Abstract

We report on steady-state measurements on the anisotropy of autofluorescence from malignant and normal breast tissue as a function of tissue thickness. For thin tissue sections the anisotropy from normal tissue was found to be smaller compared with that from malignant tissue. However, the opposite result was obtained for thicker tissues. A phenomenological model was also developed to simulate the dependence of anisotropy on tissue thickness.

© 2001 Optical Society of America

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References

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  1. K. Kincade, “Optical diagnostics images tissues and tumors,” Laser Focus World (February1996), pp. 71–79.
  2. E. Servick-Muraca, D. Benaron, eds., Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996).
  3. R. Richards Kortum, E. Servick-Muraca, “Quantitative optical spectroscopy for tissue diagnosis,” Annu. Rev. Phys. Chem. 47, 556–606 (1996).
  4. G. A. Wagnieres, W. M. Star, B. C. Wilson, “In-vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol. 68, 603–632 (1998).
  5. D. B. Tata, M. Foresti, J. Cordero, P. Tomashefsky, M. A. Alfano, R. R. Alfano, “Fluorescence polarization spectroscopy and time-resolved fluorescence kinetics of native cancerous and normal rat kidney tissues,” Biophys. J. 50, 463–469 (1986).
    [CrossRef] [PubMed]
  6. A. Pradhan, S. S. Jena, B. V. Laxmi, A. Agarwal, “Fluorescence depolarization of normal and diseased skin tissues,” in Optical Biopsy II, R. R. Alfano, A. Katzir, eds., Proc. SPIE3250, 78–82 (1998).
    [CrossRef]
  7. J. Lackowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983).
    [CrossRef]
  8. F. W. J. Teale, “Fluorescence depolarization by light scattering in turbid solutions,” Photochem. Photobiol. 10, 363–374 (1969).
    [CrossRef] [PubMed]
  9. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, pp. 182–183.
  10. C. F. Bohren, D. R. Hoffman, “Absorption and scattering of light by small particles,” (Wiley, New York, 1983).
  11. N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical parameters of human breast tissue,” in Proceedings of the National Laser Symposium (Center for Laser Technology and Department of Physics, Indian Institute of Technology Kanpur, Kanpur, India, 1998), pp. 217–218.
  12. N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissues,” Appl. Opt. 40, 176–184 (2001).
    [CrossRef]
  13. P. K. Gupta, S. K. Majumder, A. Uppal, “Breast cancer diagnosis using N2 laser excited autofluorescence spectroscopy,” Lasers Surg. Med. 21, 417–422 (1997).
    [CrossRef]
  14. S. K. Majumder, P. K. Gupta, B. Jain, A. Uppal, “UV excited autofluorescence spectroscopy of human breast tissues for discriminating cancerous tissue from benign tumor and normal tissue,” Lasers Life Sci. 8, 249–264 (1998).
  15. W. F. Cheong, “Summary of optical properties,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. Van Gemert, eds. (Plenum, New York, 1995), Chap. 8.
  16. D. Bicont, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
    [CrossRef]
  17. F. C. Mackintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
    [CrossRef]

2001 (1)

1998 (2)

S. K. Majumder, P. K. Gupta, B. Jain, A. Uppal, “UV excited autofluorescence spectroscopy of human breast tissues for discriminating cancerous tissue from benign tumor and normal tissue,” Lasers Life Sci. 8, 249–264 (1998).

G. A. Wagnieres, W. M. Star, B. C. Wilson, “In-vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol. 68, 603–632 (1998).

1997 (1)

P. K. Gupta, S. K. Majumder, A. Uppal, “Breast cancer diagnosis using N2 laser excited autofluorescence spectroscopy,” Lasers Surg. Med. 21, 417–422 (1997).
[CrossRef]

1996 (2)

K. Kincade, “Optical diagnostics images tissues and tumors,” Laser Focus World (February1996), pp. 71–79.

R. Richards Kortum, E. Servick-Muraca, “Quantitative optical spectroscopy for tissue diagnosis,” Annu. Rev. Phys. Chem. 47, 556–606 (1996).

1994 (1)

D. Bicont, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

1989 (1)

F. C. Mackintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

1986 (1)

D. B. Tata, M. Foresti, J. Cordero, P. Tomashefsky, M. A. Alfano, R. R. Alfano, “Fluorescence polarization spectroscopy and time-resolved fluorescence kinetics of native cancerous and normal rat kidney tissues,” Biophys. J. 50, 463–469 (1986).
[CrossRef] [PubMed]

1969 (1)

F. W. J. Teale, “Fluorescence depolarization by light scattering in turbid solutions,” Photochem. Photobiol. 10, 363–374 (1969).
[CrossRef] [PubMed]

Agarwal, A.

A. Pradhan, S. S. Jena, B. V. Laxmi, A. Agarwal, “Fluorescence depolarization of normal and diseased skin tissues,” in Optical Biopsy II, R. R. Alfano, A. Katzir, eds., Proc. SPIE3250, 78–82 (1998).
[CrossRef]

Alfano, M. A.

D. B. Tata, M. Foresti, J. Cordero, P. Tomashefsky, M. A. Alfano, R. R. Alfano, “Fluorescence polarization spectroscopy and time-resolved fluorescence kinetics of native cancerous and normal rat kidney tissues,” Biophys. J. 50, 463–469 (1986).
[CrossRef] [PubMed]

Alfano, R. R.

D. B. Tata, M. Foresti, J. Cordero, P. Tomashefsky, M. A. Alfano, R. R. Alfano, “Fluorescence polarization spectroscopy and time-resolved fluorescence kinetics of native cancerous and normal rat kidney tissues,” Biophys. J. 50, 463–469 (1986).
[CrossRef] [PubMed]

Bicont, D.

D. Bicont, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Hoffman, “Absorption and scattering of light by small particles,” (Wiley, New York, 1983).

Brosseau, C.

D. Bicont, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Cheong, W. F.

W. F. Cheong, “Summary of optical properties,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. Van Gemert, eds. (Plenum, New York, 1995), Chap. 8.

Cordero, J.

D. B. Tata, M. Foresti, J. Cordero, P. Tomashefsky, M. A. Alfano, R. R. Alfano, “Fluorescence polarization spectroscopy and time-resolved fluorescence kinetics of native cancerous and normal rat kidney tissues,” Biophys. J. 50, 463–469 (1986).
[CrossRef] [PubMed]

Foresti, M.

D. B. Tata, M. Foresti, J. Cordero, P. Tomashefsky, M. A. Alfano, R. R. Alfano, “Fluorescence polarization spectroscopy and time-resolved fluorescence kinetics of native cancerous and normal rat kidney tissues,” Biophys. J. 50, 463–469 (1986).
[CrossRef] [PubMed]

Ghosh, N.

N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissues,” Appl. Opt. 40, 176–184 (2001).
[CrossRef]

N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical parameters of human breast tissue,” in Proceedings of the National Laser Symposium (Center for Laser Technology and Department of Physics, Indian Institute of Technology Kanpur, Kanpur, India, 1998), pp. 217–218.

Gupta, P. K.

N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissues,” Appl. Opt. 40, 176–184 (2001).
[CrossRef]

S. K. Majumder, P. K. Gupta, B. Jain, A. Uppal, “UV excited autofluorescence spectroscopy of human breast tissues for discriminating cancerous tissue from benign tumor and normal tissue,” Lasers Life Sci. 8, 249–264 (1998).

P. K. Gupta, S. K. Majumder, A. Uppal, “Breast cancer diagnosis using N2 laser excited autofluorescence spectroscopy,” Lasers Surg. Med. 21, 417–422 (1997).
[CrossRef]

N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical parameters of human breast tissue,” in Proceedings of the National Laser Symposium (Center for Laser Technology and Department of Physics, Indian Institute of Technology Kanpur, Kanpur, India, 1998), pp. 217–218.

Hoffman, D. R.

C. F. Bohren, D. R. Hoffman, “Absorption and scattering of light by small particles,” (Wiley, New York, 1983).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, pp. 182–183.

Jain, B.

S. K. Majumder, P. K. Gupta, B. Jain, A. Uppal, “UV excited autofluorescence spectroscopy of human breast tissues for discriminating cancerous tissue from benign tumor and normal tissue,” Lasers Life Sci. 8, 249–264 (1998).

Jena, S. S.

A. Pradhan, S. S. Jena, B. V. Laxmi, A. Agarwal, “Fluorescence depolarization of normal and diseased skin tissues,” in Optical Biopsy II, R. R. Alfano, A. Katzir, eds., Proc. SPIE3250, 78–82 (1998).
[CrossRef]

Kincade, K.

K. Kincade, “Optical diagnostics images tissues and tumors,” Laser Focus World (February1996), pp. 71–79.

Lackowicz, J.

J. Lackowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983).
[CrossRef]

Laxmi, B. V.

A. Pradhan, S. S. Jena, B. V. Laxmi, A. Agarwal, “Fluorescence depolarization of normal and diseased skin tissues,” in Optical Biopsy II, R. R. Alfano, A. Katzir, eds., Proc. SPIE3250, 78–82 (1998).
[CrossRef]

Mackintosh, F. C.

F. C. Mackintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Majumder, S. K.

N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissues,” Appl. Opt. 40, 176–184 (2001).
[CrossRef]

S. K. Majumder, P. K. Gupta, B. Jain, A. Uppal, “UV excited autofluorescence spectroscopy of human breast tissues for discriminating cancerous tissue from benign tumor and normal tissue,” Lasers Life Sci. 8, 249–264 (1998).

P. K. Gupta, S. K. Majumder, A. Uppal, “Breast cancer diagnosis using N2 laser excited autofluorescence spectroscopy,” Lasers Surg. Med. 21, 417–422 (1997).
[CrossRef]

N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical parameters of human breast tissue,” in Proceedings of the National Laser Symposium (Center for Laser Technology and Department of Physics, Indian Institute of Technology Kanpur, Kanpur, India, 1998), pp. 217–218.

Martinez, A. S.

D. Bicont, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Mohanty, S. K.

N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissues,” Appl. Opt. 40, 176–184 (2001).
[CrossRef]

N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical parameters of human breast tissue,” in Proceedings of the National Laser Symposium (Center for Laser Technology and Department of Physics, Indian Institute of Technology Kanpur, Kanpur, India, 1998), pp. 217–218.

Pine, D. J.

F. C. Mackintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Pradhan, A.

A. Pradhan, S. S. Jena, B. V. Laxmi, A. Agarwal, “Fluorescence depolarization of normal and diseased skin tissues,” in Optical Biopsy II, R. R. Alfano, A. Katzir, eds., Proc. SPIE3250, 78–82 (1998).
[CrossRef]

Richards Kortum, R.

R. Richards Kortum, E. Servick-Muraca, “Quantitative optical spectroscopy for tissue diagnosis,” Annu. Rev. Phys. Chem. 47, 556–606 (1996).

Schmitt, J. M.

D. Bicont, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Servick-Muraca, E.

R. Richards Kortum, E. Servick-Muraca, “Quantitative optical spectroscopy for tissue diagnosis,” Annu. Rev. Phys. Chem. 47, 556–606 (1996).

Star, W. M.

G. A. Wagnieres, W. M. Star, B. C. Wilson, “In-vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol. 68, 603–632 (1998).

Tata, D. B.

D. B. Tata, M. Foresti, J. Cordero, P. Tomashefsky, M. A. Alfano, R. R. Alfano, “Fluorescence polarization spectroscopy and time-resolved fluorescence kinetics of native cancerous and normal rat kidney tissues,” Biophys. J. 50, 463–469 (1986).
[CrossRef] [PubMed]

Teale, F. W. J.

F. W. J. Teale, “Fluorescence depolarization by light scattering in turbid solutions,” Photochem. Photobiol. 10, 363–374 (1969).
[CrossRef] [PubMed]

Tomashefsky, P.

D. B. Tata, M. Foresti, J. Cordero, P. Tomashefsky, M. A. Alfano, R. R. Alfano, “Fluorescence polarization spectroscopy and time-resolved fluorescence kinetics of native cancerous and normal rat kidney tissues,” Biophys. J. 50, 463–469 (1986).
[CrossRef] [PubMed]

Uppal, A.

S. K. Majumder, P. K. Gupta, B. Jain, A. Uppal, “UV excited autofluorescence spectroscopy of human breast tissues for discriminating cancerous tissue from benign tumor and normal tissue,” Lasers Life Sci. 8, 249–264 (1998).

P. K. Gupta, S. K. Majumder, A. Uppal, “Breast cancer diagnosis using N2 laser excited autofluorescence spectroscopy,” Lasers Surg. Med. 21, 417–422 (1997).
[CrossRef]

Wagnieres, G. A.

G. A. Wagnieres, W. M. Star, B. C. Wilson, “In-vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol. 68, 603–632 (1998).

Weitz, D. A.

F. C. Mackintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Wilson, B. C.

G. A. Wagnieres, W. M. Star, B. C. Wilson, “In-vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol. 68, 603–632 (1998).

Zhu, J. X.

F. C. Mackintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Annu. Rev. Phys. Chem. (1)

R. Richards Kortum, E. Servick-Muraca, “Quantitative optical spectroscopy for tissue diagnosis,” Annu. Rev. Phys. Chem. 47, 556–606 (1996).

Appl. Opt. (1)

Biophys. J. (1)

D. B. Tata, M. Foresti, J. Cordero, P. Tomashefsky, M. A. Alfano, R. R. Alfano, “Fluorescence polarization spectroscopy and time-resolved fluorescence kinetics of native cancerous and normal rat kidney tissues,” Biophys. J. 50, 463–469 (1986).
[CrossRef] [PubMed]

Laser Focus World (1)

K. Kincade, “Optical diagnostics images tissues and tumors,” Laser Focus World (February1996), pp. 71–79.

Lasers Life Sci. (1)

S. K. Majumder, P. K. Gupta, B. Jain, A. Uppal, “UV excited autofluorescence spectroscopy of human breast tissues for discriminating cancerous tissue from benign tumor and normal tissue,” Lasers Life Sci. 8, 249–264 (1998).

Lasers Surg. Med. (1)

P. K. Gupta, S. K. Majumder, A. Uppal, “Breast cancer diagnosis using N2 laser excited autofluorescence spectroscopy,” Lasers Surg. Med. 21, 417–422 (1997).
[CrossRef]

Photochem. Photobiol. (2)

G. A. Wagnieres, W. M. Star, B. C. Wilson, “In-vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol. 68, 603–632 (1998).

F. W. J. Teale, “Fluorescence depolarization by light scattering in turbid solutions,” Photochem. Photobiol. 10, 363–374 (1969).
[CrossRef] [PubMed]

Phys. Rev. B (1)

F. C. Mackintosh, J. X. Zhu, D. J. Pine, D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[CrossRef]

Phys. Rev. E (1)

D. Bicont, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Other (7)

W. F. Cheong, “Summary of optical properties,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. Van Gemert, eds. (Plenum, New York, 1995), Chap. 8.

A. Pradhan, S. S. Jena, B. V. Laxmi, A. Agarwal, “Fluorescence depolarization of normal and diseased skin tissues,” in Optical Biopsy II, R. R. Alfano, A. Katzir, eds., Proc. SPIE3250, 78–82 (1998).
[CrossRef]

J. Lackowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, pp. 182–183.

C. F. Bohren, D. R. Hoffman, “Absorption and scattering of light by small particles,” (Wiley, New York, 1983).

N. Ghosh, S. K. Mohanty, S. K. Majumder, P. K. Gupta, “Measurement of optical parameters of human breast tissue,” in Proceedings of the National Laser Symposium (Center for Laser Technology and Department of Physics, Indian Institute of Technology Kanpur, Kanpur, India, 1998), pp. 217–218.

E. Servick-Muraca, D. Benaron, eds., Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996).

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Figures (9)

Fig. 1
Fig. 1

Wavelength dependence of (a) single-scattering efficiency (Q s ) and (b) reduced-scattering efficiency (Q s ′) for 0.61-µm-diameter microsphere suspension.

Fig. 2
Fig. 2

Typical polarized fluorescence spectra from a tissue phantom (microsphere concentration 0.53 × 1010/c.c. and NADH concentration 2.7 µM). The excitation wavelength used was 340 nm. Solid curve, spectra with excitation and emission polarizer oriented vertically (I ); dashed curve, spectra with excitation polarizer oriented vertically and emission polarizer oriented horizontally (I ). The inset shows the spectral dependence of G.

Fig. 3
Fig. 3

Values for anisotropy of fluorescence at 440 nm from the tissue phantom as a function of the sum of scattering coefficients (μ s tot = μ s ex + μ s em). Squares, experimentally measured values; circles, values predicted by the model.

Fig. 4
Fig. 4

(a) Typical polarized fluorescence spectra from malignant breast tissue with 340-nm excitation. Solid curve, spectra with excitation and emission polarizer oriented vertically (I ); dashed curve, spectra with excitation polarizer oriented vertically and emission polarizer oriented horizontally (I ). (b) Typical polarized fluorescence spectra from normal breast tissue with 340-nm excitation. Solid curve, spectra with excitation and emission polarizer oriented vertically (I ); dashed curve, spectra with excitation polarizer oriented vertically and emission polarizer oriented horizontally (I ).

Fig. 5
Fig. 5

Mean anisotropy spectra of 2-mm-thick malignant (dashed curve) and normal (solid curve) breast tissues with 340-nm excitation.

Fig. 6
Fig. 6

Mean anisotropy spectra of 2-mm-thick malignant (dashed curve) and normal (solid curve) breast tissues with 460-nm excitation.

Fig. 7
Fig. 7

Variation of the value for anisotropy of 440-nm fluorescence from malignant (open circles) and normal (filled circles) breast tissues as a function of tissue thickness. The excitation wavelength used was 340 nm. The error bars in the figure represent standard deviation. The solid and the dashed curve profiles show theoretical fits for normal and malignant tissues, respectively. An expanded view of the dependence of the anisotropy on tissue thickness for thickness less than 0.1 mm is shown in the inset.

Fig. 8
Fig. 8

Variation of the value for anisotropy of 540-nm fluorescence from malignant (open circles) and normal (filled circles) breast tissues as a function of tissue thickness. The excitation wavelength used was 460 nm. The error bars in the figure represent standard deviation. The solid and the dashed curve profiles show theoretical fits for normal and malignant tissues, respectively. An expanded view of the dependence of the anisotropy on tissue thickness for thickness less than 0.1 mm is shown in the inset.

Fig. 9
Fig. 9

(a) Dependence of the estimates for μ s tot on the anisotropy reduction factor per scattering event. The estimates for μ s tot for malignant (open circles) and for normal tissues (filled circles) was obtained with the theoretical model to fit the measured thickness dependence of anisotropy of 340-nm-excited fluorescence at 440 nm. The ratio of estimates for μ s tot of malignant and normal tissues is shown with triangles. The inset shows dependence of the estimates for μeff tot for malignant (open diamonds) and normal (filled diamonds) tissues on the anisotropy reduction factor per scattering event. (b) Dependence of the estimates for μ s tot on uncertainty in tissue thickness. The estimates for μ s tot for malignant (open circles) and normal tissue (filled circles) was obtained with the theoretical model to fit the measured thickness dependence of anisotropy of 340-nm-excited fluorescence at 440 nm. The ratio of estimates for μ s tot of malignant and normal tissues is shown with triangles. (c) Dependence of the estimates for μeff tot on uncertainty in tissue thickness. The estimates for μeff tot for malignant (open circles) and normal tissues (filled circles) was obtained with the theoretical model to fit the measured thickness dependence of anisotropy of 340-nm-excited fluorescence at 440 nm. The ratio of estimates for μeff tot of malignant and normal tissues is shown with triangles.

Tables (1)

Tables Icon

Table 1 Values for Transport Parameters μ s tot and μeff tot of Normal and Malignant Breast Tissues That Provide Best Theoretical Fit to the Experimentally Measured Dependence Anisotropy on Tissue Thickness

Equations (21)

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

n1z=z×μsex.
n2z=z×μsem.
Az=A0×0.7n1z+n2z,
Aobs=iIifAii Iif,
Iz=C2ex exp-μeffexz+Aex exp-μtexz,
C2ex=-Aex1+μtexhex/1+μeffexhex-Q1ex/2π1+μeffexhex,
Aex=Q0ex/μtex2-μeffex2,
μeffex=3 μaex×μtrex1/2,
μtrex=μaex+μsex,
μsex=μsex1-gex,
Q0ex=3μsexμtrex+3μsexμtexgexI0/4π,
hex=2/3μtrex,
Q1ex=μsexgex/μtrexI0,
Iz=C2ex exp-μeffex z.
IfzC2ex exp-μeffexz×φC2em exp-μeffemz,
Aobs=A00texp-μefftotz×0.7n1z+n2zdz0texp-μefftotzdz.
Aobs=A0μefftot/μefftot-ln0.7×μstot×(1-exp-μefftott×0.7μstott/1-exp-μefftott),
μefftot=μeffex+μeffem,
μstot=μsex+μsem.
A=I-GI/I+2GI.
μs=N×A×Qs,  μs=N×A×Qs,

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