Multicanonical Monte-Carlo simulations of light propagation in biological media
Optics Express, Vol. 13, Issue 24, pp. 9822-9833 (2005)
http://dx.doi.org/10.1364/OPEX.13.009822
Acrobat PDF (2276 KB)
Abstract
Monte-Carlo simulation is an important tool in the field of biomedical optics, but suffers from significant computational expense. In this paper, we present the multicanonical Monte-Carlo (MMC) method for improving the efficiency of classical Monte Carlo simulations of light propagation in biological media. The MMC is an adaptive importance sampling technique that iteratively equilibrates at the optimal importance distribution with little (if any) a priori knowledge of how to choose and bias the importance proposal distribution. We illustrate the efficiency of this method by evaluating the probability density function (pdf) for the radial distance of photons exiting from a semi-infinite homogeneous tissue as well as the pdf for the maximum penetration depth of photons propagating in an inhomogeneous tissue. The results agree very well with diffusion theory as well as classical Monte-Carlo simulations. A six to sevenfold improvement in computational time is achieved by the MMC algorithm in calculating pdf values as low as 10^{-8}. This result suggests that the MMC method can be useful in efficiently studying numerous applications of light propagation in complex biological media where the remitted photon yield is low.
© 2005 Optical Society of America
1. Introduction
1 . S. T. Flock , M. S. Patterson , B. C. Wilson , and D. R. Wyman , “ Monte Carlo modeling of light propagation in highly scattering tissues - 1. Model predictions and comparison with diffusion theory ,” IEEE Trans. Biomed. Eng. 36 , 1162 – 1167 ( 1989 ). [CrossRef] [PubMed]
5 . L. Wang , S. L. Jacques , and L. Zheng , “ MCML - Monte Carlo modeling of light transport in multi-layered tissues ,” Comput. Methods and Programs in Biomed. 47 , 131 – 146 ( 1995 ). [CrossRef]
5 . L. Wang , S. L. Jacques , and L. Zheng , “ MCML - Monte Carlo modeling of light transport in multi-layered tissues ,” Comput. Methods and Programs in Biomed. 47 , 131 – 146 ( 1995 ). [CrossRef]
2 . J. M. Schmitt and K. Ben-Letaief , “ Efficient Monte Carlo simulation of confocal microscopy in biological tissue ,” J. Opt. Soc. Am. A 13 , 952 – 961 ( 1996 ). [CrossRef]
5 . L. Wang , S. L. Jacques , and L. Zheng , “ MCML - Monte Carlo modeling of light transport in multi-layered tissues ,” Comput. Methods and Programs in Biomed. 47 , 131 – 146 ( 1995 ). [CrossRef]
2 . J. M. Schmitt and K. Ben-Letaief , “ Efficient Monte Carlo simulation of confocal microscopy in biological tissue ,” J. Opt. Soc. Am. A 13 , 952 – 961 ( 1996 ). [CrossRef]
7 . B. A. Berg and T. Neuhaus , “ Multicanonical ensemble: A new approach to simulate first-order phase transitions ”, Phys. Rev. Lett. 68 , 9 – 12 ( 1992 ). [CrossRef] [PubMed]
7 . B. A. Berg and T. Neuhaus , “ Multicanonical ensemble: A new approach to simulate first-order phase transitions ”, Phys. Rev. Lett. 68 , 9 – 12 ( 1992 ). [CrossRef] [PubMed]
8 . D. Yevick , “ Multicanonical communication system modeling - application to PMD statistics ,” IEEE Photon. Tech. Lett. 14 , 1512 – 1514 ( 2002 ). [CrossRef]
9 . R. HolzlÖhner and C. R. Menyuk , “ Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems ,” Opt. Lett. 28 , 1894 – 1896 ( 2003 ). [CrossRef] [PubMed]
10 . A. Bilenca and G. Eisenstein , “ Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier ,” J. Quantum Electron. 41 , 36 – 44 ( 2005 ). [CrossRef]
2. Multicanonical Monte-Carlo (MMC) algorithm
7 . B. A. Berg and T. Neuhaus , “ Multicanonical ensemble: A new approach to simulate first-order phase transitions ”, Phys. Rev. Lett. 68 , 9 – 12 ( 1992 ). [CrossRef] [PubMed]
12 . C. Andrieu , N. De Freitas , A. Doucet , and M. I. Jordan , “ An introduction to MCMC for machine learning ,” Machine Learning 50 , 5 – 43 ( 2003 ). [CrossRef]
12 . C. Andrieu , N. De Freitas , A. Doucet , and M. I. Jordan , “ An introduction to MCMC for machine learning ,” Machine Learning 50 , 5 – 43 ( 2003 ). [CrossRef]
12 . C. Andrieu , N. De Freitas , A. Doucet , and M. I. Jordan , “ An introduction to MCMC for machine learning ,” Machine Learning 50 , 5 – 43 ( 2003 ). [CrossRef]
12 . C. Andrieu , N. De Freitas , A. Doucet , and M. I. Jordan , “ An introduction to MCMC for machine learning ,” Machine Learning 50 , 5 – 43 ( 2003 ). [CrossRef]
13 . N. Metropolis , A. Rosenbluth , M. Rosenbluth , M. Teller , and E. Teller , “ Equation of state calculations by fast computing machines ,” J. Chem. Phys. 21 , 1087 – 1092 ( 1953 ). [CrossRef]
12 . C. Andrieu , N. De Freitas , A. Doucet , and M. I. Jordan , “ An introduction to MCMC for machine learning ,” Machine Learning 50 , 5 – 43 ( 2003 ). [CrossRef]
3. Application of the MMC method to light propagation in biological media
4 . 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 , 159 – 170 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-3-159 [PubMed]
5 . L. Wang , S. L. Jacques , and L. Zheng , “ MCML - Monte Carlo modeling of light transport in multi-layered tissues ,” Comput. Methods and Programs in Biomed. 47 , 131 – 146 ( 1995 ). [CrossRef]
5 . L. Wang , S. L. Jacques , and L. Zheng , “ MCML - Monte Carlo modeling of light transport in multi-layered tissues ,” Comput. Methods and Programs in Biomed. 47 , 131 – 146 ( 1995 ). [CrossRef]
5 . L. Wang , S. L. Jacques , and L. Zheng , “ MCML - Monte Carlo modeling of light transport in multi-layered tissues ,” Comput. Methods and Programs in Biomed. 47 , 131 – 146 ( 1995 ). [CrossRef]
4. Simulation results and discussion
4.1 Radially resolved steady state diffuse reflectance pdf for photons propagating in a semi-infinite homogeneous random medium
14 . T. J. Farrell , M. S. Patterson , and B. Wilson , “ A diffusion theory model of spatially resolved, steady-state diffusive reflectance for the noninvasive determination of tissue optical properties in vivo ,” Med. Phys. 19 , 879 – 888 ( 1992 ). [CrossRef] [PubMed]
14 . T. J. Farrell , M. S. Patterson , and B. Wilson , “ A diffusion theory model of spatially resolved, steady-state diffusive reflectance for the noninvasive determination of tissue optical properties in vivo ,” Med. Phys. 19 , 879 – 888 ( 1992 ). [CrossRef] [PubMed]
4.2 pdf of the maximum penetration depth of photons that propagate and exit a two-layered random medium
15 . G. Alexandrakis , T. J. Farrell , and M. S. Patterson , “ Accuracy of the Diffusion Approximation in Determining the Optical Properties of a Two-Layer Turbid Medium ,” Appl. Opt. 37 , 7401 – 7409 ( 1998 ). [CrossRef]
5. Conclusions
2 . J. M. Schmitt and K. Ben-Letaief , “ Efficient Monte Carlo simulation of confocal microscopy in biological tissue ,” J. Opt. Soc. Am. A 13 , 952 – 961 ( 1996 ). [CrossRef]
Acknowledgments
References and links
1 . | S. T. Flock , M. S. Patterson , B. C. Wilson , and D. R. Wyman , “ Monte Carlo modeling of light propagation in highly scattering tissues - 1. Model predictions and comparison with diffusion theory ,” IEEE Trans. Biomed. Eng. 36 , 1162 – 1167 ( 1989 ). [CrossRef] [PubMed] |
2 . | J. M. Schmitt and K. Ben-Letaief , “ Efficient Monte Carlo simulation of confocal microscopy in biological tissue ,” J. Opt. Soc. Am. A 13 , 952 – 961 ( 1996 ). [CrossRef] |
3 . | G. Yao and L. Wang , “ Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media ,” Phys. Med. Biol. 44 , 2307 – 2320 ( 1999 ). [CrossRef] [PubMed] |
4 . | 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 , 159 – 170 ( 2002 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-3-159 [PubMed] |
5 . | L. Wang , S. L. Jacques , and L. Zheng , “ MCML - Monte Carlo modeling of light transport in multi-layered tissues ,” Comput. Methods and Programs in Biomed. 47 , 131 – 146 ( 1995 ). [CrossRef] |
6 . | A. Ishimaru Wave Propagation and Scattering in Random Media ( Academic Press, Inc., San Diego 1978 ). |
7 . | B. A. Berg and T. Neuhaus , “ Multicanonical ensemble: A new approach to simulate first-order phase transitions ”, Phys. Rev. Lett. 68 , 9 – 12 ( 1992 ). [CrossRef] [PubMed] |
8 . | D. Yevick , “ Multicanonical communication system modeling - application to PMD statistics ,” IEEE Photon. Tech. Lett. 14 , 1512 – 1514 ( 2002 ). [CrossRef] |
9 . | R. HolzlÖhner and C. R. Menyuk , “ Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems ,” Opt. Lett. 28 , 1894 – 1896 ( 2003 ). [CrossRef] [PubMed] |
10 . | A. Bilenca and G. Eisenstein , “ Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier ,” J. Quantum Electron. 41 , 36 – 44 ( 2005 ). [CrossRef] |
11 . | D. P. Landau and K. Binder , A Guide to Monte Carlo Simulations in Statistical Physics ( Cambridge, MA/New York , 2000 ). |
12 . | C. Andrieu , N. De Freitas , A. Doucet , and M. I. Jordan , “ An introduction to MCMC for machine learning ,” Machine Learning 50 , 5 – 43 ( 2003 ). [CrossRef] |
13 . | N. Metropolis , A. Rosenbluth , M. Rosenbluth , M. Teller , and E. Teller , “ Equation of state calculations by fast computing machines ,” J. Chem. Phys. 21 , 1087 – 1092 ( 1953 ). [CrossRef] |
14 . | T. J. Farrell , M. S. Patterson , and B. Wilson , “ A diffusion theory model of spatially resolved, steady-state diffusive reflectance for the noninvasive determination of tissue optical properties in vivo ,” Med. Phys. 19 , 879 – 888 ( 1992 ). [CrossRef] [PubMed] |
15 . | G. Alexandrakis , T. J. Farrell , and M. S. Patterson , “ Accuracy of the Diffusion Approximation in Determining the Optical Properties of a Two-Layer Turbid Medium ,” Appl. Opt. 37 , 7401 – 7409 ( 1998 ). [CrossRef] |
OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(290.1350) Scattering : Backscattering
ToC Category:
Research Papers
History
Original Manuscript: October 4, 2005
Revised Manuscript: October 3, 2005
Published: November 28, 2005
Citation
A. Bilenca, A. Desjardins, B. Bouma, and G. Tearney, "Multicanonical Monte-Carlo simulations of light propagation in biological media," Opt. Express 13, 9822-9833 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-24-9822
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References
- S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues – 1. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162-1167 (1989). [CrossRef] [PubMed]
- J. M. Schmitt and K. Ben-Letaief, “Efficient Monte Carlo simulation of confocal microscopy in biological tissue,” J. Opt. Soc. Am. A 13, 952-961 (1996). [CrossRef]
- G. Yao and L. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44, 2307-2320 (1999). [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, 159-170 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-3-159">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-3-159</a> [PubMed]
- L. Wang, S. L. Jacques, and L. Zheng, “MCML – Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods and Programs in Biomed. 47, 131-146 (1995). [CrossRef]
- A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, Inc., San Diego 1978).
- B. A. Berg and T. Neuhaus, “Multicanonical ensemble: A new approach to simulate first-order phase transitions,” Phys. Rev. Lett. 68, 9-12 (1992). [CrossRef] [PubMed]
- D. Yevick, “Multicanonical communication system modeling – application to PMD statistics,” IEEE Photon. Tech. Lett. 14, 1512-1514 (2002). [CrossRef]
- R. Holzlöhner and C. R. Menyuk, “Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems,” Opt. Lett. 28, 1894-1896 (2003). [CrossRef] [PubMed]
- A. Bilenca and G. Eisenstein, “Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier,” J. Quantum Electron. 41, 36-44 (2005). [CrossRef]
- D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge, MA/New York, 2000).
- C. Andrieu, N. De Freitas, A. Doucet, and M. I. Jordan, “An introduction to MCMC for machine learning,” Machine Learning 50, 5–43 (2003). [CrossRef]
- N. Metropolis, A. Rosenbluth, M. Rosenbluth, M. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087-1092 (1953). [CrossRef]
- T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffusive reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879-888 (1992). [CrossRef] [PubMed]
- G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the Diffusion Approximation in Determining the Optical Properties of a Two-Layer Turbid Medium,” Appl. Opt. 37, 7401-7409 (1998). [CrossRef]
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