Calculation of relative biological effectiveness for proton beams using biological weighting functions

Calculation of biological effectiveness of SOBP proton beams: a TOPAS Monte Carlo study

Objective.This study aims to investigate the biological effectiveness of Spread-Out Bragg-Peak (SOBP) proton beams with initial kinetic energies 50-250 MeV at different depths in water using TOPAS Monte Carlo code.Approach.The study modelled SOBP proton beams using TOPAS time feature. Various LET-based models and Repair-Misrepair-Fixation model were employed to calculate Relative Biological Effectiveness (RBE) for V79 cell lines at different on-axis depths based on TOPAS. Microdosimetric Kinetic Model and biological weighting function-based models, which utilize microdosimetric distributions, were also used to estimate the RBE. A phase-space-based method was adopted for calculating microdosimetric distributions.Main results.The trend of variation of RBE with depth is similar in all the RBE models, but the absolute RBE values vary based on the calculation models. RBE sharply increases at the distal edge of SOBP proton beams. In the entrance region of all the proton beams, RBE values at 4 Gy i.e. RBE(4 Gy) resulting from different models are in the range of 1.04-1.07, comparable to clinically used generic RBE of 1.1. Moving from the proximal to distal end of the SOBP, RBE(4 Gy) is in the range of 1.15-1.33, 1.13-1.21, 1.11-1.17, 1.13-1.18 and 1.17-1.21, respectively for 50, 100, 150, 200 and 250 MeV SOBP beams, whereas at the distal dose fall-off region, these values are 1.68, 1.53, 1.44, 1.42 and 1.40, respectively.Significance.The study emphasises application of depth-, dose- and energy- dependent RBE values in clinical application of proton beams.

Microdosimetry-based investigation of biological effectiveness of252Cf brachytherapy source: TOPAS Monte Carlo study

Objective.To investigate biological effectiveness of252Cf brachytherapy source using Monte Carlo-calculated microdosimetric distributions.Approach.252Cf source capsule was placed at the center of the spherical water phantom and phase-space data were scored as a function of radial distance in water (R= 1-5 cm) using TOPAS Monte Carlo code. The phase-space data were used to calculate microdosimetric distributions at 1μm site size. Using these distributions, Relative Biological Effectiveness (RBE), mean quality factor (Q̅) and Oxygen Enhancement Ratio (OER) were calculated as a function ofR.Main results.The overall shapes of the microdosimetric distributions are comparable at all the radial distances in water. However, slight variation in the bin-wise yield is observed withR. RBE,Q̅and OER are insensitive to R over the range 1-5 cm. Microdosimetric kinetic model based RBE values are about 2.3 and 2.8 for HSG tumour cells and V79 cells, respectively, whereas biological weighting function-based RBE is about 2.8. ICRP 60 and ICRU 40 recommendation-basedQ̅values are about 14.5 and 16, respectively. Theory of dual radiation action based RBE is 11.4. The calculated value of OER is 1.6.Significance.This study demonstrates the relative insensitivity of RBE,Q̅and OER radially away from the252Cf source along the distances of 1-5 cm in water.

GPU-accelerated calculation of proton microdosimetric spectra as a function of target size, proton energy, and bounding volume size

Objective.Shortcomings of dose-averaged linear energy transfer (LETD), the quantity which is most commonly used to quantify proton relative biological effectiveness, have long been recognized. Microdosimetric spectra may overcome the limitations of LETDbut are extremely computationally demanding to calculate. A systematic library of lineal energy spectra for monoenergetic protons could enable rapid determination of microdosimetric spectra in a clinical environment. The objective of this work was to calculate and validate such a library of lineal energy spectra.Approach. SuperTrack, a GPU-accelerated CUDA/C++ based application, was developed to superimpose tracks calculated using Geant4 onto targets of interest and to compute microdosimetric spectra. Lineal energy spectra of protons with energies from 0.1 to 100 MeV were determined in spherical targets of diameters from 1 nm to 10μm and in bounding voxels with side lengths of 5μm and 3 mm.Main results.Compared to an analogous Geant4-based application, SuperTrack is up to 3500 times more computationally efficient if each track is resampled 1000 times. Dose spectra of lineal energy and dose-mean lineal energy calculated with SuperTrack were consistent with values published in the literature and with comparison to a Geant4 simulation. Using SuperTrack, we developed the largest known library of proton microdosimetric spectra as a function of primary proton energy, target size, and bounding volume size.Significance. SuperTrack greatly increases the computational efficiency of the calculation of microdosimetric spectra. The elevated lineal energy observed in a 3 mm side length bounding volume suggests that lineal energy spectra determined experimentally or computed in small bounding volumes may not be representative of the lineal energy spectra in voxels of a dose calculation grid. The library of lineal energy spectra calculated in this work could be integrated with a treatment planning system for rapid determination of lineal energy spectra in patient geometries.

A practical approach for continuous in situ characterization of radiation quality factors in space

The space radiation environment is qualitatively different from Earth, and its radiation hazard is generally quantified relative to photons using quality factors that allow assessment of biologically-effective dose. Two approaches exist for estimating radiation quality factors in complex low/intermediate-dose radiation environments: one is a fluence-based risk cross-section approach, which requires very detailed in silico characterization of the radiation field and biological cross sections, and thus cannot realistically be used for in situ monitoring. By contrast, the microdosimetric approach, using measured (or calculated) distributions of microdosimetric energy deposition together with empirical biological weighting functions, is conceptually and practically simpler. To demonstrate feasibility of the microdosimetric approach, we estimated a biological weighting function for one specific endpoint, heavy-ion-induced tumorigenesis in APC^1638N/+ mice, which was unfolded from experimental results after a variety of heavy ion exposures together with corresponding calculated heavy ion microdosimetric energy deposition spectra. Separate biological weighting functions were unfolded for targeted and non-targeted effects, and these differed substantially. We folded these biological weighting functions with microdosimetric energy deposition spectra for different space radiation environments, and conclude that the microdosimetric approach is indeed practical and, in conjunction with in-situ measurements of microdosimetric spectra, can allow continuous readout of biologically-effective dose during space flight.

Radiobiological impact of gadolinium neutron capture from proton therapy and alternative neutron sources using TOPAS-nBio

PURPOSE

A multi-scale investigation of the biological properties of gadolinium neutron capture (GdNC) therapy with applications in particle therapy is conducted using the TOPAS Monte Carlo (MC) simulation code. The simulation results are used to quantify the amount of gadolinium dose enhancement produced as a result of the secondary neutron production from proton therapy scaled by measured data.

MATERIALS AND METHODS

MC modeling was performed using the radiobiology extension TOol for PArticle Simulation TOPAS-nBio MC simulation code to study the radiobiological effects produced from GdNC on a segment of DNA, a spherical cellular model, and from the modeling of previous experimental measurements. The average RBE values were calculated from two methods, microdosimetric kinematic (MK) and biological weighting r(y) within a 2 nm DNA segment for GdNC. The single-strand breaks (SSBs) and double-strand breaks (DSBs) were calculated from within the nucleus of a 20 µm diameter, spherical cell model. From a previous experimental proton therapy measurement using a spread-out Bragg peak (SOBP) of 4.5-9.5 cm and a delivered absorbed dose of 10.4 Gy, the amount of Gd neutron captures was calculated and used to quantify the amount of GdNC absolute dose from particle therapy.

RESULTS

The average RBE from microdosimetric kinematic and biological weighting was 1.35, and 1.70 for a 10% cell survival on HSG cell-line and weighting function data from early intestinal tolerance of mice. From a central isotropic GdNC source, the energy deposition is found to decrease from roughly 2.7 eV per capture down to approximately 0.01 eV per capture, a drop of two orders of magnitude within 50 nm. This result suggests that Gd needs to be close to the DNA (within 10-20 nm) in order for neutron capture to induce a significant dose enhancement due to the short-range electrons emitted after Gd neutron capture. Within a spherical cell model, the SSBs, and DSBs were determined to be 39 and 1.5 per neutron capture, respectively. From the total neutron captures produced from an experimental proton therapy measurement on a 3000 PPM Gd solution, an insignificant absolute Gd dose enhancement was quantified to be 5.4 × 10^-6  Gy per Gy of administered proton dose.

CONCLUSION

From this study and literature review, the production of secondary thermal neutrons from proton therapy is determined to be a limiting factor and unlikely to produce a clinically useful dose enhancement for secondary neutron capture therapy. Moreover, alternative neutron sources, such as, a compact deuterium-tritium (D-T) neutron generator, a "high yield" deuterium-deuterium (D-D) generator, or an industrial strength (100 mg) ²⁵² Cf source were investigated, with the ²⁵² Cf source the most likely to be capable of producing enough neutrons for 1 Gy of localized GdNC absolute dose within a reasonable treatment time.

Development of a new microdosimetric biological weighting function for the RBE10 assessment in case of the V79 cell line exposed to ions from 1H to 238U

An improved biological weighting function (IBWF) is proposed to phenomenologically relate microdosimetric lineal energy probability density distributions with the relative biological effectiveness (RBE) for the in vitro clonogenic cell survival (surviving fraction = 10%) of the most commonly used mammalian cell line, i.e. the Chinese hamster lung fibroblasts (V79). The IBWF, intended as a simple and robust tool for a fast RBE assessment to compare different exposure conditions in particle therapy beams, was determined through an iterative global-fitting process aimed to minimize the average relative deviation between RBE calculations and literature in vitro data in case of exposure to various types of ions from ¹H to ²³⁸U. By using a single particle- and energy- independent function, it was possible to establish an univocal correlation between lineal energy and clonogenic cell survival for particles spanning over an unrestricted linear energy transfer range of almost five orders of magnitude (0.2 keV µm^-1 to 15 000 keV µm^-1 in liquid water). The average deviation between IBWF-derived RBE values and the published in vitro data was ∼14%. The IBWF results were also compared with corresponding calculations (in vitro RBE₁₀ for the V79 cell line) performed using the modified microdosimetric kinetic model (modified MKM). Furthermore, RBE values computed with the reference biological weighting function (BWF) for the in vivo early intestine tolerance in mice were included for comparison and to further explore potential correlations between the BWF results and the in vitro RBE as reported in previous studies. The results suggest that the modified MKM possess limitations in reproducing the experimental in vitro RBE₁₀ for the V79 cell line in case of ions heavier than ²⁰Ne. Furthermore, due to the different modelled endpoint, marked deviations were found between the RBE values assessed using the reference BWF and the IBWF for ions heavier than ²H. Finally, the IBWF was unchangingly applied to calculate RBE values by processing lineal energy density distributions experimentally measured with eight different microdosimeters in 19 ¹H and ¹²C beams at ten different facilities (eight clinical and two research ones). Despite the differences between the detectors, irradiation facilities, beam profiles (pristine or spread out Bragg peak), maximum beam energy, beam delivery (passive or active scanning), energy degradation system (water, PMMA, polyamide or low-density polyethylene), the obtained IBWF-based RBE trends were found to be in good agreement with the corresponding ones in case of computer-simulated microdosimetric spectra (average relative deviation equal to 0.8% and 5.7% for ¹H and ¹²C ions respectively).

A microdosimetric analysis of the interactions of mono-energetic neutrons with human tissue

Nuclear reactions induced during high-energy radiotherapy produce secondary neutrons that, due to their carcinogenic potential, constitute an important risk for the development of iatrogenic cancer. Experimental and epidemiological findings indicate a marked energy dependence of neutron relative biological effectiveness (RBE) for carcinogenesis, but little is reported on its physical basis. While the exact mechanism of radiation carcinogenesis is yet to be fully elucidated, numerical microdosimetry can be used to predict the biological consequences of a given irradiation based on its microscopic pattern of energy depositions. Building on recent studies, this work investigated the physics underlying neutron RBE by using the microdosimetric quantity dose-mean lineal energy (y‾_D) as a proxy. A simulation pipeline was constructed to explicitly calculate the y‾_D of radiation fields that consisted of (i) the open source Monte Carlo toolkit Geant4, (ii) its radiobiological extension Geant4-DNA, and (iii) a weighted track-sampling algorithm. This approach was used to study mono-energetic neutrons with initial kinetic energies between 1 eV and 10 MeV at multiple depths in a tissue-equivalent phantom. Spherical sampling volumes with diameters between 2 nm and 1 μm were considered. To obtain a measure of RBE, the neutron y‾_D values were divided by those of 250 keV X-rays that were calculated in the same way. Qualitative agreement was found with published radiation protection factors and simulation data, allowing for the dependencies of neutron RBE on depth and energy to be discussed in the context of the neutron interaction cross sections and secondary particle distributions in human tissue.

Proton Irradiation Increases the Necessity for Homologous Recombination Repair Along with the Indispensability of Non-Homologous End Joining

Technical improvements in clinical radiotherapy for maximizing cytotoxicity to the tumor while limiting negative impact on co-irradiated healthy tissues include the increasing use of particle therapy (e.g., proton therapy) worldwide. Yet potential differences in the biology of DNA damage induction and repair between irradiation with X-ray photons and protons remain elusive. We compared the differences in DNA double strand break (DSB) repair and survival of cells compromised in non-homologous end joining (NHEJ), homologous recombination repair (HRR) or both, after irradiation with an equal dose of X-ray photons, entrance plateau (EP) protons, and mid spread-out Bragg peak (SOBP) protons. We used super-resolution microscopy to investigate potential differences in spatial distribution of DNA damage foci upon irradiation. While DNA damage foci were equally distributed throughout the nucleus after X-ray photon irradiation, we observed more clustered DNA damage foci upon proton irradiation. Furthermore, deficiency in essential NHEJ proteins delayed DNA repair kinetics and sensitized cells to both, X-ray photon and proton irradiation, whereas deficiency in HRR proteins sensitized cells only to proton irradiation. We assume that NHEJ is indispensable for processing DNA DSB independent of the irradiation source, whereas the importance of HRR rises with increasing energy of applied irradiation.

The microdosimetric extension in TOPAS: development and comparison with published data

Microdosimetric energy depositions have been suggested as a key variable for the modeling of the relative biological effectiveness (RBE) in proton and ion radiation therapy. However, microdosimetry has been underutilized in radiation therapy. Recent advances in detector technology allow the design of new mico- and nano-dosimeters. At the same time Monte Carlo (MC) simulations have become more widely used in radiation therapy. In order to address the growing interest in the field, a microdosimetric extension was developed in TOPAS. The extension provides users with the functionality to simulate microdosimetric spectra as well as the contribution of secondary particles to the spectra, calculate microdosimetric parameters, and determine RBE with a biological weighting function approach or with the microdosimetric kinetic (MK) model. Simulations were conducted with the extension and the results were compared with published experimental data and other simulation results for three types of microdosimeters, a spherical tissue equivalent proportional counter (TEPC), a cylindrical TEPC and a solid state microdosimeter. The corresponding microdosimetric spectra obtained with TOPAS from the plateau region to the distal tail of the Bragg curve generally show good agreement with the published data.

Report of the AAPM TG-256 on the relative biological effectiveness of proton beams in radiation therapy

The biological effectiveness of proton beams relative to photon beams in radiation therapy has been taken to be 1.1 throughout the history of proton therapy. While potentially appropriate as an average value, actual relative biological effectiveness (RBE) values may differ. This Task Group report outlines the basic concepts of RBE as well as the biophysical interpretation and mathematical concepts. The current knowledge on RBE variations is reviewed and discussed in the context of the current clinical use of RBE and the clinical relevance of RBE variations (with respect to physical as well as biological parameters). The following task group aims were designed to guide the current clinical practice: Assess whether the current clinical practice of using a constant RBE for protons should be revised or maintained. Identifying sites and treatment strategies where variable RBE might be utilized for a clinical benefit. Assess the potential clinical consequences of delivering biologically weighted proton doses based on variable RBE and/or LET models implemented in treatment planning systems. Recommend experiments needed to improve our current understanding of the relationships among in vitro, in vivo, and clinical RBE, and the research required to develop models. Develop recommendations to minimize the effects of uncertainties associated with proton RBE for well-defined tumor types and critical structures.

Validation of the physical and RBE-weighted dose estimator based on PHITS coupled with a microdosimetric kinetic model for proton therapy

The microdosimetric kinetic model (MKM) is widely used for estimating relative biological effectiveness (RBE)-weighted doses for various radiotherapies because it can determine the surviving fraction of irradiated cells based on only the lineal energy distribution, and it is independent of the radiation type and ion species. However, the applicability of the method to proton therapy has not yet been investigated thoroughly. In this study, we validated the RBE-weighted dose calculated by the MKM in tandem with the Monte Carlo code PHITS for proton therapy by considering the complete simulation geometry of the clinical proton beam line. The physical dose, lineal energy distribution, and RBE-weighted dose for a 155 MeV mono-energetic and spread-out Bragg peak (SOBP) beam of 60 mm width were evaluated. In estimating the physical dose, the calculated depth dose distribution by irradiating the mono-energetic beam using PHITS was consistent with the data measured by a diode detector. A maximum difference of 3.1% in the depth distribution was observed for the SOBP beam. In the RBE-weighted dose validation, the calculated lineal energy distributions generally agreed well with the published measurement data. The calculated and measured RBE-weighted doses were in excellent agreement, except at the Bragg peak region of the mono-energetic beam, where the calculation overestimated the measured data by ~15%. This research has provided a computational microdosimetric approach based on a combination of PHITS and MKM for typical clinical proton beams. The developed RBE-estimator function has potential application in the treatment planning system for various radiotherapies.

Difference in the relative biological effectiveness and DNA damage repair processes in response to proton beam therapy according to the positions of the spread out Bragg peak

Background

Cellular responses to proton beam irradiation are not yet clearly understood, especially differences in the relative biological effectiveness (RBE) of high-energy proton beams depending on the position on the Spread-Out Bragg Peak (SOBP). Towards this end, we investigated the differences in the biological effect of a high-energy proton beam on the target cells placed at different positions on the SOBP, using two human esophageal cancer cell lines with differing radiosensitivities.

Methods

Two human esophageal cancer cell lines (OE21, KYSE450) with different radiosensitivities were irradiated with a 235-MeV proton beam at 4 different positions on the SOBP (position #1: At entry; position #2: At the proximal end of the SOBP; position #3: Center of the SOBP; position #4: At the distal end of the SOBP), and the cell survivals were assessed by the clonogenic assay. The RBE₁₀ for each position of the target cell lines on the SOBP was determined based on the results of the cell survival assay conducted after photon beam irradiation. In addition, the number of DNA double-strand breaks was estimated by quantitating the number of phospho-histone H2AX (γH2AX) foci formed in the nuclei by immunofluorescence analysis.

Results

In regard to differences in the RBE of a proton beam according to the position on the SOBP, the RBE value tended to increase as the position on the SOBP moved distally. Comparison of the residual number of γH2AX foci at the end 24 h after the irradiation revealed, for both cell lines, a higher number of foci in the cells irradiated at the distal end of the SOPB than in those irradiated at the proximal end or center of the SOBP.

Conclusions

The results of this study demonstrate that the RBE of a high-energy proton beam and the cellular responses, including the DNA damage repair processes, to high-energy proton beam irradiation, differ according to the position on the SOBP, irrespective of the radiosensitivity levels of the cell lines.

Electronic supplementary material

The online version of this article (doi:10.1186/s13014-017-0849-1) contains supplementary material, which is available to authorized users.

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.

Analytical linear energy transfer model including secondary particles: calculations along the central axis of the proton pencil beam

In proton therapy, the relative biological effectiveness (RBE) depends on various types of parameters such as linear energy transfer (LET). An analytical model for LET calculation exists (Wilkens' model), but secondary particles are not included in this model. In the present study, we propose a correction factor, L sec, for Wilkens' model in order to take into account the LET contributions of certain secondary particles. This study includes secondary protons and deuterons, since the effects of these two types of particles can be described by the same RBE-LET relationship. L sec was evaluated by Monte Carlo (MC) simulations using the GATE/GEANT4 platform and was defined by the ratio of the LET d distributions of all protons and deuterons and only primary protons. This method was applied to the innovative Pencil Beam Scanning (PBS) delivery systems and L sec was evaluated along the beam axis. This correction factor indicates the high contribution of secondary particles in the entrance region, with L sec values higher than 1.6 for a 220 MeV clinical pencil beam. MC simulations showed the impact of pencil beam parameters, such as mean initial energy, spot size, and depth in water, on L sec. The variation of L sec with these different parameters was integrated in a polynomial function of the L sec factor in order to obtain a model universally applicable to all PBS delivery systems. The validity of this correction factor applied to Wilkens' model was verified along the beam axis of various pencil beams in comparison with MC simulations. A good agreement was obtained between the corrected analytical model and the MC calculations, with mean-LET deviations along the beam axis less than 0.05 keV μm(-1). These results demonstrate the efficacy of our new correction of the existing LET model in order to take into account secondary protons and deuterons along the pencil beam axis.

Radiobiological intercomparison of the 160 MeV and 230 MeV proton therapy beams at the Harvard Cyclotron Laboratory and at Massachusetts General Hospital

The purpose of this study was to determine the relative biological effectiveness (RBE) along the axis of two range-modulated proton beams (160 and 230 MeV). Both the depth and the dose dependence of RBE were investigated. Chinese hamster V79-WNRE cells, suspended in medium containing gelatin and cooled to 2 °C, were used to obtain complete survival curves at multiple positions throughout the entrance and 10 cm spread-out Bragg peak (SOBP). Simultaneous measurements of the survival response to (60)Co gamma rays served as the reference data for the proton RBE determinations. For both beams the RBE increased significantly with depth in the 10 cm SOBP, particularly in the distal half of the SOBP, then rose even more sharply at the distal edge, the most distal position measured. At a 4 Gy dose of gamma radiation (S = 0.34) the average RBE values for the entrance, proximal half, distal half and distal edge were 1.07 ± 0.01, 1.10 ± 0.01, 1.17 ± 0.01 and 1.21 ± 0.01, respectively, and essentially the same for both beams. At a 2 Gy dose of gamma radiation (S = 0.71) the average RBE values rose to 1.13 ± 0.03, 1.15 ± 0.02, 1.26 ± 0.02 and 1.30 ± 0.02, respectively, for the same four regions of the SOBP. The difference between the 4 Gy and 2 Gy RBE values reflects the dose dependence of RBE as measured in these V79-WNRE cells, which have a low α/β value, as do other widely used cell lines that also show dose-dependent RBE values. Late-responding tissues are also characterized by low α/β values, so it is possible that these cell lines may be predictive for the response of such tissues (e.g., spinal cord, optic nerve, kidney, liver, lung). However, in the very small number of studies of late-responding tissues performed to date there appears to be no evidence of an increased RBE for protons at low doses. Similarly, RBE measurements using early responding in vivo systems (mostly mouse jejunum, an early-responding tissue which has a large α/β ∼ 10 Gy) have generally shown little or no detectable dose dependence. It is useful to compare the RBE values reported here to the commonly used generic clinical RBE of 1.1, which assumes no dependence on depth or on dose. Our proximal RBEs obviously avoid the depth-related increase in RBE and for doses of 4 Gy or more, the low-dose increase in RBE is also minimized, as shown in this article. Thus the proximal RBE at a 4 Gy dose of 1.10 ± 0.01, quoted above, represents an interesting point of congruence with the clinical RBE for conditions where it could reasonably be expected in the measurements reported here. The depth dependence of RBE reported here is consistent with the majority of measurements, both in vitro and in vivo, by other investigators. The dose dependence of RBE, on the other hand, is tissue specific but has not yet been demonstrated for protons by RBE values in late-responding normal tissue systems. This indicates a need for additional RBE determination as function of dose, especially in late-responding tissues.

Future development of biologically relevant dosimetry

Proton and ion beams are radiotherapy modalities of increasing importance and interest. Because of the different biological dose response of these radiations as compared with high-energy photon beams, the current approach of treatment prescription is based on the product of the absorbed dose to water and a biological weighting factor, but this is found to be insufficient for providing a generic method to quantify the biological outcome of radiation. It is therefore suggested to define new dosimetric quantities that allow a transparent separation of the physical processes from the biological ones. Given the complexity of the initiation and occurrence of biological processes on various time and length scales, and given that neither microdosimetry nor nanodosimetry on their own can fully describe the biological effects as a function of the distribution of energy deposition or ionization, a multiscale approach is needed to lay the foundation for the aforementioned new physical quantities relating track structure to relative biological effectiveness in proton and ion beam therapy. This article reviews the state-of-the-art microdosimetry, nanodosimetry, track structure simulations, quantification of reactive species, reference radiobiological data, cross-section data and multiscale models of biological response in the context of realizing the new quantities. It also introduces the European metrology project, Biologically Weighted Quantities in Radiotherapy, which aims to investigate the feasibility of establishing a multiscale model as the basis of the new quantities. A tentative generic expression of how the weighting of physical quantities at different length scales could be carried out is presented.

Range modulation in proton therapy planning: a simple method for mitigating effects of increased relative biological effectiveness at the end-of-range of clinical proton beams

Background

The increase in relative biological effectiveness (RBE) of proton beams at the distal edge of the spread out Bragg peak (SOBP) is a well-known phenomenon that is difficult to quantify accurately in vivo. For purposes of treatment planning, disallowing the distal SOBP to fall within vulnerable tissues hampers sparing to the extent possible with proton beam therapy (PBT). We propose the distal RBE uncertainty may be straightforwardly mitigated with a technique we call “range modulation”. With range modulation, the distal falloff is smeared, reducing both the dose and average RBE over the terminal few millimeters of the SOBP.

Methods

One patient plan was selected to serve as an example for direct comparison of image-guided radiotherapy plans using non-range modulation PBT (NRMPBT), and range-modulation PBT (RMPBT). An additional plan using RMPBT was created to represent a re-treatment scenario (RMPBTrt) using a vertex beam. Planning statistics regarding dose, volume of the planning targets, and color images of the plans are shown.

Results

The three plans generated for this patient reveal that in all cases dosimetric and device manufacturing advantages are able to be achieved using RMPBT. Organ at risk (OAR) doses to critical structures such as the cochleae, optic apparatus, hypothalamus, and temporal lobes can be selectively spared using this method. Concerns about the location of the RBE that did significantly impact beam selection and treatment planning no longer have the same impact on the process, allowing these structures to be spared dose and subsequent associated issues.

Conclusions

This present study has illustrated that RMPBT can improve OAR sparing while giving equivalent coverage to target volumes relative to traditional PBT methods while avoiding the increased RBE at the end of the beam. It has proven easy to design and implement and robust in our planning process. The method underscores the need to optimize treatment plans in PBT for both traditional energy dose in gray (Gy) and biologic dose (RBE).

A model of radiation-induced cell killing: insights into mechanisms and applications for hadron therapy

A mechanism-based, two-parameter biophysical model of cell killing was developed with the aim of elucidating the mechanisms underlying radiation-induced cell death and predicting cell killing by different radiation types, including protons and carbon ions at energies and doses of interest for cancer therapy. The model assumed that certain chromosome aberrations (dicentrics, rings and large deletions, called "lethal aberrations") lead to clonogenic inactivation, and that aberrations derive from μm-scale misrejoining of chromatin fragments, which in turn are produced by "dirty" double-strand breaks called "cluster lesions" (CLs). The average numbers of CLs per Gy per cell were left as a semi-free parameter and the threshold distance for chromatin-fragment rejoining was defined the second parameter. The model was "translated" into Monte Carlo code and provided simulated survival curves, which were compared with survival data on V79 cells exposed to protons, carbon ions and X rays. The agreement was good between simulations and survival data and supported the assumptions of the model at least for doses up to a few Gy. Dicentrics, rings and large deletions were found to be lethal not only for AG1522 cells exposed to X rays, as already reported by others, but also for V79 cells exposed to protons and carbon ions of different energies. Furthermore, the derived CL yields suggest that the critical DNA lesions leading to clonogenic inactivation are more complex than "clean" DSBs. After initial validation, the model was applied to characterize the particle and LET dependence of proton and carbon cell killing. Consistent with the proton data, the predicted fraction of inactivated cells after 2 Gy protons was 40-50% below 7.7 keV/μm, increased by a factor ∼1.6 between 7.7-30.5 keV/μm, and decreased by a factor ∼1.1 between 30.5-34.6 keV/μm. These LET values correspond to proton energies below a few MeV, which are always present in the distal region of hadron therapy spread-out Bragg peaks (SOBP). Consistent with the carbon data, the predicted fraction of inactivated cells after 2 Gy carbon was 40-50% between 13.7-32.4 keV/μm, it increased by a factor ∼1.7 between 32.4-153.5 keV/μm, and decreased by a factor ∼1.1 between 153.5-339.1 keV/μm. Finally, we applied the model to predict cell death at different depths along a carbon SOBP used for preclinical experiments at HIMAC in Chiba, Japan. The predicted fraction of inactivated cells was found to be roughly constant (less than 10%) along the SOBP, suggesting that this approach may be applied to predict cell killing of therapeutic carbon beams and that, more generally, dicentrics, rings and deletions at the first mitosis may be regarded as a biological dose for these beams. This study advanced our understanding of the mechanisms of radiation-induced cell death and characterized the particle and LET dependence of proton and carbon cell killing along a carbon SOBP. The model does not use RBE values, which can be a source of uncertainty. More generally, this model is a mechanism-based tool that in minutes can predict cell inactivation by protons or carbon ions of a given energy and dose, based on an experimental photon curve and in principle, a single (experimental) survival point for the considered ion type and energy.

Microdosimetric calculation of relative biological effectiveness for design of therapeutic proton beams

The authors attempt to establish the relative biological effectiveness (RBE) calculation for designing therapeutic proton beams on the basis of microdosimetry. The tissue-equivalent proportional counter (TEPC) was used to measure microdosimetric lineal energy spectra for proton beams at various depths in a water phantom. An RBE-weighted absorbed dose is defined as an absorbed dose multiplied by an RBE for cell death of human salivary gland (HSG) tumor cells in this study. The RBE values were calculated by a modified microdosimetric kinetic model using the biological parameters for HSG tumor cells. The calculated RBE distributions showed a gradual increase to about 1cm short of a beam range and a steep increase around the beam range for both the mono-energetic and spread-out Bragg peak (SOBP) proton beams. The calculated RBE values were partially compared with a biological experiment in which the HSG tumor cells were irradiated by the SOBP beam except around the distal end. The RBE-weighted absorbed dose distribution for the SOBP beam was derived from the measured spectra for the mono-energetic beam by a mixing calculation, and it was confirmed that it agreed well with that directly derived from the microdosimetric spectra measured in the SOBP beam. The absorbed dose distributions to planarize the RBE-weighted absorbed dose were calculated in consideration of the RBE dependence on the prescribed absorbed dose and cellular radio-sensitivity. The results show that the microdosimetric measurement for the mono-energetic proton beam is also useful for designing RBE-weighted absorbed dose distributions for range-modulated proton beams.

Direct Response to Proton Beam Linear Energy Transfer (LET) in a Novel Polymer Gel Dosimeter Formulation

Linear energy transfer (LET) of clinical proton beams is an important parameter influencing the biological effects of radiation. This work demonstrates LET-induced response enhancement in novel formulations of polymer gel dosimeters, potentially useful for LET mapping of clinical proton beams. A series of four polymer gel dosimeters (labeled A through D), prepared based on the BANG3-Pro2 formulation, but with varying concentrations of polymerization modifiers, were irradiated by a clinical proton beam with a spread out Bragg peak modulation (SOBP) and read out using the OCTOPUS-IQ optical CT scanner. The evaluation of optical density profiles in the SOBP (constant physical dose) revealed response deviations at the distal end consistent with variations in gel composition. Maximum response deviations were as follows: −3% (under-response) for gel A, and over-response of 2%, 12%, and 17% for gels B, C, and D, respectively, relative to the mean dose in the center of the SOBP. This enhancement in optical response was correlated to LET by analytical calculations. Gels A and B showed no measurable dependence on LET. Gel C responded linearly in the limited range from 1.5 to 3.5 keV/μm. LET response of gel D was linear up to at least 5.5 keV/μm, with the threshold at about 1.3 keV/μm. These results suggest that it may be possible to develop a polymer gel system with direct optical response to LET for mapping of LET distributions for particle therapy beams.

Cutaneous graft-versus-host disease after proton-based craniospinal irradiation for recurrent Philadelphia-positive acute lymphoblastic leukaemia

Treatment of recurrent acute lymphoblastic leukaemia (ALL) often involves allogeneic stem-cell transplantation (alloSCT) and disease recurrence in the central nervous system may require craniospinal irradiation. Although graft-versus-host disease (GVHD) is a known risk after alloSCT, cutaneous manifestation within radiation fields is rarely seen. The authors report a case of a 25-year-old man with Philadelphia+ALL recurring in the central nervous system after a homologous SCT. Craniospinal radiation was delivered with proton therapy to a total dose of 24 cobalt-Gray-equivalents in 12 fractions. Eight weeks after the proton therapy, significant cutaneous GVHD had developed within the radiation fields. This was treated successfully with tacrolimus (4 mg/day), a short course of methylprednisolone, and topical treatment with 0.1% triamcinolone cream, 0.05% clobetasol ointment. Cutaneous GVHD after SCT can be seen within proton radiation fields probably due to an inherent higher skin dose.

Dose and dose averaged LET comparison of ¹H, ⁴He, ⁶Li, ⁸Be, ¹⁰B, ¹²C, ¹⁴N, and ¹⁶O ion beams forming a spread-out Bragg peak

PURPOSE

Modern clinical accelerators are capable of producing ion beams from protons up to neon. This work compares the depth dose distribution and corresponding dose averaged linear energy transfer (LET) distribution, which is related to the biological effectiveness, for different ion beams (¹H, ⁴He, ⁶Li, ⁸Be, ¹⁰B, ¹²C, ¹⁴N, and ¹⁶O) using multi-energetic spectra in order to configure spread-out Bragg peaks (SOBP).

METHODS

Monte Carlo simulations were performed in order to configure a 5 cm SOBP at 8 cm depth in water for all the different ion beams. Physical dose and dose averaged LET distributions as a function of depth were then calculated and compared. The superposition of dose distribution of all ions is also presented for a two opposing fields configuration. Additional simulations were performed for (12)C beams to investigate the dependence of dose and dose averaged LET distributions on target depth and size, as well as beam configuration. These included simulations for a 3 cm SOBP at 7, 10, and 13 cm depth in water, a 6 cm SOBP at 7 depth in water, and two opposing fields of 6 cm SOBP.

RESULTS

Alpha particles and protons present superior physical depth dose distributions relative to the rest of the beams studied. Dose averaged LET distributions results suggest higher biological effectiveness in the target volume for carbon, nitrogen and oxygen ions. This is coupled, however, with relatively high LET values-especially for the last two ion species-outside the SOBP where healthy tissue would be located. Dose averaged LET distributions for ⁸Be and ¹⁰B beams show that they could be attractive alternatives to ¹²C for the treatment of small, not deeply seated lesions. The potential therapeutic effect of different ion beams studied in this work depends on target volume and position, as well as the number of beams used.

CONCLUSIONS

The optimization of beam modality for specific tumor cites remains an open question that warrants further investigation and clinically relevant results.

Radiobiological characterization of two therapeutic proton beams with different initial energy spectra used at the Institut Curie Proton Therapy Center in Orsay

PURPOSE

Treatment planning in proton therapy uses a generic value for the relative biological efficiency (RBE) of 1.1 throughout the spread-out Bragg peak (SOBP) generated. In this article, we report on the variation of the RBE with depth in the SOBP of the 76- and 201-MeV proton beams used for treatment at the Institut Curie Proton Therapy Center in Orsay.

METHODS AND MATERIALS

The RBE (relative to (137)Cs γ-rays) of the two modulated proton beams at three positions in the SOBP was determined in two human tumor cells using as endpoints clonogenic cell survival and the incidence of DNA double-strand breaks (DSBs) as measured by pulse-field gel electrophoresis without and with enzymatic treatment to reveal clustered lesions.

RESULTS

The RBE for induced cell killing by the 76-MeV beam increased with depth in the SOBP. However for the 201-MeV protons, it was close to that for (137)Cs γ-rays and did not vary significantly. The incidence of DSBs and clustered lesions was higher for protons than for (137)Cs γ-rays, but did not depend on the proton energy or the position in the SOBP.

CONCLUSIONS

Until now, little attention has been paid to the variation of RBE with depth in the SOBP as a function of the nominal energy of the primary proton beam and the molecular nature of the DNA damage. The RBE increase in the 76-MeV SOBP implies that the tumor tissues at the distal end receives a higher biologically equivalent dose than at the proximal end, despite a homogeneous physical dose. This is not the case for the 201-MeV energy beam. The precise determination of the effects of incident beam energy, modulation, and depth in tissues on the linear energy transfer-RBE relationship is essential for treatment planning.

Determination of the dose-depth distribution of proton beam using resazurin assay in vitro and diode laser-induced fluorescence detection

In this study the dose-depth distribution pattern of proton beams was investigated by inactivation of human cells exposed to high-LET (linear energy transfer) protons. The proton beams accelerated up to 45 MeV were horizontally extracted from the cyclotron, and were delivered to the cells acutely through a home made prototype over a range of physical depths (in the form of a variable water column). The biological systems used here were two in vitro cell lines, including human embryonic kidney cells (HEK 293), and human breast adenocarcinoma cell line (MCF-7). Cells were exposed to unmodulated proton beam radiation at a dose of 50 Gy similar to that used in therapy. Resazurin metabolism assay was investigated for measurement of cell response to irradiation as a simple and non-destructive assay. In the resazurin reduction test the non-fluorescent probe dye is reduced to pink and highly fluorescent resorufin. The dose-depth distribution of proton beam obtained based on the highly sensitive laser-induced fluorometric determination of resorufin was found to coincide well with the data collected using conventional film based dosimetry. The resazurin method yielded data comparable with the optical micrographs of the irradiated cells, showing the least cell survival at the measured Bragg-peak position of 10 mm. In addition, fused silica capillary was used as a sample container to increase the probability for irradiated laser beam to probe and excite resorufin in small sample volume of the capillary. The developed method has the potential to serve as a non-destructive, sample-thrifty, and time saving tool to realize more realistic, practical dose-depth distribution of proton beam compared to conventional in vitro cell viability assessment techniques.

The influence of RBE variations in a clinical proton treatment plan for a hypopharynx cancer

Currently, most clinical range-modulated proton beams are assumed to have a fixed overall relative biological effectiveness (RBE) of 1.1. However, it is well known that the RBE increases with depth in the spread-out Bragg peak (SOBP) and becomes about 10% higher than mid-SOBP RBE at 2 mm from the distal edge (Paganetti 2003 Technol. Cancer Res. Treat. 2 413-26) and can reach values of 1.3-1.4 in vitro at the distal edge (Robertson et al 1975 Cancer 35 1664-77, Courdi et al 1994 Br. J. Radiol. 67 800-4). We present a fast method for applying a variable RBE correction with linear energy transfer (LET) dependent tissue-specific parameters based on the alpharef/betaref ratios suitable for implementation in a treatment planning system. The influence of applying this variable RBE correction on a clinical multiple beam proton dose plan is presented here. The treatment plan is evaluated by RBE weighted dose volume histograms (DVHs) and the calculation of tumour control probability (TCP) and normal tissue complication probability (NTCP) values. The variable RBE correction yields DVHs for the clinical target volumes (CTVs), a primary advanced hypopharynx cancer and subclinical disease in the lymph nodes, that are slightly higher than those achieved by multiplying the absorbed dose with RBE=1.1. Although, more importantly, the RBE weighted DVH for an organ at risk, the spinal cord is considerably increased for the variable RBE. As the spinal cord in this particular case is located 8 mm behind the planning target volume (PTV) and hence receives only low total doses, the NTCP values are zero in spite of the significant increase in the RBE weighted DVHs for the variable RBE. However, high NTCP values for the non-target normal tissue were obtained when applying the variable RBE correction. As RBE variations tend to be smaller for in vivo systems, this study-based on in vitro data since human tissue RBE values are scarce and have large uncertainties-can be interpreted as showing the upper limits of the possible effects of utilizing a variable RBE correction. In conclusion, the results obtained here still indicate a significant difference in introducing a variable RBE compared to applying a generic RBE of 1.1, suggesting it is worth considering such a correction in clinical proton therapy planning, especially when risk organs are located immediately behind the target volume.

Significance and implementation of RBE variations in proton beam therapy

Key to radiation therapy is to apply a high tumor-destroying dose while protecting healthy tissue, especially near organs at risk. To optimize treatment for ion therapy not the dose but the dose multiplied by the relative biological effectiveness (RBE) is decisive. Proton therapy has been based on the use of a generic RBE, which is applied to all treatments independent of dose/fraction, position in the spread-out Bragg peak (SOBP), initial beam energy or the particular tissue. Dependencies of the RBE on various physical and biological properties are disregarded. The variability of RBE in clinical situations is believed to be within 10-20%. This is in the same range of effects that receive high attention these days, i.e., patient set-up uncertainties, organ motion effects, and dose calculation accuracy all affecting proton as well as conventional radiation therapy. Elevated RBE values can be expected near the edges of the target, thus probably near critical structures. This is because the edges show lower doses and, depending on the treatment plan, may be identical with the beam's distal edge, where dose is deposited in part by high-LET protons. We assess the rationale for the continued use of a generic RBE and whether the magnitude of RBE variation with treatment parameters is small relative to our abilities to determine RBE's. Two aspects have to be considered. Firstly, the available information from experimental studies and secondly, our ability to calculate RBE values for a given treatment plan based on parameters extracted from such experiments. We analyzed published RBE values for in vitro and in vivo endpoints. The values for cell survival in vitro indicate a substantial spread between the diverse cell lines. The average value at mid SOBP over all dose levels is approximately 1.2 in vitro and approximately 1.1 in vivo. Both in vitro and in vivo data indicate a statistically significant increase in RBE for lower doses per fraction, which is much smaller for in vivo systems. The experimental in vivo data indicate that continued employment of a generic RBE value of 1.1 is reasonable. At present, there seems to be too much uncertainty in the RBE value for any human tissue to propose RBE values specific for tissue, dose/fraction, etc. There is a clear need for prospective assessments of normal tissue reactions in proton irradiated patients and determinations of RBE values for several late responding tissues in animal systems, especially as a function of dose in the range of 1-4 Gy. However, there is a measurable increase in RBE over the terminal few mm of the SOBP, which results in an extension of the bio-effective range of the beam of a few mm. This needs to be considered in treatment planning, particularly for single field plans or for an end of range in or close to a critical structure. To assess our ability to calculate RBE values we studied two approaches, which are both based on the track structure theory of radiation action. RBE calculations are difficult since both the physical input parameters, i.e., LET distributions, and, even more so, the biological input parameters, i.e., local cellular response, have to be known with high accuracy. Track structure theory provides a basis for predicting dose-response curves for particle irradiation. However, designed for heavy ion applications the models show weaknesses in the prediction of proton radiation effects. We conclude that, at present, RBE modeling in treatment planning involves significant uncertainties. To incorporate RBE variations in treatment planning there has to be a reliable biological model to calculate RBE values based on the physical characteristics of the radiation field and based on well-known biological input parameters. In order to do detailed model calculations more experimental data, in particular for in vivo endpoints, are needed

Relative biological effectiveness (RBE), quality factor (Q), and radiation weighting factor (w(R)). A report of the International Commission on Radiological Protection

The effect of ionising radiation is influenced by the dose, the dose rate, and the quality of the radiation. Before 1990, dose-equivalent quantities were defined in terms of a quality factor, Q(L), that was applied to the absorbed dose at a point in order to take into account the differences in the effects of different types of radiation. In its 1990 recommendations, the ICRP introduced a modified concept. For radiological protection purposes, the absorbed dose is averaged over an organ or tissue, T, and this absorbed dose average is weighted for the radiation quality in terms of the radiation weighting factor, w(R), for the type and energy of radiation incident on the body. The resulting weighted dose is designated as the organ- or tissue-equivalent dose, H(T). The sum of the organ-equivalent doses weighted by the ICRP organ-weighting factors, w(T), is termed the effective dose, E. Measurements can be performed in terms of the operational quantities, ambient dose equivalent, and personal dose equivalent. These quantities continue to be defined in terms of the absorbed dose at the reference point weighted by Q(L). The values for w(R) and Q(L) in the 1990 recommendations were based on a review of the biological and other information available, but the underlying relative biological effectiveness (RBE) values and the choice of w(R) values were not elaborated in detail. Since 1990, there have been substantial developments in biological and dosimetric knowledge that justify a re-appraisal of w(R) values and how they may be derived. This re-appraisal is the principal objective of the present report. The report discusses in some detail the values of RBE with regard to stochastic effects, which are central to the selection of w(R) and Q(L). Those factors and the dose-equivalent quantities are restricted to the dose range of interest to radiation protection, i.e. to the general magnitude of the dose limits. In special circumstances where one deals with higher doses that can cause deterministic effects, the relevant RBE values are applied to obtain a weighted dose. The question of RBE values for deterministic effects and how they should be used is also treated in the report, but it is an issue that will demand further investigations. This report is one of a set of documents being developed by ICRP Committees in order to advise the ICRP on the formulation of its next Recommendations for Radiological Protection. Thus, while the report suggests some future modifications, the w(R) values given in the 1990 recommendations are still valid at this time. The report provides a scientific background and suggests how the ICRP might proceed with the derivation of w(R) values ahead of its forthcoming recommendations.

Proton beam radiosurgery for vestibular schwannoma: tumor control and cranial nerve toxicity

OBJECTIVE

We sought to determine the tumor control rate and cranial nerve function outcomes in patients with vestibular schwannomas who were treated with proton beam stereotactic radiosurgery.

METHODS

Between November 1992 and August 2000, 88 patients with vestibular schwannomas were treated at the Harvard Cyclotron Laboratory with proton beam stereotactic radiosurgery in which two to four convergent fixed beams of 160-MeV protons were applied. The median transverse diameter was 16 mm (range, 2.5-35 mm), and the median tumor volume was 1.4 cm(3) (range, 0.1-15.9 cm(3)). Surgical resection had been performed previously in 15 patients (17%). Facial nerve function (House-Brackmann Grade 1) and trigeminal nerve function were normal in 79 patients (89.8%). Eight patients (9%) had good or excellent hearing (Gardner-Robertson [GR] Grade 1), and 13 patients (15%) had serviceable hearing (GR Grade 2). A median dose of 12 cobalt Gray equivalents (range, 10-18 cobalt Gray equivalents) was prescribed to the 70 to 108% isodose lines (median, 70%). The median follow-up period was 38.7 months (range, 12-102.6 mo).

RESULTS

The actuarial 2- and 5-year tumor control rates were 95.3% (95% confidence interval [CI], 90.9-99.9%) and 93.6% (95% CI, 88.3-99.3%). Salvage radiosurgery was performed in one patient 32.5 months after treatment, and a craniotomy was required 19.1 months after treatment in another patient with hemorrhage in the vicinity of a stable tumor. Three patients (3.4%) underwent shunting for hydrocephalus, and a subsequent partial resection was performed in one of these patients. The actuarial 5-year cumulative radiological reduction rate was 94.7% (95% CI, 81.2-98.3%). Of the 21 patients (24%) with functional hearing (GR Grade 1 or 2), 7 (33.3%) retained serviceable hearing ability (GR Grade 2). Actuarial 5-year normal facial and trigeminal nerve function preservation rates were 91.1% (95% CI, 85-97.6%) and 89.4% (95% CI, 82-96.7%). Univariate analysis revealed that prescribed dose (P = 0.005), maximum dose (P = 0.006), and the inhomogeneity coefficient (P = 0.03) were associated with a significant risk of long-term facial neuropathy. No other cranial nerve deficits or cancer relapses were observed.

CONCLUSION

Proton beam stereotactic radiosurgery has been shown to be an effective means of tumor control. A high radiological response rate was observed. Excellent facial and trigeminal nerve function preservation rates were achieved. A reduced prescribed dose is associated with a significant decrease in facial neuropathy.

Relative biological effectiveness (RBE) values for proton beam therapy

PURPOSE

Clinical proton beam therapy has been based on the use of a generic relative biological effectiveness (RBE) of 1.0 or 1.1, since the available evidence has been interpreted as indicating that the magnitude of RBE variation with treatment parameters is small relative to our abilities to determine RBEs. As substantial clinical experience and additional experimental determinations of RBE have accumulated and the number of proton radiation therapy centers is projected to increase, it is appropriate to reassess the rationale for the continued use of a generic RBE and for that RBE to be 1.0-1.1.

METHODS AND MATERIALS

Results of experimental determinations of RBE of in vitro and in vivo systems are examined, and then several of the considerations critical to a decision to move from a generic to tissue-, dose/fraction-, and LET-specific RBE values are assessed. The impact of an error in the value assigned to RBE on normal tissue complication probability (NTCP) is discussed. The incidence of major morbidity in proton-treated patients at Massachusetts General Hospital (MGH) for malignant tumors of the skull base and of the prostate is reviewed. This is followed by an analysis of the magnitude of the experimental effort to exclude an error in RBE of >or=10% using in vivo systems.

RESULTS

The published RBE values, using colony formation as the measure of cell survival, from in vitro studies indicate a substantial spread between the diverse cell lines. The average value at mid SOBP (Spread Out Bragg Peak) over all dose levels is approximately 1.2, ranging from 0.9 to 2.1. The average RBE value at mid SOBP in vivo is approximately 1.1, ranging from 0.7 to 1.6. Overall, both in vitro and in vivo data indicate a statistically significant increase in RBE for lower doses per fraction, which is much smaller for in vivo systems. There is agreement that there is a measurable increase in RBE over the terminal few millimeters of the SOBP, which results in an extension of the bioeffective range of the beam in the range of 1-2 mm. There is no published report to indicate that the RBE of 1.1 is low. However, a substantial proportion of patients treated at approximately 2 cobalt Gray equivalent (CGE)/fraction 5 or more years ago were treated by a combination of both proton and photon beams. Were the RBE to be erroneously underestimated by approximately 10%, the increase in complication frequency would be quite serious were the complication incidence for the reference treatment >or=3% and the slope of the dose response curves steep, e.g., a gamma(50) approximately 4. To exclude >or=1.2 as the correct RBE for a specific condition or tissue at the 95% confidence limit would require relatively large and multiple assays.

CONCLUSIONS

At present, there is too much uncertainty in the RBE value for any human tissue to propose RBE values specific for tissue, dose/fraction, proton energy, etc. The experimental in vivo and clinical data indicate that continued employment of a generic RBE value and for that value to be 1.1 is reasonable. However, there is a local "hot region" over the terminal few millimeters of the SOBP and an extension of the biologically effective range. This needs to be considered in treatment planning, particularly for single field plans or for an end of range in or close to a critical structure. There is a clear need for prospective assessments of normal tissue reactions in proton irradiated patients and determinations of RBE values for several late responding tissues in laboratory animal systems, especially as a function of dose/fraction in the range of 1-4 Gy.

Nuclear interactions in proton therapy: dose and relative biological effect distributions originating from primary and secondary particles

The dose distribution delivered in charged particle therapy is due to both primary and secondary particles. The secondaries, originating from non-elastic nuclear interactions, are of interest for three reasons. First, if fast Monte Carlo treatment planning is envisaged, the question arises whether all nuclear interaction products deliver a significant contribution to the total dose and, hence, need to be tracked. Second, there could be an enhanced relative biological effectiveness (RBE) due to low energy and/or heavy secondaries. Third, neutrons originating from nuclear interactions may deliver dose outside the target volume. The particle yield from different nuclear interaction channels as a function of proton penetration depth was studied theoretically for different proton beam energies. Three-dimensional dose distributions from primary and secondary particles were simulated for an unmodulated 160 MeV proton beam with and without including a slice of bone material and for a spread-out Bragg peak (SOBP) of 3 x 3 x 3 cm3 in water. Secondary protons deliver up to 10% of the total dose proximal to the Bragg peak of an unmodulated proton beam and they affect the flatness of the SOBP. Furthermore, they cause a dose build-up due to forward emission of secondary particles from nuclear interactions. The dose deposited by d, t, 3He and alpha-particles was found to contribute less than 0.1% of the total dose. The dose distal to the target volume caused by liberated neutrons was studied for four proton beam energies in the range of 160-250 MeV and found to be below 0.05% (2 cm distal to SOBP) of the prescribed target dose for a 3 x 3 x 3 cm3 target. RBE values relative to 60Co were calculated proximal to and within the SOBP. The RBE proximal to the Bragg peak (100% dose) is influenced by secondary particles (mainly protons and a-particles) with a strong dose dependency resulting in RBE values up to 1.2 (2 Gy; inactivation of V79). Depending on the endpoint considered, secondary particles cause a shift in RBE by up to 8% at 2 Gy. In contrast, the RBE in the Bragg peak is almost entirely determined by primary protons due to a decreasing secondary particle fluence with depth. RBE values up to 1.3 (2 Gy; inactivation of V79) at 1 cm distal to the Bragg peak maximum were found. The inactivations of human skin fibroblasts and mouse lymphoma cells were also analysed and reveal a substantial tissue dependency of the total RBE. The outcome of this study shows that elevated RBE values occur not only at the distal edge of the SOBP. Although the variations are modest, and in most cases might have no observable clinical effect, they might have to be considered in certain treatment situations. The biological effect downstream of the target caused by neutrons was analysed using a radiation quality factor of 10. The biological dose was found to be below 0.5% of the prescribed target dose (for a 3 x 3 x 3 cm3 SOBP) but depends on the size of the SOBP. This dose should not be significant with respect to late effects, e.g. cancer induction.

Dose and dose rate effects of whole-body proton irradiation on leukocyte populations and lymphoid organs: part I

The goal of part I of this study was to evaluate the effects of whole-body proton irradiation on lymphoid organs and specific leukocyte populations. C57BL/6 mice were exposed to the entry region of the proton Bragg curve to total doses of 0.5 gray (Gy), 1.5 Gy, and 3.0 Gy, each delivered at a low dose rate (LDR) of 1 cGy/min and high dose rate (HDR) of 80 cGy/min. Non-irradiated and 3 Gy HDR gamma-irradiated groups were included as controls. At 4 days post-irradiation, highly significant radiation dose-dependent reductions were observed in the mass of both lymphoid organs and the numbers of leukocytes and T (CD3(+)), T helper (CD3(+)/CD4(+)), T cytotoxic (CD3(+)/CD8(+)), and B (CD19(+)) cells in both blood and spleen. A less pronounced dose effect was noted for natural killer (NK1.1(+) NK) cells in spleen. Monocyte, but not granulocyte, counts in blood were highly dose-dependent. The numbers for each population generally tended to be lower with HDR than with LDR radiation; a significant dose rate effect was found in the percentages of T and B cells, monocytes, and granulocytes and in CD4(+):CD8(+) ratios. These data indicate that mononuclear cell response to the entry region of the proton Bragg curve is highly dependent upon the total dose and that dose rate effects are evident with some cell types. Results from gamma- and proton-irradiated groups (both at 3 Gy HDR) were similar, although proton-irradiation gave consistently lower values in some measurements.

Techniques for precision irradiation of the lateral half of the rat cervical spinal cord using 150 MeV protons [corrected]

Techniques for high precision irradiation experiments with protons, to investigate the volume dependence of the tolerance dose of the rat cervical spinal cord are described. In the present study, 50% of the lateral cross section of the spinal cord was irradiated. The diameter of the cross section of this part of the rat spinal cord is at maximum 3.5 mm. Therefore, a dedicated procedure was developed to comply with the needs for a very high positioning accuracy and high spatial resolution dosimetry. By using 150 MeV protons a steep dose gradient (20-80% = 1 mm) in the centre of the spinal cord was achieved. This yields a good dose contrast between the left and right halves of the cord. A home-made digital x-ray imager with a pixel resolution of 0.18 mm/pixel was used for position verification of the spinal cord. A positioning accuracy of 0.09 mm was obtained by using information of multiple pixels. The average position stability during the irradiation was found to be 0.08 mm (1 SD) without significant systematic deviations. Profiles of the dose distribution were measured with a 2D dosimetry system consisting of a scintillating screen and a CCD camera. Dose volume histograms of the whole spinal cord as well as separately of the white and grey matters were calculated using MRI imaging of the cross section of the rat cervical spinal cord. From the irradiation of 20 animals a dose-response curve has been established. MRI showed radiation-induced damage at the high dose side of the spinal cord. Analysis of the preliminary dose-response data shows a significant dose-volume effect. With the described procedure and equipment it is possible to perform high precision irradiations on selected parts of the spinal cord.

Collimator scatter and 2D dosimetry in small proton beams

Monte Carlo simulations have been performed to determine the influence of collimator-scattered protons from a 150 MeV proton beam on the dose distribution behind a collimator. Slit-shaped collimators with apertures between 2 and 20 mm have been simulated. The Monte Carlo code GEANT 3.21 has been validated against one-dimensional dose measurements with a scintillating screen, observed by a CCD camera. In order to account for the effects of the spatial response of the CCD/scintillator system, the line-spread function was determined by comparison with measurements made with a diamond detector. The line-spread function of the CCD/scintillator system is described by a Gaussian distribution with a standard deviation of 0.22 mm. The Monte Carlo simulations show that protons that hit the collimator on the entrance face and leave it through the wall of the aperture make the largest scatter contribution. Scatter on air is the major contribution to the extent of the penumbra. From the energy spectra it is derived that protons with a relative biological effectiveness greater than 1 cause at most 1% more damage in tissue than what would be expected from the physical dose.

Monte Carlo simulation of fast neutron spectra: mean lineal energy estimation with an effectiveness function and correlation to RBE

PURPOSE

Intercomparisons of radiotherapy trials conducted at different fast neutron facilities are complicated by the dependence of the relative biologic effectiveness (RBE) of the different beams on the fast neutrons spectra. To obtain a better understanding of the influence of neutron energy on radiation quality, Monte Carlo simulations were performed to calculate fast neutron (FN) spectra at different irradiation positions. To allow for comparisons with experimental data, the positions were chosen to be the same as that used by other investigators to obtain microdosimetry readings and radiobiological data.

METHODS AND MATERIALS

The primary neutron yield for beryllium targets bombarded with protons at the National Accelerator Center, Louvain, Nice, and Orleans facilities were calculated using the FLUKA code. Neutron transport simulations were performed with MCNP-4A, giving FN spectra for various phantom depths, hardening filter thickness, and field sizes. Using an effectiveness function, FN energy groups were correlated with mean lineal energies (y*-values) obtained experimentally by other workers.

RESULTS

Calculations confirm earlier measurements that a decrease in beam quality by a hardening filter is the result of a reduction in the low-energy neutron component, i.e., neutrons below 3 MeV. Variations in RBE due to changes in field size and different phantom depths could also be explained by variations of neutrons with energies between 3-15 MeV. The effectiveness function allows one to calculate changes in y* observed for the NAC beam with great accuracy (R(2) = 0.99, p < 0.0001). Also, when this function is applied to beams with different neutron energies, y* calculated values show a very significant correlation with measured RBE values (R(2) = 0.98, p < 0.0001).

CONCLUSION

The effectiveness function appears to be suitable to predict changes in y*-values and variations in RBE, using FN spectra simulated for various neutron therapy facilities.

Estimation of optimum dose per fraction for high LET radiations: implications for proton radiotherapy

PURPOSE

For high linear energy transfer (LET) radiations, the relative biologic effect (RBE) changes with dose per fraction. Methods for calculating the optimum dose per fraction for high LET radiations should therefore include an allowance for RBE.

METHODS AND MATERIALS

The linear-quadratic (LQ) model, and the associated biologic effective dose (BED) concept, has previously been extended to incorporate the RBE effect. Differential calculus is now used to calculate the optimum dose per fraction (z), when high-LET radiation is used, which is given by the solution for z of (g - LATE(alpha/beta)(L)/TUM(alpha/beta)L . RBE(M( z(2))) - 2 . f . g . K . z - (LATE)(alpha/beta)(L) . f . K . RBE(M) = 0 where g is the normal tissue sparing factor, RBE(M) is the maximum RBE value, f the mean interfraction interval, K the daily low-LET BED equivalent dose for clonogen repopulation and (LATE)(alpha/beta)(L) and (TUM)(alpha/beta)(L) are the respective late reacting normal tissue and tumor fractionation sensitivities for low-LET radiation.

RESULTS

The optimum dose per fraction for proton therapy is generally lower than that calculated for photons but there is not a simple relationship between the magnitude of the reduction and the assumed value of RBE(M.) Thus(,) generic values of RBE(M) cannot always be used in such calculations. In some cases, where tumor alpha/beta ratios are low (around 5-6 Gy) and where there is good normal tissue sparing, the optimum dose per fraction is relatively large, typically 4-8 Gy.

CONCLUSION

BED equations that include the RBE parameter, together with low-LET alpha/beta ratios and repopulation dose equivalents, constitute a rational model of high-LET radiotherapy. In the case of proton beam therapy, a wide range of optimum dose per fraction is predicted.