Research Papers: Imaging

Radiative transfer equation modeling by streamline diffusion modified continuous Galerkin method

[+] Author Affiliations
Feixiao Long, Xavier Intes, Shiva P. Kotha

Rensselaer Polytechnic Institute, Department of Biomedical Engineering, 110 8th Street, Troy, New York 12180, United States

Fengyan Li

Rensselaer Polytechnic Institute, Department of Mathematical Science, 110 8th Street, Troy, New York 12180, United States

J. Biomed. Opt. 21(3), 036003 (Mar 08, 2016). doi:10.1117/1.JBO.21.3.036003
History: Received October 28, 2015; Accepted February 15, 2016
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Abstract.  Optical tomography has a wide range of biomedical applications. Accurate prediction of photon transport in media is critical, as it directly affects the accuracy of the reconstructions. The radiative transfer equation (RTE) is the most accurate deterministic forward model, yet it has not been widely employed in practice due to the challenges in robust and efficient numerical implementations in high dimensions. Herein, we propose a method that combines the discrete ordinate method (DOM) with a streamline diffusion modified continuous Galerkin method to numerically solve RTE. Additionally, a phase function normalization technique was employed to dramatically reduce the instability of the DOM with fewer discrete angular points. To illustrate the accuracy and robustness of our method, the computed solutions to RTE were compared with Monte Carlo (MC) simulations when two types of sources (ideal pencil beam and Gaussian beam) and multiple optical properties were tested. Results show that with standard optical properties of human tissue, photon densities obtained using RTE are, on average, around 5% of those predicted by MC simulations in the entire/deeper region. These results suggest that this implementation of the finite element method-RTE is an accurate forward model for optical tomography in human tissues.

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© 2016 Society of Photo-Optical Instrumentation Engineers

Citation

Feixiao Long ; Fengyan Li ; Xavier Intes and Shiva P. Kotha
"Radiative transfer equation modeling by streamline diffusion modified continuous Galerkin method", J. Biomed. Opt. 21(3), 036003 (Mar 08, 2016). ; http://dx.doi.org/10.1117/1.JBO.21.3.036003


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