Abstract

Solving inverse problems requires multiple forward calculations of measured signals. We present a fast method combining graphic processing unit-accelerated Monte Carlo simulations of individual photons and a new perturbation scheme for a 300-fold speedup in comparison to conventional CPU-based approaches. The method allows rapid calculations of the diffuse reflectance and transmittance signals from a turbid sample of absorption coefficient μa, scattering coefficient μs, and anisotropy factor g based on the principle of correlated sampling. To demonstrate its strong utility, we have applied the method for determining the optical parameters of diluted intralipid samples with satisfactory results.

© 2013 Optical Society of America

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2011 (1)

2010 (1)

2007 (1)

C. Chen, J. Q. Lu, K. Li, S. Zhao, R. S. Brock, and X. H. Hu, Med. Phys. 34, 2939 (2007).
[CrossRef]

2006 (1)

2005 (1)

2003 (2)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

X. Ma, J. Q. Lu, and X. H. Hu, Opt. Lett. 28, 2204 (2003).
[CrossRef]

2001 (2)

1999 (1)

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, Comput. Meth. Prog. Bio. 47, 131 (1995).

1993 (1)

1984 (1)

H. Rief, Ann. Nucl. Energy 11, 455 (1984).
[CrossRef]

Alerstam, E.

Andersson-Engels, S.

Bevilacqua, F.

Brock, R. S.

C. Chen, J. Q. Lu, K. Li, S. Zhao, R. S. Brock, and X. H. Hu, Med. Phys. 34, 2939 (2007).
[CrossRef]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

Cariveau, M.

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, Phys. Med. Biol. 46, 167 (2001).
[CrossRef]

Chen, C.

C. Chen, J. Q. Lu, K. Li, S. Zhao, R. S. Brock, and X. H. Hu, Med. Phys. 34, 2939 (2007).
[CrossRef]

C. Chen, J. Q. Lu, H. Ding, K. M. Jacobs, Y. Du, and X. H. Hu, Opt. Express 14, 7420 (2006).
[CrossRef]

Ding, H.

Dong, K.

Du, Y.

C. Chen, J. Q. Lu, H. Ding, K. M. Jacobs, Y. Du, and X. H. Hu, Opt. Express 14, 7420 (2006).
[CrossRef]

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, Phys. Med. Biol. 46, 167 (2001).
[CrossRef]

Dunn, A. K.

Gelbard, E. M.

J. Spanier and E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, 1969).

Han, T. D.

Hayakawa, C. K.

Hu, X. H.

C. Chen, J. Q. Lu, K. Li, S. Zhao, R. S. Brock, and X. H. Hu, Med. Phys. 34, 2939 (2007).
[CrossRef]

C. Chen, J. Q. Lu, H. Ding, K. M. Jacobs, Y. Du, and X. H. Hu, Opt. Express 14, 7420 (2006).
[CrossRef]

X. Ma, J. Q. Lu, H. Ding, and X. H. Hu, Opt. Lett. 30, 412 (2005).
[CrossRef]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

X. Ma, J. Q. Lu, and X. H. Hu, Opt. Lett. 28, 2204 (2003).
[CrossRef]

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, Phys. Med. Biol. 46, 167 (2001).
[CrossRef]

Z. Song, K. Dong, X. H. Hu, and J. Q. Lu, Appl. Opt. 38, 2944 (1999).
[CrossRef]

Jacobs, K. M.

C. Chen, J. Q. Lu, H. Ding, K. M. Jacobs, Y. Du, and X. H. Hu, Opt. Express 14, 7420 (2006).
[CrossRef]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Meth. Prog. Bio. 47, 131 (1995).

Kalmus, G. W.

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, Phys. Med. Biol. 46, 167 (2001).
[CrossRef]

Li, K.

C. Chen, J. Q. Lu, K. Li, S. Zhao, R. S. Brock, and X. H. Hu, Med. Phys. 34, 2939 (2007).
[CrossRef]

Lilge, L.

Lu, J. Q.

C. Chen, J. Q. Lu, K. Li, S. Zhao, R. S. Brock, and X. H. Hu, Med. Phys. 34, 2939 (2007).
[CrossRef]

C. Chen, J. Q. Lu, H. Ding, K. M. Jacobs, Y. Du, and X. H. Hu, Opt. Express 14, 7420 (2006).
[CrossRef]

X. Ma, J. Q. Lu, H. Ding, and X. H. Hu, Opt. Lett. 30, 412 (2005).
[CrossRef]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

X. Ma, J. Q. Lu, and X. H. Hu, Opt. Lett. 28, 2204 (2003).
[CrossRef]

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, Phys. Med. Biol. 46, 167 (2001).
[CrossRef]

Z. Song, K. Dong, X. H. Hu, and J. Q. Lu, Appl. Opt. 38, 2944 (1999).
[CrossRef]

Ma, X.

X. Ma, J. Q. Lu, H. Ding, and X. H. Hu, Opt. Lett. 30, 412 (2005).
[CrossRef]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

X. Ma, J. Q. Lu, and X. H. Hu, Opt. Lett. 28, 2204 (2003).
[CrossRef]

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, Phys. Med. Biol. 46, 167 (2001).
[CrossRef]

Prahl, S. A.

Rief, H.

H. Rief, Ann. Nucl. Energy 11, 455 (1984).
[CrossRef]

Rose, J.

Sassaroli, A.

Song, Z.

Spanier, J.

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]

J. Spanier and E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, 1969).

Tromberg, B. J.

van Gemert, M. J. C.

Venugopalan, V.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Meth. Prog. Bio. 47, 131 (1995).

Welch, A. J.

Yang, P.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

Yip Lo, W. C.

You, J. S.

Zhao, S.

C. Chen, J. Q. Lu, K. Li, S. Zhao, R. S. Brock, and X. H. Hu, Med. Phys. 34, 2939 (2007).
[CrossRef]

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, Comput. Meth. Prog. Bio. 47, 131 (1995).

Ann. Nucl. Energy (1)

H. Rief, Ann. Nucl. Energy 11, 455 (1984).
[CrossRef]

Appl. Opt. (2)

Biomed. Opt. Express (1)

Comput. Meth. Prog. Bio. (1)

L. Wang, S. L. Jacques, and L. Zheng, Comput. Meth. Prog. Bio. 47, 131 (1995).

Med. Phys. (1)

C. Chen, J. Q. Lu, K. Li, S. Zhao, R. S. Brock, and X. H. Hu, Med. Phys. 34, 2939 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Med. Biol. (2)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, Phys. Med. Biol. 46, 167 (2001).
[CrossRef]

Other (1)

J. Spanier and E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, 1969).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the source-sample-detector configuration (not to scale) with beam center at (x0,0,0), diameter B, and a top-hat beam profile.

Fig. 2.
Fig. 2.

Rd and Td versus μs and g with μa=0.1mm1, dR=dT=60mm, x0=0mm, B=6.35mm, θ0=45°; d=1mm, w=25mm, sample height along the y axis is 25 mm, W=1mm, D=3mm, refractive index n=1.349 for the sample, and n=1.519 for the holder. Symbols are simulation results, and solid curves are guides for the eye.

Fig. 3.
Fig. 3.

Dependence of ΔRd/Rd, and ΔTd/Td on μs and g with μa=0.05mm1, μs0=10.0mm1, g0=0.5, and θR=θT=70°; all other parameters are the same as those in Fig. 2.

Fig. 4.
Fig. 4.

Dependence of ΔRd/Rd and ΔTd/Td on μs and g with μa=0.1mm1, μs0=10.0mm1, g0=0.5, and θR=θT=70°; all other parameters are the same as those in Fig. 2.

Fig. 5.
Fig. 5.

Wavelength dependence of optical parameters inversely determined from three samples of d=1,2,3mm with symbols representing the mean values and error bars the standard deviations. Inset, the relative difference Δ between the parameters determined by the new method and those with full GPU-iMC simulations for the sample with d=2mm. The solid curves are guides for the eye.

Equations (3)

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

La=ln(RND)μa,Lsi=ln(RND)μsandLs=i=1jLsi.
Ls=[1+(1)mΔμsμs0+(1)mΔg1g0]1Ls0,
Ls=[1+(1)mΔμsμs0+(1)mΔg]1Ls0,

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