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Tissue optics for a slab geometry in the diffusion approximation

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Abstract

This paper solves the radiative transport equation in a slab using the diffusion approximation in one-dimension. The absorption and scattering coefficients as well as the first moment of the phase function are shown to follow directly from measurement of the diffuse transmission and the collimated transmission, and the diffuse reflection.

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References

  1. Chandrasekhar S.Radiative transfer. New York: Dover Publications, 1960

    Google Scholar 

  2. Ishimaru A.Wave propagation and scattering in random media. New York: Academic Press, 1978

    Google Scholar 

  3. Wilson BC, Patterson MS. The physics of photodynamic therapy.Phys Med Biol 1986,31:327–60

    Article  PubMed  CAS  Google Scholar 

  4. Kaminow IP, Wiesenfeld JM, Choy DSJ. Argon laser disintegration of thrombus and atherosclerotic plaque.Appl Optics 1984,23:1301–2

    CAS  Google Scholar 

  5. Eichler J, Knopf J, Lenz M. Measurements on the depth of penetration of light (0.35–1.0 μ) in tissue.Rad Environm Biophys 1977,14:239–42

    Article  CAS  Google Scholar 

  6. Kubelka P. New contributions to the optics of intensely light scattering materials. Part I.J Opt Soc Am 1948,38:448–57

    PubMed  CAS  Google Scholar 

  7. Kottler F. Turbid media with plane-parallel surfaces.J Opt Soc Am 1960,50:483–90

    Google Scholar 

  8. Wan S, Anderson RR, Parrish JA. Analytical modeling for the optical properties of the skin with in vitro and in vivo applications.Photochem Photobiol 1981,34:493–9

    PubMed  CAS  Google Scholar 

  9. Anderson RR, Parrish JA. The optics of human skin.J Invest Dermatol 1981,77:13–9

    Article  PubMed  CAS  Google Scholar 

  10. Ertefai S, Profio AE. Spectral transmittance and contrast in breast diaphanography.Med Phys 1985,12:393–400

    Article  PubMed  CAS  Google Scholar 

  11. Van Gemert MJC, Verdaasdonk R, Stassen ES et al. Optical properties of human blood vessel wall and plaque.Lasers Surg Med 1985,5:235–7

    Article  PubMed  Google Scholar 

  12. Prince MR, Deutsch FT, Margolis R et al. Preferential light absorption in atheromas: Implication for laser angioplasty.J Clin Invest 1986,78:295–302

    Article  PubMed  CAS  Google Scholar 

  13. Van Gemert MJC, Berenbaum MC, Gijbers GHM. Wavelength and light-dose dependence in tumour phototherapy with haematoporphyrin-derivative.Br J Cancer 1985,52:43–9

    PubMed  Google Scholar 

  14. Atkins JT. Absoption and scattering of light in turbid media, Ph.D. Dissertation, University of Delaware, June 1965, Dissertation abstract: B27, No. 6, 1944, 1966

  15. Reichman J. Determination of absorption and scattering coefficients for non-homogeneous media. 1: Theory.Appl Optics 1973,12:1811–15

    CAS  Google Scholar 

  16. Diffey BL. A mathematical model for ultraviolet optics of skin.Phys Med Biol 1983,28:647–57

    Article  PubMed  CAS  Google Scholar 

  17. Everett MA, Yeargers E, Sayre RM, Olsen RL. Penetration of epidermis by ultraviolet rays.Photochem Photobiol 1966,5:533–42

    Article  PubMed  CAS  Google Scholar 

  18. Reynolds L, Johnson CC, Ishimaru A. Diffuse reflectance from a finite blood medium: application to the modeling of fiberoptic catheters.Appl Optics 1978,15:2059–67

    Google Scholar 

  19. Groenhuis RAJ, Ferwerda HA, Ten Bosch JJ. Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory.Appl Optics 1983,22:2456–67

    CAS  Google Scholar 

  20. Svaasand LO, Ellingsen R. Optical properties of human brain.Photochem Photobiol 1983,38:293–9

    PubMed  CAS  Google Scholar 

  21. Muller PJ, Wilson BC. An update on the penetration depth of 630 nm light in normal and maligannt human brain tissue in vivo.Phys Med Biol 1986,31:1295–7

    Article  PubMed  CAS  Google Scholar 

  22. Marijnissen JPA, Star WM. Phanton measurements for light dosimetry using isotropic and small aperture detectors. In: Doiron DR, Gomer CJ (eds)Porphyrin localization and treatment of tumors. New York: Alan Liss, 1984:133–48

    Google Scholar 

  23. Marijnissen JPA, Star WM, van Delft JL, Franken NAP. Light intensity measurements in optical phantoms and in vivo during HPD-photoradiation treatment using a miniature light detector with isotropic response. In: Jori G, Perria C (eds)Photodynamic therapy of tumors and other diseases. Padova: Libreria Progetto, 1985:387–90

    Google Scholar 

  24. Gijsbers GHM, Breederveld D, van Gemert MJC et al. In vivo fluorescence excitation and emission spectra of hematoporphyrin derivative (HpD).Lasers Life Sci 1986,1:29–48

    Google Scholar 

  25. Brinkworth BJ. Interpretation of the Kubelka-Munk coefficients in reflection theory.Appl Optics 1972,11:1434–5

    Google Scholar 

  26. Klier K. Absorption and scattering in plane parallel turbid media.J Opt Soc Am 1972,62:882–5

    Article  Google Scholar 

  27. Van Gemert MJC, Star WM. Relations between the Kubelka-Munk and the transport equation models for anisotropic scattering.Lasers Life Sci. 1987 (in press)

  28. Bell GI, Glasstone S.Nuclear Reactor Theory. Van Nostrand Reinhold, 1970, Chapters 1–3

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Van Gemert, M.J.C., Welch, A.J., Star, W.M. et al. Tissue optics for a slab geometry in the diffusion approximation. Laser Med Sci 2, 295–302 (1987). https://doi.org/10.1007/BF02594174

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  • DOI: https://doi.org/10.1007/BF02594174

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