Purpose: To develop a novel Grid Based Boltzmann Solver with inclusion of magnetic fields and evaluate its accuracy on bulk density assigned patient CT plans for the feasibility of its application to an MRI-only treatment planning workflow.
Methods: An energy-adaptive space-angle discontinuous finite element framework was developed to solve the LBTE in magnetic fields, including novel techniques to stabilize the Lorentz force operator at oblique beam orientations. Patient CT scans for anatomical sites of lung, liver, and brain were automatically segmented into discrete regions corresponding to air, lung, adipose, muscle, cartilage, and bone, each parameterized by a single mass density (0.0012, 0.26, 0.80, 1.05, 1.15, 1.85 g/cm3 respectively). Deterministic dose distributions for multi-beam treatment plans were compared against Geant4 reference Monte Carlo using 3D gamma analysis for magnetic field configurations of 0.5T parallel, and 1.5T perpendicular. Runtimes for a prototype implementation of the deterministic calculation in Matlab were noted for an Intel i7-6700K processor.
Results: At all anatomical sites over 95% (99%) of points passed the 1%/1mm (2%/2mm) criterion in the presence of Bâ‚€ = 0.5T parallel, using an adaptive forward-peaked mesh, with an average runtime of 7m40s per beam. With Bâ‚€ = 1.5T perpendicular, over 94% (99%) of points passed the 1%/1mm (2%/2mm) criterion using an adaptive isotropic mesh, with an average runtime of 9m19s per beam. The deterministic solution was unconditionally stable, while benefitting from the absence of statistical uncertainty and ray-effect artifacts.
Conclusion: Excellent agreement with Monte Carlo was demonstrated for an energy-adaptive deterministic dose calculation in strong magnetic fields using bulk-density assignments such as those used for MRI-only treatment planning. Magnetic field effects, most pronounced in air and lung, were modeled with high accuracy and solved with unconditional stability. Runtimes benefitted from reduced computational complexity of an energy adaptive angular meshing strategy.
Funding Support, Disclosures, and Conflict of Interest: This work is supported by Alberta Innovates Health Solutions and NSERC. Dr. B.G. Fallone is a cofounder and CEO of MagnetTx Oncology Solutions.