Abstract

A diffusion model describing the propagation of photon flux in the epidermal, dermal, and subcutaneous tissue layers of the skin is presented. Assuming that the skin is illuminated by a collimated, finite-aperture source, we develop expressions relating photon flux density within the skin and intensities re-emitted from the skin surface to the optical properties of the individual layers. Model simulations show that the rate at which re-emitted intensities diminish with radial distance away from the source can provide information about absorption and scattering in underlying tissues. Re-emitted intensities measured from homogeneous and two-layer tissue phantoms compare favorably with model predictions. We demonstrate potential applications of the model by estimating the absorption (Σa) and transport-corrected scattering (Σs) coefficients of dermis and subcutis from intensities measured from intact skin and by predicting the magnitude of the optical-density variations measured by a photoplethysmograph.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. A. Arndt, J. M. Noe, S. Rosen, eds., Cutaneous Laser Therapy (Wiley, London, 1983).
  2. T. J. Dougherty, J. E. Kaufman, A. Goldfarb, K. R. Weishaupt, D. G. Boyle, A. Mittleman, “Photoradiation therapy for the treatment of malignant tumors,” Cancer Res. 38, 2628–2635 (1978).
    [PubMed]
  3. R. F. Bonner, T. R. Clem, P. D. Bowen, R. L. Bowman, “Laser-Doppler continuous real-time monitor of pulsatile and mean blood flow in tissue microcirculation,” in Scattering Techniques Applied to Supramolecular and Non-Equilibrium Systems, S. H. Chen, B. Chu, R. Nossal, eds. (Plenum, New York, 1981), pp. 685–702.
    [CrossRef]
  4. K. K. Tremper, S. J. Barker, “Pulse oximetry,” Anesthesiology 70, 98–109 (1989).
    [CrossRef] [PubMed]
  5. K. R. Chapman, F. L. W. Liu, R. M. Watson, A. S. Rebuck, “Range of accuracy of two-wavelength oximetry,” Chest 4, 540–542 (1986).
    [CrossRef]
  6. R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applications in in vivoremittance spectroscopy,” in Proceedings of the Symposium on Bioengineering and the Skin (MTP, London, 1980), pp. 253–313.
  7. S. Wan, R. R. Anderson, J. A. Parrish, “Analytical modeling for the optical properties of the skin with in vitroand in vivoapplications,” Photochem. Photobiol. 34, 493–499 (1981).
    [PubMed]
  8. R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model for photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
    [CrossRef] [PubMed]
  9. R. Nossal, J. Kiefer, G. H. Weiss, R. Bonner, H. Taitelbaum, S. Havlin, “Photon migration in layered media,” Appl. Opt. 27, 3382–3391 (1988).
    [CrossRef] [PubMed]
  10. 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]
  11. S. Chandraseklar, Radiative Transfer (Dover, New York, 1960).
  12. R. L. Longini, R. Zdrojkowski, “A note on the theory of backscattering of light by living tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
    [CrossRef]
  13. R. J. Zdrojkowski, N. R. Pisharoty, “Optical transmission and reflection by blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
    [CrossRef]
  14. L. Reynolds, C. Johnson, A. Ishimaru, “Diffuse reflectance from a finite blood medium: applications to the modeling of fiber optic catheters,” Appl. Opt. 15, 2059–2067 (1976).
    [CrossRef] [PubMed]
  15. S. Takatani, M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
    [CrossRef]
  16. L. O. Reynolds, “Optical diffuse reflectance and transmittance from an anisotropically scattering finite blood medium.” Ph.D. dissertation (University of Washington, Seattle, Wash., 1975).
  17. R. A. J. Groenhuis, H. A. Ferwerda, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined by reflection measurements. 1: Theory,” Appl. Opt. 22, 2456–2462 (1983).
    [CrossRef] [PubMed]
  18. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 9, pp. 175–186.
    [CrossRef]
  19. H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 1, Chap. 14, pp. 477–492.
  20. M. Keijzar, W. M. Star, P. R. M. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988).
    [CrossRef]
  21. S. Takatani, “On the theory and development of a non-invasive tissue reflectance oximeter,” Ph.D. dissertation (Case Western Reserve University, Cleveland, Ohio, 1978).
  22. W. A. G. Bruls, J. C. van der Leun, “Forward scattering properties of human epidermal layers,” Photochem. Photobiol. 40, 231–242 (1984).
    [CrossRef] [PubMed]
  23. M. J. C. van Gemert, J. P. H. Henning, “A model approach to laser coagulation of dermal vascular lesions,” Arch. Dermatol. Res. 270, 429–439 (1981).
    [CrossRef] [PubMed]
  24. B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
    [CrossRef]
  25. S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
    [CrossRef] [PubMed]
  26. J. P. A. Marynissen, W. M. Star, “Phantom measurements for light dosimetry using isotropic and small aperture detectors,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, Gomen, eds. (Liss, New York, 1984), pp. 133–138.
  27. J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in vivomeasurement of blood oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
    [CrossRef]
  28. F. P. Bolin, L. E. Preuss, R. C. Taylor, R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2303 (1989).
    [CrossRef] [PubMed]
  29. A. J. Groenhuis, J. J. Ten Bosch, H. A. Ferwerda, “Scattering and absorption of turbid materials determined from reflection measurements. 2: Measuring method and calibration,” Appl. Opt. 22, 2463–2467 (1983).
    [CrossRef] [PubMed]
  30. S. B. Wilson, V. A. Spence, “A tissue heat transfer model relating dynamic skin temperature changes to the physiological parameters,” Phys. Med. Biol. 33, 894–897 (1988).
    [CrossRef]
  31. T. J. Ryan, “Structure, pattern, and shape of blood vessels of the skin,” in The Physiology and Pathophysiology of the Skin, A. Janet, ed. (Academic, New York, 1973), Vol. 2, Chap. 16.
  32. R. J. Zdrojkowski, R. L. Longini, “Optical transmission through whole blood illuminated with highly collimated light,” J. Opt. Soc. Am. 59, 898–903 (1969).
  33. J. T. Whitton, J. D. Everall, “The thickness of the epidermis,” Br. J. Dermatol. 89, 467–476 (1973).
    [CrossRef] [PubMed]
  34. B. J. Brinkworth, “Interpretation of the Kubelka–Munk coefficients in reflection theory,” Appl. Opt. 11, 1434–1435 (1972).
    [CrossRef] [PubMed]

1989 (3)

1988 (3)

1987 (2)

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model for photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

1986 (3)

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in vivomeasurement of blood oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

K. R. Chapman, F. L. W. Liu, R. M. Watson, A. S. Rebuck, “Range of accuracy of two-wavelength oximetry,” Chest 4, 540–542 (1986).
[CrossRef]

1984 (1)

W. A. G. Bruls, J. C. van der Leun, “Forward scattering properties of human epidermal layers,” Photochem. Photobiol. 40, 231–242 (1984).
[CrossRef] [PubMed]

1983 (2)

1981 (2)

M. J. C. van Gemert, J. P. H. Henning, “A model approach to laser coagulation of dermal vascular lesions,” Arch. Dermatol. Res. 270, 429–439 (1981).
[CrossRef] [PubMed]

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical modeling for the optical properties of the skin with in vitroand in vivoapplications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

1979 (1)

S. Takatani, M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

1978 (1)

T. J. Dougherty, J. E. Kaufman, A. Goldfarb, K. R. Weishaupt, D. G. Boyle, A. Mittleman, “Photoradiation therapy for the treatment of malignant tumors,” Cancer Res. 38, 2628–2635 (1978).
[PubMed]

1976 (1)

1973 (1)

J. T. Whitton, J. D. Everall, “The thickness of the epidermis,” Br. J. Dermatol. 89, 467–476 (1973).
[CrossRef] [PubMed]

1972 (1)

1970 (1)

R. J. Zdrojkowski, N. R. Pisharoty, “Optical transmission and reflection by blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
[CrossRef]

1969 (1)

1968 (1)

R. L. Longini, R. Zdrojkowski, “A note on the theory of backscattering of light by living tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
[CrossRef]

Anderson, R. R.

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical modeling for the optical properties of the skin with in vitroand in vivoapplications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applications in in vivoremittance spectroscopy,” in Proceedings of the Symposium on Bioengineering and the Skin (MTP, London, 1980), pp. 253–313.

Barker, S. J.

K. K. Tremper, S. J. Barker, “Pulse oximetry,” Anesthesiology 70, 98–109 (1989).
[CrossRef] [PubMed]

Bolin, F. P.

Bonner, R.

Bonner, R. F.

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model for photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
[CrossRef] [PubMed]

R. F. Bonner, T. R. Clem, P. D. Bowen, R. L. Bowman, “Laser-Doppler continuous real-time monitor of pulsatile and mean blood flow in tissue microcirculation,” in Scattering Techniques Applied to Supramolecular and Non-Equilibrium Systems, S. H. Chen, B. Chu, R. Nossal, eds. (Plenum, New York, 1981), pp. 685–702.
[CrossRef]

Bowen, P. D.

R. F. Bonner, T. R. Clem, P. D. Bowen, R. L. Bowman, “Laser-Doppler continuous real-time monitor of pulsatile and mean blood flow in tissue microcirculation,” in Scattering Techniques Applied to Supramolecular and Non-Equilibrium Systems, S. H. Chen, B. Chu, R. Nossal, eds. (Plenum, New York, 1981), pp. 685–702.
[CrossRef]

Bowman, R. L.

R. F. Bonner, T. R. Clem, P. D. Bowen, R. L. Bowman, “Laser-Doppler continuous real-time monitor of pulsatile and mean blood flow in tissue microcirculation,” in Scattering Techniques Applied to Supramolecular and Non-Equilibrium Systems, S. H. Chen, B. Chu, R. Nossal, eds. (Plenum, New York, 1981), pp. 685–702.
[CrossRef]

Boyle, D. G.

T. J. Dougherty, J. E. Kaufman, A. Goldfarb, K. R. Weishaupt, D. G. Boyle, A. Mittleman, “Photoradiation therapy for the treatment of malignant tumors,” Cancer Res. 38, 2628–2635 (1978).
[PubMed]

Brinkworth, B. J.

Bruls, W. A. G.

W. A. G. Bruls, J. C. van der Leun, “Forward scattering properties of human epidermal layers,” Photochem. Photobiol. 40, 231–242 (1984).
[CrossRef] [PubMed]

Burns, D. M.

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

Chandraseklar, S.

S. Chandraseklar, Radiative Transfer (Dover, New York, 1960).

Chapman, K. R.

K. R. Chapman, F. L. W. Liu, R. M. Watson, A. S. Rebuck, “Range of accuracy of two-wavelength oximetry,” Chest 4, 540–542 (1986).
[CrossRef]

Clem, T. R.

R. F. Bonner, T. R. Clem, P. D. Bowen, R. L. Bowman, “Laser-Doppler continuous real-time monitor of pulsatile and mean blood flow in tissue microcirculation,” in Scattering Techniques Applied to Supramolecular and Non-Equilibrium Systems, S. H. Chen, B. Chu, R. Nossal, eds. (Plenum, New York, 1981), pp. 685–702.
[CrossRef]

Dougherty, T. J.

T. J. Dougherty, J. E. Kaufman, A. Goldfarb, K. R. Weishaupt, D. G. Boyle, A. Mittleman, “Photoradiation therapy for the treatment of malignant tumors,” Cancer Res. 38, 2628–2635 (1978).
[PubMed]

Everall, J. D.

J. T. Whitton, J. D. Everall, “The thickness of the epidermis,” Br. J. Dermatol. 89, 467–476 (1973).
[CrossRef] [PubMed]

Ference, R. J.

Ferwerda, H. A.

Flock, S. T.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Goldfarb, A.

T. J. Dougherty, J. E. Kaufman, A. Goldfarb, K. R. Weishaupt, D. G. Boyle, A. Mittleman, “Photoradiation therapy for the treatment of malignant tumors,” Cancer Res. 38, 2628–2635 (1978).
[PubMed]

Graham, M. D.

S. Takatani, M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

Groenhuis, A. J.

Groenhuis, R. A. J.

Havlin, S.

Henning, J. P. H.

M. J. C. van Gemert, J. P. H. Henning, “A model approach to laser coagulation of dermal vascular lesions,” Arch. Dermatol. Res. 270, 429–439 (1981).
[CrossRef] [PubMed]

Hu, J.

R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applications in in vivoremittance spectroscopy,” in Proceedings of the Symposium on Bioengineering and the Skin (MTP, London, 1980), pp. 253–313.

Ishimaru, A.

Johnson, C.

Kaufman, J. E.

T. J. Dougherty, J. E. Kaufman, A. Goldfarb, K. R. Weishaupt, D. G. Boyle, A. Mittleman, “Photoradiation therapy for the treatment of malignant tumors,” Cancer Res. 38, 2628–2635 (1978).
[PubMed]

Keijzar, M.

Kiefer, J.

Liu, F. L. W.

K. R. Chapman, F. L. W. Liu, R. M. Watson, A. S. Rebuck, “Range of accuracy of two-wavelength oximetry,” Chest 4, 540–542 (1986).
[CrossRef]

Longini, R. L.

R. J. Zdrojkowski, R. L. Longini, “Optical transmission through whole blood illuminated with highly collimated light,” J. Opt. Soc. Am. 59, 898–903 (1969).

R. L. Longini, R. Zdrojkowski, “A note on the theory of backscattering of light by living tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
[CrossRef]

Marynissen, J. P. A.

J. P. A. Marynissen, W. M. Star, “Phantom measurements for light dosimetry using isotropic and small aperture detectors,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, Gomen, eds. (Liss, New York, 1984), pp. 133–138.

Meindl, J. D.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in vivomeasurement of blood oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

Mihm, F. G.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in vivomeasurement of blood oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

Mittleman, A.

T. J. Dougherty, J. E. Kaufman, A. Goldfarb, K. R. Weishaupt, D. G. Boyle, A. Mittleman, “Photoradiation therapy for the treatment of malignant tumors,” Cancer Res. 38, 2628–2635 (1978).
[PubMed]

Nossal, R.

Parrish, J. A.

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical modeling for the optical properties of the skin with in vitroand in vivoapplications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applications in in vivoremittance spectroscopy,” in Proceedings of the Symposium on Bioengineering and the Skin (MTP, London, 1980), pp. 253–313.

Patterson, M. S.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

Pisharoty, N. R.

R. J. Zdrojkowski, N. R. Pisharoty, “Optical transmission and reflection by blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
[CrossRef]

Preuss, L. E.

Rebuck, A. S.

K. R. Chapman, F. L. W. Liu, R. M. Watson, A. S. Rebuck, “Range of accuracy of two-wavelength oximetry,” Chest 4, 540–542 (1986).
[CrossRef]

Reynolds, L.

Reynolds, L. O.

L. O. Reynolds, “Optical diffuse reflectance and transmittance from an anisotropically scattering finite blood medium.” Ph.D. dissertation (University of Washington, Seattle, Wash., 1975).

Ryan, T. J.

T. J. Ryan, “Structure, pattern, and shape of blood vessels of the skin,” in The Physiology and Pathophysiology of the Skin, A. Janet, ed. (Academic, New York, 1973), Vol. 2, Chap. 16.

Schmitt, J. M.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in vivomeasurement of blood oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

Spence, V. A.

S. B. Wilson, V. A. Spence, “A tissue heat transfer model relating dynamic skin temperature changes to the physiological parameters,” Phys. Med. Biol. 33, 894–897 (1988).
[CrossRef]

Star, W. M.

M. Keijzar, W. M. Star, P. R. M. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988).
[CrossRef]

J. P. A. Marynissen, W. M. Star, “Phantom measurements for light dosimetry using isotropic and small aperture detectors,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, Gomen, eds. (Liss, New York, 1984), pp. 133–138.

Storchi, P. R. M.

Taitelbaum, H.

Takatani, S.

S. Takatani, M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

S. Takatani, “On the theory and development of a non-invasive tissue reflectance oximeter,” Ph.D. dissertation (Case Western Reserve University, Cleveland, Ohio, 1978).

Taylor, R. C.

Ten Bosch, J. J.

Tremper, K. K.

K. K. Tremper, S. J. Barker, “Pulse oximetry,” Anesthesiology 70, 98–109 (1989).
[CrossRef] [PubMed]

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 1, Chap. 14, pp. 477–492.

van der Leun, J. C.

W. A. G. Bruls, J. C. van der Leun, “Forward scattering properties of human epidermal layers,” Photochem. Photobiol. 40, 231–242 (1984).
[CrossRef] [PubMed]

van Gemert, M. J. C.

M. J. C. van Gemert, J. P. H. Henning, “A model approach to laser coagulation of dermal vascular lesions,” Arch. Dermatol. Res. 270, 429–439 (1981).
[CrossRef] [PubMed]

Wan, S.

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical modeling for the optical properties of the skin with in vitroand in vivoapplications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

Watson, R. M.

K. R. Chapman, F. L. W. Liu, R. M. Watson, A. S. Rebuck, “Range of accuracy of two-wavelength oximetry,” Chest 4, 540–542 (1986).
[CrossRef]

Weishaupt, K. R.

T. J. Dougherty, J. E. Kaufman, A. Goldfarb, K. R. Weishaupt, D. G. Boyle, A. Mittleman, “Photoradiation therapy for the treatment of malignant tumors,” Cancer Res. 38, 2628–2635 (1978).
[PubMed]

Weiss, G. H.

Whitton, J. T.

J. T. Whitton, J. D. Everall, “The thickness of the epidermis,” Br. J. Dermatol. 89, 467–476 (1973).
[CrossRef] [PubMed]

Wilson, B. C.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

Wilson, S. B.

S. B. Wilson, V. A. Spence, “A tissue heat transfer model relating dynamic skin temperature changes to the physiological parameters,” Phys. Med. Biol. 33, 894–897 (1988).
[CrossRef]

Zdrojkowski, R.

R. L. Longini, R. Zdrojkowski, “A note on the theory of backscattering of light by living tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
[CrossRef]

Zdrojkowski, R. J.

R. J. Zdrojkowski, N. R. Pisharoty, “Optical transmission and reflection by blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
[CrossRef]

R. J. Zdrojkowski, R. L. Longini, “Optical transmission through whole blood illuminated with highly collimated light,” J. Opt. Soc. Am. 59, 898–903 (1969).

Anesthesiology (1)

K. K. Tremper, S. J. Barker, “Pulse oximetry,” Anesthesiology 70, 98–109 (1989).
[CrossRef] [PubMed]

Appl. Opt. (8)

Arch. Dermatol. Res. (1)

M. J. C. van Gemert, J. P. H. Henning, “A model approach to laser coagulation of dermal vascular lesions,” Arch. Dermatol. Res. 270, 429–439 (1981).
[CrossRef] [PubMed]

Br. J. Dermatol. (1)

J. T. Whitton, J. D. Everall, “The thickness of the epidermis,” Br. J. Dermatol. 89, 467–476 (1973).
[CrossRef] [PubMed]

Cancer Res. (1)

T. J. Dougherty, J. E. Kaufman, A. Goldfarb, K. R. Weishaupt, D. G. Boyle, A. Mittleman, “Photoradiation therapy for the treatment of malignant tumors,” Cancer Res. 38, 2628–2635 (1978).
[PubMed]

Chest (1)

K. R. Chapman, F. L. W. Liu, R. M. Watson, A. S. Rebuck, “Range of accuracy of two-wavelength oximetry,” Chest 4, 540–542 (1986).
[CrossRef]

IEEE Trans. Biomed. Eng. (4)

R. L. Longini, R. Zdrojkowski, “A note on the theory of backscattering of light by living tissue,” IEEE Trans. Biomed. Eng. BME-15, 4–10 (1968).
[CrossRef]

R. J. Zdrojkowski, N. R. Pisharoty, “Optical transmission and reflection by blood,” IEEE Trans. Biomed. Eng. BME-17, 122–128 (1970).
[CrossRef]

S. Takatani, M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in vivomeasurement of blood oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98–107 (1986).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Lasers Med. Sci. (1)

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

Med. Phys. (1)

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Photochem. Photobiol. (2)

S. Wan, R. R. Anderson, J. A. Parrish, “Analytical modeling for the optical properties of the skin with in vitroand in vivoapplications,” Photochem. Photobiol. 34, 493–499 (1981).
[PubMed]

W. A. G. Bruls, J. C. van der Leun, “Forward scattering properties of human epidermal layers,” Photochem. Photobiol. 40, 231–242 (1984).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

S. B. Wilson, V. A. Spence, “A tissue heat transfer model relating dynamic skin temperature changes to the physiological parameters,” Phys. Med. Biol. 33, 894–897 (1988).
[CrossRef]

Other (10)

T. J. Ryan, “Structure, pattern, and shape of blood vessels of the skin,” in The Physiology and Pathophysiology of the Skin, A. Janet, ed. (Academic, New York, 1973), Vol. 2, Chap. 16.

K. A. Arndt, J. M. Noe, S. Rosen, eds., Cutaneous Laser Therapy (Wiley, London, 1983).

S. Chandraseklar, Radiative Transfer (Dover, New York, 1960).

J. P. A. Marynissen, W. M. Star, “Phantom measurements for light dosimetry using isotropic and small aperture detectors,” in Porphyrin Localization and Treatment of Tumors, D. R. Doiron, Gomen, eds. (Liss, New York, 1984), pp. 133–138.

L. O. Reynolds, “Optical diffuse reflectance and transmittance from an anisotropically scattering finite blood medium.” Ph.D. dissertation (University of Washington, Seattle, Wash., 1975).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 9, pp. 175–186.
[CrossRef]

H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 1, Chap. 14, pp. 477–492.

S. Takatani, “On the theory and development of a non-invasive tissue reflectance oximeter,” Ph.D. dissertation (Case Western Reserve University, Cleveland, Ohio, 1978).

R. R. Anderson, J. Hu, J. A. Parrish, “Optical radiation transfer in the human skin and applications in in vivoremittance spectroscopy,” in Proceedings of the Symposium on Bioengineering and the Skin (MTP, London, 1980), pp. 253–313.

R. F. Bonner, T. R. Clem, P. D. Bowen, R. L. Bowman, “Laser-Doppler continuous real-time monitor of pulsatile and mean blood flow in tissue microcirculation,” in Scattering Techniques Applied to Supramolecular and Non-Equilibrium Systems, S. H. Chen, B. Chu, R. Nossal, eds. (Plenum, New York, 1981), pp. 685–702.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Geometry of the multilayer skin model.

Fig. 2
Fig. 2

Contour plots of photon-flux density in simulated homogeneous skin tissue having different absorption (Σa) and transport-corrected scattering ( Σ s ) coefficients. (a) High-absorption, high-scattering medium (Σa = 0.1 mm−1, Σ s = 5 mm 1). (b) Low-absorption, high-scattering medium (Σa = 0.03 mm−1, Σ s = 5 mm 1). (c) High-absorption, low-scattering medium (Σa = 0.1 mm−1, Σ s = 1 mm 1). (d) Low-absorption low-scattering medium (Σa = 0.03 mm−1, Σ s = 1 mm 1). For these simulations, the source beam (Ψ0 = 1, a = 1 mm) was assumed to impinge upon the medium with its axis passing through the origin perpendicular to the top surface. Layer thicknesses were as follows: z0 = 0, z1 = d = 20 mm.

Fig. 3
Fig. 3

Logarithm of reflectance from a homogeneous tissue plotted as a function of the center-to-center distance between the source and detector for various values of the medium’s absorption coefficient: (a) Σ s = 1 mm 1, (b) Σ s = 2 mm 1. Curves were generated from Eq. (27) with Ψ0 = 1, a = b = 1 mm, z0 = 0, z1 = d = 20 mm.

Fig. 4
Fig. 4

Example of table for estimating Σa (mm−1) and Σ s ( mm 1 ) from the slope (c2) and offset (−ln c1) of model-derived ln R-versus-rb curves for a homogeneous tissue medium. Model parameters are the same as those listed in the caption of Fig. 3, except a = b = 1.5 mm. The constants c2 and ln c1 were determined by fitting model curves for n = 0 over the range 6.5 < rb < 10.5 mm.

Fig. 5
Fig. 5

Simulated surface emission profiles showing the effect of varying the absorption coefficient of an embedded tissue layer on remitted intensities over a range of source–detector separations. Model parameters: a = b = 1.0 mm, z = 0, z1 = 2 mm, z2 = 5 mm.

Fig. 6
Fig. 6

Simulated surface emission profiles showing the effect of varying the thickness of a layer of skin tissue (dermis) lying above a deeper tissue layer (subcutis): (a) high-over-low absorption case (Σa1 = 0.05 mm−1, Σa2 = 0.01 mm−1), (b) low-over-high absorption case (Σa1 = 0.01 mm−1, Σa2 = 0.05 mm−1). Model parameters: a = b = 1.0 mm, Σ s 1 = Σ s 1 = 1 mm 1, z0 = 0, d = 7 mm.

Fig. 7
Fig. 7

Diagram of experimental apparatus used by the authors to measure surface emission profiles on tissue phantoms and skin. S/H, sample-and-hold amplifier.

Fig. 8
Fig. 8

Comparison of experimental and predicted remitted-intensity curves for single-layer tissue phantoms containing increasing concentrations of an absorbing dye. Solid curves are generated by the model for the indicated Σa values that were obtained from spectrophotometric measurements (at 660 nm). The concentration of milk in the phantoms was 15%, yielding a reduced scattering coefficient of 0.75 mm−1. Model parameters: a = b = 1.5 mm; z0 = 0, z1 = d = 10 mm.

Fig. 9
Fig. 9

Comparison of remitted-intensity curves for one- and two-layer tissue phantoms. The figure inset shows the geometry of the homogeneous and layered phantoms on which the reflectances were measured. The scattering coefficient of these phantoms was the same as that of the phantoms from which the measurements in Fig. 8 were made ( Σ s = 0.75 mm 1 ). The theoretical curves were generated by using values of absorption coefficients obtained from spectrophotometric measurements (at 660 nm): Σa1 = Σa2 = 0.029 mm−1 (one-layer phantom); Σa1 = 0.029 mm−1, Σa2 = 0.002 mm−1 (two-layer phantom).

Fig. 10
Fig. 10

Surface-emission profiles generated by the model using optical parameters that were obtained by fitting log-reflectance values measured on the forearms of an African-American subject and a Caucasian subject. For both subjects, the thicknesses of the epidermis, the dermis, and the subcutis were assumed to be 66 μm, 1.2 mm, and 6 mm, respectively. Fitted optical parameters are as follows: African-American, Σa0, Σs0 = 17.5, 5.5 mm−1 (at 660 nm); Σa0, Σs0 = 10.0, 5.0 mm−1 (at 950 nm); Σa1, Σ s 1 = 0.022, 0.85 mm−1 (at 660 and 950 nm); Σa2, Σ s 2 = 0.014, 0.55 mm−1 (at 660 and 950 nm). Caucasian, Σa0, Σs0 = 9.5, 5.5 mm−1 (at 660 nm); Σa0, Σs0 = 6.0, 5.0 mm−1 (at 950 nm); Σa1, Σ s 1 = 0.035, 1.5 mm−1 (at 660 and 950 nm); Σa2, Σ s 1 = 0.015, 1.1 mm−1 (at 660 and 950 nm).

Fig. 11
Fig. 11

Simulation of the effect of source-detector separation on the amplitude of pulsatile intensities measured by a reflectance plethysmograph for pulsating top-layer and pulsating bottom-layer cases. Amplitude is expressed in terms of ΔR/R, the peak-to-peak reflectance change divided by the steady-state reflectance. Model parameters: a = b = 1.5 mm; z0 = 66 μm, z1 = 1.5 mm, z2 = 3.0 mm; Σa and Σ s of bloodless dermis (both layers) = 0.015 mm−1 and 1.3 mm−1, respectively; steady-state blood volume fraction Vb = 0.06 (0.03 venous, 0.03 arterial); pulsatile blood volume fraction ΔVb = 0.005; oxygen saturation S = 0.97 (arterial), 0.87 (venous); hematocrit 0.35.

Tables (1)

Tables Icon

Table 1 Optical Scattering and Absorption Coefficients of Tissues Measured at 633 nm, as Published by Various Authors

Equations (30)

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

D 2 Ψ ( ρ ) + Σ a Ψ ( ρ ) = S ( ρ ) ,
Σ s = Σ s ( 1 g ) .
Ψ ( ρ ) = 1 D V S ( ρ ) G ( ρ | ρ ) d V ,
S 1 ( r , z ) = Ψ 0 Σ s 1 exp [ ( Σ s 0 + Σ a 0 ) z 0 ] × exp [ ( Σ s 1 + Σ a 1 ) z ] R ( r ) = Ψ 0 Σ s 1 exp ( Σ t 0 z 0 ) exp ( Σ t 1 z ) R ( r ) ,
S 2 ( r , z ) = Ψ 0 n 2 n 1 Σ s 2 exp [ ( Σ s 0 + Σ a 0 ) z 0 ] × exp [ ( Σ s 1 + Σ a 1 ) z 1 ] exp [ ( Σ s 2 + Σ a 2 ) ( z z 1 ) ] R ( r ) = Ψ 0 n 2 n 1 Σ s 2 exp ( Σ t 0 z 0 ) exp ( Σ t 1 z 1 ) × exp [ Σ t 2 ( z z 1 ) ] R ( r ) .
D 1 Ψ 1 ( r , z ) z = D 2 Ψ 2 ( r , z ) z , z = z 1
Ψ 1 ( r , z ) Ψ 2 ( r , z ) = ( n 1 n 2 ) 2 , z = z 1 .
Ψ 1 ( z ) 2 b 1 3 Σ t 1 Ψ 1 ( z ) z = 0 , z = 0 ,
Ψ 2 ( z ) + 2 b 2 3 Σ t 2 Ψ 2 ( z ) z = 0 , z = d ,
G 1 = n = 1 ϕ n 1 ( z ) ϕ n 1 ( z ) N n G ( r | r ) ,
G 2 = n = 1 ϕ n 2 ( z ) ϕ n 2 ( z ) N n G ( r | r ) .
N n = 0 d ϕ n 2 ( z ) d z = 0 z 1 ϕ n 1 2 ( z ) d z + z 1 d ϕ n 2 2 ( z ) d z = A 1 2 2 + z 1 ( 1 A 1 2 ) 2 + 1 4 k n 1 [ sin ( 2 γ n 1 ) sin ( 2 k n 1 z 1 + 2 γ n 1 ) ] + A 1 2 4 k n 1 { sin ( 2 γ n 2 ) sin [ 2 k n 2 ( d z 1 ) + 2 γ n 2 ] }
ϕ n 1 ( z ) = sin ( k n 1 z + γ n 1 ) ,
ϕ n 2 ( z ) = A 1 sin [ k n 2 ( d z ) + γ n 2 ] ,
A 1 = ( n 2 n 1 ) 2 sin ( k n 1 z 1 + γ n 1 ) sin [ k n 2 ( d z 1 ) + γ n 2 ] .
γ n 1 = tan 1 ( 2 b 1 3 Σ t 1 k n 1 ) ,
γ n 2 = tan 1 ( 2 b 2 3 Σ t 2 k n 2 ) .
n 2 2 D 1 k n 1 tan ( k n 1 z 1 + γ n 1 ) = n 1 2 D 2 k n 2 tan [ k n 2 ( d z 1 ) + γ n 2 ] .
( 2 r 2 + 1 r r λ n 2 ) G ( r | r ) = 0 ,
λ n 2 = k n 1 2 + Σ a 1 D 1 = k n 2 2 + Σ a 2 D 2 .
G ( r | r ) = ( 1 / 2 π ) { K 0 ( λ n r ) I 0 ( λ n r ) r < r I 0 ( λ n r ) K 0 ( λ n r ) r > r .
Ψ 1 ( r , z ) = Ψ 0 exp ( Σ t 0 z 0 ) n = 1 A 1 sin ( k n 1 z + γ n 1 ) N n × ( Σ s 1 D 1 B n 1 + A 1 n 2 Σ s 2 n 1 D 2 B n 2 ) × { ( 1 / λ n 2 ) [ 1 λ n a I 0 ( λ n r ) K 1 ( λ n a ) ] r < a ( a / λ n ) I 1 ( λ n a ) K 0 ( λ n r ) r > a ,
Ψ 2 ( r , z ) = Ψ 0 exp ( Σ t 0 z 0 ) n = 1 A 1 sin [ k n 2 ( d z ) + γ n 2 ] N n × ( Σ s 1 D 1 B n 1 + A 1 n 2 Σ s 2 n 1 D 2 B n 2 ) × { ( 1 / λ n 2 ) [ 1 λ n a I 0 ( λ n r ) K 1 ( λ n a ) ] r < a ( a / λ n ) I 1 ( λ n a ) K 0 ( λ n r ) r > a ,
B n 1 = ( 1 Σ t 1 2 + k n 1 2 ) { Σ t 1 sin γ n 1 + k n 1 cos γ n 1 exp ( Σ t 1 z 1 ) [ Σ t 1 sin ( k n 1 z 1 + γ n 1 ) + k n 1 cos ( k n 1 z 1 + γ n 1 ) ] } ,
B n 2 = { exp [ ( Σ t 1 Σ t 2 ) z 1 ] Σ t 2 2 + k n 2 2 } ( exp ( Σ t 2 d ) ( k n 2 cos γ n 2 Σ t 2 sin γ n 2 ) + exp ( Σ t 2 z 1 ) { Σ t 2 sin [ k n 2 ( d z 1 ) + γ n 2 ] k n 2 cos [ k n 2 ( d z 1 ) + γ n 2 } ) .
I ( r x ) = exp ( Σ t 0 z 0 ) 0 r x D 1 Ψ 1 ( r , z ) z r d r , z = 0 = Ψ 0 exp ( 2 Σ t 0 z 0 ) n = 1 k n 1 cos ( γ n 1 ) N n × ( Σ s 1 B n 1 + A 1 D 1 n 2 Σ s 2 n 1 D 2 B n 2 ) × [ a 2 2 λ n 2 a r x λ n 2 I 1 ( λ n a ) K 1 ( λ n r x ) ] , r > r x .
R = b 4 r b [ I ( r b + b ) I ( r b b ) ] 0 a Ψ 0 r d r = b 2 a 2 r b [ I ( r b + b ) I ( r b b ) ] ,
Σ a 1 = ( 1 V b ) Σ a t + V b [ Σ a b r ( 1 S ) + Σ a b o S ] ,
Σ s 1 = ( 1 V b ) Σ s t + V b Σ s b ,
R = c 1 ( r b ) n exp ( c 2 r b ) ,

Metrics