Abstract

We describe a fast mesh-based Monte Carlo (MC) photon migration algorithm for static and time-resolved imaging in 3D complex media. Compared with previous works using voxel-based media discretization, a mesh-based approach can be more accurate in modeling targets with curved boundaries or locally refined structures. We implement an efficient ray-tracing technique using Plücker Coordinates. The Barycentric coordinates computed from Plücker-formed ray-tracing enables us to use linear Lagrange basis functions to model both media properties and fluence distribution, leading to further improvement in accuracy. The Plücker-coordinate ray-polygon intersection test can be extended to hexahedral or high-order elements. Excellent agreement is found when comparing mesh-based MC with the analytical diffusion model and 3D voxel-based MC code in both homogeneous and heterogeneous cases. Realistic time-resolved imaging results are observed for a complex human brain anatomy using mesh-based MC. We also include multi-threading support in the software and will port it to a graphics processing unit platform in the near future.

© 2010 OSA

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    [CrossRef] [PubMed]

2010 (2)

2009 (2)

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
[CrossRef] [PubMed]

Q. Fang and D. Boas, “Tetrahedral mesh generation from volumetric binary and gray-scale images,” Proceedings of IEEE International Symposium on Biomedical Imaging 2009, 1142–1145 (2009).

2008 (2)

T. Binzoni, T. S. Leung, R. Giust, D. Rüfenacht, and A. H. Gandjbakhche, “Light transport in tissue by 3D Monte Carlo: influence of boundary voxelization,” Comput. Methods Programs Biomed. 89(1), 14–23 (2008).
[CrossRef] [PubMed]

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (1)

2004 (2)

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(6), 578–580 (2004).
[CrossRef] [PubMed]

Y. Xu, Q. Zhang, and H. Jiang, “Optical image reconstruction of non-scattering and low scattering heterogeneities in turbid media based on the diffusion approximation model,” J. Opt. A, Pure Appl. Opt. 6(1), 29–35 (2004).
[CrossRef]

2003 (2)

Y. Fukui, Y. Ajichi, and E. Okada, “Monte Carlo prediction of near-infrared light propagation in realistic adult and neonatal head models,” Appl. Opt. 42(16), 2881–2887 (2003).
[CrossRef] [PubMed]

N. Platis and T. Theoharis, “Fast ray-tetrahedron intersection using Plücker coordinates,” Journal of Graphics Tools 8(4), 37–48 (2003).

2002 (3)

M. Meyer, H. Lee, A. Barr, and M. Desbrun, “Generalized Barycentric Coordinates on Irregular Polygons,” Journal of Graphics Tools 7(1), 13–22 (2002).

A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich, and H.-J. Schwarzmaier, “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range,” Phys. Med. Biol. 47(12), 2059–2073 (2002).
[CrossRef] [PubMed]

D. A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10(3), 159–170 (2002).
[PubMed]

2000 (3)

A. Colasanti, G. Guida, A. Kisslinger, R. Liuzzi, M. Quarto, P. Riccio, G. Roberti, and F. Villani, “Multiple processor version of a Monte Carlo code for photon transport in turbid media,” Comput. Phys. Commun. 132(1–2), 84–93 (2000).
[CrossRef]

J. Ripoll, M. Nieto-Vesperinas, S. R. Arridge, and H. Dehghani, “Boundary conditions for light propagation in diffusive media with nonscattering regions,” J. Opt. Soc. Am. A 17(9), 1671–1681 (2000).
[CrossRef] [PubMed]

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27(1), 252–264 (2000).
[CrossRef] [PubMed]

1999 (1)

J. Vollmer, R. Mencel, and H. Müller, ““Improved Laplacian smoothing of noisy surface meshes,” In Proc,” EuroGraphics 99, 131–138 (1999).

1998 (2)

D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans, “Design and construction of a realistic digital brain phantom,” IEEE Trans. Med. Imaging 17(3), 463–468 (1998).
[CrossRef] [PubMed]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[CrossRef] [PubMed]

1997 (2)

1995 (1)

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML - Monte Carlo modeling of light transport in multilayered tissues,” Comput. Meth. Prog. Bio. 47(2), 131–146 (1995).
[CrossRef]

1994 (1)

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91(11), 4887–4891 (1994).
[CrossRef] [PubMed]

1993 (2)

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2 Pt 1), 299–309 (1993).
[CrossRef] [PubMed]

1991 (1)

1983 (1)

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Abdoulaev, G. S.

Adam, G.

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Ajichi, Y.

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[CrossRef] [PubMed]

Alerstam, E.

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[CrossRef] [PubMed]

Andersson-Engels, S.

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[CrossRef] [PubMed]

Arridge, S. R.

J. Ripoll, M. Nieto-Vesperinas, S. R. Arridge, and H. Dehghani, “Boundary conditions for light propagation in diffusive media with nonscattering regions,” J. Opt. Soc. Am. A 17(9), 1671–1681 (2000).
[CrossRef] [PubMed]

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27(1), 252–264 (2000).
[CrossRef] [PubMed]

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2 Pt 1), 299–309 (1993).
[CrossRef] [PubMed]

Bal, G.

Barbour, R. L.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[CrossRef] [PubMed]

Barnett, A. H.

Barr, A.

M. Meyer, H. Lee, A. Barr, and M. Desbrun, “Generalized Barycentric Coordinates on Irregular Polygons,” Journal of Graphics Tools 7(1), 13–22 (2002).

Binzoni, T.

T. Binzoni, T. S. Leung, R. Giust, D. Rüfenacht, and A. H. Gandjbakhche, “Light transport in tissue by 3D Monte Carlo: influence of boundary voxelization,” Comput. Methods Programs Biomed. 89(1), 14–23 (2008).
[CrossRef] [PubMed]

Boas, D.

Q. Fang and D. Boas, “Tetrahedral mesh generation from volumetric binary and gray-scale images,” Proceedings of IEEE International Symposium on Biomedical Imaging 2009, 1142–1145 (2009).

Boas, D. A.

Chance, B.

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91(11), 4887–4891 (1994).
[CrossRef] [PubMed]

Colasanti, A.

A. Colasanti, G. Guida, A. Kisslinger, R. Liuzzi, M. Quarto, P. Riccio, G. Roberti, and F. Villani, “Multiple processor version of a Monte Carlo code for photon transport in turbid media,” Comput. Phys. Commun. 132(1–2), 84–93 (2000).
[CrossRef]

Collins, D. L.

D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans, “Design and construction of a realistic digital brain phantom,” IEEE Trans. Med. Imaging 17(3), 463–468 (1998).
[CrossRef] [PubMed]

Contini, D.

Cope, M.

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[CrossRef] [PubMed]

Culver, J. P.

Custo, A.

Dehghani, H.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27(1), 252–264 (2000).
[CrossRef] [PubMed]

J. Ripoll, M. Nieto-Vesperinas, S. R. Arridge, and H. Dehghani, “Boundary conditions for light propagation in diffusive media with nonscattering regions,” J. Opt. Soc. Am. A 17(9), 1671–1681 (2000).
[CrossRef] [PubMed]

Delorme, J. F.

Delpy, D. T.

D. R. Kirkby and D. T. Delpy, “Parallel operation of Monte Carlo simulations on a diverse network of computers,” Phys. Med. Biol. 42(6), 1203–1208 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2 Pt 1), 299–309 (1993).
[CrossRef] [PubMed]

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[CrossRef] [PubMed]

Desbrun, M.

M. Meyer, H. Lee, A. Barr, and M. Desbrun, “Generalized Barycentric Coordinates on Irregular Polygons,” Journal of Graphics Tools 7(1), 13–22 (2002).

Dunn, A. K.

Essenpreis, M.

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[CrossRef] [PubMed]

Evans, A. C.

D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans, “Design and construction of a realistic digital brain phantom,” IEEE Trans. Med. Imaging 17(3), 463–468 (1998).
[CrossRef] [PubMed]

Fang, Q.

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
[CrossRef] [PubMed]

Q. Fang and D. Boas, “Tetrahedral mesh generation from volumetric binary and gray-scale images,” Proceedings of IEEE International Symposium on Biomedical Imaging 2009, 1142–1145 (2009).

Firbank, M.

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[CrossRef] [PubMed]

French, P. J.

Fukui, Y.

Gallant, P.

Gandjbakhche, A. H.

T. Binzoni, T. S. Leung, R. Giust, D. Rüfenacht, and A. H. Gandjbakhche, “Light transport in tissue by 3D Monte Carlo: influence of boundary voxelization,” Comput. Methods Programs Biomed. 89(1), 14–23 (2008).
[CrossRef] [PubMed]

Giust, R.

T. Binzoni, T. S. Leung, R. Giust, D. Rüfenacht, and A. H. Gandjbakhche, “Light transport in tissue by 3D Monte Carlo: influence of boundary voxelization,” Comput. Methods Programs Biomed. 89(1), 14–23 (2008).
[CrossRef] [PubMed]

Guida, G.

A. Colasanti, G. Guida, A. Kisslinger, R. Liuzzi, M. Quarto, P. Riccio, G. Roberti, and F. Villani, “Multiple processor version of a Monte Carlo code for photon transport in turbid media,” Comput. Phys. Commun. 132(1–2), 84–93 (2000).
[CrossRef]

Hasegawa, Y.

Hielscher, A. H.

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(6), 578–580 (2004).
[CrossRef] [PubMed]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[CrossRef] [PubMed]

Hillman, E. M.

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2 Pt 1), 299–309 (1993).
[CrossRef] [PubMed]

M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[CrossRef] [PubMed]

Holmes, C. J.

D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans, “Design and construction of a realistic digital brain phantom,” IEEE Trans. Med. Imaging 17(3), 463–468 (1998).
[CrossRef] [PubMed]

Jacques, S. L.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML - Monte Carlo modeling of light transport in multilayered tissues,” Comput. Meth. Prog. Bio. 47(2), 131–146 (1995).
[CrossRef]

Jiang, H.

Y. Xu, Q. Zhang, and H. Jiang, “Optical image reconstruction of non-scattering and low scattering heterogeneities in turbid media based on the diffusion approximation model,” J. Opt. A, Pure Appl. Opt. 6(1), 29–35 (2004).
[CrossRef]

Kabani, N. J.

D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans, “Design and construction of a realistic digital brain phantom,” IEEE Trans. Med. Imaging 17(3), 463–468 (1998).
[CrossRef] [PubMed]

Kirkby, D. R.

D. R. Kirkby and D. T. Delpy, “Parallel operation of Monte Carlo simulations on a diverse network of computers,” Phys. Med. Biol. 42(6), 1203–1208 (1997).
[CrossRef] [PubMed]

Kisslinger, A.

A. Colasanti, G. Guida, A. Kisslinger, R. Liuzzi, M. Quarto, P. Riccio, G. Roberti, and F. Villani, “Multiple processor version of a Monte Carlo code for photon transport in turbid media,” Comput. Phys. Commun. 132(1–2), 84–93 (2000).
[CrossRef]

Kollokian, V.

D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans, “Design and construction of a realistic digital brain phantom,” IEEE Trans. Med. Imaging 17(3), 463–468 (1998).
[CrossRef] [PubMed]

Lee, H.

M. Meyer, H. Lee, A. Barr, and M. Desbrun, “Generalized Barycentric Coordinates on Irregular Polygons,” Journal of Graphics Tools 7(1), 13–22 (2002).

Leung, T. S.

T. Binzoni, T. S. Leung, R. Giust, D. Rüfenacht, and A. H. Gandjbakhche, “Light transport in tissue by 3D Monte Carlo: influence of boundary voxelization,” Comput. Methods Programs Biomed. 89(1), 14–23 (2008).
[CrossRef] [PubMed]

Li, J.

Liang, J.

Liuzzi, R.

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M. Meyer, H. Lee, A. Barr, and M. Desbrun, “Generalized Barycentric Coordinates on Irregular Polygons,” Journal of Graphics Tools 7(1), 13–22 (2002).

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J. Vollmer, R. Mencel, and H. Müller, ““Improved Laplacian smoothing of noisy surface meshes,” In Proc,” EuroGraphics 99, 131–138 (1999).

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D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91(11), 4887–4891 (1994).
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A. Colasanti, G. Guida, A. Kisslinger, R. Liuzzi, M. Quarto, P. Riccio, G. Roberti, and F. Villani, “Multiple processor version of a Monte Carlo code for photon transport in turbid media,” Comput. Phys. Commun. 132(1–2), 84–93 (2000).
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A. Colasanti, G. Guida, A. Kisslinger, R. Liuzzi, M. Quarto, P. Riccio, G. Roberti, and F. Villani, “Multiple processor version of a Monte Carlo code for photon transport in turbid media,” Comput. Phys. Commun. 132(1–2), 84–93 (2000).
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A. Colasanti, G. Guida, A. Kisslinger, R. Liuzzi, M. Quarto, P. Riccio, G. Roberti, and F. Villani, “Multiple processor version of a Monte Carlo code for photon transport in turbid media,” Comput. Phys. Commun. 132(1–2), 84–93 (2000).
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D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91(11), 4887–4891 (1994).
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Appl. Opt. (5)

Comput. Meth. Prog. Bio. (1)

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML - Monte Carlo modeling of light transport in multilayered tissues,” Comput. Meth. Prog. Bio. 47(2), 131–146 (1995).
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Comput. Phys. Commun. (1)

A. Colasanti, G. Guida, A. Kisslinger, R. Liuzzi, M. Quarto, P. Riccio, G. Roberti, and F. Villani, “Multiple processor version of a Monte Carlo code for photon transport in turbid media,” Comput. Phys. Commun. 132(1–2), 84–93 (2000).
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EuroGraphics (1)

J. Vollmer, R. Mencel, and H. Müller, ““Improved Laplacian smoothing of noisy surface meshes,” In Proc,” EuroGraphics 99, 131–138 (1999).

IEEE Trans. Med. Imaging (1)

D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans, “Design and construction of a realistic digital brain phantom,” IEEE Trans. Med. Imaging 17(3), 463–468 (1998).
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J. Biomed. Opt. (1)

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
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J. Opt. A, Pure Appl. Opt. (1)

Y. Xu, Q. Zhang, and H. Jiang, “Optical image reconstruction of non-scattering and low scattering heterogeneities in turbid media based on the diffusion approximation model,” J. Opt. A, Pure Appl. Opt. 6(1), 29–35 (2004).
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J. Opt. Soc. Am. A (1)

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N. Platis and T. Theoharis, “Fast ray-tetrahedron intersection using Plücker coordinates,” Journal of Graphics Tools 8(4), 37–48 (2003).

M. Meyer, H. Lee, A. Barr, and M. Desbrun, “Generalized Barycentric Coordinates on Irregular Polygons,” Journal of Graphics Tools 7(1), 13–22 (2002).

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D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91(11), 4887–4891 (1994).
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Supplementary Material (1)

» Media 1: AVI (1689 KB)     

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Figures (4)

Fig. 1
Fig. 1

(a) Diagram of Plücker-formed ray-polygon intersection test and (b) other commonly used polyhedral elements.

Fig. 2
Fig. 2

Comparisons between MMCM with voxel-based MC code, MCX, and the diffusion model for a homogeneous cubic domain: (a) the time-domain response (TPSF) at position (30,14,10) mm, and (b) CW fluence contour plots (with 10db spacing) in plane y = 30 mm.

Fig. 3
Fig. 3

Validations of MMCM in heterogeneous media. We show the mesh cross-cut-views and the fluence contour plots (with 10db spacing) of two mesh configurations: (a)-(b) a high-density uniform mesh and (c)-(d) a mesh with higher density at the surface of the spherical inclusion and near source.

Fig. 4
Fig. 4

Test of MMCM with a complex 3D brain atlas: (a) 3D-cut and (b) sagittal-cut views of the FE mesh; (c) the CW fluence and (d) time-resolved fluence (TPSF), both in log10-scale, extracted at plane x = 76 mm (Media 1). The tissue layers, from exterior to interior, are scalp/skull, cerebro-spinal fluid (CSF), gray matter and white matter, respectively. The boundaries of the tissue layers are overlapped in (c) and (d).

Tables (2)

Tables Icon

Table 1 Memory utility and speed comparisons for MMCM and MCX for a heterogeneous simulation.

Tables Icon

Table 2 Optical parameters in various brain tissue types for the human brain atlas simulation. The properties for scalp/skull and cerebro-spinal fluid (CSF) are based on [11] and those for gray and white matters are based on [40] at 630 nm.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

x    = p + ( q p ) t
d    = q p m = p × q
w i = U r V e i + V r U e i
u i = w i / i w i
p = i u i p i .

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