Energy Spectra of Protons and Generated Secondary Electrons around the Bragg Peak in Materials of Interest in Proton Therapy

MR-guided ion therapy: Detector response in magnetic fields during carbon ion irradiation

BACKGROUND

Combining carbon ion therapy with on-bed MR imaging has the potential to bring particle therapy to a new level of precision. However, the introduction of magnetic fields brings challenges for dosimetry and quality assurance. For protons, a small, but significant change in detector response was shown in the presence of magnetic fields previously. For carbon ion beams, so far no such experiments have been performed.

PURPOSE

To investigate the influence of external magnetic fields on the response of air-filled ionization chambers.

METHODS

Four commercially available ionization chambers, three thimble type (Farmer, Semiflex, and PinPoint), and a plane parallel (Bragg peak) detector were investigated. Detectors were aligned in water such that their effective point of measurement was located at 2 cm depth. Irradiations were performed using10 × 10 cm 2 $10\times 10\nobreakspace \mathrm{cm}^2$ square fields for carbon ions of 186.1, 272.5, and 402.8 MeV/u employing magnetic field strengths of 0, 0.25, 0.5, and 1 T. In addition, the detector response for protons and carbon ions was compared taking into account the secondary electron spectra and employing protons of 252.7 MeV for comparison.

RESULTS

For all four detectors, a statistically significant change in detector response, dependent on the magnetic field strength, was found. The effect was more pronounced for higher energies. The highest effects were found at 0.5 T for the PinPoint detector with a change in detector response of 1.1%. The response of different detector types appeared to be related to the cavity diameter. For proton and carbon ion irradiation with similar secondary electron spectra, the change in detector response was larger for carbon ions compared to protons.

CONCLUSION

A small, but significant dependence of the detector response was found for carbon ion irradiation in a magnetic field. The effect was found to be larger for smaller cavity diameters and at medium magnetic field strengths. Changes in detector response were more pronounced for carbon ions compared to protons.

Intermediate LET-like effect in distal part of proton Bragg peak revealed by track-ends imaging during super-Fricke radiolysis

Upstream of the efficiency of proton or carbon ion beams in cancer therapy, and to optimize hadrontherapy results, we analysed the chemistry of Fricke solutions in track-end of 64-MeV protons and 1.14-GeV carbon ions. An original optical setup is designed to determine the primary track-segment yields along the last millimetres of the ion track with a sub-millimetre resolution. The Fe3+-yield falls in the Bragg peak to (4.9 ± 0.4) × 10-7 mol/J and 1.9 × 10-7 mol/J, under protons and carbon ions respectively. Beyond the Bragg peak, a yield recovery is observed over 1 mm for proton beams. It is attributed to the intermediate-LET of protons in this region where their energy decreases and energy distribution becomes broader, in relation with the longitudinal straggling of the beam. Consequently to this LET decrease in the distal part of the Bragg peak, Fe3+-yield increases. For the first time, this signature is highlighted at the chemical level under proton irradiation. Nevertheless, this phenomenon is not identified for carbon ion beams since their straggling is lower. It would need a greater spatial resolution to be observed.

Monte Carlo simulation for proton dosimetry in magnetic fields: Fano test and magnetic field correction factorskBfor Farmer-type ionization chambers

Objective. In this contribution we present a special Fano test for charged particles in presence of magnetic fields in the MC code TOol for PArticle Simulation (TOPAS), as well as the determination of magnetic field correction factorskBfor Farmer-type ionization chambers using proton beams.Approach. Customized C++ extensions for TOPAS were implemented to model the special Fano tests in presence of magnetic fields for electrons and protons. The Geant4-specific transport parameters,DRoverRandfinalRange,were investigated to optimize passing rate and computation time. ThekBwas determined for the Farmer-type PTW 30013 ionization chamber, and 5 custom built ionization chambers with same geometry but varying inner radius, testing magnetic flux density ranging from 0 to 1.0 T and two proton beam energies of 157.43 and 221.05 MeV.Main results. Using the investigated parameters, TOPAS passed the Fano test within 0.39 ± 0.15% and 0.82 ± 0.42%, respectively for electrons and protons. The chamber response (kB,M,Q) gives a maximum at different magnetic flux densities depending of the chamber size, 1.0043 at 1.0 T for the smallest chamber and 1.0051 at 0.2 T for the largest chamber. The local dose differencecBremained ≤ 0.1% for both tested energies. The magnetic field correction factorkB, for the chamber PTW 30013, varied from 0.9946 to 1.0036 for both tested energies.Significance. The developed extension for the special Fano test in TOPAS MC code with the adjusted transport parameters, can accurately transport electron and proton particles in magnetic field. This makes TOPAS a valuable tool for the determination ofkB. The ionization chambers we tested showed thatkBremains small (≤0.72%). To the best of our knowledge, this is the first calculations ofkBfor proton beams. This work represents a significant step forward in the development of MRgPT and protocols for proton dosimetry in presence of magnetic field.

Gold-Nanoparticles-Enhanced Production of Reactive Oxygen Species in Cells at Spread-Out Bragg Peak under Proton Beam Radiation

This study investigates the radiobiological effects of gold nanoparticles (GNPs) as radiosensitizers for proton beam therapy (PBT). Specifically, we explore the enhanced production of reactive oxygen species (ROS) in GNP-loaded tumor cells irradiated by a 230 MeV proton beam in a spread-out Bragg peak (SOBP) zone obtained by a passive scattering system. Our findings indicate that the radiosensitization enhancement factor is 1.24 at 30% cell survival fraction, 8 days after 6 Gy proton beam irradiation. Since protons deposit the majority of their energy at the SOBP region and interact with GNPs to induce more ejected electrons from the high-Z GNPs, these ejected electrons then react with water molecules to produce excessive ROS that can damage cellular organelles. Laser scanning confocal microscopy reveals the excessive ROS induced inside the GNP-loaded cells immediately after proton irradiation. Furthermore, the damage to cytoskeletons and mitochondrial dysfunction in GNP-loaded cells caused by the induced ROS becomes significantly severe, 48 h after proton irradiation. Our biological evidence suggests that the cytotoxicity of GNP-enhanced ROS production has the potential to increase the tumoricidal efficacy of PBT.

Impact of secondary particles on the magnetic field generated by a proton pencil beam: a finite-element analysis based on Geant4-DNA simulations

PURPOSE

To investigate the static magnetic field generated by a proton pencil beam as a candidate for range verification by means of Monte Carlo simulations, thereby improving upon existing analytical calculations. We focus on the impact of statistical current fluctuations and secondary protons and electrons.

METHODS

We considered a pulsed beam (10 μ ${\umu}$ s pulse duration) during the duty cycle with a peak beam current of 0.2 μ $\umu$ A and an initial energy of 100 MeV. We ran Geant4-DNA Monte Carlo simulations of a proton pencil beam in water and extracted independent particle phase spaces. We calculated longitudinal and radial current density of protons and electrons, serving as an input for a magnetic field estimation based on a finite element analysis in a cylindrical geometry. We made sure to allow for non-solenoidal current densities as is the case of a stopping proton beam.

RESULTS

The rising proton charge density toward the range is not perturbed by energy straggling and only lowered through nuclear reactions by up to 15%, leading to an approximately constant longitudinal current. Their relative low density however (at most 0.37 protons/mm³ for the 0.2  μ ${\umu}$ A current and a beam cross-section of 2.5 mm), gives rise to considerable current density fluctuations. The radial proton current resulting from lateral scattering and being two orders of magnitude weaker than the longitudinal current is subject to even stronger fluctuations. Secondary electrons with energies above 10 eV, that far outnumber the primary protons, reduce the primary proton current by only 10% due to their largely isotropic flow. A small fraction of electrons (<1%), undergoing head-on collisions, constitutes the relevant electron current. In the far-field, both contributions to the magnetic field strength (longitudinal and lateral) are independent of the beam spot size. We also find that the nuclear reaction-related losses cause a shift of 1.3 mm to the magnetic field profile relative to the actual range, which is further enlarged to 2.4 mm by the electron current (at a distance of ρ = 50 $\rho =50$  mm away from the central beam axis). For ρ > 45 $\rho &gt;45$  mm, the shift increases linearly. While the current density variations cause significant magnetic field uncertainty close to the central beam axis with a relative standard deviation (RSD) close to 100%, they average out at a distance of 10 cm, where the RSD of the total magnetic field drops below 2%.

CONCLUSIONS

With the small influence of the secondary electrons together with the low RSD, our analysis encourages an experimental detection of the magnetic field through sensitive instrumentation, such as optical magnetometry or SQUIDs.

Modeling RBE with other quantities than LET significantly improves prediction of in vitro cell survival for proton therapy

BACKGROUND

For proton therapy, a relative biological effectiveness (RBE) of 1.1 has broadly been applied clinically. However, as unexpected toxicities have been observed by the end of the proton tracks, variable RBE models have been proposed. Typically, the dose-averaged linear energy transfer (LET_d ) has been used as an input variable for these models but the way the LET_d was defined, calculated, or determined was not always consistent, potentially impacting the corresponding RBE value.

PURPOSE

This study compares consistently calculated LET_d with other quantities as input variables for a phenomenological RBE model and attempts to determine which quantity that can best predicts proton RBE. The comparison was performed within the frame of introducing a new model for the proton RBE.

METHODS

High-throughput experimental setups of in vitro cell survival studies for proton RBE determination are simulated using the SHIELD-HIT12A Monte Carlo particle transport code. Together with LET, z ∗ 2 / β 2 $z^{*2}/\beta ^2$ , here called effective Q (Q_eff ), and Q are scored. Each quantity is calculated using the dose and track averaging methods, because the scoring includes all hadronic particles, all protons or only primaries. A phenomenological linear-quadratic-based RBE model is subsequently applied to the in vitro data with the various beam quality descriptors used as input variables and the goodness of fit is determined and compared using a bootstrapping approach. Both linear and nonlinear fit functions were tested.

RESULTS

Versions of Q_eff and Q outperform LET with a statistically significant margin, with the best nonlinear and linear fit having a relative root mean square error (RMSE) for RBE_2Gy ± one standard error of 1.55 ± 0.04 (Q_{eff, t, primary} ) and 2.84 ± 0.07 (Q_{eff, d, primary} ), respectively. For comparison, the corresponding best nonlinear and linear fits for LET_{d, all protons} had a relative RMSE of 2.07 ± 0.06 and 3.39 ± 0.08, respectively. Applying Welch's t-test for comparing the calculated RMSE of RBE_2Gy resulted in two-tailed p-values of <0.002 for all Q and Q_eff quantities compared to LET_{d, all protons} .

CONCLUSIONS

The study shows that Q or Q_eff could be better RBE descriptors that dose averaged LET.

Energy Deposition around Swift Carbon-Ion Tracks in Liquid Water

Energetic carbon ions are promising projectiles used for cancer radiotherapy. A thorough knowledge of how the energy of these ions is deposited in biological media (mainly composed of liquid water) is required. This can be attained by means of detailed computer simulations, both macroscopically (relevant for appropriately delivering the dose) and at the nanoscale (important for determining the inflicted radiobiological damage). The energy lost per unit path length (i.e., the so-called stopping power) of carbon ions is here theoretically calculated within the dielectric formalism from the excitation spectrum of liquid water obtained from two complementary approaches (one relying on an optical-data model and the other exclusively on ab initio calculations). In addition, the energy carried at the nanometre scale by the generated secondary electrons around the ion's path is simulated by means of a detailed Monte Carlo code. For this purpose, we use the ion and electron cross sections calculated by means of state-of-the art approaches suited to take into account the condensed-phase nature of the liquid water target. As a result of these simulations, the radial dose around the ion's path is obtained, as well as the distributions of clustered events in nanometric volumes similar to the dimensions of DNA convolutions, contributing to the biological damage for carbon ions in a wide energy range, covering from the plateau to the maximum of the Bragg peak.

Technical note: Extraction of proton pencil beam energy spectrum from measured integral depth dose in a cyclotron proton beam system

PURPOSE

Proton pencil beam energy spectrum is an essential parameter for calculations of dose and linear energy transfer. We extract the energy spectrum from measured integral depth dose (IDD).

METHODS

A measured IDD (measIDD) in water is decomposed into many IDDs of mono-energetic pencil beams (monoIDDs) in water. A simultaneous iterative technique is used to do the decomposition that extracts the energy spectrum of protons from the measIDD. The monoIDDs are generated by our analytic random walk model-based proton dose calculation algorithm. The linear independence of the monoIDDs is considered and high spatial resolution monoIDDs are used to improve their linear independence. To validate the extraction, first we use synthesized IDDs (synIDD) with Gaussian energy spectrum and compare the extracted energy spectrum with the Gaussian; second, for the energy spectrum extracted from measIDDs, the accuracy of the extraction is validated by comparing the calculated IDD from the energy spectrum with the measIDD. The measIDDs are derived from commissioning of a cyclotron proton pencil beam system with a Bragg peak ionization chamber. The nominal energy of the pencil beams is from 70 to 245 MeV. The monoIDDs are generated for energies from 0.05 to 275 MeV in steps of 0.05 MeV with a spatial resolution of 1 mm.

RESULTS

The difference of the extracted and original Gaussian energy spectrum peaked at 75 and 80 MeV was <1%. As the energy decreased, the difference increased but was reduced by using 0.1-mm monoIDDs. The difference was not sensitive to the energy interval of monoIDDs when the interval increased from 0.05 to 1 MeV. For the energy spectrum extraction from measIDDs, there was a main peak near the nominal energy but the spectrum was not in Gaussian distribution. In three example cases (70, 160, and 245 MeV), the relative differences of the measIDDs and calculated IDDs were within 3.4%, 2.9%, and 4.7% of the Bragg peak value, respectively. Fitting the spectrum by Gaussian distribution, we had σ = 0.87, 1.51, and 0.86 MeV, respectively, for these three examples, and the relative differences of the resultant calculated IDDs from the measIDDs were within 4.7%, 7.4%, and 4.5%, respectively.

CONCLUSIONS

Our algorithm accurately extracted the energy spectrum from the synIDDs and measIDDs. High-resolution monoIDDs are necessary to extract low-energy spectrum. Energy spectrum extraction from measIDD reveals important information for beam modeling.