Magnetic field effects on particle beams and their implications for dose calculation in MR-guided particle therapy.

To investigate and model effects of magnetic fields on proton and carbon ion beams for dose calculation. In a first step, Monte Carlo simulations using Gate 7.1/Geant4.10.0.p03 were performed for proton and carbon ion beams in magnetic fields ranging from 0 to 3 T. Initial particle energies ranged from 60 to 250 MeV (protons) and 120 to 400 MeV/u (carbon ions), respectively. The resulting dose distributions were analyzed focusing on beam deflection, dose deformation, as well as the impact of material heterogeneities. In a second step, a numerical algorithm was developed to calculate the lateral beam position. Using the Runge-Kutta method, an iterative solution of the relativistic Lorentz equation, corrected for the changing particle energy during penetration, was performed. For comparison, a γ-index analysis was utilized, using a criteria of 2%/2 mm of the local maximum. A tilt in the dose distribution within the Bragg peak area was observed, leading to non-negligible dose distribution changes. The magnitude was found to depend on the magnetic field strength as well as on the initial beam energy. Comparison of the 3 T dose distribution with non-B field (nominal) dose distributions, resulted in a γmean (mean value of the γ distribution) of 0.6, with 14.4% of the values above 1 and γ1 % (1% of all points have an equal or higher γ value) of 1.8. The presented numerical algorithm calculated the lateral beam offset with maximum errors of less than 2% with calculation times of less than 5 μs. The impact of tissue interfaces on the proton dose distributions was found to be less than 2% for a dose voxel size of 1 × 1 × 1 mm3 . Non-negligible dose deformations at the Bragg peak area were identified for high initial energies and strong magnetic fields. A fast numerical algorithm based on the solution of the energy-corrected relativistic Lorentz equation was able to describe the beam path, taking into account the particle energy, magnetic field, and material.

Fuchs H ，Moser P ，Gröschl M ，Georg D ... -  《-》

A pencil beam algorithm for magnetic resonance image-guided proton therapy.

The feasibility of magnetic resonance image (MRI)-based proton therapy is based, among several other factors, on the implementation of appropriate extensions on current dose calculation methods. This work aims to develop a pencil beam algorithm (PBA) for dose calculation of proton beams within magnetic field regions of up to 3 T. Monte Carlo (MC) simulations using the GATE 7.1/GEANT4.9.4p02 toolkit were performed to generate calibration and benchmarking data for the PBA. Dose distributions from proton beams in the clinical required energy range 60-250 MeV impinging on a 400 × 400 × 400 mm3 water phantom and transverse magnetic fields ranging from 0 to 3 T were considered. Energy depositions in homogeneous and heterogeneous phantoms filled with water, adipose, bone, and air were evaluated for proton energies of 80, 150, and 240 MeV, combining a trajectory calculation method and look-up tables (LUT). A novel parametrization model, using independent tailed Gauss fitting functions, was employed to describe the nonsymmetric shape of lateral beam profiles. Integrated depth-dose curves (IDD), lateral dose profiles, and two-dimensional dose distributions calculated with the PBA were compared with results from MC simulations to assess the performance of the algorithm. A gamma index criterion of 2%/2 mm was used for analysis. A close to perfect agreement was observed for PB-based dose calculations in water in magnetic fields of 0.5, 1.5, and 3 T. IDD functions showed differences between the PBA and MC of less than 0.1% before the Bragg peak, and deviations of 2-8% in the distal energy falloff region. Gamma index pass rates higher than 99% and mean values lower than 0.1 were encountered for all analyzed configurations. For homogeneous phantoms, only the full bone configuration offered deviations in the Bragg peak position of up to 1.7% and overestimations of the lateral beam spot width for high-energy protons and magnetic field intensities. An excellent agreement between PBA and MC dose calculation was also achieved using slab-like and lateral heterogeneous phantoms, with gamma index passing rates above 98% and mean values between 0.1 and 0.2. As expected, agreement reduced for high-energy protons and high-intensity magnetic fields, although results remained good enough to be considered for future implementation in clinical practice. The proposed pencil beam algorithm for protons can accurately account for dose distortion effects induced by external magnetic fields. The application of an analytical model for dose estimation and corrections reduces the calculation times considerably, making the presented PBA a suitable candidate for integration in a treatment planning system.

Padilla-Cabal F ，Georg D ，Fuchs H 《-》

Benchmarking a GATE/Geant4 Monte Carlo model for proton beams in magnetic fields.

Magnetic resonance guidance in proton therapy (MRPT) is expected to improve its current performance. The combination of magnetic fields with clinical proton beam lines poses several challenges for dosimetry, treatment planning and dose delivery. Proton beams are deflected by magnetic fields causing considerable changes in beam trajectories and also a retraction of the Bragg peak positions. A proper prediction and compensation of these effects is essential to ensure accurate dose calculations. This work aims to develop and benchmark a Monte Carlo (MC) beam model for dose calculation of MRPT for static magnetic fields up to 1 T. Proton beam interactions with magnetic fields were simulated using the GATE/Geant4 toolkit. The transport of charged particle in custom 3D magnetic field maps was implemented for the first time in GATE. Validation experiments were done using a horizontal proton pencil beam scanning system with energies between 62.4 and 252.7 MeV and a large gap dipole magnet (B = 0-1 T), positioned at the isocenter and creating magnetic fields transverse to the beam direction. Dose was measured with Gafchromic EBT3 films within a homogeneous PMMA phantom without and with bone and tissue equivalent material slab inserts. Linear energy transfer (LET) quenching of EBT3 films was corrected using a linear model on dose-averaged LET method to ensure a realistic dosimetric comparison between simulations and experiments. Planar dose distributions were measured with the films in two different configurations: parallel and transverse to the beam direction using single energy fields and spread-out Bragg peaks. The MC model was benchmarked against lateral deflections and spot sizes in air of single beams measured with a Lynx PT detector, as well as dose distributions using EBT3 films. Experimental and calculated dose distributions were compared to test the accuracy of the model. Measured proton beam deflections in air at distances of 465, 665, and 1155 mm behind the isocenter after passing the magnetic field region agreed with MC-predicted values within 4 mm. Differences between calculated and measured beam full width at half maximum (FWHM) were lower than 2 mm. For the homogeneous phantom, measured and simulated in-depth dose profiles showed range and average dose differences below 0.2 mm and 1.2%, respectively. Simulated central beam positions and widths differed <1 mm to the measurements with films. For both heterogenous phantoms, differences within 1 mm between measured and simulated central beam positions and widths were obtained, confirming a good agreement of the MC model. A GATE/Geant4 beam model for protons interacting with magnetic fields up to 1 T was developed and benchmarked to experimental data. For the first time, the GATE/Geant4 model was successfully validated not only for single energy beams, but for SOBP, in homogeneous and heterogeneous phantoms. EBT3 film dosimetry demonstrated to be a powerful dosimetric tool, once the film response function is LET corrected, for measurements in-line and transverse to the beam direction in magnetic fields. The proposed MC beam model is foreseen to support treatment planning and quality assurance (QA) activities toward MRPT.

Padilla-Cabal F ，Alejandro Fragoso J ，Franz Resch A ，Georg D ，Fuchs H ... -  《-》

Technical Note: Experimental verification of magnetic field-induced beam deflection and Bragg peak displacement for MR-integrated proton therapy.

Given its sensitivity to anatomical variations, proton therapy is expected to benefit greatly from integration with magnetic resonance imaging for online anatomy monitoring during irradiation. Such an integration raises several challenges, as both systems mutually interact. The proton beam will experience quasi-continuous energy loss and energy-dependent electromagnetic deflection at the same time, giving rise to a deflected beam trajectory and an altered dose distribution with a displaced Bragg peak. So far, these effects have only been predicted using Monte Carlo and analytical models, but no clear consensus has been reached and experimental benchmark data are lacking. We measured proton beam trajectories and Bragg peak displacement in a homogeneous phantom placed inside a magnetic field and compared them to simulations. Planar dose distributions of proton pencil beams (80-180 MeV) traversing the field of a 0.95 T NdFeB permanent magnet while depositing energy in a PMMA slab phantom were measured using EBT3 radiochromic films and simulated using the Geant4 toolkit. Deflected beam trajectories and the Bragg peak displacement were extracted from the measured planar dose distributions and compared against the simulations. The lateral beam deflection was clearly visible on the EBT3 films and ranged from 1 to 10 mm for 80 to 180 MeV, respectively. Simulated and measured beam trajectories and Bragg peak displacement agreed within 0.8 mm for all studied proton energies. These results prove that the magnetic field-induced Bragg peak displacement is both measurable and accurately predictable in a homogeneous phantom at 0.95 T, and allows Monte Carlo simulations to be used as gold standard for proton beam trajectory prediction in similar frameworks for MR-integrated proton therapy.

Schellhammer SM ，Gantz S ，Lühr A ，Oborn BM ，Bussmann M ，Hoffmann AL ... -  《-》

An analytical solution to proton Bragg peak deflection in a magnetic field.

Wolf R ，Bortfeld T 《-》