Abstract

As a widely used numerical solution for the radiation transport equation (RTE), the discrete ordinates can predict the propagation of photons through biological tissues more accurately relative to the diffusion equation. The discrete ordinates reduce the RTE to a serial of differential equations that can be solved by source iteration (SI). However, the tremendous time consumption of SI, which is partly caused by the expensive computation of each SI step, limits its applications. In this paper, we present a graphics processing unit (GPU) parallel accelerated SI method for discrete ordinates. Utilizing the calculation independence on the levels of the discrete ordinate equation and spatial element, the proposed method reduces the time cost of each SI step by parallel calculation. The photon reflection at the boundary was calculated based on the results of the last SI step to ensure the calculation independence on the level of the discrete ordinate equation. An element sweeping strategy was proposed to detect the calculation independence on the level of the spatial element. A GPU parallel frame called the compute unified device architecture was employed to carry out the parallel computation. The simulation experiments, which were carried out with a cylindrical phantom and numerical mouse, indicated that the time cost of each SI step can be reduced up to a factor of 228 by the proposed method with a GTX 260 graphics card.

© 2011 Optical Society of America

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  1. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
    [CrossRef]
  2. R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
    [CrossRef]
  3. V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006).
    [CrossRef]
  4. V. Ntziachristos, J. Ripoll, LH. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
    [CrossRef]
  5. G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
    [CrossRef]
  6. K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
    [CrossRef]
  7. S. Patwardhan, S. Bloch, S. Achilefu, and J. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice,” Opt. Express 13, 2564–2577 (2005).
    [CrossRef]
  8. E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911(2003).
    [CrossRef]
  9. E. D. Aydin, C. R. E. Oliveira, and A. J. H. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).
    [CrossRef]
  10. A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. 220, 441–470 (2006).
    [CrossRef]
  11. J. C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Radiative transport in fluorescence-enhanced frequency-domain photon migration,” Med. Phys. 33, 4685–4700 (2006).
    [CrossRef]
  12. E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport (Wiley, 1984).
  13. T. A. Wareing, J. M. McGhee, J. E. Morel, and S. D. Pautz, “Discontinuous finite element SN methods on three-dimensional unstructured grids,” Nucl. Sci. Eng. 138, 256–268 (2001).
  14. A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345(2005).
    [CrossRef]
  15. A. D. Klose and A. H. Hielscher, “Fluorescence tomography with simulated data based on the equation of radiative transfer,” Opt. Lett. 28, 1019–1021 (2003).
    [CrossRef]
  16. K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain,” Opt. Lett. 29, 578–580 (2004).
    [CrossRef]
  17. H. Gao and H. K. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192(2009).
    [CrossRef]
  18. M. L. Adams, T. A. Wareing, and W. F. Walters, “Characteristic methods in thick diffusive problems,” Nucl. Sci. Eng. 130, 18–46 (1998).
  19. M. L. Adams and E. W. Larsen, “Fast iterative methods for discrete-ordinates particle transport calculations,” Prog. Nucl. Energy 40, 3–159 (2002).
    [CrossRef]
  20. G. Longoni, A. Haghighat, C. Yi, and G. E. Sjoden, “Benchmarking of PENTRAN-SSN parallel transport code and fast preconditioning algorithm using the VENUS-2 MOX-fueled benchmark problem,” J. ASTM Int. 3, 321–330 (2006).
  21. V. Kucukboyaci, A. Haghighat, and G. E. Sjoden, “Performance of PENTRAN 3-D parallel particle transport code on the IBM SP2 and PCTRAN cluster,” Lect. Notes Comput. Sci. 2131, 36–43 (2001).
    [CrossRef]
  22. G. Ghita, G. Sjoden, and J. Baciak, “A Methodology for experimental and 3-D computational radiation transport assessments of Pu-Be neutron sources,” Nucl. Technol. 159, 319–331(2007).
  23. NVIDIA, http://www.nvidia. com.
  24. V. Lebedev, “Values of the nodes and weights of ninth to seventeenth order Gauss–Markov quadrature formulae invariant under the octahedron group with inversion,” USSR Comput. Math. Math. Phys. 15, 44–51 (1975).
    [CrossRef]
  25. V. Lebedev, “Quadratures on a sphere,” USSR Comput. Math. Math. Phys. 16, 10–24 (1976).
    [CrossRef]
  26. A. Kienle, F. K. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett. 26, 1571–1573 (2001).
    [CrossRef]
  27. J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
  28. L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
    [CrossRef]
  29. D. Boas, J. Culver, J. Stott, and A. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10, 159–169 (2002).
  30. N. N. Ren, J. M. Liang, X. C. Qu, J. F. Li, B. J. Lu, and J. Tian, “GPU-based Monte Carlo simulation for light propagation in complex heterogeneous tissues,” Opt. Express 18, 6811–6823(2010).
    [CrossRef]
  31. B. Dogdas, D. Stout, A. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587 (2007).
    [CrossRef]
  32. G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50, 4225–4241 (2005).
    [CrossRef]
  33. A. Nicholls and B. Honig, “A rapid finite difference algorithm utilizing successive over-relaxation to solve the Poisson-Boltzmann equation,” J. Comput. Chem. 12, 435–445 (1991).
    [CrossRef]
  34. J. V. Dave and J. Gazdag, “A modified Fourier transform method for multiple scattering calculations in a plane parallel Mie atmosphere,” Appl. Opt. 9, 1457–1466 (1970).
    [CrossRef]
  35. S. Ito and T. Oguchi, “Approximate solutions of the vector radiative transfer equation for linearly polarized light in discrete random media,” J. Opt. Soc. Am. A 6, 1852–1858(1989).
    [CrossRef]
  36. V. P. Budak and A. V. Kozelskii, “Accuracy and applicability domain of the small angle approximation,” Atmos. Oceanic Opt. 18, 32–37 (2005).
  37. Y. A. Ilyushin and V. P. Budak, “Narrow-beam propagation in a two-dimensional scattering medium,” J. Opt. Soc. Am. A 28, 76–81 (2011).
    [CrossRef]
  38. S. A. Rukolaine and V. S. Yuferev, “Discrete ordinates quadrature schemes based on the angular interpolation of radiation intensity,” J. Quant. Spectrosc. Radiat. Transfer 69, 257–275(2001).
    [CrossRef]

2011 (1)

2010 (1)

2009 (1)

H. Gao and H. K. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192(2009).
[CrossRef]

2007 (2)

B. Dogdas, D. Stout, A. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587 (2007).
[CrossRef]

G. Ghita, G. Sjoden, and J. Baciak, “A Methodology for experimental and 3-D computational radiation transport assessments of Pu-Be neutron sources,” Nucl. Technol. 159, 319–331(2007).

2006 (5)

G. Longoni, A. Haghighat, C. Yi, and G. E. Sjoden, “Benchmarking of PENTRAN-SSN parallel transport code and fast preconditioning algorithm using the VENUS-2 MOX-fueled benchmark problem,” J. ASTM Int. 3, 321–330 (2006).

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. 220, 441–470 (2006).
[CrossRef]

J. C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Radiative transport in fluorescence-enhanced frequency-domain photon migration,” Med. Phys. 33, 4685–4700 (2006).
[CrossRef]

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006).
[CrossRef]

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

2005 (6)

S. Patwardhan, S. Bloch, S. Achilefu, and J. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice,” Opt. Express 13, 2564–2577 (2005).
[CrossRef]

V. Ntziachristos, J. Ripoll, LH. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[CrossRef]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345(2005).
[CrossRef]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50, 4225–4241 (2005).
[CrossRef]

V. P. Budak and A. V. Kozelskii, “Accuracy and applicability domain of the small angle approximation,” Atmos. Oceanic Opt. 18, 32–37 (2005).

2004 (1)

2003 (3)

A. D. Klose and A. H. Hielscher, “Fluorescence tomography with simulated data based on the equation of radiative transfer,” Opt. Lett. 28, 1019–1021 (2003).
[CrossRef]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911(2003).
[CrossRef]

2002 (3)

E. D. Aydin, C. R. E. Oliveira, and A. J. H. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).
[CrossRef]

D. Boas, J. Culver, J. Stott, and A. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10, 159–169 (2002).

M. L. Adams and E. W. Larsen, “Fast iterative methods for discrete-ordinates particle transport calculations,” Prog. Nucl. Energy 40, 3–159 (2002).
[CrossRef]

2001 (4)

A. Kienle, F. K. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett. 26, 1571–1573 (2001).
[CrossRef]

V. Kucukboyaci, A. Haghighat, and G. E. Sjoden, “Performance of PENTRAN 3-D parallel particle transport code on the IBM SP2 and PCTRAN cluster,” Lect. Notes Comput. Sci. 2131, 36–43 (2001).
[CrossRef]

S. A. Rukolaine and V. S. Yuferev, “Discrete ordinates quadrature schemes based on the angular interpolation of radiation intensity,” J. Quant. Spectrosc. Radiat. Transfer 69, 257–275(2001).
[CrossRef]

T. A. Wareing, J. M. McGhee, J. E. Morel, and S. D. Pautz, “Discontinuous finite element SN methods on three-dimensional unstructured grids,” Nucl. Sci. Eng. 138, 256–268 (2001).

1999 (1)

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

1998 (1)

M. L. Adams, T. A. Wareing, and W. F. Walters, “Characteristic methods in thick diffusive problems,” Nucl. Sci. Eng. 130, 18–46 (1998).

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

1991 (1)

A. Nicholls and B. Honig, “A rapid finite difference algorithm utilizing successive over-relaxation to solve the Poisson-Boltzmann equation,” J. Comput. Chem. 12, 435–445 (1991).
[CrossRef]

1990 (1)

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef]

1989 (1)

1984 (1)

E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport (Wiley, 1984).

1976 (1)

V. Lebedev, “Quadratures on a sphere,” USSR Comput. Math. Math. Phys. 16, 10–24 (1976).
[CrossRef]

1975 (1)

V. Lebedev, “Values of the nodes and weights of ninth to seventeenth order Gauss–Markov quadrature formulae invariant under the octahedron group with inversion,” USSR Comput. Math. Math. Phys. 15, 44–51 (1975).
[CrossRef]

1970 (1)

Abdoulaev, G. S.

Achilefu, S.

Adams, M. L.

M. L. Adams and E. W. Larsen, “Fast iterative methods for discrete-ordinates particle transport calculations,” Prog. Nucl. Energy 40, 3–159 (2002).
[CrossRef]

M. L. Adams, T. A. Wareing, and W. F. Walters, “Characteristic methods in thick diffusive problems,” Nucl. Sci. Eng. 130, 18–46 (1998).

Alexandrakis, G.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50, 4225–4241 (2005).
[CrossRef]

Alfano, R. R.

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[CrossRef]

Aydin, E. D.

E. D. Aydin, C. R. E. Oliveira, and A. J. H. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).
[CrossRef]

Baciak, J.

G. Ghita, G. Sjoden, and J. Baciak, “A Methodology for experimental and 3-D computational radiation transport assessments of Pu-Be neutron sources,” Nucl. Technol. 159, 319–331(2007).

Bal, G.

Bloch, S.

Boas, D.

Budak, V. P.

Y. A. Ilyushin and V. P. Budak, “Narrow-beam propagation in a two-dimensional scattering medium,” J. Opt. Soc. Am. A 28, 76–81 (2011).
[CrossRef]

V. P. Budak and A. V. Kozelskii, “Accuracy and applicability domain of the small angle approximation,” Atmos. Oceanic Opt. 18, 32–37 (2005).

Chatziioannou, A.

B. Dogdas, D. Stout, A. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587 (2007).
[CrossRef]

Chatziioannou, A. F.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50, 4225–4241 (2005).
[CrossRef]

Cheng, J.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Cong, W.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Culver, J.

Dave, J. V.

Dogdas, B.

B. Dogdas, D. Stout, A. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587 (2007).
[CrossRef]

Dunn, A.

Forster, F. K.

Gao, H.

H. Gao and H. K. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192(2009).
[CrossRef]

Gazdag, J.

Ghita, G.

G. Ghita, G. Sjoden, and J. Baciak, “A Methodology for experimental and 3-D computational radiation transport assessments of Pu-Be neutron sources,” Nucl. Technol. 159, 319–331(2007).

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[CrossRef]

Goddard, A. J. H.

E. D. Aydin, C. R. E. Oliveira, and A. J. H. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).
[CrossRef]

Graves, E. E.

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911(2003).
[CrossRef]

Haghighat, A.

G. Longoni, A. Haghighat, C. Yi, and G. E. Sjoden, “Benchmarking of PENTRAN-SSN parallel transport code and fast preconditioning algorithm using the VENUS-2 MOX-fueled benchmark problem,” J. ASTM Int. 3, 321–330 (2006).

V. Kucukboyaci, A. Haghighat, and G. E. Sjoden, “Performance of PENTRAN 3-D parallel particle transport code on the IBM SP2 and PCTRAN cluster,” Lect. Notes Comput. Sci. 2131, 36–43 (2001).
[CrossRef]

Han, W.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[CrossRef]

Hibst, R.

Hielscher, A. H.

Honig, B.

A. Nicholls and B. Honig, “A rapid finite difference algorithm utilizing successive over-relaxation to solve the Poisson-Boltzmann equation,” J. Comput. Chem. 12, 435–445 (1991).
[CrossRef]

Ilyushin, Y. A.

Ito, S.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Jiang, M.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Joshi, A.

J. C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Radiative transport in fluorescence-enhanced frequency-domain photon migration,” Med. Phys. 33, 4685–4700 (2006).
[CrossRef]

Kienle, A.

Klose, A. D.

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. 220, 441–470 (2006).
[CrossRef]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345(2005).
[CrossRef]

A. D. Klose and A. H. Hielscher, “Fluorescence tomography with simulated data based on the equation of radiative transfer,” Opt. Lett. 28, 1019–1021 (2003).
[CrossRef]

Kozelskii, A. V.

V. P. Budak and A. V. Kozelskii, “Accuracy and applicability domain of the small angle approximation,” Atmos. Oceanic Opt. 18, 32–37 (2005).

Kucukboyaci, V.

V. Kucukboyaci, A. Haghighat, and G. E. Sjoden, “Performance of PENTRAN 3-D parallel particle transport code on the IBM SP2 and PCTRAN cluster,” Lect. Notes Comput. Sci. 2131, 36–43 (2001).
[CrossRef]

Kumar, D.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Larsen, E. W.

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. 220, 441–470 (2006).
[CrossRef]

M. L. Adams and E. W. Larsen, “Fast iterative methods for discrete-ordinates particle transport calculations,” Prog. Nucl. Energy 40, 3–159 (2002).
[CrossRef]

Leahy, R. M.

B. Dogdas, D. Stout, A. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587 (2007).
[CrossRef]

Lebedev, V.

V. Lebedev, “Quadratures on a sphere,” USSR Comput. Math. Math. Phys. 16, 10–24 (1976).
[CrossRef]

V. Lebedev, “Values of the nodes and weights of ninth to seventeenth order Gauss–Markov quadrature formulae invariant under the octahedron group with inversion,” USSR Comput. Math. Math. Phys. 15, 44–51 (1975).
[CrossRef]

Lewis, E. E.

E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport (Wiley, 1984).

Li, H.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Li, J. F.

Li, Y.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Liang, J. M.

Liu, F.

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef]

Longoni, G.

G. Longoni, A. Haghighat, C. Yi, and G. E. Sjoden, “Benchmarking of PENTRAN-SSN parallel transport code and fast preconditioning algorithm using the VENUS-2 MOX-fueled benchmark problem,” J. ASTM Int. 3, 321–330 (2006).

Lu, B. J.

Luo, J.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Lv, Y.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

McGhee, J.

J. C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Radiative transport in fluorescence-enhanced frequency-domain photon migration,” Med. Phys. 33, 4685–4700 (2006).
[CrossRef]

McGhee, J. M.

T. A. Wareing, J. M. McGhee, J. E. Morel, and S. D. Pautz, “Discontinuous finite element SN methods on three-dimensional unstructured grids,” Nucl. Sci. Eng. 138, 256–268 (2001).

Miller, W. F.

E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport (Wiley, 1984).

Morel, J. E.

T. A. Wareing, J. M. McGhee, J. E. Morel, and S. D. Pautz, “Discontinuous finite element SN methods on three-dimensional unstructured grids,” Nucl. Sci. Eng. 138, 256–268 (2001).

Nicholls, A.

A. Nicholls and B. Honig, “A rapid finite difference algorithm utilizing successive over-relaxation to solve the Poisson-Boltzmann equation,” J. Comput. Chem. 12, 435–445 (1991).
[CrossRef]

Ntziachristos, V.

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006).
[CrossRef]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345(2005).
[CrossRef]

V. Ntziachristos, J. Ripoll, LH. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911(2003).
[CrossRef]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef]

Oguchi, T.

Oliveira, C. R. E.

E. D. Aydin, C. R. E. Oliveira, and A. J. H. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).
[CrossRef]

Pan, T.

J. C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Radiative transport in fluorescence-enhanced frequency-domain photon migration,” Med. Phys. 33, 4685–4700 (2006).
[CrossRef]

Patwardhan, S.

Pautz, S. D.

T. A. Wareing, J. M. McGhee, J. E. Morel, and S. D. Pautz, “Discontinuous finite element SN methods on three-dimensional unstructured grids,” Nucl. Sci. Eng. 138, 256–268 (2001).

Qian, X.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Qu, X. C.

Rannou, F. R.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50, 4225–4241 (2005).
[CrossRef]

Rasmussen, J. C.

J. C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Radiative transport in fluorescence-enhanced frequency-domain photon migration,” Med. Phys. 33, 4685–4700 (2006).
[CrossRef]

Ren, K.

Ren, N. N.

Ripoll, J.

V. Ntziachristos, J. Ripoll, LH. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911(2003).
[CrossRef]

Rukolaine, S. A.

S. A. Rukolaine and V. S. Yuferev, “Discrete ordinates quadrature schemes based on the angular interpolation of radiation intensity,” J. Quant. Spectrosc. Radiat. Transfer 69, 257–275(2001).
[CrossRef]

Sevick-Muraca, E. M.

J. C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Radiative transport in fluorescence-enhanced frequency-domain photon migration,” Med. Phys. 33, 4685–4700 (2006).
[CrossRef]

Shen, H.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Sjoden, G.

G. Ghita, G. Sjoden, and J. Baciak, “A Methodology for experimental and 3-D computational radiation transport assessments of Pu-Be neutron sources,” Nucl. Technol. 159, 319–331(2007).

Sjoden, G. E.

G. Longoni, A. Haghighat, C. Yi, and G. E. Sjoden, “Benchmarking of PENTRAN-SSN parallel transport code and fast preconditioning algorithm using the VENUS-2 MOX-fueled benchmark problem,” J. ASTM Int. 3, 321–330 (2006).

V. Kucukboyaci, A. Haghighat, and G. E. Sjoden, “Performance of PENTRAN 3-D parallel particle transport code on the IBM SP2 and PCTRAN cluster,” Lect. Notes Comput. Sci. 2131, 36–43 (2001).
[CrossRef]

Stott, J.

Stout, D.

B. Dogdas, D. Stout, A. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587 (2007).
[CrossRef]

Tian, J.

N. N. Ren, J. M. Liang, X. C. Qu, J. F. Li, B. J. Lu, and J. Tian, “GPU-based Monte Carlo simulation for light propagation in complex heterogeneous tissues,” Opt. Express 18, 6811–6823(2010).
[CrossRef]

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Walters, W. F.

M. L. Adams, T. A. Wareing, and W. F. Walters, “Characteristic methods in thick diffusive problems,” Nucl. Sci. Eng. 130, 18–46 (1998).

Wang, G.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Wang, LH.

V. Ntziachristos, J. Ripoll, LH. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

Wareing, T.

J. C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Radiative transport in fluorescence-enhanced frequency-domain photon migration,” Med. Phys. 33, 4685–4700 (2006).
[CrossRef]

Wareing, T. A.

T. A. Wareing, J. M. McGhee, J. E. Morel, and S. D. Pautz, “Discontinuous finite element SN methods on three-dimensional unstructured grids,” Nucl. Sci. Eng. 138, 256–268 (2001).

M. L. Adams, T. A. Wareing, and W. F. Walters, “Characteristic methods in thick diffusive problems,” Nucl. Sci. Eng. 130, 18–46 (1998).

Weissleder, R.

V. Ntziachristos, J. Ripoll, LH. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911(2003).
[CrossRef]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef]

Yi, C.

G. Longoni, A. Haghighat, C. Yi, and G. E. Sjoden, “Benchmarking of PENTRAN-SSN parallel transport code and fast preconditioning algorithm using the VENUS-2 MOX-fueled benchmark problem,” J. ASTM Int. 3, 321–330 (2006).

Yoo, K. M.

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef]

Yuferev, V. S.

S. A. Rukolaine and V. S. Yuferev, “Discrete ordinates quadrature schemes based on the angular interpolation of radiation intensity,” J. Quant. Spectrosc. Radiat. Transfer 69, 257–275(2001).
[CrossRef]

Zhao, H. K.

H. Gao and H. K. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192(2009).
[CrossRef]

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Zhou, T.

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

Annu. Rev. Biomed. Eng. (1)

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006).
[CrossRef]

Appl. Opt. (1)

Atmos. Oceanic Opt. (1)

V. P. Budak and A. V. Kozelskii, “Accuracy and applicability domain of the small angle approximation,” Atmos. Oceanic Opt. 18, 32–37 (2005).

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Curr. Med. Imaging Rev. (1)

G. Wang, W. Cong, Y. Li, W. Han, D. Kumar, X. Qian, H. Shen, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo. “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2, 453–457 (2006).
[CrossRef]

J. ASTM Int. (1)

G. Longoni, A. Haghighat, C. Yi, and G. E. Sjoden, “Benchmarking of PENTRAN-SSN parallel transport code and fast preconditioning algorithm using the VENUS-2 MOX-fueled benchmark problem,” J. ASTM Int. 3, 321–330 (2006).

J. Comput. Chem. (1)

A. Nicholls and B. Honig, “A rapid finite difference algorithm utilizing successive over-relaxation to solve the Poisson-Boltzmann equation,” J. Comput. Chem. 12, 435–445 (1991).
[CrossRef]

J. Comput. Phys. (2)

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. 220, 441–470 (2006).
[CrossRef]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345(2005).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (1)

S. A. Rukolaine and V. S. Yuferev, “Discrete ordinates quadrature schemes based on the angular interpolation of radiation intensity,” J. Quant. Spectrosc. Radiat. Transfer 69, 257–275(2001).
[CrossRef]

Lect. Notes Comput. Sci. (1)

V. Kucukboyaci, A. Haghighat, and G. E. Sjoden, “Performance of PENTRAN 3-D parallel particle transport code on the IBM SP2 and PCTRAN cluster,” Lect. Notes Comput. Sci. 2131, 36–43 (2001).
[CrossRef]

Med. Phys. (3)

J. C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Radiative transport in fluorescence-enhanced frequency-domain photon migration,” Med. Phys. 33, 4685–4700 (2006).
[CrossRef]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911(2003).
[CrossRef]

E. D. Aydin, C. R. E. Oliveira, and A. J. H. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).
[CrossRef]

Nat. Biotechnol. (1)

V. Ntziachristos, J. Ripoll, LH. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

Nat. Med. (1)

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef]

Nucl. Sci. Eng. (2)

T. A. Wareing, J. M. McGhee, J. E. Morel, and S. D. Pautz, “Discontinuous finite element SN methods on three-dimensional unstructured grids,” Nucl. Sci. Eng. 138, 256–268 (2001).

M. L. Adams, T. A. Wareing, and W. F. Walters, “Characteristic methods in thick diffusive problems,” Nucl. Sci. Eng. 130, 18–46 (1998).

Nucl. Technol. (1)

G. Ghita, G. Sjoden, and J. Baciak, “A Methodology for experimental and 3-D computational radiation transport assessments of Pu-Be neutron sources,” Nucl. Technol. 159, 319–331(2007).

Opt. Express (3)

Opt. Lett. (3)

Phys. Med. Biol. (3)

B. Dogdas, D. Stout, A. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587 (2007).
[CrossRef]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50, 4225–4241 (2005).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef]

Prog. Nucl. Energy (1)

M. L. Adams and E. W. Larsen, “Fast iterative methods for discrete-ordinates particle transport calculations,” Prog. Nucl. Energy 40, 3–159 (2002).
[CrossRef]

Transp. Theory Stat. Phys. (1)

H. Gao and H. K. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192(2009).
[CrossRef]

USSR Comput. Math. Math. Phys. (2)

V. Lebedev, “Values of the nodes and weights of ninth to seventeenth order Gauss–Markov quadrature formulae invariant under the octahedron group with inversion,” USSR Comput. Math. Math. Phys. 15, 44–51 (1975).
[CrossRef]

V. Lebedev, “Quadratures on a sphere,” USSR Comput. Math. Math. Phys. 16, 10–24 (1976).
[CrossRef]

Other (3)

NVIDIA, http://www.nvidia. com.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport (Wiley, 1984).

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