Abstract

The scattering of He–Ne laser light by an average-sized human red blood cell (RBC) is investigated numerically. The RBC is modeled as an axisymmetric, low-contrast dielectric, biconcave disk. The interaction problem is treated numerically by means of a boundary-element methodology. The differential scattering cross sections (DSCS’s) corresponding to various cell orientations are calculated. The numerical results obtained for the exact RBC geometry are compared with those corresponding to a scattering problem in which the cell is assumed to be either a volume-equivalent sphere or an oblate spheroid. A parametric study demonstrating the dependence of the DSCS on the wavelength of the incident wave and the cell’s refractive index is presented.

© 1999 Optical Society of America

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References

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  1. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  2. J. Plasek, T. Marik, “Determination of undeformable erythrocytes in blood samples using light scattering,” Appl. Opt. 21, 4335–4338 (1982).
    [CrossRef] [PubMed]
  3. J. M. Steinke, A. P. Shepherd, “Comparison of Mie theory and the light scattering of red blood cells,” Appl. Opt. 27, 4027–4033 (1988).
    [CrossRef] [PubMed]
  4. M. Hammer, D. Schweitzer, B. Michel, E. Thamm, A. Kolb, “Single scattering by red blood cells,” Appl. Opt. 37, 7410–7418 (1998).
    [CrossRef]
  5. V. Twersky, “Absorption and multiple scattering by biological suspensions,” J. Opt. Soc. Am. 60, 1084–1093 (1970).
    [CrossRef] [PubMed]
  6. V. S. Lee, L. Tarassenko, “Absorption and multiple scattering by suspensions of aligned red blood cells,” J. Opt. Soc. Am. A 8, 1135–1141 (1991).
    [CrossRef] [PubMed]
  7. J. Kim, J. C. Lin, “Successive order scattering transport approximation for laser light propagation in whole blood medium,” IEEE Trans. Biomed. Eng. 45, 505–510 (1998).
    [CrossRef] [PubMed]
  8. A. H. Gandjbakhche, P. Mills, P. Snabre, “Light-scattering technique for the study of orientation and deformation of red blood cells in a concentrated suspension,” Appl. Opt. 33, 1070–1078 (1994).
    [CrossRef] [PubMed]
  9. G. N. Constantinides, D. Gintides, S. E. Kattis, K. Kiriaki, C. A. Paraskeva, A. C. Payatakes, D. Polyzos, S. V. Tsinopoulos, S. N. Yannopoulos, “Computation of light scattering by axisymmetric nonspherical particles and comparison with experimental results,” Appl. Opt. 37, 7310–7319 (1998).
    [CrossRef]
  10. Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues (Springer-Verlag, New York, 1981).
    [CrossRef]
  11. G. J. Streekstra, A. G. Hoekstra, E. J. Nijhof, R. M. Heethaar, “Light scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction,” Appl. Opt. 32, 2266–2272 (1993).
    [CrossRef] [PubMed]
  12. H. C. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  13. M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
    [CrossRef]
  14. A. M. K. Nilsson, P. Alsholm, A. Karlsson, S. Andersson-Engels, “T-matrix computations of light scattering by red blood cells,” Appl. Opt. 37, 2735–2748 (1998).
    [CrossRef]
  15. D. H. Tycko, M. H. Metz, E. A. Epstein, A. Grinbaum, “Flow-cytometric light scattering measurements of red blood cell volume and hemoglobin concentration,” Appl. Opt. 24, 1355–1365 (1985).
    [CrossRef]
  16. G. J. Streekstra, A. G. Hoekstra, R. M. Heethaar, “Anomalous diffraction by arbitrarily oriented ellipsoids: applications in ektacytometry,” Appl. Opt. 33, 7288–7296 (1994).
    [CrossRef] [PubMed]
  17. P. Mazeron, S. Muller, “Light scattering by ellipsoids in a physical optics approximation,” Appl. Opt. 35, 3726–3735 (1996).
    [CrossRef] [PubMed]
  18. P. Mazeron, S. Muller, H. El. Azouri, “On intensity reinforcement in small-angle light scattering patterns of erythrocytes under shear,” Eur. Biophys. J. 26, 247–252 (1997).
    [CrossRef]
  19. P. Mazeron, S. Muller, H. El. Azouri, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34, 99–110 (1997).
    [CrossRef] [PubMed]
  20. G. S. Stamatakos, D. Yova, N. K. Uzunoglu, “Integral equation model of light scattering by an oriented monodisperse system of triaxial dielectric ellipsoids: application in ektacytometry,” Appl. Opt. 36, 6503–6512 (1997).
    [CrossRef]
  21. J. T. Soini, A. V. Chernyshev, A. N. Shvalov, V. P. Maltsev, “Measurement of scattering patterns from individual nonspherical particles using scanning flow cytometer,” in Light Scattering by Nonspherical Particles, K. Lumme, J. W. Hovenier, K. Muinonen, J. Rahola, H. Laitinen, eds. (Observatory, University of Helsinki, Helsinki, Finland, 1997).
  22. J. D. Klett, R. A. Sutherland, “Approximate methods for modeling the scattering properties of nonspherical particles: evaluation of the Wentzel–Kramers–Brillouin method,” Appl. Opt. 31, 373–386 (1992).
    [CrossRef] [PubMed]
  23. A. N. Shvalov, J. T. Soini, A. V. Chernyshev, P. A. Tarasov, E. Soini, V. P. Maltsev, “Light-scattering properties of individual erythrocytes,” Appl. Opt. 38, 230–235 (1999).
    [CrossRef]
  24. S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “3D boundary element method in electromagnetic wave scattering by small biological bodies,” in Third Hellenic-European Conference on Mathematics and Informatics: HERMIS ’96, E. A. Lipitakes, ed. (LEA, Athens, Greece, 1996).
  25. P. Mazeron, S. Muller, “Dielectric or absorbing particles: EM surface fields and scattering,” J. Opt. 29, 68–77 (1998).
    [CrossRef]
  26. S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies,” Comput. Mech. 21, 306–315 (1998).
    [CrossRef]
  27. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  28. S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “An advanced BE/FFT methodology for solving electromagnetic wave scattering problems with axisymmetric dielectric particles,” Eng. Anal. Boundary Elements 23, 155–165 (1999).
    [CrossRef]
  29. D. S. Jones, The Theory of Electromagnetism (Pergamon, London, 1964).
  30. IMSL Math/Library User’s Manual, Version 3.0 (Visual Numerics, Inc., Houston, Tex., 1994).
  31. W. C. O. Tsang, “The size and shape of human red blood cells,” M.S. thesis (University of California at San Diego, San Diego, Calif., 1975).

1999 (2)

A. N. Shvalov, J. T. Soini, A. V. Chernyshev, P. A. Tarasov, E. Soini, V. P. Maltsev, “Light-scattering properties of individual erythrocytes,” Appl. Opt. 38, 230–235 (1999).
[CrossRef]

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “An advanced BE/FFT methodology for solving electromagnetic wave scattering problems with axisymmetric dielectric particles,” Eng. Anal. Boundary Elements 23, 155–165 (1999).
[CrossRef]

1998 (6)

P. Mazeron, S. Muller, “Dielectric or absorbing particles: EM surface fields and scattering,” J. Opt. 29, 68–77 (1998).
[CrossRef]

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies,” Comput. Mech. 21, 306–315 (1998).
[CrossRef]

M. Hammer, D. Schweitzer, B. Michel, E. Thamm, A. Kolb, “Single scattering by red blood cells,” Appl. Opt. 37, 7410–7418 (1998).
[CrossRef]

J. Kim, J. C. Lin, “Successive order scattering transport approximation for laser light propagation in whole blood medium,” IEEE Trans. Biomed. Eng. 45, 505–510 (1998).
[CrossRef] [PubMed]

G. N. Constantinides, D. Gintides, S. E. Kattis, K. Kiriaki, C. A. Paraskeva, A. C. Payatakes, D. Polyzos, S. V. Tsinopoulos, S. N. Yannopoulos, “Computation of light scattering by axisymmetric nonspherical particles and comparison with experimental results,” Appl. Opt. 37, 7310–7319 (1998).
[CrossRef]

A. M. K. Nilsson, P. Alsholm, A. Karlsson, S. Andersson-Engels, “T-matrix computations of light scattering by red blood cells,” Appl. Opt. 37, 2735–2748 (1998).
[CrossRef]

1997 (3)

P. Mazeron, S. Muller, H. El. Azouri, “On intensity reinforcement in small-angle light scattering patterns of erythrocytes under shear,” Eur. Biophys. J. 26, 247–252 (1997).
[CrossRef]

P. Mazeron, S. Muller, H. El. Azouri, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34, 99–110 (1997).
[CrossRef] [PubMed]

G. S. Stamatakos, D. Yova, N. K. Uzunoglu, “Integral equation model of light scattering by an oriented monodisperse system of triaxial dielectric ellipsoids: application in ektacytometry,” Appl. Opt. 36, 6503–6512 (1997).
[CrossRef]

1996 (1)

1994 (3)

1993 (1)

1992 (1)

1991 (1)

1988 (1)

1985 (1)

1982 (1)

1970 (1)

Alsholm, P.

Andersson-Engels, S.

Azouri, H. El.

P. Mazeron, S. Muller, H. El. Azouri, “On intensity reinforcement in small-angle light scattering patterns of erythrocytes under shear,” Eur. Biophys. J. 26, 247–252 (1997).
[CrossRef]

P. Mazeron, S. Muller, H. El. Azouri, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34, 99–110 (1997).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Chernyshev, A. V.

A. N. Shvalov, J. T. Soini, A. V. Chernyshev, P. A. Tarasov, E. Soini, V. P. Maltsev, “Light-scattering properties of individual erythrocytes,” Appl. Opt. 38, 230–235 (1999).
[CrossRef]

J. T. Soini, A. V. Chernyshev, A. N. Shvalov, V. P. Maltsev, “Measurement of scattering patterns from individual nonspherical particles using scanning flow cytometer,” in Light Scattering by Nonspherical Particles, K. Lumme, J. W. Hovenier, K. Muinonen, J. Rahola, H. Laitinen, eds. (Observatory, University of Helsinki, Helsinki, Finland, 1997).

Constantinides, G. N.

Epstein, E. A.

Fung, Y. C.

Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues (Springer-Verlag, New York, 1981).
[CrossRef]

Gandjbakhche, A. H.

Gintides, D.

Grinbaum, A.

Hammer, M.

Heethaar, R. M.

Hoekstra, A. G.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Jones, D. S.

D. S. Jones, The Theory of Electromagnetism (Pergamon, London, 1964).

Karlsson, A.

Kattis, S. E.

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “An advanced BE/FFT methodology for solving electromagnetic wave scattering problems with axisymmetric dielectric particles,” Eng. Anal. Boundary Elements 23, 155–165 (1999).
[CrossRef]

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies,” Comput. Mech. 21, 306–315 (1998).
[CrossRef]

G. N. Constantinides, D. Gintides, S. E. Kattis, K. Kiriaki, C. A. Paraskeva, A. C. Payatakes, D. Polyzos, S. V. Tsinopoulos, S. N. Yannopoulos, “Computation of light scattering by axisymmetric nonspherical particles and comparison with experimental results,” Appl. Opt. 37, 7310–7319 (1998).
[CrossRef]

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “3D boundary element method in electromagnetic wave scattering by small biological bodies,” in Third Hellenic-European Conference on Mathematics and Informatics: HERMIS ’96, E. A. Lipitakes, ed. (LEA, Athens, Greece, 1996).

Kim, J.

J. Kim, J. C. Lin, “Successive order scattering transport approximation for laser light propagation in whole blood medium,” IEEE Trans. Biomed. Eng. 45, 505–510 (1998).
[CrossRef] [PubMed]

Kiriaki, K.

Klett, J. D.

Kolb, A.

Lee, V. S.

Lin, J. C.

J. Kim, J. C. Lin, “Successive order scattering transport approximation for laser light propagation in whole blood medium,” IEEE Trans. Biomed. Eng. 45, 505–510 (1998).
[CrossRef] [PubMed]

Maltsev, V. P.

A. N. Shvalov, J. T. Soini, A. V. Chernyshev, P. A. Tarasov, E. Soini, V. P. Maltsev, “Light-scattering properties of individual erythrocytes,” Appl. Opt. 38, 230–235 (1999).
[CrossRef]

J. T. Soini, A. V. Chernyshev, A. N. Shvalov, V. P. Maltsev, “Measurement of scattering patterns from individual nonspherical particles using scanning flow cytometer,” in Light Scattering by Nonspherical Particles, K. Lumme, J. W. Hovenier, K. Muinonen, J. Rahola, H. Laitinen, eds. (Observatory, University of Helsinki, Helsinki, Finland, 1997).

Marik, T.

Mazeron, P.

P. Mazeron, S. Muller, “Dielectric or absorbing particles: EM surface fields and scattering,” J. Opt. 29, 68–77 (1998).
[CrossRef]

P. Mazeron, S. Muller, H. El. Azouri, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34, 99–110 (1997).
[CrossRef] [PubMed]

P. Mazeron, S. Muller, H. El. Azouri, “On intensity reinforcement in small-angle light scattering patterns of erythrocytes under shear,” Eur. Biophys. J. 26, 247–252 (1997).
[CrossRef]

P. Mazeron, S. Muller, “Light scattering by ellipsoids in a physical optics approximation,” Appl. Opt. 35, 3726–3735 (1996).
[CrossRef] [PubMed]

Metz, M. H.

Michel, B.

Mills, P.

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

Muller, S.

P. Mazeron, S. Muller, “Dielectric or absorbing particles: EM surface fields and scattering,” J. Opt. 29, 68–77 (1998).
[CrossRef]

P. Mazeron, S. Muller, H. El. Azouri, “On intensity reinforcement in small-angle light scattering patterns of erythrocytes under shear,” Eur. Biophys. J. 26, 247–252 (1997).
[CrossRef]

P. Mazeron, S. Muller, H. El. Azouri, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34, 99–110 (1997).
[CrossRef] [PubMed]

P. Mazeron, S. Muller, “Light scattering by ellipsoids in a physical optics approximation,” Appl. Opt. 35, 3726–3735 (1996).
[CrossRef] [PubMed]

Nijhof, E. J.

Nilsson, A. M. K.

Paraskeva, C. A.

Payatakes, A. C.

Plasek, J.

Polyzos, D.

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “An advanced BE/FFT methodology for solving electromagnetic wave scattering problems with axisymmetric dielectric particles,” Eng. Anal. Boundary Elements 23, 155–165 (1999).
[CrossRef]

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies,” Comput. Mech. 21, 306–315 (1998).
[CrossRef]

G. N. Constantinides, D. Gintides, S. E. Kattis, K. Kiriaki, C. A. Paraskeva, A. C. Payatakes, D. Polyzos, S. V. Tsinopoulos, S. N. Yannopoulos, “Computation of light scattering by axisymmetric nonspherical particles and comparison with experimental results,” Appl. Opt. 37, 7310–7319 (1998).
[CrossRef]

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “3D boundary element method in electromagnetic wave scattering by small biological bodies,” in Third Hellenic-European Conference on Mathematics and Informatics: HERMIS ’96, E. A. Lipitakes, ed. (LEA, Athens, Greece, 1996).

Schweitzer, D.

Shepherd, A. P.

Shvalov, A. N.

A. N. Shvalov, J. T. Soini, A. V. Chernyshev, P. A. Tarasov, E. Soini, V. P. Maltsev, “Light-scattering properties of individual erythrocytes,” Appl. Opt. 38, 230–235 (1999).
[CrossRef]

J. T. Soini, A. V. Chernyshev, A. N. Shvalov, V. P. Maltsev, “Measurement of scattering patterns from individual nonspherical particles using scanning flow cytometer,” in Light Scattering by Nonspherical Particles, K. Lumme, J. W. Hovenier, K. Muinonen, J. Rahola, H. Laitinen, eds. (Observatory, University of Helsinki, Helsinki, Finland, 1997).

Snabre, P.

Soini, E.

Soini, J. T.

A. N. Shvalov, J. T. Soini, A. V. Chernyshev, P. A. Tarasov, E. Soini, V. P. Maltsev, “Light-scattering properties of individual erythrocytes,” Appl. Opt. 38, 230–235 (1999).
[CrossRef]

J. T. Soini, A. V. Chernyshev, A. N. Shvalov, V. P. Maltsev, “Measurement of scattering patterns from individual nonspherical particles using scanning flow cytometer,” in Light Scattering by Nonspherical Particles, K. Lumme, J. W. Hovenier, K. Muinonen, J. Rahola, H. Laitinen, eds. (Observatory, University of Helsinki, Helsinki, Finland, 1997).

Stamatakos, G. S.

Steinke, J. M.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Streekstra, G. J.

Sutherland, R. A.

Tarasov, P. A.

Tarassenko, L.

Thamm, E.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

Tsang, W. C. O.

W. C. O. Tsang, “The size and shape of human red blood cells,” M.S. thesis (University of California at San Diego, San Diego, Calif., 1975).

Tsinopoulos, S. V.

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “An advanced BE/FFT methodology for solving electromagnetic wave scattering problems with axisymmetric dielectric particles,” Eng. Anal. Boundary Elements 23, 155–165 (1999).
[CrossRef]

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies,” Comput. Mech. 21, 306–315 (1998).
[CrossRef]

G. N. Constantinides, D. Gintides, S. E. Kattis, K. Kiriaki, C. A. Paraskeva, A. C. Payatakes, D. Polyzos, S. V. Tsinopoulos, S. N. Yannopoulos, “Computation of light scattering by axisymmetric nonspherical particles and comparison with experimental results,” Appl. Opt. 37, 7310–7319 (1998).
[CrossRef]

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “3D boundary element method in electromagnetic wave scattering by small biological bodies,” in Third Hellenic-European Conference on Mathematics and Informatics: HERMIS ’96, E. A. Lipitakes, ed. (LEA, Athens, Greece, 1996).

Twersky, V.

Tycko, D. H.

Uzunoglu, N. K.

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Yannopoulos, S. N.

Yova, D.

Appl. Opt. (13)

J. Plasek, T. Marik, “Determination of undeformable erythrocytes in blood samples using light scattering,” Appl. Opt. 21, 4335–4338 (1982).
[CrossRef] [PubMed]

J. M. Steinke, A. P. Shepherd, “Comparison of Mie theory and the light scattering of red blood cells,” Appl. Opt. 27, 4027–4033 (1988).
[CrossRef] [PubMed]

M. Hammer, D. Schweitzer, B. Michel, E. Thamm, A. Kolb, “Single scattering by red blood cells,” Appl. Opt. 37, 7410–7418 (1998).
[CrossRef]

A. H. Gandjbakhche, P. Mills, P. Snabre, “Light-scattering technique for the study of orientation and deformation of red blood cells in a concentrated suspension,” Appl. Opt. 33, 1070–1078 (1994).
[CrossRef] [PubMed]

G. N. Constantinides, D. Gintides, S. E. Kattis, K. Kiriaki, C. A. Paraskeva, A. C. Payatakes, D. Polyzos, S. V. Tsinopoulos, S. N. Yannopoulos, “Computation of light scattering by axisymmetric nonspherical particles and comparison with experimental results,” Appl. Opt. 37, 7310–7319 (1998).
[CrossRef]

A. M. K. Nilsson, P. Alsholm, A. Karlsson, S. Andersson-Engels, “T-matrix computations of light scattering by red blood cells,” Appl. Opt. 37, 2735–2748 (1998).
[CrossRef]

D. H. Tycko, M. H. Metz, E. A. Epstein, A. Grinbaum, “Flow-cytometric light scattering measurements of red blood cell volume and hemoglobin concentration,” Appl. Opt. 24, 1355–1365 (1985).
[CrossRef]

G. J. Streekstra, A. G. Hoekstra, R. M. Heethaar, “Anomalous diffraction by arbitrarily oriented ellipsoids: applications in ektacytometry,” Appl. Opt. 33, 7288–7296 (1994).
[CrossRef] [PubMed]

P. Mazeron, S. Muller, “Light scattering by ellipsoids in a physical optics approximation,” Appl. Opt. 35, 3726–3735 (1996).
[CrossRef] [PubMed]

G. J. Streekstra, A. G. Hoekstra, E. J. Nijhof, R. M. Heethaar, “Light scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction,” Appl. Opt. 32, 2266–2272 (1993).
[CrossRef] [PubMed]

G. S. Stamatakos, D. Yova, N. K. Uzunoglu, “Integral equation model of light scattering by an oriented monodisperse system of triaxial dielectric ellipsoids: application in ektacytometry,” Appl. Opt. 36, 6503–6512 (1997).
[CrossRef]

J. D. Klett, R. A. Sutherland, “Approximate methods for modeling the scattering properties of nonspherical particles: evaluation of the Wentzel–Kramers–Brillouin method,” Appl. Opt. 31, 373–386 (1992).
[CrossRef] [PubMed]

A. N. Shvalov, J. T. Soini, A. V. Chernyshev, P. A. Tarasov, E. Soini, V. P. Maltsev, “Light-scattering properties of individual erythrocytes,” Appl. Opt. 38, 230–235 (1999).
[CrossRef]

Biorheology (1)

P. Mazeron, S. Muller, H. El. Azouri, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34, 99–110 (1997).
[CrossRef] [PubMed]

Comput. Mech. (1)

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies,” Comput. Mech. 21, 306–315 (1998).
[CrossRef]

Eng. Anal. Boundary Elements (1)

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “An advanced BE/FFT methodology for solving electromagnetic wave scattering problems with axisymmetric dielectric particles,” Eng. Anal. Boundary Elements 23, 155–165 (1999).
[CrossRef]

Eur. Biophys. J. (1)

P. Mazeron, S. Muller, H. El. Azouri, “On intensity reinforcement in small-angle light scattering patterns of erythrocytes under shear,” Eur. Biophys. J. 26, 247–252 (1997).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

J. Kim, J. C. Lin, “Successive order scattering transport approximation for laser light propagation in whole blood medium,” IEEE Trans. Biomed. Eng. 45, 505–510 (1998).
[CrossRef] [PubMed]

J. Opt. (1)

P. Mazeron, S. Muller, “Dielectric or absorbing particles: EM surface fields and scattering,” J. Opt. 29, 68–77 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

Other (9)

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues (Springer-Verlag, New York, 1981).
[CrossRef]

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

D. S. Jones, The Theory of Electromagnetism (Pergamon, London, 1964).

IMSL Math/Library User’s Manual, Version 3.0 (Visual Numerics, Inc., Houston, Tex., 1994).

W. C. O. Tsang, “The size and shape of human red blood cells,” M.S. thesis (University of California at San Diego, San Diego, Calif., 1975).

S. V. Tsinopoulos, S. E. Kattis, D. Polyzos, “3D boundary element method in electromagnetic wave scattering by small biological bodies,” in Third Hellenic-European Conference on Mathematics and Informatics: HERMIS ’96, E. A. Lipitakes, ed. (LEA, Athens, Greece, 1996).

J. T. Soini, A. V. Chernyshev, A. N. Shvalov, V. P. Maltsev, “Measurement of scattering patterns from individual nonspherical particles using scanning flow cytometer,” in Light Scattering by Nonspherical Particles, K. Lumme, J. W. Hovenier, K. Muinonen, J. Rahola, H. Laitinen, eds. (Observatory, University of Helsinki, Helsinki, Finland, 1997).

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Figures (14)

Fig. 1
Fig. 1

DSCS normalized by a 2 plotted versus the scattering angle θ for a sphere with a relative refractive index of m = 1.05 and a dimensionless frequency of k ex a = 50. Shown is a comparison between the results obtained with the analytical Mie theory (solid curve) and the numerical results obtained with the BE–FFT method (filled circles).

Fig. 2
Fig. 2

Representation of the biconcave RBC model on the ρ–z plane. The angle τ is formed by the X 3 axis and the axis of symmetry z and indicates the orientation of the RBC with respect to the incident wave, which is propagating in the 3 direction with its electric field polarized in the 1 direction.

Fig. 3
Fig. 3

Evaluated DSCS’s for (a) face-on, (b) oblique, (c) rim-on He–Ne laser light illumination of a biconcave-disk-shaped RBC plotted versus the scattering angle θ.

Fig. 4
Fig. 4

Comparison between DSCS values calculated for He–Ne laser illumination of a real RBC and a volume-equivalent sphere on (a) the parallel and (b) the perpendicular scattering planes.

Fig. 5
Fig. 5

Comparison between DSCS values calculated for face-on He–Ne laser illumination of a RBC and a size- and a volume-equivalent oblate spheroid on (a) the parallel and (b) the perpendicular scattering planes.

Fig. 6
Fig. 6

Comparison among DSCS values calculated for rim-on He–Ne laser illumination of a RBC and a size- and a volume-equivalent oblate spheroid on (a) the parallel and (b) the perpendicular scattering plane.

Fig. 7
Fig. 7

Evaluation of RBC intensity scattering patterns: (a) Position of the forward and the backward screens. (b) Geometry of the screen.

Fig. 8
Fig. 8

Forward light-intensity scattering patterns calculated for face-on He–Ne laser illumination of (a) a size–volume-equivalent oblate spheroid and (b) a RBC.

Fig. 9
Fig. 9

Backward light-intensity scattering patterns calculated for face-on He–Ne laser illumination of (a) a size–volume-equivalent oblate spheroid and (b) a RBC.

Fig. 10
Fig. 10

Forward light-intensity scattering patterns calculated for rim-on He–Ne laser illumination of (a) a size–volume-equivalent oblate spheroid and (b) a RBC.

Fig. 11
Fig. 11

Backward light-intensity scattering patterns calculated for rim-on He–Ne laser illumination of (a) a size–volume-equivalent oblate spheroid and (b) a RBC.

Fig. 12
Fig. 12

Evaluation of RBC integrated light intensity: (a) Positions of the forward, side 1 (parallel scattering plane), side 2 (perpendicular scattering plane), and backward detectors. (b) Geometry of the detector.

Fig. 13
Fig. 13

Scattering cross section C sca det scattered from an average-sized RBC and collected by the four detectors for the cases of (a) face-on and (b) rim-on incidences plotted versus the exterior wave number k ex.

Fig. 14
Fig. 14

Scattering cross section C sca det scattered from an average-sized RBC and collected by the four detectors for the cases of (a) face-on and (b) rim-on incidences plotted versus the relative refractive index m.

Equations (25)

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c˜x·Ψexx+Sq˜exx, y, ω·Ψ˜exydSy=S φ˜exx, y, ω·TexydSy+UIx,
Ĩ-c˜x·Ψinx+Sq˜inx, y, ω·Ψ˜inydSy=Sφ˜inx, y, ω·TinydSy,
c˜x=0˜for xVĨ,for xR3-V12Ĩfor xS.
φ˜x, y, ω=-Gx, y, ωĨ,
q˜x, y, ω=yGx, y, ωnˆ-nˆyGx, y, ω+nˆ·yGx, y, ωĨ,
Ψinx=B˜·Ψexx,  μexTinx=μinTexx,  xS,
B˜=Ĩ-nˆnˆ+ωexωin-iσ nˆnˆ,
Ψexx-UIx=U0Iexp-ikexR-ikexRgθRˆ, kˆ; dˆθˆ+gϕRˆ, kˆ; dˆφˆ,  R=|y-x|,
gθRˆ, kˆ; dˆ=kex4πU0IS-kexθˆRˆ-Rˆθˆ : nˆΨexy+iθˆ·TexyexpikexRˆ·ydSy,
gϕRˆ, kˆ; dˆ=kex4πU0IS-kexφˆRˆ-Rˆφˆ : nˆΨexy+iφˆ·TexyexpikexRˆ·ydSy,
ab : cd=a·db·c,
Rˆ=y-x|y-x|,
σD=limR R2|Ψexx-UIx|2U0I2=|gθRˆ, kˆ; dˆ|2+|gϕRˆ, kˆ; dˆ|2kex2.
HnexGnexHninG˜nin·ΨnexTnex=UnI0,
zρ=1-ρa21/2C0+C2ρa2+C4ρa4,
zρ=1-ρa21/20.72+4.152 ρa2-3.426ρa4.
m¯=1.335+0.001823Hb+8.6526×10-6 Hb2,
IA=σDARA2 II,
RA2=z2+x1A2+x2A2=z21+tan θ cos φ2+tan θ sin φ2
IA=σDA1+tan θ cos φ2+tan θ sin φ2IIz2=σRIIz2.
Cscadet=θγ,τφγ,τ σDθγ, τ, φγ, τsin θγ, τdθdφ,
θγ, τ=γ,  φγ, τ=τ,
θγ, τ=180-γ,  φγ, τ=τ,
θγ, τ=-tan-1cos2 γ+sin2 γ sin2 τ1/2sin γ cos τ,  φγ, τ=tan-1sin γ sin τcos γ,
θγ, τ=-tan-1cos2 γ+sin2 γ cos2 τ1/2sin γ sin τ,  φγ, τ=tan-1cos γsin γ cos τ,

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