Proton RBE models: commonalities and differences

Benchmarking proton RBE models

Objective.To biologically optimise proton therapy, models which can accurately predict variations in proton relative biological effectiveness (RBE) are essential. Current phenomenological models show large disagreements in RBE predictions, due to different model assumptions and differences in the data to which they were fit. In this work, thirteen RBE models were benchmarked against a comprehensive proton RBE dataset to evaluate predictions when all models are fit using the same data and fitting techniques, and to assess the statistical robustness of the models.Approach.Model performance was initially evaluated by fitting to the full dataset, and then a cross-validation approach was applied to assess model generalisability and robustness. The impact of weighting the fit and the choice of biological endpoint (either single or multiple survival levels) was also evaluated.Main results.Fitting the models to a common dataset reduced differences between their predictions, however significant disagreements remained due to different underlying assumptions. All models performed poorly under cross-validation in the weighted fits, suggesting that some uncertainties on the experimental data were significantly underestimated, resulting in over-fitting and poor performance on unseen data. The simplest model, which depends linearly on the LET but has no tissue or dose dependence, performed best for a single survival level. However, when fitting to multiple survival levels simultaneously, more complex models with tissue dependence performed better. All models had significant residual uncertainty in their predictions compared to experimental data.Significance.This analysis highlights that poor quality of error estimation on the dose response parameters introduces substantial uncertainty in model fitting. The significant residual error present in all approaches illustrates the challenges inherent in fitting to large, heterogeneous datasets and the importance of robust statistical validation of RBE models.

Characterizing Proton-Induced Biological Effects in a Mouse Spinal Cord Model: A Comparison of Bragg Peak and Entrance Beam Response in Single and Fractionated Exposures

PURPOSE

Proton relative biological effectiveness (RBE) is a dynamic variable influenced by factors like linear energy transfer (LET), dose, tissue type, and biological endpoint. The standard fixed proton RBE of 1.1, currently used in clinical planning, may not accurately represent the true biological effects of proton therapy (PT) in all cases. This uncertainty can contribute to radiation-induced normal tissue toxicity in patients. In late-responding tissues such as the spinal cord, toxicity can cause devastating complications. This study investigated spinal cord tolerance in mice subjected to proton irradiation and characterized the influence of fractionation on proton- induced myelopathy at entrance (ENT) and Bragg peak (BP) positions.

METHODS AND MATERIALS

Cervical spinal cords of 8-week-old C57BL/6J female mice were irradiated with single- or multi-fractions (18x) using lateral opposed radiation fields at 1 of 2 positions along the Bragg curve: ENT (dose-mean LET = 1.2 keV/μm) and BP (LET = 6.9 keV/μm). Mice were monitored over 1 year for changes in weight, mobility, and general health, with radiation-induced myelopathy as the primary biological endpoint. Calculations of the RBE of the ENT and BP curve (RBEENT/BP) were performed.

RESULTS

Single-fraction RBEENT/BP for 50% effect probability (tolerance dose (TD50), grade II paresis, determined using log-logistic model fitting) was 1.10 ± 0.06 (95% CI) and for multifraction treatments it was 1.19 ± 0.05 (95% CI). Higher incidence and faster onset of paralysis were seen in mice treated at the BP compared with ENT.

CONCLUSIONS

The findings challenge the universally fixed RBE value in PT, indicating up to a 25% mouse spinal cord RBEENT/BP variation for multifraction treatments. These results highlight the importance of considering fractionation in determining RBE for PT. Robust characterization of proton-induced toxicity, aided by in vivo models, is paramount for refining clinical decision-making and mitigating potential patient side effects.

Variable RBE in proton radiotherapy: a comparative study with the predictive Mayo Clinic Florida microdosimetric kinetic model and phenomenological models of cell survival

Objectives. (1) To examine to what extent the cell- and exposure- specific information neglected in the phenomenological proton relative biological effectiveness (RBE) models could influence the computed RBE in proton therapy. (2) To explore similarities and differences in the formalism and the results between the linear energy transfer (LET)-based phenomenological proton RBE models and the microdosimetry-based Mayo Clinic Florida microdosimetric kinetic model (MCF MKM). (3) To investigate how the relationship between the RBE and the dose-mean proton LET is affected by the proton energy spectrum and the secondary fragments.Approach. We systematically compared six selected phenomenological proton RBE models with the MCF MKM in track-segment simulations, monoenergetic proton beams in a water phantom, and two spread-out Bragg peaks. A representative comparison within vitrodata for human glioblastoma cells (U87 cell line) is also included.Main results. Marked differences were observed between the results of the phenomenological proton RBE models, as reported in previous studies. The dispersion of these models' results was found to be comparable to the spread in the MCF MKM results obtained by varying the cell-specific parameters neglected in the phenomenological models. Furthermore, while single cell-specific correlation between RBE and the dose-mean proton LET seems reasonable above 2 keVμm-1, caution is necessary at lower LET values due to the relevant contribution of secondary fragments. The comparison within vitrodata demonstrates comparable agreement between the MCF MKM predictions and the results of the phenomenological models.Significance. The study highlights the importance of considering cell-specific characteristics and detailed radiation quality information for accurate RBE calculations in proton therapy. Furthermore, these results provide confidence in the use of the MCF MKM for clonogenic survival RBE calculations in proton therapy, offering a more mechanistic approach compared to phenomenological models.

Monte Carlo simulations of cell survival in proton SOBP

Objective. The objective of this study is to develop a multi-scale modeling approach that accurately predicts radiation-induced DNA damage and survival fraction in specific cell lines.Approach. A Monte Carlo based simulation framework was employed to make the predictions. The FLUKA Monte Carlo code was utilized to estimate absorbed doses and fluence energy spectra, which were then used in the Monte Carlo Damage Simulation code to compute DNA damage yields in Chinese hamster V79 cell lines. The outputs were converted into cell survival fractions using a previously published theoretical model. To reduce the uncertainties of the predictions, new values for the parameters of the theoretical model were computed, expanding the database of experimental points considered in the previous estimation. Simulated results were validated against experimental data, confirming the applicability of the framework for proton beams up to 230 MeV. Additionally, the impact of secondary particles on cell survival was estimated.Main results. The simulated survival fraction versus depth in a glycerol phantom is reported for eighteen different configurations. Two proton spread out Bragg peaks at several doses were simulated and compared with experimental data. In all cases, the simulations follow the experimental trends, demonstrating the accuracy of the predictions up to 230 MeV.Significance. This study holds significant importance as it contributes to the advancement of models for predicting biological responses to radiation, ultimately contributing to more effective cancer treatment in proton therapy.

Proposing a Clinical Model for RBE Based on Proton Track-End Counts

PURPOSE

In proton therapy, the clinical application of linear energy transfer (LET) optimization remains contentious, in part because of challenges associated with the definition and calculation of LET and its exact relationship with relative biological effectiveness (RBE) because of large variation in experimental in vitro data. This has raised interest in other metrics with favorable properties for biological optimization, such as the number of proton track ends in a voxel. In this work, we propose a novel model for clinical calculations of RBE, based on proton track end counts.

METHODS AND MATERIALS

We developed an effective dose concept to translate between the total proton track-end count per unit mass in a voxel and a proton RBE value. Dose, track end, and dose-averaged LET (LETd) distributions were simulated using Monte Carlo models for a series of water phantoms, in vitro radiobiological studies, and patient treatment plans. We evaluated the correlation between track ends and regions of elevated biological effectiveness in comparison to LETd-based models of RBE.

RESULTS

Track ends were found to correlate with biological effects in in vitro experiments with an accuracy comparable to LETd. In patient simulations, our track end model identified the same biological hotspots as predicted by LETd-based radiobiological models of proton RBE.

CONCLUSIONS

These results suggest that, for clinical optimization and evaluation, an RBE model based on proton track end counts may match LETd-based models in terms of information provided while also offering superior statistical properties.

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.

Linear Energy Transfer and Relative Biological Effectiveness Investigation of Various Structures for a Cohort of Proton Patients With Brain Tumors

Purpose

The current knowledge on biological effects associated with proton therapy is limited. Therefore, we investigated the distributions of dose, dose-averaged linear energy transfer (LET_d), and the product between dose and LET_d (DLET_d) for a patient cohort treated with proton therapy. Different treatment planning system features and visualization tools were explored.

Methods and Materials

For a cohort of 24 patients with brain tumors, the LET_d, DLET_d, and dose was calculated for a fixed relative biological effectiveness value and 2 variable models: plan-based and phenomenological. Dose threshold levels of 0, 5, and 20 Gy were imposed for LET_d visualization. The relationship between physical dose and LET_d and the frequency of LET_d hotspots were investigated.

Results

The phenomenological relative biological effectiveness model presented consistently higher dose values. For lower dose thresholds, the LET_d distribution was steered toward higher values related to low treatment doses. Differences up to 26.0% were found according to the threshold. Maximum LET_d values were identified in the brain, periventricular space, and ventricles. An inverse relationship between LET_d and dose was observed. Frequency information to the domain of dose and LET_d allowed for the identification of clusters, which steer the mean LET_d values, and the identification of higher, but sparse, LET_d values.

Conclusions

Identifying, quantifying, and recording LET distributions in a standardized fashion is necessary, because concern exists over a link between toxicity and LET hotspots. Visualizing DLET_d or dose × LET_d during treatment planning could allow for clinicians to make informed decisions.

Comparing biological effectiveness guided plan optimization strategies for cranial proton therapy: potential and challenges

BACKGROUND

To introduce and compare multiple biological effectiveness guided (BG) proton plan optimization strategies minimizing variable relative biological effectiveness (RBE) induced dose burden in organs at risk (OAR) while maintaining plan quality with a constant RBE.

METHODS

Dose-optimized (DOSEopt) proton pencil beam scanning reference treatment plans were generated for ten cranial patients with prescription doses ≥ 54 Gy(RBE) and ≥ 1 OAR close to the clinical target volume (CTV). For each patient, four additional BG plans were created. BG objectives minimized either proton track-ends, dose-averaged linear energy transfer (LET_d), energy depositions from high-LET protons or variable RBE-weighted dose (D_RBE) in adjacent serially structured OARs. Plan quality (RBE = 1.1) was assessed by CTV dose coverage and robustness (2 mm setup, 3.5% density), dose homogeneity and conformity in the planning target volumes and adherence to OAR tolerance doses. LET_d, D_RBE (Wedenberg model, α/β_CTV = 10 Gy, α/β_OAR = 2 Gy) and resulting normal tissue complication probabilities (NTCPs) for blindness and brainstem necrosis were derived. Differences between DOSEopt and BG optimized plans were assessed and statistically tested (Wilcoxon signed rank, α = 0.05).

RESULTS

All plans were clinically acceptable. DOSEopt and BG optimized plans were comparable in target volume coverage, homogeneity and conformity. For recalculated D_RBE in all patients, all BG plans significantly reduced near-maximum D_RBE to critical OARs with differences up to 8.2 Gy(RBE) (p < 0.05). Direct D_RBE optimization primarily reduced absorbed dose in OARs (average ΔD_mean = 2.0 Gy; average ΔLET_d,mean = 0.1 keV/µm), while the other strategies reduced LET_d (average ΔD_mean < 0.3 Gy; average ΔLET_d,mean = 0.5 keV/µm). LET-optimizing strategies were more robust against range and setup uncertaintes for high-dose CTVs than D_RBE optimization. All BG strategies reduced NTCP for brainstem necrosis and blindness on average by 47% with average and maximum reductions of 5.4 and 18.4 percentage points, respectively.

CONCLUSIONS

All BG strategies reduced variable RBE-induced NTCPs to OARs. Reducing LET_d in high-dose voxels may be favourable due to its adherence to current dose reporting and maintenance of clinical plan quality and the availability of reported LET_d and dose levels from clinical toxicity reports after cranial proton therapy. These optimization strategies beyond dose may be a first step towards safely translating variable RBE optimization in the clinics.

An empirical model of proton RBE based on the linear correlation between x-ray and proton radiosensitivity

BACKGROUND

Proton relative biological effectiveness (RBE) is known to depend on physical factors of the proton beam, such as its linear energy transfer (LET), as well as on cell-line specific biological factors, such as their ability to repair DNA damage. However, in a clinical setting, proton RBE is still considered to have a fixed value of 1.1 despite the existence of several empirical models that can predict proton RBE based on how a cell's survival curve (linear-quadratic model [LQM]) parameters α and β vary with the LET of the proton beam. Part of the hesitation to incorporate variable RBE models in the clinic is due to the great noise in the biological datasets on which these models are trained, often making it unclear which model, if any, provides sufficiently accurate RBE predictions to warrant a departure from RBE = 1.1.

PURPOSE

Here, we introduce a novel model of proton RBE based on how a cell's intrinsic radiosensitivity varies with LET, rather than its LQM parameters.

METHODS AND MATERIALS

We performed clonogenic cell survival assays for eight cell lines exposed to 6 MV x-rays and 1.2, 2.6, or 9.9 keV/µm protons, and combined our measurements with published survival data (n = 397 total cell line/LET combinations). We characterized how radiosensitivity metrics of the form DSF% , (the dose required to achieve survival fraction [SF], e.g., D10% ) varied with proton LET, and calculated the Bayesian information criteria associated with different LET-dependent functions to determine which functions best described the underlying trends. This allowed us to construct a six-parameter model that predicts cells' proton survival curves based on the LET dependence of their radiosensitivity, rather than the LET dependence of the LQM parameters themselves. We compared the accuracy of our model to previously established empirical proton RBE models, and implemented our model within a clinical treatment plan evaluation workflow to demonstrate its feasibility in a clinical setting.

RESULTS

Our analyses of the trends in the data show that DSF% is linearly correlated between x-rays and protons, regardless of the choice of the survival level (e.g., D10% , D37% , or D50% are similarly correlated), and that the slope and intercept of these correlations vary with proton LET. The model we constructed based on these trends predicts proton RBE within 15%-30% at the 68.3% confidence level and offers a more accurate general description of the experimental data than previously published empirical models. In the context of a clinical treatment plan, our model generally predicted higher RBE-weighted doses than the other empirical models, with RBE-weighted doses in the distal portion of the field being up to 50.7% higher than the planned RBE-weighted doses (RBE = 1.1) to the tumor.

CONCLUSIONS

We established a new empirical proton RBE model that is more accurate than previous empirical models, and that predicts much higher RBE values in the distal edge of clinical proton beams.

An ion-independent phenomenological relative biological effectiveness (RBE) model for proton therapy

BACKGROUND

A relative biological effectiveness (RBE) of 1.1 is used for proton therapy though clinical evidence of varying RBE was raised. Clinical studies on RBE variability have been conducted for decades for carbon radiation, which could advance the understanding of the clinical proton RBE given an ion-independent RBE model. In this work, such a model, linear and simple, using the beam quantity Q = Z²/E (Z = ion charge, E = kinetic energy per nucleon) was tested and compared to the commonly used, proton-specific and linear energy transfer (LET) based Wedenberg RBE model.

MATERIAL AND METHODS

The Wedenberg and Q models, both predicting RBE_max and RBE_min (i.e., RBE at vanishing and very high dose, respectively), are compared in terms of ion-dependence and prediction power. An experimental in-vitro data ensemble covering 115 publications for various ions was used as dataset.

RESULTS

The model parameter of the Q model was observed to be similar for different ions (in contrast to LET). The Q model was trained without any prior knowledge of proton data. For proton RBE, the differences between experimental data and corresponding predictions of the Wedenberg or the Q model were highly comparable.

CONCLUSIONS

A simple linear RBE model using Q instead of LET was proposed and tested to be able to predict proton RBE using model parameter trained based on only RBE data of other particles in a clinical proton energy range for a large in-vitro dataset. Adding (pre)clinical knowledge from carbon ion therapy may, therefore, reduce the dominating biological uncertainty in proton RBE modelling. This would translate in reduced RBE related uncertainty in proton therapy treatment planning.

Impact of a spatially dependent dose delivery time structure on the biological effectiveness of scanning proton therapy

PURPOSE

In the scanning beam delivery of protons, different portions of the target are irradiated with different linear energy transfer protons with various time intervals and irradiation times. This research aimed to evaluate the spatially dependent biological effectiveness of protracted irradiation in scanning proton therapy.

METHODS

One and two parallel opposed fields plans were created in water phantom with the prescribed dose of 2 Gy. Three scenarios (instantaneous, continuous, and layered scans) were used with the corresponding beam delivery models. The biological dose (physical dose × relative biological effectiveness) was calculated using the linear quadratic model and the theory of dual radiation action to quantitatively evaluate the dose delivery time effect. In addition, simulations using clinical plans (postoperative seminoma and prostate tumor cases) were conducted to assess the impact of the effects on the dose volume histogram parameters and homogeneity coefficient (HC) in targets.

RESULTS

In a single-field plan of water phantom, when the treatment time was 19 min, the layered-scan scenario showed a decrease of <0.2% (almost 3.3%) in the biological dose from the plan on the distal (proximal) side because of the high (low) dose rate. This is in contrast to the continuous scenario, where the biological dose was almost uniformly decreased over the target by approximately 3.3%. The simulation with clinical geometry showed that the decrease rates in D_99% were 0.9% and 1.5% for every 10 min of treatment time prolongation for postoperative seminoma and prostate tumor cases, respectively, whereas the increase rates in HC were 0.7% and 0.2%.

CONCLUSIONS

In protracted irradiation in scanning proton therapy, the spatially dependent dose delivery time structure in scanning beam delivery can be an important factor for accurate evaluation of biological effectiveness.

The Organ Sparing Potential of Different Biological Optimization Strategies in Proton Therapy

Purpose

Variable relative biological effectiveness (RBE) models allow for differences in linear energy transfer (LET), physical dose, and tissue type to be accounted for when quantifying and optimizing the biological damage of protons. These models are complex and fraught with uncertainties, and therefore, simpler RBE optimization strategies have also been suggested. Our aim was to compare several biological optimization strategies for proton therapy by evaluating their performance in different clinical cases.

Methods and Materials

Two different optimization strategies were compared: full variable RBE optimization and differential RBE optimization, which involve applying fixed RBE for the planning target volume (PTV) and variable RBE in organs at risk (OARs). The optimization strategies were coupled to 2 variable RBE models and 1 LET-weighted dose model, with performance demonstrated on 3 different clinical cases: brain, head and neck, and prostate tumors.

Results

In cases with low (α/β)x in the tumor, the full RBE optimization strategies had a large effect, with up to 10% reduction in RBE-weighted dose to the PTV and OARs compared with the reference plan, whereas smaller variations (<5%) were obtained with differential optimization. For tumors with high (α/β)x, the differential RBE optimization strategy showed a greater reduction in RBE-weighted dose to the OARs compared with the reference plan and the full RBE optimization strategy.

Conclusions

Differences between the optimization strategies varied across the studied cases, influenced by both biological and physical parameters. Whereas full RBE optimization showed greater OAR sparing, awareness of underdosage to the target must be carefully considered.

Predict Treatment Response by Magnetic Resonance Diffusion Weighted Imaging: A Preliminary Study on 46 Meningiomas Treated with Proton-Therapy

Objective: a considerable subgroup of meningiomas (MN) exhibit indolent and insidious growth. Strategies to detect earlier treatment responses based on tumour biology rather than on size can be useful. We aimed to characterize therapy-induced changes in the apparent diffusion coefficient (ADC) of MN treated with proton-therapy (PT), determining whether the pre- and early post-treatment ADC values may predict tumour response. Methods: Forty-four subjects with MN treated with PT were retrospectively enrolled. All patients underwent conventional magnetic resonance imaging (MRI) including diffusion-weighted imaging (DWI) at baseline and each 3 months for a follow-up period up to 36 months after the beginning of PT. Mean relative ADC (rADCm) values of 46 MN were measured at each exam. The volume variation percentage (VV) for each MN was calculated. The Wilcoxon test was used to assess the differences in rADCm values between pre-treatment and post-treatment exams. Patients were grouped in terms of VV (threshold −20%). A p < 0.05 was considered statistically significant for all the tests. Results: A significant progressive increase of rADCm values was detected at each time point when compared to baseline rADCm (p < 0.05). Subjects that showed higher pre-treatment rADCm values had no significant volume changes or showed volume increase, while subjects that showed a VV < −20% had significantly lower pre-treatment rADCm values. Higher and earlier rADCm increases (3 months) are related to greater volume reduction. Conclusion: In MN treated with PT, pre-treatment rADCm values and longitudinal rADCm changes may predict treatment response.