Canonical and Involutory Transformations of the Variational Problems of Transport Theory

Kaplan, S.; Davis, James A.

doi:10.13182/nse67-a17466

Cited by 61 publications

(14 citation statements)

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“…Indefinite number of variational principles may be associated with the even-parity problem. [37][38][39] One of them is a self-adjoint minimum principle, with the related quadratic functional being defined as 40,32…”

Section: ͑10͒mentioning

confidence: 99%

A comparison between transport and diffusion calculations using a finite element‐spherical harmonics radiation transport method

2002

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Most researchers choose the diffusion approximation to the transport equation as the model to describe photon migration in biological tissues. However, the applicability of this approximation is limited and, in certain cases, invalid. In this paper we introduce a two-dimensional, finite element-spherical harmonics (FE-P(N)) radiation transport method for the simulation of light propagation in tissue. The propagation of light is investigated first in a layered cylinder, which can be seen as a very simplistic approximation of a human head. Effects of the anisotropy factor g on the photon migration is then examined in homogeneous and heterogeneous media for different values of g and mu(s). The influence of void-like heterogeneities and channels in which absorption and scattering are very small compared with the surrounding medium on the transport of photons is also investigated. Significant differences between transport and diffusion calculations are shown to occur in all cases.

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Section: ͑10͒mentioning

confidence: 99%

A comparison between transport and diffusion calculations using a finite element‐spherical harmonics radiation transport method

2002

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“…The EP and OP equations have been numerically solved within the neutron transport community for decades 0021 [3][4][5][6][7][8]. These equations have been traditionally used to solve only the steady-state neutron transport equation.…”

Section: Introductionmentioning

confidence: 99%

Spatial discretizations for self-adjoint forms of the radiative transfer equations

Morel

Adams

Noh

et al. 2006

Journal of Computational Physics

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“…This leads to a representation of Eq. 1 that allows to introduce a variational principle [31,32] and to use the finite element method to solve the problem numerically. For more details concerning this approach see reference [30].…”

Section: Image Reconstruction Algorithmmentioning

confidence: 99%

Optical tomographic brain imaging with diffusion and transport-theory-based algorithms

et al. 2003

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There has been considerable discussion concerning the effects of the cerebrospinal fluid on measurements of bloodrelated parameters in the human brain, and if diffusion-theory-based image reconstruction algorithms can accurately account for the light propagation in the head. All of these studies have been performed either with synthetic data generate from numerical models or from phantom studies. We present here the first comparative study that involves clinical data from optical tomographic measurements. Data obtained from the human forehead during a Valsalva maneuver were input to two different model-based iterative image reconstruction algorithms recently developed in our laboratories. One code is based on the equation of radiative transfer, while the other algorithm uses a diffusion model to describe the light propagation in the head. Both codes use finite-element formulations of the respective theories and were used to obtain three-dimensional volumetric images of oxy, dexoy and total hemoglobin. The reconstructed overall spatial heterogeneity in changes of these parameters is similar using both algorithms. The two codes differ mostly in the amplitude of the observed changes. In general the transport based codes reconstructs changes 10-40% stronger than the diffusion code.

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Canonical and Involutory Transformations of the Variational Problems of Transport Theory

Cited by 61 publications

References 0 publications

A comparison between transport and diffusion calculations using a finite element‐spherical harmonics radiation transport method

A comparison between transport and diffusion calculations using a finite element‐spherical harmonics radiation transport method

Spatial discretizations for self-adjoint forms of the radiative transfer equations

Optical tomographic brain imaging with diffusion and transport-theory-based algorithms

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