Abstract

We present an explicit model for the diffuse reflectance due to a collimated beam of light incident normally on layered tissues. This model is derived using the corrected diffusion approximation applied to a layered medium, and it takes the form of a convolution with an explicit kernel and the incident beam profile. This model corrects the standard diffusion approximation over all source–detector separation distances provided the beam is sufficiently wide compared to the scattering mean free path. We validate this model through comparison with Monte Carlo simulations. Then we use this model to estimate the optical properties of an epithelial layer from Monte Carlo simulation data. Using measurements at small source–detector separations and this model, we are able to estimate the absorption coefficient, scattering coefficient, and anisotropy factor of epithelial tissues efficiently with reasonable accuracy.

© 2013 Optical Society of America

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References

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    [CrossRef]
  19. C. Kortun, Y. R. Hijazi, and D. Arifler, J. Biomed. Opt. 13, 034014 (2008).
    [CrossRef]

2012

2011

2008

C. Kortun, Y. R. Hijazi, and D. Arifler, J. Biomed. Opt. 13, 034014 (2008).
[CrossRef]

I. Seo, C. K. Hayakawa, and V. Venugopalan, Med. Phys. 35, 681 (2008).
[CrossRef]

S.-H. Tseng, C. K. Hayakawa, J. Spanier, and A. J. Durkin, IEEE Trans. Biomed. Eng. 55, 335 (2008).
[CrossRef]

2006

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, Int. J. Num. Math. Eng. 65, 383 (2006).

G. Zonios and A. Dimou, Opt. Express 14, 8661 (2006).
[CrossRef]

1998

1997

1992

T. J. Farrell, M. S. Patterson, and B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef]

1990

G. C. Pomraning, J. Quant. Spectrosc. Radiat. Transfer 44, 317 (1990).
[CrossRef]

Alexandrakis, G.

Arifler, D.

C. Kortun, Y. R. Hijazi, and D. Arifler, J. Biomed. Opt. 13, 034014 (2008).
[CrossRef]

Bays, R.

Cotran, R. S.

R. S. Cotran, S. L. Robbins, and V. Kumar, Robbins Pathological Basis of Disease (W. B. Saunders, 1994).

Cuccia, D.

Dimou, A.

Dögnitz, N.

Durkin, A. J.

S.-H. Tseng, C. K. Hayakawa, J. Spanier, and A. J. Durkin, IEEE Trans. Biomed. Eng. 55, 335 (2008).
[CrossRef]

Fareell, T. J.

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef]

Gardner, A.

Guo, L.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. G. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587 (2011).
[CrossRef]

Hanlon, E. G.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. G. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587 (2011).
[CrossRef]

Hayakawa, C.

Hayakawa, C. K.

S.-H. Tseng, C. K. Hayakawa, J. Spanier, and A. J. Durkin, IEEE Trans. Biomed. Eng. 55, 335 (2008).
[CrossRef]

I. Seo, C. K. Hayakawa, and V. Venugopalan, Med. Phys. 35, 681 (2008).
[CrossRef]

Hijazi, Y. R.

C. Kortun, Y. R. Hijazi, and D. Arifler, J. Biomed. Opt. 13, 034014 (2008).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

Itzkan, I.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. G. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587 (2011).
[CrossRef]

Kaipio, J. P.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, Int. J. Num. Math. Eng. 65, 383 (2006).

Kienle, A.

Kim, A. D.

Kolehmainen, V.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, Int. J. Num. Math. Eng. 65, 383 (2006).

Kortun, C.

C. Kortun, Y. R. Hijazi, and D. Arifler, J. Biomed. Opt. 13, 034014 (2008).
[CrossRef]

Kumar, V.

R. S. Cotran, S. L. Robbins, and V. Kumar, Robbins Pathological Basis of Disease (W. B. Saunders, 1994).

Martinelli, M.

Patterson, M. S.

Perelman, L. T.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. G. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587 (2011).
[CrossRef]

Pomraning, G. C.

G. C. Pomraning, J. Quant. Spectrosc. Radiat. Transfer 44, 317 (1990).
[CrossRef]

Prahl, S. A.

S. A. Prahl, in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch and M. J. C. van Gemert, eds. (Plenum, 1995), Chap. 7, pp. 207–231.

Qiu, L.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. G. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587 (2011).
[CrossRef]

Robbins, S. L.

R. S. Cotran, S. L. Robbins, and V. Kumar, Robbins Pathological Basis of Disease (W. B. Saunders, 1994).

Rohde, S. B.

Seo, I.

I. Seo, C. K. Hayakawa, and V. Venugopalan, Med. Phys. 35, 681 (2008).
[CrossRef]

Spanier, J.

M. Martinelli, A. Gardner, D. Cuccia, C. Hayakawa, J. Spanier, and V. Venugopalan, Opt. Express 19, 19627 (2011).
[CrossRef]

S.-H. Tseng, C. K. Hayakawa, J. Spanier, and A. J. Durkin, IEEE Trans. Biomed. Eng. 55, 335 (2008).
[CrossRef]

Tarvainen, T.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, Int. J. Num. Math. Eng. 65, 383 (2006).

Tseng, S.-H.

S.-H. Tseng, C. K. Hayakawa, J. Spanier, and A. J. Durkin, IEEE Trans. Biomed. Eng. 55, 335 (2008).
[CrossRef]

Turzhitsky, V.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. G. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587 (2011).
[CrossRef]

van den Bergh, H.

Vauhkonen, M.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, Int. J. Num. Math. Eng. 65, 383 (2006).

Venugopalan, V.

Vitkin, E.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. G. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587 (2011).
[CrossRef]

Wagnières, G.

Wang, L. V.

L. V. Wang, J. Opt. Soc. Am. A 15, 936 (1998).
[CrossRef]

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

Wilson, B.

T. J. Farrell, M. S. Patterson, and B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef]

Wu, H.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

Zonios, G.

Appl. Opt.

IEEE Trans. Biomed. Eng.

S.-H. Tseng, C. K. Hayakawa, J. Spanier, and A. J. Durkin, IEEE Trans. Biomed. Eng. 55, 335 (2008).
[CrossRef]

Int. J. Num. Math. Eng.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, Int. J. Num. Math. Eng. 65, 383 (2006).

J. Biomed. Opt.

C. Kortun, Y. R. Hijazi, and D. Arifler, J. Biomed. Opt. 13, 034014 (2008).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

G. C. Pomraning, J. Quant. Spectrosc. Radiat. Transfer 44, 317 (1990).
[CrossRef]

Med. Phys.

I. Seo, C. K. Hayakawa, and V. Venugopalan, Med. Phys. 35, 681 (2008).
[CrossRef]

T. J. Farrell, M. S. Patterson, and B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef]

Nat. Commun.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Guo, I. Itzkan, E. G. Hanlon, and L. T. Perelman, Nat. Commun. 2, 587 (2011).
[CrossRef]

Opt. Express

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

R. S. Cotran, S. L. Robbins, and V. Kumar, Robbins Pathological Basis of Disease (W. B. Saunders, 1994).

S. A. Prahl, in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch and M. J. C. van Gemert, eds. (Plenum, 1995), Chap. 7, pp. 207–231.

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Figures (2)

Fig. 1.
Fig. 1.

Comparison of the diffuse reflectance by Monte Carlo simulations (circle symbols), the convolution model (solid curve), and the standard diffusion approximation (dashed curve). The optical properties, taken from Kienle et al. [6], for the top layer are μa1=0.02mm1, μs1=6.5mm1, and g1=0.80, and the optical properties for the bottom layer are μa2=0.01mm1, μs2=6mm1, and g2=0.80. The layer thickness is z0=0.25mm, the refractive index is nrel=1.4, and NA=1.

Fig. 2.
Fig. 2.

Comparison of the diffuse reflectance by Monte Carlo simulations (circle symbols) and the convolution model (solid curve). The optical properties, taken from Kortun et al. [19], for the top layer are μa1=0.12mm1, μs1=1.644mm1, and g1=0.80, and the optical properties for the bottom layer are μa2=0.097mm1, μs2=10.32mm1, and g2=0.80. The layer thickness is z0=0.25mm, the refractive index is nrel=1.4, and NA=1.

Equations (11)

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

R(x,y)=K*f(x,y),
K^=Rc+c[Ra(1+χ)+3κ1γ1Rb(1χ)]a(1+χ)+3κ1bγ1(1χ).
κ12ϕ1μa1ϕ1=0,in0<z<z0,
κ22ϕ2μa2ϕ2=0,inz>z0,
aϕ13κ1bzϕ1=cfonz=0,
ϕ1=ϕ2,andκ1zϕ1=κ2zϕ2,onz=z0.
μψz+μt1ψ=μs111h(μ,μ;g1)ψ(μ,z)dμ,
ψa(μ,0)r(μ)ψa(μ,0)=1r(μ),
ψb(μ,0)r(μ)ψb(μ,0)=μ+μr(μ),
ψc(μ,0)r(μ)ψc(μ,0)=(2π)1δ(μ1),
minμa1,μs1,g112dm22.

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