Abstract

Noncontact, frequency-domain measurements of diffusely reflected light are used to quantify optical properties of two-layer tissuelike turbid media. The irradiating source is a sinusoidal intensity-modulated plane wave, with modulation frequencies ranging from 10 to 1500 MHz. Frequency-dependent phase and amplitude of diffusely reflected photon density waves are simultaneously fitted to a diffusion-based two-layer model to quantify absorption (μa) and reduced scattering (μs′) parameters of each layer as well as the upper-layer thickness (l). Study results indicate that the optical properties of two-layer media can be determined with a percent accuracy of the order of ±9% and ±5% for μa and μs′, respectively. The accuracy of upper-layer thickness (l) estimation is as good as ±6% when optical properties of upper and lower layers are known. Optical property and layer thickness prediction accuracy degrade significantly when more than three free parameters are extracted from data fits. Problems with convergence are encountered when all five free parameters (μa and μs′ of upper and lower layers and thickness l) must be deduced.

© 2000 Optical Society of America

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2000

T. H. Pham, O. Coquoz, J. B. Fishkin, E. A. Anderson, B. J. Tromberg, “A broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

1999

L. O. Svaasand, T. Spott, J. B. Fishkin, T. H. Pham, B. J. Tromberg, M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

1998

V. Quaresima, S. J. Matcher, M. Ferrari, “Identification and quantification of intrinsic optical contrast for near-infrared mammography,” Photochem. Photobiol. 67, 4–14 (1998).
[CrossRef] [PubMed]

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, J. P. Freyer, “Evidence of intrinsic differences in the light scattering properties of tumorigenic and nontumorigenic cells,” Cancer 84, 366–374 (1998).
[CrossRef]

J. F. de Boer, S. M. Srinivas, A. Malekafzali, Z. Chen, J. S. Nelson, “Imaging thermally damaged tissue by polarization sensitive optical coherence tomography,” Opt. Exp. 3, 212–218 (1998).
[CrossRef]

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

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

1997

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

1996

R. A. de Blasi, R. Sfareni, B. Pietranico, A. M. Mega, M. Ferrari, “Non invasive measurement of brachioradial muscle VO2-blood flow relationship during graded isometric exercise,” Adv. Exp. Med. Biol. 388, 293–298 (1996).
[CrossRef] [PubMed]

A. H. Hielscher, H. L. Liu, B. Chance, F. K. Tittel, S. L. Jacques, “Time-resolved photon emission from layered turbid media,” Appl. Opt. 35, 719–728 (1996).
[CrossRef] [PubMed]

1995

J. B. Fishkin, P. So, A. E. Cerussi, S. Fantini, M. A. Franceschini, E. Gratton, “Frequency-domain method for measuring spectral properties in multiple-scattering media: methemoglobin absorption spectrum in a tissuelike phantom,” Appl. Opt. 34, 1143–1155 (1995).
[CrossRef] [PubMed]

L. O. Svaasand, L. T. Norvang, E. J. Fiskerstrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine stains,” Lasers Med. Sci. 10, 55–65 (1995).
[CrossRef]

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

1994

1993

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

1992

T. J. Farrell, M. S. Patterson, “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]

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

1991

1990

J. M. Schmitt, G. Z. Zhou, E. C. Walker, R. T. Wall, “Multilayer model of photon diffusion in skin,” J. Opt. Soc. Am. A 7, 2141–2153 (1990).
[CrossRef] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

1989

1980

1964

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comp. J. (Cambridge) 7, 308–313 (1964).

Anderson, E. A.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. A. Anderson, B. J. Tromberg, “A broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

Anderson, E. R.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

Bays, R.

Berns, M. W.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. H. Pham, B. J. Tromberg, M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

L. O. Svaasand, L. T. Norvang, E. J. Fiskerstrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine stains,” Lasers Med. Sci. 10, 55–65 (1995).
[CrossRef]

Boas, D. A.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Butler, J.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

Cahn, M.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

Cerussi, A. E.

Chance, B.

Chen, Z.

J. F. de Boer, S. M. Srinivas, A. Malekafzali, Z. Chen, J. S. Nelson, “Imaging thermally damaged tissue by polarization sensitive optical coherence tomography,” Opt. Exp. 3, 212–218 (1998).
[CrossRef]

Cope, M.

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

M. Cope, “The development of a near infrared spectroscopy system and its application for non-invasive monitoring of cerebral blood and tissue oxygenation in the newborn infant,” Ph.D. dissertation (University College London, London, UK, 1991), pp. 56–78.

Coquoz, O.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. A. Anderson, B. J. Tromberg, “A broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

Dayan, I.

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

de Blasi, R. A.

R. A. de Blasi, R. Sfareni, B. Pietranico, A. M. Mega, M. Ferrari, “Non invasive measurement of brachioradial muscle VO2-blood flow relationship during graded isometric exercise,” Adv. Exp. Med. Biol. 388, 293–298 (1996).
[CrossRef] [PubMed]

de Boer, J. F.

J. F. de Boer, S. M. Srinivas, A. Malekafzali, Z. Chen, J. S. Nelson, “Imaging thermally damaged tissue by polarization sensitive optical coherence tomography,” Opt. Exp. 3, 212–218 (1998).
[CrossRef]

Delpy, D. T.

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Dognitz, N.

Duck, F. A.

F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference Book (Academic, New York, 1990), pp. 43–60.
[CrossRef]

Edwards, A. D.

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Eick, A. A.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, J. P. Freyer, “Evidence of intrinsic differences in the light scattering properties of tumorigenic and nontumorigenic cells,” Cancer 84, 366–374 (1998).
[CrossRef]

Elwell, C.

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Fantini, S.

Farrell, T. J.

T. J. Farrell, M. S. Patterson, “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]

Feng, T. C.

Ferrari, M.

V. Quaresima, S. J. Matcher, M. Ferrari, “Identification and quantification of intrinsic optical contrast for near-infrared mammography,” Photochem. Photobiol. 67, 4–14 (1998).
[CrossRef] [PubMed]

R. A. de Blasi, R. Sfareni, B. Pietranico, A. M. Mega, M. Ferrari, “Non invasive measurement of brachioradial muscle VO2-blood flow relationship during graded isometric exercise,” Adv. Exp. Med. Biol. 388, 293–298 (1996).
[CrossRef] [PubMed]

Fishkin, J. B.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. A. Anderson, B. J. Tromberg, “A broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. H. Pham, B. J. Tromberg, M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

J. B. Fishkin, P. So, A. E. Cerussi, S. Fantini, M. A. Franceschini, E. Gratton, “Frequency-domain method for measuring spectral properties in multiple-scattering media: methemoglobin absorption spectrum in a tissuelike phantom,” Appl. Opt. 34, 1143–1155 (1995).
[CrossRef] [PubMed]

Fiskerstrand, E. J.

L. O. Svaasand, L. T. Norvang, E. J. Fiskerstrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine stains,” Lasers Med. Sci. 10, 55–65 (1995).
[CrossRef]

Flannery, B. P.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, N.Y., 1992), pp. 408–412.

Franceschini, M. A.

Frank, G. L.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Freyer, J. P.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, J. P. Freyer, “Evidence of intrinsic differences in the light scattering properties of tumorigenic and nontumorigenic cells,” Cancer 84, 366–374 (1998).
[CrossRef]

Furutsu, K.

Graton, E.

Gratton, E.

Gross, J. D.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

Haskell, R. C.

Havlin, S.

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

Hielscher, A. H.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, J. P. Freyer, “Evidence of intrinsic differences in the light scattering properties of tumorigenic and nontumorigenic cells,” Cancer 84, 366–374 (1998).
[CrossRef]

A. H. Hielscher, H. L. Liu, B. Chance, F. K. Tittel, S. L. Jacques, “Time-resolved photon emission from layered turbid media,” Appl. Opt. 35, 719–728 (1996).
[CrossRef] [PubMed]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), pp. 175–190.
[CrossRef]

Jacques, S. L.

Johnson, T. M.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, J. P. Freyer, “Evidence of intrinsic differences in the light scattering properties of tumorigenic and nontumorigenic cells,” Cancer 84, 366–374 (1998).
[CrossRef]

Kienle, A.

Liu, H.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Liu, H. L.

Maier, J. S.

Malekafzali, A.

J. F. de Boer, S. M. Srinivas, A. Malekafzali, Z. Chen, J. S. Nelson, “Imaging thermally damaged tissue by polarization sensitive optical coherence tomography,” Opt. Exp. 3, 212–218 (1998).
[CrossRef]

Mank, A. J.

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

Matcher, S. J.

V. Quaresima, S. J. Matcher, M. Ferrari, “Identification and quantification of intrinsic optical contrast for near-infrared mammography,” Photochem. Photobiol. 67, 4–14 (1998).
[CrossRef] [PubMed]

McAdams, M. S.

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comp. J. (Cambridge) 7, 308–313 (1964).

Mega, A. M.

R. A. de Blasi, R. Sfareni, B. Pietranico, A. M. Mega, M. Ferrari, “Non invasive measurement of brachioradial muscle VO2-blood flow relationship during graded isometric exercise,” Adv. Exp. Med. Biol. 388, 293–298 (1996).
[CrossRef] [PubMed]

Moes, C. J. M.

Mourant, J. R.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, J. P. Freyer, “Evidence of intrinsic differences in the light scattering properties of tumorigenic and nontumorigenic cells,” Cancer 84, 366–374 (1998).
[CrossRef]

Nauta, J. M.

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comp. J. (Cambridge) 7, 308–313 (1964).

Nelson, J. S.

J. F. de Boer, S. M. Srinivas, A. Malekafzali, Z. Chen, J. S. Nelson, “Imaging thermally damaged tissue by polarization sensitive optical coherence tomography,” Opt. Exp. 3, 212–218 (1998).
[CrossRef]

L. O. Svaasand, L. T. Norvang, E. J. Fiskerstrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine stains,” Lasers Med. Sci. 10, 55–65 (1995).
[CrossRef]

Nooren, C. A.

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

Norvang, L. T.

L. O. Svaasand, L. T. Norvang, E. J. Fiskerstrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine stains,” Lasers Med. Sci. 10, 55–65 (1995).
[CrossRef]

Patterson, M. S.

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

T. J. Farrell, M. S. Patterson, “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]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

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

Paunescu, L. A.

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Pham, D.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

Pham, T. H.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. A. Anderson, B. J. Tromberg, “A broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. H. Pham, B. J. Tromberg, M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

Pietranico, B.

R. A. de Blasi, R. Sfareni, B. Pietranico, A. M. Mega, M. Ferrari, “Non invasive measurement of brachioradial muscle VO2-blood flow relationship during graded isometric exercise,” Adv. Exp. Med. Biol. 388, 293–298 (1996).
[CrossRef] [PubMed]

Posthumus, R.

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

Prahl, S. A.

Press, W. H.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, N.Y., 1992), pp. 408–412.

Quaresima, V.

V. Quaresima, S. J. Matcher, M. Ferrari, “Identification and quantification of intrinsic optical contrast for near-infrared mammography,” Photochem. Photobiol. 67, 4–14 (1998).
[CrossRef] [PubMed]

Reynolds, E. O.

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Richardson, C.

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Roodenburg, J. L.

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

Schmitt, J. M.

Sfareni, R.

R. A. de Blasi, R. Sfareni, B. Pietranico, A. M. Mega, M. Ferrari, “Non invasive measurement of brachioradial muscle VO2-blood flow relationship during graded isometric exercise,” Adv. Exp. Med. Biol. 388, 293–298 (1996).
[CrossRef] [PubMed]

So, P.

Speelman, O. C.

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

Spott, T.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. H. Pham, B. J. Tromberg, M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

Srinivas, S. M.

J. F. de Boer, S. M. Srinivas, A. Malekafzali, Z. Chen, J. S. Nelson, “Imaging thermally damaged tissue by polarization sensitive optical coherence tomography,” Opt. Exp. 3, 212–218 (1998).
[CrossRef]

Star, W. M.

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

Stopps, E. K. S.

L. O. Svaasand, L. T. Norvang, E. J. Fiskerstrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine stains,” Lasers Med. Sci. 10, 55–65 (1995).
[CrossRef]

Svaasand, L. O.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. H. Pham, B. J. Tromberg, M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

L. O. Svaasand, L. T. Norvang, E. J. Fiskerstrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine stains,” Lasers Med. Sci. 10, 55–65 (1995).
[CrossRef]

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2743 (1994).
[CrossRef]

Teukolsky, S. A.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, N.Y., 1992), pp. 408–412.

Tittel, F. K.

Tromberg, B. J.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. A. Anderson, B. J. Tromberg, “A broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. H. Pham, B. J. Tromberg, M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2743 (1994).
[CrossRef]

Tsay, T. T.

van den Bergh, H.

van der Zee, P.

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Venugopalan, V.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

Vetterling, W. T.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, N.Y., 1992), pp. 408–412.

Wagnieres, G.

Walker, E. C.

Wall, R. T.

Weiss, G. H.

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

Wilson, B. C.

Witjes, M. J.

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

Wyatt, J. S.

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Yodh, A. G.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Zhang, Y.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Zhou, G. Z.

Adv. Exp. Med. Biol.

R. A. de Blasi, R. Sfareni, B. Pietranico, A. M. Mega, M. Ferrari, “Non invasive measurement of brachioradial muscle VO2-blood flow relationship during graded isometric exercise,” Adv. Exp. Med. Biol. 388, 293–298 (1996).
[CrossRef] [PubMed]

Appl. Opt.

Cancer

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, J. P. Freyer, “Evidence of intrinsic differences in the light scattering properties of tumorigenic and nontumorigenic cells,” Cancer 84, 366–374 (1998).
[CrossRef]

Comp. J. (Cambridge)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comp. J. (Cambridge) 7, 308–313 (1964).

J. Appl. Physiol.

A. D. Edwards, C. Richardson, P. van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

J. Mod. Opt.

I. Dayan, S. Havlin, 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.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Lasers Med. Sci.

L. O. Svaasand, L. T. Norvang, E. J. Fiskerstrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine stains,” Lasers Med. Sci. 10, 55–65 (1995).
[CrossRef]

Med. Phys.

T. J. Farrell, M. S. Patterson, “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. Exp.

J. F. de Boer, S. M. Srinivas, A. Malekafzali, Z. Chen, J. S. Nelson, “Imaging thermally damaged tissue by polarization sensitive optical coherence tomography,” Opt. Exp. 3, 212–218 (1998).
[CrossRef]

Philos. Trans. R. Soc. London Series B

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. H. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Series B 352, 661–668 (1997).
[CrossRef]

Photochem. Photobiol.

M. J. Witjes, A. J. Mank, O. C. Speelman, R. Posthumus, C. A. Nooren, J. M. Nauta, J. L. Roodenburg, W. M. Star, “Distribution of aluminum phthalocyanine disulfonate in an oral squamous cell carcinoma model. In vivo fluorescence imaging compared with ex vivo analytical methods,” Photochem. Photobiol. 65, 685–693 (1997).
[PubMed]

V. Quaresima, S. J. Matcher, M. Ferrari, “Identification and quantification of intrinsic optical contrast for near-infrared mammography,” Photochem. Photobiol. 67, 4–14 (1998).
[CrossRef] [PubMed]

Phys. Med. Biol.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. H. Pham, B. J. Tromberg, M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. A. Anderson, B. J. Tromberg, “A broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

Other

W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, N.Y., 1992), pp. 408–412.

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[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic depicts the parameters of two-layer turbid media. The top layer is characterized by the absorption coefficient (μ a1), reduced scattering coefficient (μ s1′), and thickness (l). μ a2 and μ s2′ denote, respectively, the absorption and reduced scattering coefficients of the bottom layer. The refractive indices of both layers are n, and air is n 0 = 1. The light source is an intensity-modulated plane wave. The source strength decays exponentially at rates that depend on layer optical properties.

Fig. 2
Fig. 2

Schematic outline of components and construction of the frequency-domain instrument that was used to measure amplitude and phase of photon density waves for frequencies ranging from 10 to 1500 MHz. (b) A two-compartment container was used to hold the top and bottom layer liquid phantoms; layers were separated by a thin, transparent polyvinyl film. Light emitted from the 100-µm source fiber was expanded to form a 5-cm-diameter illumination spot. GPIB, general-purpose interface bus; APD, avalanche photodiode.

Fig. 3
Fig. 3

Plots show response of PPDW phase and amplitude as the top-layer thickness (l) is increased from 0.00 to 10.40 mm. Optical properties of the layers were μ a1 = 0.0054 mm-1, μ s1′ = 0.310 mm-1, μ a2 = 0.0056 mm-1, and μ s2′ = 0.630 mm-1. (a) Measured phase is compared with (b) simulated phase, and (c) measured amplitude is compared with (d) simulated amplitude. Simulated phase and amplitude were calculated from known properties of the two-layer media.

Fig. 4
Fig. 4

Example showing agreement between experimental data and results of the fit: (a) experimental phase (■) (solid curves); (b) experimental amplitude (■). Experimental phase and amplitude are from data set 1, and the properties of the two-layer medium were l = 1.55 mm, μ a1 = 0.0054 mm-1, μ s1′ = 0.310 mm-1, μ a2 = 0.0056 mm-1, and μ s2′ = 0.630 mm-1. Fit data are from use of the simplex (Nelder–Mead) algorithm to simultaneously fit phase and amplitude data to extract l and μ s1′.

Fig. 5
Fig. 5

PPDW phase and amplitude data were acquired from two-layer media with properties specified in Table 1. Phase and amplitude measurements were fit to model functions [Eq. (14)] to estimate one variable. Only the experimentally varied property was calculated, whereas other parameters were set to real values. The true value for each data set is specified on the x axis of the subplots. Results of one-variable fits are shown in subplots (a) through (e) for the five data sets of Table 1 [(a) through (e) correspond to sets 1 through 5, respectively]. Fit values for different initial guesses are specified on the subplots as initial guess 1 (♦) and initial guess 2 (▲), and solid lines indicate expected values.

Fig. 6
Fig. 6

Representative results of two-variable fits for data set 5 are plotted in (a) and (b). Reduced scattering of the bottom layer (μ s2′) was experimentally increased, whereas the other properties were held constant (l = 2.35 mm, μ a1 = 0.0054 mm-1, μ s1′ = 0.310 mm-1, and μ a2 = 0.0054 mm-1). FDPM amplitude and phase data were simultaneously fit to model functions to calculate optical properties (μ a2 and μ s2′) of the bottom layer, whereas the remaining parameters (μ a1, μ s1′, and l) were assigned to real values. (a) Fit μ s2′ values for two different initial guesses are plotted (♦, ▲) and expected values are shown as a solid line. (b) Fit μ a2 values (♦, ▲) and expected μ a2 values (solid line). μ a2 was kept constant in the experiment, and thus expected values appear as a horizontal line in (b).

Fig. 7
Fig. 7

Representative results of three-variable fit for data set 1 are shown in (a)–(c). Thickness l was experimentally increased whereas the other four properties were kept constant (μ a1 = 0.0054 mm-1, μ s1′ = 0.310 mm-1, μ a2 = 0.0056 mm-1 and μ s2′ = 0.630 mm-1). FDPM amplitude and phase data were simultaneously fit to model functions to calculate three parameters (μ a1, μ s1′, and l) of the top layer. μ a2 and μ s2′ were set to real values. (a) Fit values of l for two different initial guesses (♦, ▲) and expected l values (solid line). (b) Fit μ a1 values with different initial guesses (♦, ▲) and expected μ a1 values (solid line). (c) Fit μ s1′ values for different initial guesses (♦, ▲) and expected μ s1′ values (solid line).

Fig. 8
Fig. 8

Representative results of five-variable fit for data set 4 are shown in (a)–(c). μ a2 was experimentally increased whereas the other four properties were kept constant (l = 2.10 mm, μ a1 = 0.0054 mm-1, μ s1′ = 0.310 mm-1, and μ s2′ = 0.630 mm-1). Amplitude and phase data were simultaneously fit to model functions to estimate all five parameters (μ a1, μ s1′, μ a2, μ s2′, and l). (a) Fit μ a2 values for different initial guesses (♦, ▲) and expected μ a2 values (solid line). (b) Thickness (l) and μ s2′. On the left y axis of (b), fit (♦) and expected (solid line) thickness values are plotted against real μ a2 values. On the right y axis of (b), fit (■) and expected (dashed line) μ s2′ values are plotted versus real μ a2 values. (c) Properties of the top layer (μ a1 and μ s1′): fit (♦) and expected (solid line) μ a1 on the left y axis; fit (■) and expected (dashed line) μ s1′ on the right y axis.

Tables (2)

Tables Icon

Table 1 Properties of Two-Layer Media for the Five Experimental Data Sets

Tables Icon

Table 2 Uncertainties in the Estimation of the Fit Parameter (l, μ a , μ s ′) for One-, Two-, and Three-Variable Fits a

Equations (16)

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

2-3μaμtr-3μtrc1+μaμtrt-3c22t2ϕ=-3μtr-3ctq,
2-1δc2=-qζc,
δc=3μaμtr-3ω2c2+i1+μaμtr3μtrωc-1/2,
ζc=3μtr1+i ωcμtr.
j=-ζcϕ.
q1=P0μs,1 exp-μtr,1+i ωcz, 0<zl,  q2=P0μs,2 exp-μtr,1lexp-μtr,2+i ωc×z-l, l<z,
ϕ1|z=l-=ϕ2|z=l+,  j1|z=l-=j2|z=l+.
j|z=0+=ηϕ|z=0+, with η=1-Reff21+Reff,
ϕ1=ψ1 exp-μtr,1+i ωcz+A1 exp-zδc,1+A2 expzδc,1, 0<zl,  ϕ2=ψ2 exp-μtr,2+i ωcz-l+A3 exp-zδc,2, l<z,
ψ1=P0δc,12μs,1ζc,11-δc,12μtr,1+i ωc2,  ψ2=P0δc,22μs,2ζc,21-δc,22μtr,2+i ωc2exp-μtr,1+i ωcl.
α11α12α13α21α22α23α31α32α33A1A2A3=β1β2β3, or αA=β,
α11=exp-lδc,1,α12=explδc,1,α13=exp-lδc,2,α21=ζc,1δc,1 exp-lδc,1,α22=-ζc,1δc,1 explδc,1,α23=-ζc,2δc,2 exp-lδc,2,α31=η-ζc,1δc,1,α32=η+ζc,1δc,1,α33=0,
β1=ψ2-ψ1 exp-μtr,1+i ωcl,  β2=ψ2ζc,2μtr,2+i ωc-ψ1ζc,1μtr,1 + i ωc×exp-μtr,1+i ωcl,  β3=ψ1ζc,1μtr,1+i ωc-ηψ1,
γ=-j|z=0P0=|γ|exp-iθγ.
θir=θcalωi-θγωi,  Airωi=Acalωi|γωi|,
χ2=iθi-θγωi; μa1, μs1, μa2, μs2, lσθ,i2+Ai-|γ|ωi; μa1, μs1, μa2, μs2, lσ|γ|,i2,

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