Abstract

The general two-layer inverse problem in biomedical photon migration is to estimate the absorption and scattering coefficients of each layer as well as the top-layer thickness. We attempted to solve this problem, using experimental and simulated spatially resolved frequency-domain (FD) reflectance for optical properties typical of skin overlying muscle or skin overlying fat in the near infrared. Two forward models of light propagation were used: a two-layer diffusion solution [Appl. Opt. 37, 779 (1998)] and a hybrid Monte Carlo (MC) diffusion model [Appl. Opt. 37, 7401 (1998)]. MC-simulated FD reflectance data were fitted as relative measurements to the hybrid and the pure diffusion models. It was found that the hybrid model could determine all the optical properties of the two-layer media studied to ∼5%. Also, the same accuracy could be achieved by means of fitting MC-simulated cw reflectance data as absolute measurements, but fitting them as relative ones is an ill-posed problem. In contrast, two-layer diffusion could not retrieve the top-layer optical properties as accurately for FD data and was ill-posed for both relative and absolute cw data. The hybrid and the pure diffusion models were also fitted to experimental FD reflectance measurements from two-layer tissue-simulating phantoms representative of skin-on-fat and skin-on-muscle baseline optical properties. Both the hybrid and the diffusion models could determine the optical properties of the lower layer. The hybrid model demonstrated its potential to retrieve quantitatively the transport scattering coefficient of skin (the upper layer), which was not possible with the pure diffusion model. Systematic discrepancies between model and experiment may compromise the accuracy of the deduced top-layer optical properties. Identifying and eliminating such discrepancies is critical to practical application of the method.

© 2001 Optical Society of America

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References

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  1. R. A. De Blasi, N. Almenräder, P. Aurisicchio, M. Ferrari, “Comparison of two methods of measuring forearm oxygen consumption (V̇O2) by near infrared spectroscopy,” J. Biomed. Opt. 2, 171–175 (1997).
    [CrossRef] [PubMed]
  2. M. Nitzav, A. Babchencko, B. Khanokh, H. Taitelbaum, “Measurement of oxygen saturation in venous blood by dynamic near infrared spectroscopy,” J. Biomed. Opt. 5, 155–162 (2000).
    [CrossRef]
  3. M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematoporphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
    [CrossRef] [PubMed]
  4. R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of non-invasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
    [CrossRef] [PubMed]
  5. J. R. Mourant, T. M. Johnson, G. Los, I. J. Bigio, “Non-invasive measurement of chemotherapy drug concentrations in tissue: preliminary demonstrations of in vivo measurements,” Phys. Med. Biol. 44, 1397–1417 (1999).
    [CrossRef] [PubMed]
  6. J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, M. Essenpreis, G. Schmelzeisen-Redeker, D. Bocker, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahl-Christiansen, H. Orskov, “Correlation between blood glucose concentration in diabetics and non-invasively measured tissue optical scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. 37, 7401–7410 (1998).
    [CrossRef]
  12. T. H. Pham, T. Spott, L. O. Svaasand, B. J. Tromberg, “Quantifying the properties of two-layer turbid media with frequency-domain diffuse reflectance,” Appl. Opt. 39, 4733–4745 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2001 (1)

D. E. Hyde, T. J. Farrell, M. S. Patterson, “A diffusion theory model of spatially resolved fluorescence from depth dependent fluorophore concentrations,” Phys. Med. Biol. 46, 369–383 (2001).
[CrossRef] [PubMed]

2000 (3)

1999 (3)

1998 (4)

1997 (3)

R. A. De Blasi, N. Almenräder, P. Aurisicchio, M. Ferrari, “Comparison of two methods of measuring forearm oxygen consumption (V̇O2) by near infrared spectroscopy,” J. Biomed. Opt. 2, 171–175 (1997).
[CrossRef] [PubMed]

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of non-invasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, M. Essenpreis, G. Schmelzeisen-Redeker, D. Bocker, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahl-Christiansen, H. Orskov, “Correlation between blood glucose concentration in diabetics and non-invasively measured tissue optical scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
[CrossRef] [PubMed]

1996 (2)

1995 (1)

1994 (1)

1993 (1)

1988 (1)

1987 (1)

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematoporphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Alexandrakis, G.

Almenräder, N.

R. A. De Blasi, N. Almenräder, P. Aurisicchio, M. Ferrari, “Comparison of two methods of measuring forearm oxygen consumption (V̇O2) by near infrared spectroscopy,” J. Biomed. Opt. 2, 171–175 (1997).
[CrossRef] [PubMed]

Aurisicchio, P.

R. A. De Blasi, N. Almenräder, P. Aurisicchio, M. Ferrari, “Comparison of two methods of measuring forearm oxygen consumption (V̇O2) by near infrared spectroscopy,” J. Biomed. Opt. 2, 171–175 (1997).
[CrossRef] [PubMed]

Babchencko, A.

M. Nitzav, A. Babchencko, B. Khanokh, H. Taitelbaum, “Measurement of oxygen saturation in venous blood by dynamic near infrared spectroscopy,” J. Biomed. Opt. 5, 155–162 (2000).
[CrossRef]

Beauvoit, B.

B. Beauvoit, B. Chance, “Time-resolved spectroscopy of mitochondria, cells and tissues under normal and pathological conditions,” Mol. Cell. Biochem. 184, 445–455 (1998).
[CrossRef] [PubMed]

Berger, M.

Bigio, I. J.

J. R. Mourant, T. M. Johnson, G. Los, I. J. Bigio, “Non-invasive measurement of chemotherapy drug concentrations in tissue: preliminary demonstrations of in vivo measurements,” Phys. Med. Biol. 44, 1397–1417 (1999).
[CrossRef] [PubMed]

Bocker, D.

Bohren, C. F.

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

Bruulsema, J. T.

Burns, D. M.

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematoporphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Chance, B.

B. Beauvoit, B. Chance, “Time-resolved spectroscopy of mitochondria, cells and tissues under normal and pathological conditions,” Mol. Cell. Biochem. 184, 445–455 (1998).
[CrossRef] [PubMed]

De Blasi, R. A.

R. A. De Blasi, N. Almenräder, P. Aurisicchio, M. Ferrari, “Comparison of two methods of measuring forearm oxygen consumption (V̇O2) by near infrared spectroscopy,” J. Biomed. Opt. 2, 171–175 (1997).
[CrossRef] [PubMed]

Diamond, K. R.

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of non-invasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

Engstrom, R. W.

R. W. Engstrom, Photomultiplier Handbook (RCA, Lancaster, Pa., 1980), pp. 32, 47–52.

Essenpreis, M.

Fantini, S.

Faris, G. W.

M. Gerken, G. W. Faris, “Frequency-domain immersion technique for accurate optical property measurements of turbid media,” Opt. Lett. 24, 1726–1728 (1999).
[CrossRef]

M. Gerken, G. W. Faris, “High precision frequency-domain measurements of the optical properties of turbid media,” Opt. Lett. 24, 930–932 (1999).
[CrossRef]

M. Gerken, G. W. Faris, “High accuracy optical property measurements using a frequency domain technique,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 593–600 (1999).
[CrossRef]

Farrell, T. J.

Feather, J. W.

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematoporphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Feng, T.-C.

Ferrari, M.

R. A. De Blasi, N. Almenräder, P. Aurisicchio, M. Ferrari, “Comparison of two methods of measuring forearm oxygen consumption (V̇O2) by near infrared spectroscopy,” J. Biomed. Opt. 2, 171–175 (1997).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1996), Chaps. 10, 13, and 15.

Franceschini, M. A.

Gerken, M.

M. Gerken, G. W. Faris, “Frequency-domain immersion technique for accurate optical property measurements of turbid media,” Opt. Lett. 24, 1726–1728 (1999).
[CrossRef]

M. Gerken, G. W. Faris, “High precision frequency-domain measurements of the optical properties of turbid media,” Opt. Lett. 24, 930–932 (1999).
[CrossRef]

M. Gerken, G. W. Faris, “High accuracy optical property measurements using a frequency domain technique,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 593–600 (1999).
[CrossRef]

Graaff, R.

H. C. van de Hulst, R. Graaff, “Aspects of similarity in tissue optics with strong forward scattering,” Phys. Med. Biol. 41, 2519–2531 (1996).
[CrossRef] [PubMed]

Gratton, E.

Haskell, R. C.

Hayward, J. E.

Heinemann, L.

Hibst, R.

Huffman, D. R.

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

Hyde, D. E.

D. E. Hyde, T. J. Farrell, M. S. Patterson, “A diffusion theory model of spatially resolved fluorescence from depth dependent fluorophore concentrations,” Phys. Med. Biol. 46, 369–383 (2001).
[CrossRef] [PubMed]

Ishimaru, A.

A. Ishimaru, Wave Propagation in Scattering and Random Media (Academic, New York, 1978), Chaps. 7 and 9.

Jacques, S. L.

Johnson, T. M.

J. R. Mourant, T. M. Johnson, G. Los, I. J. Bigio, “Non-invasive measurement of chemotherapy drug concentrations in tissue: preliminary demonstrations of in vivo measurements,” Phys. Med. Biol. 44, 1397–1417 (1999).
[CrossRef] [PubMed]

Khanokh, B.

M. Nitzav, A. Babchencko, B. Khanokh, H. Taitelbaum, “Measurement of oxygen saturation in venous blood by dynamic near infrared spectroscopy,” J. Biomed. Opt. 5, 155–162 (2000).
[CrossRef]

Kienle, A.

Koschinsky, T.

Kumar, G.

Lilge, L.

Los, G.

J. R. Mourant, T. M. Johnson, G. Los, I. J. Bigio, “Non-invasive measurement of chemotherapy drug concentrations in tissue: preliminary demonstrations of in vivo measurements,” Phys. Med. Biol. 44, 1397–1417 (1999).
[CrossRef] [PubMed]

Maier, J. S.

McAdams, M. S.

Mourant, J. R.

J. R. Mourant, T. M. Johnson, G. Los, I. J. Bigio, “Non-invasive measurement of chemotherapy drug concentrations in tissue: preliminary demonstrations of in vivo measurements,” Phys. Med. Biol. 44, 1397–1417 (1999).
[CrossRef] [PubMed]

Nitzav, M.

M. Nitzav, A. Babchencko, B. Khanokh, H. Taitelbaum, “Measurement of oxygen saturation in venous blood by dynamic near infrared spectroscopy,” J. Biomed. Opt. 5, 155–162 (2000).
[CrossRef]

Orskov, H.

Patterson, M. S.

D. E. Hyde, T. J. Farrell, M. S. Patterson, “A diffusion theory model of spatially resolved fluorescence from depth dependent fluorophore concentrations,” Phys. Med. Biol. 46, 369–383 (2001).
[CrossRef] [PubMed]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Monte Carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain,” Appl. Opt. 39, 2235–2244 (2000).
[CrossRef]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. 37, 7401–7410 (1998).
[CrossRef]

T. J. Farrell, M. S. Patterson, 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]

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, M. Essenpreis, G. Schmelzeisen-Redeker, D. Bocker, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahl-Christiansen, H. Orskov, “Correlation between blood glucose concentration in diabetics and non-invasively measured tissue optical scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
[CrossRef] [PubMed]

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of non-invasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, 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).
[CrossRef] [PubMed]

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematoporphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Paunescu, L. A.

Pham, T. H.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1996), Chaps. 10, 13, and 15.

Pushka, W.

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematoporphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Saidi, I. S.

Sandahl-Christiansen, J.

Schmelzeisen-Redeker, G.

Schmitt, J. M.

Spott, T.

Steiner, R.

Svaasand, L. O.

Taitelbaum, H.

M. Nitzav, A. Babchencko, B. Khanokh, H. Taitelbaum, “Measurement of oxygen saturation in venous blood by dynamic near infrared spectroscopy,” J. Biomed. Opt. 5, 155–162 (2000).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1996), Chaps. 10, 13, and 15.

Tittel, F. K.

Tromberg, B. J.

Tsay, T.-T.

van de Hulst, H. C.

H. C. van de Hulst, R. Graaff, “Aspects of similarity in tissue optics with strong forward scattering,” Phys. Med. Biol. 41, 2519–2531 (1996).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1996), Chaps. 10, 13, and 15.

Wang, L.

Weersink, R. A.

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of non-invasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

Wilson, B. C.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, 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).
[CrossRef] [PubMed]

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematoporphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

Appl. Opt. (8)

T. J. Farrell, M. S. Patterson, 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]

J. M. Schmitt, G. Kumar, “Optical scattering properties of soft tissue: a discrete particle model,” Appl. Opt. 37, 2788–2797 (1988).
[CrossRef]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. 37, 7401–7410 (1998).
[CrossRef]

M. A. Franceschini, S. Fantini, L. A. Paunescu, J. S. Maier, E. Gratton, “Influence of a superficial layer in the quantitative spectroscopic study of strongly scattering media,” Appl. Opt. 37, 7447–7458 (1998).
[CrossRef]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Monte Carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain,” Appl. Opt. 39, 2235–2244 (2000).
[CrossRef]

I. S. Saidi, S. L. Jacques, F. K. Tittel, “Mie and Rayleigh modeling of visible-light scattering in neonatal skin,” Appl. Opt. 34, 7410–7418 (1995).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, 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).
[CrossRef] [PubMed]

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

J. Biomed. Opt. (2)

R. A. De Blasi, N. Almenräder, P. Aurisicchio, M. Ferrari, “Comparison of two methods of measuring forearm oxygen consumption (V̇O2) by near infrared spectroscopy,” J. Biomed. Opt. 2, 171–175 (1997).
[CrossRef] [PubMed]

M. Nitzav, A. Babchencko, B. Khanokh, H. Taitelbaum, “Measurement of oxygen saturation in venous blood by dynamic near infrared spectroscopy,” J. Biomed. Opt. 5, 155–162 (2000).
[CrossRef]

J. Opt. Soc. Am. A (2)

Mol. Cell. Biochem. (1)

B. Beauvoit, B. Chance, “Time-resolved spectroscopy of mitochondria, cells and tissues under normal and pathological conditions,” Mol. Cell. Biochem. 184, 445–455 (1998).
[CrossRef] [PubMed]

Opt. Lett. (3)

Photochem. Photobiol. (2)

M. S. Patterson, B. C. Wilson, J. W. Feather, D. M. Burns, W. Pushka, “The measurement of dihematoporphyrin ether concentration in tissue by reflectance spectrophotometry,” Photochem. Photobiol. 46, 337–343 (1987).
[CrossRef] [PubMed]

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of non-invasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

Phys. Med. Biol. (3)

J. R. Mourant, T. M. Johnson, G. Los, I. J. Bigio, “Non-invasive measurement of chemotherapy drug concentrations in tissue: preliminary demonstrations of in vivo measurements,” Phys. Med. Biol. 44, 1397–1417 (1999).
[CrossRef] [PubMed]

D. E. Hyde, T. J. Farrell, M. S. Patterson, “A diffusion theory model of spatially resolved fluorescence from depth dependent fluorophore concentrations,” Phys. Med. Biol. 46, 369–383 (2001).
[CrossRef] [PubMed]

H. C. van de Hulst, R. Graaff, “Aspects of similarity in tissue optics with strong forward scattering,” Phys. Med. Biol. 41, 2519–2531 (1996).
[CrossRef] [PubMed]

Other (7)

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

R. W. Engstrom, Photomultiplier Handbook (RCA, Lancaster, Pa., 1980), pp. 32, 47–52.

H. Kume, ed., Photomultiplier Tube: Principle to Application (Hamamatsu Photonics K. K., Hamamatsu City, Japan, 1994), pp. 36, 47–49.

A. Ishimaru, Wave Propagation in Scattering and Random Media (Academic, New York, 1978), Chaps. 7 and 9.

M. Gerken, G. W. Faris, “High accuracy optical property measurements using a frequency domain technique,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 593–600 (1999).
[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1996), Chaps. 10, 13, and 15.

“Appendix B, Degassing Procedures,” in IEEE Guide for Medical Ultrasound Field Parameter Measurements, IEEE Std. 790-1989, F. W. Kremkau, W. T. Coakley, P. D. Edmonds, L. A. Frizzel, G. R. Harris, W. A. Riley, R. A. Robinson, eds. (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 91–94.

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Figures (10)

Fig. 1
Fig. 1

(a) Two-layer phantom and FD system probe design. The source and detector fibers have been left out for clarity. (b) Bottom view of the probe face plate.

Fig. 2
Fig. 2

%err for the retrieved value of μ a1 in the MC-simulated skin-on-fat case when two-layer diffusion (white bars) and the hybrid model (gray bars) are used. The abscissa values indicate the smallest source–detector distance included in the fits (see text). Error bars indicate the 95% confidence intervals on each fitted optical property %err value.

Fig. 3
Fig. 3

As in Fig. 2 but for μ s1′ in the skin-on-fat case.

Fig. 4
Fig. 4

As in Fig. 2 but for μ s1′ in the skin-on-muscle case.

Fig. 5
Fig. 5

%err for the retrieved skin-on-fat optical properties (Table 1, column 1) when MC data generated with a Mie theory phase function (g = 0.9, white bars) or a HG phase function (g = 0.8, gray bars) are fitted as relative measurements to the hybrid model with HG (g = 0.8).

Fig. 6
Fig. 6

%err for the retrieved skin-on-fat optical properties from fitting skin-on-fat (Table 1, column 1) cw MC data to the hybrid model as relative (white bars) or absolute (gray bars) measurements.

Fig. 7
Fig. 7

(a) rf amplitude reflectance [ACR(ρ)] measurements, plotted as ln[ρ2 ACR(ρ)], for a skin-on-fat phantom (open diamonds), l = 3 mm, versus the hybrid model calculations for the best-fit optical properties (solid curve) and those based on the infinite medium measurements (dashed curve). (b) Phase-delay measurements and corresponding hybrid model calculations [symbol and curve styles as in Fig. 7(a)]. The experimental measurement error estimates are comparable with the size of the symbols and have been left out for clarity.

Fig. 8
Fig. 8

%err for the retrieved skin-on-fat, l = 3 mm, optical properties as determined by the hybrid model (gray bars) and pure two-layer diffusion (white bars).

Fig. 9
Fig. 9

(a) As in Fig. 7(a) but for a skin-on-muscle, l = 3 mm, phantom. (b) As in Fig. 9(a) but for the phase-delay data.

Fig. 10
Fig. 10

As in Fig. 8 but for a skin-on-muscle, l = 3 mm, phantom.

Tables (2)

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Table 1 Two Sets of Tissue Optical Propertiesa

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Table 2 Liquid Phantom Optical Propertiesa

Equations (5)

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Φρ, z, ω=12π0 ϕs, z, ωsJ0sρds,
Rρ, ω=14 Φρ, z=0, ω+12 D1Φρ, z, ωzz=0.
ACRρ, ω=(ImRρ, ω2+ReRρ, ω2)1/2,
θρ, ω=tan-1ImRρ, ωReRρ, ω.
%err=μfit-μMC/μMC×100.

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