Journal article
A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields
Physics in medicine & biology, Vol.63(3), pp.035018-035018
01/30/2018
DOI: 10.1088/1361-6560/aaa2b1
PMID: 29256449
Abstract
Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.
Details
- Title: Subtitle
- A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields
- Creators
- R Yang - University of Alberta Department of Oncology, 11560 University Ave, Edmonton, Alberta T6G 1Z2, CanadaO Zelyak - University of Alberta Department of Oncology, 11560 University Ave, Edmonton, Alberta T6G 1Z2, CanadaB G Fallone - Cross Cancer Institute Department of Medical Physics, 11560 University Ave, Edmonton, Alberta T6G 1Z2, CanadaJ St-Aubin - Author to whom any correspondence should be addressed
- Resource Type
- Journal article
- Publication Details
- Physics in medicine & biology, Vol.63(3), pp.035018-035018
- Publisher
- IOP Publishing
- DOI
- 10.1088/1361-6560/aaa2b1
- PMID
- 29256449
- ISSN
- 0031-9155
- eISSN
- 1361-6560
- Number of pages
- 17
- Grant note
- 201500137; 20160065 / Alberta Innovates - Health Solutions (https://doi.org/10.13039/501100000145)
- Language
- English
- Date published
- 01/30/2018
- Academic Unit
- Radiation Oncology
- Record Identifier
- 9984047980202771
Metrics
16 Record Views