Abstract

The quantification of a nonuniform quantum yield or fluorophore absorption distribution is of major interest in molecular imaging of biological tissue. We introduce what is believed to be the first fluorescence image reconstruction algorithm based on the equation of radiative transfer that recovers the spatial distribution of light-emitting fluorophores inside a highly scattering medium from measurements made on the surface of the medium. We obtain images of either the quantum yield or the fluorophore absorption.

© 2003 Optical Society of America

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References

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  1. R. Weissleder and U. Mahmood, Radiology 219, 316 (2001).
    [CrossRef] [PubMed]
  2. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983).
    [CrossRef]
  3. M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, Opt. Lett. 21, 158 (1996).
    [CrossRef] [PubMed]
  4. D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, Appl. Opt. 36, 2260 (1997).
    [CrossRef] [PubMed]
  5. J. Chang, H. L. Graber, and R. L. Barbour, J. Opt. Soc. Am. A 14, 288 (1997).
    [CrossRef]
  6. H. Jiang, Appl. Opt. 37, 5337 (1998).
    [CrossRef]
  7. V. Ntziachristos and R. Weissleder, Opt. Lett. 26, 893 (2001).
    [CrossRef]
  8. M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. Sevick-Muraca, Proc. Natl. Acad. Sci. USA 99, 9619 (2002).
    [CrossRef]
  9. A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, Phys. Med. Biol. 43, 1285 (1998).
    [CrossRef] [PubMed]
  10. A. D. Kim and A. Ishimaru, Appl. Opt. 37, 5313 (1998).
    [CrossRef]
  11. R. Aronson and N. Corngold, J. Opt. Soc. Am. A 16, 1066 (1999).
    [CrossRef]
  12. S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, Med. Phys. 27, 252 (2000).
    [CrossRef] [PubMed]
  13. B. Chen, K. Stamnes, and J. J. Stamnes, Appl. Opt. 40, 6356 (2001).
    [CrossRef]
  14. A. H. Hielscher, A. D. Klose, and K. M. Hanson, IEEE Trans. Med. Imag. 18, 262 (1999).
    [CrossRef]
  15. A. D. Klose and A. H. Hielscher, J. Quant. Spectrosc. Radiat. Transfer 72, 715 (2002).
    [CrossRef]
  16. M. L. Adams and E. W. Larsen, Prog. Nucl. Eng. 40, 3 (2002).
    [CrossRef]
  17. B. G. Carlson and K. D. Lathrop, in Computing Methods in Reactor Physics, H. Greenspan, ed. (Gordon and Breach, New York, 1968), pp. 166–266.
  18. A. D. Klose and A. H. Hielscher, Inverse Problems 19, 387 (2003).
    [CrossRef]

2003 (1)

A. D. Klose and A. H. Hielscher, Inverse Problems 19, 387 (2003).
[CrossRef]

2002 (3)

A. D. Klose and A. H. Hielscher, J. Quant. Spectrosc. Radiat. Transfer 72, 715 (2002).
[CrossRef]

M. L. Adams and E. W. Larsen, Prog. Nucl. Eng. 40, 3 (2002).
[CrossRef]

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. Sevick-Muraca, Proc. Natl. Acad. Sci. USA 99, 9619 (2002).
[CrossRef]

2001 (3)

2000 (1)

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, Med. Phys. 27, 252 (2000).
[CrossRef] [PubMed]

1999 (2)

R. Aronson and N. Corngold, J. Opt. Soc. Am. A 16, 1066 (1999).
[CrossRef]

A. H. Hielscher, A. D. Klose, and K. M. Hanson, IEEE Trans. Med. Imag. 18, 262 (1999).
[CrossRef]

1998 (3)

H. Jiang, Appl. Opt. 37, 5337 (1998).
[CrossRef]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, Phys. Med. Biol. 43, 1285 (1998).
[CrossRef] [PubMed]

A. D. Kim and A. Ishimaru, Appl. Opt. 37, 5313 (1998).
[CrossRef]

1997 (2)

1996 (1)

Adams, M. L.

M. L. Adams and E. W. Larsen, Prog. Nucl. Eng. 40, 3 (2002).
[CrossRef]

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, Phys. Med. Biol. 43, 1285 (1998).
[CrossRef] [PubMed]

Aronson, R.

Arridge, S. R.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, Med. Phys. 27, 252 (2000).
[CrossRef] [PubMed]

Barbour, R. L.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, Phys. Med. Biol. 43, 1285 (1998).
[CrossRef] [PubMed]

J. Chang, H. L. Graber, and R. L. Barbour, J. Opt. Soc. Am. A 14, 288 (1997).
[CrossRef]

Boas, D. A.

Carlson, B. G.

B. G. Carlson and K. D. Lathrop, in Computing Methods in Reactor Physics, H. Greenspan, ed. (Gordon and Breach, New York, 1968), pp. 166–266.

Chance, B.

Chang, J.

Chen, A. U.

Chen, B.

Corngold, N.

Dehghani, H.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, Med. Phys. 27, 252 (2000).
[CrossRef] [PubMed]

Eppstein, M. J.

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. Sevick-Muraca, Proc. Natl. Acad. Sci. USA 99, 9619 (2002).
[CrossRef]

Godavarty, A.

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. Sevick-Muraca, Proc. Natl. Acad. Sci. USA 99, 9619 (2002).
[CrossRef]

Graber, H. L.

Hanson, K. M.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, IEEE Trans. Med. Imag. 18, 262 (1999).
[CrossRef]

Hawrysz, D. J.

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. Sevick-Muraca, Proc. Natl. Acad. Sci. USA 99, 9619 (2002).
[CrossRef]

Hielscher, A. H.

A. D. Klose and A. H. Hielscher, Inverse Problems 19, 387 (2003).
[CrossRef]

A. D. Klose and A. H. Hielscher, J. Quant. Spectrosc. Radiat. Transfer 72, 715 (2002).
[CrossRef]

A. H. Hielscher, A. D. Klose, and K. M. Hanson, IEEE Trans. Med. Imag. 18, 262 (1999).
[CrossRef]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, Phys. Med. Biol. 43, 1285 (1998).
[CrossRef] [PubMed]

Ishimaru, A.

Jiang, H.

Kim, A. D.

Klose, A. D.

A. D. Klose and A. H. Hielscher, Inverse Problems 19, 387 (2003).
[CrossRef]

A. D. Klose and A. H. Hielscher, J. Quant. Spectrosc. Radiat. Transfer 72, 715 (2002).
[CrossRef]

A. H. Hielscher, A. D. Klose, and K. M. Hanson, IEEE Trans. Med. Imag. 18, 262 (1999).
[CrossRef]

Lakowicz, J. R.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983).
[CrossRef]

Larsen, E. W.

M. L. Adams and E. W. Larsen, Prog. Nucl. Eng. 40, 3 (2002).
[CrossRef]

Lathrop, K. D.

B. G. Carlson and K. D. Lathrop, in Computing Methods in Reactor Physics, H. Greenspan, ed. (Gordon and Breach, New York, 1968), pp. 166–266.

Li, X. D.

Mahmood, U.

R. Weissleder and U. Mahmood, Radiology 219, 316 (2001).
[CrossRef] [PubMed]

Ntziachristos, V.

O’Leary, M. A.

Okada, E.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, Med. Phys. 27, 252 (2000).
[CrossRef] [PubMed]

Paithankar, D. Y.

Patterson, M. S.

Pogue, B. W.

Schweiger, M.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, Med. Phys. 27, 252 (2000).
[CrossRef] [PubMed]

Sevick-Muraca, E.

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. Sevick-Muraca, Proc. Natl. Acad. Sci. USA 99, 9619 (2002).
[CrossRef]

Sevick-Muraca, E. M.

Stamnes, J. J.

Stamnes, K.

Weissleder, R.

Yodh, A. G.

Appl. Opt. (4)

IEEE Trans. Med. Imag. (1)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, IEEE Trans. Med. Imag. 18, 262 (1999).
[CrossRef]

Inverse Problems (1)

A. D. Klose and A. H. Hielscher, Inverse Problems 19, 387 (2003).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (1)

A. D. Klose and A. H. Hielscher, J. Quant. Spectrosc. Radiat. Transfer 72, 715 (2002).
[CrossRef]

Med. Phys. (1)

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, Med. Phys. 27, 252 (2000).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Med. Biol. (1)

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, Phys. Med. Biol. 43, 1285 (1998).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. Sevick-Muraca, Proc. Natl. Acad. Sci. USA 99, 9619 (2002).
[CrossRef]

Prog. Nucl. Eng. (1)

M. L. Adams and E. W. Larsen, Prog. Nucl. Eng. 40, 3 (2002).
[CrossRef]

Radiology (1)

R. Weissleder and U. Mahmood, Radiology 219, 316 (2001).
[CrossRef] [PubMed]

Other (2)

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983).
[CrossRef]

B. G. Carlson and K. D. Lathrop, in Computing Methods in Reactor Physics, H. Greenspan, ed. (Gordon and Breach, New York, 1968), pp. 166–266.

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Figures (2)

Fig. 1
Fig. 1

(a) Original quantum yield distribution η. (b) Reconstructed quantum yield distribution η. (c) Reconstructed fluorescence yield distribution ημaxm.

Fig. 2
Fig. 2

(a) Original fluorescence absorption μaxm. (b) Reconstructed fluorescence absorption μaxm by means of Eq. (1). (c) Reconstructed fluorescence absorption μaxm by means of Eq. (2).

Equations (7)

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

Ω·ψx+μax+μaxm+μsxψx=Sx+μsx4πpΩ,ΩψxΩdΩ,
Ω·ψm+μam+μsmψm=14πημaxmϕx+μsm4πpΩ,ΩψmΩdΩ.
4πpΩ,ΩψΩdΩk=1KwkpΩk,ΩkψΩk,
Aψ=Bψ+S,
Aψz+1=Bψz+S
pd:=ϕd=n·Ω>0ψrd,ΩdΩ,
φd=1Dpd-mdmd2.

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