Abstract

In general it is not possible to write an analytic expression for the fluorescence signal generated by a fluorophore distributed in a scattering medium such as tissue. However, by assuming that the scattering properties of the tissue are the same at the excitation and emission wavelengths, we have derived a simple relation between the fluorescence and the scatter signals. Along with diffusion theory, this was used to write expressions for the fluorescence signal detected at the tissue surface in both the time and the frequency domains. Experiments using the fluorophore aluminum chlorosulfonated phthalocyanine in tissue-simulating materials confirmed the accuracy of the model. Applications to in υiυo spectroscopy are discussed.

© 1994 Optical Society of America

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References

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  1. S. Andersson-Engels, B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol. 3, 66–79 (1992).
  2. A. E. Profio, J. Sarnaik, “Fluorescence of HpD for tumor detection and dosimetry in photoradiation therapy,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 163–175.
  3. W. J. M. van der Putten, M. J. C. van Gemert, “A modelling approach to the detection of subcutaneous tumours by haematoporphyrin-derivative fluorescence,” Phys. Med. Biol. 28, 639–645 (1983).
    [CrossRef] [PubMed]
  4. A. F. Gmitro, F. W. Cutruzzola, M. S. Stetz, L. I. Deckelbaum, “Measurement depth of laser-induced tissue fluorescence with application to laser angioplasty,” Appl. Opt. 27, 1844–1849 (1988).
    [CrossRef] [PubMed]
  5. R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
    [CrossRef] [PubMed]
  6. W. R. Potter, T. S. Mang, “Photofrin II levels by in vivo fluorescence photometry,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 177–186.
  7. M. Keijzer, R. R. Richards-Kortum, S. L. Jacques, M. S. Feld, “Fluorescence spectroscopy of turbid media: autofluorescence of the human aorta,” Appl. Opt. 28, 4286–4292 (1989).
    [CrossRef] [PubMed]
  8. W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  9. J. Wu, M. S. Feld, R. P. Rava, “Analytical model for extracting intrinsic fluorescence in a turbid media,” Appl. Opt. 32, 3585–3595 (1993).
    [CrossRef] [PubMed]
  10. M. S. Patterson, S. J. Madsen, J. D. Moulton, B. C. Wilson, “Diffusion equation representation of photon migration in tissue,” in Microwave Theory and Techniques Symposium (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 905–908.
  11. M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  12. J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).
  13. M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
    [CrossRef] [PubMed]
  14. B. W. Henderson, T. J. Dougherty, eds., Photodynamic Therapy: Basic Principles and Clinical Applications (Dekker, New York, 1992).
  15. J. H. Brannon, D. Magde, “Picosecond laser photophysics. Group 3A phthalocyanines,” J. Am. Chem. Soc. 102, 62–65 (1980).
    [CrossRef]
  16. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983).
    [CrossRef]
  17. H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
    [CrossRef] [PubMed]
  18. S. J. Madsen, M. S. Patterson, B. C. Wilson, “The use of India ink as an optical absorber in tissue-simulating phantoms,” Phys. Med. Biol. 37, 985–993 (1992).
    [CrossRef] [PubMed]
  19. I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
    [CrossRef]
  20. G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]
  21. E. Gratton, M. Limkeman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J. 44, 315–324 (1983).
    [CrossRef] [PubMed]
  22. B. M. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency-domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
    [CrossRef]
  23. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980) pp. 331–339.
  24. M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. II: Optical properties of tissues and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
    [CrossRef]
  25. T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion-theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
    [CrossRef] [PubMed]
  26. M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time-resolved light-scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).
  27. N. J. Turro, Modern Molecular Photochemistry (Benjamin/Cummings, Menlo Park, Calif., 1978), p. 109.

1993 (1)

1992 (3)

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion-theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

S. Andersson-Engels, B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol. 3, 66–79 (1992).

S. J. Madsen, M. S. Patterson, B. C. Wilson, “The use of India ink as an optical absorber in tissue-simulating phantoms,” Phys. Med. Biol. 37, 985–993 (1992).
[CrossRef] [PubMed]

1991 (3)

1990 (1)

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1989 (5)

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

B. M. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency-domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
[CrossRef]

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

M. Keijzer, R. R. Richards-Kortum, S. L. Jacques, M. S. Feld, “Fluorescence spectroscopy of turbid media: autofluorescence of the human aorta,” Appl. Opt. 28, 4286–4292 (1989).
[CrossRef] [PubMed]

1988 (1)

1983 (2)

E. Gratton, M. Limkeman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J. 44, 315–324 (1983).
[CrossRef] [PubMed]

W. J. M. van der Putten, M. J. C. van Gemert, “A modelling approach to the detection of subcutaneous tumours by haematoporphyrin-derivative fluorescence,” Phys. Med. Biol. 28, 639–645 (1983).
[CrossRef] [PubMed]

1980 (1)

J. H. Brannon, D. Magde, “Picosecond laser photophysics. Group 3A phthalocyanines,” J. Am. Chem. Soc. 102, 62–65 (1980).
[CrossRef]

1973 (1)

Andersson-Engels, S.

S. Andersson-Engels, B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol. 3, 66–79 (1992).

Berndt, K. W.

Brannon, J. H.

J. H. Brannon, D. Magde, “Picosecond laser photophysics. Group 3A phthalocyanines,” J. Am. Chem. Soc. 102, 62–65 (1980).
[CrossRef]

Chance, B.

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time-resolved light-scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Cutruzzola, F. W.

Dawson, J. B.

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

Deckelbaum, L. I.

Driver, I.

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

Duderstadt, J. J.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Farrell, T. J.

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion-theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Feather, J. W.

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

Feddersen, B. M.

B. M. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency-domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
[CrossRef]

Feld, M. S.

J. Wu, M. S. Feld, R. P. Rava, “Analytical model for extracting intrinsic fluorescence in a turbid media,” Appl. Opt. 32, 3585–3595 (1993).
[CrossRef] [PubMed]

M. Keijzer, R. R. Richards-Kortum, S. L. Jacques, M. S. Feld, “Fluorescence spectroscopy of turbid media: autofluorescence of the human aorta,” Appl. Opt. 28, 4286–4292 (1989).
[CrossRef] [PubMed]

R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Fitzmaurice, M.

R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Gmitro, A. F.

Gratton, E.

B. M. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency-domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
[CrossRef]

E. Gratton, M. Limkeman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J. 44, 315–324 (1983).
[CrossRef] [PubMed]

Hale, G. M.

Hamilton, L. J.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Jacques, S. L.

Keijzer, M.

King, P. R.

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

Kramer, J. R.

R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Lakowicz, J. R.

Limkeman, M.

E. Gratton, M. Limkeman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J. 44, 315–324 (1983).
[CrossRef] [PubMed]

Madsen, S. J.

S. J. Madsen, M. S. Patterson, B. C. Wilson, “The use of India ink as an optical absorber in tissue-simulating phantoms,” Phys. Med. Biol. 37, 985–993 (1992).
[CrossRef] [PubMed]

M. S. Patterson, S. J. Madsen, J. D. Moulton, B. C. Wilson, “Diffusion equation representation of photon migration in tissue,” in Microwave Theory and Techniques Symposium (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 905–908.

Magde, D.

J. H. Brannon, D. Magde, “Picosecond laser photophysics. Group 3A phthalocyanines,” J. Am. Chem. Soc. 102, 62–65 (1980).
[CrossRef]

Mang, T. S.

W. R. Potter, T. S. Mang, “Photofrin II levels by in vivo fluorescence photometry,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 177–186.

Moes, C. J. M.

Moulton, J. D.

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time-resolved light-scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).

M. S. Patterson, S. J. Madsen, J. D. Moulton, B. C. Wilson, “Diffusion equation representation of photon migration in tissue,” in Microwave Theory and Techniques Symposium (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 905–908.

Patterson, M. S.

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion-theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

S. J. Madsen, M. S. Patterson, B. C. Wilson, “The use of India ink as an optical absorber in tissue-simulating phantoms,” Phys. Med. Biol. 37, 985–993 (1992).
[CrossRef] [PubMed]

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. II: Optical properties of tissues and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
[CrossRef]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time-resolved light-scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).

M. S. Patterson, S. J. Madsen, J. D. Moulton, B. C. Wilson, “Diffusion equation representation of photon migration in tissue,” in Microwave Theory and Techniques Symposium (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 905–908.

Piston, D. W.

B. M. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency-domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
[CrossRef]

Potter, W. R.

W. R. Potter, T. S. Mang, “Photofrin II levels by in vivo fluorescence photometry,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 177–186.

Prahl, S. A.

H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
[CrossRef] [PubMed]

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Profio, A. E.

A. E. Profio, J. Sarnaik, “Fluorescence of HpD for tumor detection and dosimetry in photoradiation therapy,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 163–175.

Querry, M. R.

Ratliff, N. B.

R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Rava, R. P.

J. Wu, M. S. Feld, R. P. Rava, “Analytical model for extracting intrinsic fluorescence in a turbid media,” Appl. Opt. 32, 3585–3595 (1993).
[CrossRef] [PubMed]

R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Richards-Kortum, R.

R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Richards-Kortum, R. R.

Sarnaik, J.

A. E. Profio, J. Sarnaik, “Fluorescence of HpD for tumor detection and dosimetry in photoradiation therapy,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 163–175.

Stetz, M. S.

Tong, L. L.

R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

Turro, N. J.

N. J. Turro, Modern Molecular Photochemistry (Benjamin/Cummings, Menlo Park, Calif., 1978), p. 109.

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980) pp. 331–339.

van der Putten, W. J. M.

W. J. M. van der Putten, M. J. C. van Gemert, “A modelling approach to the detection of subcutaneous tumours by haematoporphyrin-derivative fluorescence,” Phys. Med. Biol. 28, 639–645 (1983).
[CrossRef] [PubMed]

van Gemert, M. J. C.

H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
[CrossRef] [PubMed]

W. J. M. van der Putten, M. J. C. van Gemert, “A modelling approach to the detection of subcutaneous tumours by haematoporphyrin-derivative fluorescence,” Phys. Med. Biol. 28, 639–645 (1983).
[CrossRef] [PubMed]

van Marie, J.

van Staveren, H. J.

Welch, A. J.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Wilson, B. C.

S. Andersson-Engels, B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol. 3, 66–79 (1992).

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion-theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

S. J. Madsen, M. S. Patterson, B. C. Wilson, “The use of India ink as an optical absorber in tissue-simulating phantoms,” Phys. Med. Biol. 37, 985–993 (1992).
[CrossRef] [PubMed]

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. II: Optical properties of tissues and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
[CrossRef]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time-resolved light-scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).

M. S. Patterson, S. J. Madsen, J. D. Moulton, B. C. Wilson, “Diffusion equation representation of photon migration in tissue,” in Microwave Theory and Techniques Symposium (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 905–908.

Wu, J.

Wyman, D. R.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. II: Optical properties of tissues and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
[CrossRef]

Appl. Opt. (7)

Biophys. J. (1)

E. Gratton, M. Limkeman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J. 44, 315–324 (1983).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

R. Richards-Kortum, R. P. Rava, M. Fitzmaurice, L. L. Tong, N. B. Ratliff, J. R. Kramer, M. S. Feld, “A one-layer model of laser-induced fluorescence for diagnosis of disease in human tissue: applications to atherosclerosis,” IEEE Trans. Biomed. Eng. 36, 1222–1232 (1989).
[CrossRef] [PubMed]

J. Am. Chem. Soc. (1)

J. H. Brannon, D. Magde, “Picosecond laser photophysics. Group 3A phthalocyanines,” J. Am. Chem. Soc. 102, 62–65 (1980).
[CrossRef]

J. Cell. Pharmacol. (1)

S. Andersson-Engels, B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol. 3, 66–79 (1992).

Lasers Med. Sci. (1)

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. II: Optical properties of tissues and resulting fluence distributions,” Lasers Med. Sci. 6, 379–390 (1991).
[CrossRef]

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion-theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Phys. Med. Biol. (3)

W. J. M. van der Putten, M. J. C. van Gemert, “A modelling approach to the detection of subcutaneous tumours by haematoporphyrin-derivative fluorescence,” Phys. Med. Biol. 28, 639–645 (1983).
[CrossRef] [PubMed]

S. J. Madsen, M. S. Patterson, B. C. Wilson, “The use of India ink as an optical absorber in tissue-simulating phantoms,” Phys. Med. Biol. 37, 985–993 (1992).
[CrossRef] [PubMed]

I. Driver, J. W. Feather, P. R. King, J. B. Dawson, “The optical properties of aqueous suspensions of Intralipid, a fat emulsion,” Phys. Med. Biol. 34, 1927–1930 (1989).
[CrossRef]

Rev. Sci. Instrum. (1)

B. M. Feddersen, D. W. Piston, E. Gratton, “Digital parallel acquisition in frequency-domain fluorometry,” Rev. Sci. Instrum. 60, 2929–2936 (1989).
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Figures (8)

Fig. 1
Fig. 1

Schematic illustration of fluorescence spectroscopy in a turbid medium such as biological tissue. Excitation photons (wavelength λx) are delivered to the tissue by an optical fiber at the origin, and a fraction of these reach the detector at distance ρ through many different multiple-scattering paths. Fluorescence photons (wavelength λm) are generated throughout the tissue, and some also reach the detector. If the optical properties of the tissue are identical at λx and λm, a fluorescence photon generated at location r′ at time t′ has the same probability of being at location r at time t as does an excitation photon that is also at r′ at t′.

Fig. 2
Fig. 2

Extinction coefficient (solid curve) and fluorescence-emission spectrum (excitation wavelength of 650 nm) for ALSPC in saline. The emission spectrum has not been corrected for the wavelength-dependent response of the detector. However, because the same detector is used for all experiments, this correction is not required in the calculations described in the text.

Fig. 3
Fig. 3

Schematic diagram of the frequency-domain system. Selection of the filter in front of the detector PMT permits the measurement of scattered light alone, fluorescent light alone, or the sum of these two components.

Fig. 4
Fig. 4

Measurements of the phase and modulation of scattered light, fluorescent light, and scattered-plus-fluorescent light as functions of the source–detector distance. The curves are the result of calculations described in the text. Measurements were performed at (a) 60 MHz and (b) 140 MHz. The phantom consisted of 1% Intralipid plus 0.5-μg/mL ALSPC. The excitation wavelength was 633 nm, and the fluorescence component was detected at 680 nm. For the measurement of scatter plus fluorescence, no wavelength discrimination was employed.

Fig. 5
Fig. 5

Measurements of the phase and modulation of the total (i.e., scatter-plus-fluorescence) signal under the same conditions as for Fig. 4, except that the excitation wavelength was 670 nm. In this case, good agreement with experimental results was achieved when the model was used to calculate the components of fluorescence in 10-nm-wavelength intervals. These components were then summed at each source–detector distance to estimate the total signal.

Fig. 6
Fig. 6

Measurements of the phase and modulation of fluorescence-plus-scatter light as functions of the excitation wavelength. The phantom consisted of 1% Intralipid plus sufficient India ink to increase the absorption coefficient to 0.015 mm−1. Measurements were performed before and after the addition of 0.5-μg/mL ALSPC. The source–detector separation was 20 mm.

Fig. 7
Fig. 7

Ratio of steady-state fluorescence (at 680 nm) to steady-state scatter (at 633 nm) versus the source–detector separation. Experimental conditions were the same as for Fig. 4. Both the experimental data and the model predictions have been normalized to their respective values at ρ = 35 nm.

Fig. 8
Fig. 8

Calculated steady-state fluorescence (photons/mm2 at the surface for each excitation photon) as a function of the ALSPC concentration for the geometry illustrated in Fig. 1. For the host tissue we have assumed that (1 − gs = 1.0 mm−1 and the absorption coefficient is 0.01, 0.03, or 0.1 mm−1. We have also assumed that fluorescence excitation occurs at 610 nm and that detection is performed through a 680-nm, 10-nm bandpass filter (50% transmission at peak). In (a), ρ = 1 mm, the fluorescence signal increases almost linearly with ALSPC concentration and depends little on the tissue-absorption coefficient. In (b), when ρ is increased to 7 mm, the dependence of fluorescence signal on ALSPC concentration is nonlinear, and the signal amplitude is also much more sensitive to the optical properties of the host tissue. The dashed curves are the model predictions, including secondary fluorescence, as explained in the text. Experiments were performed under these conditions for ρ = 7 mm, and the relative fluorescence signal is shown by the open circles. These data have been normalized to match the maximum signal to the model prediction.

Equations (30)

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μ f x = C x .
H ( r , μ a x + μ f x , μ s x , g x , n x , t ) μ f x Φ ( λ x , λ m ) d 3 r d λ m d t ,
F x m ( r , t ) = μ f x Φ x m t r H x ( r , t ) × E m ( r r , t t ) d 3 r d t ,
F x m ( r , t ) * 1 τ exp ( t / τ ) .
N f ( r , t ) N x ( r , t ) = μ f x Φ x m c 0 t d t
= μ f x Φ x m c t .
β x = c ( μ a x + μ f x ) ,
β m = c ( μ a m + μ f m ) .
N f ( r , t ) N x ( r , t ) = μ fx Φ xm c 0 t exp [ ( β x β m , ) ( t t ) ] d t ,
= μ fx Φ xm c β x β m { exp [ ( β x β m ) t ] 1 } .
N x ( r , t ) = N o ( r , t ) exp ( β x t ) ,
N f ( r , t ) = μ f x Φ x m c β x β m N o ( r , t ) exp ( β m t ) exp ( β x t ) ] ,
= μ f x Φ x m c β x β m [ N m ( r , t ) N x ( r , t ) ] ,
N f ( r ) = μ f x Φ x m c β x β m [ N m ( r ) N x ( r ) ] ,
R x ( ρ , t ) = D z H x ( ρ , z , t ) , z = 0 ,
R x ( ρ , t ) = z o ( 4 π D c ) 3 / 2 t 5 / 2 exp ( ρ 2 + z o 2 4 Dct ) exp ( β x t ) ,
z o = 1 μ s ( 1 g ) ,
D 1 3 μ s ( 1 g ) .
F x m ( ρ , t ) = μ f x Φ x m c z o ( 4 π D c ) 3 / 2 ( β x β m ) t 5 / 2 × exp ( ρ 2 + z o 2 4 D c t ) [ exp ( β m t ) exp ( β x t ) ] .
M ( f ) = [ Sig ( f ) Sig ( 0 ) ] [ Src ( f ) Src ( 0 ) ] 1 ,
R ˜ x ( ρ , f ) = z o exp ( Ψ i ) ( 1 + Ψ o 2 + 2 Ψ i ) 1 / 2 2 π ( ρ 2 + z o 2 ) 3 / 2 × { cos [ Ψ r tan 1 ( Ψ r 1 + Ψ i ) ] + i sin [ Ψ r tan 1 ( Ψ r 1 + Ψ i ) ] } ,
Ψ o = [ ( ρ 2 + z o 2 ) β x 2 + ( 2 π f ) 2 D c ] 1 / 2 ,
Ψ i = Ψ o cos [ 1 2 tan 1 ( 2 π f β x ) ] ,
Ψ r = Ψ o sin [ 1 2 tan 1 ( 2 π f β x ) ] .
θ x ( ρ , f ) = tan 1 I m [ R ˜ x ( ρ , f ) ] e [ R x ( ρ , f ) ] ,
M x ( ρ , f ) = ( e 2 [ R ˜ x ( ρ , r ) ] + I m 2 [ R ˜ x ( ρ , f ) ] e 2 [ R ˜ x ( ρ , 0 ) ] + I m 2 [ R ˜ x ( ρ , 0 ) ] ) 1 / 2 .
F ˜ x m ( ρ , f ) = μ f x Φ x m c β x β m [ R ˜ m ( ρ , f ) R ˜ x ( ρ , f ) ] ,
F ˜ x m ( ρ , f ) = μ f x Φ x m c β x β m [ R ˜ m ( ρ , f ) R ˜ x ( ρ , f ) ] [ 1 i 2 π f τ 1 + ( 2 π f τ ) 2 ] .
T ˜ x m ( ρ , f ) = R ˜ x ( ρ , f ) + μ f x Φ x m c β x β m × [ R ˜ m ( ρ , f ) R ˜ x ( ρ , f ) ] [ 1 i 2 π f τ 1 + ( 2 π f τ ) 2 ] .
μ f x = μ f m ( λ ) I m ( λ ) d λ I m ( λ ) d λ = 0 . 0228 mm 1 μ g 1 mL .

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