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Applied Optics

Applied Optics


  • Vol. 32, Iss. 4 — Feb. 1, 1993
  • pp: 504–516

Scaling relationships for theories of anisotropic random walks applied to tissue optics

A. H. Gandjbakhche, R. Nossal, and R. F. Bonner  »View Author Affiliations

Applied Optics, Vol. 32, Issue 4, pp. 504-516 (1993)

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Monte Carlo simulations are used to discern scaling relationships for photon migration occurring within homogeneous, anisotropic scattering media of semi-infinite extent. Special attention is given to events associated with short path lengths. Empirical scaling relationships for path lengths and surface intensities are shown to agree with a consistency equation derived in an earlier study of anisotropic random walks. They are augmented here by a procedure that accounts for concomitant scaling of optical absorption coefficients. Results then are used to transform expressions that were obtained previously by analytical random-walk theory developed for an isotropic scattering model of photon migration. Quantities that are studied include the diffuse surface reflectance, the depth distribution of the fluence, and the time-resolved intensity of backreflected photons.

© 1993 Optical Society of America

Original Manuscript: December 17, 1991
Published: February 1, 1993

A. H. Gandjbakhche, R. Nossal, and R. F. Bonner, "Scaling relationships for theories of anisotropic random walks applied to tissue optics," Appl. Opt. 32, 504-516 (1993)

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  1. R. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model for photon migration in turbid biological tissue,” J. Opt. Soc. Am. A 4, 423–432 (1987). [CrossRef] [PubMed]
  2. R. Nossal, J. Kiefer, G. H. Weiss, R. Bonner, H. Taitelbaum, S. Havlin, “Photon migration in layered media,” Appl. Opt. 27, 3382–3391 (1988). [CrossRef] [PubMed]
  3. R. Nossal, R. F. Bonner, G. H. Weiss, “The influence of path length on remote optical sensing of properties of biological tissue,” Appl. Opt. 28, 2238–2244 (1989). [CrossRef] [PubMed]
  4. G. H. Weiss, R. Nossal, R. F. Bonner, “Statistics of penetration depth of photons re-emitted from irradiated tissue,” J. Mod. Opt. 36, 349–359 (1989). [CrossRef]
  5. R. Nossal, R. F. Bonner, “Differential time-resolved detection of absorbance changes in composite structures,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Soc. Photo-Opt. Instrum. Eng.1431, 21–28 (1991).
  6. M. Stern, “In vivo evaluation of microcirculation by coherent light scattering,” Nature (London) 254, 56–58 (1975). [CrossRef]
  7. R. Bonner, R. Nossal, “Model for laser Doppler measurements of blood flow in tissue,” Appl. Opt. 20, 2097–2107 (1981); R. Bonner, R. Nossal, “Principles of laser-Doppler flowmetry,” in Laser-Doppler Blood Flowmetry, A. P. Shepherd, P. Å. Öberg, ed. (Kluwer, Boston, Mass., 1990), Chap. 2, p. 17. [CrossRef] [PubMed]
  8. 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]
  9. B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Yound, 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]
  10. J. M. Schmitt, G. X. Zhou, E. C. Walker, R. T. Wall, “A multilayer model of photon diffusion in skin,” J. Opt. Soc. Am. A 14, 2141–2153 (1990). [CrossRef]
  11. C. C. Johnson, “Optical diffusion in blood,” IEEE Trans. Biomed. Eng. BME-17, 129–133 (1970). [CrossRef]
  12. A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061 (1977). [CrossRef]
  13. M. 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]
  14. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988). [CrossRef] [PubMed]
  15. D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990). [CrossRef]
  16. R. Nossal, J. M. Schmitt, “Measuring photon pathlengths by quasielastic light scattering in a multiply scattering medium,” in Photon Correlation Spectroscopy: Multicomponent System, K. S. Schmitt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1430, 37–47 (1991).
  17. A. H. Gandjbakhche, R. F. Bonner, R. Nossal, “Scaling relationships for anisotropic random walks,” J. Stat. Phys. 69, 35–53 (1992). [CrossRef]
  18. K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990). [CrossRef] [PubMed]
  19. K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967), Chap. 8, p. 194.
  20. J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976), Chap. 4, p. 217.
  21. L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]
  22. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980), Vol. 2, Chap. 14, p. 477.
  23. D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for the interaction parameters in radiation transport,” Appl. Opt. 28, 5243–5249 (1989). [CrossRef] [PubMed]
  24. G. Yoon, S. A. Prahl, A. J. Welch, “Accuracies of the diffusion approximation and its similarity relations for laser irradiated biological media,” Appl. Opt. 28, 2250–2261 (1989). [CrossRef] [PubMed]
  25. M. P. Arnfield, J. Tulip, M. S. McPhee, “Optical propagation in tissue with anisotropic scattering,” IEEE Trans. Biomed. Eng. 35, 372–380 (1988). [CrossRef] [PubMed]
  26. G. E. Roberts, H. Kaufman, Table of Laplace Transforms (Saunders, Philadelphia, Pa., 1966), p. 22.

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