Journal article
Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy
Physics in medicine & biology, Vol.63(1), pp.015011-015011
12/14/2017
DOI: 10.1088/1361-6560/aa959a
PMID: 29064370
Abstract
Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.
Details
- Title: Subtitle
- Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy
- Creators
- Oleksandr Zelyak - University of Alberta Department of Oncology, 11560 University Ave, Edmonton, Alberta T6G 1Z2, CanadaB Gino Fallone - Cross Cancer Institute Department of Medical Physics, 11560 University Ave, Edmonton, Alberta T6G 1Z2, CanadaJoel St-Aubin - Cross Cancer Institute Department of Medical Physics, 11560 University Ave, Edmonton, Alberta T6G 1Z2, Canada
- Resource Type
- Journal article
- Publication Details
- Physics in medicine & biology, Vol.63(1), pp.015011-015011
- Publisher
- IOP Publishing
- DOI
- 10.1088/1361-6560/aa959a
- PMID
- 29064370
- ISSN
- 0031-9155
- eISSN
- 1361-6560
- Number of pages
- 16
- Grant note
- AIHS CRIO TEAM grant 20160065 / Alberta Innovates Health Solutions
- Language
- English
- Date published
- 12/14/2017
- Academic Unit
- Radiation Oncology
- Record Identifier
- 9984046903502771
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