuming α/β values on voxel level, three variable RBE models were applied to the proton dose plans. The impact of the variable RBE was studied in the plan comparison, which was based on the dose distribution, DVHs, and normal tissue complication probabilities (NTCP) for the rectum. Subsequently, the physical proton dose was reoptimized for each proton plan based on the LETd distribution, to achieve a homogeneous RBE-weighted target dose when applying a specific RBE model and still fulfill the clinical goals for the rectum and bladder. All the photon and proton plans assuming RBE=1.1 met the clinical goals with similar target coverage. The proton plans fulfilled the robustness criteria in terms of range and setup uncertainty. Applying the variable RBE models generally resulted in higher target doses and rectum NTCP compared to the photon plans. The increase was most pronounced for the fractionation dose of 2Gy(RBE), whereas it was of less magnitude and more dependent on model and α/β assumption for the hypofractionated schedules. The reoptimized proton plans proved to be robust and showed similar target coverage and doses to the organs at risk as the proton plans optimized with a constant RBE. Model predicted RBE values may differ substantially from 1.1. This is most pronounced for fractionation doses of around 2Gy(RBE) with higher doses to the target and the OARs, whereas the effect seems to be of less importance for the hypofractionated schedules. This could result in misleading conclusions when comparing proton plans to photon plans. By accounting for a variable RBE in the optimization process, robust and clinically acceptable dose plans, with the potential of lowering rectal NTCP, may be generated by reoptimizing the physical dose. However, the direction and magnitude of the changes in the physical proton dose to the prostate are dependent on RBE model and α/β assumptions and should therefore be used conservatively.

Incorporation of relative biological effectiveness uncertainties into proton plan robustness evaluation

Background: The constant relative biological effectiveness (RBE) of 1.1 is typically assumed in proton therapy. This study presents a method of incorporating the variable RBE and its uncertainties into the proton plan robustness evaluation.Material and methods: The robustness evaluation was split into two parts. In part one, the worst-case physical dose was estimated using setup and range errors, including the fractionation dependence. The results were fed into part two, in which the worst-case RBE-weighted doses were estimated using a Monte Carlo method for sampling the input parameters of the chosen RBE model. The method was applied to three prostate, breast and head and neck (H&N) plans for several fractionation schedules using two RBE models. The uncertainties in the model parameters, linear energy transfer and α/β were included. The resulting DVH error bands were compared with the use of a constant RBE without uncertainties.Results: All plans were evaluated as robust using the constant RBE. Applying the proposed methodology using the variable RBE models broadens the DVH error bands for all structures studied. The uncertainty in α/β was the dominant factor. The variable RBE also shifted the nominal DVHs towards higher doses for most OARs, whereas the direction of this shift for the clinical target volumes (CTVs) depended on the treatment site, RBE model and fractionation schedule. The average RBE within the CTV, using one of the RBE models and 2 Gy(RBE) per fraction, varied between 1.11–1.26, 1.06–1.16 and 1.14–1.25 for the breast, H&N and prostate patients, respectively.Conclusions: A method of incorporating RBE uncertainties into the robustness evaluation has been proposed. By disregarding the variable RBE and its uncertainties, the variation in the RBE-weighted CTV and OAR doses may be underestimated. This could be an essential factor to take into account, especially in normal tissue complication probabilities based comparisons between proton and photon plans.

Hydrogel rectum-prostate spacers mitigate the uncertainties in proton relative biological effectiveness associated with anterior-oblique beams

Aim: Anterior-oblique (AO) proton beams can form an attractive option for prostate patients receiving external beam radiotherapy (EBRT) as they avoid the femoral heads. For a cohort with hydrogel prostate-rectum spacers, we asked whether it was possible to generate AO proton plans robust to end-of-range elevations in linear energy transfer (LET) and modeled relative biological effectiveness (RBE). Additionally we considered how rectal spacers influenced planned dose distributions for AO and standard bilateral (SB) proton beams versus intensity-modulated radiotherapy (IMRT).Material and methods: We studied three treatment strategies for 10 patients with rectal spacers: (A) AO proton beams, (B) SB proton beams and (C) IMRT. For strategy (A) dose and LET distributions were simulated (using the TOPAS Monte Carlo platform) and the McNamara model was used to calculate proton RBE as a function of LET, dose per fraction, and photon α/β. All calculations were performed on pretreatment scans: inter- and intra-fractional changes in anatomy/set-up were not considered.Results: For 9/10 patients, rectal spacers enabled generation of AO proton plans robust to modeled RBE elevations: rectal dose constraints were fulfilled even when the variable RBE model was applied with a conservative α/β = 2 Gy. Amongst a subset of patients the proton rectal doses for the planning target volume plans were remarkably low: for 2/10 SB plans and 4/10 AO plans, ≤10% of the rectum received ≥20 Gy. AO proton plans delivered integral doses a factor of approximately three lower than IMRT and spared the femoral heads almost entirely.Conclusion: Typically, rectal spacers enabled the generation of anterior beam proton plans that appeared robust to modeled variation in RBE. However, further analysis of day-to-day robustness would be required prior to a clinical implementation of AO proton beams. Such beams offer almost complete femoral head sparing, but their broader value relative to IMRT and SB protons remains unclear.

SU‐F‐T‐132: Variable RBE Models Predict Possible Underestimation of Vaginal Dose for Anal Cancer Patients Treated Using Single‐Field Proton Treatments

Purpose:Anal cancer patients treated using a posterior proton beam may be at risk of vaginal wall injury due to the increased linear energy transfer (LET) and relative biological effectiveness (RBE) at the beam distal edge. We investigate the vaginal dose received.Methods:Five patients treated for anal cancer with proton pencil beam scanning were considered, all treated to a prescription dose of 54 Gy(RBE) over 28–30 fractions. Dose and LET distributions were calculated using the Monte Carlo simulation toolkit TOPAS. In addition to the standard assumption of a fixed RBE of 1.1, variable RBE was considered via the application of published models. Dose volume histograms (DVHs) were extracted for the planning treatment volume (PTV) and vagina, the latter being used to calculate the vaginal normal tissue complication probability (NTCP).Results:Compared to the assumption of a fixed RBE of 1.1, the variable RBE model predicts a dose increase of approximately 3.3 ± 1.7 Gy at the end of beam range. NTCP parameters for the vagina are incomplete in the current literature, however, inferring value ranges from the existing data we use D50 = 50 Gy and LKB model parameters a=1–2 and m=0.2–0.4. We estimate the NTCP for the vagina to be 37–48% and 42–47% for the fixed and variable RBE cases, respectively. Additionally, a difference in the dose distribution was observed between the analytical calculation and Monte Carlo methods. We find that the target dose is overestimated on average by approximately 1–2%.Conclusion:For patients treated with posterior beams, the vaginal wall may coincide with the distal end of the proton beam and may receive a substantial increase in dose if variable RBE models are applied compared to using the current clinical standard of RBE equal to 1.1. This could potentially lead to underestimating toxicities when treating with protons.

Investigating the Implications of a Variable RBE on Proton Dose Fractionation Across a Clinical Pencil Beam Scanned Spread-Out Bragg Peak

PurposeTo investigate the clinical implications of a variable relative biological effectiveness (RBE) on proton dose fractionation. Using acute exposures, the current clinical adoption of a generic, constant cell killing RBE has been shown to underestimate the effect of the sharp increase in linear energy transfer (LET) in the distal regions of the spread-out Bragg peak (SOBP). However, experimental data for the impact of dose fractionation in such scenarios are still limited.Methods and MaterialsHuman fibroblasts (AG01522) at 4 key depth positions on a clinical SOBP of maximum energy 219.65 MeV were subjected to various fractionation regimens with an interfraction period of 24 hours at Proton Therapy Center in Prague, Czech Republic. Cell killing RBE variations were measured using standard clonogenic assays and were further validated using Monte Carlo simulations and parameterized using a linear quadratic formalism.ResultsSignificant variations in the cell killing RBE for fractionated exposures along the proton dose profile were observed. RBE increased sharply toward the distal position, corresponding to a reduction in cell sparing effectiveness of fractionated proton exposures at higher LET. The effect was more pronounced at smaller doses per fraction. Experimental survival fractions were adequately predicted using a linear quadratic formalism assuming full repair between fractions. Data were also used to validate a parameterized variable RBE model based on linear α parameter response with LET that showed considerable deviations from clinically predicted isoeffective fractionation regimens.ConclusionsThe RBE-weighted absorbed dose calculated using the clinically adopted generic RBE of 1.1 significantly underestimates the biological effective dose from variable RBE, particularly in fractionation regimens with low doses per fraction. Coupled with an increase in effective range in fractionated exposures, our study provides an RBE dataset that can be used by the modeling community for the optimization of fractionated proton therapy.

Can We Advance Proton Therapy for Prostate? Considering Alternative Beam Angles and Relative Biological Effectiveness Variations When Comparing Against Intensity Modulated Radiation Therapy

For prostate treatments, robust evidence regarding the superiority of either intensity modulated radiation therapy (IMRT) or proton therapy is currently lacking. In this study we investigated the circumstances under which proton therapy should be expected to outperform IMRT, particularly the proton beam orientations and relative biological effectiveness (RBE) assumptions. For 8 patients, 4 treatment planning strategies were considered: (A) IMRT; (B) passively scattered standard bilateral (SB) proton beams; (C) passively scattered anterior oblique (AO) proton beams, and (D) AO intensity modulated proton therapy (IMPT). For modalities (B)-(D) the dose and linear energy transfer (LET) distributions were simulated using the TOPAS Monte Carlo platform and RBE was calculated according to 3 different models. Assuming a fixed RBE of 1.1, our implementation of IMRT outperformed SB proton therapy across most normal tissue metrics. For the scattered AO proton plans, application of the variable RBE models resulted in substantial hotspots in rectal RBE weighted dose. For AO IMPT, it was typically not possible to find a plan that simultaneously met the tumor and rectal constraints for both fixed and variable RBE models. If either a fixed RBE of 1.1 or a variable RBE model could be validated in vivo, then it would always be possible to use AO IMPT to dose-boost the prostate and improve normal tissue sparing relative to IMRT. For a cohort without rectum spacer gels, this study (1) underlines the importance of resolving the question of proton RBE within the framework of an IMRT versus proton debate for the prostate and (2) highlights that without further LET/RBE model validation, great care must be taken if AO proton fields are to be considered for prostate treatments.

TU‐G‐108‐08: Variable RBE and Incidence of Radiation Pneumonitis in Lung Patients Treated with Proton Therapy

Purpose: To determine the correlation between the Relative Biological Effectiveness (RBE)‐weighted dose and radiation pneumonitis (RP) incidence in cancer patients treated with proton therapy. Methods: The Monte Carlo proton dose calculation system MC2 based on MCNPX was used to recalculate treatment plans taken from the clinical treatment planning system (TPS) and compute the dose‐averaged LET in each voxel of the CT based patient model. The linear scaling model (LSM) for proton RBE was used with biological coefficients for RP to compute the variable RBE‐weighted dose distributions. These were compared with the constant RBE‐weighted doses computed by the TPS and currently used in our clinical practice. A restaging FDG PET/CT was registered to the treatment planning CT and the standard uptake values (SUV) were used as a measure of radiation dose response. Results: The variable RBE model results in higher biological dose at the distal ends of proton beams and the corresponding lung volumes receiving elevated doses can be significant if the beam is terminating inside the low density lung tissue. Preliminary results for the first two patients in the study show that the regions of elevated variable RBE‐weighted doses inside the lung are well correlated to the high SUV values in the restaging PET. Both patients were diagnosed with grade 3 RP after completing the treatment. Conclusion: The preliminary results indicate that variable RBE‐weighted doses may provide additional insight into toxicity risk for patients treated with proton radiotherapy. The complete study will include the analysis of many more patients diagnosed with grade 3 RP or higher, treated with protons in our institution. NCI grant P01CA021239

TH‐F‐105‐05: Comparison of Results for RBE‐Weighted Dose From Two RBE Models for Proton Therapy Treatment Plans

Purpose: To evaluate the differences between relative biological effectiveness (RBE)‐weighted doses calculated with either the linear quadratic (LQ) or repair‐misrepair‐fixation (RMF) RBE model for intensity modulated proton therapy (IMPT) treatment plans. Methods: The commercial treatment planning system (TPS) used at MD Anderson Cancer Center (MDACC) does not provide the LET information necessary in order to utilize variable RBE models to calculate RBE‐weighted dose for treatment plans. To obtain this information the Monte Carlo code MCNPX was used to recalculate IMPT treatment plans for patients with central nervous system (CNS) disease taken from the TPS and record the track‐averaged LET in each voxel of the dose distribution. The dose‐averaged LET was approximated from the track‐averaged LET by use of an appropriate scaling factor. The Monte Carlo Damage Simulation (MCDS) software was used to parameterize the number of double‐strand breaks generated in cells by protons according to their stopping power. This information, along with relevant biological coefficients, was then used to generate RBE‐weighted dose distributions according to the LQ and RMF RBE models. Plan evaluation metrics, such as a conformality index and heterogeneity index, were used for plan comparison. Results: The LQ RBE model produces higher RBE‐weighted doses, particularly in the target volume, compared to the RMF model. Doses predicted by the RMF model in nearby organs at risk can at times be several Gray lower than those predicted by the LQ model. Both models predict equivalently heterogeneous target dose distributions, while the RMF model predicts more conformal target dose. Conclusion: Calculation of proton treatment plan dose incorporating either the LQ or RMF models of variable RBE produces observable differences in the resultant dose distributions. Further investigation, including utilization of different biological coefficients, is required to determine the implications for all of the associated normal tissues. UTMDACC Sister Institution Network Fund Grant (SINF MDACC‐DKFZ)

Is Constant RBE Accurate Enough for Determination of Biological Effects in Proton Therapy?

The relative biological effectiveness (RBE) of protons currently used in clinical practice is assigned a constant value of 1.1, despite the evidence that the actual RBE of protons varies as a function of proton energy, linear energy transfer (LET), dose per treatment fraction, tissue type, and clinical endpoint. The purpose of this study is to compare the performance of the traditional, constant RBE model, and two variable RBE models in explaining the radiation induced brain necrosis indicated on follow-up imaging studies for a patient treated with postoperative proton radiation therapy for malignant meningioma. In this study, treatment plan information is extracted from a clinical treatment planning system (TPS) and used to recalculate physical proton dose and linear energy transfer (LET) distributions using Monte Carlo simulations. One constant and two variable RBE models which account for tissue specific parameters, LET, biological endpoint, and dose per treatment fraction are applied on a voxel-by-voxel basis to compute three biologically effective dose distributions. These dose distributions are subsequently correlated to follow-up imaging studies which have indicated the presence of radiation induced necrosis in the treated region of the patient being analyzed. Corresponding areas of toxicity and dose/RBE computed with three different models are compared to determine which model performs the best in explaining the radiation induced toxicity. Areas of increased biologically effective dose computed using variable RBE models compared to the original dose distribution calculated by the clinical TPS using a constant RBE model are found to correspond to areas of radiation induced brain necrosis. Variable RBE doses were up to 8% higher in the region of toxicity. Variable RBE models perform better in explaining the radiation induced brain necrosis.

Application of Constant vs. Variable Relative Biological Effectiveness in Treatment Planning of Intensity-Modulated Proton Therapy

To investigate in a simulation study whether using a variable relative biological effectiveness (RBE) in calculation and optimization of intensity-modulated proton therapy (IMPT) instead of using an RBE of 1.1 would result in significant changes in the RBE-weighted dose (RWD) distributions. For 4 patients with head-and-neck tumors, three IMPT plans were prepared respectively. The first plan was physically optimized (IMPT-PO plan), and the RWD was calculated with a constant RBE of 1.1. Then the plan's RWD was recalculated (IMPT-R plan) using a variable RBE model taking into account the linear energy transfer (LET) and tissue-specific radiobiological parameters. The third IMPT plan was optimized using a biological optimization routine (IMPT-BO plan). Comparing the IMPT-PO and IMPT-R plans, we observed that the RWD in radioresistant tissues was more sensitive to the LET than in radiosensitive tissues. The IMPT-R plans were in general more inhomogeneous than the IMPT-PO plans. The differences of RWD distributions for all volumes between IMPT-PO and IMPT-BO plans complied with predefined dose-volume constraints. The average LET was significantly lower in IMPT-BO plans than in IMPT-R plans. In radioresistant normal tissues caution has to be used regarding the LET distribution because these are most sensitive to changes in the LET. Biological optimization of IMPT plans based on the organ-specific biological parameters and LET distributions is feasible.