Geodesic
Optical radiation propagation modeling in a phantom of biological tissue by the supercomputer MBC1000/M
Matematičeskoe modelirovanie, Tome 18 (2006) no. 1, pp. 29-42 
L. P. Bass; O. V. Nikolaeva; V. S. Kuznetsov; A. V. Bykov; A. V. Priezzhev; A. A. Dergachev. Optical radiation propagation modeling in a phantom of biological tissue by the supercomputer MBC1000/M. Matematičeskoe modelirovanie, Tome 18 (2006) no. 1, pp. 29-42. http://geodesic.mathdoc.fr/item/MM_2006_18_1_a3/
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     author = {L. P. Bass and O. V. Nikolaeva and V. S. Kuznetsov and A. V. Bykov and A. V. Priezzhev and A. A. Dergachev},
     title = {Optical radiation propagation modeling in a phantom of biological tissue by the supercomputer {MBC1000/M}},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {29--42},
     year = {2006},
     volume = {18},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_1_a3/}
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%A A. A. Dergachev
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Voir la notice de l'article provenant de la source Math-Net.Ru

The direct problem of biological tissue sounding by a laser source of small aperture is considered. Radiation propagation through tissue is modeled by the transport equation. The grid algorithm is presented to solve it. The technique relies on analytical representation of unscattered light intensity and hemi-analytical method of once-scattered light intensity calculation. Numerical results are presented. They show advantages of considered algorithm of radiative fields calculation in comparison with the statistical modeling method and simplified approach, which leans upon the diffusion equation.

[1] Zimnyakov D. A., Tuchin V. V., “Opticheskaya tomografiya tkanei”, Kvantovaya elektronika, 32:10 (2002), 849–867

[2] Priezzhev A. V., Tuchin V. V., Shubochkin L. P., Lazernaya diagnostika v biologii i meditsine, Nauka, M., 1989

[3] Tuchin V. V., Lazery i volokonnaya optika v biomeditsinskikh issledovaniyakh, Izd-vo Saratovskogo un-ta, Saratov, 1998

[4] Yodh A., Trombrg B., Sevick-Muraca E., Pine D., “Special Section: Diffusing photons in turbid media”, J. Opt. Soc. Am. A, 14 (1997), 136–342 | DOI

[5] Isimaru A., Rasprostranenie i rasseyanie voln v sluchaino-neodnorodnykh sredakh, Mir, M., 1981

[6] Kandidov V. P., “Metod Monte-Karlo v nelineinoi statisticheskoi optike”, UFN, 166:12 (1996), 1309–1338 | DOI

[7] Bass L. P., Voloschenko A. M., Germogenova T. A., Metody diskretnykh ordinat v zadachakh o perenose izlucheniya, IPMatem. AN SSSR, M., 1986

[8] Bass L. P., Germogenova T. A., Kuznetsov V. S., Nikolaeva O. V., “Raduga-5.1 i Raduga-5.1(P)–programmy dlya resheniya statsionarnogo uravneniya perenosa v 2-kh i 3-kh mernykh geometriyakh na odno- i mnogoprotsessornykh EVM”, Sbornik dokladov seminara “Algoritmy i programmy dlya neitronno-fizicheskikh raschetov yadernykh reaktorov (Neitronika-2001)” (30 oktyabrya–2 noyabrya), Obninsk, 2001

[9] Klose A. D., et al., “Optical tomography using the time-independent equation of radiative transfer - Part I: forward model”, JQSRT, 72 (2002), 691–713

[10] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Gos. izd-vo fiz.-mat. lit., M., 1962, 1100 pp. | MR

[11] Habetler G, Matkowsky B., “Uniform Asymptotic Expansion in Transport Theory with Small Mean Free Paths and the Diffusion Approximation”, J. Math. Phys., 16 (1975), 846–854 | DOI | MR | Zbl

[12] Germogenova T. A., “Regulyarnye komponenty asimptoticheskikh priblizhenii k resheniyam uravneniya perenosa v opticheski plotnykh sredakh”, ZhVMiMF, 37 (1997), 464–482 | MR | Zbl

[13] Germogenova T. A., Zadachi s sosredotochennymi istochnikami v statsionarnoi teorii perenosa, preprint No 23, IPM im. M. V. Keldysha, M., 1971 | MR

[14] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1967 | MR

[15] Landesman M., Morel J. E., “Angular Fokker–Planck Decomposition and Representation Techniques”, Nucl. Sci. Eng., 103 (1989), 1–11

[16] Fawzi Y. S., Abo-Bakr M. Y., El-Batanony M. H. and Kadah Y. M., “Determination of the optical properties of a two-layer tissue model by detecting photons migrating at progressively increasing depths”, Appl. Opt., 42:38 (2003), 6398–6411 | DOI