Abstract

Flux density distributions were measured in large tissue sections illuminated with 633- and 1064-nm laser radiation delivered by an optical fiber. The results were modeled by solving the 2-D diffusion approximation for an incident Gaussian beam and fitting the data with nonlinear regression. It is shown that the radial average flux density is exponentially attenuated for an arbitrary incident irradiance profile.

© 1990 Optical Society of America

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  1. B. C. Wilson, G. Adam, “A Monte Carlo Model for the Absorption and Flux Distributions of Light in Tissue,” Med. Phys. 10, 824–830 (1983).
    [CrossRef] [PubMed]
  2. P. Parsa, S. L. Jacques, N. S. Nishoika, “Optical Properties of Rat Liver Between 350 and 2200 nm,” Appl. Opt. 28, 2325–2330 (1989).
    [CrossRef] [PubMed]
  3. A. E. Profio, “Light Transport in Tissue,” Appl. Opt. 28, 2216–2222 (1989).
    [CrossRef] [PubMed]
  4. M. Motamedi, S. Rastegar, G. LeCarpentier, A. J. Welch, “Light and Temperature Distribution in Laser Irradiated Tissue: the Influence of Anisotropic Scattering and Refractive Index,” Appl. Opt. 28, 2230–2237 (1989).
    [CrossRef] [PubMed]
  5. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  6. L. Reynolds, C. C. Johnson, A. Ishimaru, “Diffuse Reflectance from a Finite Blood Medium: Application to the Modeling of a Fiber Optic Catheter,” Appl. Opt. 15, 2059–2067 (1976).
    [CrossRef] [PubMed]
  7. R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and Absorption of Turbid Materials Determined From Reflection Measurements. 1: Theory,” Appl. Opt. 22, 2456–2462 (1983).
    [CrossRef] [PubMed]
  8. D. R. Doiron, “Photophysics of and Instrumentation for Porphyrin Detection and Activation,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, Eds. (Alan A. Liss, New York, 1984), p. 41.
  9. F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive Index of Some Mammalian Tissues Using a Fiber Optic Cladding Method,” Appl. Opt. 28, 2297–2303 (1989).
    [CrossRef] [PubMed]
  10. J. L. Karagiannes, Z. Zhang, B. Grossweiner, L. I. Grossweiner, “Applications of the 1-D Diffusion Approximation to the Optics of Tissues and Tissue Phantoms,” Appl. Opt. 28, 2311–2317 (1989).
    [CrossRef] [PubMed]
  11. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 717.
  12. W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. 1, 149–167 (1987).
    [CrossRef]
  13. B. C. Wilson, M. S. Patterson, D. M. Burns, “The Effect of Photosensitizer Concentration in Tissue on the Penetration Depth of Photoactivating Light,” Laser Med. Sci. 1, 235–244 (1986).
    [CrossRef]
  14. S. L. Jacques, S. A. Prahl, “Modeling Optical and Thermal Distributions in Tissue During Laser Irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
    [CrossRef] [PubMed]
  15. H. C. van de Hulst, Multiple Light Scattering Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 2.
  16. W. A. G. Bruls, J. C. van der Leun, “Forward Scattering Properties of Human Epidermal Layers,” Photochem. Photobiol. 40, 231–242 (1984).
    [CrossRef] [PubMed]
  17. B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect Versus Direct Techniques for the Measurement of the Optical Properties of Tissues,” Photochem. Photobiol. 46, 601–608 (1987).
    [CrossRef] [PubMed]
  18. G. Yoon, S. A. Prahl, A. J. Welch, “Accuracies of the Diffusion Approximation and Its Similarity Relations for Laser-Irradiated Biological Media,” Appl. Opt. 28, 2250–2255 (1989).
    [CrossRef] [PubMed]

1989 (6)

1987 (3)

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. 1, 149–167 (1987).
[CrossRef]

S. L. Jacques, S. A. Prahl, “Modeling Optical and Thermal Distributions in Tissue During Laser Irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect Versus Direct Techniques for the Measurement of the Optical Properties of Tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

1986 (1)

B. C. Wilson, M. S. Patterson, D. M. Burns, “The Effect of Photosensitizer Concentration in Tissue on the Penetration Depth of Photoactivating Light,” Laser Med. Sci. 1, 235–244 (1986).
[CrossRef]

1984 (1)

W. A. G. Bruls, J. C. van der Leun, “Forward Scattering Properties of Human Epidermal Layers,” Photochem. Photobiol. 40, 231–242 (1984).
[CrossRef] [PubMed]

1983 (2)

1976 (1)

Adam, G.

B. C. Wilson, G. Adam, “A Monte Carlo Model for the Absorption and Flux Distributions of Light in Tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Bolin, F. P.

Bruls, W. A. G.

W. A. G. Bruls, J. C. van der Leun, “Forward Scattering Properties of Human Epidermal Layers,” Photochem. Photobiol. 40, 231–242 (1984).
[CrossRef] [PubMed]

Burns, D. M.

B. C. Wilson, M. S. Patterson, D. M. Burns, “The Effect of Photosensitizer Concentration in Tissue on the Penetration Depth of Photoactivating Light,” Laser Med. Sci. 1, 235–244 (1986).
[CrossRef]

Doiron, D. R.

D. R. Doiron, “Photophysics of and Instrumentation for Porphyrin Detection and Activation,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, Eds. (Alan A. Liss, New York, 1984), p. 41.

Ference, R. J.

Ferwerda, H. A.

Flock, S. T.

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect Versus Direct Techniques for the Measurement of the Optical Properties of Tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 717.

Groenhuis, R. A. J.

Grossweiner, B.

Grossweiner, L. I.

Ishimaru, A.

Jacques, S. L.

P. Parsa, S. L. Jacques, N. S. Nishoika, “Optical Properties of Rat Liver Between 350 and 2200 nm,” Appl. Opt. 28, 2325–2330 (1989).
[CrossRef] [PubMed]

S. L. Jacques, S. A. Prahl, “Modeling Optical and Thermal Distributions in Tissue During Laser Irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

Johnson, C. C.

Karagiannes, J. L.

LeCarpentier, G.

Marijnissen, J. P. A.

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. 1, 149–167 (1987).
[CrossRef]

Motamedi, M.

Nishoika, N. S.

Parsa, P.

Patterson, M. S.

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect Versus Direct Techniques for the Measurement of the Optical Properties of Tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, D. M. Burns, “The Effect of Photosensitizer Concentration in Tissue on the Penetration Depth of Photoactivating Light,” Laser Med. Sci. 1, 235–244 (1986).
[CrossRef]

Prahl, S. A.

G. Yoon, S. A. Prahl, A. J. Welch, “Accuracies of the Diffusion Approximation and Its Similarity Relations for Laser-Irradiated Biological Media,” Appl. Opt. 28, 2250–2255 (1989).
[CrossRef] [PubMed]

S. L. Jacques, S. A. Prahl, “Modeling Optical and Thermal Distributions in Tissue During Laser Irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

Preuss, L. E.

Profio, A. E.

Rastegar, S.

Reynolds, L.

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 717.

Star, W. M.

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. 1, 149–167 (1987).
[CrossRef]

Taylor, R. C.

Ten Bosch, J. J.

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 2.

van der Leun, J. C.

W. A. G. Bruls, J. C. van der Leun, “Forward Scattering Properties of Human Epidermal Layers,” Photochem. Photobiol. 40, 231–242 (1984).
[CrossRef] [PubMed]

van Gemert, M. J. C.

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. 1, 149–167 (1987).
[CrossRef]

Welch, A. J.

Wilson, B. C.

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect Versus Direct Techniques for the Measurement of the Optical Properties of Tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, D. M. Burns, “The Effect of Photosensitizer Concentration in Tissue on the Penetration Depth of Photoactivating Light,” Laser Med. Sci. 1, 235–244 (1986).
[CrossRef]

B. C. Wilson, G. Adam, “A Monte Carlo Model for the Absorption and Flux Distributions of Light in Tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Yoon, G.

Zhang, Z.

Appl. Opt. (8)

L. Reynolds, C. C. Johnson, A. Ishimaru, “Diffuse Reflectance from a Finite Blood Medium: Application to the Modeling of a Fiber Optic Catheter,” Appl. Opt. 15, 2059–2067 (1976).
[CrossRef] [PubMed]

R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and Absorption of Turbid Materials Determined From Reflection Measurements. 1: Theory,” Appl. Opt. 22, 2456–2462 (1983).
[CrossRef] [PubMed]

A. E. Profio, “Light Transport in Tissue,” Appl. Opt. 28, 2216–2222 (1989).
[CrossRef] [PubMed]

M. Motamedi, S. Rastegar, G. LeCarpentier, A. J. Welch, “Light and Temperature Distribution in Laser Irradiated Tissue: the Influence of Anisotropic Scattering and Refractive Index,” Appl. Opt. 28, 2230–2237 (1989).
[CrossRef] [PubMed]

G. Yoon, S. A. Prahl, A. J. Welch, “Accuracies of the Diffusion Approximation and Its Similarity Relations for Laser-Irradiated Biological Media,” Appl. Opt. 28, 2250–2255 (1989).
[CrossRef] [PubMed]

F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive Index of Some Mammalian Tissues Using a Fiber Optic Cladding Method,” Appl. Opt. 28, 2297–2303 (1989).
[CrossRef] [PubMed]

J. L. Karagiannes, Z. Zhang, B. Grossweiner, L. I. Grossweiner, “Applications of the 1-D Diffusion Approximation to the Optics of Tissues and Tissue Phantoms,” Appl. Opt. 28, 2311–2317 (1989).
[CrossRef] [PubMed]

P. Parsa, S. L. Jacques, N. S. Nishoika, “Optical Properties of Rat Liver Between 350 and 2200 nm,” Appl. Opt. 28, 2325–2330 (1989).
[CrossRef] [PubMed]

J. Photochem. Photobiol. (1)

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light Dosimetry: Status and Prospects,” J. Photochem. Photobiol. 1, 149–167 (1987).
[CrossRef]

Laser Med. Sci. (1)

B. C. Wilson, M. S. Patterson, D. M. Burns, “The Effect of Photosensitizer Concentration in Tissue on the Penetration Depth of Photoactivating Light,” Laser Med. Sci. 1, 235–244 (1986).
[CrossRef]

Lasers Surg. Med. (1)

S. L. Jacques, S. A. Prahl, “Modeling Optical and Thermal Distributions in Tissue During Laser Irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

Med. Phys. (1)

B. C. Wilson, G. Adam, “A Monte Carlo Model for the Absorption and Flux Distributions of Light in Tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Photochem. Photobiol. (2)

W. A. G. Bruls, J. C. van der Leun, “Forward Scattering Properties of Human Epidermal Layers,” Photochem. Photobiol. 40, 231–242 (1984).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect Versus Direct Techniques for the Measurement of the Optical Properties of Tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

Other (4)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

D. R. Doiron, “Photophysics of and Instrumentation for Porphyrin Detection and Activation,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, Eds. (Alan A. Liss, New York, 1984), p. 41.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980), p. 717.

H. C. van de Hulst, Multiple Light Scattering Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 2.

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