Abstract

We investigated the dependence of the diffusion coefficient on the absorption coefficient by studying the propagation of light emitted by an isotropic source in an infinitely extended medium. Comparisons with both experimental and numerical results showed that the diffusion equation gives a better description of photon migration when the diffusion coefficient is assumed to be independent of absorption.

© 1997 Optical Society of America

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  1. K. Furutsu, J. Opt. Soc. Am. 70, 360 (1980).
    [CrossRef]
  2. M. Patterson, B. Chance, and B. C. Wilson, Appl. Opt. 28, 2331 (1989).
    [CrossRef] [PubMed]
  3. S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
    [CrossRef] [PubMed]
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), p. 175.
    [CrossRef]
  5. E. P. Zege, A. I. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991), pp. 20, 72.
  6. R. A. Groenhuis, H. A. Ferwerda, and J. J. ten Bosch, Appl. Opt. 22, 2456 (1983).
    [CrossRef] [PubMed]
  7. K. Furutsu and Y. Yamada, Phys. Rev. E 50, 3634 (1994).
    [CrossRef]
  8. D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation: I. theory,” Appl. Opt. (to be published).
  9. V. G. Kolinko, F. F. M. de Mul, J. Greve, and A. V. Priezzhev, Appl. Opt. 35, 4541 (1996).
    [CrossRef] [PubMed]
  10. S. Kumar, K. Mitra, and Y. Yamada, Appl. Opt. 35, 3372 (1996).
    [CrossRef] [PubMed]
  11. P. Bruscaglioni and G. Zaccanti, in Scattering in Volumes and Surfaces, M. Nieto Vesperinas and J. C. Dainty, eds. (Elsevier, New York, 1990), pp. 53–71.
  12. G. Zaccanti, Appl. Opt. 30, 2031 (1991).
    [CrossRef] [PubMed]
  13. B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
    [CrossRef]
  14. H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, and M. J. C. van Gemert, Appl. Opt. 30, 4507 (1991).
    [CrossRef] [PubMed]

1996

1994

K. Furutsu and Y. Yamada, Phys. Rev. E 50, 3634 (1994).
[CrossRef]

1992

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

1991

1989

1986

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

1983

1980

Arridge, S. R.

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

Bruscaglioni, P.

P. Bruscaglioni and G. Zaccanti, in Scattering in Volumes and Surfaces, M. Nieto Vesperinas and J. C. Dainty, eds. (Elsevier, New York, 1990), pp. 53–71.

Burns, D. M.

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

Chance, B.

Contini, D.

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation: I. theory,” Appl. Opt. (to be published).

Cope, M.

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

de Mul, F. F. M.

Delpy, D. T.

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

Ferwerda, H. A.

Furutsu, K.

K. Furutsu and Y. Yamada, Phys. Rev. E 50, 3634 (1994).
[CrossRef]

K. Furutsu, J. Opt. Soc. Am. 70, 360 (1980).
[CrossRef]

Greve, J.

Groenhuis, R. A.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), p. 175.
[CrossRef]

Ivanov, A. I.

E. P. Zege, A. I. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991), pp. 20, 72.

Katsev, I. L.

E. P. Zege, A. I. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991), pp. 20, 72.

Kolinko, V. G.

Kumar, S.

Martelli, F.

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation: I. theory,” Appl. Opt. (to be published).

Mitra, K.

Moes, C. J. M.

Patterson, M.

Patterson, M. S.

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

Prahl, S. A.

Priezzhev, A. V.

ten Bosch, J. J.

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Wilson, B. C.

M. Patterson, B. Chance, and B. C. Wilson, Appl. Opt. 28, 2331 (1989).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

Yamada, Y.

Zaccanti, G.

G. Zaccanti, Appl. Opt. 30, 2031 (1991).
[CrossRef] [PubMed]

P. Bruscaglioni and G. Zaccanti, in Scattering in Volumes and Surfaces, M. Nieto Vesperinas and J. C. Dainty, eds. (Elsevier, New York, 1990), pp. 53–71.

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation: I. theory,” Appl. Opt. (to be published).

Zege, E. P.

E. P. Zege, A. I. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991), pp. 20, 72.

Appl. Opt.

J. Opt. Soc. Am.

Lasers Med. Sci.

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

Phys. Med. Biol.

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

Phys. Rev. E

K. Furutsu and Y. Yamada, Phys. Rev. E 50, 3634 (1994).
[CrossRef]

Other

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation: I. theory,” Appl. Opt. (to be published).

P. Bruscaglioni and G. Zaccanti, in Scattering in Volumes and Surfaces, M. Nieto Vesperinas and J. C. Dainty, eds. (Elsevier, New York, 1990), pp. 53–71.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), p. 175.
[CrossRef]

E. P. Zege, A. I. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, New York, 1991), pp. 20, 72.

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Figures (3)

Fig. 1
Fig. 1

Examples of experimental results obtained for a suspension of polystyrene spheres (diameter 0.798 µm, μs=1.25 µm-1): lnrϕr is shown versus r for different values of μa. The straight lines represent the linear best fits of the experimental results.

Fig. 2
Fig. 2

μa/D obtained from the square of the slope of lnrϕr for measurements carried out on polystyrene and on Liposyne 10%. The linear dependence of μa/D on μa indicates that D does not depend on absorption. The curves expected from the DE for the values of μa and μs that are considered when the μa-dependent (dotted lines), and the μa-independent (solid lines) diffusion coefficient is assumed are also shown.

Fig. 3
Fig. 3

Results of Monte Carlo simulations: (a) Time-resolved irradiance at a distance r=10 mm (solid curve) for a medium with μs=1 mm-1 and μa=0.1 mm-1. The results expected from the DE when D1 (dotted curve) or D2 (dashed curve) is assumed are also shown. (b) Percent differences between the Monte Carlo results and the DE when both D1 (dotted curve) and D2 (dashed curve) are considered.

Equations (7)

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

1vt-D2+μaϕr, t=δrδt,
ϕr, t=θtv exp-r24Dvt-μavt4πDvt3/2,
θt=1for t00for t<0.
D1=13μs+μa,
D2=13μs.
ϕr=14πDrexp-rμa/D,
lnrϕr=ln14πD-rμa/D.

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