Analytical approximate solutions of the time-domain diffusion equation in layered slabs

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 19, Issue 1, 2002, Pages 71-80

  Martelli, Fabrizio ^a,b   Sassaroli, Angelo ^b   Yamada, Yukio ^b,c   Zaccanti, Giovanni ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

^b NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

^c UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; MONTE CARLO METHODS; PHOTONS; REFRACTIVE INDEX;

PHOTON MIGRATION;

DIFFUSION;

ARTICLE; DIAGNOSTIC IMAGING; DIFFUSION; PHOTON; THEORETICAL MODEL; TIME;

DIAGNOSTIC IMAGING; DIFFUSION; MODELS, THEORETICAL; PHOTONS; TIME FACTORS;

EID: 0036370225     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.19.000071     Document Type: Article

References (33)

1. M. Patterson, B. Chance, and B. C. Wilson, "Time-resolved reflectance and transmittance for the non-invasive determination of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
2. S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
3. D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory," Appl. Opt. 36, 4587-4599 (1997).
4. M. Niwayama, L. Lin, J. Shao, T. Shiga, N. Kudo, and K. Yamamoto, "Quantitative measurement of muscle oxygenation by NIRS: Analysis of the influence of a subcutaneous fat layer and skin," in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, and B. J. Tromberg, eds., Proc. SPIE 3597, 291-299 (1999).
5. A. Kienle and T. Glanzmann, "In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model, " Phys. Med. Biol. 44, 2689-2702 (1999).
6. S. Takatani and M. D. Graham, "Theoretical analysis of diffuse reflectance from a two-layer tissue model," IEEE Trans. Biomed. Eng. BME-26, 656-664 (1979).
7. M. Keijer, W. M. Star, and P. R. M. Storchi, "Optical diffusion in layered media," Appl. Opt. 27, 1820-1824 (1988).
8. R. Nossal, J. Kiefer, G. H. Weiss, R. Bonner, H. Taitelbaum, and S. Havlin, "Photon migration in layer media," Appl. Opt. 27, 3382-3391 (1988).
9. H. Taitelbaum, S. Havlin, and G. H. Weiss, "Approximate theory of photon migration in a two-layer medium," Appl. Opt. 28, 2245-2249 (1989).
10. J. M. Schmitt, G. X. Zhou, E. C. Walker, and R. T. Wall, "Multilayer model of photon diffusion in skin," J. Opt. Soc. Am. A 7, 2141-2153 (1990).
11. I. Dayan, S. Havlin, and G. H. Weiss, "Photon migration in a two-layer turbid medium: A diffusion analysis," J. Mod. Opt. 39, 1567-1582 (1992).
12. A. H. Hielscher, H. Liu, B. Chance, F. K. Tittel, and S. L. Jacques, "Time resolved photon emission from layered turbid media," Appl. Opt. 35, 719-728 (1996).
13. E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and 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).
14. A. Kienle, M. S. Patterson, N. Dognitz, R. Bays, G. Wagnieres, and H. van de Bergh, "Noninvasive determination of the optical properties of two-layered turbid medium," Appl. Opt. 37, 779-791 (1998).
15. A. Kienle, T. Glanzmann, G. Wagnieres, and H. van de Bergh, "Investigation of two-layered media with time-resolved reflectance," Appl. Opt. 37, 6852-6862 (1998).
16. G. Alexandrakis, T. J. Farrel, and M. Patterson, "Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium," Appl. Opt. 37, 7401-7409 (1998).
17. T. J. Farrell, M. S. Patterson, and M. Essenpreis, "Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry,"Appl. Opt. 37, 1958-1972 (1998).
18. M. A. Franceschini, S. Fantini, L. A. Paunescu, J. S. Maier, and E. Gratton, "Influence of a superficial layer in the quantitative spectroscopic study of strongly scattering media," Appl. Opt. 37, 7447-7458 (1998).
19. J.-M. Tualle, J. Prat, E. Tinet, and S. Avrillier, "Real-space Green's function calculation for the solution of the diffusion equation in stratified turbid media," J. Opt. Soc. Am. A 17, 2046-2055 (2000).
20. K. Furutsu, "Diffusion equation derived from space-time transport equation," J. Opt. Soc. Am. 70, 360-366 (1980).
21. K. Furutsu and Y. Yamada, "Diffusion approximation for a dissipative random medium and the applications," Phys. Rev. E 50, 3634-3640 (1994).
22. F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, "Refractive index of some mammalian tissues using a fiber optic cladding method," Appl. Opt. 28, 2297-2303 (1989).
23. R. Aronson, "Boundary conditions for diffusion of light," J. Opt. Soc. Am. A 12, 2532-2539 (1995).
24. R. C. Haskell, L. O. Svaasand, T. T. Say, T. C. Feng, M. S. McAdams, and B. J. Tromberg, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).
25. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part I (McGraw-Hill, New York, 1953), Chap. 7.
26. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford U. Press, Oxford, UK, 1959), Chap. XIV.
27. G. F. Roach, Green's Functions (Van Nostrand Reinhold, London, 1970), Chap. 9.
28. G. Zaccanti, L. Alianelli, C. Blumetti, and S. Carraresi, "Method for measuring the mean time of flight spent by photons inside a volume element of a highly diffusing medium," Opt. Lett. 24, 1290-1292 (1999).
29. F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, "Method for measuring the diffusion coefficient of homogeneous and layered media," Opt. Lett. 25, 1508-1510 (2000).
30. G. Zaccanti, "Monte Carlo study of light propagation in optically thick media: point source case," Appl. Opt. 30, 2031-2041 (1991).
31. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1988).
32. F. Martelli, A. Sassaroli, and Y. Yamada, "Analytical solution of the time-dependent photon diffusion equation for a layered medium," in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, and B. J. Tromberg, eds., Proc. SPIE 3597, 79-89 (1999).
33. J. Ripoll and M. Nieto-Vesperinas, "Index mismatch for diffuse photon density waves at both flat and rough diffuse-diffuse interfaces," J. Opt. Soc. Am. A 16, 1947-1957 (1999).