Relative biological effectiveness of oxygen ion beams in the rat spinal cord: Dependence on linear energy transfer and dose and comparison with model predictions.

Background and purpose: Ion beams exhibit an increased relative biological effectiveness (RBE) with respect to photons. This study determined the RBE of oxygen ion beams as a function of linear energy transfer (LET) and dose in the rat spinal cord. Materials and methods: The spinal cord of rats was irradiated at four different positions of a 6 cm spread-out Bragg-peak (LET: 26, 66, 98 and 141 keV/µm) using increasing levels of single and split oxygen ion doses. Dose-response curves were established for the endpoint paresis grade II and based on ED50 (dose at 50 % effect probability), the RBE was determined and compared to model predictions. Results: When LET increased from 26 to 98 keV/µm, ED50 decreased from 17.2 ± 0.3 Gy to 13.5 ± 0.4 Gy for single and from 21.7 ± 0.4 Gy to 15.5 ± 0.5 Gy for split doses, however, at 141 keV/µm, ED50 rose again to 15.8 ± 0.4 Gy and 17.2 ± 0.4 Gy, respectively. As a result, the RBE increased from 1.43 ± 0.05 to 1.82 ± 0.08 (single dose) and from 1.58 ± 0.04 to 2.21 ± 0.08 (split dose), respectively, before declining again to 1.56 ± 0.06 for single and 1.99 ± 0.06 for split doses at the highest LET. Deviations from RBE-predictions were model-dependent. Conclusion: This study established first RBE data for the late reacting central nervous system after single and split doses of oxygen ions. The data was used to validate the RBE-dependence on LET and dose of three RBE-models. This study extends the existing data base for protons, helium and carbon ions and provides important information for future patient treatments with oxygen ions.

Evaluation of Helium Ion Radiotherapy in Combination with Gemcitabine in Pancreatic Cancer In Vitro.

BACKGROUND: Pancreatic cancer is one of the most aggressive and lethal cancers. New treatment strategies are highly warranted. Particle radiotherapy could offer a way to overcome the radioresistant nature of pancreatic cancer because of its biological and physical characteristics. Within particles, helium ions represent an attractive therapy option to achieve the highest possible conformity while at the same time protecting the surrounding normal tissue. The aim of this study was to evaluate the cytotoxic efficacy of helium ion irradiation in pancreatic cancer in vitro. METHODS: Human pancreatic cancer cell lines AsPC-1, BxPC-3 and Panc-1 were irradiated with photons and helium ions at various doses and treated with gemcitabine. Photon irradiation was performed with a biological cabin X-ray irradiator, and helium ion irradiation was performed with a spread-out Bragg peak using the raster scanning technique at the Heidelberg Ion Beam Therapy Center (HIT). The cytotoxic effect on pancreatic cancer cells was measured with clonogenic survival. The survival curves were compared to the predicted curves that were calculated via the modified microdosimetric kinetic model (mMKM). RESULTS: The experimental relative biological effectiveness (RBE) of helium ion irradiation ranged from 1.0 to 1.7. The predicted survival curves obtained via mMKM calculations matched the experimental survival curves. Mainly additive cytotoxic effects were observed for the cell lines AsPC-1, BxPC-3 and Panc-1. CONCLUSION: Our results demonstrate the cytotoxic efficacy of helium ion radiotherapy in pancreatic cancer in vitro as well as the capability of mMKM calculation and its value for biological plan optimization in helium ion therapy for pancreatic cancer. A combined treatment of helium irradiation and chemotherapy with gemcitabine leads to mainly additive cytotoxic effects in pancreatic cancer cell lines. The data generated in this study may serve as the radiobiological basis for future experimental and clinical works using helium ion radiotherapy in pancreatic cancer treatment.

Effects of cellular radioresponse on therapeutic helium-, carbon-, oxygen-, and neon-ion beams: a simulation study.

Objective. Helium, oxygen, and neon ions in addition to carbon ions will be used for hypofractionated multi-ion therapy to maximize the therapeutic effectiveness of charged-particle therapy. To use new ions in cancer treatments based on the dose-fractionation protocols established in carbon-ion therapy, this study examined the cell-line-specific radioresponse to therapeutic helium-, oxygen-, and neon-ion beams within wide dose ranges.Approach. Response of cells to ions was described by the stochastic microdosimetric kinetic model. First, simulations were made for the irradiation of one-field spread-out Bragg peak beams in water with helium, carbon, oxygen, and neon ions to achieve uniform survival fractions at 37%, 10%, and 1% for human salivary gland tumor (HSG) cells, the reference cell line for the Japanese relative biological effectiveness weighted dose system, within the target region defined at depths from 90 to 150 mm. The HSG cells were then replaced by other cell lines with different radioresponses to evaluate differences in the biological dose distributions of each ion beam with respect to those of carbon-ion beams.Main results. For oxygen- and neon-ion beams, the biological dose distributions within the target region were almost equivalent to those of carbon-ion beams, differing by less than 5% in most cases. In contrast, for helium-ion beams, the biological dose distributions within the target region were largely different from those of carbon-ion beams, more than 10% in several cases.Significance.From the standpoint of tumor control evaluated by the clonogenic cell survival, this study suggests that the dose-fractionation protocols established in carbon-ion therapy could be reasonably applied to oxygen- and neon-ion beams while some modifications in dose prescription would be needed when the protocols are applied to helium-ion beams. This study bridges the gap between carbon-ion therapy and hypofractionated multi-ion therapy.

Modeling for predicting survival fraction of cells after ultra-high dose rate irradiation.

Objective. FLASH radiotherapy (FLASH-RT) with ultra-high dose rate (UHDR) irradiation (i.e. > 40 Gy s-1) spares the function of normal tissues while preserving antitumor efficacy, known as the FLASH effect. The biological effects after conventional dose rate-radiotherapy (CONV-RT) with ≤0.1 Gy s-1have been well modeled by considering microdosimetry and DNA repair processes, meanwhile modeling of radiosensitivities under UHDR irradiation is insufficient. Here, we developed anintegrated microdosimetric-kinetic(IMK)model for UHDR-irradiationenabling the prediction of surviving fraction after UHDR irradiation.Approach.TheIMK model for UHDR-irradiationconsiders the initial DNA damage yields by the modification of indirect effects under UHDR compared to CONV dose rate. The developed model is based on the linear-quadratic (LQ) nature with the dose and dose square coefficients, considering the reduction of DNA damage yields as a function of dose rate.Main results.The estimate by the developed model could successfully reproduce thein vitroexperimental dose-response curve for various cell line types and dose rates.Significance.The developed model would be useful for predicting the biological effects under the UHDR irradiation.

Biological dosimetric impact of dose-delivery time for hypoxic tumour with modified microdosimetric kinetic model.

Background: An improved microdosimetric kinetic model (MKM) can address radiobiological effects with prolonged delivery times. However, these do not consider the effects of oxygen. The current study aimed to evaluate the biological dosimetric effects associated with the dose delivery time in hypoxic tumours with improved MKM for photon radiation therapy. Materials and methods: Cell survival was measured under anoxic, hypoxic, and oxic conditions using the Monte Carlo code PHITS. The effect of the dose rate of 0.5-24 Gy/min for the biological dose (Dbio) was estimated using the microdosimetric kinetic model. The dose per fraction and pressure of O2 (pO2) in the tumour varied from 2 to 20 Gy and from 0.01 to 5.0% pO2, respectively. Results: The ratio of the Dbio at 1.0-24 Gy/min to that at 0.5 Gy/min (RDR) was higher at higher doses. The maximum RDR was 1.09 at 1.0 Gy/min, 1.12 at 12 Gy/min, and 1.13 at 24 Gy/min. The ratio of the Dbio at 0.01-2.0% of pO2 to that at 5.0% of pO2 (Roxy) was within 0.1 for 2-20 Gy of physical dose. The maximum Roxy was 0.42 at 0.01% pO2, 0.76 at 0.4% pO2, 0.89 at 1% pO2, and 0.96 at 2% pO2. Conclusion: Our proposed model can estimate the cell killing and biological dose under hypoxia in a clinical and realistic patient. A shorter dose-delivery time with a higher oxygen distribution increased the radiobiological effect. It was more effective at higher doses per fraction than at lower doses.

A systematic analysis of the particle irradiation data ensemble in the key of the microdosimetric kinetic model: Should clonogenic data be used for clinical relative biological effectiveness?

PURPOSE: To perform a systematic analysis of the Particle Irradiation Data Ensemble (PIDE) database for clonogenic survival assays in the context of the Microdosimetric Kinetic Model (MKM). METHODS AND MATERIAL: Our study used data from the PIDE database containing data on various cell lines and radiation types. Two main parameters of the MKM were determined experiment-wise: the domain radius, which accounts for the increase of the linear parameter as a function of LET or lineal energy, and the nucleus radius, which accounts for the overkilling effect at LET high enough. We used experiments with LET less and more than 75 keV/µm to determine domain and nucleus radius, respectively. Experiments with cells in asynchronous phase of the cell cycle and monoenergetic beams were considered, and data from 294 out of 461 available experiments with protons, alpha, and carbon beams were used. RESULTS: Domain and nucleus radii were determined for 32 cell lines as the median among cell-specific experiments after filtering experiments using protons, α-particles, and carbon ions, including 28 human cells and 12 rodent cells. The median values found for domain radii were 380 nm for normal human cells, 390 nm for tumor human cells, 295 nm for normal rodent cells, and 525 nm for tumor rodent cells (only one experiment with rodent tumor cells) with large variability across cell lines and across experiments on each cell line. CONCLUSIONS: Large inter-experiment variabilities were found for the same cell lines, based on enormous experimental uncertainties and different experimental conditions. Our analysis raises questions about how convenient is to use clonogenic data to feed RBE models to be utilized in the clinical practice in particle therapy.

Extension of matRad with a modified microdosimetric kinetic model for carbon ion treatment planning: Comparison with Monte Carlo calculation.

BACKGROUND: Treatment planning is essential for in silico particle therapy studies. matRad is an open-source research treatment planning system (TPS) based on the local effect model, which is a type of relative biological effectiveness (RBE) model. PURPOSE: This study aims to implement a microdosimetric kinetic model (MKM) in matRad and develop an automation algorithm for Monte Carlo (MC) dose recalculation using the TOPAS code. In addition, we provide the developed MKM extension as open-source tool for users. METHODS: Carbon beam data were generated using TOPAS MC pencil beam irradiation. We parameterized the TOPAS MC beam data with a double-Gaussian fit and modeled the integral depth doses and lateral spot profiles in the range of 100-430 MeV/u. To implement the MKM, the specific energy data table for Z = 1-6 and integrated depth-specific energy data were acquired based on the Kiefer-Chatterjee track structure and TOPAS MC simulation, respectively. Generic data were integrated into matRad, and treatment planning was performed based on these data. The optimized plan parameters were automatically converted into MC simulation input. Finally, the matRad TPS and TOPAS MC simulations were compared using the RBE-weighted dose calculation results. A comparison was made for three geometries: homogeneous water phantom, inhomogeneous phantom, and patient. RESULTS: The RBE-weighted dose (DRBE ) distribution agreed with TOPAS MC within 1.8% for all target sizes for the homogeneous phantom. For the inhomogeneous phantom, the relative difference in the range of 80% of the prescription dose in the distal fall-off region (R80) between the matRad TPS and TOPAS MC was 0.6% (1.1 mm). DRBE between the TPS and the MC was within 4.0%. In the patient case, the difference in the dose-volume histogram parameters for the target volume between the TPS and the MC was less than 2.7%. The relative difference in R80 was 0.7% (1.2 mm). CONCLUSIONS: The MKM was successfully implemented in matRad TPS, and the RBE-weighted dose was comparable to that of TOPAS MC. The MKM-implemented matRad was released as an open-source tool. Further investigations with MC simulations can be conducted using this tool, providing a good option for carbon ion research.

Formation of spread-out Bragg peak for helium-ion beam using microdosimetric kinetic model.

PURPOSE: To evaluate the applicability of microdosimetric kinetic model (MKM) to helium-ion therapy by forming a spread-out Bragg peak (SOBP) of a helium-ion beam using the MKM developed for carbon-ion radiotherapy and confirming the predictions in biological experiments. METHODS: Using a ridge filter, a 90-mm wide SOBP for a 210 MeV/u helium-ion beam was created in a broad beam delivery system. The ridge filter was designed such that a uniform biological response was achieved with a cell survival rate of 7% over the SOBP region. Biological experiments were then performed using the SOBP beam in a human salivary gland (HSG) cell line to measure the cell survival rates. RESULTS: The biological responses were uniform in the SOBP region, as expected by the MKM; however, the mean of the measured cell survival rates was (11.2 ± 0.6) % in the SOBP region, which was 60% higher than the designed rate. When investigating the biological parameters of the HSG cell line used in the experiments, we found that they were altered slightly from the MKM parameters used for carbon-ion radiotherapy. The new ß parameter reproduced the measured survival rates within 6.5% in the SOBP region. CONCLUSION: We produced biologically uniform SOBP using MKM for carbon-ion radiotherapy. The measured survival rates in the SOBP region were higher than expected, and the survival rates were reproduced by modifying the MKM parameter. This study was limited to one SOBP, and further investigations are required to prove that MKM is generally applicable to helium-ion radiotherapy.

Influence of selection of domain shape on parameters of microdosimetric kinetic model / 中华放射医学与防护杂志

Objective:To calculate the single-event dose-averaged specific energy of particles delivered in spherical domains based on the track structure model and using triple integration, and to investigate the influence of the domain shape on the key model parameters of microdosimetric kinetic model (MKM) and its corresponding physical significance.Methods:The domains are assumed to be cylinders and spheres, respectively. With α 0, domain radius, rd, and nucleus radius, Rn, as undetermined coefficients, the nuclear charge numbers, kinetic energies and their corresponding LETs of three kinds of charged particles ( 3He, 12C, 20Ne) as independent variables, D10 as dependent variable, the mean value of squared residuals, J2, between the D10 calculated values and D10 experimental values as the optimization objective, the final fitting values of the above undetermined coefficients of human salivary gland (HSG) cells and Chinese hamster lung (V79) cells obtained after iteration by the robust least square method are the optimal model parameter values of MKM. Results:For HSG cells, cylindrical domain: α 0=0.073/Gy, rd=0.29 μm, Rn=4.1 μm, J2=0.039 7 Gy 2; spherical domain: α 0=0.023/Gy, rd=0.29 μm, Rn=4.4 μm, J2=0.039 3 Gy 2; For V79 cells, cylindrical domain: α 0=0.114/Gy, rd=0.25 μm, Rn=3.8 μm, J2=0.097 4 Gy 2; spherical domain: α 0=0.095/Gy, rd=0.26 μm, Rn=4.1 μm, J2=0.096 9 Gy 2. Conclusions:For the same type of cells, cylindrical and spherical domains were selected respectively, and there are significant differences in MKM parameters obtained by fitting. The fitting values of the domain radius, rd of the two shapes of domains show no significant difference, while the fitting values of α0 of spherical domains are smaller than those of cylindrical domains, the fitting values of nucleus radius, Rn, of spherical domain are larger than those of cylindrical domains, closer to the nucleus radius observed by fluorescence microscopy. In the low LET (<20 keV/μm) region, D10 calculated according to the parameters of the two different shapes of domains are different, so the selection of the domain shape will cause differences in the relative biological effectiveness(RBE) calculation of proton in the region near Bragg peak.

Modelling the HPRT-gene mutation induction of particle beams: systematicin vitrodata collection, analysis and microdosimetric kinetic model implementation.

Objective. Since the early years, particle therapy treatments have been associated with concerns for late toxicities, especially secondary cancer risk (SCR). Nowadays, this concern is related to patients for whom long-term survival is expected (e.g. breast cancer, lymphoma, paediatrics). In the aim to contribute to this research, we present a dedicated statistical and modelling analysis aiming at improving our understanding of the RBE for mutation induction (RBEM˜) for different particle species.Approach. We built a new database based on a systematic collection of RBE data for mutation assays of the gene encoding for the purine salvage enzyme hypoxanthine-guanine phosphoribosyltransferase from literature (105 entries, distributed among 3 cell lines and 16 particle species). The data were employed to perform statistical and modelling analysis. For the latter, we adapted the microdosimetric kinetic model (MKM) to describe the mutagenesis in analogy to lethal lesion induction.Main results. Correlation analysis between RBE for survival (RBES) andRBEM˜reveals significant correlation between these two quantities (ρ= 0.86,p< 0.05). The correlation gets stronger when looking at subsets of data based on cell line and particle species. We also show that the MKM can be successfully employed to describeRBEM˜,obtaining comparably good agreement with the experimental data. Remarkably, to improve the agreement with experimental data the MKM requires, consistently in all the analysed cases, a reduced domain size for the description of mutation induction compared to that adopted for survival.Significance. We were able to show that RBESandRBEM˜are strongly related quantities. We also showed for the first time that the MKM could be successfully applied to the description of mutation induction, representing an endpoint different from the more traditional cell killing. In analogy to the RBES,RBEM˜can be implemented into treatment planning system evaluations.

Development of modified microdosimetric kinetic model for relative biological effectiveness in proton therapy.

To predict the biological effects of ionising radiation, the quantity of biological dose is introduced instead of the physical absorbed dose. In proton therapy, a constant relative biological effectiveness (RBE) of 1.1 is usually applied clinically as recommended by the International Commission of Radiation Units and Measurements. This study presents a new model, based on the modified microdosimetric kinetic model (MMKM), for calculating variable RBE values based on experimental data on the induction of DNA double-strand breaks (DSBs) within cells. The MMKM was proposed based on experimental data for the yield of DSBs in mammalian cells, which allows modification of the yield of primary lesions in the MKM. In this approach, a unique function named f(LET), which describes the relation between RBE and linear energy transfer (LET), was considered for charged particles. In the presented model (DMMKM), the MMKM approach was developed further by considering different f(LET)s for different relevant ions involved in energy deposition events in proton therapy. Although experimental data represent the dependence of the yield of primary lesions on the ion species, the DSB yield (assumed as the main primary lesion) is assumed independent of the ion species in the MMKM. In the DMMKM, by considering the yield of primary lesions as a function of the ion species, the α and ß values are in better agreement with the experimental data as compared to those of the MKM and MMKM approaches. The biological dose in the DMMKM is predicted to be lower than that in the MMKM. Further, in the proposed model, the variation of the ß parameter is higher than the constant value assumed in the MKM, at the distal end of the spread-out Bragg peak (SOBP). Moreover, the level of cell death estimated by the MMKM at the SOBP region is higher than that obtained based on the DMMKM. It is concluded that considering modified f(LET)s in the model developed here is more consistent with experimental results than when MMKM and MKM approaches are considered. The DMMKM examines the biological effects with full detail and will, therefore, be effective in improving proton therapy.

Relative biological effectiveness of single and split helium ion doses in the rat spinal cord increases strongly with linear energy transfer.

BACKGROUND AND PURPOSE: Determination of the relative biological effectiveness (RBE) of helium ions as a function of linear energy transfer (LET) for single and split doses using the rat cervical spinal cord as model system for late-responding normal tissue. MATERIAL AND METHODS: The rat cervical spinal cord was irradiated at four different positions within a 6 cm spread-out Bragg-peak (SOBP) (LET 2.9, 9.4, 14.4 and 20.7 keV/µm) using increasing levels of single or split doses of helium ions. Dose-response curves were determined and based on TD50-values (dose at 50% effect probability using paresis II as endpoint), RBE-values were derived for the endpoint of radiation-induced myelopathy. RESULTS: With increasing LET, RBE-values increased from 1.13 ± 0.04 to 1.42 ± 0.05 (single dose) and 1.12 ± 0.03 to 1.50 ± 0.04 (split doses) as TD50-values decreased from 21.7 ± 0.3 Gy to 17.3 ± 0.3 Gy (single dose) and 30.6 ± 0.3 Gy to 22.9 ± 0.3 Gy (split doses), respectively. RBE-models (LEM I and IV, mMKM) deviated differently for single and split doses but described the RBE variation in the high-LET region sufficiently accurate. CONCLUSION: This study established the LET-dependence of the RBE for late effects in the central nervous system after single and split doses of helium ions. The results extend the existing database for protons and carbon ions and allow systematic testing of RBE-models. While the RBE-values of helium were generally lower than for carbon ions, the increase at the distal edge of the Bragg-peak was larger than for protons, making detailed RBE-modeling necessary.

Brainstem NTCP and Dose Constraints for Carbon Ion RT-Application and Translation From Japanese to European RBE-Weighted Dose.

BACKGROUND AND PURPOSE: The Italian National Center of Oncological Hadrontherapy (CNAO) has applied dose constraints for carbon ion RT (CIRT) as defined by Japan's National Institute of Radiological Sciences (NIRS). However, these institutions use different models to predict the relative biological effectiveness (RBE). CNAO applies the Local Effect Model I (LEM I), which in most clinical situations predicts higher RBE than NIRS's Microdosimetric Kinetic Model (MKM). Equal constraints therefore become more restrictive at CNAO. Tolerance doses for the brainstem have not been validated for LEM I-weighted dose (D LEM I). However, brainstem constraints and a Normal Tissue Complication Probability (NTCP) model were recently reported for MKM-weighted dose (D MKM), showing that a constraint relaxation to D MKM|0.7 cm3 <30 Gy (RBE) and D MKM|0.1 cm3 <40 Gy (RBE) was feasible. The aim of this work was to evaluate the brainstem NTCP associated with CNAO's current clinical practice and to propose new brainstem constraints for LEM I-optimized CIRT at CNAO. MATERIAL AND METHODS: We reproduced the absorbed dose of 30 representative patient treatment plans from CNAO. Subsequently, we calculated both D LEM I and D MKM, and the relationship between D MKM and D LEM I for various brainstem dose metrics was analyzed. Furthermore, the NTCP model developed for D MKM was applied to estimate the NTCPs of the delivered plans. RESULTS: The translation of CNAO treatment plans to D MKM confirmed that the former CNAO constraints were conservative compared with D MKM constraints. Estimated NTCPs were 0% for all but one case, in which the NTCP was 2%. The relationship D MKM/D LEM I could be described by a quadratic regression model which revealed that the validated D MKM constraints corresponded to D LEM I|0.7 cm3 <41 Gy (RBE) (95% CI, 38-44 Gy (RBE)) and D LEM I|0.1 cm3 <49 Gy (RBE) (95% CI, 46-52 Gy (RBE)). CONCLUSION: Our study demonstrates that RBE-weighted dose translation is of crucial importance in order to exchange experience and thus harmonize CIRT treatments globally. To mitigate uncertainties involved, we propose to use the lower bound of the 95% CI of the translation estimates, i.e., D LEM I|0.7 cm3 <38 Gy (RBE) and D LEM I|0.1 cm3 <46 Gy (RBE) as brainstem dose constraints for 16 fraction CIRT treatments optimized with LEM I.

Radiobiological effects of the interruption time with Monte Carlo Simulation on multiple fields in photon beams.

PURPOSE: The interruption time is the irradiation interruption that occurs at sites and operations such as the gantry, collimator, couch rotation, and patient setup within the field in radiotherapy. However, the radiobiological effect of prolonging the treatment time by the interruption time for tumor cells is little evaluated. We investigated the effect of the interruption time on the radiobiological effectiveness with photon beams based on a modified microdosimetric kinetic (mMK) model. METHODS: The dose-mean lineal energy yD (keV/µm) of 6-MV photon beams was calculated by the particle and heavy ion transport system (PHITS). We set the absorbed dose to 2 or 8 Gy, and the interruption time (τ) was set to 1, 3, 5, 10, 30, and 60 min. The biological parameters such as α0, ß0, and DNA repair constant rate (a + c) values were acquired from a human non-small-cell lung cancer cell line (NCI-H460) for the mMK model. We used two-field and four-field irradiation with a constant dose rate (3 Gy/min); the photon beams were paused for interruption time τ. We calculated the relative biological effectiveness (RBE) to evaluate the interruption time's effect compared with no interrupted as a reference. RESULTS: The yD of 6-MV photon beams was 2.32 (keV/µm), and there was little effect by changing the water depth (standard deviation was 0.01). The RBE with four-field irradiation for 8 Gy was decreased to 0.997, 0.975, 0.900, and 0.836 τ = 1, 10, 30, 60 min, respectively. In addition, the RBE was affected by the repair constant rate (a + c) value, the greater the decrease in RBE with the longer the interruption time when the (a + c) value was large. CONCLUSION: The ~10-min interruption of 6-MV photon beams did not significantly impact the radiobiological effectiveness, since the RBE decrease was <3%. Nevertheless, the RBE's effect on tumor cells was decreased about 30% by increasing the 60 min interruption time at 8 Gy with four-field irradiation. It is thus necessary to make the interruption time as short as possible.

Estimations of relative biological effectiveness of secondary fragments in carbon ion irradiation of water using CR-39 plastic detector and microdosimetric kinetic model.

PURPOSE: To estimate relative biological effectiveness (RBE) ascribed to secondary fragments in a lateral distribution of carbon ion irradiation. The RBE was estimated with the microdosimetric kinetic (MK) model and measured linear energy transfer (LET) obtained with CR-39 plastic detectors. METHODS: A water phantom was irradiated by a 12 C pencil beam with energy of 380 MeV/u at the Gunma University Heavy Ion Medical Center (GHMC), and CR-39 detectors were exposed to secondary fragments. Because CR-39 was insensitive to low LET, we conducted Monte Carlo simulations with Geant4 to calculate low LET particles. The spectra of low LET particles were combined with experimental spectra to calculate RBE. To estimate accuracy of RBE, we calculated RBE by changing yield of low LET particles by ± 10% and ± 40%. RESULTS: At a small angle, maximum RBE by secondary fragments was 1.3 for 10% survival fractions. RBE values of fragments gradually decreased as the angle became larger. The shape of the LET spectra in the simulation reproduced the experimental spectra, but there was a discrepancy between the simulation and experiment for the relative yield of fragments. When the yield of low LET particles was changed by ± 40%, the change in RBE was smaller than 10%. CONCLUSIONS: An RBE of 1.3 was expected for secondary fragments emitted at a small angle. Although, we observed a discrepancy in the relative yield of secondary fragments between simulation and experiment, precision of RBE was not so sensitive to the yield of low LET particles.

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.

Markov chain Monte Carlo analysis for the selection of a cell-killing model under high-dose-rate irradiation.

PURPOSE: High-dose-rate irradiation with 6 MV linac x rays is a wide-spread means to treat cancer tissue in radiotherapy. The treatment planning relies on a mathematical description of surviving fraction (SF), such as the linear-quadratic model (LQM) formula. However, even in the case of high-dose-rate treatment, the repair kinetics of DNA damage during dose-delivery time plays a function in predicting the dose-SF relation. This may call the SF model selection into question when considering the dose-delivery time or dose-rate effects (DREs) in radiotherapy and in vitro cell experiments. In this study, we demonstrate the importance of dose-delivery time at high-dose-rate irradiations used in radiotherapy by means of Bayesian estimation. METHODS: To evaluate the model selection for SF, three types of models, the LQM and two microdosimetric-kinetic models with and without DREs (MKMDR and MKM) were applied to describe in vitroSF data (our work and references). The parameters in each model were evaluated by a Markov chain Monte Carlo (MCMC) simulation. RESULTS: The MCMC analysis shows that the cell survival curve by the MKMDR fits the experimental data the best in terms of the deviance information criterion (DIC). In the fractionated regimen with 30 fractions to a total dose of 60 Gy, the final cell survival estimated by the MKMDR was higher than that by the LQM. This suggests that additional fractions are required for attaining the total dose equivalent to yield the same effect as the conventional regimen using the LQM in fractionated radiotherapy. CONCLUSIONS: Damage repair during dose-delivery time plays a key role in precisely estimating cell survival even at a high dose rate in radiotherapy. Consequently, it was suggested that the cell-killing model without repair factor during a short dose-delivery time may overestimate actual cell killing in fractionated radiotherapy.

Modeling cell survival and change in amount of DNA during protracted irradiation.

Hyper-radiosensitivity (HRS) is a well-known bioresponse under low-dose or low-dose-rate exposures. Although disorder of the DNA repair function, non-targeted effects and accumulation of cells in G2 have been experimentally observed, the mechanism for inducing HRS by long-term irradiation is still unclear. On the basis of biological experiments and a theoretical study, we have shown that change in the amount of DNA associated with accumulation of cells in G2 enhances radiosensitivity. To demonstrate continuous irradiation with 250 kVp X-rays, we adopted a fractionated regimen of 0.186 or 1.00 Gy per fraction at intervals of 1 h (i.e. 0.186 Gy/h, 1.00 Gy/h on average) to Chinese Hamster Ovary (CHO)-K1 cells. The change in the amount of DNA during irradiation was quantified by flow cytometric analysis with propidium iodide (PI). Concurrently, we attempted a theoretical evaluation of the DNA damage by using a microdosimetric-kinetic (MK) model that was modified to incorporate the change in the amount of DNA. Our experimental results showed that the fraction of the cells in G2/M phase increased by 6.7% with 0.186 Gy/h and by 22.1% with 1.00 Gy/h after the 12th irradiation. The MK model considering the change in amount of DNA during the irradiation exhibited a higher radiosensitivity at a high dose range, which could account for the experimental clonogenic survival. The theoretical results suggest that HRS in the high dose range is associated with an increase in the total amount of DNA during irradiation.

Evaluation of the cell survival curve under radiation exposure based on the kinetics of lesions in relation to dose-delivery time.

We have investigated the dose rate effects on cell damage caused by photon-beam irradiation. During a relatively long dose-delivery time with a low dose rate, lesions created in cells may undergo some reactions, such as DNA repair. In order to investigate these reactions quantitatively, we adopted the microdosimetric-kinetic (MK) model and deduced a cell surviving fraction (SF) formula for continuous irradiation. This model enabled us to estimate the SF from dose and dose rate. The parameters in the MK model were determined so as to generate the SF, and we attempted to evaluate the dose rate effects on the SF. To deduce the cell-specific parameters in the SF formula, including the dose rate, we performed a split-dose experiment and a single-dose experiment with a constant dose-delivery time (10 min) (to retain the condition for equivalent behavior of cell lesions) by means of a clonogenic assay. Then, using the MK model parameters, the SFs were reproduced for a variety of dose rates (1.0, 0.31, 0.18, 0.025 and 0.0031 Gy/min) and were compared with reported experimental data. The SF curves predicted by the MK model agreed well with the experimental data, suggesting that the dose rate effects appear in the kinetics of cell lesions during the dose-delivery time. From fitting the analysis of the model formula to the experimental data, it was shown that the MK model could illustrate the characteristics of log-SF in a rectilinear form at a high dose range with a relatively low dose rate.

Quantitative estimation of DNA damage by photon irradiation based on the microdosimetric-kinetic model.

The microdosimetric-kinetic (MK) model is one of the models that can describe the fraction of cells surviving after exposure to ionizing radiation. In the MK model, there are specific parameters, k and yD, where k is an inherent parameter to represent the number of potentially lethal lesions (PLLs) and yD indicates the dose-mean lineal energy in keV/µm. Assuming the PLLs to be DNA double-strand breaks (DSBs), the rate equations are derived for evaluating the DSB number in the cell nucleus. In this study, we estimated the ratio of DSBs for two types of photon irradiation (6 MV and 200 kVp X-rays) in Chinese hamster ovary (CHO-K1) cells and human non-small cell lung cancer (H1299) cells by observing the surviving fraction. The estimated ratio was then compared with the ratio of γ-H2AX foci using immunofluorescent staining. For making a comparison of the number of DSBs among a variety of radiation energy cases, we next utilized the survival data in the literature for both cells exposed to other photon types, such as (60)Co γ-rays, (137)Cs γ-rays and 100 kVp X-rays. The ratio of DSBs based on the MK model with conventional data was consistent with the ratio of γ-H2AX foci numbers, confirming that the γ-H2AX focus is indicative of DSBs. It was also shown that the larger yD is, the larger the DSB number is. These results suggest that k and yD represent the characteristics of the surviving fraction and the biological effects for photon irradiation.