Abstract

When a picosecond light pulse is incident upon a turbid medium such as tissue, the temporal distribution of diffusely reflected and transmitted photons depends on the optical absorption and scattering properties of the medium. From diffusion theory it is possible to derive analytic expressions for the pulse shape in terms of the optical interaction coefficients of a homogeneous semi-infinite medium. Experimental tests of this simple model in tissue-simulating liquid phantoms of different geometries are presented here. The results of these tests show that, in a semi-infinite phantom, the application of the diffusion model provides estimates of the absorption and transport-scattering coefficients that are accurate to better than 10%. Comparable accuracy was also obtained with this simple model for finite slab, cylindrical, and spherical volumes as long as the objects were of sufficient size. For smaller volumes the absorption coefficient was overestimated because of the significant loss of photons at the boundaries of the object.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
    [CrossRef] [PubMed]
  2. 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. Comp. 26, 289–294 (1988).
    [CrossRef]
  3. B. C. Wilson, M. S. Patterson, “The physics of photodynamic therapy,” Phys. Med. Biol. 31, 327–360 (1986).
    [CrossRef] [PubMed]
  4. S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
    [CrossRef] [PubMed]
  5. M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).
  6. B. C. Wilson, Y. D. Park, Y. Hefetz, M. S. Patterson, S. J. Madsen, S. L. Jacques, “The potential of time-resolved reflectance measurements for the noninvasive determination of tissue optical properties,” in Thermal and Optical Interactions with Biological and Related Composite Materials, M. J. Berry, G. M. Harpole, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1064, 97–106 (1989).
  7. K. M. Yoo, R. R. Alfano, “Determination of the scattering and absorption lengths from the temporal profile of a backscattered pulse,” Opt. Lett. 15, 276–278 (1990).
    [CrossRef] [PubMed]
  8. K. M. Yoo, R. R. Alfano, “Coherent backscattering of light from biological tissues,” Appl. Opt. 29, 3237–3239 (1990).
    [CrossRef] [PubMed]
  9. M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time resolved light scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).
  10. 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]
  11. S. J. Madsen, M. S. Patterson, B. C. Wilson, Y. D. Park, J. D. Moulton, S. L. Jacques, Y. Hefetz, “Time resolved diffuse reflectance and transmittance studies in tissue simulating phantoms,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds, Proc. Soc. Photo-Opt. Instrum. Eng.1431, 42–51 (1991).
  12. G. Eason, A. Veitch, R. Nisbeth, F. Turnbull, “The theory of the backscattering of light by blood,” J. Phys. D 11, 1463–1479 (1978).
    [CrossRef]
  13. H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
    [CrossRef] [PubMed]
  14. A. E. Profio, J. Sarnaik, “Fluorescence of HPD for tumor detection and dosimetry in photoradiation therapy,” in Porphyrin Photosensitization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 163–175.
  15. 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]
  16. B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–607 (1987).
    [CrossRef] [PubMed]
  17. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969), pp. 208–213.
  18. K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
    [CrossRef] [PubMed]
  19. 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]
  20. S. L. Jacques, “Time-resolved reflectance spectroscopy in turbid tissues,” IEEE Trans. Biomed. Eng. 36, 1155–1161 (1989).
    [CrossRef] [PubMed]

1991 (1)

1990 (3)

1989 (2)

1988 (2)

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (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. Comp. 26, 289–294 (1988).
[CrossRef]

1987 (3)

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. 6, 494–503 (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]

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–607 (1987).
[CrossRef] [PubMed]

1986 (2)

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]

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

1978 (1)

G. Eason, A. Veitch, R. Nisbeth, F. Turnbull, “The theory of the backscattering of light by blood,” J. Phys. D 11, 1463–1479 (1978).
[CrossRef]

Alfano, R. R.

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969), pp. 208–213.

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]

Chance, B.

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]

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time resolved light scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).

Cope, M.

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. Comp. 26, 289–294 (1988).
[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. Comp. 26, 289–294 (1988).
[CrossRef]

Eason, G.

G. Eason, A. Veitch, R. Nisbeth, F. Turnbull, “The theory of the backscattering of light by blood,” J. Phys. D 11, 1463–1479 (1978).
[CrossRef]

Flock, S. T.

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–607 (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]

Fountain, M.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Greenfeld, R.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Hefetz, Y.

S. J. Madsen, M. S. Patterson, B. C. Wilson, Y. D. Park, J. D. Moulton, S. L. Jacques, Y. Hefetz, “Time resolved diffuse reflectance and transmittance studies in tissue simulating phantoms,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds, Proc. Soc. Photo-Opt. Instrum. Eng.1431, 42–51 (1991).

B. C. Wilson, Y. D. Park, Y. Hefetz, M. S. Patterson, S. J. Madsen, S. L. Jacques, “The potential of time-resolved reflectance measurements for the noninvasive determination of tissue optical properties,” in Thermal and Optical Interactions with Biological and Related Composite Materials, M. J. Berry, G. M. Harpole, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1064, 97–106 (1989).

Holtom, G.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Jacques, S. L.

S. L. Jacques, “Time-resolved reflectance spectroscopy in turbid tissues,” IEEE Trans. Biomed. Eng. 36, 1155–1161 (1989).
[CrossRef] [PubMed]

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

B. C. Wilson, Y. D. Park, Y. Hefetz, M. S. Patterson, S. J. Madsen, S. L. Jacques, “The potential of time-resolved reflectance measurements for the noninvasive determination of tissue optical properties,” in Thermal and Optical Interactions with Biological and Related Composite Materials, M. J. Berry, G. M. Harpole, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1064, 97–106 (1989).

S. J. Madsen, M. S. Patterson, B. C. Wilson, Y. D. Park, J. D. Moulton, S. L. Jacques, Y. Hefetz, “Time resolved diffuse reflectance and transmittance studies in tissue simulating phantoms,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds, Proc. Soc. Photo-Opt. Instrum. Eng.1431, 42–51 (1991).

Kent, J.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Liu, F.

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Madsen, S. J.

S. J. Madsen, M. S. Patterson, B. C. Wilson, Y. D. Park, J. D. Moulton, S. L. Jacques, Y. Hefetz, “Time resolved diffuse reflectance and transmittance studies in tissue simulating phantoms,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds, Proc. Soc. Photo-Opt. Instrum. Eng.1431, 42–51 (1991).

B. C. Wilson, Y. D. Park, Y. Hefetz, M. S. Patterson, S. J. Madsen, S. L. Jacques, “The potential of time-resolved reflectance measurements for the noninvasive determination of tissue optical properties,” in Thermal and Optical Interactions with Biological and Related Composite Materials, M. J. Berry, G. M. Harpole, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1064, 97–106 (1989).

McCully, K.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Moes, C. J. M.

Moulton, J. D.

M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time resolved light scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).

S. J. Madsen, M. S. Patterson, B. C. Wilson, Y. D. Park, J. D. Moulton, S. L. Jacques, Y. Hefetz, “Time resolved diffuse reflectance and transmittance studies in tissue simulating phantoms,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds, Proc. Soc. Photo-Opt. Instrum. Eng.1431, 42–51 (1991).

Nioka, S.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Nisbeth, R.

G. Eason, A. Veitch, R. Nisbeth, F. Turnbull, “The theory of the backscattering of light by blood,” J. Phys. D 11, 1463–1479 (1978).
[CrossRef]

Park, Y. D.

B. C. Wilson, Y. D. Park, Y. Hefetz, M. S. Patterson, S. J. Madsen, S. L. Jacques, “The potential of time-resolved reflectance measurements for the noninvasive determination of tissue optical properties,” in Thermal and Optical Interactions with Biological and Related Composite Materials, M. J. Berry, G. M. Harpole, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1064, 97–106 (1989).

S. J. Madsen, M. S. Patterson, B. C. Wilson, Y. D. Park, J. D. Moulton, S. L. Jacques, Y. Hefetz, “Time resolved diffuse reflectance and transmittance studies in tissue simulating phantoms,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds, Proc. Soc. Photo-Opt. Instrum. Eng.1431, 42–51 (1991).

Patterson, M. S.

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]

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, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–607 (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]

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

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

S. J. Madsen, M. S. Patterson, B. C. Wilson, Y. D. Park, J. D. Moulton, S. L. Jacques, Y. Hefetz, “Time resolved diffuse reflectance and transmittance studies in tissue simulating phantoms,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds, Proc. Soc. Photo-Opt. Instrum. Eng.1431, 42–51 (1991).

M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time resolved light scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).

B. C. Wilson, Y. D. Park, Y. Hefetz, M. S. Patterson, S. J. Madsen, S. L. Jacques, “The potential of time-resolved reflectance measurements for the noninvasive determination of tissue optical properties,” in Thermal and Optical Interactions with Biological and Related Composite Materials, M. J. Berry, G. M. Harpole, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1064, 97–106 (1989).

Prahl, S. A.

Profio, A. E.

A. E. Profio, J. Sarnaik, “Fluorescence of HPD for tumor detection and dosimetry in photoradiation therapy,” in Porphyrin Photosensitization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 163–175.

Sarnaik, J.

A. E. Profio, J. Sarnaik, “Fluorescence of HPD for tumor detection and dosimetry in photoradiation therapy,” in Porphyrin Photosensitization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 163–175.

Schwartz, E.

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

Turnbull, F.

G. Eason, A. Veitch, R. Nisbeth, F. Turnbull, “The theory of the backscattering of light by blood,” J. Phys. D 11, 1463–1479 (1978).
[CrossRef]

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Veitch, A.

G. Eason, A. Veitch, R. Nisbeth, F. Turnbull, “The theory of the backscattering of light by blood,” J. Phys. D 11, 1463–1479 (1978).
[CrossRef]

Wilson, B. C.

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]

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, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–607 (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, 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]

S. J. Madsen, M. S. Patterson, B. C. Wilson, Y. D. Park, J. D. Moulton, S. L. Jacques, Y. Hefetz, “Time resolved diffuse reflectance and transmittance studies in tissue simulating phantoms,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds, Proc. Soc. Photo-Opt. Instrum. Eng.1431, 42–51 (1991).

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time resolved light scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).

B. C. Wilson, Y. D. Park, Y. Hefetz, M. S. Patterson, S. J. Madsen, S. L. Jacques, “The potential of time-resolved reflectance measurements for the noninvasive determination of tissue optical properties,” in Thermal and Optical Interactions with Biological and Related Composite Materials, M. J. Berry, G. M. Harpole, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1064, 97–106 (1989).

Yoo, K. M.

Anal. Biochem. (1)

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[CrossRef] [PubMed]

Appl. Opt. (3)

IEEE Trans. Biomed. Eng. (1)

S. L. Jacques, “Time-resolved reflectance spectroscopy in turbid tissues,” IEEE Trans. Biomed. Eng. 36, 1155–1161 (1989).
[CrossRef] [PubMed]

J. Phys. D (1)

G. Eason, A. Veitch, R. Nisbeth, F. Turnbull, “The theory of the backscattering of light by blood,” J. Phys. D 11, 1463–1479 (1978).
[CrossRef]

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]

Lasers Surg. Med. (1)

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

Med. Biol. Eng. Comp. (1)

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. Comp. 26, 289–294 (1988).
[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]

Opt. Lett. (1)

Photochem. Photobiol. (1)

B. C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–607 (1987).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

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

Phys. Rev. Lett. (1)

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Other (6)

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969), pp. 208–213.

A. E. Profio, J. Sarnaik, “Fluorescence of HPD for tumor detection and dosimetry in photoradiation therapy,” in Porphyrin Photosensitization and Treatment of Tumors, D. R. Doiron, C. J. Gomer, eds. (Liss, New York, 1984), pp. 163–175.

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflectance spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

B. C. Wilson, Y. D. Park, Y. Hefetz, M. S. Patterson, S. J. Madsen, S. L. Jacques, “The potential of time-resolved reflectance measurements for the noninvasive determination of tissue optical properties,” in Thermal and Optical Interactions with Biological and Related Composite Materials, M. J. Berry, G. M. Harpole, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1064, 97–106 (1989).

M. S. Patterson, J. D. Moulton, B. C. Wilson, B. Chance, “Applications of time resolved light scattering measurements to photodynamic therapy dosimetry,” in Photodynamic Therapy: Mechanisms II, T. J. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1203, 62–75 (1990).

S. J. Madsen, M. S. Patterson, B. C. Wilson, Y. D. Park, J. D. Moulton, S. L. Jacques, Y. Hefetz, “Time resolved diffuse reflectance and transmittance studies in tissue simulating phantoms,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds, Proc. Soc. Photo-Opt. Instrum. Eng.1431, 42–51 (1991).

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 (8)

Fig. 1
Fig. 1

Experimental apparatus for the measurement of time-resolved diffuse reflectance: - - - - -, electronic; —, optical; HV, high voltage.

Fig. 2
Fig. 2

Pulse shape as a function of added absorber for the 100-mm thick slab phantom (ρ = 70 mm). The solid curves represent fits to the experimental data (dots) using the simple diffusion model of Eq. (5). The absorption coefficient is the sum of the Intralipid and ink coefficients as determined by steady-state methods.

Fig. 3
Fig. 3

Pulse shape as a function of transport-scattering coefficient for the 100-mm thick slab phantom (ρ = 70 mm). The solid curves represent fits to the experimental data (dots) made by using the simple diffusion model of Eq. (5).

Fig. 4
Fig. 4

Summary of results in the thick-slab (d = 100 mm) phantom. The solid line represents equivalence between the steady-state and time-resolved values. (a) μa time-resolved versus μa steady-state values for μs′ = 0.5 mm−1 and ρ = 70 mm; (b) μa time-resolved versus μa steady-state values for μs′ = 0.5 mm−1 and ρ = 30 mm; (c) μa time-resolved versus μa steady-state values for μs′ = 1.0 mm−1 and ρ = 70 mm; (d) μa time-resolved versus μa steady-state values for μs′ = 1.0 mm−1 and ρ = 30 mm; (e) μs′ time-resolved versus μs′ steady-state values for ρ = 70 mm; and (f) μs′ time-resolved versus μs′ steady-state values for ρ = 30 mm.

Fig. 5
Fig. 5

Comparisons of the predictions of the diffusion model and Monte Carlo results. The diffusion model results have been matched to the Monte Carlo data at 170 ps. Better absolute agreement can be obtained with a more exact boundary condition.9 The reflectance corresponds to the number of photons reaching the surface per unit time per unit area per incident photon.

Fig. 6
Fig. 6

Summary of results in the slab geometry: (a) estimated absorption coefficient versus slab thickness and (b) estimated transport-scattering coefficient versus slab thickness. The solid lines correspond to the steady-state value, whose uncertainty is given by the dashed lines.

Fig. 7
Fig. 7

Summary of results in the spherical geometry: (a) estimated absorption coefficient versus sphere radius and (b) estimated transport-scattering coefficient versus sphere radius. The steady-state value and its uncertainty are indicated by the solid and dashed lines, respectively.

Fig. 8
Fig. 8

Summary of results in the cylindrical geometry: (a) estimated absorption coefficient versus cylinder radius and (b) estimated transport-scattering coefficient versus cylinder radius. The steady-state value and its uncertainty are indicated by the solid and dashed lines, respectively.

Equations (5)

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

1 c t φ ( r , t ) - D 2 φ ( r , t ) + μ α φ ( r , t ) = S ( r , t ) ,
D = [ 3 ( μ a + μ s ) ] - 1 ,
μ s = ( 1 - g ) μ s
z 0 = [ ( 1 - g ) μ s ] - 1 ,
R ( ρ , t ) = ( 4 π D c ) - 3 / 2 z 0 t - 5 / 2 exp ( - μ a c t ) exp ( - ρ 2 + z 0 2 4 D c t ) .

Metrics