Abstract

We introduce a novel and efficient method to provide solutions to inverse photon migration problems in heterogeneous turbid media. The method extracts derivative information from a single Monte Carlo simulation to permit the rapid determination of rates of change in the detected photon signal with respect to perturbations in background tissue optical properties. We then feed this derivative information to a nonlinear optimization algorithm to determine the optical properties of the tissue heterogeneity under examination. We demonstrate the use of this approach to solve rapidly a two-region inverse problem of photon migration in the transport regime, for which diffusion-approximation-based approaches are not applicable.

© 2001 Optical Society of America

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References

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  1. F. Bevilacqua, D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, and C. Depeursinge, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
    [CrossRef]
  2. J. R. Mourant, J. Boyer, A. H. Hielscher, and I. J. Bigio, “Influence of the scattering phase function on light transport measurements in turbid media performed with small source–detector separations,” Opt. Lett. 21, 546–548 (1996).
    [CrossRef] [PubMed]
  3. V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
    [CrossRef]
  4. J. Spanier and E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, Reading, Mass., 1969).
  5. A. Sassaroli, C. Blumeti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37, 7392–7400 (1998).
    [CrossRef]
  6. G. Dejonghe, “Etudes d’effets differentials par la méthode de Monte Carlo dans le cadre de l’equation du transport. Applications aux calculs de protection et de neutronique,” Ph.D. dissertation (Université Paris XI, Orsay, France, 1982).
  7. H. Rief, “Generalized Monte Carlo perturbation algorithms for correlated sampling and a second-order Taylor series approach,” Ann. Nucl. Energy 9, 455–476 (1984).
    [CrossRef]
  8. M. G. C. Hall, “Cross-section adjustment with Monte Carlo sensitivities: application to the Winfrith iron benchmark,” Nucl. Sci. Eng. 81, 423–431 (1982).
  9. R. Hornung, T. H. Pham, K. A. Keefe, M. W. Berns, Y. Tadir, and B. J. Tromberg, “Quantitative near-infrared spectroscopy of cervical dysplasia in vivo,” Hum. Reprod. 14, 2908–2916 (1999).
    [CrossRef] [PubMed]
  10. M. Testorf, U. Osterberg, B. Pogue, and K. Paulsen, “Sampling of time- and frequency-domain signals in Monte Carlo simulations of photon migration,” Appl. Opt. 38, 236–245 (1999).
    [CrossRef]

1999 (3)

1998 (2)

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

A. Sassaroli, C. Blumeti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37, 7392–7400 (1998).
[CrossRef]

1996 (1)

1984 (1)

H. Rief, “Generalized Monte Carlo perturbation algorithms for correlated sampling and a second-order Taylor series approach,” Ann. Nucl. Energy 9, 455–476 (1984).
[CrossRef]

1982 (1)

M. G. C. Hall, “Cross-section adjustment with Monte Carlo sensitivities: application to the Winfrith iron benchmark,” Nucl. Sci. Eng. 81, 423–431 (1982).

Alianelli, L.

Berns, M. W.

R. Hornung, T. H. Pham, K. A. Keefe, M. W. Berns, Y. Tadir, and B. J. Tromberg, “Quantitative near-infrared spectroscopy of cervical dysplasia in vivo,” Hum. Reprod. 14, 2908–2916 (1999).
[CrossRef] [PubMed]

Bevilacqua, F.

Bigio, I. J.

Blumeti, C.

Boyer, J.

Contini, D.

Dejonghe, G.

G. Dejonghe, “Etudes d’effets differentials par la méthode de Monte Carlo dans le cadre de l’equation du transport. Applications aux calculs de protection et de neutronique,” Ph.D. dissertation (Université Paris XI, Orsay, France, 1982).

Depeursinge, C.

Gelbard, E. M.

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

Gross, J. D.

Hall, M. G. C.

M. G. C. Hall, “Cross-section adjustment with Monte Carlo sensitivities: application to the Winfrith iron benchmark,” Nucl. Sci. Eng. 81, 423–431 (1982).

Hielscher, A. H.

Hornung, R.

R. Hornung, T. H. Pham, K. A. Keefe, M. W. Berns, Y. Tadir, and B. J. Tromberg, “Quantitative near-infrared spectroscopy of cervical dysplasia in vivo,” Hum. Reprod. 14, 2908–2916 (1999).
[CrossRef] [PubMed]

Ismaelli, A.

Keefe, K. A.

R. Hornung, T. H. Pham, K. A. Keefe, M. W. Berns, Y. Tadir, and B. J. Tromberg, “Quantitative near-infrared spectroscopy of cervical dysplasia in vivo,” Hum. Reprod. 14, 2908–2916 (1999).
[CrossRef] [PubMed]

Marquet, P.

Martelli, F.

Mourant, J. R.

Osterberg, U.

Paulsen, K.

Pham, T. H.

R. Hornung, T. H. Pham, K. A. Keefe, M. W. Berns, Y. Tadir, and B. J. Tromberg, “Quantitative near-infrared spectroscopy of cervical dysplasia in vivo,” Hum. Reprod. 14, 2908–2916 (1999).
[CrossRef] [PubMed]

Piguet, D.

Pogue, B.

Rief, H.

H. Rief, “Generalized Monte Carlo perturbation algorithms for correlated sampling and a second-order Taylor series approach,” Ann. Nucl. Energy 9, 455–476 (1984).
[CrossRef]

Sassaroli, A.

Spanier, J.

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

Tadir, Y.

R. Hornung, T. H. Pham, K. A. Keefe, M. W. Berns, Y. Tadir, and B. J. Tromberg, “Quantitative near-infrared spectroscopy of cervical dysplasia in vivo,” Hum. Reprod. 14, 2908–2916 (1999).
[CrossRef] [PubMed]

Testorf, M.

Tromberg, B. J.

F. Bevilacqua, D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, and C. Depeursinge, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
[CrossRef]

R. Hornung, T. H. Pham, K. A. Keefe, M. W. Berns, Y. Tadir, and B. J. Tromberg, “Quantitative near-infrared spectroscopy of cervical dysplasia in vivo,” Hum. Reprod. 14, 2908–2916 (1999).
[CrossRef] [PubMed]

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

Venugopalan, V.

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

You, J. S.

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

Zaccanti, G.

Ann. Nucl. Energy (1)

H. Rief, “Generalized Monte Carlo perturbation algorithms for correlated sampling and a second-order Taylor series approach,” Ann. Nucl. Energy 9, 455–476 (1984).
[CrossRef]

Appl. Opt. (3)

Hum. Reprod. (1)

R. Hornung, T. H. Pham, K. A. Keefe, M. W. Berns, Y. Tadir, and B. J. Tromberg, “Quantitative near-infrared spectroscopy of cervical dysplasia in vivo,” Hum. Reprod. 14, 2908–2916 (1999).
[CrossRef] [PubMed]

Nucl. Sci. Eng. (1)

M. G. C. Hall, “Cross-section adjustment with Monte Carlo sensitivities: application to the Winfrith iron benchmark,” Nucl. Sci. Eng. 81, 423–431 (1982).

Opt. Lett. (1)

Phys. Rev. E (1)

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: an extension for highly absorbing media and small source–detector separations,” Phys. Rev. E 58, 2395–2407 (1998).
[CrossRef]

Other (2)

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

G. Dejonghe, “Etudes d’effets differentials par la méthode de Monte Carlo dans le cadre de l’equation du transport. Applications aux calculs de protection et de neutronique,” Ph.D. dissertation (Université Paris XI, Orsay, France, 1982).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the proposed method for solving inverse photon migration problems in heterogeneous media.

Fig. 2
Fig. 2

Values of μa and μs° as predicted by our proposed pMC method for μa perturbations in (a) the top layer and (b) the bottom layer. Error bars represent 1σ confidence intervals and, where they are not visible, are smaller than the symbol.

Fig. 3
Fig. 3

Values of μa and μs° as predicted by our proposed pMC method for μs perturbations in (a) the top layer and (b) the bottom layer. Error bars represent 1σ confidence intervals and, where they are not visible, are smaller than the symbol.

Equations (1)

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ξ^=ξμ^s/μ^tμs/μtjμ^tμtjexp-μ^t-μtS

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