Abstract

Most instruments used to measure tissue optical properties noninvasively employ data-analysis algorithms that rely on the simplifying assumption that the tissue is semi-infinite and homogeneous. The influence of a layered tissue architecture on the determination of the scattering and absorption coefficients has been investigated in this study. Reflectance as a function of distance from a point source for a two-layered tissue architecture that simulates skin overlying fat was calculated by using a Monte Carlo code. These data were analyzed by using a diffusion theory model for a homogeneous semi-infinite medium to calculate the scatter and absorption coefficients. Depending on the algorithm and the radial distance, the estimated tissue optical properties were different from those of either layer, and under some circumstances, physically impossible. In addition, the sensitivity and cross talk of the estimated optical properties to changes in input optical properties were calculated for different layered geometries. For typical optical properties of skin, the sensitivity to changes in optical properties is highly dependent on the layered architecture, the measurement distance, and the fitting algorithm. Furthermore, a change in the input absorption coefficient may result in an apparent change in the measured scatter coefficient, and a change in the input scatter coefficient may result in an apparent change in the measured absorption coefficient.

© 1998 Optical Society of America

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1997 (4)

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Non-invasive in vivo measurements of photosensitizer uptake using diffuse reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

M. G. Nichols, E. L. Hull, T. H. Foster, “Design and testing of a white-light steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt. 36, 1–12 (1997).
[CrossRef]

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).
[CrossRef]

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

1996 (3)

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]

B. W. Pogue, M. S. Patterson, “Error assessment of a wavelength tunable frequency domain system for noninvasive tissue spectroscopy,” J. Biomed. Opt. 1, 311–323 (1996).
[CrossRef] [PubMed]

B. J. Tromberg, L. O. Svaasand, M. K. Fehr, S. J. Madsen, P. Wyss, B. Sansone, Y. Tadir, “A mathematical model for light dosimetry in photodynamic destruction of human endometrium,” Phys. Med. Biol. 41, 233–237 (1996).
[CrossRef]

1994 (6)

1992 (4)

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. C. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (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]

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

1990 (1)

1989 (2)

1988 (2)

R. Nossal, J. Keifer, G. Weiss, R. Bonner, H. Taitelbaum, S. Havlin, “Photon migration in layered media,” Appl. Opt. 27, 3382–3391 (1988).
[CrossRef] [PubMed]

M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
[CrossRef] [PubMed]

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]

1986 (1)

B. C. Wilson, M. S. Patterson, “The physics of photodynamic therapy,” Phys. Med. Biol. 31, 327–360 (1986).
[CrossRef] [PubMed]

1941 (1)

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Anderson, E. R.

Barbieri, B.

Berger, M.

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Bocker, D.

Böcker, D.

Bonner, R.

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.

Cope, M.

M. Kohl, M. Essenpreis, M. Cope, D. Bocker, “Influence of glucose concentration upon light scattering in tissue simulating phantoms,” Opt. Lett. 19, 2170–2172 (1994).
[CrossRef] [PubMed]

M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
[CrossRef] [PubMed]

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]

Delpy, D. T.

M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
[CrossRef] [PubMed]

Diamond, K. R.

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Non-invasive in vivo measurements of photosensitizer uptake using diffuse reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

Essenpreis, M.

Fantini, S.

Farrell, T. J.

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

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

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

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Application in Photodynamic Therapy, G. J. Gomer, ed., Vol. IS06 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990), pp. 219–231.

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]

Fehr, M. K.

B. J. Tromberg, L. O. Svaasand, M. K. Fehr, S. J. Madsen, P. Wyss, B. Sansone, Y. Tadir, “A mathematical model for light dosimetry in photodynamic destruction of human endometrium,” Phys. Med. Biol. 41, 233–237 (1996).
[CrossRef]

Feng, T. C.

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2724–2741 (1994).
[CrossRef]

Fishkin, S.

Foster, T. H.

M. G. Nichols, E. L. Hull, T. H. Foster, “Design and testing of a white-light steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt. 36, 1–12 (1997).
[CrossRef]

Fraceschini, M. A.

Franceshini, M.

Gerald, C. F.

C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1990).

Gratton, E.

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Gutsche, A. S.

S. L. Jacques, A. S. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. Van der Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

Haskell, R. C.

S. J. Madsen, E. R. Anderson, R. C. Haskell, B. J. Tromberg, “Portable high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy,” Opt. Lett. 19, 1934–1936 (1994).
[CrossRef] [PubMed]

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2724–2741 (1994).
[CrossRef]

Havlin, S.

Hayward, J. E.

Hefetz, Y.

Heinemann, L.

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Hibst, R.

Hull, E. L.

M. G. Nichols, E. L. Hull, T. H. Foster, “Design and testing of a white-light steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt. 36, 1–12 (1997).
[CrossRef]

Jacques, S. C.

Jacques, S. L.

S. L. Jacques, A. S. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. Van der Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

Keifer, J.

Kienle, A.

Kohl, M.

Kölzer, J.

Koschinsky, T.

Lilge, L.

Madsen, S. J.

Maier, J. S.

McAdams, M.

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2724–2741 (1994).
[CrossRef]

Mitic, G.

Nichols, M. G.

M. G. Nichols, E. L. Hull, T. H. Foster, “Design and testing of a white-light steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems,” Appl. Opt. 36, 1–12 (1997).
[CrossRef]

Nossal, R.

Orskov, H.

Otto, J.

Park, Y. D.

Patterson, M. S.

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).
[CrossRef]

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahl-Christiansen, H. Orskov, M. Essenpreis, G. Schmelzeisen-Redeker, D. Böcker, “Correlation between blood glucose concentration in diabetics and noninvasively 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, “Non-invasive in vivo measurements of photosensitizer uptake using diffuse 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]

B. W. Pogue, M. S. Patterson, “Error assessment of a wavelength tunable frequency domain system for noninvasive tissue spectroscopy,” J. Biomed. Opt. 1, 311–323 (1996).
[CrossRef] [PubMed]

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. C. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

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

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

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

B. C. Wilson, M. S. Patterson, “The physics of photodynamic therapy,” Phys. Med. Biol. 31, 327–360 (1986).
[CrossRef] [PubMed]

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Application in Photodynamic Therapy, G. J. Gomer, ed., Vol. IS06 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990), pp. 219–231.

Plies, E.

Pogue, B. W.

B. W. Pogue, M. S. Patterson, “Error assessment of a wavelength tunable frequency domain system for noninvasive tissue spectroscopy,” J. Biomed. Opt. 1, 311–323 (1996).
[CrossRef] [PubMed]

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]

Sandahl-Christiansen, J.

Sansone, B.

B. J. Tromberg, L. O. Svaasand, M. K. Fehr, S. J. Madsen, P. Wyss, B. Sansone, Y. Tadir, “A mathematical model for light dosimetry in photodynamic destruction of human endometrium,” Phys. Med. Biol. 41, 233–237 (1996).
[CrossRef]

Schmelzeisen-Redeker, G.

Schmitt, J. M.

Schwartz, J.

S. L. Jacques, A. S. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. Van der Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

Sölkner, G.

Steiner, R.

Svaasand, L. O.

B. J. Tromberg, L. O. Svaasand, M. K. Fehr, S. J. Madsen, P. Wyss, B. Sansone, Y. Tadir, “A mathematical model for light dosimetry in photodynamic destruction of human endometrium,” Phys. Med. Biol. 41, 233–237 (1996).
[CrossRef]

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2724–2741 (1994).
[CrossRef]

Tadir, Y.

B. J. Tromberg, L. O. Svaasand, M. K. Fehr, S. J. Madsen, P. Wyss, B. Sansone, Y. Tadir, “A mathematical model for light dosimetry in photodynamic destruction of human endometrium,” Phys. Med. Biol. 41, 233–237 (1996).
[CrossRef]

Taitelbaum, H.

Tittel, F. K.

S. L. Jacques, A. S. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. Van der Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

Tromberg, B. J.

B. J. Tromberg, L. O. Svaasand, M. K. Fehr, S. J. Madsen, P. Wyss, B. Sansone, Y. Tadir, “A mathematical model for light dosimetry in photodynamic destruction of human endometrium,” Phys. Med. Biol. 41, 233–237 (1996).
[CrossRef]

S. J. Madsen, E. R. Anderson, R. C. Haskell, B. J. Tromberg, “Portable high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy,” Opt. Lett. 19, 1934–1936 (1994).
[CrossRef] [PubMed]

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2724–2741 (1994).
[CrossRef]

Tsay, T. T.

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C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1990).

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T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

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

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. C. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved transmittance and reflectance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
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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).
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B. C. Wilson, M. S. Patterson, “The physics of photodynamic therapy,” Phys. Med. Biol. 31, 327–360 (1986).
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B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Application in Photodynamic Therapy, G. J. Gomer, ed., Vol. IS06 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990), pp. 219–231.

Wyss, P.

B. J. Tromberg, L. O. Svaasand, M. K. Fehr, S. J. Madsen, P. Wyss, B. Sansone, Y. Tadir, “A mathematical model for light dosimetry in photodynamic destruction of human endometrium,” Phys. Med. Biol. 41, 233–237 (1996).
[CrossRef]

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[CrossRef] [PubMed]

H. Taitelbaum, S. Havlin, G. H. Weiss, “Approximate theory of photon migration in a two-layer medium,” Appl. Opt. 28, 2245–2249 (1989).
[CrossRef] [PubMed]

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

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. C. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

S. Fantini, M. Franceshini, S. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting diode-based technique,” Appl. Opt. 33, 5204–5213 (1994).
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[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]

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L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

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B. W. Pogue, M. S. Patterson, “Error assessment of a wavelength tunable frequency domain system for noninvasive tissue spectroscopy,” J. Biomed. Opt. 1, 311–323 (1996).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

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. A (3)

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M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
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Med. Phys. (1)

T. J. Farrell, M. S. Patterson, B. C. 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. Lett. (4)

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, “Non-invasive in vivo measurements of photosensitizer uptake using diffuse reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[CrossRef] [PubMed]

Phys. Med. Biol. (3)

B. C. Wilson, M. S. Patterson, “The physics of photodynamic therapy,” Phys. Med. Biol. 31, 327–360 (1986).
[CrossRef] [PubMed]

B. J. Tromberg, L. O. Svaasand, M. K. Fehr, S. J. Madsen, P. Wyss, B. Sansone, Y. Tadir, “A mathematical model for light dosimetry in photodynamic destruction of human endometrium,” Phys. Med. Biol. 41, 233–237 (1996).
[CrossRef]

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of a neural network to determine tissue optical properties from spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

Other (4)

C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1990).

B. C. Wilson, T. J. Farrell, M. S. Patterson, “An optical fiber-based diffuse reflectance spectrometer for non-invasive investigation of photodynamic sensitizers in vivo,” in Future Directions and Application in Photodynamic Therapy, G. J. Gomer, ed., Vol. IS06 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990), pp. 219–231.

S. L. Jacques, A. S. Gutsche, J. Schwartz, L. Wang, F. K. Tittel, “Video reflectometry to extract optical properties of tissue in vivo,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. Van der Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 211–226.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

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Figures (14)

Fig. 1
Fig. 1

Typical steady-state reflectance data measured by using a video reflectometer at 750 nm on a human volunteer. Measured reflectance is plotted against radial distance (symbols) and best fit, obtained by using a two-layered Monte Carlo simulation (curve).

Fig. 2
Fig. 2

Steady-state reflectance as a function of radial distance, generated by using a two-layered Monte Carlo simulation and baseline optical properties. The extreme top and bottom curves are for single-layer simulations with optical properties corresponding to a lower fat layer and an upper skin layer, respectively. The middle curves, from top to bottom, correspond to the thickness of the skin layer, changing from 0.5 to 4.0 mm in steps of 0.5 mm.

Fig. 3
Fig. 3

Phase difference for 300-MHz modulated intensity reflectance as a function of radial distance, generated by using a two-layer Monte Carlo simulation and baseline optical properties. (a) The dashed curves are for single-layer simulations corresponding to skin optical properties and fat optical properties; the solid curves, from top to bottom, correspond to skin layer thicknesses of 2, 4, and 8 mm. (b) Curves are identical to (a); the range of data plotted is greater.

Fig. 4
Fig. 4

Time-resolved reflectance at (a) 5 mm, (b) 15 mm as a function of time, generated by using a two-layer Monte Carlo simulation with an upper layer thickness of 3.0 mm and baseline optical properties. Smooth curves were calculated by using diffusion theory for a homogeneous tissue and correspond to skin optical properties (lower smooth curve) and fat optical properties (upper smooth curve). The middle curve is two-layered Monte Carlo reflectance.

Fig. 5
Fig. 5

Nonlinear least squares fit to Monte Carlo simulations, using a homogeneous steady-state reflectance model for different top-layer thicknesses. Data are multiplied by radial distance squared to enhance visualization of fit. Smooth curves are least-squares fits and noisy curves are Monte Carlo data. (a) Curves are for a single-layer simulation: the upper curve represents fat optical properties and the lower curve represents skin optical properties. (b) Curves are for two-layered simulations: from bottom to top, the curves represent interface depths of 1.0, 1.5, 2.0, and 2.5 mm, respectively.

Fig. 6
Fig. 6

Plot of fitted optical properties as a function of interface depth. Baseline optical properties were used for Monte Carlo simulations, and a complete set of steady-state data between 1 and 10 mm was fit by using the Marquardt algorithm. Dotted lines represent optical properties for skin and fat layers. (a) Scatter coefficient as function of interface depth. (b) Absorption coefficient as function of interface depth.

Fig. 7
Fig. 7

Nonlinear least-squares fit to Monte Carlo simulations, using a homogeneous time-resolved reflectance model. Smooth curves are least-squares fits and noisy curves are Monte Carlo data. Upper curves represent time-resolved reflectance at 5 mm radial distance; lower curves represent time-resolved reflectance at 15 mm.

Fig. 8
Fig. 8

Plot of percentage change in the measured optical property as a function of percentage change in the input optical property. Relative reflectance data were obtained from 1 to 10 mm by using an interface depth of 1.5 mm and were fit by using a neural network algorithm. For all plots the symbols represent: ○, change in the optical property in both layers; △, change in the optical property in the upper layer; ▽, change in the optical property in the lower layer. (a) Sensitivity to change in the scatter coefficient. (b) Cross talk of change in the scatter coefficient into the measured absorption coefficient. (c) Cross talk of change in the absorption coefficient into the measured scatter coefficient. (d) Sensitivity to change in the absorption coefficient.

Fig. 9
Fig. 9

Plot of sensitivity and cross talk as a function of interface depth. Data were fit by using a neural network algorithm. For all plots the symbols represent: ○, change in the optical property in both layers; △, change in the optical property in the upper layer; ▽, change in the optical property in the lower layer. (a) Sensitivity to change in the scatter coefficient. (b) Cross talk of change in the scatter coefficient into the measured absorption coefficient. (c) Sensitivity to change in the absorption coefficient. (d) Cross talk of change in the absorption coefficient into the measured scatter coefficient.

Fig. 10
Fig. 10

Nonlinear least-squares fit to Monte Carlo simulations, using a homogeneous steady-state reflectance model plotted as a function of radial distance for different fitting ranges. Smooth curves are least-squares fits and the noisy curve is Monte Carlo data generated by using a two-layered model and an interface depth of 1.5 mm.

Fig. 11
Fig. 11

Steady-state reflectance calculated by using a homogeneous diffusion theory model plotted as a function of radial distance. Data are multiplied by radial distance squared to enhance visualization. All curves have a scatter coefficient of 2.0 mm-1. Curves from bottom to top represent absorption coefficients of 0.1, 0.01, 0.001, 0.0001, and 0.00001 mm-1, respectively. Note the kink in the curves for low values of the absorption coefficient, which is also characteristic of the curves for two-layered media.

Fig. 12
Fig. 12

Photon density as a function of depth for a semi-infinite beam normally incident on a semi-infinite tissue. The lower curve is calculated for a two-layered tissue, using the baseline optical properties and an interface depth of 1.5 mm. The upper curve uses the optical properties obtained by fitting the two-layered Monte Carlo data with a homogeneous model.

Fig. 13
Fig. 13

Simulated scatter and absorption spectra obtained by fitting two-layered Monte Carlo data, using the homogeneous model. The interface depth was 1.5 mm and a neural network algorithm was used. For each figure the scatter coefficient does not change with wavelength, while the absorption coefficient changes by 100% at the position of a simulated absorption peak. The absorption coefficient changes (a) only in the upper layer, (b) only in the lower layer.

Fig. 14
Fig. 14

Absorption and scatter spectra obtained on rabbit dorsal skin 24 h following an injection of AlPcS4. The concentration of drug in the skin is approximately ten times that in the underlying muscle. The absorption spectrum for AlPcS4 is shown in the inset.

Tables (6)

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Table 1 Baseline Optical Properties Used for Monte Carlo Simulations

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Table 2 Summary of Fitting Algorithms Used for Data Analysis

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Table 3 Summary of Optical Properties Estimated from Baseline Simulations and a 1.5-mm Skin Layer

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Table 4 Sensitivity and Cross Talk to Optical Property Changes by Using a Neural Network

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Table 5 Sensitivity and Cross Talk to Optical Property Changes in the Upper Skin Layer Only

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Table 6 Cross Talk and Sensitivity to Optical Property Changes in the Bottom Fat Layer Only

Equations (5)

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

R ρ = 1 4 π μ t μ eff + 1 r 1 exp - μ eff r 1 r 1 2 + 4 3   A + 1 μ eff + 1 r 2 exp - μ eff r 2 r 2 2 ,
r 1 = z 0 2 + ρ 2 ,     r 2 = z 0 + 2 z b 2 + ρ 2 ,
R ρ ,   t = 1 2 4 π Dc - 3 / 2 t - 5 / 2 exp - μ a ct × z 0 exp - r 1 2 4 Dct + z 0 + 2 z b exp - r 2 2 4 Dct .
R ρ ,   t = z 0 4 π k + 1 r 1 exp - kr 1 - i ω t + 4 3   A + 1 k + 1 r 2 exp - kr 2 - i ω t ,
k = μ a + i ω / c D .

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