Abstract

A scaling Monte Carlo method has been developed to calculate diffuse reflectance from multilayered media with a wide range of optical properties in the ultraviolet–visible wavelength range. This multilayered scaling method employs the photon trajectory information generated from a single baseline Monte Carlo simulation of a homogeneous medium to scale the exit distance and exit weight of photons for a new set of optical properties in the multilayered medium. The scaling method is particularly suited to simulating diffuse reflectance spectra or creating a Monte Carlo database to extract optical properties of layered media, both of which are demonstrated in this paper. Particularly, it was found that the root-mean-square error (RMSE) between scaled diffuse reflectance, for which the anisotropy factor and refractive index in the baseline simulation were, respectively, 0.9 and 1.338, and independently simulated diffuse reflectance was less than or equal to 5% for source–detector separations from 200to1500μm when the anisotropy factor of the top layer in a two-layered epithelial tissue model was varied from 0.8 to 0.99; in contrast, the RMSE was always less than 5% for all separations (from 0to1500μm) when the anisotropy factor of the bottom layer was varied from 0.7 to 0.99. When the refractive index of either layer in the two-layered tissue model was varied from 1.3 to 1.4, the RMSE was less than 10%. The scaling method can reduce computation time by more than 2 orders of magnitude compared with independent Monte Carlo simulations.

© 2007 Optical Society of America

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2006 (3)

2005 (4)

W. Verkruysse, R. Zhang, B. Choi, G. Lucassen, L. O. Svaasand, and J. S. Nelson, "A library based fitting method for visual reflectance spectroscopy of human skin," Phys. Med. Biol. 50, 57-70 (2005).
[CrossRef] [PubMed]

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[CrossRef]

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, "Refractive index of tissue measured with confocal microscopy," J. Biomed. Opt. 10, 44014 (2005).
[CrossRef] [PubMed]

L. Jiancheng, L. Zhenhua, W. Chunyong, and H. Anzhi, "Experimental measurement of the refractive index of biological tissues by total internal reflection," Appl. Opt. 44, 1845-1849 (2005).
[CrossRef]

2004 (1)

2003 (8)

J. Swartling, A. Pifferi, A. M. K. Enejder, and S. Andersson-Engels, "Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues," J. Opt. Soc. Am. A 20, 714-727 (2003).
[CrossRef]

S. Merritt, F. Bevilacqua, A. J. Durkin, D. J. Cuccia, R. Lanning, B. J. Tromberg, G. Gulsen, H. Yu, J. Wang, and O. Nalcioglu, "Coregistration of diffuse optical spectroscopy and magnetic resonance imaging in a rat tumor model," Appl. Opt. 42, 2951-2959 (2003).
[CrossRef] [PubMed]

V. Tsenova and E. V. Stoykova, "Refractive index measurement in human tissue samples," in Proc. SPIE 5226, 413-417 (2003).
[CrossRef]

Q. Liu, C. Zhu, and N. Ramanujam, "Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum," J. Biomed. Opt. 8, 223-236 (2003).
[CrossRef] [PubMed]

P. Laven, "Refractive index of water as a function of wavelength," http://www.philiplaven.com/p20.html (2003).

X-5 Monte Carlo Team, "MCNP Vol. I: Overview and Theory," http://mcnp-green.lanl.gov/manual.html (Diagnostics Applications Group, Los Alamos National Laboratory, 2003), pp. 130-158.

I. Pavlova, K. Sokolov, R. Drezek, A. Malpica, M. Follen, and R. Richards-Kortum, "Microanatomical and biochemical origins of normal and precancerous cervical autofluorescence using laser-scanning fluorescence confocal microscopy," Photochem. Photobiol. 77, 550-555 (2003).
[CrossRef] [PubMed]

T. Collier, D. Arifler, A. Malpica, M. Follen, and R. Richards-Kortum, "Determination of epithelial tissue scattering coefficient using confocal microscopy," IEEE J. Sel. Top. Quantum Electron. 9, 307-313 (2003).
[CrossRef]

2001 (3)

R. Drezek, C. Brookner, I. Pavlova, I. Boiko, A. Malpica, R. Lotan, M. Follen, and R. Richards-Kortum, "Autofluorescence microscopy of fresh cervical-tissue sections reveals alterations in tissue biochemistry with dysplasia," Photochem. Photobiol. 73, 636-641 (2001).
[CrossRef] [PubMed]

R. Drezek, K. Sokolov, U. Utzinger, I. Boiko, A. Malpica, M. Follen, and R. Richards-Kortum, "Understanding the contributions of NADH and collagen to cervical tissue fluorescence spectra: modeling, measurements, and implications," J. Biomed. Opt. 6, 385-396 (2001).
[CrossRef] [PubMed]

C. K. Hayakawa, T. Spanier, F. Bevilacqua, A. K. Dunn, J. S. You, B. J. Tromberg, and V. Venugopalan, "Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues," Opt. Lett. 26, 1335-1337 (2001).
[CrossRef]

2000 (1)

1999 (4)

1998 (1)

1997 (1)

The Condor Team, "Condor--high throughput computing," http://www.cs.wisc.edu/condor/ (1997-2006).

1996 (3)

1995 (3)

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, and J. G. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett. 20, 2258-2260 (1995).
[CrossRef] [PubMed]

W.-F. Cheong, "Appendix to Chapter 8: summary of optical properties," in Optical-Thermal Response of Laser-Irradiated Tissue, A.J.Welch and M.J. C.van Gemert, eds. (Plenum, 1995), pp. 275-303.

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

1993 (1)

1992 (1)

T. J. Farrell, M. S. Patterson, and B. Wilson, "A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

1989 (1)

D. R. Wyman, M. S. Patterson, and B. C. Wilson, "Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles," J. Comput. Phys. 81, 137-150 (1989).
[CrossRef]

1985 (1)

1983 (1)

F. C. Bohren and R. D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

1965 (1)

I. H. Malittson, "Refractive index versus wavelength reference table measured at 20°C: synthetic fused silica," http://www.polymicro.com/catalog/alowbar12.htm (1965).

Aalders, M. C.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

Alianelli, L.

Andersson-Engels, S.

Anzhi, H.

Arifler, D.

T. Collier, D. Arifler, A. Malpica, M. Follen, and R. Richards-Kortum, "Determination of epithelial tissue scattering coefficient using confocal microscopy," IEEE J. Sel. Top. Quantum Electron. 9, 307-313 (2003).
[CrossRef]

Avrillier, S.

Backman, V.

Battistelli, E.

Bevilacqua, F.

Blumetti, C.

Bohren, F. C.

F. C. Bohren and R. D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Boiko, I.

R. Drezek, K. Sokolov, U. Utzinger, I. Boiko, A. Malpica, M. Follen, and R. Richards-Kortum, "Understanding the contributions of NADH and collagen to cervical tissue fluorescence spectra: modeling, measurements, and implications," J. Biomed. Opt. 6, 385-396 (2001).
[CrossRef] [PubMed]

R. Drezek, C. Brookner, I. Pavlova, I. Boiko, A. Malpica, R. Lotan, M. Follen, and R. Richards-Kortum, "Autofluorescence microscopy of fresh cervical-tissue sections reveals alterations in tissue biochemistry with dysplasia," Photochem. Photobiol. 73, 636-641 (2001).
[CrossRef] [PubMed]

Bouma, B. E.

Breslin, T. M.

Brezinski, M. E.

Brookner, C.

R. Drezek, C. Brookner, I. Pavlova, I. Boiko, A. Malpica, R. Lotan, M. Follen, and R. Richards-Kortum, "Autofluorescence microscopy of fresh cervical-tissue sections reveals alterations in tissue biochemistry with dysplasia," Photochem. Photobiol. 73, 636-641 (2001).
[CrossRef] [PubMed]

Bruscaglioni, P.

Cheong, W.-F.

W.-F. Cheong, "Appendix to Chapter 8: summary of optical properties," in Optical-Thermal Response of Laser-Irradiated Tissue, A.J.Welch and M.J. C.van Gemert, eds. (Plenum, 1995), pp. 275-303.

Chikoidze, E.

R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, E. Chikoidze, and R. Cubeddu, "Determination of visible near-IR absorption coefficients of mammalian fat using time- and spatially resolved diffuse reflectance and transmission spectroscopy," J. Biomed. Opt. 10, 54004 (2005).
[CrossRef]

Choi, B.

W. Verkruysse, R. Zhang, B. Choi, G. Lucassen, L. O. Svaasand, and J. S. Nelson, "A library based fitting method for visual reflectance spectroscopy of human skin," Phys. Med. Biol. 50, 57-70 (2005).
[CrossRef] [PubMed]

Chunyong, W.

Collier, T.

T. Collier, D. Arifler, A. Malpica, M. Follen, and R. Richards-Kortum, "Determination of epithelial tissue scattering coefficient using confocal microscopy," IEEE J. Sel. Top. Quantum Electron. 9, 307-313 (2003).
[CrossRef]

Contini, D.

Cross, F. W.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

Cubeddu, R.

R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, E. Chikoidze, and R. Cubeddu, "Determination of visible near-IR absorption coefficients of mammalian fat using time- and spatially resolved diffuse reflectance and transmission spectroscopy," J. Biomed. Opt. 10, 54004 (2005).
[CrossRef]

Cuccia, D. J.

Dassel, A. C. M.

de Mul, F.

Decraemer, W. F.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, "Refractive index of tissue measured with confocal microscopy," J. Biomed. Opt. 10, 44014 (2005).
[CrossRef] [PubMed]

Depeursinge, C.

Dirckx, J. J. J.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, "Refractive index of tissue measured with confocal microscopy," J. Biomed. Opt. 10, 44014 (2005).
[CrossRef] [PubMed]

Doornbos, R. M. P.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

Drezek, R.

I. Pavlova, K. Sokolov, R. Drezek, A. Malpica, M. Follen, and R. Richards-Kortum, "Microanatomical and biochemical origins of normal and precancerous cervical autofluorescence using laser-scanning fluorescence confocal microscopy," Photochem. Photobiol. 77, 550-555 (2003).
[CrossRef] [PubMed]

R. Drezek, C. Brookner, I. Pavlova, I. Boiko, A. Malpica, R. Lotan, M. Follen, and R. Richards-Kortum, "Autofluorescence microscopy of fresh cervical-tissue sections reveals alterations in tissue biochemistry with dysplasia," Photochem. Photobiol. 73, 636-641 (2001).
[CrossRef] [PubMed]

R. Drezek, K. Sokolov, U. Utzinger, I. Boiko, A. Malpica, M. Follen, and R. Richards-Kortum, "Understanding the contributions of NADH and collagen to cervical tissue fluorescence spectra: modeling, measurements, and implications," J. Biomed. Opt. 6, 385-396 (2001).
[CrossRef] [PubMed]

Dunn, A. K.

Durkin, A. J.

Enejder, A. M. K.

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, "A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Feld, M. S.

Fitzmaurice, M.

Follen, M.

T. Collier, D. Arifler, A. Malpica, M. Follen, and R. Richards-Kortum, "Determination of epithelial tissue scattering coefficient using confocal microscopy," IEEE J. Sel. Top. Quantum Electron. 9, 307-313 (2003).
[CrossRef]

I. Pavlova, K. Sokolov, R. Drezek, A. Malpica, M. Follen, and R. Richards-Kortum, "Microanatomical and biochemical origins of normal and precancerous cervical autofluorescence using laser-scanning fluorescence confocal microscopy," Photochem. Photobiol. 77, 550-555 (2003).
[CrossRef] [PubMed]

R. Drezek, C. Brookner, I. Pavlova, I. Boiko, A. Malpica, R. Lotan, M. Follen, and R. Richards-Kortum, "Autofluorescence microscopy of fresh cervical-tissue sections reveals alterations in tissue biochemistry with dysplasia," Photochem. Photobiol. 73, 636-641 (2001).
[CrossRef] [PubMed]

R. Drezek, K. Sokolov, U. Utzinger, I. Boiko, A. Malpica, M. Follen, and R. Richards-Kortum, "Understanding the contributions of NADH and collagen to cervical tissue fluorescence spectra: modeling, measurements, and implications," J. Biomed. Opt. 6, 385-396 (2001).
[CrossRef] [PubMed]

N. Ramanujam, R. Richards-Kortum, S. Thomsen, A. Mahadevan-Jansen, and M. Follen, "Low temperature fluorescence imaging of freeze-trapped human cervical tissues," Opt. Express 8, 335-343 (2000).
[CrossRef]

Fujimoto, J. G.

Gilchrist, K. W.

Graaff, R.

Gross, J. D.

Gulsen, G.

Hayakawa, C. K.

Hee, M. R.

Hibst, R.

Huffman, R. D.

F. C. Bohren and R. D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Ismaelli, A.

Jacques, S. L.

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

Jiancheng, L.

Kienle, A.

Koelink, M.

Kuypers, L. C.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, "Refractive index of tissue measured with confocal microscopy," J. Biomed. Opt. 10, 44014 (2005).
[CrossRef] [PubMed]

Lang, R.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

Lanning, R.

Laven, P.

P. Laven, "Refractive index of water as a function of wavelength," http://www.philiplaven.com/p20.html (2003).

Lilge, L.

Liu, Q.

Lotan, R.

R. Drezek, C. Brookner, I. Pavlova, I. Boiko, A. Malpica, R. Lotan, M. Follen, and R. Richards-Kortum, "Autofluorescence microscopy of fresh cervical-tissue sections reveals alterations in tissue biochemistry with dysplasia," Photochem. Photobiol. 73, 636-641 (2001).
[CrossRef] [PubMed]

Lucassen, G.

W. Verkruysse, R. Zhang, B. Choi, G. Lucassen, L. O. Svaasand, and J. S. Nelson, "A library based fitting method for visual reflectance spectroscopy of human skin," Phys. Med. Biol. 50, 57-70 (2005).
[CrossRef] [PubMed]

Mahadevan-Jansen, A.

Malittson, I. H.

I. H. Malittson, "Refractive index versus wavelength reference table measured at 20°C: synthetic fused silica," http://www.polymicro.com/catalog/alowbar12.htm (1965).

Malpica, A.

I. Pavlova, K. Sokolov, R. Drezek, A. Malpica, M. Follen, and R. Richards-Kortum, "Microanatomical and biochemical origins of normal and precancerous cervical autofluorescence using laser-scanning fluorescence confocal microscopy," Photochem. Photobiol. 77, 550-555 (2003).
[CrossRef] [PubMed]

T. Collier, D. Arifler, A. Malpica, M. Follen, and R. Richards-Kortum, "Determination of epithelial tissue scattering coefficient using confocal microscopy," IEEE J. Sel. Top. Quantum Electron. 9, 307-313 (2003).
[CrossRef]

R. Drezek, C. Brookner, I. Pavlova, I. Boiko, A. Malpica, R. Lotan, M. Follen, and R. Richards-Kortum, "Autofluorescence microscopy of fresh cervical-tissue sections reveals alterations in tissue biochemistry with dysplasia," Photochem. Photobiol. 73, 636-641 (2001).
[CrossRef] [PubMed]

R. Drezek, K. Sokolov, U. Utzinger, I. Boiko, A. Malpica, M. Follen, and R. Richards-Kortum, "Understanding the contributions of NADH and collagen to cervical tissue fluorescence spectra: modeling, measurements, and implications," J. Biomed. Opt. 6, 385-396 (2001).
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Manoharan, R.

Marquet, P.

Martelli, F.

Merritt, S.

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[CrossRef] [PubMed]

Palmer, G. M.

Patterson, M. S.

A. Kienle and M. S. Patterson, "Determination of the optical properties of turbid media from a single Monte Carlo simulation," Phys. Med. Biol. 41, 2221-2227 (1996).
[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 the optical scattering and absorption coefficients of biological tissue," Appl. Opt. 35, 2304-2314 (1996).
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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef] [PubMed]

R. Drezek, K. Sokolov, U. Utzinger, I. Boiko, A. Malpica, M. Follen, and R. Richards-Kortum, "Understanding the contributions of NADH and collagen to cervical tissue fluorescence spectra: modeling, measurements, and implications," J. Biomed. Opt. 6, 385-396 (2001).
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R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, E. Chikoidze, and R. Cubeddu, "Determination of visible near-IR absorption coefficients of mammalian fat using time- and spatially resolved diffuse reflectance and transmission spectroscopy," J. Biomed. Opt. 10, 54004 (2005).
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W. Verkruysse, R. Zhang, B. Choi, G. Lucassen, L. O. Svaasand, and J. S. Nelson, "A library based fitting method for visual reflectance spectroscopy of human skin," Phys. Med. Biol. 50, 57-70 (2005).
[CrossRef] [PubMed]

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Tearney, G. J.

Thomsen, S.

Tinet, E.

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R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, E. Chikoidze, and R. Cubeddu, "Determination of visible near-IR absorption coefficients of mammalian fat using time- and spatially resolved diffuse reflectance and transmission spectroscopy," J. Biomed. Opt. 10, 54004 (2005).
[CrossRef]

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V. Tsenova and E. V. Stoykova, "Refractive index measurement in human tissue samples," in Proc. SPIE 5226, 413-417 (2003).
[CrossRef]

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R. Drezek, K. Sokolov, U. Utzinger, I. Boiko, A. Malpica, M. Follen, and R. Richards-Kortum, "Understanding the contributions of NADH and collagen to cervical tissue fluorescence spectra: modeling, measurements, and implications," J. Biomed. Opt. 6, 385-396 (2001).
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[CrossRef]

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W. Verkruysse, R. Zhang, B. Choi, G. Lucassen, L. O. Svaasand, and J. S. Nelson, "A library based fitting method for visual reflectance spectroscopy of human skin," Phys. Med. Biol. 50, 57-70 (2005).
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T. J. Farrell, M. S. Patterson, and B. Wilson, "A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

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W. Verkruysse, R. Zhang, B. Choi, G. Lucassen, L. O. Svaasand, and J. S. Nelson, "A library based fitting method for visual reflectance spectroscopy of human skin," Phys. Med. Biol. 50, 57-70 (2005).
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L. Wang, S. L. Jacques, and L. Zheng, "MCML--Monte Carlo modeling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
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G. M. Palmer and N. Ramanujam, "Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms," Appl. Opt. 45, 1062-1071 (2006).
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G. M. Palmer, C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanujam, "Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis," Appl. Opt. 45, 1072-1078 (2006).
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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).
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L. Wang, S. L. Jacques, and L. Zheng, "MCML--Monte Carlo modeling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

T. Collier, D. Arifler, A. Malpica, M. Follen, and R. Richards-Kortum, "Determination of epithelial tissue scattering coefficient using confocal microscopy," IEEE J. Sel. Top. Quantum Electron. 9, 307-313 (2003).
[CrossRef]

J. Biomed. Opt. (4)

R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, E. Chikoidze, and R. Cubeddu, "Determination of visible near-IR absorption coefficients of mammalian fat using time- and spatially resolved diffuse reflectance and transmission spectroscopy," J. Biomed. Opt. 10, 54004 (2005).
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[CrossRef] [PubMed]

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J. Comput. Phys. (1)

D. R. Wyman, M. S. Patterson, and B. C. Wilson, "Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles," J. Comput. Phys. 81, 137-150 (1989).
[CrossRef]

J. Opt. Soc. Am. A (4)

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, and B. Wilson, "A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo," Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Photochem. Photobiol. (2)

R. Drezek, C. Brookner, I. Pavlova, I. Boiko, A. Malpica, R. Lotan, M. Follen, and R. Richards-Kortum, "Autofluorescence microscopy of fresh cervical-tissue sections reveals alterations in tissue biochemistry with dysplasia," Photochem. Photobiol. 73, 636-641 (2001).
[CrossRef] [PubMed]

I. Pavlova, K. Sokolov, R. Drezek, A. Malpica, M. Follen, and R. Richards-Kortum, "Microanatomical and biochemical origins of normal and precancerous cervical autofluorescence using laser-scanning fluorescence confocal microscopy," Photochem. Photobiol. 77, 550-555 (2003).
[CrossRef] [PubMed]

Phys. Med. Biol. (3)

W. Verkruysse, R. Zhang, B. Choi, G. Lucassen, L. O. Svaasand, and J. S. Nelson, "A library based fitting method for visual reflectance spectroscopy of human skin," Phys. Med. Biol. 50, 57-70 (2005).
[CrossRef] [PubMed]

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, "The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy," Phys. Med. Biol. 44, 967-981 (1999).
[CrossRef] [PubMed]

A. Kienle and M. S. Patterson, "Determination of the optical properties of turbid media from a single Monte Carlo simulation," Phys. Med. Biol. 41, 2221-2227 (1996).
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Proc. SPIE (1)

V. Tsenova and E. V. Stoykova, "Refractive index measurement in human tissue samples," in Proc. SPIE 5226, 413-417 (2003).
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Figures (8)

Fig. 1
Fig. 1

Principle of the scaling method as applied in (a) a homogeneous medium and (b) a two-layered medium. In both (a) and (b), the horizontal bold line is the air–medium interface, the solid lines with arrows represent the trajectory of a photon in a baseline medium, and the dashed lines with arrows represent the scaled trajectory of the same photon in a new medium with a different set of optical properties. The incident locations of the two trajectories were supposed to overlap, but they were purposefully shifted away from each other in the above figures for better differentiation. The baseline transport coefficient ( μ t ) is μ t 0 in both (a) and (b). For homogeneous scaling in (a), it is assumed that the new μ t is half of μ t 0 . For the layered scaling in (b), it is assumed that the μ t of the top layer is twice μ t 0 and the μ t of the bottom layer is half of μ t 0 . In (b), the horizontal dashed line in the middle stands for the layer interface in the two-layered medium, while the horizontal solid line in the bottom represents the corresponding location of the layer interface in the baseline medium as if the baseline medium were two-layered with a pseudolayer interface.

Fig. 2
Fig. 2

Schematics of two-layered and three-layered epithelial tissue models for testing the accuracy of the multilayered scaling method. The optical properties of the top layer are shown in Fig. 3a, the optical properties of the bottom layer are shown in Fig. 3b, and the optical properties of the middle layer are shown in Fig. 3c. It should be noted that the thicknesses of the top layer and the middle layer in (b) add up to the thickness of the top layer in (a).

Fig. 3
Fig. 3

Absorption and reduced scattering coefficients of the (a) top layer, (b) bottom layer, and (c) middle layer at a range of wavelengths from 360 to 660 nm in a two-layered and a three-layered theoretical epithelial tissue model.

Fig. 4
Fig. 4

Diffuse reflectance as a function of the source–detector separation at a single wavelength ( 500 nm ) for the original two-layered epithelial tissue model. The star symbols in the inset are the percent deviations of the scaled reflectance value relative to the mean of six independently simulated reflectance values as calculated in Eq. (1) for each separation. The open circles in the inset represent zero percent deviation. The error bar indicates 95% confidence interval (CI) of the percent deviation of simulated reflectance values relative to its expected value, which was calculated according to Eq. (2).

Fig. 5
Fig. 5

(a) Simulated and scaled diffuse reflectance and (b) percent deviation of scaled reflectance relative to simulated reflectance [calculated according to Eq. (1)] as a function of wavelength at four separations (0, 200, 800, and 1500 μ m in the order from the top to the bottom) for the original two-layered epithelial tissue model. The 95% CI of the percent deviation of simulated reflectance relative to its expected value was calculated according to Eq. (2) and illustrated by the error bars in (b). The open circles in (b) are the mean of the percent deviation of simulated reflectance relative to its expected value, which is always zero because the expected value was estimated by the mean of simulated reflectance.

Fig. 6
Fig. 6

Simulated reflectance as a function of separation from a modified two-layered epithelial tissue model at a wavelength of 500 nm , where the refractive index of the medium above the tissue model was varied from 1.0 to 1.338 to 1.462 and to 1.6 and other parameters were kept identical to those in the original two-layered epithelial tissue model. The scaled reflectance as a function of separation is also shown, for which the refractive index of the medium above the tissue model was 1.462 in the baseline simulation. The inset graph shows the percent deviation of scaled reflectance relative to simulated reflectance for different refractive indices as a function of separation. The dashed line in the inset represents zero percent deviation.

Fig. 7
Fig. 7

Simulated reflectance as a function of separation at a wavelength of 500 nm for a modified two-layered epithelial tissue model, in which the phase function was calculated from Mie theory[30] and other parameters including absorption and reduced scattering coefficients were kept identical to the original two-layered epithelial tissue model. The reflectance simulated for the original two-layered epithelial tissue model and the scaled reflectance, in which the HG phase function was used, are also shown for comparison. The inset graph shows the percent deviation of scaled reflectance relative to the two sets of simulated reflectance. The dashed line in the inset represents zero deviation.

Fig. 8
Fig. 8

(a) Schematic of a flat-tip fiber-optic probe geometry for diffuse reflectance measurement from a semi-infinite two-layered epithelial tissue phantom and (b) the scaled version of the phantom and the probe geometry. In (a), μ t 1 and μ t 2 are the transport coefficients of the top and bottom layers, α 1 and α 2 are the albedos of the two layers, the thickness of the top layer is d 1 , the diameter of both source and detector fibers is D, and the source–detector separation is ρ. In (b), the transport coefficients of the top and bottom layers are μ t 1 N and μ t 2 N , the albedos of the two layers are still α 1 and α 2 , the thickness of the top layer becomes d 1 × N , the diameter of both source and detector fibers is D × N , and the source–detector separation is ρ × N . Two representative photon trajectories were drawn in both (a) and (b) to illustrate the scaling operation.

Tables (8)

Tables Icon

Table 1 Effect of Anisotropy Factor of Tissue Layer on RMSE a

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Table 2 Effect of Refractive Index of Tissue Layer on RMSE a

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Table 3 Effect of Refractive Indices of Fiber Core and Tissue Model on Specular Reflectance a

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Table 4 Effect of Phase Function on RMSE a

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Table 5 Effect of One Additional Layer and Layer Thickness on RMSE a

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Table 6 Effect of Anisotropy Factor of Tissue Layer on RMSE of Estimated Optical Properties a

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Table 7 Effect of Refractive Index of Tissue Layer on RMSE of Estimated Optical Properties a

Tables Icon

Table 8 Effect of Phase Function on RMSE of Estimated Optical Properties a

Equations (9)

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

d 1 = d 1 × μ t 1 μ t 0 ,
d 2 = d 2 × μ t 2 μ t 0 ,
d n = d n × μ t n μ t 0 .
r = i = 1 n ( r i × μ t 0 μ t i ) ,
w = i = 1 n ( α i α 0 ) N i × w 0 ,
Percent Deviation = Scaled - Simulated Simulated × 100 ,
95 % CI = mean 1.96 × std m , mean + 1.96 × std m ,
RMSE = i = 1 n ( Scaled i - Simulated i Simulated i × 100 ) 2 n ,

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