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.

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.

Sensitivity study of the microdosimetric kinetic model parameters for carbon ion radiotherapy

In carbon ion therapy treatment planning, the relative biological effectiveness (RBE) is accounted for by optimization of the RBE-weighted dose (biological dose). The RBE calculation methods currently applied clinically in carbon ion therapy are derived from the microdosimetric kinetic model (MKM) in Japan and the local effect model (LEM) in Europe. The input parameters of these models are based on fit to experimental data subjected to uncertainties. We therefore performed a sensitivity study of the MKM input parameters, i.e. the domain radius (r _d ), the nucleus radius (R _n ) and the parameters of the linear quadratic (LQ) model (α _x and β). The study was performed with the FLUKA Monte Carlo code, using spread out Bragg peak (SOBP) scenarios in water and a biological dose distribution in a clinical patient case. Comparisons were done between biological doses estimated applying the MKM with parameters based on HSG cells, and with HSG parameters varied separately by  ±{5, 25, 50}%. Comparisons were also done between parameter sets from different cell lines (HSG, V79, CHO and T1), as well as versions of the LEM. Of the parameters, r _d had the largest impact on the biological dose distribution, especially on the absolute dose values. Increasing this parameter by 25% decreased the biological dose level at the center of a 3 Gy(RBE) SOBP by 14%. Variations in R _n only influenced the biological dose distribution towards the particle range, and variations in α _x resulted in minor changes in the biological dose, with an increasing impact towards the particle range. β had the overall smallest influence on the SOBPs, but the impact could become more pronounced if alternative (LET dependent) implementations are used. The resulting percentage change in the SOBPs was generally less than the percentage change in the parameters. The patient case showed similar effects as with the SOBPs in water, and parameter variations had similar impact on the biological dose when using the clinical MKM and the general MKM. The clinical LEM calculated the highest biological doses to both tumor and surrounding healthy tissues, with a median target dose (D _50%) of 40.5 Gy(RBE), while the MKM with HSG and V79 parameters resulted in a D _50% of 34.2 and 36.9 Gy(RBE), respectively. In all, the observed change in biological dose distribution due to parameter variations demonstrates the importance of accurate input parameters when applying the MKM in treatment planning.

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.

Monte Carlo simulations of a low energy proton beamline for radiobiological experiments

BACKGROUND

In order to determine the relative biological effectiveness (RBE) of protons with high accuracy, radiobiological experiments with detailed knowledge of the linear energy transfer (LET) are needed. Cell survival data from high LET protons are sparse and experiments with low energy protons to achieve high LET values are therefore required. The aim of this study was to quantify LET distributions from a low energy proton beam by using Monte Carlo (MC) simulations, and to further compare to a proton beam representing a typical minimum energy available at clinical facilities.

MATERIALS AND METHODS

A Markus ionization chamber and Gafchromic films were employed in dose measurements in the proton beam at Oslo Cyclotron Laboratory. Dose profiles were also calculated using the FLUKA MC code, with the MC beam parameters optimized based on comparisons with the measurements. LET spectra and dose-averaged LET (LET_d) were then estimated in FLUKA, and compared with LET calculated from an 80 MeV proton beam.

RESULTS

The initial proton energy was determined to be 15.5 MeV, with a Gaussian energy distribution of 0.2% full width at half maximum (FWHM) and a Gaussian lateral spread of 2 mm FWHM. The LET_d increased with depth, from approximately 5 keV/μm in the entrance to approximately 40 keV/μm in the distal dose fall-off. The LET_d values were considerably higher and the LET spectra were much narrower than the corresponding spectra from the 80 MeV beam.

CONCLUSIONS

MC simulations accurately modeled the dose distribution from the proton beam and could be used to estimate the LET at any position in the setup. The setup can be used to study the RBE for protons at high LET_d, which is not achievable in clinical proton therapy facilities.

A phenomenological biological dose model for proton therapy based on linear energy transfer spectra

PURPOSE

The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET_d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model.

METHOD

The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET_d based models for a simulated spread out Bragg peak (SOBP) scenario.

RESULTS

The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22).

CONCLUSION

The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were observed for the SOBP scenario, both non-linear LET spectrum- and linear LET_d based models should be further evaluated in clinically realistic scenarios.