Minimal skin dose increase in longitudinal rotating biplanar linac-MR systems: examination of radiation energy and flattening filter design.

The magnetic fields of linac-MR systems modify the path of contaminant electrons in photon beams, which alters patient entrance skin dose. Also, the increased SSD of linac-MR systems reduces the maximum achievable dose rate. To accurately quantify the changes in entrance skin dose, the authors use EGSnrc Monte Carlo calculations that incorporate 3D magnetic field of the Alberta 0.5 T longitudinal linac-MR system. The Varian 600C linac head geometry assembled on the MRI components is used in the BEAMnrc simulations for 6 MV and 10 MV beam models and skin doses are calculated at an average depth of 70 µm using DOSXYZnrc. 3D modeling shows that magnetic fringe fields decay rapidly and are small at the linac head. SSDs between 100 and 120 cm result in skin-dose increases of between ~6%-19% and ~1%-9% for the 6 and 10 MV beams, respectively. For 6 MV, skin dose increases from ~10.5% to ~1.5% for field-size increases of 5 × 5 cm(2) to 20 × 20 cm(2). For 10 MV, skin dose increases by ~6% for a 5 × 5 cm(2) field, and decreases by ~1.5% for a 20 × 20 cm(2) field. Furthermore, the proposed reshaped flattening filter increases the dose rate from the current 355 MU min(-1) to 529 MU min(-1) (6 MV) or 604 MU min(-1) (10 MV), while the skin-dose increases by only an additional ~2.6% (all percent increases in skin dose are relative to D max). This study suggests that there is minimal increase in the entrance skin dose and minimal/no decrease in the dose rate of the Alberta longitudinal linac-MR system. The even lower skin dose increase at 10 MV offers further advantages in future designs of linac-MR prototypes.

Discontinuous finite element space-angle treatment of the first order linear Boltzmann transport equation with magnetic fields: Application to MRI-guided radiotherapy.

PURPOSE: The advent of magnetic resonance imaging (MRI) guided radiotherapy systems demands the incorporation of the magnetic field into dose calculation algorithms of treatment planning systems. This is due to the fact that the Lorentz force of the magnetic field perturbs the path of the relativistic electrons, hence altering the dose deposited by them. Building on the previous work, the authors have developed a discontinuous finite element space-angle treatment of the linear Boltzmann transport equation to accurately account for the effects of magnetic fields on radiotherapy doses. METHODS: The authors present a detailed description of their new formalism and compare its accuracy to geant4 Monte Carlo calculations for magnetic fields parallel and perpendicular to the radiation beam at field strengths of 0.5 and 3 T for an inhomogeneous 3D slab geometry phantom comprising water, bone, and air or lung. The accuracy of the authors' new formalism was determined using a gamma analysis with a 2%/2 mm criterion. RESULTS: Greater than 98.9% of all points analyzed passed the 2%/2 mm gamma criterion for the field strengths and orientations tested. The authors have benchmarked their new formalism against Monte Carlo in a challenging radiation transport problem with a high density material (bone) directly adjacent to a very low density material (dry air at STP) where the effects of the magnetic field dominate collisions. CONCLUSIONS: A discontinuous finite element space-angle approach has been proven to be an accurate method for solving the linear Boltzmann transport equation with magnetic fields for cases relevant to MRI guided radiotherapy. The authors have validated the accuracy of this novel technique against geant4, even in cases of strong magnetic field strengths and low density air.

A deterministic solution of the first order linear Boltzmann transport equation in the presence of external magnetic fields.

PURPOSE: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today's treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields. METHODS: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf_macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm(2) field as well as a smaller 2 × 2 cm(2) field. RESULTS: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm's high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization. CONCLUSIONS: The feasibility of including magnetic field effects in a deterministic solution to the first order linear Boltzmann transport equation is shown. The results show a high degree of accuracy when compared against Monte Carlo calculations in all magnetic field strengths and orientations tested.

Skin dose in longitudinal and transverse linac-MRIs using Monte Carlo and realistic 3D MRI field models.

PURPOSE: The magnetic fields of linac-MR systems modify the path of contaminant electrons in photon beams, which alters patient skin dose. To accurately quantify the magnitude of changes in skin dose, the authors use Monte Carlo calculations that incorporate realistic 3D magnetic field models of longitudinal and transverse linac-MR systems. METHODS: Finite element method (FEM) is used to generate complete 3D magnetic field maps for 0.56 T longitudinal and transverse linac-MR magnet assemblies, as well as for representative 0.5 and 1.0 T Helmholtz MRI systems. EGSnrc simulations implementing these 3D magnetic fields are performed. The geometry for the BEAMnrc simulations incorporates the Varian 600C 6 MV linac, magnet poles, the yoke, and the magnetic shields of the linac-MRIs. Resulting phase-space files are used to calculate the central axis percent depth-doses in a water phantom and 2D skin dose distributions for 70 µm entrance and exit layers using DOSXYZnrc. For comparison, skin doses are also calculated in the absence of magnetic field, and using a 1D magnetic field with an unrealistically large fringe field. The effects of photon field size, air gap (longitudinal configuration), and angle of obliquity (transverse configuration) are also investigated. RESULTS: Realistic modeling of the 3D magnetic fields shows that fringe fields decay rapidly and have a very small magnitude at the linac head. As a result, longitudinal linac-MR systems mostly confine contaminant electrons that are generated in the air gap and have an insignificant effect on electrons produced further upstream. The increase in the skin dose for the longitudinal configuration compared to the zero B-field case varies from ∼1% to ∼14% for air gaps of 5-31 cm, respectively. (All dose changes are reported as a % of D(max).) The increase is also field-size dependent, ranging from ∼3% at 20 × 20 cm(2) to ∼11% at 5 × 5 cm(2). The small changes in skin dose are in contrast to significant increases that are calculated for the unrealistic 1D magnetic field. For the transverse configuration, the entrance skin dose is equal or smaller than that of the zero B-field case for perpendicular beams. For a 10 × 10 cm(2) oblique beam the transverse magnetic field decreases the entry skin dose for oblique angles less than ±20° and increases it by no more than 10% for larger angles up to ±45°. The exit skin dose is increased by 42% for a 10 × 10 cm(2) perpendicular beam, but appreciably drops and approaches the zero B-field case for large oblique angles of incidence. CONCLUSIONS: For longitudinal linac-MR systems only a small increase in the entrance skin dose is predicted, due to the rapid decay of the realistic magnetic fringe fields. For transverse linac-MR systems, changes to the entrance skin dose are small for most scenarios. For the same geometry, on the exit side a fairly large increase is observed for perpendicular beams, but significantly drops for large oblique angles of incidence. The observed effects on skin dose are not expected to limit the application of linac-MR systems in either the longitudinal or transverse configuration.

SU-E-T-469: The Effects of Patient Anatomy and Parallel Magnetic Fields on Beamlet Dose Distributions.

PURPOSE: Beamlets are generated in a patient geometry in the presence of a magnetic field to investigate the effects of tissue density and magnetic field on beamlet dose distributions, which is important for the optimization of photon fluence to be delivered by a linac-MR system. METHODS: 50×50 mm2 fields were placed with isocenter in the middle of a patient's right lung. Each treatment field was decomposed into 100 beamlets (each 5×5 mm2 ). BEAMnrc scored the particle phase space at 100.2 cm from the source in the linac-MR geometry (isocentre at 126 cm) with parallel magnetic fields of 0, 0.56, and 3T. DOSXYZnrc was modified to score the energy deposited by particles from this phase space as a function of the beamlet the particle passed through. The calculation volume of 70×46×64 voxels encompassed the patient with a voxel size of 3×3×3 mm3 . Each beamlet was normalized to the dose calculated to a 3×3×3 mm3 voxel with isocenter at 5cm depth in a flat water tank without a magnetic field. RESULTS: Beamlet files were calculated on Western Canada's high performance computing cluster (Westgrid) using 100 processors, enabling simulation of 109 histories in less than 3 hours. The resulting files, which contained 3D dose distributions for all 100 beamlets, were 81 MB per field. The Monte Carlo uncertainty was also stored. The gyroradii for 1 MeV electron traversing field lines at 20 degrees are 2.9mm and 0.5mm for 0.56 and 3T fields respectively. The 0.56T parallel magnetic field has a small effect compared to the distortion of the beamlet introduced by the presence of lung. CONCLUSIONS: The effect of tissue heterogeneities is more significant than the effect of a 0.56T parallel magnetic field. A 3T field refocuses the dose in lung to the beamlet path and significantly reduces the lateral electron scatter.

WE-E-BRB-06: Monte Carlo Calculations of the Skin Dose for Longitudinal Linac-MR System Using Realistic Three-Dimensional Magnetic Field Modeling.

PURPOSE: This study quantifies the effects of the magnetic field of a longitudinal linac-MR system (B-field parallel to beam direction) on skin dose due to the confinement of contaminant electrons, using Monte Carlo calculations and realistic 3-D models of the magnetic field. METHODS: The complete realistic 3-D magnetic fields generated by the bi-planar Linac-MR magnet assembly are calculated with the finite element method using Opera- 3D. EGSnrc simulations are performed in the presence of ∼0.6T and IT MRI fields that have realistic rapid fall-off of the fringe field. The simulation geometry includes a Varian 600C 6MV linac, the yoke and magnetic shields of the MRIs, and features an isocentre distance of 126 cm. Phase spaces at the surface of a water phantom are scored using BEAMnrc; DOSXYZnrc is used to score the resulting CAX percent depth-doses in the phantom and the 2D skin dose distributions in the first 70 urn layer. For comparison, skin doses are also calculated in the absence of magnetic field and using a 1-D magnetic field with an unrealistic fringe field. The effects of field size and air gap (between phantom surface and magnet pole) are also examined. RESULTS: Analysis of the phase-space and dose distributions reveals that significant containment of electrons occurs primarily close to the uniform magnetic field region. The increase in skin dose due to the magnetic field depends on the air gap, varying from 1% to 13% for air gaps of 5 to 31 cm, respectively. The increase is also field-size dependent, varying from 3% at 20×20 cm2 to 11% at 5×5 cm2. CONCLUSIONS: Calculations based on various realistic MRI 3D magnetic-field maps that appropriately account for the rapid decay of the fringe field show that the increase in the patient skin dose of a longitudinal Linac-MR system is clinically insignificant.