Abstract

We perform a detailed comparison study of Monte Carlo (MC) simulations and discrete-ordinate radiative-transfer (DISORT) calculations of spectral radiances in a 1D coupled air–tissue (CAT) system consisting of horizontal plane-parallel layers. The MC and DISORT models have the same physical basis, including coupling between the air and the tissue, and we use the same air and tissue input parameters for both codes. We find excellent agreement between radiances obtained with the two codes, both above and in the tissue. Our tests cover typical optical properties of skin tissue at the 280, 540, and 650  nm wavelengths. The normalized volume scattering function for internal structures in the skin is represented by the one-parameter Henyey–Greenstein function for large particles and the Rayleigh scattering function for small particles. The CAT-DISORT code is found to be approximately 1000 times faster than the CAT-MC code. We also show that the spectral radiance field is strongly dependent on the inherent optical properties of the skin tissue.

© 2007 Optical Society of America

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    [PubMed]
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2005 (2)

2004 (1)

K. P. Nielsen, L. Zhao, P. Juzenas, K. Stamnes, J. J. Stamnes, and J. Moan, "Reflectance spectra of pigmented and nonpigmented skin in the UV spectral region," Photochem. Photobiol. 80, 450-455 (2004).
[PubMed]

2003 (1)

2001 (2)

1999 (1)

A. R. Degheidy and M. S. A. Krim, "Effects of Fresnel and diffused reflectivities on light transport in a half-space medium," J. Quant. Spectrosc. Radiat. Transfer 61, 751-757 (1999).

1996 (1)

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[PubMed]

1994 (1)

1991 (1)

1989 (1)

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, "A Monte Carlo model of light propagation in tissue," in Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller and D. H. Sliney, eds., in Proc. SPIE IS 5, 102-111 (1989).

1981 (1)

S. Wan, R. Anderson, and J. A. Parrish, "Analytical modeling for the optical properties of the skin with in vitro and in vivo applications," Photochem. Photobiol. 34, 493-499 (1981).
[PubMed]

1941 (1)

L. C. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 93, 70-83 (1941).

1920 (2)

L. Rayleigh, "A re-examination of the light scattered by gases in respect of polarization. I. Experiments on the common gases," Proc. R. Soc. London 97, 435-450 (1920).

L. Rayleigh, "A re-examination of the light scattered by gases in respect of polarization. II. Experiments on helium and argon," Proc. R. Soc. London 98, 57-64 (1920).

1871 (1)

L. Rayleigh, "On the light from the sky, its polarization and colour," Philos. Mag. 41, 107-120, 274-279, 447-454 (1871).

Anderson, R.

S. Wan, R. Anderson, and J. A. Parrish, "Analytical modeling for the optical properties of the skin with in vitro and in vivo applications," Photochem. Photobiol. 34, 493-499 (1981).
[PubMed]

Ben-Letaief, K.

Bilenca, A.

Born, M.

M. Born and E. Wolf. Principles of Optics (Cambridge U. Press, 1980).

Bouma, B.

Chen, B.

Degheidy, A. R.

A. R. Degheidy and M. S. A. Krim, "Effects of Fresnel and diffused reflectivities on light transport in a half-space medium," J. Quant. Spectrosc. Radiat. Transfer 61, 751-757 (1999).

Desjardins, A.

Erga, S. R.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1992).

Frette, Ø.

Gentili, B.

Gjerstad, K. I.

Greenstein, J. L.

L. C. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 93, 70-83 (1941).

Hamre, B.

Henyey, L. C.

L. C. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 93, 70-83 (1941).

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[PubMed]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, "A Monte Carlo model of light propagation in tissue," in Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller and D. H. Sliney, eds., in Proc. SPIE IS 5, 102-111 (1989).

Jiang, S.

Jin, Z.

Juzenas, P.

K. P. Nielsen, L. Zhao, P. Juzenas, K. Stamnes, J. J. Stamnes, and J. Moan, "Reflectance spectra of pigmented and nonpigmented skin in the UV spectral region," Photochem. Photobiol. 80, 450-455 (2004).
[PubMed]

Keijzer, M.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, "A Monte Carlo model of light propagation in tissue," in Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller and D. H. Sliney, eds., in Proc. SPIE IS 5, 102-111 (1989).

Krim, M. S. A.

A. R. Degheidy and M. S. A. Krim, "Effects of Fresnel and diffused reflectivities on light transport in a half-space medium," J. Quant. Spectrosc. Radiat. Transfer 61, 751-757 (1999).

Li, W.

Lotsberg, J. K.

Moan, J.

K. P. Nielsen, L. Zhao, P. Juzenas, K. Stamnes, J. J. Stamnes, and J. Moan, "Reflectance spectra of pigmented and nonpigmented skin in the UV spectral region," Photochem. Photobiol. 80, 450-455 (2004).
[PubMed]

Mobley, C. D.

C. D. Mobley, Light and Water (Cambridge U. Press, 1994).

Morel, A.

Nielsen, K. P.

K. P. Nielsen, L. Zhao, P. Juzenas, K. Stamnes, J. J. Stamnes, and J. Moan, "Reflectance spectra of pigmented and nonpigmented skin in the UV spectral region," Photochem. Photobiol. 80, 450-455 (2004).
[PubMed]

Parrish, J. A.

S. Wan, R. Anderson, and J. A. Parrish, "Analytical modeling for the optical properties of the skin with in vitro and in vivo applications," Photochem. Photobiol. 34, 493-499 (1981).
[PubMed]

Prahl, S. A.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, "A Monte Carlo model of light propagation in tissue," in Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller and D. H. Sliney, eds., in Proc. SPIE IS 5, 102-111 (1989).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1992).

Rayleigh, L.

L. Rayleigh, "A re-examination of the light scattered by gases in respect of polarization. I. Experiments on the common gases," Proc. R. Soc. London 97, 435-450 (1920).

L. Rayleigh, "A re-examination of the light scattered by gases in respect of polarization. II. Experiments on helium and argon," Proc. R. Soc. London 98, 57-64 (1920).

L. Rayleigh, "On the light from the sky, its polarization and colour," Philos. Mag. 41, 107-120, 274-279, 447-454 (1871).

Schmitt, J. M.

Stamnes, J. J.

Stamnes, K.

Svaasand, L. O.

L. O. Svaasand, "Optical dosimetry for direct and interstitial photoradiation therapy of malignant tumors," in Porphyrin Localization and Treatment of Tumors, D.Doiron and C.Gomer, eds. (Wiley, 1984), pp. 91-114.

Tearney, G.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1992).

Thomas, G. E.

G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, 1999).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1992).

Wan, S.

S. Wan, R. Anderson, and J. A. Parrish, "Analytical modeling for the optical properties of the skin with in vitro and in vivo applications," Photochem. Photobiol. 34, 493-499 (1981).
[PubMed]

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[PubMed]

Welch, A. J.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, "A Monte Carlo model of light propagation in tissue," in Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller and D. H. Sliney, eds., in Proc. SPIE IS 5, 102-111 (1989).

Wolf., E.

M. Born and E. Wolf. Principles of Optics (Cambridge U. Press, 1980).

Yan, B.

Zhao, L.

K. P. Nielsen, L. Zhao, P. Juzenas, K. Stamnes, J. J. Stamnes, and J. Moan, "Reflectance spectra of pigmented and nonpigmented skin in the UV spectral region," Photochem. Photobiol. 80, 450-455 (2004).
[PubMed]

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[PubMed]

Appl. Opt. (6)

Astrophys. J. (1)

L. C. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 93, 70-83 (1941).

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[PubMed]

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

J. Quant. Spectrosc. Radiat. Transfer (1)

A. R. Degheidy and M. S. A. Krim, "Effects of Fresnel and diffused reflectivities on light transport in a half-space medium," J. Quant. Spectrosc. Radiat. Transfer 61, 751-757 (1999).

Opt. Express (1)

Philos. Mag. (1)

L. Rayleigh, "On the light from the sky, its polarization and colour," Philos. Mag. 41, 107-120, 274-279, 447-454 (1871).

Photochem. Photobiol. (2)

K. P. Nielsen, L. Zhao, P. Juzenas, K. Stamnes, J. J. Stamnes, and J. Moan, "Reflectance spectra of pigmented and nonpigmented skin in the UV spectral region," Photochem. Photobiol. 80, 450-455 (2004).
[PubMed]

S. Wan, R. Anderson, and J. A. Parrish, "Analytical modeling for the optical properties of the skin with in vitro and in vivo applications," Photochem. Photobiol. 34, 493-499 (1981).
[PubMed]

Proc. R. Soc. London (2)

L. Rayleigh, "A re-examination of the light scattered by gases in respect of polarization. I. Experiments on the common gases," Proc. R. Soc. London 97, 435-450 (1920).

L. Rayleigh, "A re-examination of the light scattered by gases in respect of polarization. II. Experiments on helium and argon," Proc. R. Soc. London 98, 57-64 (1920).

Proc. SPIE IS (1)

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, "A Monte Carlo model of light propagation in tissue," in Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller and D. H. Sliney, eds., in Proc. SPIE IS 5, 102-111 (1989).

Other (5)

C. D. Mobley, Light and Water (Cambridge U. Press, 1994).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1992).

L. O. Svaasand, "Optical dosimetry for direct and interstitial photoradiation therapy of malignant tumors," in Porphyrin Localization and Treatment of Tumors, D.Doiron and C.Gomer, eds. (Wiley, 1984), pp. 91-114.

M. Born and E. Wolf. Principles of Optics (Cambridge U. Press, 1980).

G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, 1999).

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Figures (12)

Fig. 1
Fig. 1

Flowchart of the CAT-MC program.

Fig. 2
Fig. 2

Normalized volume scattering functions in the upper epidermis for λ = 280   nm , λ = 540   nm , and λ = 650   nm .

Fig. 3
Fig. 3

Angle of incidence is θ i = 0 ° . (a), (c), and (e) Show radiances reflected from the skin tissue for λ = 280   nm , λ = 540   nm , and λ = 650   nm , respectively. (b), (d), and (f) Show the relative error between CAT-MC and CAT-DISORT values for (a), (c), and (e), respectively.

Fig. 4
Fig. 4

Angle of incidence is θ i = 0 ° . (a), (c), and (e) Show radiances at a depth of 10   μm for λ = 280   nm , λ = 540   nm , and λ = 650   nm , respectively. (b), (d), and (f) Show the relative error between CAT-MC and CAT-DISORT values for (a), (c), and (e), respectively.

Fig. 5
Fig. 5

Angle of incidence is θ i = 0 ° . (a), (c), and (e) Show radiances at a depth of 30   μm for λ = 280   nm , λ = 540   nm , and λ = 650   nm , respectively. (b), (d), and (f) Show the relative error between CAT-MC and CAT-DISORT values for (a), (c), and (e), respectively.

Fig. 6
Fig. 6

Angle of incidence is θ i = 0 ° . (a), (c), and (e) Show radiances at a depth of 50   μm for λ = 280   nm , λ = 540   nm , and λ = 650   nm , respectively. (b), (d), and (f) Show the relative error between CAT-MC and CAT-DISORT values for (a), (c), and (e), respectively.

Fig. 7
Fig. 7

Angle of incidence is θ i = 0 ° . (a) and (c) Show radiances at a depth of 1.05   mm for λ = 540   nm and λ = 650   nm , respectively. (b) and (d) Show the relative error between CAT-MC and CAT-DISORT values for (a) and (c), respectively.

Fig. 8
Fig. 8

Angle of incidence is θ i = 45 ° . (a), (c), and (e) Show radiances reflected from the skin tissue for λ = 280   nm , λ = 540   nm , and λ = 650   nm , respectively. (b), (d), and (f) Show the relative error between CAT-MC and CAT-DISORT values for (a), (c), and (e), respectively.

Fig. 9
Fig. 9

Angle of incidence is θ i = 45 ° . (a), (c), and (e) Show radiances at a depth of 10   μm for λ = 280   nm , λ = 540   nm , and λ = 650   nm , respectively. (b), (d), and (f) Show the relative error between CAT-MC and CAT- DISORT values for (a), (c), and (e), respectively.

Fig. 10
Fig. 10

Angle of incidence is θ i = 45 ° . (a), (c), and (e) Show radiances at a depth of 30   μm for λ = 280   nm , λ = 540   nm , and λ = 650   nm , respectively. (b), (d), and (f) Show the relative error between CAT-MC and CAT- DISORT values for (a), (c), and (e), respectively.

Fig. 11
Fig. 11

Angle of incidence is θ i = 45 ° . (a), (c), and (e) Show radiances at a depth of 50   μm for λ = 280   nm , λ = 540   nm , and λ = 650   nm , respectively. (b), (d), and (f) Show the relative error between CAT-MC and CAT- DISORT values for (a), (c), and (e), respectively.

Fig. 12
Fig. 12

Angle of incidence is θ i = 45 ° . (a) and (c) Show radiances at a depth of 1.05   mm for λ = 540   nm and λ = 650   nm , respectively. (b) and (d) Show the relative error between CAT-MC and CAT-DISORT values for (a) and (c), respectively.

Tables (3)

Tables Icon

Table 1 Optical Properties of Skin Tissue for λ = 280 nm

Tables Icon

Table 2 Optical Properties of Skin Tissue for λ = 540 nm

Tables Icon

Table 3 Optical Properties of Skin Tissue for λ = 650 nm

Equations (33)

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α = 1 d s ( d Φ α Φ i ) ,
σ = 1 d s ( d Φ σ Φ i ) .
β ( Ω ^ , Ω ^ ) = 1 d s d ω d 2 Φ σ Φ i [ mm 1 sr 1 ] .
1 d s 4 π 1 d ω d 2 Φ σ Φ i  d ω = 1 d s d Φ σ Φ i = σ = 4 π β ( Ω ^ , Ω ^ ) d ω = 0 2 π 0 π β ( cos Θ , ϕ ) sin Θ d Θ d ϕ ,
σ = 2 π 0 π β ( cos Θ ) sin Θ d Θ = 2 π 1 1 β ( μ ) .
p ( cos Θ ) = 4 π β ( cos Θ ) 4 π β ( cos Θ ) d ω = β ( cos Θ ) 1 / 2 [ 1 1 β ( μ ) ] ,
1 4 π 4 π p ( cos Θ ) d ω = 1 .
g = cos Θ = 1 4 π 4 π p ( cos Θ ) cos Θ d ω = 1 2 0 π p ( cos Θ ) cos Θ sin Θ d Θ = 1 2 1 1 p ( μ ) μdμ .
p ( cos Θ ) = 1 g 2 ( 1 + g 2 2 g cos Θ ) 3 / 2 .
p ( cos Θ ) = 3 3 + f ( 1 + f cos 2 Θ ) ,
a σ σ + α ,
d τ = ( σ + α ) d z ,
η 1 = σ s k i n σ s k i n + σ m e l + σ R a y ,
η 2 = σ s k i n + σ m e l σ s k i n + σ m e l + σ R a y ,
Φ = Φ i e τ s .
Φ n o r m a l i z e d = c e c s .
P ( s ) = 0 s c e c s d s = 1 e c s ,
s = ln ( 1 ρ 2 ) c ,
s = ln ( ρ 2 ) c ,
R = 1 2 ( R TE + R TM ) ,
R = 1 2 ( sin 2 ( θ i θ t ) sin 2 ( θ i + θ t ) + tan 2 ( θ i θ t ) tan 2 ( θ i + θ t ) ) ,
μ d L ( τ , μ , ϕ ) d τ = L ( τ , μ , ϕ ) a 4 π 0 2 π d ϕ 1 1 p ( τ , μ , ϕ ;  μ , ϕ ) × L ( τ , μ , ϕ ) d μ S * ( τ , μ , ϕ ) .
cos Θ = cos θ cos θ + sin θ sin θ cos ( ϕ ϕ ) .
S a i r * ( τ , μ , ϕ ) = a ( τ ) F 0 4 π p ( τ , μ 0 , ϕ 0 ;  μ , ϕ ) e τ / μ 0 + a ( τ ) F 0 4 π ρ s ( μ 0 ; n r e l ) × p ( τ , μ 0 , ϕ 0 ;  μ , ϕ ) e ( 2 τ a τ ) / μ 0 ,
S s k i n * ( τ , μ , ϕ ) = a ( τ ) F 0 4 π μ 0 μ 0 n T ( μ 0 ; n r e l ) × p ( τ , μ 0 n , ϕ 0 ;  μ , ϕ ) e τ a / μ 0 e ( τ τ a ) / μ 0 n ,
p ( cos Θ ) = p ( μ , ϕ ;  μ , ϕ ) m = 0 2 N 1 ( 2 δ 0 , m ) × p m ( μ ,  μ ) cos m ( ϕ ϕ ) ,
p m ( μ , μ ) = l = m 2 N 1 ( 2 l + 1 ) χ l Λ l m ( μ ) Λ l m ( μ ) .
Λ l m ( μ ) ( l m ) ! ( l + m ) ! P l m ( μ ) ,
L ( τ , μ , ϕ ) = m = 0 2 N 1 L m ( τ , μ ) cos m ( ϕ ϕ 0 ) ,
d L m ( τ , μ ) d τ = L m ( τ , μ ) S * m ( τ , μ ) a ( τ ) 2 1 1 p m ( τ , μ , μ ) L m ( τ , μ ) ,
N 2 = ROUND ( n r e l 2 N 1 ) ,
L p ( τ , ± μ i a ) = j = 1 N 1 C j p g j p a ( ± μ i a ) e k j p a τ + C j p g j p a ( ± μ i a ) e k j p a τ + U p ( τ , ± μ i a ) ,
L q ( τ , ± μ i t ) = j = 1 N 2 C j q g j q t ( ± μ i t ) e k j q t τ + C j q g j q t ( ± μ i t ) e k j q t τ + U q ( τ , ± μ i t ) ,

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