Abstract

Elastic light scattering by mature red blood cells (RBCs) was theoretically and experimentally analyzed by use of the discrete dipole approximation (DDA) and scanning flow cytometry (SFC), respectively. SFC permits measurement of the angular dependence of the light-scattering intensity (indicatrix) of single particles. A mature RBC is modeled as a biconcave disk in DDA simulations of light scattering. We have studied the effect of RBC orientation related to the direction of the light incident upon the indicatrix. Numerical calculations of indicatrices for several axis ratios and volumes of RBC have been carried out. Comparison of the simulated indicatrices and indicatrices measured by SFC showed good agreement, validating the biconcave disk model for a mature RBC. We simulated the light-scattering output signals from the SFC with the DDA for RBCs modeled as a disk–sphere and as an oblate spheroid. The biconcave disk, the disk–sphere, and the oblate spheroid models have been compared for two orientations, i.e., face-on and rim-on incidence, relative to the direction of the incident beam. Only the oblate spheroid model for rim-on incidence gives results similar to those of the rigorous biconcave disk model.

© 2005 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, 1983).
  2. M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).
  3. S. M. Lewis, B. J. Bain, I. Bates, M. I. Levene, Dacie & Lewis Practical Haematology (Saunders, 2001).
  4. J. M. Steinke, A. P. Shepherd, “Comparison of Mie theory and the light scattering of red blood cells,” Appl. Opt. 21, 4335–4338 (1982).
  5. G. J. Streekstra, A. G. Hoekstra, E. J. Nijhof, R. M. Heethar, “Light scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction,” Appl. Opt. 32, 2266–2272 (1993).
    [CrossRef] [PubMed]
  6. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  7. 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]
  8. P. Mazeron, S. Muller, “Light scattering by ellipsoids in physical optics approximation,” Appl. Opt. 35, 3726–3735 (1996).
    [CrossRef] [PubMed]
  9. J. He, A. Karlsson, J. Swartling, S. Andersson-Engels, “Light scattering by multiple red blood cells,” J. Opt. Soc. Am. A 21, 1953–1961 (2004).
    [CrossRef]
  10. 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]
  11. P. Mazeron, S. Muller, “Dielectric or absorbing particles: EM surface fields and scattering,” J. Opt. 29, 68–77 (1998).
    [CrossRef]
  12. S. V. Tsinopoulos, D. Polyzos, “Scattering of He–Ne laser light by an average-sized red-blood cell,” Appl. Opt. 38, 5499–5510 (1999).
    [CrossRef]
  13. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [CrossRef]
  14. B. T. Draine, “The discrete dipole approximation for light-scattering by irregular targets,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), pp. 131–145.
    [CrossRef]
  15. A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulation of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
    [CrossRef]
  16. V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243–255 (2000).
    [CrossRef]
  17. Y. C. Fung, W. C. Tsang, P. Patitucci, “High-resolution data on the geometry of red blood cells,” Biorheology 18, 369–385 (1981).
    [PubMed]
  18. P. Mazeron, S. Muller, H. El. Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34, 99–110 (1997).
    [CrossRef] [PubMed]
  19. E. M. Purcel, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
  20. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  21. S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986).
    [CrossRef]
  22. A. G. Hoekstra, P. M. A. Sloot, “Dipolar unit size in coupled-dipole calculations of the scattering matrix elements,” Opt. Lett. 18, 1211–1213 (1993).
    [CrossRef] [PubMed]
  23. V. P. Maltsev, K. A. Semyanov, Characterisation of Bio-Particles from Light Scattering, Inverse and Ill-Posed Problems Series (VSP, Utrecht, 2004).
    [CrossRef]
  24. K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110–5115 (2004).
    [CrossRef] [PubMed]
  25. K. A. Semyanov, P. A. Tarasov, J. T. Soini, A. K. Petrov, V. P. Maltsev, “Calibration free method to determine the size and hemoglobin concentration of individual red blood cells from light scattering,” Appl. Opt. 39, 5884–5889 (2000).
    [CrossRef]
  26. E. Eremina, Y. Eremin, T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244, 15–23 (2005).
    [CrossRef]

2005 (1)

E. Eremina, Y. Eremin, T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244, 15–23 (2005).
[CrossRef]

2004 (2)

2000 (2)

1999 (2)

1998 (3)

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]

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

A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulation of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

1994 (1)

1993 (2)

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

1986 (1)

S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986).
[CrossRef]

1982 (1)

1981 (1)

Y. C. Fung, W. C. Tsang, P. Patitucci, “High-resolution data on the geometry of red blood cells,” Biorheology 18, 369–385 (1981).
[PubMed]

1973 (1)

E. M. Purcel, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Alsholm, P.

Andersson-Engels, S.

Azouzi, H. El.

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

Bain, B. J.

S. M. Lewis, B. J. Bain, I. Bates, M. I. Levene, Dacie & Lewis Practical Haematology (Saunders, 2001).

Bates, I.

S. M. Lewis, B. J. Bain, I. Bates, M. I. Levene, Dacie & Lewis Practical Haematology (Saunders, 2001).

Bohren, C. F.

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

Chernyshev, A. V.

Draine, B. T.

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

B. T. Draine, “The discrete dipole approximation for light-scattering by irregular targets,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), pp. 131–145.
[CrossRef]

Eremin, Y.

E. Eremina, Y. Eremin, T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244, 15–23 (2005).
[CrossRef]

Eremina, E.

E. Eremina, Y. Eremin, T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244, 15–23 (2005).
[CrossRef]

Flatau, P. J.

Fung, Y. C.

Y. C. Fung, W. C. Tsang, P. Patitucci, “High-resolution data on the geometry of red blood cells,” Biorheology 18, 369–385 (1981).
[PubMed]

Grimminck, M. D.

A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulation of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
[CrossRef]

He, J.

Heethar, R. M.

Hoekstra, A. G.

Huffman, D. R.

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

Karlsson, A.

Levene, M. I.

S. M. Lewis, B. J. Bain, I. Bates, M. I. Levene, Dacie & Lewis Practical Haematology (Saunders, 2001).

Lewis, S. M.

S. M. Lewis, B. J. Bain, I. Bates, M. I. Levene, Dacie & Lewis Practical Haematology (Saunders, 2001).

Maltsev, V. P.

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. Azouzi, “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 physical optics approximation,” Appl. Opt. 35, 3726–3735 (1996).
[CrossRef] [PubMed]

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. Azouzi, “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 physical optics approximation,” Appl. Opt. 35, 3726–3735 (1996).
[CrossRef] [PubMed]

Nijhof, E. J.

Nilsson, A. M. K.

Patitucci, P.

Y. C. Fung, W. C. Tsang, P. Patitucci, “High-resolution data on the geometry of red blood cells,” Biorheology 18, 369–385 (1981).
[PubMed]

Pennypacker, C. R.

E. M. Purcel, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Petrov, A. K.

Polyzos, D.

Purcel, E. M.

E. M. Purcel, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Salzman, G. C.

S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986).
[CrossRef]

Semyanov, K. A.

Shepherd, A. P.

Shvalov, A. N.

Singham, S. B.

S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986).
[CrossRef]

Sloot, P. M. A.

A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulation of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
[CrossRef]

A. G. Hoekstra, P. M. A. Sloot, “Dipolar unit size in coupled-dipole calculations of the scattering matrix elements,” Opt. Lett. 18, 1211–1213 (1993).
[CrossRef] [PubMed]

Soini, E.

Soini, J. T.

Steinke, J. M.

Streekstra, G. J.

Swartling, J.

Tarasov, P. A.

Tsang, W. C.

Y. C. Fung, W. C. Tsang, P. Patitucci, “High-resolution data on the geometry of red blood cells,” Biorheology 18, 369–385 (1981).
[PubMed]

Tsinopoulos, S. V.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Wriedt, T.

E. Eremina, Y. Eremin, T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244, 15–23 (2005).
[CrossRef]

Zharinov, A. E.

Appl. Opt. (8)

J. M. Steinke, A. P. Shepherd, “Comparison of Mie theory and the light scattering of red blood cells,” Appl. Opt. 21, 4335–4338 (1982).

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

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]

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

S. V. Tsinopoulos, D. Polyzos, “Scattering of He–Ne laser light by an average-sized red-blood cell,” Appl. Opt. 38, 5499–5510 (1999).
[CrossRef]

K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110–5115 (2004).
[CrossRef] [PubMed]

K. A. Semyanov, P. A. Tarasov, J. T. Soini, A. K. Petrov, V. P. Maltsev, “Calibration free method to determine the size and hemoglobin concentration of individual red blood cells from light scattering,” Appl. Opt. 39, 5884–5889 (2000).
[CrossRef]

Astrophys. J. (2)

E. M. Purcel, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Biorheology (2)

Y. C. Fung, W. C. Tsang, P. Patitucci, “High-resolution data on the geometry of red blood cells,” Biorheology 18, 369–385 (1981).
[PubMed]

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

Int. J. Mod. Phys. C (1)

A. G. Hoekstra, M. D. Grimminck, P. M. A. Sloot, “Large scale simulation of elastic light scattering by a fast discrete dipole approximation,” Int. J. Mod. Phys. C 9, 87–102 (1998).
[CrossRef]

J. Chem. Phys. (1)

S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986).
[CrossRef]

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. A (2)

Opt. Commun. (1)

E. Eremina, Y. Eremin, T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244, 15–23 (2005).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243–255 (2000).
[CrossRef]

Other (6)

B. T. Draine, “The discrete dipole approximation for light-scattering by irregular targets,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), pp. 131–145.
[CrossRef]

V. P. Maltsev, K. A. Semyanov, Characterisation of Bio-Particles from Light Scattering, Inverse and Ill-Posed Problems Series (VSP, Utrecht, 2004).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

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

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).

S. M. Lewis, B. J. Bain, I. Bates, M. I. Levene, Dacie & Lewis Practical Haematology (Saunders, 2001).

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Figures (9)

Fig. 1
Fig. 1

Shape of a mature RBC and its orientation with respect to the incident radiation. xyz is a laboratory reference frame and xyz′ is a reference frame tied to the RBC (z′ is the axis of symmetry); inc and sca are propagation vectors for incident and scattering radiation, respectively.

Fig. 2
Fig. 2

Relative errors of DDA simulations for several discretization sizes. The DDA simulations were compared with the exact solutions of Mie theory for a sphere with diameter d = 4.56 μm and relative index of refraction m = 1.10.

Fig. 3
Fig. 3

(a) Initial and (b) modified indicatrices calculated by DDA for five orientations of the single biconcave disk related to the direction of the incident light beam.

Fig. 4
Fig. 4

Modified indicatrices of biconcave disks with different diameters and fixed volume.

Fig. 5
Fig. 5

Modified indicatrices of biconcave disks with different volumes and fixed diameter.

Fig. 6
Fig. 6

Experimental and theoretical modified indicatrices of individual mature RBCs. Values of χ2 differences are shown.

Fig. 7
Fig. 7

Distribution of mature RBCs over an orientation angle obtained by use of the χ2 test.

Fig. 8
Fig. 8

Modified indicatrices of the biconcave disk and the diameter-volume-equivalent disk–sphere: (a) rim-on and (b) face-on incidence.

Fig. 9
Fig. 9

Modified indicatrices of the biconcave disk and the diameter-volume-equivalent oblate spheroid: (a) rim-on and (b) face-on incidence.

Tables (1)

Tables Icon

Table 1 Parameters of RBCs for Preliminary Calculationsa

Equations (10)

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T ( x ) = 0.65 1 - x 2 ( 0.1583 + 1.5262 x 2 - 0.8579 x 4 ) ,
T ( x ) = ɛ d 1 - x 2 ( 0.1583 + 1.5262 x 2 - 0.8579 x 4 ) ,
I s ( θ ) = 0 2 π [ S 11 ( θ ,     φ ) + S 14 ( θ ,     φ ) ] d φ ,
χ 2 = i = 1 N [ I exp ( θ i ) - I theor ( θ i ) ] 2 w 2 ( θ i ) N ,
w ( θ i ) = sin 2 ( π θ i - 10 ° 50 ° - 10 ° ) ,
- π π S ( θ ,     φ ) d φ = - π 0 S ( θ ,     φ ) d φ + 0 π S ( θ ,     φ ) d φ = 0 π [ S ( θ ,     φ ) + S ( θ ,     - φ ) ] d φ .
S ( θ ,     φ ) = S - φ ( θ ,     0 ) ,             S ( θ ,     - φ ) = S φ ( θ ,     0 ) ,
P z x P - φ = ( R φ P z x R φ ) p - φ = ( R φ P z x ) p 0 = R φ p 0 = p φ ,
[ S 11 S 12 0 0 S 21 S 22 0 0 0 0 S 33 S 34 0 0 S 43 S 44 ] .
S i j ( φ ) d φ = 0

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