Inelastic Nuclear Interactions Research Articles

GPU-based fast Monte Carlo dose calculation for proton therapy

Accurate radiation dose calculation is essential for successful proton radiotherapy. Monte Carlo (MC) simulation is considered to be the most accurate method. However, the long computation time limits it from routine clinical applications. Recently, graphics processing units (GPUs) have been widely used to accelerate computationally intensive tasks in radiotherapy. We have developed a fast MC dose calculation package, gPMC, for proton dose calculation on a GPU. In gPMC, proton transport is modeled by the class II condensed history simulation scheme with a continuous slowing down approximation. Ionization, elastic and inelastic proton nucleus interactions are considered. Energy straggling and multiple scattering are modeled. Secondary electrons are not transported and their energies are locally deposited. After an inelastic nuclear interaction event, a variety of products are generated using an empirical model. Among them, charged nuclear fragments are terminated with energy locally deposited. Secondary protons are stored in a stack and transported after finishing transport of the primary protons, while secondary neutral particles are neglected. gPMC is implemented on the GPU under the CUDA platform. We have validated gPMC using the TOPAS/Geant4 MC code as the gold standard. For various cases including homogeneous and inhomogeneous phantoms as well as a patient case, good agreements between gPMC and TOPAS/Geant4 are observed. The gamma passing rate for the 2%/2 mm criterion is over 98.7% in the region with dose greater than 10% maximum dose in all cases, excluding low-density air regions. With gPMC it takes only 6–22 s to simulate 10 million source protons to achieve ∼1% relative statistical uncertainty, depending on the phantoms and energy. This is an extremely high efficiency compared to the computational time of tens of CPU hours for TOPAS/Geant4. Our fast GPU-based code can thus facilitate the routine use of MC dose calculation in proton therapy.

The impact of modeling nuclear fragmentation on delivered dose and radiobiology in ion therapy

The importance of nuclear interactions for ion therapy arises from the influence of the particle spectrum on, first, radiobiology and therefore also on treatment planning, second, the accuracy of measuring dose and, third, the delivered dose distribution. This study tries to determine the qualitative as well as the quantitative influence of the modeling of inelastic nuclear interactions on ion therapy. Thereby, three key disciplines are investigated, namely dose delivery, dose assessment and radiobiology. In order to perform a quantitative analysis, a relative comparison between six different descriptions of nuclear interactions is carried out for carbon ions. The particle transport is simulated with the Monte Carlo code SHIELD-HIT10A while dose planning and radiobiology are covered by the analytic treatment planning program for particles TRiP, which determines the relative biological effectiveness (RBE) with the local effect model. The obtained results show that the physical dose distribution can in principle be significantly influenced by the modeling of fragmentation (about 10% for a 20% change in all inelastic nuclear cross sections for a target volume ranging from 15 to 25 cm). While the impact of nuclear fragmentation on stopping power ratios can be neglected, the fluence correction factor may be influenced by the applied nuclear models. In contrast to the results for the physical dose, the variation of the RBE is only small (about 1% for a 20% change in all inelastic nuclear cross sections) suggesting a relatively weak dependence of radiobiology on the detailed composition of the particle energy spectrum of the mixed radiation field. Also, no significant change (about 0.2 mm) of the lateral penumbra of the RBE-weighted dose is observed.

Inelastic nuclear interactions at protons multiple passage in bent crystals

Inelastic nuclear interactions for relativistic channeled and quasi-channeled protons in a bent crystal are theoretically studied. Multiple passage of projectiles through experimental setup was in details analyzed. Paying attention to the features observed, simulation results have been compared with known experimental data.

Nuclear interactions at volume reflection: Perturbative treatment

Excess of nuclear interaction probability at volume reflection is evaluated within the approximation of dominance of the continuous planar potential and thin nuclear concentrations. The domain of the adopted approximations is determined. An estimate of the volume capture probability is provided. The theoretical predictions for inelastic nuclear interaction probability and for the final beam divergence are compared with the results of recent experiments, with satisfactory agreement within the theory applicability domain.

Elevated LET components in clinical proton beams

This paper assesses the contribution of secondary particles to pencil and passively scattered proton beams, in particular when considering the dose-averaged linear energy transfer (LETd) in biological treatment planning. Proton Monte Carlo simulations are performed in water phantoms and for two patients, considering all primary and secondary particles, including recoils from inelastic nuclear interactions. Our results show that secondary protons exhibit LETd values up to a factor 10 higher than those of the primary protons at the same depth. Thus, secondary protons have a significant impact on the LETd. Their contribution increases the LETd by ∼50% along the central axis and even >200% in the penumbra. Furthermore, the LET maximum after the peak changes from 12 to 15 keV µm−1 when adding secondary protons to the primary contribution. This is important when modeling LETd with analytical methods. The contribution of recoils (A > 3) is observed to be 1.2% in the entrance region considering a prostate case. The degree of biological damage inflicted by recoils remains hard to quantify, but is discussed on the basis of detailed energy spectra. The results highlight the role of secondary protons in LET-based radiobiological effectiveness calculations for proton therapy and when analyzing radiobiological experiments. Furthermore, the findings demonstrate the impact of inhomogeneities on the LET and the subtle changes between the LET distributions of passively scattered and actively scanned beams.

A Monte Carlo evaluation of carbon and lithium ions dose distributions in water

Purpose: To compare dose distributions on the central- and off-axis for 12C and 7Li ion beams simulated by the codes SHIELD-HIT (Heavy Ion Transport) and FLUKA (FLUKtuierende KAskade), and compare with experimental data for 300 MeV/u 12C and 185 MeV/u 7Li ion beams.Materials and methods: The general purpose Monte Carlo codes, SHIELD-HIT10 and FLUKA 2008.3d.1 were used for the ion dose distribution calculations. SHIELD-HIT transports hadrons and atomic nuclei of arbitrary charge and mass number in an energy range from 1 keV/u up to 1 GeV/u. Similarly, FLUKA transports charged hadrons in an energy range from 100 keV up to 20 TeV. Neutrons are transported down to thermal energies in both codes. Inelastic nuclear interactions are modelled in SHIELD-HIT by the Many Stage Dynamical Model (MSDM), whereas in FLUKA the Pre-Equilibrium Approach to Nuclear Thermalisation (PEANUT) package which includes a Generalized Intra-Nuclear Cascade model was used.Results: The dose distributions in water irradiated with 300 MeV/u 12C and 185 MeV/u 7Li ion beams were simulated with the two codes. Studies were performed of the energy deposition both on the central axis and at lateral distances up to 10 cm off-axis. The dose distributions calculated by SHIELD-HIT and FLUKA were compared with published experimental data. The dose mean lineal energy , frequency mean lineal energy , dose mean specific energy , and frequency mean specific energy were calculated with the ion track-structure code PITS99 (Positive Ion Track Structure 99), coupled with the electron code KURBUC for the primary and secondary ions average energies at 1 mm before the Bragg peak.Conclusion: The Monte Carlo codes show good agreement with experimental results for off-axis dose distributions. The disagreements in the Bragg peak region for the central-axis dose distributions imply that further improvements especially in the nuclear interaction models are required to increase the accuracy of the codes.

MO-G-BRC-05: Impact of Secondary Particles on Linear Energy Transfer for Biological Treatment Planning in Proton Therapy

Purpose: To assess the contribution of secondary particles to pencil and passively scatteredproton beams, in particular to determine the impact on linear energy transfer (LET), a central quantity in biological treatment planning. Methods: ProtonMonte Carlo simulations were performed directly in patient geometries considering all primary and secondary particles, including recoils stemming from inelastic nuclear interactions. Simulations were conducted for a prostate and a head&neck case to investigate the impact of different initial proton energies. Results: Examination of the results reveals that secondary protons exhibit LET‐ values up to a factor 10 higher than those of the primary protons in the same region. This causes significant changes to the dose‐averaged LET when including secondary protons, from 50% along the central axis of the beam to >200% in the penumbra. Furthermore the LET‐maximum increases from 12 to 15 MeV/mm. The contribution of recoils (A>3) was observed to be 1.2% in the entrance region of the prostate case, increasing slightly compared to the same beam in a water phantom. The degree of biological damage inflicted by recoils remains hard to quantify, but can be discussed on account of detailed energy spectra of the preeminent particles. Conclusions: These results indicate that secondary protons have a significant influence on LET and should therefore be incorporated into RBE calculations for proton therapy, as well as into radiobiological experiments. The contribution of heavier secondary particles is complex, yet may have an impact on precise measurements of the radiobiological effectiveness (RBE) of protons, especially in the plateau region of high‐energy beams. In addition the LET distributions presented demonstrate the impact of inhomogeneities on the LET and the subtle changes between the LET distributions of passively scattered and actively scanned beams. The latter observation suggests higher RBE variations in active scanning than in passively scattered fields. The project was supported by the Federal Share of program income earned by Massachusetts General Hospital on C06 CA059267, Proton Therapy Research and Treatment Center.

A fast numerical method for calculating the 3D proton dose profile in a single-ring wobbling spreading system

Based on the determination of protons fluence at the phantom's surface, a 3D dose distribution is calculated inside a water phantom using a fast method. The dose contribution of secondary particles, originating from inelastic nuclear interactions, is also taken into account. This is achieved by assuming that 60% of the energy transferred to secondary particles is locally absorbed. Secondary radiation delivers approximately 16.8% of the total dose in the plateau region of the Bragg curve for monoenergetic protons of energy 190 MeV. The physical dose beyond the Bragg peak is obtained for a proton beam of 190 MeV using a Geant4 simulation. It is found that the dose beyond the Bragg peak is <0.02% of the maximum dose and is mainly delivered by protons produced via reactions of the secondary neutrons. The relative dose profile is also calculated by simulation of the proposed beam line in Geant4 code. The dose profile produced by our method agrees, within 2%, with the results predicted by the Fermi Eyges distribution function and the results of the Geant4 simulation. It is expected that the fast numerical approach proposed herein may be utilised in 3D deterministic treatment planning programs, to model proton propagation in order to analyse the effect of modifying the beam line.

First results on the SPS beam collimation with bent crystals

Experiments were performed at the CERN SPS with 120 GeV/c stored proton beams to assess the possibility of beam halo collimation assisted by bent crystals. A bent crystal was used to deflect horizontally by an angle of about 170 μrad the beam halo protons in channeling states directing them into a 60 cm long tungsten absorber. The halo loss rate due to nuclear inelastic interactions of protons in the aligned crystal was up to five times smaller than for its amorphous orientation. Channeled fractions, (75±4)% and (85±5)% for the two tested silicon crystals, were measured by intercepting the deflected beam with another collimator located between the crystals and the absorber. The pixel detector (MEDIPIX) installed in a Roman pot inside the beam pipe was used to obtain visual images of the deflected beam.

Probability of inelastic nuclear interactions of high-energy protons in a bent crystal

Probability of inelastic nuclear interactions in a short bent silicon crystal for its orientations optimal for channeling and volume reflection was investigated using 400 GeV/c protons of the CERN SPS. The contribution of nuclear interactions from channeled protons was observed to be about 3–4% of the probability for the amorphous orientation. For the crystal orientation optimal for volume reflection the nuclear interaction probability of protons was a few percents larger than in the amorphous case. It was shown that in the limiting case of a quasi parallel beam realizing for the collider beam halo the inelastic nuclear losses should decrease by more than five times, which is an additional advantage of a crystal as a primary collimator for the LHC collimation system.

On azimuthal anisotropy in fragmentation of a classical relativistic string

A fragmenting relativistic string is widely used for modeling particle production via quark–gluon strings formed in hadronic and nuclear inelastic interactions at high energies. In this note we focus on motion and fragmentation of a relativistic string with non-zero transverse separation of its ends and study this scenario as a possible mechanism for bringing anisotropy into the azimuthal angle distribution of produced particles in inelastic interactions of hadrons.

Testing the engineering sample of the NUCLEON setup on a pion beam

Results from testing the sample of the setup for the NUCLEON experiment aimed at studying the energy spectra and the charge composition of cosmic rays in the energy range of 1012–1015 eV are presented. The sample has been made approach the actual setup to the maximum degree. Charged particle beams with energies of 200–350 GeV have been used for testing. The problem of selecting high-energy events and the accuracy of energy measurements using the method being developed are discussed. This method is based on measuring the spatial flux density of secondary particles that are produced in the first act of inelastic nuclear interaction inside the target of the setup and pass through a thin converter layer in which the electromagnetic component is multiplied. The event selection efficiency is shown to be rather high. The precision in determining the energy (90–80%) using this method is in good agreement with simulation results (∼100-80%). The results of the study fully comply with the requirements of the NUCLEON experiment.

MO‐EE‐A2‐01: Nuclear Model Evaluation of Uncertainties in Therapeutic Absorbed Dose and Secondary Neutron Production in Proton Radiotherapy Using MCNPX

Purpose: To evaluate differences in nuclear physics models of MCNPX for uncertainties in 1) the dosimetric characteristics of the therapeutic dose for SOBP and cross‐field profiles and 2) stray neutron fields produced in a proton therapy unit using the default Bertini model option as the baseline. Methods and Materials: The general purpose Monte Carlo N‐Particle eXtended (MCNPX) code was used to calculate the therapeutic absorbed dose and spectral neutron fluence with three nuclear model options: the Bertini Model, the Cascade Exciton Model (CEM), and the Liège Intra‐Nuclear Cascade Model (INCL4). Each model is included as a physics option in MCNPX. For initial beam energy of 160 MeV, dose calculations were carried out in a water phantom positioned 24 cm downstream of the nozzle exit while in‐air calculations of the neutron spectral fluence were tallied in spheres positioned at isocenter, 100 cm downstream of isocenter and at lateral distances of ± 100 cm off‐axis. Calculations of secondary neutrons produced external to the nozzle housing were evaluated among the models for several parameters including the ambient neutron dose equivalent per therapeutic absorbed dose. Results: Our results indicate that calculations of the therapeutic absorbed dose were in close agreement (⩽1% difference) for all nuclear model options. On the other hand, the differences in the neutron spectral fluence calculations typically varied by a factor of 2 or more among the models. Conclusions: We found that all three inelastic nuclear interaction models provided excellent agreement in the therapeutic dose distributions. However, we observed substantial differences in the neutron spectral fluence calculations that suggest further investigation may be desirable for estimating the out of field radiation exposure uncertainties among the models.

Testing the prototype of the NUCLEON setup on the pion beam of the SPS accelerator (CERN)

A technique for determining the energy of primary cosmic rays in the range of 1012–1015 eV has been developed. The idea behind this technique consists in measuring the spatial flux density of secondary particles produced in the first act of inelastic nuclear interaction inside a target and passed through a thin converter layer in which the electromagnetic component (photons from decays of neutral pions) is multiplied. This technique has been developed by generalizing the well-known Castagnoli method (for measuring the angular characteristics of tracks of secondary particles produced in the first act of inelastic nuclear interaction inside a target), and its application offers a chance to design instruments for scientific studies such that their mass is relatively low while their luminosity is high. It is proposed to use this technique in a satellite-based NUCLEON experiment. The technique has been tested on charged particle beams of the SPS accelerator at CERN. Results of these tests confirm that, using this method, it is possible to measure the particle energy and, therefore, perform an orbital scientific experiment with the proposed equipment.

MCNP5 for proton radiography

The developmental version of MCNP5 has recently been extended to provide for continuous-energy transport of high-energy protons. This enhancement involves the incorporation of several significant new physics models into the code. Multiple Coulomb scattering is treated with an advanced model that takes account of projectile and nuclear target form factors. In the next version, this model will provide a coupled sampling of both angular deflection and collisional energy loss, including straggling. The proton elastic scattering model is also new, based on recent theoretical work. Charged particle transport in the presence of magnetic fields is accomplished either by using transfer maps from the COSY INFINITY code (in void regions) or by using an algorithm adapted from the MARS code (in void regions or in scattering materials). Work is underway to validate and implement the latest versions of the Cascade-Exciton Model and the Los Alamos Quark-Gluon String Model, which will process inelastic nuclear interactions and generate secondary particles.

Energy dependence of majority carrier defect introduction rates in p+n GaAs photodiodes irradiated with protons

Traps introduced into p+n GaAs diodes, grown by molecular beam epitaxy, by room temperature irradiation with 1, 4, 10, 50, and 53MeV protons, have been studied using deep--level transient spectroscopy. Five distinct majority carrier (electron) traps were observed after irradiation. The activation energies, capture cross sections, and introduction rates of the traps were measured. Good agreement was found between the energy dependence of the introduction rates for each trap and the calculated elastic nonionizing energy loss for protons incident upon GaAs (i.e., excluding the effects of inelastic nuclear interactions).

A systematic Monte Carlo study of secondary electron fluence perturbation in clinical proton beams (70-250 MeV) for cylindrical and spherical ion chambers.

Current dosimetry protocols for clinical protons do not take into account any secondary electron fluence perturbation in ion chambers. In this work, we performed a systematic study of secondary electron fluence perturbation factors for spherical and cylindrical ion chambers in proton beams (70-250 MeV). The electron fluence perturbation factor, pe, was calculated using Monte Carlo transport of protons and secondary electrons. The influence of proton energy, cavity wall material (graphite, water, A150, PMMA, polystyrene), cavity radius, cavity wall thickness and positioning depth in water is studied. The influence of inelastic nuclear proton interactions is briefly discussed. It was found that pe depends on wall material; the largest values for pe were obtained for ion chambers with A150 walls (pe=1.009), the smallest values for graphite walls. The perturbation factor was found to be largely independent of proton energy. A slight decrease of pe with cavity radius was obtained, especially for low energy protons. The wall thickness was found to have no effect on pe in the range studied (0.025-0.1 cm). The depth of the cavity in a water phantom was also found to have an insignificant effect on pe. Based on the results in the paper for spherical and cylindrical ion chambers, a method to calculate pe for a thimble ion chamber is presented. The results presented in this paper for cylindrical and spherical ion chambers are in contradiction to the calculated electron fluence perturbation factors for planar ion chambers in the paper by Casnati et al.

Nuclear interactions of 160 MeV protons stopping in copper: a test of Monte Carlo nuclear models.

To estimate the influence of nuclear interactions on dose or biological effect one uses Monte Carlo programs which include nuclear models. We introduce an experimental method to check these models at proton therapy energies. We have measured the distribution of charge deposited by 160 MeV protons stopping in a stack of insulated copper plates. A buildup region ahead of the main peak contains approximately 20% of the total charge and is entirely due to charged secondaries from inelastic nuclear interactions. The acceptance for charged secondaries is 100%. Therefore the data are a good benchmark for nuclear models. We have simulated the stack using GEANT with two nuclear models. FLUKA agrees fairly well with the measurement but GHEISHA, designed for much higher energies, does not. The experimental method will work for many other materials, including insulators. Therefore it can also be used for light nuclei.

Monte Carlo study of fluence perturbation effects on cavity dose response in clinical proton beams

Current protocols for clinical proton beam dosimetry have not implemented any chamber-dependent correction factors for absorbed dose determination. The present work initiates a Monte Carlo study of these factors with emphasis on proton fluence perturbation effects and preliminary calculations of perturbation effects from secondary electrons. The proton Monte Carlo code PTRAN was modified to allow simulation of proton transport in non-homogeneous geometries of both unmodulated and modulated beams. The dose to water derived from the dose calculated in an air cavity agrees well with results from analytical calculations assuming a displacement of the point of measurement. For unmodulated beams small differences, limited to 0.8%, could be partially attributed to proton multiple scattering. Effects of replacing water around the cavity with wall material are explained by the introduction of a water-equivalent wall thickness. For modulated beams no significant perturbation effects arise. Secondary electron spectra are calculated analytically. Preliminary electron transport calculations with EGS4 show that wall perturbations of the order of 1% could result. Perturbation effects caused by the energy transport of secondary particles from inelastic nuclear interactions have not been studied here. Inclusion of inelastic nuclear energy transfers in the cavity dose, assuming total local absorption, indicate that separate scaling of this contribution with the ratio of total inelastic nuclear cross sections could be important.

PET dosimetry in proton radiotherapy: a Monte Carlo study

We have used a Monte Carlo program to evaluate the applicability of positron emission tomography to in vivo dosimetry for proton radiotherapy. The transport program PTRAN was utilized to estimate the distribution of positron emitter nuclei produced by proton nuclear inelastic interactions in tissue. A comparison of Monte Carlo results with experimental data available in the literature shows that PET can be a useful tool in proton radiotherapy especially for in vivo Bragg peak localization.