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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References

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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)

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]

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]

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]

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)

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]

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]

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]

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]

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]

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)

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

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

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.

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

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Figures (6)

Fig. 1
Fig. 1

Experimental arrangement. Laser light delivered by the optical fiber is collimated and incident on the tissue sample. The front face of the tissue contacts a sugar solution of approximately the same water content. The needle optical probe is inserted at the rear face through a Lucite plate.

Fig. 2
Fig. 2

Semilogarithmic plot of the optical signals at 633 nm in the gelatin phantom vs the square radius at various depths. A Gaussian function is linear on this plot. The upper light shows the incident beam profiles at the front face of the tissue.

Fig. 3
Fig. 3

Semilogarithmic dependence of the radial averaged flux density on depth calculated by numerical integration of the experimental data: A, gelatin phantom, 633 nm; B, potato tuber, 1064 nm; C, bovine muscle, 633 nm. The lines are normalized to 100 at z = 0 with slope κd from Table I.

Fig. 4
Fig. 4

Experimental flux density profile for bovine muscle at 633 mm. The vertical scale is arbitrary

Fig. 5
Fig. 5

Experimental flux density profile for bovine muscle at 1064 nm. The vertical scale is arbitrary.

Fig. 6
Fig. 6

Calculated flux density profile for bovine muscle at 1064 nm based on chi-square minimization of the data fit to Eqs. (2) and (5). The vertical scale is the same as in Fig. 5.

Tables (1)

Tables Icon

Table I Analysis of Flux Density Profiles

Equations (11)

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ϕ ( z ) = 0 r ϕ ( r , z ) d r ,
2 ϕ ( r , z ) / r 2 + ( 1 / r ) ϕ ( r , z ) / r + 2 ϕ ( r , z ) / z 2 - κ d 2 ϕ ( r , z ) = - λ A exp ( - r 2 / b 0 2 ) exp ( - z / z 0 ) ,
ϕ ( r , z ) = 0 k J 0 ( k r ) f ( k , z ) d k .
h ( r , z ) = 0 k J 0 ( k r ) g ( k , z ) d k .
2 f / z 2 - ( k 2 + κ d 2 ) f = - ( 2 λ / b 0 2 ) A exp ( - z / z 0 ) exp ( - b 0 2 k 2 / 4 ) ,
f ( k , z ) = ( 1 / 2 ) A b 0 2 exp ( - k 2 b 0 2 / 4 ) { exp ( - ( k 2 + κ d 2 ) + λ [ exp ( - z / z 0 ) - exp ( - z ( k 2 + κ d 2 ) ] ÷ [ ( k 2 + κ d 2 ) - 1 / z 0 2 ] } .
ϕ ( 0 , z ) = ϕ 0 [ exp ( - κ d z ) - π ( z / b ) exp ( z 2 / b 2 + κ d 2 b 0 2 / 4 ) × erfc ( z / b 0 + κ d b o / 2 ) } .
ϕ ( 0 , z ) = ϕ 0 exp ( - κ d z ) ( κ d b 0 / 2 ) / [ κ d b 0 / 2 + z / b 0 ] .
ϕ ( z ) = ϕ ( 0 ) exp ( - κ d z ) ,
r 2 = 0 r 3 ϕ ( r , z ) d r / ϕ ( z ) .
r 2 = r 2 0 + 2 z / κ d .

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