Advanced

Evaluation of a radiative transfer equation and diffusion approximation hybrid forward solver for fluorescence molecular imaging

Gorpas, Dimitris and Andersson-Engels, Stefan LU (2012) In Journal of Biomedical Optics 17(12).
Abstract
The solution of the forward problem in fluorescence molecular imaging strongly influences the successful convergence of the fluorophore reconstruction. The most common approach to meeting this problem has been to apply the diffusion approximation. However, this model is a first-order angular approximation of the radiative transfer equation, and thus is subject to some well-known limitations. This manuscript proposes a methodology that confronts these limitations by applying the radiative transfer equation in spatial regions in which the diffusion approximation gives decreased accuracy. The explicit integro differential equations that formulate this model were solved by applying the Galerkin finite element approximation. The required... (More)
The solution of the forward problem in fluorescence molecular imaging strongly influences the successful convergence of the fluorophore reconstruction. The most common approach to meeting this problem has been to apply the diffusion approximation. However, this model is a first-order angular approximation of the radiative transfer equation, and thus is subject to some well-known limitations. This manuscript proposes a methodology that confronts these limitations by applying the radiative transfer equation in spatial regions in which the diffusion approximation gives decreased accuracy. The explicit integro differential equations that formulate this model were solved by applying the Galerkin finite element approximation. The required spatial discretization of the investigated domain was implemented through the Delaunay triangulation, while the azimuthal discretization scheme was used for the angular space. This model has been evaluated on two simulation geometries and the results were compared with results from an independent Monte Carlo method and the radiative transfer equation by calculating the absolute values of the relative errors between these models. The results show that the proposed forward solver can approximate the radiative transfer equation and the Monte Carlo method with better than 95% accuracy, while the accuracy of the diffusion approximation is approximately 10% lower. (c) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.JBO.17.12.126010] (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
fluorescence molecular imaging, forward problem, hybrid model, radiative, transfer equation, diffusion approximation, finite elements
in
Journal of Biomedical Optics
volume
17
issue
12
publisher
Published by SPIE--the International Society for Optical Engineering in cooperation with International Biomedical Optics Society
external identifiers
  • wos:000314504400018
  • scopus:84878324285
ISSN
1083-3668
DOI
10.1117/1.JBO.17.12.126010
language
English
LU publication?
yes
id
a3f42da2-0e90-4972-9a78-0740599c141c (old id 3568081)
date added to LUP
2013-03-25 13:21:45
date last changed
2017-08-06 03:13:00
@article{a3f42da2-0e90-4972-9a78-0740599c141c,
  abstract     = {The solution of the forward problem in fluorescence molecular imaging strongly influences the successful convergence of the fluorophore reconstruction. The most common approach to meeting this problem has been to apply the diffusion approximation. However, this model is a first-order angular approximation of the radiative transfer equation, and thus is subject to some well-known limitations. This manuscript proposes a methodology that confronts these limitations by applying the radiative transfer equation in spatial regions in which the diffusion approximation gives decreased accuracy. The explicit integro differential equations that formulate this model were solved by applying the Galerkin finite element approximation. The required spatial discretization of the investigated domain was implemented through the Delaunay triangulation, while the azimuthal discretization scheme was used for the angular space. This model has been evaluated on two simulation geometries and the results were compared with results from an independent Monte Carlo method and the radiative transfer equation by calculating the absolute values of the relative errors between these models. The results show that the proposed forward solver can approximate the radiative transfer equation and the Monte Carlo method with better than 95% accuracy, while the accuracy of the diffusion approximation is approximately 10% lower. (c) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.JBO.17.12.126010]},
  articleno    = {126010},
  author       = {Gorpas, Dimitris and Andersson-Engels, Stefan},
  issn         = {1083-3668},
  keyword      = {fluorescence molecular imaging,forward problem,hybrid model,radiative,transfer equation,diffusion approximation,finite elements},
  language     = {eng},
  number       = {12},
  publisher    = {Published by SPIE--the International Society for Optical Engineering in cooperation with International Biomedical Optics Society},
  series       = {Journal of Biomedical Optics},
  title        = {Evaluation of a radiative transfer equation and diffusion approximation hybrid forward solver for fluorescence molecular imaging},
  url          = {http://dx.doi.org/10.1117/1.JBO.17.12.126010},
  volume       = {17},
  year         = {2012},
}