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

Proton relative biological effectiveness for the induction of DNA double strand breaks based on Geant4

Uncertainties in the relative biological effectiveness (RBE) of proton remains a major barrier to the biological optimization of proton therapy. A large amount of experimental data suggest that proton RBE is variable. As an evolving Monte Carlo code toolkit, Geant4-DNA is able to simulate the initial DNA damage caused by particle beams through physical and chemical interactions at the nanometer scale over a short period of time. This contributes to evaluating the radiobiological effects induced by ionizing radiation. Based on the Geant4-DNA toolkit, this study constructed a DNA geometric model containing 6.32Gbp, simulated the relationship between radiochemical yields (G-values) and their corresponding chemical constructors, and calculated a detailed calculation of the sources of damage and the complexity of damage in DNA strand breaks. The damage model constructed in this study can simulate the relative biological effectiveness (RBE) in the proton Bragg peak region. The results indicate that: (1) When the electron energy is below 400 keV, the yield of OH·account for 18.1% to 25.3% of the total water radiolysis yields. (2) Under the influence of histone clearance function, the yield of indirect damage account for over 72.93% of the yield of DNA strand breaks (SBs). When linear energy transfer (LET) increased from 29.79 (keV/μm) to 64.29 (keV/μm), the yield of double strand breaks (DSB) increased from 17.27% to 32.65%. (3) By investigating the effect of proton Bragg peak depth on the yield of direct DSB (DSBdirect) and total DSB (DSBtotal), theRBEDSBtotandRBEDSBdirlevels of cells show that the RBE value of protons reaches 2.2 in the Bragg peak region.

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.

Investigation of ionization chamber perturbation factors using proton beam and Fano cavity test for the Monte Carlo simulation code PHITS

The reference dose for clinical proton beam therapy is based on ionization chamber dosimetry. However, data on uncertainties in proton dosimetry are lacking, and multifaceted studies are required. Monte Carlo simulations are useful tools for calculating ionization chamber dosimetry in radiation fields and are sensitive to the transport algorithm parameters when particles are transported in a heterogeneous region. We aimed to evaluate the proton transport algorithm of the Particle and Heavy Ion Transport Code System (PHITS) using the Fano test. The response of the ionization chamber f Q and beam quality correction factors k Q were calculated using the same parameters as those in the Fano test and compared with those of other Monte Carlo codes for verification. The geometry of the Fano test consisted of a cylindrical gas-filled cavity sandwiched between two cylindrical walls. f Q was calculated as the ratio of the absorbed dose in water to the dose in the cavity in the chamber. We compared the f Q calculated using PHITS with that of a previous study, which was calculated using other Monte Carlo codes (Geant4, FULKA, and PENH) under similar conditions. The flight mesh, a parameter for charged particle transport, passed the Fano test within 0.15%. This was shown to be sufficiently accurate compared with that observed in previous studies. The f Q calculated using PHITS were 1.116 ± 0.002 and 1.124 ± 0.003 for NACP-02 and PTW-30013, respectively, and the k Q were 0.981 ± 0.008 and 1.027 ± 0.008, respectively, at 150 MeV. Our results indicate that PHITS can calculate the f Q and k Q with high precision.

Comparison of 126 MeV antiproton and proton—a FLUKA-based microdosimetric approach

Objective. This study aims at comparing dosimetric parameters of 126 MeV antiprotons and protons using microdosimetric approach. Approach. Microdosimetric distributions of 126 MeV proton and antiproton beams at 1 μm site size are calculated using the Monte Carlo-based FLUKA code. The distributions are calculated at various depths along the central axis in water phantom as well as at different off-axis locations. The study also includes calculations of secondary radiations produced by antiprotons and protons. Mean quality factor, Q ¯ is calculated using the ICRP 60 and ICRU 40 recommendations. The Relative Biological Effectiveness (RBE) of HSG tumour cell at 10% survival level is calculated based on Microdosimetric Kinetic Model. Main results. Q ¯ I C R P , Q ¯ ICRU and RBE for antiprotons are higher by a factor of about 3.60, 3.41 and 1.24, respectively, at Bragg-peak and higher by a factor of about 1.41, 1.76 and 1.05, respectively, at plateau region of depth-dose profile when compared to protons. At 15 cm depth along the central axis, Q ¯ ICRP , Q ¯ ICRU and RBE for protons are higher by a factor of about 1.42, 1.66 and 1.26, respectively, when compared to antiprotons. At the off-axis distance (Ld ) of 6 cm (at 11.5 cm depth in water), Q ¯ ICRP and Q ¯ ICRU of protons are higher than that of antiproton whereas the trend is opposite at off-axis distance of 4 cm. At Ld = 4 cm (at 11.5 cm depth in water), RBE of antiprotons is higher by about 4% than protons whereas at Ld = 6 cm, RBE of protons is higher by about 13% than antiprotons. Significance. The study shows that antiproton radiotherapy is advantageous as compared to protons considering enhancements in the absorbed dose and RBE-weighed dose values at the Bragg-peak.

Development of the DICOM-based Monte Carlo dose reconstruction system for a retrospective study on the secondary cancer risk in carbon ion radiotherapy

Objective. A retrospective study on secondary cancer risk on carbon ion radiotherapy (CIRT) is ongoing at the Heavy Ion Medical Accelerator in Chiba (HIMAC). The reconstruction of the whole-body patient dose distribution is the key issue in the study because dose distribution only around the planning target volume was evaluated in the treatment planning system. Approach. We therefore developed a new dose reconstruction system based on the Particle and Heavy Ion Transport code System (PHITS) coupled with the treatment plan DICOM data set by extending the functionalities of RadioTherapy package based on PHITS (RT-PHITS). In the system, the geometry of patient-specific beam devices such as the range shifter, range compensator, and collimators as well as the individual patient’s body are automatically reconstructed. Various functions useful for retrospective analysis on the CIRT are implemented in the system, such as those for separately deducing dose contributions from different secondary particles and their origins. Main results. The accuracy of the developed system was validated by comparing the dose distribution to the experimental data measured in a water tank and using a treatment plan on an anthropomorphic phantom. Significance. The extended RT-PHITS will be used in epidemiological studies based on clinical data from HIMAC.

On the calculation of the relative biological effectiveness of ion radiation therapy using a biological weighting function, the microdosimetric kinetic model (MKM) and subsequent corrections (non-Poisson MKM and modified MKM)

Objective. To investigate similarities and differences in the formalism, processing, and the results of relative biological effectiveness (RBE) calculations with a biological weighting function (BWF), the microdosimetric kinetic model (MKM) and subsequent modifications (non-Poisson MKM, modified MKM). This includes: (a) the extension of the V79-RBE10% BWF to model the RBE for other clonogenic survival levels; (b) a novel implementation of MKMs as weighting functions; (c) a benchmark against Chinese Hamster lung fibroblast (V79) in vitro data; (d) a study on the effect of pre- or post- processing the average biophysical quantities used for the RBE calculations; (e) a possible modification of the modified MKM parameters to improve the model accuracy at high linear energy transfer (LET). Methodology. Lineal energy spectra were simulated for two spherical targets (diameter = 0.464 or 1.0 μm) using PHITS for 1H, 4He, 12C, 20Ne, 40Ar, 56Fe and 132Xe ions. The results of the in silico calculations were compared with published in vitro data. Main results. All models appear to underestimate the RBE α of hydrogen ions. All MKMs generally overestimate the RBE50%, RBE10% and RBE1% for ions with an LET greater than ∼200 keV μm−1. This overestimation is greater for small surviving fractions and is likely due to the assumption of a radiation-independent quadratic term of clonogenic survival (ß). The overall RBE trends seem to be best described by the novel ‘post-processing average’ implementation of the non-Poisson MKM. In case of calculations with the non-Poisson MKM, pre- or post- processing the average biophysical quantities affects the computed RBE values significantly. Significance. This study presents a systematic analysis of the formalism and results of widely used microdosimetric models of clonogenic survival for ions relevant for cancer particle therapy and space radiation protection. Points for improvements were highlighted and will contribute to the development of upgraded biophysical models.

Microdosimetric characterization of a clinical proton therapy beam: comparison between simulated lineal energy distributions in spherical water targets and experimental measurements with a silicon detector

Objective Treatment planning based on computer simulations were proposed to account for the increase in the relative biological effectiveness (RBE) of proton radiotherapy beams near to the edges of the irradiated volume. Since silicon detectors could be used to validate the results of these simulations, it is important to explore the limitations of this comparison. Approach Microdosimetric measurements with a MicroPlus Bridge V2 silicon detector (thickness = 10 µm) were performed along the Bragg peak of a clinical proton beam. The lineal energy distributions, the dose mean values, and the RBE calculated with a biological weighting function were compared with simulations with PHITS (microdosimetric target = 1 µm water sphere), and published clonogenic survival in vitro RBE data for the V79 cell line. The effect of the silicon-to-water conversion was also investigated by comparing three different methodologies (conversion based on a single value, novel bin-to-bin conversions based on SRIM and PSTAR). Main results Mainly due to differences in the microdosimetric targets, the experimental dose-mean lineal energy and RBE values at the distal edge were respectively up to 53% and 28% lower than the simulated ones. Furthermore, the methodology chosen for the silicon-to-water conversion was proven to affect the dose mean lineal energy and the RBE10 up to 32% and 11% respectively. The best methodology to compensate for this underestimation was the bin-to-bin silicon-to-water conversion based on PSTAR. Significance This work represents the first comparison between PHITS-simulated lineal energy distributions in water targets and corresponding experimental spectra measured with silicon detectors. Furthermore, the effect of the silicon-to-water conversion on the RBE was explored for the first time. The proposed methodology based on the PSTAR bin-to-bin conversion appears to provide superior results with respect to commonly used single scaling factors and is recommended for future studies.

Track-structure modes in particle and heavy ion transport code system (PHITS): application to radiobiological research

PURPOSE

In radiation physics, Monte Carlo radiation transport simulations are powerful tools to evaluate the cellular responses after irradiation. When investigating such radiation-induced biological effects, it is essential to perform track structure simulations by explicitly considering each atomic interaction in liquid water at the sub-cellular and DNA scales. The Particle and Heavy-Ion Transport code System (PHITS) is a Monte Carlo code which enables to calculate track structure at DNA scale by employing the track-structure modes for electrons, protons and carbon ions. In this paper, we review the recent development status and future prospects of the track-structure modes in the PHITS code.

CONCLUSIONS

To date, the physical features of these modes have been verified using the available experimental data and Monte Carlo simulation results reported in literature. These track-structure modes can be used for calculating microdosimetric distributions to estimate cell survival and for estimating initial DNA damage yields. The use of PHITS track-structure mode is expected not only to clarify the underlying mechanisms of radiation effects but also to predict curative effects in radiation therapy. The results of PHITS simulations coupled with biophysical models will contribute to the radiobiological studies by precisely predicting radiation-induced biological effects based on the Monte Carlo approach.

Comparison between the results of a recently-developed biological weighting function (V79-RBE10BWF) and thein vitroclonogenic survival RBE10of other repair-competent asynchronized normoxic mammalian cell lines and ions not used for the development of the model

728 simulated microdosimetric lineal energy spectra (26 different ions between 1H and 238U, 28 energy points from 1 to 1000 MeV/n) were used in combination with a recently-developed biological weighting function (Parisi et al., 2020) and 571 published in vitro clonogenic survival curves in order to: 1) assess prediction intervals for the in silico results by deriving an empirical indication of the experimental uncertainty from the dispersion in the in vitro hamster lung fibroblast (V79) data used for the development of the biophysical model; 2) explore the possibility of modeling the relative biological effectiveness (RBE) of the 10% clonogenic survival of asynchronized normoxic repair-competent mammalian cell lines other than the one used for the development of the model (V79); 3) investigate the predictive power of the model through a comparison between in silico results and in vitro data for 10 ions not used for the development of the model. At first, different strategies for the assessment of the in silico prediction intervals were compared. The possible sources of uncertainty responsible for the dispersion in the in vitro data were also shortly reviewed. Secondly, also because of the relevant scatter in the in vitro data, no statistically-relevant differences were found between the RBE10 of the investigated different asynchronized normoxic repair-competent mammalian cell lines. The only exception (Chinese Hamster peritoneal fibroblasts, B14FAF28), is likely due to the limited dataset (all in vitro ion data were extracted from a single publication), systematic differences in the linear energy transfer (LET) calculations for the employed very-heavy ions, and the use of reference photon survival curves extracted from a different publication. Finally, the in silico predictions for the 10 ions not used for the model development were in good agreement with the corresponding in vitro data.

Medical application of particle and heavy ion transport code system PHITS

The Particle and Heavy Ion Transport code System (PHITS) is a general-purpose Monte Carlo simulation code that has been applied in various areas of medical physics. These include application in different types of radiotherapy, shielding calculations, application to radiation biology, and research and development of medical tools. In this article, the useful features of PHITS are explained by referring to actual examples of various medical applications.

Modelling and measurements of distributions in an adult human phantom undergoing proton scanning beam radiotherapy: lung- and prostate-located tumours

Proton radiotherapy has been shown to offer a significant dosimetric advantage in cancer patients, in comparison to conventional radiotherapy, with a decrease in dose to healthy tissue and organs at risk, because the bulk of the beam energy is deposited in the Bragg peak to be located within a tumour. However, it should be kept in mind that radiotherapy of cancer is still accompanied by adverse side effects, and a better understanding and improvement of radiotherapy can extend the life expectancy of patients following the treatment of malignant tumours. In this study, the dose distributions measured with thermoluminescent detectors (TLDs) inside a tissue-equivalent adult human phantom exposed for lung and prostate cancer using the modern proton beam scanning radiotherapy technique were compared. Since the TLD detection efficiency depends on the ionization density of the radiation to be detected, and since this efficiency is detector specific, four different types of TLDs were used to compare their response in the mixed radiation fields. Additionally, the dose distributions from two different cancer treatment modalities were compared using the selected detectors. The measured dose values were benchmarked against Monte Carlo simulations and available literature data. The results indicate an increase in the lateral dose with an increase of the primary proton energy. However, the radiation quality factor of the mixed radiation increases by 20% in the vicinity to the target for the lower initial proton energy, due to the production of secondary charged particles of low-energy and short range. For the cases presented here the MTS-N TLD detector seems to be the most optimal tool for dose measurements within the target volume, while the MCP-N TLD detector, due to an interplay of its enhanced thermal neutron response and decreased detection efficiency to highly ionising radiation, is a better choice for the out-of-field measurements. The pairs of MTS-6 and MTS-7 TLDs used also in this study allowed for a direct measurement of the neutron dose equivalent. Before it can be concluded that they offer an alternative to the time-consuming nuclear track detectors, however, more research is needed to unambiguously confirm whether this observation was just accidental or whether it only applies to certain cases. Since there is no universal detector, which would allow the determination of the dosimetric quantities relevant for risk estimation, this work expands the knowledge necessary to improve the quality of dosimetry data and might help scientists and clinicians in choosing the right tools to measure radiation doses in mixed radiation fields.

Microdosimetric-Kinetic Model for Radio-enhancement of Gold Nanoparticles: Comparison with LEM

Numerous studies have strongly supported the application of gold nanoparticles (GNPs) as radio-enhanced agents. In our previous study, the local effect model (LEM I) was adopted to predict the cell survival for MDA-MB-231 cells exposed to 150 kVp X rays after 500 µg/ml GNPs treatment. However, microdosimetric quantities could not be obtained, which were correlated with biological effects on cells. Thus, we developed microdosimetric kinetic model (MKM) for GNP radio-enhancement (GNP-MKM), which uses the microdosimetric quantities such as dose-mean lineal energy with subcellular domain size. Using the Monte Carlo simulation tool Geant4, we estimated the dose-mean lineal energy with secondary radiations from GNPs and absorbed dose in the nucleus. The variations in MKM parameters for different domain sizes, and GNP concentrations, were calculated to compare the survival fractions predicted by both models. With a domain radius of 500 nm and a threshold dose of 20 Gy, the sensitizer enhancement ratio predicted by GNP-MKM and GNP-LEM was 1.41 and 1.29, respectively. The GNP-MKM predictions were much more strongly dependent on the domain size than were the GNP-LEM on the threshold dose. These findings provide another method to predict survival fraction for the GNP radio-enhancement.

Verification of KURBUC-based ion track structure mode for proton and carbon ions in the PHITS code

The particle and heavy ion transport code system (PHITS) is a general-purpose Monte Carlo radiation transport simulation code. It has the ability to handle diverse particle types over a wide range of energy. The latest PHITS development enables the generation of track structure for proton and carbon ions (¹H⁺, ¹²C⁶⁺) based on the algorithms in the KURBUC code, which is considered as one of the most verified track-structure codes worldwide. This ion track-structure mode is referred to as the PHITS-KURBUC mode. In this study, the range, radial dose distributions, and microdosimetric distributions were calculated using the PHITS-KURBUC mode. Subsequently, they were compared with the corresponding data obtained from the original KURBUC and from other studies. These comparative studies confirm the successful inclusion of the KURBUC code in the PHITS code. As results of the synergistic effect between the macroscopic and microscopic radiation transport codes, this implementation enabled the detailed calculation of the microdosimetric and nanodosimetric quantities under complex radiation fields, such as proton beam therapy with the spread-out Bragg peak.

Study on Caenorhabditis Elegans as a Combined Model of Microdosimetry and Biology

Microdosimetry is a tool for the investigation of microscopic energy deposition of ionizing radiation. This work used Caenorhabditis elegans as a model to estimate the microdosimetric deposition level at the ⁶⁰Co gamma radiation. Monte Carlo software PHITS was employed to establish irradiated nematodes model. The dose deposition of the entire body and gonad irradiated to 100 Gy was calculated. The injury levels of radiation were evaluated by the detection of biological indicators. The result of microdosimetric experiment suggested that the dose of whole body of nematodes was estimated to be 99.9 ± 57.8 Gy, ranging from 19.6 to 332.2 Gy. The dose of gonad was predicted to be 129.4 ± 558.8 Gy (9.5-6597 Gy). The result of biological experiment suggested that there were little changes in the length of nematodes after irradiation. However, times of head thrash per minute and the spawning yield in 3 consecutive days decreased 27.1% and 94.7%, respectively. Nematodes in the irradiated group displayed heterogeneity. Through contour analysis, trends of behavior kinematics and reproductive capacity of irradiated nematodes proved to be consistent with the dose distribution levels estimated by microdosimetric model. Finally, C. elegans presented a suitable combined model of microdosimetry and biology for studying radiation.

Individual dosimetry system for targeted alpha therapy based on PHITS coupled with microdosimetric kinetic model

BACKGROUND

An individual dosimetry system is essential for the evaluation of precise doses in nuclear medicine. The purpose of this study was to develop a system for calculating not only absorbed doses but also EQDX(α/β) from the PET-CT images of patients for targeted alpha therapy (TAT), considering the dose dependence of the relative biological effectiveness, the dose-rate effect, and the dose heterogeneity.

METHODS

A general-purpose Monte Carlo particle transport code PHITS was employed as the dose calculation engine in the system, while the microdosimetric kinetic model was used for converting the absorbed dose to EQDX(α/β). PHITS input files for describing the geometry and source distribution of a patient are automatically created from PET-CT images, using newly developed modules of the radiotherapy package based on PHITS (RT-PHITS). We examined the performance of the system by calculating several organ doses using the PET-CT images of four healthy volunteers after injecting 18F-NKO-035.

RESULTS

The deposition energy map obtained from our system seems to be a blurred image of the corresponding PET data because annihilation γ-rays deposit their energies rather far from the source location. The calculated organ doses agree with the corresponding data obtained from OLINDA 2.0 within 20%, indicating the reliability of our developed system. Test calculations by replacing the labeled radionuclide from 18F to 211At suggest that large dose heterogeneity in a target volume is expected in TAT, resulting in a significant decrease of EQDX(α/β) for higher-activity injection.

CONCLUSIONS

As an extension of RT-PHITS, an individual dosimetry system for nuclear medicine was developed based on PHITS coupled with the microdosimetric kinetic model. It enables us to predict the therapeutic and side effects of TAT based on the clinical data largely available from conventional external radiotherapy.

Microdosimetric measurements as a tool to assess potential in-field and out-of-field toxicity regions in proton therapy

Relative biological effectiveness (RBE) variations are thought to be one of the primary causes of unexpected normal-tissue toxicities during tumor treatments with charged particles. Unlike carbon therapy, where treatment planning is optimized on the basis of the RBE-weighted dose, a constant RBE value of 1.1 is currently used in proton therapy. Assuming a uniform value can lead to under- or over-dosage, not just to the tumor but also to surrounding normal tissue. RBE changes have been linked with dose/fraction, the biological endpoint and beam properties. Understanding radiation quality and the associated RBE can improve the prediction of normal-tissue toxicities. In this study, we exploited microdosimetry for characterizing radiation quality in proton therapy in-field, and off-beam at 20 (beam edge), 50 (close out-of-field) and 100 (far out-of-field) mm from the beam center. We measured the lineal energy y spectra in a water phantom irradiated with 152 MeV protons, from which beam quality as well as the physical dose could be obtained. Taking advantage of the linear quadratic model and a modified version of the microdosimetric kinetic model, the microdosimetric data were combined with radiobiological parameters (α and β) of human salivary gland tumor cells for assessing cell survival RBE and RBE-weighted dose. The results indicate that if a dose of 60 Gy is delivered to the peak, the beam edge receives up to 6 Gy while the close and far out-of-field regions receive doses on the order of 10^-3 Gy and 10^-4 Gy, respectively. The RBE estimate in-beam shows large variations, ranging from 1.0 ± 0.2 at the entrance channel to 2.51 ± 0.15 at the tail. The beam edge follows a similar trend but the RBE calculated at the Bragg peak depth is 2.27 ± 0.17, i.e. twice the RBE in-beam (1.05 ± 0.15). Out-of-field, the estimated RBE is always significantly higher than 1.1 and increases with increasing lateral distance, reaching the overall highest value of 3.4 ± 0.3 at a depth of 206 mm and a lateral distance of 10 mm. The combination of RBE and dose into the biological dose points to the beam edge and the end-of-range in-beam as the areas with the highest risk of potential toxicities.

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).

Experimental validation of an analytical microdosimetric model based on Geant4-DNA simulations by using a silicon-based microdosimeter

PURPOSE

To study the agreement between proton microdosimetric distributions measured with a silicon-based cylindrical microdosimeter and a previously published analytical microdosimetric model based on Geant4-DNA in-water Monte Carlo simulations for low energy proton beams.

METHODS AND MATERIAL

Distributions for lineal energy (y) are measured for four proton monoenergetic beams with nominal energies from 2.0 MeV to 4.5 MeV, with a tissue equivalent proportional counter (TEPC) and a silicon-based microdosimeter. The actual energy for protons traversing the silicon-based microdosimeter is simulated with SRIM. Monoenergetic beams with these energies are simulated with Geant4-DNA code by simulating a water cylinder site of dimensions equal to those of the microdosimeter. The microdosimeter response is calibrated by using the distribution peaks obtained from the TEPC. Analytical calculations fory ¯ F andy ¯ D using our methodology based on spherical sites are also performed choosing the equivalent sphere to be checked against experimental results.

RESULTS

Distributions for y at silicon are converted into tissue equivalent and compared to the Geant4-DNA simulated, yielding maximum deviations of 1.03% fory ¯ F and 1.17% fory ¯ D . Our analytical method generates maximum deviations of 1.29% and 3.33%, respectively, with respect to experimental results.

CONCLUSION

Simulations in Geant4-DNA with ideal cylindrical sites in liquid water produce similar results to the measurements in an actual silicon-based cylindrical microdosimeter properly calibrated. The found agreement suggests the possibility to experimentally verify the calculated clinicaly ¯ D with our analytical method.

Linear energy transfer weighted beam orientation optimization for intensity-modulated proton therapy

PURPOSE

In intensity-modulated proton therapy (IMPT), unaccounted-for variation in biological effectiveness contributes to the discrepancy between the constant relative biological effectiveness (RBE) model prediction and experimental observation. It is desirable to incorporate biological doses in treatment planning to improve modeling accuracy and consequently achieve a higher therapeutic ratio. This study addresses this demand by developing a method to incorporate linear energy transfer (LET) into beam orientation optimization (BOO).

METHODS

Instead of RBE-weighted dose, this LET weighted BOO (LETwBOO) framework uses the dose and LET product (LET  ×  D) as the biological surrogate. The problem is formulated with a physical dose fidelity term, a LET  ×  D constraint term, and a group sparsity term. The LET  ×  D of organs at risks is penalized for minimizing the biological effect while maintaining the physical dose objectives. Group sparsity is used to reduce the number of active beams from 600-800 non-coplanar candidate beams to between 2 and 4. This LETwBOO method was tested on three skull base tumor (SBT) patients and three bilateral head-and-neck (H&N) patients. The LETwBOO plans were compared with IMPT plans using manually selected beams with only physical dose constraint (MAN) and the initial MAN plan reoptimized with additional LET  ×  D constraint (LETwMAN).

RESULTS

The LETwBOO plans show superior physical dose and LET  ×  D sparing. On average, the [mean, maximal] doses of organs at risks (OARs) in LETwBOO are reduced by [2.85, 4.6] GyRBE from the MAN plans in the SBT cases and reduced by [0.9, 2.5] GyRBE in the H&N cases, while LETwMAN is comparable to MAN. cLET × Ds of PTVs are comparable in LETwBOO and LETwMAN, where c is a scaling factor of 0.04 μm/keV. On average, in the SBT cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [1.1, 2.9] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.7, 1.7] Gy. In the H&N cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [0.8, 2.6] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.3, 1.2] Gy.

CONCLUSION

We developed a novel LET weighted BOO method for IMPT to generate plans with improved physical and biological OAR sparing compared with the plans unaccounted for biological effects from BOO.

A new approach to modeling the microdosimetry of proton therapy beams

INTRODUCTION

To revisit the formulation of the mean chord length in microdosimetry and replace it by the particle mean free path appropriate for modelings in radiobiology.

METHODS

We perform a collision-by-collision followed by event-by-event Geant4 Monte Carlo simulation and calculate double-averaged stepping length, 〈〈l〉〉, for a range of target sizes from mm down to μm and depth in water. We consider 〈〈l〉〉 to represent the particle mean free path.

RESULTS

We show that 〈〈l〉〉 continuously drops as a function of depth and asymptotically saturates to a minimum value in low energies, where it exhibits a universal scaling behavior, independent of particle nominal beam energy. We correlate 〈〈l〉〉 to linear density of DNA damage, complexities of initial lethal lesions and illustrate a relative difference between predictive RBEs in model calculations using mean chord length vs the proposed mean free path. We demonstrate consistency between rapid increase in RBE within and beyond the Bragg peak and 〈〈l〉〉, a decreasing function of depth.

DISCUSSION AND CONCLUSION

An interplay between localities in imparted energy at nanometer scale and subsequent physio-chemical processes, causalities and pathways in DNA damage requires substitution of geometrical chord length of cell nuclei by mean-free path of proton and charged particles to account for a mean distance among sequential collisions in DNA materials. To this end, the event averaging over cell volume in the current microdosimetry formalism must be superseded by the collision averaging scored within the volume. The former, is fundamentally a global attribute of the cell nuclei surfaces and boundaries and is characterized by their membrane diameters, hence such global indices are not appropriate to quantitatively represent the radiobiological strength of the particles and their RBE variabilities that is associated with the sensitivities to local structure of the collisions and their spatio-temporal collective patterns in DNA materials.

Validation of mammographic x-ray spectra generated using Particle and Heavy Ion Transport code System

A Monte Carlo (MC) code is a robust method to generate a mammographic x-ray spectrum because the geometry of a mammography system can be flexible and directly modeled in MC simulation. However, simulations from MC code need to be validated before it can be reliably used for specific applications. This study aimed to generate and validate the x-ray spectra of relevant anodes used in mammography and breast tomosynthesis using Particle and Heavy Ion Transport code System (PHITS). PHITS version 3.08 was used to generate the x-ray spectra of molybdenum (Mo), rhodium (Rh), and tungsten (W) anodes. The Mo anode spectrum derived using PHITS was compared with those obtained using other MC codes. The generated spectra of all anodes were compared with the literature. Parameters including spectral shape, K characteristic x-ray yield, heel effect, and half-value layer (HVL) were used for a comparative assessment. The differences in these assessment parameters conducted by PHITS and PHITSEGS5 simulations were studied. Regarding the comparative parameters, PHITSEGS5 simulation improved the accuracy of mammographic x-ray generation compared to PHITS simulation; K x-ray and bremsstrahlung yields of the Mo anode spectrum generated by PHITSEGS5 simulation were a better agreement with those generated by other MC code simulations. The PHITSEGS5 spectra overestimated K x-ray and low-energy bremsstrahlung photons in comparison with measured spectra. Subsequently, HVLs calculated from PHITSEGS5 spectra were 1.0% (Mo/Mo) and 7.0% (W/Al) lower than those derived from measured spectra. For Mo and Rh anodes, relative difference of HVLs calculated from PHITSEGS5 spectra and those obtained from literature and measurement were within the TRS 457 acceptance criteria (±0.02 mm Al). The observed difference exceeded the acceptance criteria for W anode. Regarding existed consistency in HVL between simulation and measurement, PHITSEGS5 simulation can be reliably used to generate x-ray spectra of Mo and Rh anodes. However, its accuracy should be improved for generating W anode spectrum.

Establishment of a New Three-Dimensional Dose Evaluation Method Considering Variable Relative Biological Effectiveness and Dose Fractionation in Proton Therapy Combined with High-Dose-Rate Brachytherapy

Purpose:

The purpose of this study is to evaluate the influence of variable relative biological effectiveness (RBE) of proton beam and dose fractionation has on dose distribution and to establish a new three-dimensional dose evaluation method for proton therapy combined with high-dose-rate (HDR) brachytherapy.

Materials and Methods:

To evaluate the influence of variable RBE and dose fractionation on dose distribution in proton beam therapy, the depth-dose distribution of proton therapy was compared with clinical dose, RBE-weighted dose, and equivalent dose in 2 Gy fractions using a linear-quadratic-linear model (EQD2_LQL). The clinical dose was calculated by multiplying the physical dose by RBE of 1.1. The RBE-weighted dose is a biological dose that takes into account RBE variation calculated by microdosimetric kinetic model implemented in Monte Carlo code. The EQD2_LQL is a biological dose that makes the RBE-weighted dose equivalent to 2 Gy using a linear-quadratic-linear (LQL) model. Finally, we evaluated the three-dimensional dose by taking into account RBE variation and LQL model for proton therapy combined with HDR brachytherapy.

Results:

The RBE-weighted dose increased at the distal of the spread-out Bragg peak (SOBP). With the difference in the dose fractionation taken into account, the EQD2_LQL at the distal of the SOBP increased more than the RBE-weighted dose. In proton therapy combined with HDR brachytherapy, a divergence of 103% or more was observed between the conventional dose estimation method and the dose estimation method we propose.

Conclusions:

Our dose evaluation method can evaluate the EQD2_LQL considering RBE changes in the dose distribution.

3D-printable lung phantom for distal falloff verification of proton Bragg peak

In proton therapy, the Bragg peak of a proton beam reportedly deteriorates when passing though heterogeneous structures such as human lungs. Previous studies have used heterogeneous random voxel phantoms, in which soft tissues and air are randomly allotted to render the phantoms the same density as human lungs, for conducting Monte Carlo (MC) simulations. However, measurements of these phantoms are complicated owing to their difficult‐to‐manufacture shape. In the present study, we used Voronoi tessellation to design a phantom that can be manufactured, and prepared a Voronoi lung phantom for which both measurement and MC calculations are possible. Our aim was to evaluate the effectiveness of this phantom as a new lung phantom for investigating proton beam Bragg peak deterioration. For this purpose, we measured and calculated the percentage depth dose and the distal falloff widths (DFW) passing through the phantom. For the 155 MeV beam, the measured and calculated DFW values with the Voronoi lung phantom were 0.40 and 0.39 cm, respectively. For the 200 MeV beam, the measured and calculated DFW values with the Voronoi lung phantom were both 0.48 cm. Our results indicate that both the measurements and MC calculations exhibited high reproducibility with plastinated lung sample from human body in previous studies. We found that better results were obtained using the Voronoi lung phantom than using other previous phantoms. The designed phantom may contribute significantly to the improvement of measurement precision. This study suggests that the Voronoi lung phantom is useful for simulating the effects of the heterogeneous structure of lungs on proton beam deterioration.

Determining the energy spectrum of clinical linear accelerator using an optimized photon beam transmission protocol

PURPOSE

The complex beam delivery techniques for patient treatment using a clinical linear accelerator (linac) may result in variations in the photon spectra, which can lead to dosimetric differences in patients that cannot be accounted for by current treatment planning systems (TPSs). Therefore, precise knowledge of the fluence and energy spectrum (ES) of the therapeutic beam is very important. However, owing to the high energy and flux of the beam, the ES cannot be measured directly, and validation of the spectrum modeled in the TPS is difficult. The aim of this study is to develop an efficient beam transmission measurement procedure for accurately reconstructing the ES of a therapeutic x-ray beam generated by a clinical linac.

METHODS

The attenuation of a 6 MV photon beam from an Elekta Synergy Platform clinical linac through different thicknesses of graphite and lead was measured using an ion chamber. The response of the ion chamber as a function of photon energy was obtained using the Monte Carlo (MC) method in the Geant4 simulation code. Using the curves obtained in the photon beam transmission measurements and the ion chamber energy response, the ES was reconstructed using an iterative algorithm based on a mathematical model of the spectrum. To evaluate the accuracy of the spectrum reconstruction method, the reconstructed ES (ES_recon ) was compared to that determined by the MC simulation (ES_MC ).

RESULTS

The ion chamber model in the Geant4 simulation was well validated by comparing the ion chamber perturbation factors determined by the TRS-398 calibration protocol and EGSnrc; the differences were within 0.57%. The number of transmission measurements was optimized to 10 for efficient spectrum reconstruction according to the rate of increase in the spectrum reconstruction accuracy. The distribution of ES_recon obtained using the measured transmission curves was clearly similar to the reference, ES_MC , and the dose distributions in water calculated using ES_recon and ES_MC were similar within a 2% local difference. However, in a heterogeneous medium, the dose discrepancy between them was >5% when a complex beam delivery technique composed of 171 control points was used.

CONCLUSIONS

The proposed measurement procedure required a total time of approximately 1 h to obtain and analyze 20 transmission measurements. In addition, it was confirmed that the transmission curve of high-Z materials influences the accuracy of spectrum reconstruction more than that of low-Z materials. A well-designed transmission measurement protocol suitable for clinical environments could be an essential tool for better dosimetric accuracy in patient treatment and for periodic verification of the beam quality.

Effect of Irradiation Time on Biological Effectiveness and Tumor Control Probability in Proton Therapy

PURPOSE

The biological effectiveness of proton beams may decrease with irradiation time because of sublethal damage repair (SLDR). The purpose of this study is to systematically evaluate this effect in hypofractionated proton therapy for various target sizes, depths, and prescribed doses per fraction.

METHODS AND MATERIALS

Plans with a single spread-out Bragg peak beam were created using a constant relative biological effectiveness (RBE) of 1.1 to cover targets of 6 different sizes located at 3 different depths in water. Biological doses of 2, 3, 5, 10, and 20 Gy (RBE) were prescribed to the targets. First, to investigate the depth variation of the biological effectiveness, the biological dose in instantaneous irradiation was recalculated based on the microdosimetric kinetic model. SLDR was then taken into account in the microdosimetric kinetic model during treatments to obtain the irradiation time-dependent biological effectiveness for irradiation time T of 5 to 60 minutes and beam interruption time τ of 0 to 60 minutes. The tumor control probabilities were calculated for single-fraction proton therapy fields of different Ts and τs, and the curative doses were evaluated at a tumor control probability of 90%.

RESULTS

The biological effectiveness decreased with longer T and τ and higher prescribed dose. The maximum decrease in the biological effectiveness was 21% with a 20 Gy (RBE) prescribed dose. In single-fraction proton therapy, the curative dose increased linearly by approximately 33% to 35% with the increase of T from 0 to 60 minutes.

CONCLUSIONS

The biological effectiveness varies largely with T and τ because of SLDR during treatments. This effect was pronounced for high prescribed doses per fraction. Thus, the effect of SLDR needs to be considered in hypofractionated and single-fraction proton therapies in relation to size and depth of the target.

A novel methodology to assess linear energy transfer and relative biological effectiveness in proton therapy using pairs of differently doped thermoluminescent detectors

A new methodology for assessing linear energy transfer (LET) and relative biological effectiveness (RBE) in proton therapy beams using thermoluminescent detectors is presented. The method is based on the different LET response of two different lithium fluoride thermoluminescent detectors (LiF:Mg,Ti and LiF:Mg,Cu,P) for measuring charged particles. The relative efficiency of the two detector types was predicted using the recently developed Microdosimetric d(z) Model in combination with the Monte Carlo code PHITS. Afterwards, the calculated ratio of the expected response of the two detector types was correlated with the fluence- and dose- mean values of the unrestricted proton LET. Using the obtained proton dose mean LET as input, the RBE was assessed using a phenomenological biophysical model of cell survival. The aforementioned methodology was benchmarked by exposing the detectors at different depths within the spread out Bragg peak (SOBP) of a clinical proton beam at iThemba LABS. The assessed LET values were found to be in good agreement with the results of radiation transport computer simulations performed using the Monte Carlo code GEANT4. Furthermore, the estimated RBE values were compared with the RBE values experimentally determined by performing colony survival measurements with Chinese Hamster Ovary (CHO) cells during the same experimental run. A very good agreement was found between the results of the proposed methodology and the results of the in vitro study.