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Finite element approach to photon propagation modeling in semi-infinite homogeneous and multilayered tissue structures

Published online by Cambridge University Press:  08 February 2006

X. Deulin  and
J. P. L'Huillier
X. Deulin
Affiliation:
Laboratoire Procédés-Matériaux-Instrumentation, LPMI, Équipe Modélisation-Instrumentation, CER ENSAM, 2 Bd du Ronceray, BP 3525, 49035 Angers, France
J. P. L'Huillier*
Affiliation:
Laboratoire Procédés-Matériaux-Instrumentation, LPMI, Équipe Modélisation-Instrumentation, CER ENSAM, 2 Bd du Ronceray, BP 3525, 49035 Angers, France
*
jean-pierre.lhuillier@angers.ensam.fr
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Abstract

A computerized model of steady–state photon diffusion within turbid media such as biological tissues, solved by means of the Finite Element Method (FEM) is presented in this paper. Assuming that the different media are illuminated by a flat collimated laser beam source, we develop the basic theory including the suitable boundary conditions along the meshed domain. Model simulations depict firstly photon-flux density patterns in the $r-z$ plane associated with axis fluence rate profiles, plotted as functions of media properties and beam sizes. A second objective was to display both the rate of re-emitted optical power integrated by an optical fibre radially displaced away from the source and the power integrated by an optical fibre axially moved inside the tissue. Simulation studies are further extended to multilayered media such as skin and aorta, in order to describe the light propagation through these tissue structures more realistically.

Keywords

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 33 , Issue 2 , February 2006 , pp. 133 - 146
Copyright
© EDP Sciences, 2006

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References

A.J Welch, M.J.C. van Gemert, Optical-Thermal response of Laser-Irradiated Tissue (Plenum Press, New-York, 1995)
Weersink, R.A., Hayward, J., Diamond, K., Patterson, M.S., Photochem. Photobiol. 66, 326 (1997) CrossRef
Hull, E.L., Nichols, M.G., Foster, T.H., Phys. Med. Biol. 43, 3381 (1998) CrossRef
Le Pommellec, J.Y., L'Huillier, J.P., Proc. SPIE 4161, 202 (2000) CrossRef
Apiou-Sbirlea, G., L'Huillier, J.P., Proc. SPIE 3192, 219 (1997) CrossRef
Walsh, J.T., Flotte, T.J., Anderson, R.R., Deutsch, T.F., Lasers Surg. Med. 8, 108 (1988) CrossRef
L'Huillier, J.P., Proc. SPIE 3195, 151 (1997) CrossRef
A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, New-York, 1978), Vol. 1
Fante, R.L., J. Opt. Soc. Am. 71, 460 (1981) CrossRef
E.D Cashwell, C.J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon Press, New-York, 1959)
Witt, A.N., Astrophys. J. (Suppl. Ser.) 35, 1 (1977) CrossRef
Prahl, S.A., Keijzer, M., Jacques, S.L., Welch, A.J., Proc. SPIE 5, 102 (1989)
Wang, L.H., Jacques, S.L., Zheng, L.Q., Comput. Meth. Prog. Bio. 47, 131 (1995) CrossRef
S. Chandrasekhar, Radiative transfer (Dover, New-York, 1960)
B. Davisson, Neutron Transport Theory (Clarendon Press, Oxford, 1957)
K.M. Case, P.F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, MA, 1967)
Jin, Z.H., Stammes, K., Appl. Optics 33, 431 (1994) CrossRef
Chick, K.M., Pollack, J.B., Cassen, P., Astrophys. J. 461, 956 (1996) CrossRef
Rhoades, W.A., Childs, R.L., Nucl. Sci. Eng. 107, 397 (1991) CrossRef
Matsumoto, T., Aoki, M., Aizawa, O., Phys. Med. Biol. 36, 329 (1991) CrossRef
Rastegar, S., Motamedi, M., Welch, A.J., Hayes, L.J., IEEE Trans. Biomed. Eng. 36, 1180 (1989) CrossRef
Hielscher, A.H., Alcouffe, R.E., Barbour, R.L., Phys. Med. Biol. 43, 1285 (1998) CrossRef
Boulnois, J.L., Lasers Med. Sci. 1, 47 (1986) CrossRef
Star, W.M., Marijnissen, J.P.A., van Gemert, M.J.C., Phys. Med. Biol. 33, 437 (1988) CrossRef
J.J. Duderstadt, L.J. Hamilton, Nuclear Reactor Analysis (Wiley, New-York, 1976)
Hemenger, R.P., Appl. Optics 16, 2007 (1977) CrossRef
Takatani, S., Graham, M.D., IEEE Trans. Biomed. Eng. 26, 656 (1979) CrossRef
Jacques, S.L., Prahl, S.A., Lasers Surg. Med. 7, 494 (1987) CrossRef
Verdaasdonk, R.M., Borst, C., Appl. Optics 30, 2159 (1991) CrossRef
Farrell, T.J., Patterson, M.S., Wilson, B.C., Med. Phys. 19, 879 (1992) CrossRef
Allen, V., McKenzie, A.L., Phys. Med. Biol. 36, 1621 (1991) CrossRef
Kienle, A., Patterson, M.S., J. Opt. Soc. Am. A 14, 246 (1997) CrossRef
Patterson, M.S., Chance, B., Wilson, B.C., Appl. Optics 28, 2331 (1989) CrossRef
Patterson, M.S., Moulton, J.D., Wilson, B.C., Berndt, K.W., Lakowicz, J.R., Appl. Optics 30, 4474 (1991) CrossRef
Reynolds, L., Johnson, C., Ishimaru, A., Appl. Optics 15, 2059 (1976) CrossRef
Groenhuis, R.A.J., Ferwerda, H.A., Ten Bosch, J.J., Appl. Optics 22, 2456 (1983) CrossRef
Schmitt, J.M., Zhou, G.X., Walker, E.C., J. Opt. Soc. Am. A 7, 2141 (1990) CrossRef
S.A. Prahl, in Optical-Thermal response of Laser-Irradiated Tissue, edited by A.J. Welch, M.J.C. van Gemert (Plenum Press, New-York, 1995)
Keijzer, M., Jacques, S.L., Prahl, S.A., Welch, A.J., Lasers Surg. Med. 9, 148 (1989) CrossRef
Paulsen, K.D., Jiang, H., Med. Phys. 22, 691 (1995) CrossRef
Arridge, S.R., Inverse Problems 15, R41 (1999) CrossRef
M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964)
E. Hecht, A. Zajac, Optics, 2nd edn. (Addison-Wesley, Reading, MA, 1990)
D.S. Burnett, Finite Element Analysis. From concepts to applications (Addison-Wesley Ed., 1987)
FlexPDE, A flexible Solution System for Partial Differential Equations, PDE Inc.
Cheong, W.F., Prahl, S.A., Welch, A.J., IEEE J. Quantum Elect. 26, 2166 (1990) CrossRef
Bolin, F.P., Preuss, L.E., Taylor, R.C., Ference, R.J., Appl. Optics 28, 2297 (1989) CrossRef
Star, W., Proc. SPIE IS5, 146 (1989)
Wang, L.H., Jacques, S.L., Zheng, L., Comp. Meth. Prog. Bio. 47, 131 (1995) CrossRef
Tuchin, V.V., Utz, S.R., Yaroslavsky, I.V., Opt. Eng. 33, 3178 (1994) CrossRef
Kienle, A., Lilge, L., Patterson, M.S., Hibst, R., Steiner R., B.C. Wilson, Appl. Optics 35, 2304 (1996) CrossRef
M.S. Patterson, E. Schwartz, B.C. Wilson, Proc. SPIE 1065, 115 1989
J.P.A. Marijnissen, W.M. Star, in Porphyrin Localization and treatement of tumors, edited by D.R. Doiron, C.J. Gomert (Liss, New-York, 1984), pp. 133–148
Wilson, B.C., Patterson, M.S., Burns, D.M., Lasers Med. Sci. 1, 235 (1986) CrossRef
Choukeife, J.E., L'Huillier, J.P., Lasers Med. Sci. 14, 286 (1999) CrossRef
M.J.C. Van Gemert, A.J. Welch, J.W. Pickering, T.O. Tan, in Optical-Thermal response of Laser-Irradiated tissue, edited by A.J. Welch, M.J.C. van Gemert (Plenum Press, New York, 1995)
Van Gemert, M.J.C., Jacques, S.L., Sterenborg, H.J.C., Star, W.M., IEEE Trans. Biomed. Eng. 36, 1146 (1989) CrossRef
Keijzer, M., Richards-Kortrum, R.R., Jacques, S.L., Feld, M., Appl. Optics 28, 4286 (1989) CrossRef