A fast, linear Boltzmann transport equation solver for computed tomography dose calculation (Acuros CTD)

Purpose To improve dose reporting of CT scans, patient‐specific organ doses are highly desired. However, estimating the dose distribution in a fast and accurate manner remains challenging, despite advances in Monte Carlo methods. In this work, we present an alternative method that deterministically solves the linear Boltzmann transport equation (LBTE), which governs the behavior of x‐ray photon transport through an object. Methods Our deterministic solver for CT dose (Acuros CTD) is based on the same approach used to estimate scatter in projection images of a CT scan (Acuros CTS). A deterministic method is used to compute photon fluence within the object, which is then converted to deposited energy by multiplying by known, material‐specific conversion factors. To benchmark Acuros CTD, we used the AAPM Task Group 195 test for CT dose, which models an axial, fan beam scan (10 mm thick beam) and calculates energy deposited in each organ of an anthropomorphic phantom. We also validated our own Monte Carlo implementation of Geant4 to use as a reference to compare Acuros against for other common geometries like an axial, cone beam scan (160 mm thick beam) and a helical scan (40 mm thick beam with table motion for a pitch of 1). Results For the fan beam scan, Acuros CTD accurately estimated organ dose, with a maximum error of 2.7% and RMSE of 1.4% when excluding organs with3provided marginal improvement to the accuracy for the cone beam scan but came at the expense of increased run time. Across the different scan geometries, run time of Acuros CTD ranged from 8 to 23 s. Conclusions In this digital phantom study, a deterministic LBTE solver was capable of fast and accurate organ dose estimates

Preconditioning a mixed discontinuous finite element method for radiation diffusion

We propose a multilevel preconditioning strategy for the iterative solution of large sparse linear systems arising from a finite element discretization of the radiation diffusion equations. In particular, these equations are solved using a mixed finite element scheme in order to make the discretization discontinuous, which is imposed by the application in which the diffusion equation will be embedded. The essence of the preconditioner is to use a continuous finite element discretization of the original, elliptic diffusion equation for preconditioning the discontinuous equations. We have found that this preconditioner is very effective and makes the iterative solution of the discontinuous diffusion equations practical for large problems. This approach should be applicable to discontinuous discretizations of other elliptic equations. We show how our preconditioner is developed and applied to radiation diffusion problems on unstructured, tetrahedral meshes and show numerical results that illustrate its effectiveness. Published in 2004 by John Wiley & Sons, Ltd

Geometrically-compatible 3-D Monte Carlo and discrete-ordinates methods

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The purpose of this project was two-fold. The first purpose was to develop a deterministic discrete-ordinates neutral-particle transport scheme for unstructured tetrahedral spatial meshes, and implement it in a computer code. The second purpose was to modify the MCNP Monte Carlo radiation transport code to use adjoint solutions from the tetrahedral-mesh discrete-ordinates code to reduce the statistical variance of Monte Carlo solutions via a weight-window approach. The first task has resulted in a deterministic transport code that is much more efficient for modeling complex 3-D geometries than any previously existing deterministic code. The second task has resulted in a powerful new capability for dramatically reducing the cost of difficult 3-D Monte Carlo calculations

Krylov iterative methods applied to multidimensional S[sub n] calculations in the presence of material discontinuities

We show that a Krylov iterative meihod, preconditioned with DSA, can be used to efficiently compute solutions to diffusive problems with discontinuities in material properties. We consider a lumped, linear discontinuous discretization of the S N transport equation with a 'partially consistent' DSA preconditioner. The Krylov method can be implemented in terms of the original S N source iteration coding with little modification. Results from numerical experiments show that replacing source iteration with a preconditioned Krylov method can efficiently solve problems that are virtually intractable with accelerated source iteration. Key Words: Krylov iterative methods, discrete ordinates, deterministic transport methods, diffusion synthetic acceleratio

Krylov subspace iterations for the calculation of K-Eigenvalues with sn transport codes

We apply the Implicitly Restarted Arnoldi Method (IRAM), a Krylov subspace iterative method, to the calculation of k-eigenvalues for criticality problems. We show that the method can be implemented with only modest changes to existing power iteration schemes in an SN transport code. Numerical results on three dimensional unstructured tetrahedral meshes are shown. Although we only compare the IRAM to unaccelerated power iteration, the results indicate that the IRAM is a potentially efficient and powerful technique, especially for problems with dominance ratios approaching unity. Key Words: criticality eigenvalues, Implicitly Restarted Arnoldi Method (IRAM), deterministic transport method

Effects of fluoxetine on functional outcomes after acute stroke (FOCUS): a pragmatic, double-blind, randomised, controlled trial

Background Results of small trials indicate that fluoxetine might improve functional outcomes after stroke. The FOCUS trial aimed to provide a precise estimate of these effects. Methods FOCUS was a pragmatic, multicentre, parallel group, double-blind, randomised, placebo-controlled trial done at 103 hospitals in the UK. Patients were eligible if they were aged 18 years or older, had a clinical stroke diagnosis, were enrolled and randomly assigned between 2 days and 15 days after onset, and had focal neurological deficits. Patients were randomly allocated fluoxetine 20 mg or matching placebo orally once daily for 6 months via a web-based system by use of a minimisation algorithm. The primary outcome was functional status, measured with the modified Rankin Scale (mRS), at 6 months. Patients, carers, health-care staff, and the trial team were masked to treatment allocation. Functional status was assessed at 6 months and 12 months after randomisation. Patients were analysed according to their treatment allocation. This trial is registered with the ISRCTN registry, number ISRCTN83290762. Findings Between Sept 10, 2012, and March 31, 2017, 3127 patients were recruited. 1564 patients were allocated fluoxetine and 1563 allocated placebo. mRS data at 6 months were available for 1553 (99·3%) patients in each treatment group. The distribution across mRS categories at 6 months was similar in the fluoxetine and placebo groups (common odds ratio adjusted for minimisation variables 0·951 [95% CI 0·839–1·079]; p=0·439). Patients allocated fluoxetine were less likely than those allocated placebo to develop new depression by 6 months (210 [13·43%] patients vs 269 [17·21%]; difference 3·78% [95% CI 1·26–6·30]; p=0·0033), but they had more bone fractures (45 [2·88%] vs 23 [1·47%]; difference 1·41% [95% CI 0·38–2·43]; p=0·0070). There were no significant differences in any other event at 6 or 12 months. Interpretation Fluoxetine 20 mg given daily for 6 months after acute stroke does not seem to improve functional outcomes. Although the treatment reduced the occurrence of depression, it increased the frequency of bone fractures. These results do not support the routine use of fluoxetine either for the prevention of post-stroke depression or to promote recovery of function. Funding UK Stroke Association and NIHR Health Technology Assessment Programme

Asymptotic diffusion accelerated discontinuous finite element methods for transport problems.

The diffusion synthetic acceleration (DSA) method has emerged as a powerful tool for accelerating the iterative convergence rate of discrete-ordinate transport calculations. However, in multi-dimensional geometries, only the diamond-differenced scheme has been efficiently solved by the DSA procedure. More advanced and accurate schemes, such as the discontinuous finite element schemes, have not been efficiently solved by DSA because applying the standard DSA procedure results in a large, complicated system of equations that cannot be collapsed into an efficiently solvable discrete diffusion equation. Here we present a new procedure for diffusion-accelerating certain discontinuous finite element schemes for slab and x-y geometry discrete-ordinates problems. The novel aspect of this procedure is that the discretized diffusion problem is derived from an asymptotic expansion of the discrete transport problem. The motivation for this procedure is that the resulting diffusion problem is relatively "simple" and easily solvable. The asymptotic expansion also shows that these discontinuous finite element schemes are highly accurate for diffusive problems with optically thick spatial meshes. Therefore, these schemes possess two very desirable properties: they are very accurate for all problems with optically thin meshes and diffusive problems with optically thick meshes, and they are efficiently solved by a diffusion-synthetic acceleration procedure. Specifically, we consider the conventional and lumped linear discontinuous schemes in slab geometry and a certain lumped bilinear discontinuous scheme in x-y geometry. In slab geometry, the new "asymptotic" DSA procedure is very efficient for problems that contain either isotropic scattering or linearly-anisotropic scattering. In x-y geometry, this procedure is very efficient provided the spatial cells do not have large aspect ratios and the system does not have highly anisotropic scattering. Also, the resulting discrete diffusion equation has a very simple five-point stencil with a one-point removal term and is very efficiently solved by the multigrid method. We provide numerical results that demonstrate the high level of accuracy and rapid convergence of the new methods.Ph.D.Nuclear Engineering and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105813/1/9208688.pdfDescription of 9208688.pdf : Restricted to UM users only

Preconditioning a mixed discontinuous finite element method for radiation diffusion

We propose a multilevel preconditioning strategy for the iterative solution of large sparse linear systems arising from a finite element discretization of the radiation diffusion equations. In particular, these equations are solved using a mixed finite element scheme in order to make the discretization discontinuous, which is imposed by the application in which the diffusion equation will be embedded. The essence of the preconditioner is to use a continuous finite element discretization of the original, elliptic diffusion equation for preconditioning the discontinuous equations. We have found that this preconditioner is very effective and makes the iterative solution of the discontinuous diffusion equations practical for large problems. This approach should be applicable to discontinuous discretizations of other elliptic equations. We show how our preconditioner is developed and applied to radiation diffusion problems on unstructured, tetrahedral meshes and show numerical results that illustrate its effectiveness. Published in 2004 by John Wiley & Sons, Ltd

Pericles and Attila results for the C5G7 MOX benchmark problems

Recently the Nuclear Energy Agency has published a new benchmark entitled, 'C5G7 MOX Benchmark.' This benchmark is to test the ability of current transport codes to treat reactor core problems without spatial homogenization. The benchmark includes both a two- and three-dimensional problem. We have calculated results for these benchmark problems with our Pericles and Attila codes. Pericles is a one-,two-, and three-dimensional unstructured grid discrete-ordinates code and was used for the twodimensional benchmark problem. Attila is a three-dimensional unstructured tetrahedral mesh discrete-ordinate code and was used for the three-dimensional problem. Both codes use discontinuous finite element spatial differencing. Both codes use diffusion synthetic acceleration (DSA) for accelerating the inner iterations