Abstract

Amplitude-modulated light launched into multiple-scattering media, e.g., tissue, results in the propagation of density waves of diffuse photons. Photon density wave characteristics in turn depend on modulation frequency (ω) and media optical properties. The damped spherical wave solutions to the homogeneous form of the diffusion equation suggest two distinct regimes of behavior: (1) a high-frequency dispersion regime where density wave phase velocity Vp has a ω dependence and (2) a low-frequency domain where Vp is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase (ϕ) and modulation (m) response to simple relations for the appropriate regime. Our results indicate that reliable estimates of tissuelike optical properties can be obtained, particularly when multiple modulation frequencies are employed.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
    [CrossRef] [PubMed]
  2. D. T. Delpy, M. Cope, P. van de Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
    [CrossRef] [PubMed]
  3. A. Ishimaru, “Diffusion of a pulse in densely distributed scatterers,” J. Opt. Soc. Am. 68, 1045–1050 (1978).
    [CrossRef]
  4. K. Shimizu, A. Ishimaru, L. Reynolds, A. P. Bruchner, “Backscattering of a picosecond pulse from densely distributed scatterers,” Appl. Opt. 18, 3484–3488 (1979).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. J. R. Singer, F. A. Grunbaum, P. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
    [CrossRef] [PubMed]
  10. R. L. Barbour, H. L. Graber, R. Aronson, J. Lubowsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 192–203 (1991).
  11. D. Benaron, M. A. Lennox, D. K. Stevenson, “Two-dimensional and 3-D images of thick tissue using time-constrained time-of-flight spectrophotometry,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1641, 35–45 (1992).
  12. R. Alfano, P.-P. Ho, K.-M. Yoo, “Photons for prompt tumour detection,” Phys. World 5, 37–40 (1992).
  13. E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantiation of time and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
    [CrossRef] [PubMed]
  14. B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfield, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698 (1988).
    [CrossRef] [PubMed]
  15. J. M. Schmitt, G.-X. Zhou, “Measurement of blood hematocrit by dual-wavelength near-IR photoplethysmography,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1641, 150–161 (1992).
  16. 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]
  17. K. Furutsu, “Diffusion equation derived from space-time transport equation,” J. Opt. Soc. Am. 70, 360–366 (1980).
    [CrossRef]
  18. M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1991).
    [CrossRef]
  19. S. L. Jacques, “Time resolved propagation of ultrashort laser pulses within turbid tissues,” Appl. Opt. 28, 2223–2229 (1989).
    [CrossRef] [PubMed]
  20. S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of fight propagation in scattering tissues—I. Model prediction and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
    [CrossRef] [PubMed]
  21. A. Ishimaru, “Diffusion of light in turbid materials,” Appl. Opt. 28, 2210–2215 (1989).
    [CrossRef] [PubMed]
  22. J. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantullin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).
  23. J. R. Lakowicz, K. Berndt, “Frequency domain measurements of photon migration in tissues,” Chem. Phys. Lett. 166, 246–252 (1990).
    [CrossRef]
  24. M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
    [CrossRef] [PubMed]
  25. L. O. Svaasand, B. J. Tromberg, “On the properties of optical waves in turbid media,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 41–51 (1991).
    [CrossRef]
  26. B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, R. C. Haskell, M. W. Bems, “Optical property measurements in turbid media using frequency domain photon migration,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 52–58 (1991).
    [CrossRef]
  27. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1959), pp. 81–83, 272–273.
  28. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), pp. 175–190.
  29. L. O. Svaasand, “Propagation of thermal waves,” Med. Phys. 9, 711–744 (1982).
    [CrossRef] [PubMed]
  30. G. W. Mitchell, K. Swift, “A dual-domain Fourier transform fluorescence lifetime spectrofluorometer,” in Time-Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, Los Angeles, 270–274 (1990).
  31. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983), p. 78.

1992

R. Alfano, P.-P. Ho, K.-M. Yoo, “Photons for prompt tumour detection,” Phys. World 5, 37–40 (1992).

1991

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantiation of time and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1991).
[CrossRef]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

1990

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]

J. R. Lakowicz, K. Berndt, “Frequency domain measurements of photon migration in tissues,” Chem. Phys. Lett. 166, 246–252 (1990).
[CrossRef]

J. R. Singer, F. A. Grunbaum, P. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

1989

1988

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

D. T. Delpy, M. Cope, P. van de Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef] [PubMed]

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

1987

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]

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]

1983

1982

L. O. Svaasand, “Propagation of thermal waves,” Med. Phys. 9, 711–744 (1982).
[CrossRef] [PubMed]

1980

1979

1978

Alfano, R.

R. Alfano, P.-P. Ho, K.-M. Yoo, “Photons for prompt tumour detection,” Phys. World 5, 37–40 (1992).

Alfano, R. R.

Aronson, R.

R. L. Barbour, H. L. Graber, R. Aronson, J. Lubowsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 192–203 (1991).

Arridge, S.

D. T. Delpy, M. Cope, P. van de Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef] [PubMed]

Barbour, R. L.

R. L. Barbour, H. L. Graber, R. Aronson, J. Lubowsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 192–203 (1991).

Bems, M. W.

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, R. C. Haskell, M. W. Bems, “Optical property measurements in turbid media using frequency domain photon migration,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 52–58 (1991).
[CrossRef]

Benaron, D.

D. Benaron, M. A. Lennox, D. K. Stevenson, “Two-dimensional and 3-D images of thick tissue using time-constrained time-of-flight spectrophotometry,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1641, 35–45 (1992).

Berndt, K.

J. R. Lakowicz, K. Berndt, “Frequency domain measurements of photon migration in tissues,” Chem. Phys. Lett. 166, 246–252 (1990).
[CrossRef]

Berndt, K. W.

Bonner, R. F.

Boretsky, R.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Bruchner, A. P.

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1959), pp. 81–83, 272–273.

Chance, B.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantiation of time and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

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

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

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Cohen, P.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Cope, M.

D. T. Delpy, M. Cope, P. van de Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef] [PubMed]

Delpy, D. T.

D. T. Delpy, M. Cope, P. van de Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef] [PubMed]

Ferwerda, H. A.

Finlander, M.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Fishkin, J.

J. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantullin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of fight propagation in scattering tissues—I. Model prediction and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

Fountain, M.

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

Furutsu, K.

Graber, H. L.

R. L. Barbour, H. L. Graber, R. Aronson, J. Lubowsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 192–203 (1991).

Gratton, E.

J. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantullin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

Greenfield, R.

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

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Groenhuis, R. A. J.

Grunbaum, F. A.

J. R. Singer, F. A. Grunbaum, P. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

Haskell, R. C.

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, R. C. Haskell, M. W. Bems, “Optical property measurements in turbid media using frequency domain photon migration,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 52–58 (1991).
[CrossRef]

Havlin, S.

Ho, P.-P.

R. Alfano, P.-P. Ho, K.-M. Yoo, “Photons for prompt tumour detection,” Phys. World 5, 37–40 (1992).

Holtom, G.

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

Ishimaru, A.

Jacques, S. L.

S. L. Jacques, “Time resolved propagation of ultrashort laser pulses within turbid tissues,” Appl. Opt. 28, 2223–2229 (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]

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1959), pp. 81–83, 272–273.

Kaufmann, K.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Kent, J.

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

Kohn, P.

J. R. Singer, F. A. Grunbaum, P. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

Lakowicz, J. R.

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

J. R. Lakowicz, K. Berndt, “Frequency domain measurements of photon migration in tissues,” Chem. Phys. Lett. 166, 246–252 (1990).
[CrossRef]

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983), p. 78.

Leigh, J.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantiation of time and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Lennox, M. A.

D. Benaron, M. A. Lennox, D. K. Stevenson, “Two-dimensional and 3-D images of thick tissue using time-constrained time-of-flight spectrophotometry,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1641, 35–45 (1992).

Levy, W.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Lubowsky, J.

R. L. Barbour, H. L. Graber, R. Aronson, J. Lubowsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 192–203 (1991).

Mantullin, W. W.

J. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantullin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

Maris, M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantiation of time and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

McCully, K.

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

Mitchell, G. W.

G. W. Mitchell, K. Swift, “A dual-domain Fourier transform fluorescence lifetime spectrofluorometer,” in Time-Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, Los Angeles, 270–274 (1990).

Miyake, H.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Moulton, J. D.

Nioka, S.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantiation of time and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

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

Nossal, R.

Patterson, M. S.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1991).
[CrossRef]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of fight propagation in scattering tissues—I. Model prediction and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

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

Prahl, S. A.

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]

Reynolds, L.

Schmitt, J. M.

J. M. Schmitt, G.-X. Zhou, “Measurement of blood hematocrit by dual-wavelength near-IR photoplethysmography,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1641, 150–161 (1992).

Sevick, E. M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantiation of time and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Shimizu, K.

Singer, J. R.

J. R. Singer, F. A. Grunbaum, P. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

Smith, D.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Stevenson, D. K.

D. Benaron, M. A. Lennox, D. K. Stevenson, “Two-dimensional and 3-D images of thick tissue using time-constrained time-of-flight spectrophotometry,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1641, 35–45 (1992).

Svaasand, L. O.

L. O. Svaasand, “Propagation of thermal waves,” Med. Phys. 9, 711–744 (1982).
[CrossRef] [PubMed]

L. O. Svaasand, B. J. Tromberg, “On the properties of optical waves in turbid media,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 41–51 (1991).
[CrossRef]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, R. C. Haskell, M. W. Bems, “Optical property measurements in turbid media using frequency domain photon migration,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 52–58 (1991).
[CrossRef]

Swift, K.

G. W. Mitchell, K. Swift, “A dual-domain Fourier transform fluorescence lifetime spectrofluorometer,” in Time-Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, Los Angeles, 270–274 (1990).

Ten Bosch, J. J.

Tromberg, B. J.

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, R. C. Haskell, M. W. Bems, “Optical property measurements in turbid media using frequency domain photon migration,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 52–58 (1991).
[CrossRef]

L. O. Svaasand, B. J. Tromberg, “On the properties of optical waves in turbid media,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 41–51 (1991).
[CrossRef]

Tsay, T.-T.

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, R. C. Haskell, M. W. Bems, “Optical property measurements in turbid media using frequency domain photon migration,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 52–58 (1991).
[CrossRef]

van de Zee, P.

D. T. Delpy, M. Cope, P. van de Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef] [PubMed]

Vande Ven, M. J.

J. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantullin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

Weiss, G. H.

Wilson, B. C.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1991).
[CrossRef]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of fight propagation in scattering tissues—I. Model prediction and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

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

Wray, S.

D. T. Delpy, M. Cope, P. van de Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef] [PubMed]

Wyatt, J.

D. T. Delpy, M. Cope, P. van de Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef] [PubMed]

Wyman, D. R.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1991).
[CrossRef]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of fight propagation in scattering tissues—I. Model prediction and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

Yodshioka, H.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Yoo, K. M.

Yoo, K.-M.

R. Alfano, P.-P. Ho, K.-M. Yoo, “Photons for prompt tumour detection,” Phys. World 5, 37–40 (1992).

Yound, M.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Zhou, G.-X.

J. M. Schmitt, G.-X. Zhou, “Measurement of blood hematocrit by dual-wavelength near-IR photoplethysmography,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1641, 150–161 (1992).

Zubelli, J. P.

J. R. Singer, F. A. Grunbaum, P. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

Anal. Biochem.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantiation of time and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

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

Appl. Opt.

Chem. Phys. Lett.

J. R. Lakowicz, K. Berndt, “Frequency domain measurements of photon migration in tissues,” Chem. Phys. Lett. 166, 246–252 (1990).
[CrossRef]

IEEE Trans. Biomed. Eng.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of fight propagation in scattering tissues—I. Model prediction and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Lasers Med. Sci.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1991).
[CrossRef]

Lasers Surg. Med.

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. Phys.

L. O. Svaasand, “Propagation of thermal waves,” Med. Phys. 9, 711–744 (1982).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Med. Biol.

D. T. Delpy, M. Cope, P. van de Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef] [PubMed]

Phys. World

R. Alfano, P.-P. Ho, K.-M. Yoo, “Photons for prompt tumour detection,” Phys. World 5, 37–40 (1992).

Proc. Natl. Acad. Sci. USA

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfield, M. Finlander, K. Kaufmann, W. Levy, M. Yound, P. Cohen, H. Yodshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef] [PubMed]

Science

J. R. Singer, F. A. Grunbaum, P. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

Other

R. L. Barbour, H. L. Graber, R. Aronson, J. Lubowsky, “Imaging of subsurface regions of random media by remote sensing,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 192–203 (1991).

D. Benaron, M. A. Lennox, D. K. Stevenson, “Two-dimensional and 3-D images of thick tissue using time-constrained time-of-flight spectrophotometry,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1641, 35–45 (1992).

J. M. Schmitt, G.-X. Zhou, “Measurement of blood hematocrit by dual-wavelength near-IR photoplethysmography,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1641, 150–161 (1992).

G. W. Mitchell, K. Swift, “A dual-domain Fourier transform fluorescence lifetime spectrofluorometer,” in Time-Resolved Laser Spectroscopy in Biochemistry II, J. R. Lakowicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1204, Los Angeles, 270–274 (1990).

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983), p. 78.

J. Fishkin, E. Gratton, M. J. Vande Ven, W. W. Mantullin, “Diffusion of intensity modulated near-infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1431, 122–135 (1991).

L. O. Svaasand, B. J. Tromberg, “On the properties of optical waves in turbid media,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 41–51 (1991).
[CrossRef]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, R. C. Haskell, M. W. Bems, “Optical property measurements in turbid media using frequency domain photon migration,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 52–58 (1991).
[CrossRef]

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1959), pp. 81–83, 272–273.

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

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 (10)

Fig. 1
Fig. 1

Theoretical frequency (MHz) versus k (mm−1) response derived from analytical solutions to Eq. (8) for the following optical properties: τ = 0.44 ns, σeff = 50 cm−1, and X = 1500 m2/s.

Fig. 2
Fig. 2

Frequency-domain instrument (see text for a detailed description). BS, beam splitter; M, display monitor; r, distance.

Fig. 3
Fig. 3

(A) Phase and (B) modulation versus frequency (5–200 MHz) for various values of r. Linear fits to (C) phase and (D) modulation versus r for selected frequencies (25, 100, 200 MHz). Measurements in 2% Intralipid; λ = 650 nm; r = 0.5, 1.0, and 1.5 cm.

Fig. 4
Fig. 4

(A) Phase and (B) modulation versus frequency for 10%, 2%, and 0.4% Intralipid; λ = 650 nm, r = 1.0 cm. Smooth curves through the data represent the best nonlinear least-squares fits to Eqs. (18) and (20).

Fig. 5
Fig. 5

Summary of optical property measurements in 10%, 2%, and 0.4% Intralipid estimated from nonlinear phase and modulation fits. σeff is linearly proportional to and β is independent of % Intralipid. All measurements were made at λ = 650 nm; r = 0.5, 1.0, and 1.5 cm.

Fig. 6
Fig. 6

A, low-frequency phase (rad) versus ω (rad/s) response for r = 1.0 cm. The slopes of the linear fits are mϕ (see text). B, phase slope (mϕ) from A for several fiber separations; the reciprocal of each B slope is the low-frequency phase velocity (see text). Measurements in 10%, 2%, and 0.4% Intralipid; λ = 650 nm.

Fig. 7
Fig. 7

Phase velocity (determined from Fig. 6B) versus (1/σeff)1/2 for 10%, 2%, and 0.4% Intralipid; λ = 650 nm. The linear relation shown is predicted by diffusion equation solutions.

Fig. 8
Fig. 8

A, Phase and B, modulation versus frequency response for 10% Intralipid with and without 1 μg/mL of TPPS4 absorber; r = 0.75 cm, λ = 514 nm.

Fig. 9
Fig. 9

Best linear fits to A phase versus ω and B −In(m) versus ω2 in the low-frequency regime where ωτ < 0.7. Measurements in 10% Intralipid with 1 and 2 μg/mL of TPPS4 absorber; r = 0.5 cm, λ = 514 nm.

Fig. 10
Fig. 10

Absorption coefficient estimated from multifrequency measurements versus concentration of TPPS4 absorber added to 10% Intralipid. Linear regression yields y = 0.022x + 0.025, where 0.025 cm−1 = β in the absence of added absorber; χ2 = 2.17.

Tables (3)

Tables Icon

Table 1 Calculated Absorption β and Effective Scattering σeff Coefficients for 0.4%. 2%, and 10% Intralipid Solutions

Tables Icon

Table 2 Absorption Coefficients and Frequency-Independent Phase Velocities Determined from Low-Frequency Data Where ωτ < 0.7

Tables Icon

Table 3 Comparison of Actual and Fitted Values of β for TPPS4 in 10% Intralipid, λ = 514 nm

Equations (27)

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

φ = Ω = 0 4 π L d Ω ,
E = Ω = 0 2 π L ( l ˆ · n ˆ ) d Ω = π L = φ 4 ,
E = φ 4 + j 2 .
E = φ 4 j 2 .
L = φ 4 π + α j · l ˆ + .
E = Ω = 0 2 π [ φ 4 π + α ( j · l ˆ ) ] ( l ˆ · n ˆ ) d Ω = φ 4 + 2 πα 3 j ,
L = φ 4 π + 3 4 π j · l ˆ + ,
j = ζ grad φ,
ζ = 1 3 [ σ ( 1 g ) + β ] = 1 3 ( σ eff + β ) ,
div j = 1 c φ t βφ + q .
X 2 φ φ t φ τ = q c ,
φ ( r , t ) = φ 0 exp ( r / δ ) r + φ 1 exp ( k r r ) r exp [ i ( k i r ω t ) ] ,
λ m = 2 π / k i ,
V p = ω / k i .
k r = 1 ( 2 X τ ) 1 / 2 { [ 1 + ( ωτ ) 2 ] 1 / 2 + 1 } 1 / 2 ,
k i = 1 ( 2 X τ ) 1 / 2 { [ 1 + ( ωτ ) 2 ] 1 / 2 1 } 1 / 2 .
V p = ω / k i = ( 2 X ω ) 1 / 2 ,
k i ωτ 2 ( X τ ) 1 / 2 ,
k r 1 ( X τ ) 1 / 2 = 1 / δ ,
k r = 1 ( X τ ) 1 / 2 × [ 1 + ( ωτ ) 2 8 + ] .
ϕ = k i r = r { β [ β + ( 1 g ) σ ] } 1 / 2 ( 3 2 ) 1 / 2 × { [ 1 + ( ω β c ) 2 ] 1 / 2 1 } 1 / 2 ,
m = ( ac / dc ) sample ( ac / dc ) source = { φ 1 exp ( k r r ) r / φ 0 exp [ r / ( X τ ) 1 / 2 ] r } ( φ 1 / φ 0 ) r = 0 = exp [ ( k r 1 δ ) r ] .
ln ( m ) r { β [ β + ( 1 g ) σ ] } 1 / 2 ( 3 2 ) 1 / 2 × ( { [ 1 + ( ω β c ) 2 ] 1 / 2 + 1 } 1 / 2 + 2 ) .
ϕ = k i r ( 3 2 σ eff ) 1 / 2 c ( 2 β ) 1 / 2 × r ω,
ln ( m ) = [ k r 1 ( X τ ) 1 / 2 ] × r ( 3 2 σ eff ) 1 / 2 c ( 2 β ) 1 / 2 × r ω 2 4 β c .
β = m ϕ 4 c × m ln ( m ) .
m ϕ = ϕ / ω = r / V p .

Metrics