Abstract

To analyze the fundamental characteristics of light transmitted through living tissues, we used the Monte Carlo method to trace the paths of the rays incident upon slabs of particles. The slabs contained either (i) two types of scattering particles in a solution or (ii) one type of particle with pigment added to the solution. Temporal analyses of the transmittance have illustrated that the differences in the optical density among the slabs having different absorption coefficients with the same scattering coefficient vary linearly with time. Also, their gradients have been shown to be proportional to the differences in the absorption coefficients, thus verifying the microscopic Beer–Lambert law in highly scattering media when temporally resolved measurement is used.

© 1991 Optical Society of America

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References

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  1. F. F. Jöbsis, “Nonivasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science, 198, 1264–1267 (1977).
    [CrossRef] [PubMed]
  2. P. van der Zee, D. T. Delpy, “Simulation of the point spread function for light in tissue by a Monte Carlo method,” in Oxygen Transport to TissueI. A. Silver, A. Silver, eds. (Plenum, New York, 1987), Vol. IX.
  3. P. van der Zee, D. T. Delpy, “Computed point spread functions for light in tissue using a measured volume scattering function,” Adv. Exp. Med. Biol. 222, 191–197 (1988).
    [PubMed]
  4. D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
    [CrossRef] [PubMed]
  5. B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
    [CrossRef] [PubMed]
  6. S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials,” Med. Phys. 14, pp. 835–843 (1987).
    [CrossRef] [PubMed]
  7. B. C. Wilson, M. S. Patterson, S. T. Flock, J. D. Moulton, “The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range,” in Light in Biology and Medicine, R. H. Douglas, J. Moan, F. Dall'Acqua, eds. (Plenum, New York, 1988), Vol. 1, pp. 45–52.
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and -unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
    [CrossRef] [PubMed]
  14. O. Hazeki, M. Tamura, “Quantitative analysis of hemoglobin oxygenation state of rat brain in situ by near-infrared spectrophotometry,” J. Appl. Physiol. 64, 796–802 (1988).
    [PubMed]
  15. A. Seiyama, O. Hazeki, M. Tamura, “Noninvasive quantitative analysis of blood oxygenation in rat skeletal muscle,” J. Biochem. 103, 419–424 (1988).
    [PubMed]
  16. Y. Nomura, O. Hazeki, T. Ariga, M. Tamura, “Exponential attenuation of light along nonlinear path through the biological model,” Adv. Exp. Med. Biol. 248, 77–80 (1989).
    [CrossRef] [PubMed]
  17. R. S. Chadwick, I.-D. Chang, “A laser study of the motion of particles suspended in a slow viscous shear flow,” J. Colloid Interface Sci. 4, 516–534 (1973).
    [CrossRef]
  18. J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976), pp. 140–144.

1989 (3)

1988 (5)

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

O. Hazeki, M. Tamura, “Quantitative analysis of hemoglobin oxygenation state of rat brain in situ by near-infrared spectrophotometry,” J. Appl. Physiol. 64, 796–802 (1988).
[PubMed]

A. Seiyama, O. Hazeki, M. Tamura, “Noninvasive quantitative analysis of blood oxygenation in rat skeletal muscle,” J. Biochem. 103, 419–424 (1988).
[PubMed]

P. van der Zee, D. T. Delpy, “Computed point spread functions for light in tissue using a measured volume scattering function,” Adv. Exp. Med. Biol. 222, 191–197 (1988).
[PubMed]

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

1987 (1)

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials,” Med. Phys. 14, pp. 835–843 (1987).
[CrossRef] [PubMed]

1986 (1)

J. M. Maarek, G. Jarry, J. Crowe, M.-H. Bui, D. Laurent, “Simulation of laser tomoscopy in a heterogeneous biological medium,” Med. Biol. Eng. Comput. 24, 407–414 (1986).
[CrossRef] [PubMed]

1983 (1)

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

1980 (1)

1977 (1)

F. F. Jöbsis, “Nonivasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science, 198, 1264–1267 (1977).
[CrossRef] [PubMed]

1973 (1)

R. S. Chadwick, I.-D. Chang, “A laser study of the motion of particles suspended in a slow viscous shear flow,” J. Colloid Interface Sci. 4, 516–534 (1973).
[CrossRef]

Adam, G.

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Ariga, T.

Y. Nomura, O. Hazeki, T. Ariga, M. Tamura, “Exponential attenuation of light along nonlinear path through the biological model,” Adv. Exp. Med. Biol. 248, 77–80 (1989).
[CrossRef] [PubMed]

Arridge, S.

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

Boretsky, R.

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

Bui, M.-H.

J. M. Maarek, G. Jarry, J. Crowe, M.-H. Bui, D. Laurent, “Simulation of laser tomoscopy in a heterogeneous biological medium,” Med. Biol. Eng. Comput. 24, 407–414 (1986).
[CrossRef] [PubMed]

Chadwick, R. S.

R. S. Chadwick, I.-D. Chang, “A laser study of the motion of particles suspended in a slow viscous shear flow,” J. Colloid Interface Sci. 4, 516–534 (1973).
[CrossRef]

Chance, B.

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

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

Chang, I.-D.

R. S. Chadwick, I.-D. Chang, “A laser study of the motion of particles suspended in a slow viscous shear flow,” J. Colloid Interface Sci. 4, 516–534 (1973).
[CrossRef]

Cohen, P.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, 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 der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef] [PubMed]

Crowe, J.

J. M. Maarek, G. Jarry, J. Crowe, M.-H. Bui, D. Laurent, “Simulation of laser tomoscopy in a heterogeneous biological medium,” Med. Biol. Eng. Comput. 24, 407–414 (1986).
[CrossRef] [PubMed]

Delpy, D. T.

P. van der Zee, D. T. Delpy, “Computed point spread functions for light in tissue using a measured volume scattering function,” Adv. Exp. Med. Biol. 222, 191–197 (1988).
[PubMed]

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

P. van der Zee, D. T. Delpy, “Simulation of the point spread function for light in tissue by a Monte Carlo method,” in Oxygen Transport to TissueI. A. Silver, A. Silver, eds. (Plenum, New York, 1987), Vol. IX.

Duderstadt, J. J.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976), pp. 140–144.

Finander, M.

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

Flock, S. T.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials,” Med. Phys. 14, pp. 835–843 (1987).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, S. T. Flock, J. D. Moulton, “The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range,” in Light in Biology and Medicine, R. H. Douglas, J. Moan, F. Dall'Acqua, eds. (Plenum, New York, 1988), Vol. 1, pp. 45–52.
[CrossRef]

Furutsu, K.

Greenfeld, R.

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

Hamilton, L. J.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976), pp. 140–144.

Hazeki, O.

Y. Nomura, O. Hazeki, T. Ariga, M. Tamura, “Exponential attenuation of light along nonlinear path through the biological model,” Adv. Exp. Med. Biol. 248, 77–80 (1989).
[CrossRef] [PubMed]

O. Hazeki, M. Tamura, “Quantitative analysis of hemoglobin oxygenation state of rat brain in situ by near-infrared spectrophotometry,” J. Appl. Physiol. 64, 796–802 (1988).
[PubMed]

A. Seiyama, O. Hazeki, M. Tamura, “Noninvasive quantitative analysis of blood oxygenation in rat skeletal muscle,” J. Biochem. 103, 419–424 (1988).
[PubMed]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 9.

Ito, S.

Jacques, S. L.

Jarry, G.

J. M. Maarek, G. Jarry, J. Crowe, M.-H. Bui, D. Laurent, “Simulation of laser tomoscopy in a heterogeneous biological medium,” Med. Biol. Eng. Comput. 24, 407–414 (1986).
[CrossRef] [PubMed]

Jöbsis, F. F.

F. F. Jöbsis, “Nonivasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science, 198, 1264–1267 (1977).
[CrossRef] [PubMed]

Kaufmann, K.

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

Laurent, D.

J. M. Maarek, G. Jarry, J. Crowe, M.-H. Bui, D. Laurent, “Simulation of laser tomoscopy in a heterogeneous biological medium,” Med. Biol. Eng. Comput. 24, 407–414 (1986).
[CrossRef] [PubMed]

Leigh, J. S.

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

Levy, W.

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

Maarek, J. M.

J. M. Maarek, G. Jarry, J. Crowe, M.-H. Bui, D. Laurent, “Simulation of laser tomoscopy in a heterogeneous biological medium,” Med. Biol. Eng. Comput. 24, 407–414 (1986).
[CrossRef] [PubMed]

Miyake, H.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, 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.

B. C. Wilson, M. S. Patterson, S. T. Flock, J. D. Moulton, “The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range,” in Light in Biology and Medicine, R. H. Douglas, J. Moan, F. Dall'Acqua, eds. (Plenum, New York, 1988), Vol. 1, pp. 45–52.
[CrossRef]

Nioka, S.

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

Nomura, Y.

Y. Nomura, O. Hazeki, T. Ariga, M. Tamura, “Exponential attenuation of light along nonlinear path through the biological model,” Adv. Exp. Med. Biol. 248, 77–80 (1989).
[CrossRef] [PubMed]

Patterson, M. S.

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive 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,” Med. Phys. 14, pp. 835–843 (1987).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, S. T. Flock, J. D. Moulton, “The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range,” in Light in Biology and Medicine, R. H. Douglas, J. Moan, F. Dall'Acqua, eds. (Plenum, New York, 1988), Vol. 1, pp. 45–52.
[CrossRef]

Seiyama, A.

A. Seiyama, O. Hazeki, M. Tamura, “Noninvasive quantitative analysis of blood oxygenation in rat skeletal muscle,” J. Biochem. 103, 419–424 (1988).
[PubMed]

Smith, D. S.

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

Tamura, M.

Y. Nomura, O. Hazeki, T. Ariga, M. Tamura, “Exponential attenuation of light along nonlinear path through the biological model,” Adv. Exp. Med. Biol. 248, 77–80 (1989).
[CrossRef] [PubMed]

A. Seiyama, O. Hazeki, M. Tamura, “Noninvasive quantitative analysis of blood oxygenation in rat skeletal muscle,” J. Biochem. 103, 419–424 (1988).
[PubMed]

O. Hazeki, M. Tamura, “Quantitative analysis of hemoglobin oxygenation state of rat brain in situ by near-infrared spectrophotometry,” J. Appl. Physiol. 64, 796–802 (1988).
[PubMed]

van der Zee, P.

P. van der Zee, D. T. Delpy, “Computed point spread functions for light in tissue using a measured volume scattering function,” Adv. Exp. Med. Biol. 222, 191–197 (1988).
[PubMed]

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

P. van der Zee, D. T. Delpy, “Simulation of the point spread function for light in tissue by a Monte Carlo method,” in Oxygen Transport to TissueI. A. Silver, A. Silver, eds. (Plenum, New York, 1987), Vol. IX.

Wilson, B. C.

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive 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,” Med. Phys. 14, pp. 835–843 (1987).
[CrossRef] [PubMed]

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

B. C. Wilson, M. S. Patterson, S. T. Flock, J. D. Moulton, “The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range,” in Light in Biology and Medicine, R. H. Douglas, J. Moan, F. Dall'Acqua, eds. (Plenum, New York, 1988), Vol. 1, pp. 45–52.
[CrossRef]

Wray, S.

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

Wyatt, J.

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

Yoshioka, H.

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

Young, M.

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

Adv. Exp. Med. Biol. (2)

P. van der Zee, D. T. Delpy, “Computed point spread functions for light in tissue using a measured volume scattering function,” Adv. Exp. Med. Biol. 222, 191–197 (1988).
[PubMed]

Y. Nomura, O. Hazeki, T. Ariga, M. Tamura, “Exponential attenuation of light along nonlinear path through the biological model,” Adv. Exp. Med. Biol. 248, 77–80 (1989).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Appl. Physiol. (1)

O. Hazeki, M. Tamura, “Quantitative analysis of hemoglobin oxygenation state of rat brain in situ by near-infrared spectrophotometry,” J. Appl. Physiol. 64, 796–802 (1988).
[PubMed]

J. Biochem. (1)

A. Seiyama, O. Hazeki, M. Tamura, “Noninvasive quantitative analysis of blood oxygenation in rat skeletal muscle,” J. Biochem. 103, 419–424 (1988).
[PubMed]

J. Colloid Interface Sci. (1)

R. S. Chadwick, I.-D. Chang, “A laser study of the motion of particles suspended in a slow viscous shear flow,” J. Colloid Interface Sci. 4, 516–534 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

Med. Biol. Eng. Comput. (1)

J. M. Maarek, G. Jarry, J. Crowe, M.-H. Bui, D. Laurent, “Simulation of laser tomoscopy in a heterogeneous biological medium,” Med. Biol. Eng. Comput. 24, 407–414 (1986).
[CrossRef] [PubMed]

Med. Phys. (2)

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials,” Med. Phys. 14, pp. 835–843 (1987).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

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

Proc. Natl. Acad. Sci. USA (1)

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, P. Cohen, H. Yoshioka, 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 (1)

F. F. Jöbsis, “Nonivasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science, 198, 1264–1267 (1977).
[CrossRef] [PubMed]

Other (4)

P. van der Zee, D. T. Delpy, “Simulation of the point spread function for light in tissue by a Monte Carlo method,” in Oxygen Transport to TissueI. A. Silver, A. Silver, eds. (Plenum, New York, 1987), Vol. IX.

B. C. Wilson, M. S. Patterson, S. T. Flock, J. D. Moulton, “The optical absorption and scattering properties of tissues in the visible and near-infrared wavelength range,” in Light in Biology and Medicine, R. H. Douglas, J. Moan, F. Dall'Acqua, eds. (Plenum, New York, 1988), Vol. 1, pp. 45–52.
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 9.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976), pp. 140–144.

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Figures (7)

Fig. 1
Fig. 1

Model of temporal analysis.

Fig. 2
Fig. 2

Relative transmittance as a function of time for an impulse incidence. The slab contains isotropically scattering particles (dashed curve, T0 with the addition of forward-biased scattering weakly absorbing particle; (solid curves, T1T4).

Fig. 3
Fig. 3

Difference of the optical density based on the curve T0 in Fig. 2, ΔOD0n(t). Because of the increase in the total scattering coefficient, ΔOD0n(t) has a curvature in the early time period.

Fig. 4
Fig. 4

Difference of the optical density based on the curve T1 in Fig. 2, ΔOD1n(t). The effect of scattering is canceled and only the difference in absorption coefficient is observed. The Beer–Lambert law holds microscopically and ΔOD1n(t) varies linearly with time and the gradients of the regression lines are proportional to the difference in the absorption coefficient.

Fig. 5
Fig. 5

Relative transmittance for the isotropically scattering particle with the addition of hemoglobin solution as an absorber.

Fig. 6
Fig. 6

Comparison of measured and predicted ΔOD1n(t). The regression lines obtained by using the transmittance data in Fig. 5 are drawn.

Fig. 7
Fig. 7

Comparison of the transmittances obtained by the Monte Carlo simulation with those predicted by the diffusion approximation.

Tables (1)

Tables Icon

Table I Comparison of the Regression Data of Monte Carlo Results with the Values for Nonscattering Cases

Equations (5)

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

L = ln ( R ) / μ t ,
E i + 1 = E i exp ( μ a 2 L ) ,
E i + 1 = E i ( μ s 2 / μ t 2 ) .
Δ OD m n ( t ) = log [ T n ( t ) / T m ( t ) ] ,
Δ OD 12 ( t ) ( μ a 2 μ a 1 ) c t log ( e ) + l 2 4 c t ( 1 D 2 1 D 1 ) log ( e ) + log l 2 c t D 1 2 l 2 c t D 2 2 + 1 2 log D 2 D 1 ,

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