Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy.
O Zelyak1, B G Fallone1,2, J St-Aubin1,2
1Department of Oncology, University of Alberta, 11560 University Ave, Edmonton, Alberta T6G 1Z2, Canada.
Physics in Medicine and Biology
|October 25, 2017
Summary
This study analyzes the stability of dose calculations in MRI-guided radiotherapy. It finds that the stationary source iteration method is unstable with magnetic fields, but GMRES significantly accelerates convergence for improved accuracy.
Area of Science:
- Medical Physics
- Computational Physics
- Radiotherapy Technology
Background:
- MRI-guided radiotherapy requires accurate dose calculations accounting for magnetic fields.
- Previous work focused on accuracy but not the stability of deterministic solvers.
Purpose of the Study:
- To perform a stability analysis of a deterministic linear Boltzmann transport equation (LBTE) solver including magnetic fields.
- To investigate convergence rate dependencies and explore acceleration methods.
Main Methods:
- Fourier analysis of the spectral radius for stationary source iteration (SI) and GMRES.
- Investigated magnetic field inclusion in the iteration source versus the streaming-collision operator.
- Analyzed discontinuous finite element method (DFEM) stability and convergence.
Main Results:
- SI is unstable when magnetic fields are in the iteration source, but stable in the streaming-collision operator.
- DFEM is stable but shows slow convergence with low density and high magnetic fields.
- GMRES significantly accelerates DFEM convergence with minimal magnetic field dependence.
Conclusions:
- The choice of magnetic field inclusion in LBTE solvers is critical for stability.
- GMRES offers a promising acceleration method for dose calculations in MRI-guided radiotherapy.
- Angular parallel computing may enhance computational efficiency.
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