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Objective. To propose a mathematical model for applying ionization detail (ID), the detailed spatial distribution of ionization along a particle track, to proton and ion beam radiotherapy treatment planning (RTP).Approach. Our model provides for selection of preferred ID parameters (Ip) for RTP, that associate closest to biological effects. Cluster dose is proposed to bridge the large gap between nanoscopicIpand macroscopic RTP. Selection ofIpis demonstrated using published cell survival measurements for protons through argon, comparing results for nineteenIp:Nk,k= 2, 3, …, 10, the number of ionizations in clusters ofkor more per particle, andFk,k= 1, 2, …, 10, the number of clusters ofkor more per particle. We then describe application of the model to ID-based RTP and propose a path to clinical translation.Main results. The preferredIpwereN4andF5for aerobic cells,N5andF7for hypoxic cells. Significant differences were found in cell survival for beams having the same LET or the preferredNk. Conversely, there was no significant difference forF5for aerobic cells andF7for hypoxic cells, regardless of ion beam atomic number or energy. Further, cells irradiated with the same cluster dose for theseIphad the same cell survival. Based on these preliminary results and other compelling results in nanodosimetry, it is reasonable to assert thatIpexist that are more closely associated with biological effects than current LET-based approaches and microdosimetric RBE-based models used in particle RTP. However, more biological variables such as cell line and cycle phase, as well as ion beam pulse structure and rate still need investigation.Significance. Our model provides a practical means to select preferredIpfrom radiobiological data, and to convertIpto the macroscopic cluster dose for particle RTP.

Current Monte Carlo simulations of DNA damage have been reported only at ambient temperature. The aim of this work is to use TOPAS-nBio to simulate the yields of DNA single-strand breaks (SSBs) and double-strand breaks (DSBs) produced in plasmids under low-LET irradiation incorporating the effect of the temperature changes in the environment. A new feature was implemented in TOPAS-nBio to incorporate reaction rates used in the simulation of the chemical stage of water radiolysis as a function of temperature. The implemented feature was verified by simulating temperature-dependentG-values of chemical species in liquid water from 20 °C to 90 °C. For radiobiology applications, temperature dependent SSB and DSB yields were calculated from 0 °C to 42 °C, the range of available published measured data. For that, supercoiled DNA plasmids dissolved in aerated solutions containing EDTA irradiated by Cobalt-60 gamma-rays were simulated. TOPAS-nBio well reproduced published temperature-dependentG-values in liquid water and the yields of SSB and DSB for the temperature range considered. For strand break simulations, the model shows that the yield of SSB and DSB increased linearly with the temperature at a rate of (2.94 ± 0.17) × 10-10Gy-1Da-1°C-1(R2 = 0.99) and (0.13 ± 0.01) × 10-10Gy-1Da-1°C-1(R2 = 0.99), respectively. The extended capability of TOPAS-nBio is a complementary tool to simulate realistic conditions for a large range of environmental temperatures, allowing refined investigations of the biological effects of radiation.

PurposeSimulation of indirect damage originating from the attack of free radical species produced by ionizing radiation on biological molecules based on the independent pair approximation is investigated in this work. In addition, a new approach, relying on the independent pair approximation that is at the origin of the independent reaction time (IRT) method, is proposed in the chemical stage of Geant4-DNA.MethodsThis new approach has been designed to respect the current Geant4-DNA chemistry framework while proposing a variant IRT method. Based on the synchronous algorithm, this implementation allows us to access the information concerning the position of radicals and may make it more convenient for biological damage simulations. Estimates of the evolution of free species as well as biological hits in a segment of DNA chromatin fiber in Geant4-DNA were compared for the dynamic time step approach of the step-by-step (SBS) method, currently used in Geant4-DNA, and this newly implemented IRT.ResultsResults show a gain in computation time of a factor of 30 for high LET particle tracks with a better than 10% agreement on the number of DNA hits between the value obtained with the IRT method as implemented in this work and the SBS method currently available in Geant4-DNA.ConclusionOffering in Geant4-DNA more efficient methods for the chemical step based on the IRT method is a task in progress. For the calculation of biological damage, information on the position of chemical species is a crucial point. This can be achieved using the method presented in this paper.

PurposeThe simulation of individual particle tracks and the chemical stage following water radiolysis in biological tissue is an effective means of improving our knowledge of the physico-chemical contribution to the biological effect of ionizing radiation. However, the step-by-step simulation of the reaction kinetics of radiolytic species is the most time-consuming task in Monte Carlo track-structure simulations, with long simulation times that are an impediment to research. In this work, we present the implementation of the independent reaction times (IRT) method in Geant4-DNA Monte Carlo toolkit to improve the computational efficiency of calculating G-values, defined as the number of chemical species created or lost per 100 eV of deposited energy.MethodsThe computational efficiency of IRT, as implemented, is compared to that from available Geant4-DNA step-by-step simulations for electrons, protons and alpha particles covering a wide range of linear energy transfer (LET). The accuracy of both methods is verified using published measured data from fast electron irradiations for • OH and eaq- for time-dependent G-values. For IRT, simulations in the presence of scavengers irradiated by cobalt-60 γ-ray and 2 MeV protons are compared with measured data for different scavenging capacities. In addition, a qualitative assessment comparing measured LET-dependent G-values with Geant4-DNA calculations in pure liquid water is presented.ResultsThe IRT improved the computational efficiency by three orders of magnitude relative to the step-by-step method while differences in G-values by 3.9% at 1 μs were found. At 7 ps, • OH and eaq- yields calculated with IRT differed from recent published measured data by 5% ± 4% and 2% ± 4%, respectively. At 1 μs, differences were 9% ± 5% and 6% ± 7% for • OH and eaq- , respectively. Uncertainties are one standard deviation. Finally, G-values at different scavenging capacities and LET-dependent G-values reproduced the behavior of measurements for all radiation qualities.ConclusionThe comprehensive validation of the Geant4-DNA capabilities to accurately simulate the chemistry following water radiolysis is an ongoing work. The implementation presented in this work is a necessary step to facilitate performing such a task.

Monte Carlo (MC) track structure simulation tools are commonly used for predicting radiation induced DNA damage by modeling the physical and chemical reactions at the nanometer scale. However, the outcome of these MC simulations is particularly sensitive to the adopted parameters which vary significantly across studies. In this study, a previously developed full model of nuclear DNA was used to describe the DNA geometry. The TOPAS-nBio MC toolkit was used to investigate the impact of physics and chemistry models as well as three key parameters (the energy threshold for direct damage, the chemical stage time length, and the probability of damage between hydroxyl radical reactions with DNA) on the induction of DNA damage. Our results show that the difference in physics and chemistry models alone can cause differences up to 34% and 16% in the DNA double strand break (DSB) yield, respectively. Additionally, changing the direct damage threshold, chemical stage length, and hydroxyl damage probability can cause differences of up to 28%, 51%, and 71% in predicted DSB yields, respectively, for the configurations in this study.

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

Inverse treatment planning in intensity modulated particle therapy (IMPT) with scanned carbon-ion beams is currently based on the optimization of RBE-weighted dose to satisfy requirements of target coverage and limited toxicity to organs-at-risk (OARs) and healthy tissues. There are many feasible IMPT plans that meet these requirements, which allows the introduction of further criteria to narrow the selection of a biologically optimal treatment plan. We propose a novel treatment planning strategy based on the simultaneous optimization of RBE-weighted dose and nanometric ionization details (ID) as a new physical characteristic of the delivered plan beyond LET. In particular, we focus on the distribution of large ionization clusters (more than 3 ionizations) to enhance the biological effect across the target volume while minimizing biological effect in normal tissues. Carbon-ion treatment plans for different patient geometries and beam configurations generated with the simultaneous optimization strategy were compared against reference plans obtained with RBE-weighted dose optimization alone. Quality indicators, inhomogeneity index and planning volume histograms of RBE-weighted dose and large ionization clusters were used to evaluate the treatment plans. We show that with simultaneous optimization, ID distributions can be optimized in carbon-ion radiotherapy without compromising the RBE-weighted dose distributions. This strategy can potentially be used to account for optimization of endpoints closely related to radiation quality to achieve better tumor control and reduce risks of complications.

Details of the pattern of ionization formed by particle tracks extends knowledge of dose effects on the nanometer scale. Ionization detail (ID), frequently characterized by ionization cluster size distributions (ICSD), is obtained through time-consuming Monte Carlo (MC) track-structure simulations. In this work, TOPAS-nBio was used to generate a highly precise database of biologically significant ID quantities, sampled with randomly oriented 2.3 nm diameter cylinders, 3.4 nm (10 base pairs) long, inside a chromatin-size cylinder, irradiated by 1-1000 MeV/u ions of Z  =  1-8. A macroscopic method developed to utilize the database using condensed-history MC was used to calculate distributions of the ICSD first moment [Formula: see text] and cumulative probability [Formula: see text] in a 20  ×  20  ×  40 cm3 water phantom irradiated with proton and carbon spread-out Bragg peak (SOBP) of 10.5 cm range, 2 cm width. Results were verified against detailed MC track-structure simulations using phase space scored at several depths. ID distributions were then obtained for intensity modulated proton and carbon radiotherapy plans in a digitized anthropomorphic phantom of a base of skull tumor to demonstrate clinical application of this approach. The database statistical uncertainties were 0.5% (3 standard deviations). Fluence-averaged ID as implemented proved unsuitable for macroscopic calculation. E dep-averaged ID agreed with track-structure results within 0.8% for protons. For carbon, maximum absolute differences of 2.9%  ±  1.6% and 5.6%  ±  1.9% for [Formula: see text], 1.7%  ±  0.8% and 1.9%  ±  0.4% (1 standard deviation) for [Formula: see text], were found in the plateau and SOBP, respectively, up to 11.5%  ±  5.6% in the tail region. Macroscopic ID calculation was demonstrated for a realistic treatment plan. Computation times with or without ID calculation were comparable in all cases. Pre-calculated nanodosimetric data may be used for condensed-history MC for nanodosimetric ID-based treatment planning in ion radiotherapy in the future. The macroscopic approach developed has the calculation speed of condensed-history MC while approaching the accuracy of full track structure simulations.

Computational simulations, such as Monte Carlo track structure simulations, offer a powerful tool for quantitatively investigating radiation interactions within cells. The modelling of the spatial distribution of energy deposition events as well as diffusion of chemical free radical species, within realistic biological geometries, can help provide a comprehensive understanding of the effects of radiation on cells. Track structure simulations, however, generally require advanced computing skills to implement. The TOPAS-nBio toolkit, an extension to TOPAS (TOol for PArticle Simulation), aims to provide users with a comprehensive framework for radiobiology simulations, without the need for advanced computing skills. This includes providing users with an extensive library of advanced, realistic, biological geometries ranging from the micrometer scale (e.g. cells and organelles) down to the nanometer scale (e.g. DNA molecules and proteins). Here we present the geometries available in TOPAS-nBio.

PurposeTo evaluate the accuracy of relative stopping power and spatial resolution of images reconstructed with simulated helium CT (HeCT) in comparison to proton CT (pCT).MethodsA Monte Carlo (MC) study with the TOPAS tool was performed to compare the accuracy of relative stopping power (RSP) reconstruction and spatial resolution of low-fluence HeCT to pCT, both using 200 MeV/u particles. An ideal setup consisting of a flat beam source and a totally absorbing energy-range detector was implemented to estimate the theoretically best achievable RSP accuracy for the calibration and reconstruction methods currently used for pCT. The phantoms imaged included a cylindrical water phantom with inserts of different materials, sizes, and positions, a Catphan phantom with a module containing high-contrast line pairs (CTP528) and a module with cylindrical inserts of different RSP (CTP404), as well as a voxelized 10-year-old female phantom. Dose to the cylindrical water phantom was also calculated. The RSP accuracy was studied for all phantoms except the CTP528 module. The latter was used for the estimation of the spatial resolution, evaluated as the modulation transfer function (MTF) at 10%.ResultsAn overall error under 0.5% was achieved for HeCT for the water phantoms with the different inserts, in all cases better than that for pCT, in some cases by a factor 3. The inserts in the CTP404 module were reconstructed with an average RSP accuracy of 0.3% for HeCT and 0.2% for pCT. Anatomic structures (brain, bones, air cavities, etc.) in the digitized head phantom were well recognizable and no artifacts were visible with both HeCT and pCT. The three main tissue materials (soft tissue, brain, and cranium) were well identifiable in the reconstructed RSP-volume distribution with both imaging modalities. Using 360 projection angles, the spatial resolution was 4 lp/cm for HeCT and 3 lp/cm for pCT. Generally, spatial resolution increased with the number of projection angles and was always higher for HeCT than for pCT for the same number of projections. When HeCT and pCT scan were performed to deliver the same dose in the phantom, the resolution for HeCT was higher than pCT.ConclusionMC simulations were used to compare HeCT and pCT image reconstruction. HeCT images had similar or better RSP accuracy and higher spatial resolution compared to pCT. Further investigation of the potential of helium ion imaging is warranted.

Flagged uniform particle splitting was implemented with two methods to improve the computational efficiency of Monte Carlo track structure simulations with TOPAS-nBio by enhancing the production of secondary electrons in ionization events. In method 1 the Geant4 kernel was modified. In method 2 Geant4 was not modified. In both methods a unique flag number assigned to each new split electron was inherited by its progeny, permitting reclassification of the split events as if produced by independent histories. Computational efficiency and accuracy were evaluated for simulations of 0.5-20 MeV protons and 1-20 MeV u-1 carbon ions for three endpoints: (1) mean of the ionization cluster size distribution, (2) mean number of DNA single-strand breaks (SSBs) and double-strand breaks (DSBs) classified with DBSCAN, and (3) mean number of SSBs and DSBs classified with a geometry-based algorithm. For endpoint (1), simulation efficiency was 3 times lower when splitting electrons generated by direct ionization events of primary particles than when splitting electrons generated by the first ionization events of secondary electrons. The latter technique was selected for further investigation. The following results are for method 2, with relative efficiencies about 4.5 times lower for method 1. For endpoint (1), relative efficiency at 128 split electrons approached maximum, increasing with energy from 47.2  ±  0.2 to 66.9  ±  0.2 for protons, decreasing with energy from 51.3  ±  0.4 to 41.7  ±  0.2 for carbon. For endpoint (2), relative efficiency increased with energy, from 20.7  ±  0.1 to 50.2  ±  0.3 for protons, 15.6  ±  0.1 to 20.2  ±  0.1 for carbon. For endpoint (3) relative efficiency increased with energy, from 31.0  ±  0.2 to 58.2  ±  0.4 for protons, 23.9  ±  0.1 to 26.2  ±  0.2 for carbon. Simulation results with and without splitting agreed within 1% (2 standard deviations) for endpoints (1) and (2), within 2% (1 standard deviation) for endpoint (3). In conclusion, standard particle splitting variance reduction techniques can be successfully implemented in Monte Carlo track structure codes.

The aim of this work is to extend a widely used proton Monte Carlo tool, TOPAS, towards the modeling of relative biological effect (RBE) distributions in experimental arrangements as well as patients. TOPAS provides a software core which users configure by writing parameter files to, for instance, define application specific geometries and scoring conditions. Expert users may further extend TOPAS scoring capabilities by plugging in their own additional C++ code. This structure was utilized for the implementation of eight biophysical models suited to calculate proton RBE. As far as physics parameters are concerned, four of these models are based on the proton linear energy transfer, while the others are based on DNA double strand break induction and the frequency-mean specific energy, lineal energy, or delta electron generated track structure. The biological input parameters for all models are typically inferred from fits of the models to radiobiological experiments. The model structures have been implemented in a coherent way within the TOPAS architecture. Their performance was validated against measured experimental data on proton RBE in a spread-out Bragg peak using V79 Chinese Hamster cells. This work is an important step in bringing biologically optimized treatment planning for proton therapy closer to the clinical practice as it will allow researchers to refine and compare pre-defined as well as user-defined models.

PurposeTo measure depth dose curves for a 67.5 ± 0.1 MeV proton beam for benchmarking and validation of Monte Carlo simulation.MethodsDepth dose curves were measured in 2 beam lines. Protons in the raw beam line traversed a Ta scattering foil, 0.1016 or 0.381 mm thick, a secondary emission monitor comprised of thin Al foils, and a thin Kapton exit window. The beam energy and peak width and the composition and density of material traversed by the beam were known with sufficient accuracy to permit benchmark quality measurements. Diodes for charged particle dosimetry from two different manufacturers were used to scan the depth dose curves with 0.003 mm depth reproducibility in a water tank placed 300 mm from the exit window. Depth in water was determined with an uncertainty of 0.15 mm, including the uncertainty in the water equivalent depth of the sensitive volume of the detector. Parallel-plate chambers were used to verify the accuracy of the shape of the Bragg peak and the peak-to-plateau ratio measured with the diodes. The uncertainty in the measured peak-to-plateau ratio was 4%. Depth dose curves were also measured with a diode for a Bragg curve and treatment beam spread out Bragg peak (SOBP) on the beam line used for eye treatment. The measurements were compared to Monte Carlo simulation done with geant4 using topas.ResultsThe 80% dose at the distal side of the Bragg peak for the thinner foil was at 37.47 ± 0.11 mm (average of measurement with diodes from two different manufacturers), compared to the simulated value of 37.20 mm. The 80% dose for the thicker foil was at 35.08 ± 0.15 mm, compared to the simulated value of 34.90 mm. The measured peak-to-plateau ratio was within one standard deviation experimental uncertainty of the simulated result for the thinnest foil and two standard deviations for the thickest foil. It was necessary to include the collimation in the simulation, which had a more pronounced effect on the peak-to-plateau ratio for the thicker foil. The treatment beam, being unfocussed, had a broader Bragg peak than the raw beam. A 1.3 ± 0.1 MeV FWHM peak width in the energy distribution was used in the simulation to match the Bragg peak width. An additional 1.3-2.24 mm of water in the water column was required over the nominal values to match the measured depth penetration.ConclusionsThe proton Bragg curve measured for the 0.1016 mm thick Ta foil provided the most accurate benchmark, having a low contribution of proton scatter from upstream of the water tank. The accuracy was 0.15% in measured beam energy and 0.3% in measured depth penetration at the Bragg peak. The depth of the distal edge of the Bragg peak in the simulation fell short of measurement, suggesting that the mean ionization potential of water is 2-5 eV higher than the 78 eV used in the stopping power calculation for the simulation. The eye treatment beam line depth dose curves provide validation of Monte Carlo simulation of a Bragg curve and SOBP with 4%/2 mm accuracy.

PurposeTo present the implementation and validation of a geometrical based variance reduction technique for the calculation of phase space data for proton therapy dose calculation.MethodsThe treatment heads at the Francis H Burr Proton Therapy Center were modeled with a new Monte Carlo tool (TOPAS based on Geant4). For variance reduction purposes, two particle-splitting planes were implemented. First, the particles were split upstream of the second scatterer or at the second ionization chamber. Then, particles reaching another plane immediately upstream of the field specific aperture were split again. In each case, particles were split by a factor of 8. At the second ionization chamber and at the latter plane, the cylindrical symmetry of the proton beam was exploited to position the split particles at randomly spaced locations rotated around the beam axis. Phase space data in IAEA format were recorded at the treatment head exit and the computational efficiency was calculated. Depth-dose curves and beam profiles were analyzed. Dose distributions were compared for a voxelized water phantom for different treatment fields for both the reference and optimized simulations. In addition, dose in two patients was simulated with and without particle splitting to compare the efficiency and accuracy of the technique.ResultsA normalized computational efficiency gain of a factor of 10-20.3 was reached for phase space calculations for the different treatment head options simulated. Depth-dose curves and beam profiles were in reasonable agreement with the simulation done without splitting: within 1% for depth-dose with an average difference of (0.2 ± 0.4)%, 1 standard deviation, and a 0.3% statistical uncertainty of the simulations in the high dose region; 1.6% for planar fluence with an average difference of (0.4 ± 0.5)% and a statistical uncertainty of 0.3% in the high fluence region. The percentage differences between dose distributions in water for simulations done with and without particle splitting were within the accepted clinical tolerance of 2%, with a 0.4% statistical uncertainty. For the two patient geometries considered, head and prostate, the efficiency gain was 20.9 and 14.7, respectively, with the percentages of voxels with gamma indices lower than unity 98.9% and 99.7%, respectively, using 2% and 2 mm criteria.ConclusionsThe authors have implemented an efficient variance reduction technique with significant speed improvements for proton Monte Carlo simulations. The method can be transferred to other codes and other treatment heads.

We design a practical procedure for measuring translational and rotational misalignment of graticule with collimator axis of rotation and collimator jaws, respectively. The procedure's quantitative results are accurate to less than 0.2 mm (at isocenter) and do not assume alignment of radiation focal spot with collimator axis of rotation. When provided with these quantitative results, the manufacturer can custom-adjust graticules to the purchaser's collimator head.