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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 7 — Jul. 1, 2002
  • pp: 1383–1389

Photon path distribution in inhomogeneous turbid media: theoretical analysis and a method of calculation

Yutaka Tsuchiya  »View Author Affiliations

JOSA A, Vol. 19, Issue 7, pp. 1383-1389 (2002)

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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

OCIS Codes
(120.3890) Instrumentation, measurement, and metrology : Medical optics instrumentation
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.5280) Medical optics and biotechnology : Photon migration
(290.7050) Scattering : Turbid media
(300.1030) Spectroscopy : Absorption

Original Manuscript: July 9, 2001
Revised Manuscript: November 6, 2001
Manuscript Accepted: November 6, 2001
Published: July 1, 2002

Yutaka Tsuchiya, "Photon path distribution in inhomogeneous turbid media: theoretical analysis and a method of calculation," J. Opt. Soc. Am. A 19, 1383-1389 (2002)

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  1. F. F. Jöbsis, “Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977). [CrossRef]
  2. B. Chance, R. R. Alfano, eds., Photon Migration and Imaging in Random Media and Tissues, Proc. SPIE1888, (1993).
  3. 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).
  4. B. Chance, R. R. Alfano, eds., Optical Tomography and Spectroscopy of Tissues: Theory, Instrumentation, Model, and Human Studies II, Proc. SPIE2979(1997).
  5. B. Chance, R. R. Alfano, B. Tromberg, eds., Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE3597 (1999).
  6. 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]
  7. S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997). [CrossRef] [PubMed]
  8. 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]
  9. 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]
  10. 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.
  11. Y. Tsuchiya, K. Ohta, T. Urakami, “Isotropic photon injection for noninvasive tissue spectroscopy,” Jpn. J. Appl. Phys. 34, 2495–2501 (1995). [CrossRef]
  12. 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]
  13. 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]
  14. 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]
  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). [CrossRef] [PubMed]
  17. 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]
  18. 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]
  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). [CrossRef] [PubMed]
  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).

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