Abstract

We present a generalized delta-Eddington phase function to simplify the radiative transfer equation to an integral equation with respect to the photon flux vector. The solution of the integral equation is highly accurate to model the photon propagation in the biological tissue over a broad range of optical parameters, especially in the visible light spectrum where the diffusion approximation breaks down. The methodology is validated in the Monte Carlo simulation and can be applied in various optical imaging applications.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 1.
  2. A. J. Welch and M. J. C. van Gemert, Optical and Thermal Response of Laser-Irradiated Tissue (Plenum, 1995).
  3. C. H. Contag and M. H. Bachmann, Annu. Rev. Biomed. Eng. 4, 235 (2002).
    [CrossRef] [PubMed]
  4. J. Ripoll, D. Yessayan, G. Zacharakis, and V. Ntziachristos, J. Opt. Soc. Am. A 22, 546 (2005).
    [CrossRef]
  5. A. D. Klose and E. W. Larsen, J. Comput. Phys. 220, 441 (2006).
    [CrossRef]
  6. J. H. Joseph, W. J. Wiscombe, and J. A. Weinman, J. Atmos. Sci. 33, 2452 (1976).
    [CrossRef]
  7. S. R. Arridge, Inverse Probl. 15, R41 (1999).
    [CrossRef]
  8. F. Natterer and F. Wubbeling, Mathematical Methods in Image Reconstruction (SIAM, 2001).
    [CrossRef]
  9. M. Keijzer, W. M. Star, and P. R. M. Storchi, Appl. Opt. 27, 1820 (1988).
    [CrossRef] [PubMed]
  10. R. A. J. Groenhuis, H. A. Ferwerda, and J. J. Ten Bosch, Appl. Opt. 22, 2456 (1983).
    [CrossRef] [PubMed]
  11. S. S. Rao, The Finite Element Method in Engineering (Butterworth-Heinemann, 1999).

2006 (1)

A. D. Klose and E. W. Larsen, J. Comput. Phys. 220, 441 (2006).
[CrossRef]

2005 (1)

2002 (1)

C. H. Contag and M. H. Bachmann, Annu. Rev. Biomed. Eng. 4, 235 (2002).
[CrossRef] [PubMed]

1999 (1)

S. R. Arridge, Inverse Probl. 15, R41 (1999).
[CrossRef]

1988 (1)

1983 (1)

1976 (1)

J. H. Joseph, W. J. Wiscombe, and J. A. Weinman, J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

Annu. Rev. Biomed. Eng. (1)

C. H. Contag and M. H. Bachmann, Annu. Rev. Biomed. Eng. 4, 235 (2002).
[CrossRef] [PubMed]

Appl. Opt. (2)

Inverse Probl. (1)

S. R. Arridge, Inverse Probl. 15, R41 (1999).
[CrossRef]

J. Atmos. Sci. (1)

J. H. Joseph, W. J. Wiscombe, and J. A. Weinman, J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

J. Comput. Phys. (1)

A. D. Klose and E. W. Larsen, J. Comput. Phys. 220, 441 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

Other (4)

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

A. J. Welch and M. J. C. van Gemert, Optical and Thermal Response of Laser-Irradiated Tissue (Plenum, 1995).

F. Natterer and F. Wubbeling, Mathematical Methods in Image Reconstruction (SIAM, 2001).
[CrossRef]

S. S. Rao, The Finite Element Method in Engineering (Butterworth-Heinemann, 1999).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Comparison between the MC simulation and PA and DA models with the optical parameters μ a = 0.35 mm 1 , μ s = 12.5 mm 1 , h = 0.9 , and f = 0.917 for (a), (b); μ a = 0.20 mm 1 , μ s = 14.5 mm 1 , h = 0.92 , and f = 0.94 for (c), (d); and μ a = 0.016 mm 1 , μ s = 9.0 mm 1 , h = 0.95 , and f = 0.967 for (e), (f). The detector positions were sorted according to increasing order of MC data.

Tables (1)

Tables Icon

Table 1 Optical Parameters Used in the Simulation

Equations (10)

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

[ s + ( μ a + μ s ) ] L ( r , s ) = μ s 4 π L ( r , s ) p ( s , s ) ds + 1 4 π Q ( r ) , r Ω ,
p ( s , s ) = 1 4 π [ ( 1 f ) ( 1 + 3 h s s ) + 2 f δ ( 1 s s ) ] ,
( s + μ ̃ t ) L ( r , s ) = μ ̃ s 4 π [ Φ ( r ) + 3 h s J ( r ) ] + 1 4 π Q ( r ) ,
J ( r ) + μ a Φ ( r ) = Q ( r ) , r Ω .
( s + μ ̃ t ) L ( r , s ) = 1 4 π β ( r ) ( 3 h μ a s ) J ( r ) + 1 4 π [ 1 + β ( r ) ] Q ( r ) ,
L ( r , s ) = 1 4 π 0 R [ β ( r ρ s ) ( 3 h μ a s + ) J ( r ρ s ) ( 1 + β ( r ρ s ) ) Q ( r ρ s ) ] w ( ρ , r , s ) d ρ + L ( r R s , s ) w ( R , r , s ) ,
L ( r R s , s ) = r d L ( r R s , s ) , s n < 0 ,
L ( r R s , s ) r d 4 π J ( r R s ) [ 3 s + ( 2 A 6 n s ) n ] ,
J ( r ) = 1 4 π Ω [ β ( r ) ( + 3 h μ a v ) J ( r ) ( 1 + β ( r ) ) Q ( r ) ] G ( r , r ) v d r r d 4 π Ω [ 3 v + ( 2 A 6 n v ) n ] J ( r ) G ( r , r ) ( n v ) v d r ,
{ J } = M { J } + { Q } ,

Metrics