Abstract

A simple two-layer tissue reflectance model is described. This work is a continuation of our investigations on modeling reflectance from two-layered tissues that we recently initiated. In the present article, we describe a variation of a two-layer model that assumes a lower absorbing and scattering layer and an upper scattering-only layer. This two-layer configuration is a realistic model for biological tissues in the visible and near-IR spectral ranges, where the upper layer may be an epithelial layer and the lower layer is a vascularized stroma layer. Application of the model yields estimates for tissue parameters, such as the thickness of the upper layer or the absorption properties of the lower layer. These parameters are of great interest for the noninvasive study of a wide range of epithelial biological tissues. The validity range and accuracy of the model are tested on tissue phantoms in both the forward and inverse modes of application.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (1)

2008 (3)

G. Zonios, I. Bassukas, and A. Dimou, “Comparative evaluation of two simple diffuse reflectance models for biological tissue applications,” Appl. Opt. 47, 4965–4973 (2008).
[CrossRef] [PubMed]

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table–based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

M. H. Schmid-Wendtner and D. Dill-Müller, “Ultrasound technology in dermatology,” Semin. Cutan. Med. Surg. 27, 44–51(2008).
[CrossRef] [PubMed]

2007 (2)

2006 (4)

2005 (1)

2004 (1)

2003 (1)

1998 (3)

A’Amar, O.

Alexandrakis, G.

Amelink, A.

Bard, M. P. L.

Bassukas, I.

Bays, R.

Bigio, I. J.

Billet, C.

Burgers, S. A.

Demetropoulos, I. N.

D. G. Papageorgiou, I. N. Demetropoulos, and I. E. Lagaris, “MERLIN-3.0—A multidimensional optimization environment,” Comput. Phys. Commun. 109, 227–249 (1998).
[CrossRef]

Dill-Müller, D.

M. H. Schmid-Wendtner and D. Dill-Müller, “Ultrasound technology in dermatology,” Semin. Cutan. Med. Surg. 27, 44–51(2008).
[CrossRef] [PubMed]

Dimou, A.

Dognitz, N.

El-Batanony, M. H.

Farrell, T. J.

Fawzi, Y. S.

Fawzy, Y. S.

German, D. C.

Giller, C. A.

Hayakawa, C.

Johns, M.

Kadah, Y. M.

Kienle, A.

Kim, A. D.

Lagaris, I. E.

D. G. Papageorgiou, I. N. Demetropoulos, and I. E. Lagaris, “MERLIN-3.0—A multidimensional optimization environment,” Comput. Phys. Commun. 109, 227–249 (1998).
[CrossRef]

Liu, H. L.

Liu, Q.

Mantis, G.

Nguyen, T. H.

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table–based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

Papageorgiou, D. G.

D. G. Papageorgiou, I. N. Demetropoulos, and I. E. Lagaris, “MERLIN-3.0—A multidimensional optimization environment,” Comput. Phys. Commun. 109, 227–249 (1998).
[CrossRef]

Patterson, M. S.

Rajaram, N.

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table–based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

Ramanujam, N.

Reif, R.

Sablong, R.

Schmid-Wendtner, M. H.

M. H. Schmid-Wendtner and D. Dill-Müller, “Ultrasound technology in dermatology,” Semin. Cutan. Med. Surg. 27, 44–51(2008).
[CrossRef] [PubMed]

Sterenborg, H. J. C. M.

Tunnell, J. W.

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table–based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

van Assendelft, O. W.

O. W. van Assendelft, Spectrophotometry of Haemoglobin Derivatives (C. C. Thomas, 1970).

van den Bergh, H.

Venugopalan, V.

Wagnieres, G.

Wiscombe, W. J.

W. J. Wiscombe, “Mie scattering calculations: advances in technique and fast vector speed computer codes,” NCAR Technical Note NCAR/TN-140+STR (National Center for Atmospheric Research, 1979).

Youssef, A.-B. M.

Zheng, H.

Zonios, G.

Appl. Opt. (8)

G. Alexandrakis, T. J. Farrell, and M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. 37, 7401–7409 (1998).
[CrossRef]

A. Kienle, M. S. Patterson, N. Dognitz, R. Bays, G. Wagnieres, and H. van den Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[CrossRef]

Y. S. Fawzi, A.-B. M. Youssef, M. H. El-Batanony, and Y. M. Kadah, “Determination of the optical properties of a two-layer tissue model by detecting photons migrating at progressively increasing depths,” Appl. Opt. 42, 6398–6411(2003).
[CrossRef] [PubMed]

Y. S. Fawzy and H. Zheng, “Determination of scattering volume fraction and particle size distribution in the superficial layer of a turbid medium by using diffuse reflectance spectroscopy,” Appl. Opt. 45, 3902–3912 (2006).
[CrossRef] [PubMed]

Q. Liu and N. Ramanujam, “Sequential estimation of optical properties of a two-layered epithelial tissue model from depth-resolved ultraviolet-visible diffuse reflectance spectra,” Appl. Opt. 45, 4776–4790 (2006).
[CrossRef] [PubMed]

R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46, 7317–7328 (2007).
[CrossRef] [PubMed]

G. Zonios, I. Bassukas, and A. Dimou, “Comparative evaluation of two simple diffuse reflectance models for biological tissue applications,” Appl. Opt. 47, 4965–4973 (2008).
[CrossRef] [PubMed]

G. Mantis and G. Zonios, “Simple two-layer reflectance model for biological tissue applications,” Appl. Opt. 48, 3490–3496(2009).
[CrossRef] [PubMed]

Comput. Phys. Commun. (1)

D. G. Papageorgiou, I. N. Demetropoulos, and I. E. Lagaris, “MERLIN-3.0—A multidimensional optimization environment,” Comput. Phys. Commun. 109, 227–249 (1998).
[CrossRef]

J. Biomed. Opt. (1)

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table–based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Semin. Cutan. Med. Surg. (1)

M. H. Schmid-Wendtner and D. Dill-Müller, “Ultrasound technology in dermatology,” Semin. Cutan. Med. Surg. 27, 44–51(2008).
[CrossRef] [PubMed]

Other (2)

W. J. Wiscombe, “Mie scattering calculations: advances in technique and fast vector speed computer codes,” NCAR Technical Note NCAR/TN-140+STR (National Center for Atmospheric Research, 1979).

O. W. van Assendelft, Spectrophotometry of Haemoglobin Derivatives (C. C. Thomas, 1970).

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Figures (6)

Fig. 1
Fig. 1

Two-layer geometry of biological tissue. The upper layer is typically an epithelial layer with light-scattering properties and negligible absorption, while the lower layer is a vascularized stroma layer rich in connective tissue, which both scatters and absorbs light.

Fig. 2
Fig. 2

(a) Diffuse reflectance as a function of the absorption coefficient for variable upper layer thickness, z, measured on a tissue phantom. Data points represent actual phantom data; solid lines represent fits to the data using Eq. (1). (b) Deviation between the model and the experimental data shown in (a). The reduced scattering coefficient value was μ s = 1.8 mm 1 for both layers.

Fig. 3
Fig. 3

Parameter values for the four parameters a 1 , a 2 , a 3 , and a 4 of Eq. (1). Data points represent actual parameter values determined using the data shown in Fig. 2a, while solid lines represent cubic spline interpolation.

Fig. 4
Fig. 4

Equation (2) can be used to describe the phantom data within a specific limited range of the phantom optical properties (see text). Solid lines represent linear fits to Eq. (2).

Fig. 5
Fig. 5

Percent error between the model [Eq. (1)] and the experimental phantom data for two different values of the reduced scattering coefficient (a) μ s = 0.9 mm 1 and (b) μ s = 2.7 mm 1 .

Fig. 6
Fig. 6

Percent error for the inverse application of the model in determining model parameters on tissue phantoms: (a) absorption coefficient, and (b) upper layer thickness.

Equations (3)

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R = μ s ( a 1 + a 2 2 erfc ( ln ( μ a / a 3 ) 2 a 4 ) ) , erfc ( x ) = 2 π x e t 2 d t .
R = A B log ( μ a ) ,
R = μ s k 1 + k 2 ( z ) μ a .

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