Feasibility of energy adaptive angular meshing for perpendicular and parallel magnetic fields in a grid based...

Area of Science:

• Computational physics
• Medical physics
• Numerical methods

Background:

• MRI-guided radiotherapy requires accurate dose calculations.
• Deterministic Grid Based Boltzmann Solvers (GBBS) are promising but computationally intensive.
• Magnetic fields introduce complexities in angular advection and meshing.

Purpose of the Study:

• Develop algorithmic techniques for forward-peaked adaptive angular meshing compatible with magnetic field advection in GBBS.
• Establish energy adaptive meshing schemes to minimize computational degrees of freedom.
• Preserve high dosimetric accuracy for parallel and perpendicular magnetic fields.

Main Methods:

• Developed a framework for independent adaptation of angular mesh resolution and basis function refinement.
• Implemented upwind stabilization techniques for accurate fluence transfer between hemispheres.
• Devised cardinal forward-peaked mesh orientations for oblique beam and magnetic field orientations.
• Investigated energy-dependent fluence anisotropy to create adaptive meshing schemes.
• Validated dose distributions against GEANT4 Monte Carlo calculations.

Main Results:

• Forward-peaked and isotropic energy adaptive meshing schemes reduced solved elements by 52.8% and 47.7% respectively.
• Achieved over 97% of points passing the gamma 1%/1 mm criterion against Monte Carlo.
• Demonstrated significant reduction in numerical degrees of freedom.

Conclusions:

• Algorithmic advancements enable energy-adaptive meshing for accurate magnetic field solutions.
• Reduced computational load while maintaining excellent dosimetric agreement with Monte Carlo.
• These techniques contribute to a faster deterministic GBBS for MRI-guided radiotherapy.