Abstract

The photon path distribution (PPD) is a measure that I have developed to express optical responses in inhomogeneous turbid media in the time and frequency domains. The PPD is defined by local photon pathlengths of possible photons having total zigzag pathlengths l between the points of light input and detection. Such a distribution is independent of absorption and is uniquely determined for the medium under quantification. I show that the PPD is derived through the local photon count of the possible photons arising from an optical impulse incident on an imaginary medium having the same optical properties as the medium under quantification, except for the absence of absorption. The formulas derived can be used to calculate the PPD simultaneously with, for example, the numerical calculation of a diffusion equation.

© 2002 Optical Society of America

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  15. J. N. Winn, L. T. Perelman, K. Chen, J. Wu, R. R. Dasari, M. A. Feld, “Distribution of the paths of early-arriving photons traversing a turbid medium,” Appl. Opt. 37, 8085–8091 (1998).
    [CrossRef]
  16. 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).
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    [CrossRef]
  19. S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
    [CrossRef] [PubMed]
  20. J. Haselgrove, J. Leigh, Y. Conway, N. G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 30–41 (1991).
    [CrossRef]
  21. J. C. Schotland, J. C. Haselgrove, J. S. Leigh, “Photon hitting density,” Appl. Opt. 32, 448–453 (1993).
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  22. S. R. Arridge, “Photon-measurement density functions Part I: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
    [CrossRef] [PubMed]
  23. Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, L79–L81 (1995).
    [CrossRef]
  24. Y. Tsuchiya, T. Urakami, “Frequency domain analysis of photon migration based on the microscopic Beer–Lambert Law,” Jpn. J. Appl. Phys. 35, 4848–4851 (1996).
    [CrossRef]
  25. Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissues based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
    [CrossRef]
  26. H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
    [CrossRef]
  27. H. Zhang, Y. Tsuchiya, M. Miwa, T. Urakami, Y. Yamashita, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: consideration of the wavelength dependence of scattering properties,” Opt. Commun. 153, 314–322 (1998).
    [CrossRef]
  28. H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small-sized phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
    [CrossRef] [PubMed]
  29. H. Zhang, Y. Tsuchiya, “Applicability of time integrated spectroscopy based on the microscopic Beer–Lambert law to finite turbid media with curved boundaries,” Opt. Rev. 7, 473–478 (2000).
    [CrossRef]
  30. Y. Tsuchiya, T. Urakami, “Optical quantitation of absorbers in variously shaped turbid media based on the microscopic Beer–Lambert law: a new approach to optical computerized tomography,” in Advances in Optical Biopsy and Optical Mammography, R. R. Alfano, ed., Ann. N.Y. Acad. Sci.838, 75–94 (1998).
  31. Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamasita, Y. Tsuchiya, “Average value method: a new approach to practical optical computed tomography for a turbid medium such as human tissue,” Jpn. J. Appl. Phys. 37, 2717–2723 (1998).
    [CrossRef]
  32. Y. Ueda, K. Ohta, Y. Yamasita, Y. Tsuchiya, “Calculation of the photon path distribution in the turbid medium,” in Second Symposium on Biomedical Optics, Proc. Opt. Soc. Jpn. 2, 6–9 (2001).

2001

Y. Tsuchiya, “Photon path distribution and optical responses of turbid media: theoretical analysis based on the microscopic Beer–Lambert law,” Phys. Med. Biol. 46, 2067–2084 (2001).
[CrossRef] [PubMed]

Y. Ueda, K. Ohta, Y. Yamasita, Y. Tsuchiya, “Calculation of the photon path distribution in the turbid medium,” in Second Symposium on Biomedical Optics, Proc. Opt. Soc. Jpn. 2, 6–9 (2001).

2000

H. Zhang, Y. Tsuchiya, “Applicability of time integrated spectroscopy based on the microscopic Beer–Lambert law to finite turbid media with curved boundaries,” Opt. Rev. 7, 473–478 (2000).
[CrossRef]

1999

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small-sized phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

1998

Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamasita, Y. Tsuchiya, “Average value method: a new approach to practical optical computed tomography for a turbid medium such as human tissue,” Jpn. J. Appl. Phys. 37, 2717–2723 (1998).
[CrossRef]

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

H. Zhang, Y. Tsuchiya, M. Miwa, T. Urakami, Y. Yamashita, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: consideration of the wavelength dependence of scattering properties,” Opt. Commun. 153, 314–322 (1998).
[CrossRef]

J. N. Winn, L. T. Perelman, K. Chen, J. Wu, R. R. Dasari, M. A. Feld, “Distribution of the paths of early-arriving photons traversing a turbid medium,” Appl. Opt. 37, 8085–8091 (1998).
[CrossRef]

A. M. Gandjbakhche, X. Chernomordik, J. C. Hebden, R. Nossal, “Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments,” Appl. Opt. 37, 1973–1981 (1998).
[CrossRef]

1997

Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissues based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
[CrossRef]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head,” Appl. Opt. 36, 21–31 (1997).
[CrossRef] [PubMed]

1996

Y. Tsuchiya, T. Urakami, “Frequency domain analysis of photon migration based on the microscopic Beer–Lambert Law,” Jpn. J. Appl. Phys. 35, 4848–4851 (1996).
[CrossRef]

1995

S. R. Arridge, “Photon-measurement density functions Part I: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, L79–L81 (1995).
[CrossRef]

Y. Tsuchiya, K. Ohta, T. Urakami, “Isotropic photon injection for noninvasive tissue spectroscopy,” Jpn. J. Appl. Phys. 34, 2495–2501 (1995).
[CrossRef]

1994

L. T. Perelman, J. Wu, I. Itzkan, S. F. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1344 (1994).
[CrossRef] [PubMed]

1993

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

J. C. Schotland, J. C. Haselgrove, J. S. Leigh, “Photon hitting density,” Appl. Opt. 32, 448–453 (1993).
[CrossRef] [PubMed]

1989

1987

P. van der Zee, D. T. Delpy, “Simulation of the point spread function for light in tissue by a Monte Carlo method,” Adv. Exp. Med. Biol. 215, 179–192 (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

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

1977

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

Adam, G.

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

Aronson, R.

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE International Series (SPIE, Bellingham, Wash., 1993), pp. 121–143.

Arridge, S. R.

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head,” Appl. Opt. 36, 21–31 (1997).
[CrossRef] [PubMed]

S. R. Arridge, “Photon-measurement density functions Part I: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “Application of finite element method for the forward model in infra-red absorption imaging,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. SPIE1768, 97–108 (1992).
[CrossRef]

Barbour, R. L.

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE International Series (SPIE, Bellingham, Wash., 1993), pp. 121–143.

Bonner, R. F.

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]

J. Haselgrove, J. Leigh, Y. Conway, N. G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 30–41 (1991).
[CrossRef]

Chang, J.

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE International Series (SPIE, Bellingham, Wash., 1993), pp. 121–143.

Chen, K.

J. N. Winn, L. T. Perelman, K. Chen, J. Wu, R. R. Dasari, M. A. Feld, “Distribution of the paths of early-arriving photons traversing a turbid medium,” Appl. Opt. 37, 8085–8091 (1998).
[CrossRef]

Chernomordik, X.

Conway, Y.

J. Haselgrove, J. Leigh, Y. Conway, N. G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 30–41 (1991).
[CrossRef]

Cope, M.

Dasari, R. R.

J. N. Winn, L. T. Perelman, K. Chen, J. Wu, R. R. Dasari, M. A. Feld, “Distribution of the paths of early-arriving photons traversing a turbid medium,” Appl. Opt. 37, 8085–8091 (1998).
[CrossRef]

Delpy, D. T.

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head,” Appl. Opt. 36, 21–31 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

P. van der Zee, D. T. Delpy, “Simulation of the point spread function for light in tissue by a Monte Carlo method,” Adv. Exp. Med. Biol. 215, 179–192 (1987).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “Application of finite element method for the forward model in infra-red absorption imaging,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. SPIE1768, 97–108 (1992).
[CrossRef]

Feld, M. A.

J. N. Winn, L. T. Perelman, K. Chen, J. Wu, R. R. Dasari, M. A. Feld, “Distribution of the paths of early-arriving photons traversing a turbid medium,” Appl. Opt. 37, 8085–8091 (1998).
[CrossRef]

Feld, S. F.

L. T. Perelman, J. Wu, I. Itzkan, S. F. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1344 (1994).
[CrossRef] [PubMed]

Firbank, M.

Gandjbakhche, A. M.

Graber, H. L.

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE International Series (SPIE, Bellingham, Wash., 1993), pp. 121–143.

Haselgrove, J.

J. Haselgrove, J. Leigh, Y. Conway, N. G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 30–41 (1991).
[CrossRef]

Haselgrove, J. C.

Havlin, S.

Hebden, J. C.

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “Application of finite element method for the forward model in infra-red absorption imaging,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. SPIE1768, 97–108 (1992).
[CrossRef]

Hiruma, T.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small-sized phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

Itzkan, I.

L. T. Perelman, J. Wu, I. Itzkan, S. F. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1344 (1994).
[CrossRef] [PubMed]

Jöbsis, F. F.

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

Leigh, J.

J. Haselgrove, J. Leigh, Y. Conway, N. G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 30–41 (1991).
[CrossRef]

Leigh, J. S.

Lu, Z.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small-sized phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

Maris, M.

J. Haselgrove, J. Leigh, Y. Conway, N. G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 30–41 (1991).
[CrossRef]

Miwa, M.

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

H. Zhang, Y. Tsuchiya, M. Miwa, T. Urakami, Y. Yamashita, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: consideration of the wavelength dependence of scattering properties,” Opt. Commun. 153, 314–322 (1998).
[CrossRef]

Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamasita, Y. Tsuchiya, “Average value method: a new approach to practical optical computed tomography for a turbid medium such as human tissue,” Jpn. J. Appl. Phys. 37, 2717–2723 (1998).
[CrossRef]

Nossal, R.

Oda, M.

Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamasita, Y. Tsuchiya, “Average value method: a new approach to practical optical computed tomography for a turbid medium such as human tissue,” Jpn. J. Appl. Phys. 37, 2717–2723 (1998).
[CrossRef]

Ohta, K.

Y. Ueda, K. Ohta, Y. Yamasita, Y. Tsuchiya, “Calculation of the photon path distribution in the turbid medium,” in Second Symposium on Biomedical Optics, Proc. Opt. Soc. Jpn. 2, 6–9 (2001).

Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamasita, Y. Tsuchiya, “Average value method: a new approach to practical optical computed tomography for a turbid medium such as human tissue,” Jpn. J. Appl. Phys. 37, 2717–2723 (1998).
[CrossRef]

Y. Tsuchiya, K. Ohta, T. Urakami, “Isotropic photon injection for noninvasive tissue spectroscopy,” Jpn. J. Appl. Phys. 34, 2495–2501 (1995).
[CrossRef]

Okada, E.

Patterson, M. S.

Perelman, L. T.

J. N. Winn, L. T. Perelman, K. Chen, J. Wu, R. R. Dasari, M. A. Feld, “Distribution of the paths of early-arriving photons traversing a turbid medium,” Appl. Opt. 37, 8085–8091 (1998).
[CrossRef]

L. T. Perelman, J. Wu, I. Itzkan, S. F. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1344 (1994).
[CrossRef] [PubMed]

Schotland, J. C.

Schweiger, M.

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head,” Appl. Opt. 36, 21–31 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “Application of finite element method for the forward model in infra-red absorption imaging,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. SPIE1768, 97–108 (1992).
[CrossRef]

Tsuchiya, Y.

Y. Tsuchiya, “Photon path distribution and optical responses of turbid media: theoretical analysis based on the microscopic Beer–Lambert law,” Phys. Med. Biol. 46, 2067–2084 (2001).
[CrossRef] [PubMed]

Y. Ueda, K. Ohta, Y. Yamasita, Y. Tsuchiya, “Calculation of the photon path distribution in the turbid medium,” in Second Symposium on Biomedical Optics, Proc. Opt. Soc. Jpn. 2, 6–9 (2001).

H. Zhang, Y. Tsuchiya, “Applicability of time integrated spectroscopy based on the microscopic Beer–Lambert law to finite turbid media with curved boundaries,” Opt. Rev. 7, 473–478 (2000).
[CrossRef]

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small-sized phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

H. Zhang, Y. Tsuchiya, M. Miwa, T. Urakami, Y. Yamashita, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: consideration of the wavelength dependence of scattering properties,” Opt. Commun. 153, 314–322 (1998).
[CrossRef]

Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamasita, Y. Tsuchiya, “Average value method: a new approach to practical optical computed tomography for a turbid medium such as human tissue,” Jpn. J. Appl. Phys. 37, 2717–2723 (1998).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissues based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Frequency domain analysis of photon migration based on the microscopic Beer–Lambert Law,” Jpn. J. Appl. Phys. 35, 4848–4851 (1996).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, L79–L81 (1995).
[CrossRef]

Y. Tsuchiya, K. Ohta, T. Urakami, “Isotropic photon injection for noninvasive tissue spectroscopy,” Jpn. J. Appl. Phys. 34, 2495–2501 (1995).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Optical quantitation of absorbers in variously shaped turbid media based on the microscopic Beer–Lambert law: a new approach to optical computerized tomography,” in Advances in Optical Biopsy and Optical Mammography, R. R. Alfano, ed., Ann. N.Y. Acad. Sci.838, 75–94 (1998).

Ueda, Y.

Y. Ueda, K. Ohta, Y. Yamasita, Y. Tsuchiya, “Calculation of the photon path distribution in the turbid medium,” in Second Symposium on Biomedical Optics, Proc. Opt. Soc. Jpn. 2, 6–9 (2001).

Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamasita, Y. Tsuchiya, “Average value method: a new approach to practical optical computed tomography for a turbid medium such as human tissue,” Jpn. J. Appl. Phys. 37, 2717–2723 (1998).
[CrossRef]

Urakami, T.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small-sized phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

H. Zhang, Y. Tsuchiya, M. Miwa, T. Urakami, Y. Yamashita, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: consideration of the wavelength dependence of scattering properties,” Opt. Commun. 153, 314–322 (1998).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissues based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Frequency domain analysis of photon migration based on the microscopic Beer–Lambert Law,” Jpn. J. Appl. Phys. 35, 4848–4851 (1996).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, L79–L81 (1995).
[CrossRef]

Y. Tsuchiya, K. Ohta, T. Urakami, “Isotropic photon injection for noninvasive tissue spectroscopy,” Jpn. J. Appl. Phys. 34, 2495–2501 (1995).
[CrossRef]

Y. Tsuchiya, T. Urakami, “Optical quantitation of absorbers in variously shaped turbid media based on the microscopic Beer–Lambert law: a new approach to optical computerized tomography,” in Advances in Optical Biopsy and Optical Mammography, R. R. Alfano, ed., Ann. N.Y. Acad. Sci.838, 75–94 (1998).

van der Zee, P.

P. van der Zee, D. T. Delpy, “Simulation of the point spread function for light in tissue by a Monte Carlo method,” Adv. Exp. Med. Biol. 215, 179–192 (1987).
[CrossRef] [PubMed]

Wang, N. G.

J. Haselgrove, J. Leigh, Y. Conway, N. G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 30–41 (1991).
[CrossRef]

Weiss, G. H.

Wilson, B. C.

Winn, J. N.

J. N. Winn, L. T. Perelman, K. Chen, J. Wu, R. R. Dasari, M. A. Feld, “Distribution of the paths of early-arriving photons traversing a turbid medium,” Appl. Opt. 37, 8085–8091 (1998).
[CrossRef]

Wu, J.

J. N. Winn, L. T. Perelman, K. Chen, J. Wu, R. R. Dasari, M. A. Feld, “Distribution of the paths of early-arriving photons traversing a turbid medium,” Appl. Opt. 37, 8085–8091 (1998).
[CrossRef]

L. T. Perelman, J. Wu, I. Itzkan, S. F. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1344 (1994).
[CrossRef] [PubMed]

Yamashita, Y.

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

H. Zhang, Y. Tsuchiya, M. Miwa, T. Urakami, Y. Yamashita, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: consideration of the wavelength dependence of scattering properties,” Opt. Commun. 153, 314–322 (1998).
[CrossRef]

Yamasita, Y.

Y. Ueda, K. Ohta, Y. Yamasita, Y. Tsuchiya, “Calculation of the photon path distribution in the turbid medium,” in Second Symposium on Biomedical Optics, Proc. Opt. Soc. Jpn. 2, 6–9 (2001).

Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamasita, Y. Tsuchiya, “Average value method: a new approach to practical optical computed tomography for a turbid medium such as human tissue,” Jpn. J. Appl. Phys. 37, 2717–2723 (1998).
[CrossRef]

Zhang, H.

H. Zhang, Y. Tsuchiya, “Applicability of time integrated spectroscopy based on the microscopic Beer–Lambert law to finite turbid media with curved boundaries,” Opt. Rev. 7, 473–478 (2000).
[CrossRef]

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small-sized phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

H. Zhang, Y. Tsuchiya, M. Miwa, T. Urakami, Y. Yamashita, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: consideration of the wavelength dependence of scattering properties,” Opt. Commun. 153, 314–322 (1998).
[CrossRef]

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

Adv. Exp. Med. Biol.

P. van der Zee, D. T. Delpy, “Simulation of the point spread function for light in tissue by a Monte Carlo method,” Adv. Exp. Med. Biol. 215, 179–192 (1987).
[CrossRef] [PubMed]

Appl. Opt.

J. N. Winn, L. T. Perelman, K. Chen, J. Wu, R. R. Dasari, M. A. Feld, “Distribution of the paths of early-arriving photons traversing a turbid medium,” Appl. Opt. 37, 8085–8091 (1998).
[CrossRef]

Appl. Opt.

J. Biomed. Opt.

H. Zhang, T. Urakami, Y. Tsuchiya, Z. Lu, T. Hiruma, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: application to small-sized phantoms having different boundary conditions,” J. Biomed. Opt. 4, 183–190 (1999).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

Y. Tsuchiya, T. Urakami, “Photon migration model for turbid biological medium having various shapes,” Jpn. J. Appl. Phys. 34, L79–L81 (1995).
[CrossRef]

Jpn. J. Appl. Phys.

Y. Tsuchiya, T. Urakami, “Frequency domain analysis of photon migration based on the microscopic Beer–Lambert Law,” Jpn. J. Appl. Phys. 35, 4848–4851 (1996).
[CrossRef]

H. Zhang, M. Miwa, Y. Yamashita, Y. Tsuchiya, “Quantitation of absorbers in turbid media using time integrated spectroscopy based on microscopic Beer–Lambert law,” Jpn. J. Appl. Phys. 37, 2724–2727 (1998).
[CrossRef]

Y. Ueda, K. Ohta, M. Oda, M. Miwa, Y. Yamasita, Y. Tsuchiya, “Average value method: a new approach to practical optical computed tomography for a turbid medium such as human tissue,” Jpn. J. Appl. Phys. 37, 2717–2723 (1998).
[CrossRef]

Y. Tsuchiya, K. Ohta, T. Urakami, “Isotropic photon injection for noninvasive tissue spectroscopy,” Jpn. J. Appl. Phys. 34, 2495–2501 (1995).
[CrossRef]

Med. Phys.

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

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Opt. Commun.

H. Zhang, Y. Tsuchiya, M. Miwa, T. Urakami, Y. Yamashita, “Time integrated spectroscopy of turbid media based on the microscopic Beer–Lambert law: consideration of the wavelength dependence of scattering properties,” Opt. Commun. 153, 314–322 (1998).
[CrossRef]

Opt. Commun.

Y. Tsuchiya, T. Urakami, “Quantitation of absorbing substances in turbid media such as human tissues based on the microscopic Beer–Lambert law,” Opt. Commun. 144, 269–280 (1997).
[CrossRef]

Opt. Rev.

H. Zhang, Y. Tsuchiya, “Applicability of time integrated spectroscopy based on the microscopic Beer–Lambert law to finite turbid media with curved boundaries,” Opt. Rev. 7, 473–478 (2000).
[CrossRef]

Phys. Med. Biol.

Y. Tsuchiya, “Photon path distribution and optical responses of turbid media: theoretical analysis based on the microscopic Beer–Lambert law,” Phys. Med. Biol. 46, 2067–2084 (2001).
[CrossRef] [PubMed]

Phys. Med. Biol.

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Phys. Rev. Lett.

L. T. Perelman, J. Wu, I. Itzkan, S. F. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1344 (1994).
[CrossRef] [PubMed]

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

Second Symposium on Biomedical Optics

Y. Ueda, K. Ohta, Y. Yamasita, Y. Tsuchiya, “Calculation of the photon path distribution in the turbid medium,” in Second Symposium on Biomedical Optics, Proc. Opt. Soc. Jpn. 2, 6–9 (2001).

Other

Y. Tsuchiya, T. Urakami, “Optical quantitation of absorbers in variously shaped turbid media based on the microscopic Beer–Lambert law: a new approach to optical computerized tomography,” in Advances in Optical Biopsy and Optical Mammography, R. R. Alfano, ed., Ann. N.Y. Acad. Sci.838, 75–94 (1998).

J. Haselgrove, J. Leigh, Y. Conway, N. G. Wang, M. Maris, B. Chance, “Monte Carlo and diffusion calculations of photon migration in non-infinite highly scattering media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 30–41 (1991).
[CrossRef]

B. Chance, R. R. Alfano, eds., Photon Migration and Imaging in Random Media and Tissues, Proc. SPIE1888, (1993).

B. Chance, R. R. Alfano, eds., Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, Proc. SPIE2389 (1995).

B. Chance, R. R. Alfano, eds., Optical Tomography and Spectroscopy of Tissues: Theory, Instrumentation, Model, and Human Studies II, Proc. SPIE2979(1997).

B. Chance, R. R. Alfano, B. Tromberg, eds., Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE3597 (1999).

H. L. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE International Series (SPIE, Bellingham, Wash., 1993), pp. 121–143.

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “Application of finite element method for the forward model in infra-red absorption imaging,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. SPIE1768, 97–108 (1992).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Example of the segmentation of a medium under quantification as well as light input point p and detection point q on the surface. We divide the medium under quantification into N nonoverlapping components, voxels x ( x = x 1 ,   x 2 ,   ,   x N ) , each assumed to have a uniform absorption, and express the absorption coefficient of the voxel x i by μ ai . The sizes and shapes of the voxels are arbitrary as long as the absorption can be assumed to be uniform in the voxels. To calculate the PPD, we further define and use an imaginary reference medium that has the same optical properties and boundary conditions as the medium under quantification, except for the absence of absorption. The imaginary reference medium is also divided in exactly the same manner as the medium under quantification.

Equations (27)

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P i = exp ( - μ ai l i ) = exp ( - μ ai ct i ) ,
l ( t ) = ct = i = 1 N l i ( t ) = c i = 1 N t i .
h ( t ) = s ( t ) exp - i = 1 N ( μ ai l i ) ,
d ln   h ( t ) = i = 1 N   ln   h ( t ) μ ai d μ ai = - i = 1 N ( l i d μ ai ) .
ln   h ( t ) = ln   s ( t ) - i = 1 N ( μ ai l i ) = ln   s ( t ) - B h .
I = 0 h ( t ) d t = 0 s ( t ) exp - i = 1 N ( μ ai l i ) d t .
ln   I = ln 0 s ( t ) d t - i = 1 N 0 μ ai L i d μ a = ln 0 s ( t ) d t - i = 1 N B Ii = ln 0 s ( t ) d t - B I ,
L i = -   ln   I μ ai = 0 l i s ( t ) exp - i = 1 N ( μ ai l i ) d t 0 s ( t ) - i = 1 N ( μ ai l i ) d t = l i I ,
i = 1 N L i = 0 ls ( t ) exp - i = 1 N ( μ ai l i ) d t 0 s ( t ) exp - i = 1 N ( μ ai l i ) d t = L .
Δ μ a = μ a 2 - μ a 1 = ( λ ) Δ C ,
Δ μ a = μ a 2 - μ a 1 = ( 2 - 1 ) C = Δ C .
Δ B h = B h 2 - B h 1 = i = 1 N ( Δ μ ai l i ) .
Δ μ ah = i = 1 N ( Δ μ ai l i ) i = 1 N l i = i = 1 N ( Δ μ ai l i ) l .
Δ B I = B I 2 - B I 1 = i = 1 N μ a 1 μ a 2 L i d μ a .
Δ B I = B I 2 - B I 1 = i = 1 N ( Δ μ ai L i ) .
U i ( t ;   t ) = U pi ( t ) U iq ( t - t ) = U pi ( t ) U qi ( t - t ) ,
U i ( t ) = 0 t U i ( t ;   t ) d t ,
U ( t ) = i = 1 N U i ( t ) = i = 1 N 0 t U i ( t ;   t ) d t .
U ( t ;   t ) = i = 1 N U i ( t ;   t ) = s ( t ) .
U ( t ) = i = 1 N 0 t U i ( t ;   t ) d t = 0 t i = 1 N U i ( t ;   t ) d t = 0 t U ( t ;   t ) d t = ts ( t ) .
l i ( t ) = U i ( t ) U ( t )   l ( t ) = U i ( t ) ts ( t )   l ( t ) = c s ( t )   U i ( t ) ,
H ( ω ) = 0 h ( t ) exp ( - j ω t ) d t = 0 s ( t ) exp - i = 1 N ( μ ai l i ) exp ( - j ω t ) d t = R + jX = A   exp ( - j ϕ ) ,
R = R ( 0 ) + c i = 1 N 0 μ ai X i ω d μ a ,
X = X ( 0 ) - c i = 1 N 0 μ ai R i ω d μ a ,
ln   A = ln   A ( 0 ) - c i = 1 N 0 μ ai ϕ i ω d μ a ,
ϕ = ϕ ( 0 ) + c i = 1 N 0 μ ai   ln   A i ω d μ a ,
ϕ i ω ϕ i ω .

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