Abstract

We report a parallel Monte Carlo algorithm accelerated by graphics processing units (GPU) for modeling time-resolved photon migration in arbitrary 3D turbid media. By taking advantage of the massively parallel threads and low-memory latency, this algorithm allows many photons to be simulated simultaneously in a GPU. To further improve the computational efficiency, we explored two parallel random number generators (RNG), including a floating-point-only RNG based on a chaotic lattice. An efficient scheme for boundary reflection was implemented, along with the functions for time-resolved imaging. For a homogeneous semi-infinite medium, good agreement was observed between the simulation output and the analytical solution from the diffusion theory. The code was implemented with CUDA programming language, and benchmarked under various parameters, such as thread number, selection of RNG and memory access pattern. With a low-cost graphics card, this algorithm has demonstrated an acceleration ratio above 300 when using 1792 parallel threads over conventional CPU computation. The acceleration ratio drops to 75 when using atomic operations. These results render the GPU-based Monte Carlo simulation a practical solution for data analysis in a wide range of diffuse optical imaging applications, such as human brain or small-animal imaging.

© 2009 OSA

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2009 (2)

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

W. C. Lo, K. Redmond, J. Luu, P. Chow, J. Rose, and L. Lilge, “Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning,” J. Biomed. Opt. 14(1), 014019 (2009).
[CrossRef] [PubMed]

2008 (3)

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]

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[CrossRef] [PubMed]

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27(8), 1152–1163 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (2)

A. Custo, W. M. Wells III, A. H. Barnett, E. M. Hillman, and D. A. Boas, “Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging,” Appl. Opt. 45(19), 4747–4755 (2006).
[CrossRef] [PubMed]

N. S. Zo?ek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Methods Programs Biomed. 84(1), 50–57 (2006).
[CrossRef] [PubMed]

2005 (1)

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[CrossRef] [PubMed]

2004 (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).
[CrossRef]

2003 (1)

2002 (2)

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]

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]

2000 (1)

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]

1998 (3)

M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998).
[CrossRef]

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]

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]

1997 (1)

1995 (2)

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]

S. C. Phatak and S. S. Rao, “Logistic map: A possible random-number generator,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(4), 3670–3678 (1995).
[CrossRef] [PubMed]

1993 (1)

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]

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]

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]

Arridge, S. R.

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]

Bacskai, B. J.

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27(8), 1152–1163 (2008).
[CrossRef] [PubMed]

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.

Boas, D. A.

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27(8), 1152–1163 (2008).
[CrossRef] [PubMed]

A. Custo, W. M. Wells III, A. H. Barnett, E. M. Hillman, and D. A. Boas, “Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging,” Appl. Opt. 45(19), 4747–4755 (2006).
[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]

Boverman, G.

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

Brooks, D. H.

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

Carp, S. A.

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

Chow, P.

W. C. Lo, K. Redmond, J. Luu, P. Chow, J. Rose, and L. Lilge, “Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning,” J. Biomed. Opt. 14(1), 014019 (2009).
[CrossRef] [PubMed]

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]

Delpy, D. T.

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]

Dietsche, G.

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[CrossRef] [PubMed]

Dunn, A. K.

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27(8), 1152–1163 (2008).
[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]

Elbert, T.

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[CrossRef] [PubMed]

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, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

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.

Gisler, T.

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[CrossRef] [PubMed]

Hielscher, A. H.

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.

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]

Iftime, D.

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[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]

Joshi, A.

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[CrossRef] [PubMed]

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]

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]

Kopans, D. B.

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

Kumar, A. T. N.

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27(8), 1152–1163 (2008).
[CrossRef] [PubMed]

Li, J.

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[CrossRef] [PubMed]

Liebert, A.

N. S. Zo?ek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Methods Programs Biomed. 84(1), 50–57 (2006).
[CrossRef] [PubMed]

Lilge, L.

W. C. Lo, K. Redmond, J. Luu, P. Chow, J. Rose, and L. Lilge, “Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning,” J. Biomed. Opt. 14(1), 014019 (2009).
[CrossRef] [PubMed]

Lo, W. C.

W. C. Lo, K. Redmond, J. Luu, P. Chow, J. Rose, and L. Lilge, “Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning,” J. Biomed. Opt. 14(1), 014019 (2009).
[CrossRef] [PubMed]

Luu, J.

W. C. Lo, K. Redmond, J. Luu, P. Chow, J. Rose, and L. Lilge, “Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning,” J. Biomed. Opt. 14(1), 014019 (2009).
[CrossRef] [PubMed]

Maniewski, R.

N. S. Zo?ek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Methods Programs Biomed. 84(1), 50–57 (2006).
[CrossRef] [PubMed]

Maret, G.

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[CrossRef] [PubMed]

Margallo-Balbás, E.

Martelli, F.

Matsumoto, M.

M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998).
[CrossRef]

McGhee, J.

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[CrossRef] [PubMed]

Miller, E. L.

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

Moore, R. H.

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

Nishimura, T.

M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998).
[CrossRef]

Okada, E.

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]

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]

Phatak, S. C.

S. C. Phatak and S. S. Rao, “Logistic map: A possible random-number generator,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(4), 3670–3678 (1995).
[CrossRef] [PubMed]

Rao, S. S.

S. C. Phatak and S. S. Rao, “Logistic map: A possible random-number generator,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(4), 3670–3678 (1995).
[CrossRef] [PubMed]

Rasmussen, J. C.

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[CrossRef] [PubMed]

Raymond, S. B.

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27(8), 1152–1163 (2008).
[CrossRef] [PubMed]

Redmond, K.

W. C. Lo, K. Redmond, J. Luu, P. Chow, J. Rose, and L. Lilge, “Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning,” J. Biomed. Opt. 14(1), 014019 (2009).
[CrossRef] [PubMed]

Rockstroh, B.

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[CrossRef] [PubMed]

Rose, J.

W. C. Lo, K. Redmond, J. Luu, P. Chow, J. Rose, and L. Lilge, “Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning,” J. Biomed. Opt. 14(1), 014019 (2009).
[CrossRef] [PubMed]

Schober, R.

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]

Schulze, P. C.

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]

Schwarzmaier, H. J.

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]

Schweiger, M.

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]

Selb, J.

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[CrossRef] [PubMed]

Skipetrov, S. E.

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[CrossRef] [PubMed]

Sled, J. G.

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]

Stott, J. J.

Svensson, T.

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]

Taddeucci, A.

Ulrich, F.

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]

van der Zee, P.

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]

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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]

Wareing, T. A.

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[CrossRef] [PubMed]

Wells III, W. M.

Xu, Y.

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]

Yaroslavsky, A. N.

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]

Yaroslavsky, I. V.

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]

Zaccanti, G.

Zhang, Q.

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[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]

Zheng, L. Q.

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]

Zijdenbos, A. P.

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]

Zolek, N. S.

N. S. Zo?ek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Methods Programs Biomed. 84(1), 50–57 (2006).
[CrossRef] [PubMed]

ACM Trans. Model. Comput. Simul. (1)

M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998).
[CrossRef]

Appl. Opt. (3)

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).
[CrossRef]

Comput. Methods Programs Biomed. (1)

N. S. Zo?ek, A. Liebert, and R. Maniewski, “Optimization of the Monte Carlo code for modeling of photon migration in tissue,” Comput. Methods Programs Biomed. 84(1), 50–57 (2006).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (3)

A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27(8), 1152–1163 (2008).
[CrossRef] [PubMed]

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[CrossRef] [PubMed]

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]

J. Biomed. Opt. (3)

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, “Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy,” J. Biomed. Opt. 10(4), 44002 (2005).
[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]

W. C. Lo, K. Redmond, J. Luu, P. Chow, J. Rose, and L. Lilge, “Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning,” J. Biomed. Opt. 14(1), 014019 (2009).
[CrossRef] [PubMed]

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).
[CrossRef]

Med. Phys. (1)

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]

Opt. Express (2)

Phys. Med. Biol. (4)

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]

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]

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]

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

S. C. Phatak and S. S. Rao, “Logistic map: A possible random-number generator,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(4), 3670–3678 (1995).
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Supplementary Material (1)

» Media 1: AVI (4137 KB)     

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Figures (7)

Fig. 1
Fig. 1

Block diagram of the parallel Monte Carlo simulation for photon migration. The curved dashed lines indicate read-only global memory access and curved solid line for read/write access..

Fig. 2
Fig. 2

Determination of the reflection interface between the medium (shaded) and air (clear) voxels: (a) case with 2 intersections and (b) case with 3 intersections.

Fig. 3
Fig. 3

Serial correlation of the logistic-lattice (N=5) based random number generator.

Fig. 4
Fig. 4

Ratios between the missing and total accumulation events for regions >3 voxels away from the source at various threads and scattering coefficients.

Fig. 5
Fig. 5

The comparisons between parallel Monte Carlo algorithm (MCX), tMCimg and the diffusion model for a semi-infinite medium: (a) the time courses at voxel (30,14,9), (b) the contour plots for t=0.1 to 2.1 ns with 0.5 ns step along plane y=30, (c) radial distribution of continuous-wave (CW) solution on the interface, (d) CW fluence contour plot (10 dB spacing) along plane y=30, (e) comparisons between atomic and non-atomic solutions near the source, and (f) domain diagram showing where the results were extracted. In (a), (c) and (e), medium refraction index is 1.37 for simulations with boundary reflections.

Fig. 6
Fig. 6

The (a) continuous-wave and (b) time-resolved solutions (Media 1) of photon migration in an MRI head anatomy (transparent overlay). The color map depicts the logarithmic fluence values.

Fig. 7
Fig. 7

Simulation speed (photon/ms) with various thread numbers and simulation parameters for (a) semi-infinite medium and (b) brain MRI atlas. “MT” - Mersenne-Twister RNG; “LL5” - Logistic-lattice of size 5; “fast” - linked with CUDA’s fast math library; “atomic” – with atomic operations (otherwise, without). The acceleration ratio compared with CPU implementation is marked along the z-axis.

Equations (6)

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

F(r,t)=P(r,t)Ea/EtijP(ri,tj)μa(ri)ΔVΔt
xn+1=f(xn)=μxn(1xn)
p(x)=1πx(1x)
un=cos1(12xn)/π
xn+1imodN=f(xnimodN)+ν(f(xni1modN)2f(xnimodN)+f(xni+1modN))
xn+1i+pmodN=f(xnimodN)+ν(f(xni1modN)2f(xnimodN)+f(xni+1modN))

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