A modified microdosimetric kinetic model for relative biological effectiveness calculation

LET-based approximation of the microdosimetric kinetic model for proton radiotherapy

BACKGROUND

Phenomenological relative biological effectiveness (RBE) models for proton therapy, based on the dose-averaged linear energy transfer (LET), have been developed to address the apparent RBE increase towards the end of the proton range. The results of these phenomenological models substantially differ due to varying empirical assumptions and fitting functions. In contrast, more theory-based approaches are used in carbon ion radiotherapy, such as the microdosimetric kinetic model (MKM). However, implementing microdosimetry-based models in LET-based proton therapy treatment planning systems poses challenges.

PURPOSE

This work presents a LET-based version of the MKM that is practical for clinical use in proton radiotherapy.

METHODS

At first, we derived an approximation of the Mayo Clinic Florida (MCF) MKM for relatively-sparsely ionizing radiation such as protons. The mathematical formalism of the proposed model is equivalent to the original MKM, but it maintains some key features of the MCF MKM, such as the determination of model parameters from measurable cell characteristics. Subsequently, we carried out Monte Carlo calculations with PHITS in different simulated scenarios to establish a heuristic correlation between microdosimetric quantities and the dose averaged LET of protons.

RESULTS

A simple allometric function was found able to describe the relationship between the dose-averaged LET of protons and the dose-mean lineal energy, which includes the contributions of secondary particles. The LET-based MKM was used to model the in vitro clonogenic survival RBE of five human and rodent cell lines (A549, AG01522, CHO, T98G, and U87) exposed to pristine and spread-out Bragg peak (SOBP) proton beams. The results of the LET-based MKM agree well with the biological data in a comparable or better way with respect to the other models included in the study. A sensitivity analysis on the model results was also performed.

CONCLUSIONS

The LET-based MKM integrates the predictive theoretical framework of the MCF MKM with a straightforward mathematical description of the RBE based on the dose-averaged LET, a physical quantity readily available in modern treatment planning systems for proton therapy.

Cell-cycle dependence on the biological effects of boron neutron capture therapy and its modification by polyvinyl alcohol

Boron neutron capture therapy (BNCT) is a unique radiotherapy of selectively eradicating tumor cells using boron compounds (e.g., 4-borono-L-phenylalanine [BPA]) that are heterogeneously taken up at the cellular level. Such heterogenicity potentially reduces the curative efficiency. However, the effects of temporospatial heterogenicity on cell killing remain unclear. With the technical combination of radiation track detector and biophysical simulations, this study revealed the cell cycle-dependent heterogenicity of BPA uptake and subsequent biological effects of BNCT on HeLa cells expressing fluorescent ubiquitination-based cell cycle indicators, as well as the modification effects of polyvinyl alcohol (PVA). The results showed that the BPA concentration in the S/G2/M phase was higher than that in the G1/S phase and that PVA enhances the biological effects both by improving the uptake and by canceling the heterogenicity. These findings might contribute to a maximization of therapeutic efficacy when BNCT is combined with PVA and/or cell cycle-specific anticancer agents.

First microdosimetric measurements with a tissue-equivalent proportional counter at the MedAustron ion-beam therapy facility

The aim of this work is to present the first microdosimetric spectra measured with a miniaturised tissue-equivalent proportional counter in the clinical environment of the MedAustron ion-beam therapy facility. These spectra were gathered with a 62.4-MeV proton beam and have been compared with microdosimetric spectra measured in the 62-MeV clinical proton beam of the CATANA beam line. Monte Carlo simulations were performed using the Geant4 toolkit GATE and a fully commissioned clinical beam line model. Finally, similarities and discrepancies of the measured data to simulations based on a simple and complex detector geometry are discussed.

Monte Carlo simulations of cell survival in proton SOBP

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

Event-by-event approach to the oxygen-effect-incorporated stochastic microdosimetric kinetic model for hypofractionated multi-ion therapy

An oxygen-effect-incorporated stochastic microdosimetric kinetic (OSMK) model was previously developed to estimate the survival fraction of cells exposed to charged-particle beams with wide dose and linear energy transfer (LET) ranges under various oxygen conditions. In the model, hypoxia-induced radioresistance was formulated based on the dose-averaged radiation quality. This approximation may cause inaccuracy in the estimation of the biological effectiveness of the radiation with wide variation in energy deposited to a sensitive volume per event, such as spread-out Bragg peak (SOBP) beams. The purpose of this study was to apply an alternative approach so as to consider the energy depositions on an event-by-event basis. The production probability of radiation-induced lesions per energy was formulated with oxygen partial pressure to account for the hypoxia-induced radioresistance. The reduction in the oxygen enhancement ratio for high-LET radiations was modeled by reducing the sensitive-volume size and increasing the saturation energy in microdosimetry. The modified OSMK model was tested against the reported survival data of three cell lines exposed to six species of ions with wide dose and LET ranges under aerobic and hypoxic conditions. The model reasonably reproduced the reported cell survival data. To evaluate the event-by-event approach, survival distributions of Chinese hamster ovary cells exposed to SOBP beams were estimated using the original and modified OSMK models. The differences in the estimated survival distributions between the models were marginal even under extreme hypoxia. The event-by-event approach improved the theoretical validity of the OSMK model. However, the original OSMK model can still provide an accurate estimation of the biological effectiveness of therapeutic radiations.

The complexity of DNA damage by radiation follows a Gamma distribution: insights from the Microdosimetric Gamma Model

Introduction

DNA damage is the main predictor of response to radiation therapy for cancer. Its Q8 quantification and characterization are paramount for treatment optimization, particularly in advanced modalities such as proton and alpha-targeted therapy.

Methods

We present a novel approach called the Microdosimetric Gamma Model (MGM) to address this important issue. The MGM uses the theory of microdosimetry, specifically the mean energy imparted to small sites, as a predictor of DNA damage properties. MGM provides the number of DNA damage sites and their complexity, which were determined using Monte Carlo simulations with the TOPAS-nBio toolkit for monoenergetic protons and alpha particles. Complexity was used together with a illustrative and simplistic repair model to depict the differences between high and low LET radiations.

Results

DNA damage complexity distributions were were found to follow a Gamma distribution for all monoenergetic particles studied. The MGM functions allowed to predict number of DNA damage sites and their complexity for particles not simulated with microdosimetric measurements (yF) in the range of those studied.

Discussion

Compared to current methods, MGM allows for the characterization of DNA damage induced by beams composed of multi-energy components distributed over any time configuration and spatial distribution. The output can be plugged into ad hoc repair models that can predict cell killing, protein recruitment at repair sites, chromosome aberrations, and other biological effects, as opposed to current models solely focusing on cell survival. These features are particularly important in targeted alpha-therapy, for which biological effects remain largely uncertain. The MGM provides a flexible framework to study the energy, time, and spatial aspects of ionizing radiation and offers an excellent tool for studying and optimizing the biological effects of these radiotherapy modalities.

Quantification of damage to plasmid DNA from 35 MeV electrons, 228 MeV protons and 300 kVp X-rays in varying hydroxyl radical scavenging environments

The pBR322 plasmid DNA was irradiated with 35 MeV electrons, 228 MeV protons and 300 kVp X-rays to quantify DNA damage and make comparisons of DNA damage between radiation modalities. Plasmid was irradiated in a medium containing hydroxyl radical scavengers in varying concentrations. This altered the amount of indirect hydroxyl-mediated DNA damage, to create an environment that is more closely associated with a biological cell. We show that increasing hydroxyl scavenger concentration significantly reduced post-irradiation DNA damage to pBR322 plasmid DNA consistently and equally with three radiation modalities. At low scavenging capacities, irradiation with both 35 MeV electrons and 228 MeV protons resulted in increased DNA damage per dose compared with 300 kVp X-rays. We quantify both single-strand break (SSB) and double-strand break (DSB) induction between the modalities as a ratio of yields relative to X-rays, referred to as relative biological effectiveness (RBE). RBESSB values of 1.16 ± 0.15 and 1.18 ± 0.08 were calculated for protons and electrons, respectively, in a low hydroxyl scavenging environment containing 1 mM Tris-HCl for SSB induction. In higher hydroxyl scavenging capacity environments (above 1.1 × 106 s-1), no significant differences in DNA damage induction were found between radiation modalities when using SSB induction as a measure of RBE. Considering DSB induction, significant differences were only found between X-rays and 35 MeV electrons, with an RBEDSB of 1.72 ± 0.91 for 35 MeV electrons, indicating that electrons result in significantly more SSBs and DSBs per unit of dose than 300 kVp X-rays.

3D printed 2D range modulators preserve radiation quality on a microdosimetric scale in proton and carbon ion beams

INTRODUCTION

Particle therapy using pencil beam scanning (PBS) faces large uncertain- ties related to ranges and target motion. One possibility to improve existing mitigation strategies is a 2D range modulator (2DRM). A 2DRM offers faster irradiation times by reducing the number of layers and spots needed to create a spread-out Bragg peak. We have investigated the impact of 2DRM on microdosimetric spectra measured in proton and carbon ion beams.

MATERIALS AND METHODS

Two 2DRMs were designed and 3D printed, one for. 124.7 MeV protons and one for 238.6 MeV/u carbon ions. Their dosimetric validation was performed using Roos and PinPoint ionization chamber and EBT3 films. Monte Carlo simulations were done using GATE. A silicon-based solid-state microdosimeter was used to collect pulse-height spectra along three depths for two irradiation modalities, PBS and a single central beam.

RESULTS

For both particle types, the original pin design had to be optimized via GATE simulations. The difference between the R80 of the simulated and measured depth dose curve was 0.1 mm. The microdosimetric spectra collected with the two irradiation modalities overlap well. Their mean lineal energy values differ over all positions by 5.2 % for the proton 2DRM and 2.1 % for the carbon ion 2DRM.

CONCLUSION

Radiation quality in terms of lineal energy was independent of the irradiation method. This supports the current approach in reference dosimetry, where the residual range is chosen as a beam quality index to select stopping power ratios.

Multiple levels of stochasticity accounted for in different radiation biophysical models: from physics to biology

PURPOSE

In the present paper we investigate how some stochastic effects are included in a class of radiobiological models with particular emphasis on how such randomnesses reflect into the predicted cell survival curve.

MATERIALS AND METHODS

We consider four different models, namely the Generalized Stochastic Microdosimetric Model GSM², in its original full form, the Dirac GSM² the Poisson GSM² and the Repair-Misrepair Model (RMR). While GSM² and the RMR models are known in literature, the Dirac and the Poisson GSM²  have been newly introduced in this work. We further numerically investigate via Monte Carlo simulation of four different particle beams, how the proposed stochastic approximations reflect into the predicted survival curves. To achieve these results, we consider different ion species at energies of interest for therapeutic applications, also including a mixed field scenario.

RESULTS

We show how the Dirac GSM², the Poisson GSM² and the RMR can be obtained from the GSM² under suitable approximations on the stochasticity considered. We analytically derive the cell survival curve predicted by the four models, characterizing rigorously the high and low dose limits. We further study how the theoretical findings emerge also using Monte Carlo numerical simulations.

CONCLUSIONS

We show how different models include different levels of stochasticity in the description of cellular response to radiation. This translates into different cell survival predictions depending on the radiation quality.

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 β 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 β 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.

Estimate of the Biological Dose in Hadrontherapy Using GATE

For the evaluation of the biological effects, Monte Carlo toolkits were used to provide an RBE-weighted dose using databases of survival fraction coefficients predicted through biophysical models. Biophysics models, such as the mMKM and NanOx models, have previously been developed to estimate a biological dose. Using the mMKM model, we calculated the saturation corrected dose mean specific energy z1D* (Gy) and the dose at 10% D10 for human salivary gland (HSG) cells using Monte Carlo Track Structure codes LPCHEM and Geant4-DNA, and compared these with data from the literature for monoenergetic ions. These two models were used to create databases of survival fraction coefficients for several ion types (hydrogen, carbon, helium and oxygen) and for energies ranging from 0.1 to 400 MeV/n. We calculated α values as a function of LET with the mMKM and the NanOx models, and compared these with the literature. In order to estimate the biological dose for SOBPs, these databases were used with a Monte Carlo toolkit. We considered GATE, an open-source software based on the GEANT4 Monte Carlo toolkit. We implemented a tool, the BioDoseActor, in GATE, using the mMKM and NanOx databases of cell survival predictions as input, to estimate, at a voxel scale, biological outcomes when treating a patient. We modeled the HIBMC 320 MeV/u carbon-ion beam line. We then tested the BioDoseActor for the estimation of biological dose, the relative biological effectiveness (RBE) and the cell survival fraction for the irradiation of the HSG cell line. We then tested the implementation for the prediction of cell survival fraction, RBE and biological dose for the HIBMC 320 MeV/u carbon-ion beamline. For the cell survival fraction, we obtained satisfying results. Concerning the prediction of the biological dose, a 10% relative difference between mMKM and NanOx was reported.

Combined DNA Damage Repair Interference and Ion Beam Therapy: Development, Benchmark, and Clinical Implications of a Mechanistic Biological Model

PURPOSE

Our purpose was to develop a mechanistic model that describes and predicts radiation response after combined DNA damage repair interference (DDRi) and particle radiation therapy.

METHODS AND MATERIALS

The heterogeneous dose distributions of protons and ⁴He ions were implemented into the "UNIfied and VERSatile bio-response Engine" (UNIVERSE). Predictions for monoenergetic and mixed fields over clinically relevant dose and linear energy transfer range were compared with experimental in vitro survival data measured in this work as well as data available in the literature, including different cell lines and DDR interferences. Ultimately, UNIVERSE predictions were investigated in a patient plan.

RESULTS

UNIVERSE accurately predicts survival of cell lines with and without DDRi in clinical settings of ion beam therapy based only on 3 parameters derived from photon data. With increasing dose or linear energy transfer, the radiosensitizing effect of DDRi decreases, resulting in diminished relative biological effect of ion beam radiation for cells subjected to DDRi in comparison to cells that are not. Similar trends were observed in patient plan recalculations; however, this analysis also suggests that DDRi + particle radiation therapy may better preserve the therapeutic window in comparison to DDRi + photon radiation therapy.

CONCLUSIONS

The presented framework represents the first mechanistic model of combined DDRi and particle radiation therapy comprehensively benchmarked in clinically relevant scenarios and a step toward more personalized treatment. It reveals potential differences between DDRi + photon radiation therapy versus DDRi + particle radiation therapy, which have not been described so far. UNIVERSE could aid in appraising the clinical viability of combined administration of radiosensitizing drugs and charged particle therapy, as well as the identification of patients with known DDR deficiencies in the tumor who might benefit from therapy with light ions, freeing limited space at heavy ion therapy centers.

Further development of spinal cord retreatment dose estimation: including radiotherapy with protons and light ions

PURPOSE

A graphical user interface (GUI) was developed to aid in the assessment of changes in the radiation tolerance of spinal cord/similar central nervous system tissues with time between two individual treatment courses.

METHODS

The GUI allows any combination of photons, protons (or ions) to be used as the initial, or retreatment, radiotherapy courses. Allowances for clinical circumstances, of reduced tolerance, can also be made. The radiobiological model was published previously and has been incorporated with additional checks and safety features, to be as safe to use as possible. The proton option includes use of a fixed RBE of 1.1 (set as the default), or a variable RBE, the latter depending on the proton linear energy transfer (LET) for organs at risk. This second LET-based approach can also be used for ions, by changing the LET parameters.

RESULTS

GUI screenshots are used to show the input and output parameters for different clinical situations used in worked examples. The results from the GUI are in agreement with manual calculations, but the results are now rapidly available without tedious and error-prone manual computations. The software outputs provide a maximum dose limit boundary, which should not be exceeded. Clinicians may also choose to further lower the number of treatment fractions, whilst using the same dose per fraction (or conversely a lower dose per fraction but with the same number of fractions) in order to achieve the intended clinical benefit as safely as possible.

CONCLUSIONS

The new GUI will allow scientific-based estimations of time related radiation tolerance changes in the spinal cord and similar central nervous tissues (optic chiasm, brainstem), which can be used to guide the choice of retreatment dose fractionation schedules, with either photons, protons or ions.

Implementation of simplified stochastic microdosimetric kinetic models into PHITS for application to radiation treatment planning

PURPOSE

The stochastic microdosimetric kinetic (SMK) model is one of the most sophisticated and precise models used in the estimation of the relative biological effectiveness of carbon-ion radiotherapy (CRT) and boron neutron capture therapy (BNCT). However, because of its complicated and time-consuming calculation procedures, it is nearly impractical to directly incorporate this model into a radiation treatment-planning system.

MATERIALS AND METHODS

Through the introduction of Taylor expansion (TE) or fast Fourier transform (FFT), we developed two simplified SMK models and implemented them into the Particle and Heavy Ion Transport code System (PHITS). To verify the implementation, we calculated the photon isoeffective doses in a cylindrical phantom placed in the radiation fields of passive CRT and accelerator-based BNCT.

RESULTS AND DISCUSSION

Our calculation suggested that both TE-based and FFT-based SMK models can reproduce the data obtained from the original SMK model very well for absorbed doses approximately below 5 Gy, whereas the TE-based SMK model overestimates the original data at higher doses. In terms of computational efficiency, the TE-based SMK model is much faster than the FFT-based SMK model.

CONCLUSION

This study enables the instantaneous calculation of the photo isoeffective dose for CRT and BNCT, considering their cellular-scale dose heterogeneities. Treatment-planning systems that use the improved PHITS as a dose-calculation engine are under development.

Fast neutron energy based modelling of biological effectiveness with implications for proton and ion beams

A practical neutron energy dependent RBE model has been developed, based on the relationship between a mono-energetic neutron energy and its likely recoil proton energy. Essentially, the linear energy transfer (LET) values of the most appropriate recoil proton energies are then used to modify the linear quadratic model radiosensitivities (α and β) from their reference LET radiation values to provide the RBE estimates. Experimental neutron studies published by Hall (including some mono-energetic beams ranging from 0.2 to 15 MeV), Broerse, Berry, and data from the Clatterbridge and Detroit clinical neutron beams, which all contain some data from a spectrum of neutron energies, are used to derive single effective neutron energies (NE_eff) for each spectral beam. These energies yield a recoil proton spectrum, but with an effective mean proton energy (being around 50% of NE_eff). The fractional increase in LET is given by the recoil proton LET divided by the proton (LET_U) value which provides the highest RBE. This ratio is then used to determine the change in the linear-quadratic model α and β parameters, from those of the reference radiation, to estimate the RBE. The predicted proton recoil RBE is then reasonably close to the experimental neutron RBE values found when taking into account the variation inherent in biological experiments. The work has some important consequences. The data of Hall et al (1975 Radiat. Res. 64 245-55) shows that the highest RBE values are found with neutron energies around 0.3-0.4 MeV, but this energy cannot possibly generate recoil proton energies which are higher, as necessary for a 0.68 MeV proton with a 30.5 keV μm^-1 LET_U (the LET value which provides the maximum obtainable RBE for a specified ion). For 0.4 MeV neutrons with proton recoil energies of around 0.2 MeV, the latter have a LET of around 62.88 keV μm^-1. This could have an impact on proton beam RBE modelling. However, this is compensated by finding that the maximum radiosensitivity for mono-energetic neutrons was around 1.7 times larger than previously suggested from experimental ion beam studies, probably due to the necessary spreading out of Bragg peaks for ion beam experimental purposes, sampling errors and particle range considerations. This semi-empirical model can be used with minimal computer support and could have applications in ionic beams and in radioprotection.

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).

Clinical Radiobiology of Fast Neutron Therapy: What Was Learnt?

Neutron therapy was developed from neutron radiobiology experiments, and had identified a higher cell kill per unit dose and an accompanying reduction in oxygen dependency. But experts such as Hal Gray were sceptical about clinical applications, for good reasons. Gray knew that the increase in relative biological effectiveness (RBE) with dose fall-off could produce marked clinical limitations. After many years of research, this treatment did not produce the expected gains in tumour control relative to normal tissue toxicity, as predicted by Gray. More detailed reasons for this are discussed in this paper. Neutrons do not have Bragg peaks and so did not selectively spare many tissues from radiation exposure; the constant neutron RBE tumour prescription values did not represent the probable higher RBE values in late-reacting tissues with low α/β values; the inevitable increase in RBE as dose falls along a beam would also contribute to greater toxicity than in a similar megavoltage photon beam. Some tissues such as the central nervous system white matter had the highest RBEs partly because of the higher percentage hydrogen content in lipid-containing molecules. All the above factors contributed to disappointing clinical results found in a series of randomised controlled studies at many treatment centres, although at the time they were performed, neutron therapy was in a catch-up phase with photon-based treatments. Their findings are summarised along with their technical aspects and fractionation choices. Better understanding of fast neutron experiments and therapy has been gained through relatively simple mathematical models—using the biological effective dose concept and incorporating the RBEmax and RBEmin parameters (the limits of RBE at low and high dose, respectively—as shown in the Appendix). The RBE itself can then vary between these limits according to the dose per fraction used. These approaches provide useful insights into the problems that can occur in proton and ion beam therapy and how they may be optimised. This is because neutron ionisations in living tissues are mainly caused by recoil protons of energy proportional to the neutron energy: these are close to the proton energies that occur close to the Bragg peak region. To some extent, neutron RBE studies contain the highest RBE ranges found within proton and ion beams near Bragg peaks. In retrospect, neutrons were a useful radiobiological tool that has continued to inform the scientific and clinical community about the essential radiobiological principles of all forms of high linear energy transfer therapy. Neutron radiobiology and its implications should be taught on training courses and studied closely by clinicians, physicists, and biologists engaged in particle beam therapies.

A Model for Estimating Dose-Rate Effects on Cell-Killing of Human Melanoma after Boron Neutron Capture Therapy

Boron neutron capture therapy (BNCT) is a type of radiation therapy for eradicating tumor cells through a ¹⁰B(n,α)⁷Li reaction in the presence of ¹⁰B in cancer cells. When delivering a high absorbed dose to cancer cells using BNCT, both the timeline of ¹⁰B concentrations and the relative long dose-delivery time compared to photon therapy must be considered. Changes in radiosensitivity during such a long dose-delivery time can reduce the probability of tumor control; however, such changes have not yet been evaluated. Here, we propose an improved integrated microdosimetric-kinetic model that accounts for changes in microdosimetric quantities and dose rates depending on the ¹⁰B concentration and investigate the cell recovery (dose-rate effects) of melanoma during BNCT irradiation. The integrated microdosimetric–kinetic model used in this study considers both sub-lethal damage repair and changes in microdosimetric quantities during irradiation. The model, coupled with the Monte Carlo track structure simulation code of the Particle and Heavy Ion Transport code System, shows good agreement with in vitro experimental data for acute exposure to ⁶⁰Co γ-rays, thermal neutrons, and BNCT with ¹⁰B concentrations of 10 ppm. This indicates that microdosimetric quantities are important parameters for predicting dose-response curves for cell survival under BNCT irradiations. Furthermore, the model estimation at the endpoint of the mean activation dose exhibits a reduced impact of cell recovery during BNCT irradiations with high linear energy transfer (LET) compared to ⁶⁰Co γ-rays irradiation with low LET. Throughout this study, we discuss the advantages of BNCT for enhancing the killing of cancer cells with a reduced dose-rate dependency. If the neutron spectrum and the timelines for drug and dose delivery are provided, the present model will make it possible to predict radiosensitivity for more realistic dose-delivery schemes in BNCT irradiations.

A Simplified Cluster Analysis of Electron Track Structure for Estimating Complex DNA Damage Yields

Complex DNA damage, defined as at least two vicinal lesions within 10-20 base pairs (bp), induced after exposure to ionizing radiation, is recognized as fatal damage to human tissue. Due to the difficulty of directly measuring the aggregation of DNA damage at the nano-meter scale, many cluster analyses of inelastic interactions based on Monte Carlo simulation for radiation track structure in liquid water have been conducted to evaluate DNA damage. Meanwhile, the experimental technique to detect complex DNA damage has evolved in recent decades, so both approaches with simulation and experiment get used for investigating complex DNA damage. During this study, we propose a simplified cluster analysis of ionization and electronic excitation events within 10 bp based on track structure for estimating complex DNA damage yields for electron and X-ray irradiations. We then compare the computational results with the experimental complex DNA damage coupled with base damage (BD) measured by enzymatic cleavage and atomic force microscopy (AFM). The computational results agree well with experimental fractions of complex damage yields, i.e., single and double strand breaks (SSBs, DSBs) and complex BD, when the yield ratio of BD/SSB is assumed to be 1.3. Considering the comparison of complex DSB yields, i.e., DSB + BD and DSB + 2BD, between simulation and experimental data, we find that the aggregation degree of the events along electron tracks reflects the complexity of induced DNA damage, showing 43.5% of DSB induced after 70 kVp X-ray irradiation can be classified as a complex form coupled with BD. The present simulation enables us to quantify the type of complex damage which cannot be measured through in vitro experiments and helps us to interpret the experimental detection efficiency for complex BD measured by AFM. This simple model for estimating complex DNA damage yields contributes to the precise understanding of the DNA damage complexity induced after X-ray and electron irradiations.

Proton RBE dependence on dose in the setting of hypofractionation

Hypofractionated radiotherapy is attractive concerning patient burden and therapy costs, but many aspects play a role when it comes to assess its safety. While exploited for conventional photon therapy and carbon ion therapy, hypofractionation with protons is only rarely applied. One reason for this is uncertainty in the described dose, mainly due to the relative biological effectiveness (RBE), which is small for protons, but not negligible. RBE is generally dose-dependent, and for higher doses as used in hypofractionation, a thorough RBE evaluation is needed. This review article focuses on the RBE variability in protons and associated issues or implications for hypofractionation.

Monte Carlo investigation of the characteristics of radioactive beams for heavy ion therapy

This work presents a simulation study evaluating relative biological effectiveness at 10% survival fraction (RBE10) of several different positron-emitting radionuclides in heavy ion treatment systems, and comparing these to the RBE10s of their non-radioactive counterparts. RBE10 is evaluated as a function of depth for three positron-emitting radioactive ion beams (¹⁰C, ¹¹C and ¹⁵O) and two stable ion beams (¹²C and ¹⁶O) using the modified microdosimetric kinetic model (MKM) in a heterogeneous skull phantom subject to a rectangular 50 mm × 50 mm × 60 mm spread out Bragg peak. We demonstrate that the RBE10 of the positron-emitting radioactive beams is almost identical to the corresponding stable isotopes. The potential improvement in PET quality assurance image quality which is obtained when using radioactive beams is evaluated by comparing the signal to background ratios of positron annihilations at different intra- and post-irradiation time points. Finally, the incidental dose to the patient resulting from the use of radioactive beams is also quantified and shown to be negligible.

A comparison of mechanism-inspired models for particle relative biological effectiveness (RBE)

BACKGROUND AND SIGNIFICANCE

The application of heavy ion beams in cancer therapy must account for the increasing relative biological effectiveness (RBE) with increasing penetration depth when determining dose prescriptions and organ at risk (OAR) constraints in treatment planning. Because RBE depends in a complex manner on factors such as the ion type, energy, cell and tissue radiosensitivity, physical dose, biological endpoint, and position within and outside treatment fields, biophysical models reflecting these dependencies are required for the personalization and optimization of treatment plans.

AIM

To review and compare three mechanism-inspired models which predict the complexities of particle RBE for various ion types, energies, linear energy transfer (LET) values and tissue radiation sensitivities.

METHODS

The review of models and mechanisms focuses on the Local Effect Model (LEM), the Microdosimetric-Kinetic (MK) model, and the Repair-Misrepair-Fixation (RMF) model in combination with the Monte Carlo Damage Simulation (MCDS). These models relate the induction of potentially lethal double strand breaks (DSBs) to the subsequent interactions and biological processing of DSB into more lethal forms of damage. A key element to explain the increased biological effectiveness of high LET ions compared to MV x rays is the characterization of the number and local complexity (clustering) of the initial DSB produced within a cell. For high LET ions, the spatial density of DSB induction along an ion's trajectory is much greater than along the path of a low LET electron, such as the secondary electrons produced by the megavoltage (MV) x rays used in conventional radiation therapy. The main aspects of the three models are introduced and the conceptual similarities and differences are critiqued and highlighted. Model predictions are compared in terms of the RBE for DSB induction and for reproductive cell survival.

RESULTS AND CONCLUSIONS

Comparisons of the RBE for DSB induction and for cell survival are presented for proton (¹ H), helium (⁴ He), and carbon (¹² C) ions for the therapeutically most relevant range of ion beam energies. The reviewed models embody mechanisms of action acting over the spatial scales underlying the biological processing of potentially lethal DSB into more lethal forms of damage. Differences among the number and types of input parameters, relevant biological targets, and the computational approaches among the LEM, MK and RMF models are summarized and critiqued. Potential experiments to test some of the seemingly contradictory aspects of the models are discussed.

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

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