Abstract

We present a two-step Monte Carlo (MC) method that is used to solve the radiative transfer equation in heterogeneous turbid media. The method exploits the one-to-one correspondence between the seed value of a random number generator and the sequence of random numbers. In the first step, a full MC simulation is run for the initial distribution of the optical properties and the “good” seeds (the ones leading to detected photons) are stored in an array. In the second step, we run a new MC simulation with only the good seeds stored in the first step, i.e., we propagate only detected photons. The effect of a change in the optical properties is calculated in a short time by using two scaling relationships. By this method we can increase the speed of a simulation up to a factor of 1300 in typical situations found in near-IR tissue spectroscopy and diffuse optical tomography, with a minimal requirement for hard disk space. Potential applications of this method for imaging of turbid media and the inverse problem are discussed.

© 2011 Optical Society of America

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  1. B. C. Wilson and G. Adam, Med. Phys. 10, 824 (1983).
    [CrossRef] [PubMed]
  2. L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
    [CrossRef] [PubMed]
  3. S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, IEEE Trans. Biomed. Eng. 36, 1162 (1989).
    [CrossRef] [PubMed]
  4. R. Graaff, M. H. Koelink, F. F. M. Demul, W. G. Zijlstra, A. C. M. Dassel, and J. G. Aarnoudse, Appl. Opt. 32, 426 (1993).
    [CrossRef] [PubMed]
  5. A. Pifferi, P. Taroni, G. Valentini, and S. Andersson-Engels, Appl. Opt. 37, 2774 (1998).
    [CrossRef]
  6. A. Kienle and M. S. Patterson, Phys. Med. Biol. 41, 2221 (1996).
    [CrossRef] [PubMed]
  7. C. K. Hayakawa, J. Spanier, F. Bevilacqua, A. K. Dunn, J. S. You, B. J. Tromberg, and V. Venugopalan, Opt. Lett. 26, 1335 (2001).
    [CrossRef]
  8. D. A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, Opt. Express 10, 159 (2002).
    [PubMed]
  9. E. Margallo-Balbás and P. J. French, Opt. Express 15, 14086 (2007).
    [CrossRef] [PubMed]
  10. H. Shen and G. Wang, Phys. Med. Biol. 55, 947 (2010).
    [CrossRef] [PubMed]
  11. Q. Fang and D. A. Boas, Opt. Express 17, 20178 (2009).
    [CrossRef] [PubMed]
  12. E. Alerstam, W. C. Y. Lo, T. D. Han, J. Rose, S. Andersson-Engels, and L. Lilge, Biomed. Opt. Express 1, 658 (2010).
    [CrossRef]
  13. N. Ren, J. Liang, X. Qu, J. Li, B. Lu, and J. Tian, Opt. Express 18, 6811 (2010).
    [CrossRef] [PubMed]
  14. A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, Appl. Opt. 37, 7392 (1998).
    [CrossRef]
  15. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

2010

2009

2007

2002

2001

1998

1996

A. Kienle and M. S. Patterson, Phys. Med. Biol. 41, 2221 (1996).
[CrossRef] [PubMed]

1995

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

1993

1989

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, IEEE Trans. Biomed. Eng. 36, 1162 (1989).
[CrossRef] [PubMed]

1983

B. C. Wilson and G. Adam, Med. Phys. 10, 824 (1983).
[CrossRef] [PubMed]

Aarnoudse, J. G.

Adam, G.

B. C. Wilson and G. Adam, Med. Phys. 10, 824 (1983).
[CrossRef] [PubMed]

Alerstam, E.

Alianelli, L.

Andersson-Engels, S.

Bevilacqua, F.

Blumetti, C.

Boas, D. A.

Contini, D.

Culver, J. P.

Dassel, A. C. M.

Demul, F. F. M.

Dunn, A. K.

Fang, Q.

Flannery, B. P.

H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, IEEE Trans. Biomed. Eng. 36, 1162 (1989).
[CrossRef] [PubMed]

French, P. J.

Graaff, R.

Han, T. D.

Hayakawa, C. K.

Ismaelli, A.

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

Kienle, A.

A. Kienle and M. S. Patterson, Phys. Med. Biol. 41, 2221 (1996).
[CrossRef] [PubMed]

Koelink, M. H.

Li, J.

Liang, J.

Lilge, L.

Lo, W. C. Y.

Lu, B.

Margallo-Balbás, E.

Martelli, F.

Patterson, M. S.

A. Kienle and M. S. Patterson, Phys. Med. Biol. 41, 2221 (1996).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, IEEE Trans. Biomed. Eng. 36, 1162 (1989).
[CrossRef] [PubMed]

Pifferi, A.

Press, H.

H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

Qu, X.

Ren, N.

Rose, J.

Sassaroli, A.

Shen, H.

H. Shen and G. Wang, Phys. Med. Biol. 55, 947 (2010).
[CrossRef] [PubMed]

Spanier, J.

Stott, J. J.

Taroni, P.

Teukolsky, S. A.

H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

Tian, J.

Tromberg, B. J.

Valentini, G.

Venugopalan, V.

Vetterling, W. T.

H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

Wang, G.

H. Shen and G. Wang, Phys. Med. Biol. 55, 947 (2010).
[CrossRef] [PubMed]

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

Wilson, B. C.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, IEEE Trans. Biomed. Eng. 36, 1162 (1989).
[CrossRef] [PubMed]

B. C. Wilson and G. Adam, Med. Phys. 10, 824 (1983).
[CrossRef] [PubMed]

Wyman, D. R.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, IEEE Trans. Biomed. Eng. 36, 1162 (1989).
[CrossRef] [PubMed]

You, J. S.

Zaccanti, G.

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

Zijlstra, W. G.

Appl. Opt.

Biomed. Opt. Express

Comput. Methods Programs Biomed.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, IEEE Trans. Biomed. Eng. 36, 1162 (1989).
[CrossRef] [PubMed]

Med. Phys.

B. C. Wilson and G. Adam, Med. Phys. 10, 824 (1983).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

A. Kienle and M. S. Patterson, Phys. Med. Biol. 41, 2221 (1996).
[CrossRef] [PubMed]

H. Shen and G. Wang, Phys. Med. Biol. 55, 947 (2010).
[CrossRef] [PubMed]

Other

H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

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Figures (3)

Fig. 1
Fig. 1

(a) and (b) Schematics of the two-step MC method. (c) Speed gain between the (a) full MC code and the (b) fast MC code plotted against the reduced scattering coefficient of the medium, for the cases of slab and semi-infinite geometries.

Fig. 2
Fig. 2

Top maps: normalized relative changes of cw intensity in the (a) semi-infinite and (c) slab geometries. Bottom maps: relative changes of phase in the (b) semi-infinite and (d) slab geometries. The changes are calculated with respect to a homogeneous medium. The source position is at ( x , y , z ) = ( 0 , 0 , 0 ) , while the positions of the detectors are ( x , y , z ) = ( 30 , 0 , 0 ) mm and ( x , y , z ) = ( 0 , 0 , 40 ) mm in the semi-infinite and slab geometries, respectively. The optical properties of the medium are μ a = 0.005 mm 1 and μ s = 0.5 mm 1 .

Fig. 3
Fig. 3

Comparison of two TPSFs obtained for the slab represented in the schematic on top. The TPSF “scaled” refers to the calculation obtained by applying the weight factor w s [Eq. (1)]; “direct” refers to the TPSF calculated by considering directly the spherical scattering perturbation in the MC code. The relative error between the two curves is also shown.

Equations (1)

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w a = exp ( i = 1 n l i Δ μ a i ) , w s = i = 1 n ( μ s i μ s 0 ) k i exp ( l i Δ μ s i ) .

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