A first collision source method for coupling Monte Carlo and discrete ordinates for localized source problems

Alcouffe, R.E.

doi:10.1007/bfb0049062

Cited by 13 publications

(7 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ray-effect arises due to the restriction of particle transport to a set of discrete directions. To mitigate 'ray-effect' , the first-collision source method was employed 36 . The fluence in each voxel is composed of uncollided photons directly from the source and collided photons scattered from other voxels, energies, and directions.…”

Section: Methodsmentioning

confidence: 99%

Photon fluence and dose estimation in computed tomography using a discrete ordinates Boltzmann solver

Norris

Liu

2020

Sci Rep

View full text Add to dashboard Cite

In this study, cone-beam single projection and axial CT scans are modeled with a software package-DOCTORS, which solves the linear Boltzmann equation using the discrete ordinates method. Phantoms include a uniform 35 cm diameter water cylinder and a non-uniform abdomen phantom. Series simulations were performed with different simulation parameters, including the number of quadrature angles, the order of Legendre polynomial expansions, and coarse and fine mesh grid. Monte Carlo simulations were also performed to benchmark DOCTORS simulations. A quantitative comparison was made between the simulation results obtained using DOCTORS and Monte Carlo methods. The deterministic simulation was in good agreement with the Monte Carlo simulation on dose estimation, with a root-mean-square-deviation difference of around 2.87%. It was found that the contribution of uncollided photon fluence directly from the source dominates the local absorbed dose in the diagnostic X-ray energy range. The uncollided photon fluence can be calculated accurately using a 'ray-tracing' algorithm. The accuracy of collided photon fluence estimation is largely affected by the pre-calculated multigroup cross-sections. The primary benefit of DOCTORS lies in its rapid computation speed. Using DOCTORS, parallel computing with GPU enables the cone-beam CT dose estimation nearly in real-time. In X-ray attenuation-based CT imaging, the mechanisms responsible for a material's attenuation are primarily the photoelectric effect and Compton and Rayleigh scattering 1-3. These interactions determine the energy transfer between photons and material as well as the photon distribution throughout the CT system. A complete description of the photon distribution and energy transfer is essential for estimating patient dose and for designing an optimized CT system. Stochastic methods (e.g., Monte Carlo simulation) have been used extensively in the past 4-20 , and are generally considered to be the gold standard for estimating photon distributions and CT doses. However, they require a large number of particle histories and, therefore, a lengthy computation time is needed to reduce statistical uncertainty to an acceptable level. There is, however, no statistical error associated with deterministic methods, so they can be comparatively efficient in large regions where the highly resolved spatial fluence must be known to within a tight uncertainty bound. While hybrid stochastic-deterministic methods advantageously combine Monte Carlo and deterministic techniques and are more computationally efficient than a pure Monte Carlo simulation, they result in a cumbersome computational framework, due to the combination of two different methodologies, and can also have lengthy computation times 21, 22. We have explored three methodologies including Monte Carlo, hybrid Monte Carlo, and deterministic methods to solve photon transport problems 23-27 , and have found that the deterministic method provides accurate results that are comparable to a Monte Carlo simulation. In addition, the ...

show abstract

Section: Methodsmentioning

confidence: 99%

Photon fluence and dose estimation in computed tomography using a discrete ordinates Boltzmann solver

Norris

Liu

2020

Sci Rep

View full text Add to dashboard Cite

show abstract

“…In this section, we introduce and analyze a hybrid spatial discretization for the RTE. The underlying formulation is based on the idea of first collision source [4] and has been used in [32] as a way to combine different angular discretizations in a fully implicit time integration scheme. Here we combine DG discretization, which performs well in the diffusion limit, with FV discretization, which uses less memory per computational cell, into a single discretization strategy.…”

Section: Discrete Ordinatesmentioning

confidence: 99%

Hybrid Discrete Ordinates Solver for the Radiative Transport Equation using Second Order Finite Volume and Discontinuous Galerkin

Heningburg

2018

View full text Add to dashboard Cite

We propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite volume (FV) method. The strategy relies on a simple operator splitting that has been used previously to combine different angular discretizations. Unlike standard FV methods with upwind fluxes, the hybrid approach is able to accurately simulate problems in scattering dominated regimes. However, it requires less memory and yields a faster computational time than a uniform DG discretization. In addition, the underlying splitting allows naturally for hybridization in both space and angle. Numerical results are given to demonstrate the efficiency of the hybrid approach in the context of discrete ordinate angular discretizations and Cartesian spatial grids.

show abstract

“…The scattering source (including both upscatter and downscatter) then becomes dft' v' f_, ft' -9 -g( r. •n )og, (r. ) = Et.g,--g( r) t;. ( n )ot_g, <r) 0 g'" l tr g"-I /--0 rrt-'--I (2)(3)(4)(5)(6)(7)(8)(9)(10) Note that because of symmetry considerations for two dimensional geometries, the moments ot,,,g,(r) are zero for m < 0.13…”

Section: Tmentioning

confidence: 99%

“…As discussed in Chapter 4, explicit outscatter is replaced with a reduction in particle weight during the response matrix calculation. This is implemented by replacing the value of c normally used with cnM = _,jo.g--g /Er.,ig, (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23) where E,i0.g_g is as defined in Eq. (6)(7)(8)(9)(10)(11)(12)(13)(14).…”

Section: Collision Events Without Fissionmentioning

confidence: 99%

See 1 more Smart Citation

A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report

Baker¹

1990

View full text Add to dashboard Cite

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi-1 bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infr_'_geprivately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views aqd opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

show abstract

A first collision source method for coupling Monte Carlo and discrete ordinates for localized source problems

Cited by 13 publications

References 2 publications

Photon fluence and dose estimation in computed tomography using a discrete ordinates Boltzmann solver

Photon fluence and dose estimation in computed tomography using a discrete ordinates Boltzmann solver

Hybrid Discrete Ordinates Solver for the Radiative Transport Equation using Second Order Finite Volume and Discontinuous Galerkin

A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report

Contact Info

Product

Resources

About