Abstract

Reflectance measurement of breast tissue is influenced by the underlying chest wall, which is often tilted as seen by the detection probe. We develop an analytical solution of light propagation in a two-layer tissue structure with tilted interface and refractive index difference between the layers. We validate the analytical solution with Monte Carlo simulations and phantom experiments, and a good agreement is seen. The influence of varying the tilting angle of the interface on the reflectance is discussed for two types of layered structures. Further, we apply the developed analytical solution to obtain the optical properties of breast tissue and chest wall from clinical data. Inverse calculation using the developed solution applied to the data obtained from Monte Carlo simulations shows that the optical properties of both layers are obtained with higher accuracy as compared to using a simple two-layer model ignoring the interface tilt. This is expected to improve the accuracy in estimating the optical properties of breast tissue, thus enhancing the accuracy of optical tomography of breast tumors.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2005

C. Xu and Q. Zhu, "Estimation of chest-wall-induced diffused wave distortion with assistance of ultrasound," Appl. Opt. 44, 4255-4264 (2005).
[CrossRef] [PubMed]

Q. Zhu, E. Cronin, A. Currier, H. S. Vine, M. Huang, N. G. Chen, and C. Xu, "Benign versus malignant breast masses: optical differentiation using US to guide optical imaging reconstruction," Radiology 237, 57-66 (2005).
[CrossRef] [PubMed]

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

2004

2003

2002

D. Boas, J. Culver, J. Stott, and A. Dunn, "Three-dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head," Opt. Express 10, 159-170 (2002).
[PubMed]

R. Srinivasan, D. Kumar, and M. Singh, "Optical tissue-equivalent phantoms for medical imaging," Trends Biomater. Artif. Organs. 15, 42-47 (2002).

2001

2000

T. H. Pham, T. Spott, L. O. Svaasand, and B. J. Tromberg, "Quantifying the properties of two-layer turbid media with frequency-domain diffuse reflectance," Appl. Opt. 39, 4733-4745 (2000).
[CrossRef]

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
[CrossRef] [PubMed]

J.-M. Tualle, J. Prat, E. Tinet, and S. Avrillier, "Real-space Green's function calculation for the solution of the diffusion equation in stratified turbid media," J. Opt. Soc. Am. A. 17, 2046-2055 (2000).
[CrossRef]

1998

1997

1996

1995

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

1994

1993

M. Firbank, M. Hiraoka, M. Essenpreis, and D. T. Delpy, "Measurement of the optical properties of the skull in the wavelength range 650-950 nm," Phys. Med. Biol. 38, 503-510 (1993).
[CrossRef] [PubMed]

1992

I. Dayan, S. Havlin, and G. H. Weiss, "Photon migration in a two-layer turbid medium. A diffusion analysis," J. Mod. Opt. 39, 1567-1582 (1992).
[CrossRef]

1990

W. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical property of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

1989

M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light-propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

Alexandrakis, G.

Anderson, E. R.

Avrillier, S.

J.-M. Tualle, J. Prat, E. Tinet, and S. Avrillier, "Real-space Green's function calculation for the solution of the diffusion equation in stratified turbid media," J. Opt. Soc. Am. A. 17, 2046-2055 (2000).
[CrossRef]

Bassi, A.

Bays, R.

Bergh, H.

Bianco, S. D.

F. Martelli, S. D. Bianco, and G. Zaccanti, "Effect of the refractive index mismatch on light propagation through diffusive layered media," Phys. Rev. E 70, 011907 (2004).
[CrossRef]

F. Martelli, S. D. Bianco, and G. Zaccanti, "Procedure for retrieving the optical properties of a two-layered medium from time-resolved reflectance measurements," Opt. Lett. 28, 1236-1238 (2003).
[CrossRef] [PubMed]

Boas, D.

Bolster, M. B.

Brenner, M.

Brooksby, B.

H. Deghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. Paulsen, "The effects of internal refractive index variation in near-infrared optical tomography: a finite element modeling approach," Phys. Med. Biol. 48, 2713-2727 (2003).
[CrossRef]

Butler, J.

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
[CrossRef] [PubMed]

Cerussi, A.

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
[CrossRef] [PubMed]

Chance, B.

Chen, N.

Chen, N. G.

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

Q. Zhu, E. Cronin, A. Currier, H. S. Vine, M. Huang, N. G. Chen, and C. Xu, "Benign versus malignant breast masses: optical differentiation using US to guide optical imaging reconstruction," Radiology 237, 57-66 (2005).
[CrossRef] [PubMed]

N. G. Chen, P. Guo, S. Yan, D. Piao, and Q. Zhu, "Simultaneous near infrared diffusive light and ultrasound imaging," Appl. Opt. 40, 6367-6280 (2001).
[CrossRef]

Cheong, W.

W. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical property of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Cope, M.

Coquoz, O.

Cronin, E.

Q. Zhu, E. Cronin, A. Currier, H. S. Vine, M. Huang, N. G. Chen, and C. Xu, "Benign versus malignant breast masses: optical differentiation using US to guide optical imaging reconstruction," Radiology 237, 57-66 (2005).
[CrossRef] [PubMed]

Cubeddu, R.

Culver, J.

Currier, A.

Q. Zhu, E. Cronin, A. Currier, H. S. Vine, M. Huang, N. G. Chen, and C. Xu, "Benign versus malignant breast masses: optical differentiation using US to guide optical imaging reconstruction," Radiology 237, 57-66 (2005).
[CrossRef] [PubMed]

Dayan, I.

I. Dayan, S. Havlin, and G. H. Weiss, "Photon migration in a two-layer turbid medium. A diffusion analysis," J. Mod. Opt. 39, 1567-1582 (1992).
[CrossRef]

Deghani, H.

H. Deghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. Paulsen, "The effects of internal refractive index variation in near-infrared optical tomography: a finite element modeling approach," Phys. Med. Biol. 48, 2713-2727 (2003).
[CrossRef]

Del Bianco, S.

Delpy, D. T.

S. J. Matcher, M. Cope, and D. T. Delpy, "In vivo measurements of the wavelength dependence of tissue-scattering coefficients between 760 and 900 nm measured with time-resolved spectroscopy," Appl. Opt. 36, 386-396 (1997).
[CrossRef] [PubMed]

M. Firbank, M. Hiraoka, M. Essenpreis, and D. T. Delpy, "Measurement of the optical properties of the skull in the wavelength range 650-950 nm," Phys. Med. Biol. 38, 503-510 (1993).
[CrossRef] [PubMed]

Dögnitz, N.

Dunn, A.

El-Batanony, M. H.

Espinoza, J.

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
[CrossRef] [PubMed]

Essenpreis, M.

T. J. Farrel, M. S. Patterson, and M. Essenpreis, "Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry," Appl. Opt. 37, 1958-1972 (1998).
[CrossRef]

M. Firbank, M. Hiraoka, M. Essenpreis, and D. T. Delpy, "Measurement of the optical properties of the skull in the wavelength range 650-950 nm," Phys. Med. Biol. 38, 503-510 (1993).
[CrossRef] [PubMed]

Farrel, T. J.

Farrell, T. J.

Fawzi, Y. S.

Feng, T. C.

Firbank, M.

M. Firbank, M. Hiraoka, M. Essenpreis, and D. T. Delpy, "Measurement of the optical properties of the skull in the wavelength range 650-950 nm," Phys. Med. Biol. 38, 503-510 (1993).
[CrossRef] [PubMed]

Fishkin, J. B.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, 1988).

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light-propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, S. T. Flock, and J. D. Moulton, "The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range," in Light in Biology and Medicine, R.H.Douglas, J.Moan, and F.Doll'Acqua, eds. (Plenum, 1988), Vol. 1, pp. 45-52.
[CrossRef]

Guo, P.

Haskell, R. C.

Havlin, S.

I. Dayan, S. Havlin, and G. H. Weiss, "Photon migration in a two-layer turbid medium. A diffusion analysis," J. Mod. Opt. 39, 1567-1582 (1992).
[CrossRef]

Hegde, P.

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

Hibst, R.

Hiraoka, M.

M. Firbank, M. Hiraoka, M. Essenpreis, and D. T. Delpy, "Measurement of the optical properties of the skull in the wavelength range 650-950 nm," Phys. Med. Biol. 38, 503-510 (1993).
[CrossRef] [PubMed]

Huang, M.

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

Q. Zhu, E. Cronin, A. Currier, H. S. Vine, M. Huang, N. G. Chen, and C. Xu, "Benign versus malignant breast masses: optical differentiation using US to guide optical imaging reconstruction," Radiology 237, 57-66 (2005).
[CrossRef] [PubMed]

M. Huang and Q. Zhu, "A two-layer model for NIR breast imaging with the assistance of ultrasound," in Proc. SPIE 5693, 121-128 (2005).

Iftimia, N.

Jacques, S. L.

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

Jagjivan, B.

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

Jiang, H.

Kadah, Y. M.

Kane, M.

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

Key, L. L.

Kienle, A.

Kumar, D.

R. Srinivasan, D. Kumar, and M. Singh, "Optical tissue-equivalent phantoms for medical imaging," Trends Biomater. Artif. Organs. 15, 42-47 (2002).

Kurtzman, S.

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

Q. Zhu, N. Chen, and S. Kurtzman, "Imaging tumor angiogenesis by use of combined near-infrared diffusive light and ultrasound," Opt. Lett. 28, 337-339 (2003).
[CrossRef] [PubMed]

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead sinplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).

Lanning, R.

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
[CrossRef] [PubMed]

Lilge, L.

Martelli, F.

Matcher, S. J.

McAdams, M.

Moulton, J. D.

B. C. Wilson, M. S. Patterson, S. T. Flock, and J. D. Moulton, "The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range," in Light in Biology and Medicine, R.H.Douglas, J.Moan, and F.Doll'Acqua, eds. (Plenum, 1988), Vol. 1, pp. 45-52.
[CrossRef]

Patterson, M. J.

Patterson, M. S.

T. J. Farrel, M. S. Patterson, and M. Essenpreis, "Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry," Appl. Opt. 37, 1958-1972 (1998).
[CrossRef]

A. Kienle, M. S. Patterson, N. Dögnitz, R. Bays, G. Wagnièrese, and H. Bergh, "Noninvasive determination of the optical properties of two-layered turbid media," Appl. Opt. 37, 779-791, (1998).
[CrossRef]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, "Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light-propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, S. T. Flock, and J. D. Moulton, "The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range," in Light in Biology and Medicine, R.H.Douglas, J.Moan, and F.Doll'Acqua, eds. (Plenum, 1988), Vol. 1, pp. 45-52.
[CrossRef]

Paulsen, K.

H. Deghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. Paulsen, "The effects of internal refractive index variation in near-infrared optical tomography: a finite element modeling approach," Phys. Med. Biol. 48, 2713-2727 (2003).
[CrossRef]

Pham, T.

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
[CrossRef] [PubMed]

Pham, T. H.

Piao, D.

Pifferi, A.

Pogue, B. W.

H. Deghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. Paulsen, "The effects of internal refractive index variation in near-infrared optical tomography: a finite element modeling approach," Phys. Med. Biol. 48, 2713-2727 (2003).
[CrossRef]

Prahl, S. A.

W. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical property of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Prat, J.

J.-M. Tualle, J. Prat, E. Tinet, and S. Avrillier, "Real-space Green's function calculation for the solution of the diffusion equation in stratified turbid media," J. Opt. Soc. Am. A. 17, 2046-2055 (2000).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, 1988).

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead sinplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).

Shah, N.

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
[CrossRef] [PubMed]

Singh, M.

R. Srinivasan, D. Kumar, and M. Singh, "Optical tissue-equivalent phantoms for medical imaging," Trends Biomater. Artif. Organs. 15, 42-47 (2002).

Spott, T.

Srinivasan, R.

R. Srinivasan, D. Kumar, and M. Singh, "Optical tissue-equivalent phantoms for medical imaging," Trends Biomater. Artif. Organs. 15, 42-47 (2002).

Steiner, R.

Stott, J.

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B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
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Tannenbaum, S.

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

Taroni, P.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, 1988).

Tinet, E.

J.-M. Tualle, J. Prat, E. Tinet, and S. Avrillier, "Real-space Green's function calculation for the solution of the diffusion equation in stratified turbid media," J. Opt. Soc. Am. A. 17, 2046-2055 (2000).
[CrossRef]

Torricelli, A.

Tromberg, B.

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
[CrossRef] [PubMed]

Tromberg, B. J.

Tsay, T. T.

Tualle, J.-M.

J.-M. Tualle, J. Prat, E. Tinet, and S. Avrillier, "Real-space Green's function calculation for the solution of the diffusion equation in stratified turbid media," J. Opt. Soc. Am. A. 17, 2046-2055 (2000).
[CrossRef]

Vettering, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, 1988).

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Q. Zhu, E. Cronin, A. Currier, H. S. Vine, M. Huang, N. G. Chen, and C. Xu, "Benign versus malignant breast masses: optical differentiation using US to guide optical imaging reconstruction," Radiology 237, 57-66 (2005).
[CrossRef] [PubMed]

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H. Deghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. Paulsen, "The effects of internal refractive index variation in near-infrared optical tomography: a finite element modeling approach," Phys. Med. Biol. 48, 2713-2727 (2003).
[CrossRef]

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[CrossRef]

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[CrossRef]

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A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, "Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996).
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[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light-propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, S. T. Flock, and J. D. Moulton, "The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range," in Light in Biology and Medicine, R.H.Douglas, J.Moan, and F.Doll'Acqua, eds. (Plenum, 1988), Vol. 1, pp. 45-52.
[CrossRef]

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead sinplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead sinplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).

Wyman, D. R.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light-propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

Xu, C.

Q. Zhu, E. Cronin, A. Currier, H. S. Vine, M. Huang, N. G. Chen, and C. Xu, "Benign versus malignant breast masses: optical differentiation using US to guide optical imaging reconstruction," Radiology 237, 57-66 (2005).
[CrossRef] [PubMed]

C. Xu and Q. Zhu, "Estimation of chest-wall-induced diffused wave distortion with assistance of ultrasound," Appl. Opt. 44, 4255-4264 (2005).
[CrossRef] [PubMed]

Xu, Y.

Yan, S.

Youssef, A. M.

Zaccanti, G.

Zarfos, K.

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

Zheng, L.

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

Zhu, Q.

Q. Zhu, E. Cronin, A. Currier, H. S. Vine, M. Huang, N. G. Chen, and C. Xu, "Benign versus malignant breast masses: optical differentiation using US to guide optical imaging reconstruction," Radiology 237, 57-66 (2005).
[CrossRef] [PubMed]

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

C. Xu and Q. Zhu, "Estimation of chest-wall-induced diffused wave distortion with assistance of ultrasound," Appl. Opt. 44, 4255-4264 (2005).
[CrossRef] [PubMed]

Q. Zhu, N. Chen, and S. Kurtzman, "Imaging tumor angiogenesis by use of combined near-infrared diffusive light and ultrasound," Opt. Lett. 28, 337-339 (2003).
[CrossRef] [PubMed]

N. G. Chen, P. Guo, S. Yan, D. Piao, and Q. Zhu, "Simultaneous near infrared diffusive light and ultrasound imaging," Appl. Opt. 40, 6367-6280 (2001).
[CrossRef]

M. Huang and Q. Zhu, "A two-layer model for NIR breast imaging with the assistance of ultrasound," in Proc. SPIE 5693, 121-128 (2005).

Appl. Opt.

J. B. Fishkin, O. Coquoz, E. R. Anderson, M. Brenner, and B. J. Tromberg, "Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject," Appl. Opt. 36, 10-20 (1997).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, "Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996).
[CrossRef] [PubMed]

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

T. J. Farrel, M. S. Patterson, and M. Essenpreis, "Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry," Appl. Opt. 37, 1958-1972 (1998).
[CrossRef]

T. H. Pham, T. Spott, L. O. Svaasand, and B. J. Tromberg, "Quantifying the properties of two-layer turbid media with frequency-domain diffuse reflectance," Appl. Opt. 39, 4733-4745 (2000).
[CrossRef]

G. Alexandrakis, T. J. Farrell, and M. J. Patterson, "Accuracy of 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. Dögnitz, R. Bays, G. Wagnièrese, and H. Bergh, "Noninvasive determination of the optical properties of two-layered turbid media," Appl. Opt. 37, 779-791, (1998).
[CrossRef]

C. Xu and Q. Zhu, "Estimation of chest-wall-induced diffused wave distortion with assistance of ultrasound," Appl. Opt. 44, 4255-4264 (2005).
[CrossRef] [PubMed]

N. G. Chen, P. Guo, S. Yan, D. Piao, and Q. Zhu, "Simultaneous near infrared diffusive light and ultrasound imaging," Appl. Opt. 40, 6367-6280 (2001).
[CrossRef]

M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
[CrossRef] [PubMed]

S. J. Matcher, M. Cope, and D. T. Delpy, "In vivo measurements of the wavelength dependence of tissue-scattering coefficients between 760 and 900 nm measured with time-resolved spectroscopy," Appl. Opt. 36, 386-396 (1997).
[CrossRef] [PubMed]

Comput. Methods Programs Biomed.

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

IEEE J. Quantum Electron.

W. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical property of biological tissues," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

IEEE Trans. Biomed. Eng.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light-propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

J. Mod. Opt.

I. Dayan, S. Havlin, and G. H. Weiss, "Photon migration in a two-layer turbid medium. A diffusion analysis," J. Mod. Opt. 39, 1567-1582 (1992).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. A.

J.-M. Tualle, J. Prat, E. Tinet, and S. Avrillier, "Real-space Green's function calculation for the solution of the diffusion equation in stratified turbid media," J. Opt. Soc. Am. A. 17, 2046-2055 (2000).
[CrossRef]

Neoplasia

B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, "Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000).
[CrossRef] [PubMed]

Q. Zhu, S. Kurtzman, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, "Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers," Neoplasia 7, 263-270 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

H. Deghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. Paulsen, "The effects of internal refractive index variation in near-infrared optical tomography: a finite element modeling approach," Phys. Med. Biol. 48, 2713-2727 (2003).
[CrossRef]

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[CrossRef] [PubMed]

Phys. Rev. E

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[CrossRef]

Radiology

Q. Zhu, E. Cronin, A. Currier, H. S. Vine, M. Huang, N. G. Chen, and C. Xu, "Benign versus malignant breast masses: optical differentiation using US to guide optical imaging reconstruction," Radiology 237, 57-66 (2005).
[CrossRef] [PubMed]

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R. Srinivasan, D. Kumar, and M. Singh, "Optical tissue-equivalent phantoms for medical imaging," Trends Biomater. Artif. Organs. 15, 42-47 (2002).

Other

B. C. Wilson, M. S. Patterson, S. T. Flock, and J. D. Moulton, "The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range," in Light in Biology and Medicine, R.H.Douglas, J.Moan, and F.Doll'Acqua, eds. (Plenum, 1988), Vol. 1, pp. 45-52.
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, 1988).

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead sinplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).

M. Huang and Q. Zhu, "A two-layer model for NIR breast imaging with the assistance of ultrasound," in Proc. SPIE 5693, 121-128 (2005).

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Figures (8)

Fig. 1
Fig. 1

Schematic of a two-layer tissue structure with tilted interface. RM is the normal to the tilted surface, and we assume n 2 > n 1.

Fig. 2
Fig. 2

Comparison of analytical and MC calculations for a two-layer structure. (a) Amplitude plots and (b) phase plots for case 1, μ a 1 = 0.05 cm−1, μ s 1′ = 6 cm−1, μ a 2 = 0.02 cm−1, μ s 2′ = 15 cm−1, and case 2, μ a 1 = 0.05 cm−1, μ s 1′ = 6 cm−1, μ a 2 = 0.08 cm−1, μ s 2′ = 30 cm−1. For the tilted case the first layer maximum thickness is 2 cm with a 13° tilting angle at the interface.

Fig. 3
Fig. 3

Phantom measurements compared with analytical results for tilted and nontilted interface. (a) Amplitude plots and (b) phase plots.

Fig. 4
Fig. 4

Simulated (a) amplitude and (b) phase plots for two-layer structures with varying tilting angles (circle, 4°; star, 8°; diamond, 11°) for case 1, μ a 1 = 0.1 cm−1, μ s 1′ = 6, μ a 2 = 0.01 cm−1, μ s 2′ = 14 cm−1, and case 2, μ a 1 = 0.05 cm−1, μ s 1′ = 6 cm−1, μ a 2 = 0.09 cm−1, μ s 2′ = 14 cm−1. The dashed line and the solid line represent reflectance at zero-degree tilt for case 1 and case 2, respectively.

Fig. 5
Fig. 5

Estimated absorption coefficient of (a) the first layer (μ a 1) and (b) the second layer (μ a 2) determined by nonlinear regression of the analytical solution to MC data plotted versus the true value of the absorption coefficient of the second layer (μ a 2). Parameters chosen for MC simulations are a maximum layer thickness of 1.2 cm, an interface tilt of 7°, μ a 1 = 0.05 cm−1, μ s 1′ = 5 cm−1, μ s 2′ = 10 cm−1, and μ a 2 varying from 0.02 to 0.11 cm−1. The solid line indicates the true value, stars represent the estimated values considering the interface tilt, and squares represent the estimated values ignoring the interface tilt.

Fig. 6
Fig. 6

Estimated reduced scattering coefficient of (a) the first layer (μ s 1′) and (b) the second layer (μ s 2′) determined by nonlinear regression of the analytical solution to MC data plotted versus the true value of reduced scattering coefficient of the second layer (μ s 2′). Parameters chosen for MC simulations are a maximum layer thickness of 1.2 cm, an interface tilt of 7°, μ a 1 = 0.05 cm−1, μ s 1′ = 5 cm−1, μ a 2 = 0.08 cm−1, and μ s 2′ varying from 8 to 14 cm−1. The solid line indicates the true value, stars represent the estimated values considering the interface tilt, and squares represent the estimated values ignoring the interface tilt.

Fig. 7
Fig. 7

(Color online) Ultrasound image obtained from a 52-year-old patient with an effective breast tissue thickness of 1.25 cm at the breast tissue–chest wall interface marked by the array of white arrows.

Fig. 8
Fig. 8

Ultrasound image obtained from a 21-year-old patient showing a maximum breast tissue thickness of about 1.75 cm reducing to 1 cm with a tilt angle of 6°. The breast tissue–chest wall interface is marked by the array of white arrows. The horizontal scale is 6.5 cm.

Tables (3)

Tables Icon

Table 1 Estimated Background Absorption and Reduced Scattering Coefficient of Breast Tissue and Chest Wall a

Tables Icon

Table 2 Estimated Background Absorption and Reduced Scattering Coefficient of Breast Tissue and Chest Wall a

Tables Icon

Table 3 Estimated Background Absorption and Reduced Scattering Coefficient of Breast Tissue and Chest Wall a

Equations (10)

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

D 1 2 Φ 1 ( r , ω ) ( μ a 1 + j ω ν m ) Φ 1 ( r , ω ) = δ ( x , y , z z 0 ) exp ( j ω ν i r ) , 0 z 1 ,
D 2 2 Φ 2 ( r , ω ) ( μ a 2 + j ω ν m ) Φ 2 ( r , ω ) = 0 , l z ,
Φ 1 ( z = z b , r ) = 0 ,
Φ 1 ( r ) = 0 ,
Φ 1 ( l , r ) Φ 2 ( l , r ) = n 1     2 n 2     2 ,
D 1 Φ 1 ( z ) z | z = l cos ( θ 1 ) = D 2 Φ 2 ( z ) z | z = l + cos ( θ 2 ) .
ϕ i ( z , s 1 , s 2 ) = Φ i ( x , y , z ) × exp [ i ( s 1 x + s 2 y ) ] d x d y .
ϕ 1 ( z , s ) = sinh [ α 1 ( z b + z 0 ) ] D 1 α 1 D 1 α 1 ϕ cosh [ α 1 ( l z ) ] + ( n 2 / n 1 ) 2 D 2 α 2 sinh [ α 1 ( l z ) ] D 1 α 1 ϕ cosh [ α 1 ( l + z b ) ] + ( n 2 / n 1 ) 2 D 2 α 2 sinh [ α 1 ( l + z b ) ]    sinh [ α 1 ( z 0 z ) ] D 1 α 1 , 0 z < z 0 ,
Φ 1 ( ρ , z = 0 ) = 1 2 π 0 ϕ 1 ( z = 0 ) s I 0 ( s ρ ) d s ,
R ( ρ ) = 2 π d Ω [ 1 R fres ( θ ) ] 1 4 π [ Φ 1 ( ρ , z = 0 ) + 3 D 1 Φ 1 ( ρ , z = 0 ) z cos ( θ 1 ) ] cos ( θ ) ,

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