Abstract

We have studied the light-scattering properties of human erythrocytes both experimentally and theoretically. In the experimental study measurements were performed with a Scanning Flow Cytometer (SFC). The SFC can measure the light-scattering pattern (indicatrix) of an individual particle over an angular range of 10–60°. We have observed polymorphism in the measured set of indicatrices. To understand the reason for this polymorphism, we have made a theoretical study of the scattering properties of erythrocytes. The Wentzel–Kramer–Brillouin approximation has been employed to calculate indicatrices of individual erythrocytes in different orientations relative to the incident light beam. The indicatrices were calculated over an angular range of 15–35°. A comparison of the experimentally measured and theoretically calculated indicatrices shows that the polymorphism is due mainly to the different orientation of the erythrocytes in the flow. The effect caused by the Poiseuille profile of the flow on an individual erythrocyte within the SFC cuvette capillary was studied theoretically by use of the Stokes approximation. Rotation of an erythrocyte was predicted by this theoretical analysis, and this prediction was further verified by comparison with experimental results.

© 1999 Optical Society of America

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References

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    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

1998 (2)

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical setup for the Scanning Flow Cytometer,” Cytometry 31, 78–84 (1998).
[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]

1997 (2)

N. K. Uzunoglu, D. Yova, G. S. Stamatakos, “Light scattering by pathological and deformed erythrocytes: an integral equation model,” J. Biomed. Opt. 2, 310–318 (1997).
[CrossRef]

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

1996 (2)

V. P. Maltsev, A. V. Chernyshev, K. A. Semyanov, E. Soini, “Absolute real-time measurement of particle size distribution with the method of flying light scattering indicatrix,” Appl. Opt. 35, 3275–3280 (1996).
[CrossRef] [PubMed]

V. N. Lopatin, N. V. Shepelevich, “Consequences of the integral wave equation in the Wentsel–Kramers–Brilluen approximation,” Opt. Spectrosc. 81, 103–106 (1996).

1995 (1)

1993 (1)

1992 (1)

1985 (1)

1981 (1)

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

1975 (1)

1973 (1)

R. Skalak, A. Tozeren, R. P. Zarda, S. Chien, “Strain energy function of red blood cell membranes,” Biophys. J. 13, 245–264 (1973).
[CrossRef] [PubMed]

1963 (1)

H. Brenner, “The Stokes resistance of an arbitrary particle,” Chem. Eng. Sci. 18, 1–25 (1963).
[CrossRef]

Alsholm, P.

Andersson-Engels, S.

Azouzi, H. El.

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

P. Mazeron, S. Muller, H. El. Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology34, 99–110 (1997).
[PubMed]

Barber, P.

Bohren, C. F.

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

Brenner, H.

H. Brenner, “The Stokes resistance of an arbitrary particle,” Chem. Eng. Sci. 18, 1–25 (1963).
[CrossRef]

Chernyshev, A. V.

Chien, S.

R. Skalak, A. Tozeren, R. P. Zarda, S. Chien, “Strain energy function of red blood cell membranes,” Biophys. J. 13, 245–264 (1973).
[CrossRef] [PubMed]

Doroshkin, A. A.

Epstein, E. A.

Fung, Y. C.

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

Grinbaum, A.

Hanninen, P. E.

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical setup for the Scanning Flow Cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

Heethaar, R. M.

Hoeksta, A. G.

Huffman, D. R.

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

Karlsson, A.

Klett, J. D.

Lopatin, V. N.

V. N. Lopatin, N. V. Shepelevich, “Consequences of the integral wave equation in the Wentsel–Kramers–Brilluen approximation,” Opt. Spectrosc. 81, 103–106 (1996).

Maltsev, V. P.

Mazeron, P.

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

P. Mazeron, S. Muller, H. El. Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology34, 99–110 (1997).
[PubMed]

Metz, M. H.

Muller, S.

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

P. Mazeron, S. Muller, H. El. Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology34, 99–110 (1997).
[PubMed]

Nijhof, E.

Nilsson, A. M. K.

Patitucci, P.

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

Prots, V. I.

Semyanov, K. A.

Shepelevich, N. V.

V. N. Lopatin, N. V. Shepelevich, “Consequences of the integral wave equation in the Wentsel–Kramers–Brilluen approximation,” Opt. Spectrosc. 81, 103–106 (1996).

Skalak, R.

R. Skalak, A. Tozeren, R. P. Zarda, S. Chien, “Strain energy function of red blood cell membranes,” Biophys. J. 13, 245–264 (1973).
[CrossRef] [PubMed]

Soini, E.

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical setup for the Scanning Flow Cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

V. P. Maltsev, A. V. Chernyshev, K. A. Semyanov, E. Soini, “Absolute real-time measurement of particle size distribution with the method of flying light scattering indicatrix,” Appl. Opt. 35, 3275–3280 (1996).
[CrossRef] [PubMed]

Soini, J. T.

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical setup for the Scanning Flow Cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

Stamatakos, G. S.

N. K. Uzunoglu, D. Yova, G. S. Stamatakos, “Light scattering by pathological and deformed erythrocytes: an integral equation model,” J. Biomed. Opt. 2, 310–318 (1997).
[CrossRef]

Steekstra, G. J.

Sutherland, R. A.

Tozeren, A.

R. Skalak, A. Tozeren, R. P. Zarda, S. Chien, “Strain energy function of red blood cell membranes,” Biophys. J. 13, 245–264 (1973).
[CrossRef] [PubMed]

Tsang, W. C. O.

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

Tycko, D. H.

Uzunoglu, N. K.

N. K. Uzunoglu, D. Yova, G. S. Stamatakos, “Light scattering by pathological and deformed erythrocytes: an integral equation model,” J. Biomed. Opt. 2, 310–318 (1997).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Yeh, C.

Yova, D.

N. K. Uzunoglu, D. Yova, G. S. Stamatakos, “Light scattering by pathological and deformed erythrocytes: an integral equation model,” J. Biomed. Opt. 2, 310–318 (1997).
[CrossRef]

Zarda, R. P.

R. Skalak, A. Tozeren, R. P. Zarda, S. Chien, “Strain energy function of red blood cell membranes,” Biophys. J. 13, 245–264 (1973).
[CrossRef] [PubMed]

Appl. Opt. (7)

Biophys. J. (1)

R. Skalak, A. Tozeren, R. P. Zarda, S. Chien, “Strain energy function of red blood cell membranes,” Biophys. J. 13, 245–264 (1973).
[CrossRef] [PubMed]

Biorheology (1)

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

Chem. Eng. Sci. (1)

H. Brenner, “The Stokes resistance of an arbitrary particle,” Chem. Eng. Sci. 18, 1–25 (1963).
[CrossRef]

Cytometry (1)

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical setup for the Scanning Flow Cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

Eur. Biophys. J. (1)

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

J. Biomed. Opt. (1)

N. K. Uzunoglu, D. Yova, G. S. Stamatakos, “Light scattering by pathological and deformed erythrocytes: an integral equation model,” J. Biomed. Opt. 2, 310–318 (1997).
[CrossRef]

Opt. Spectrosc. (1)

V. N. Lopatin, N. V. Shepelevich, “Consequences of the integral wave equation in the Wentsel–Kramers–Brilluen approximation,” Opt. Spectrosc. 81, 103–106 (1996).

Other (3)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

P. Mazeron, S. Muller, H. El. Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology34, 99–110 (1997).
[PubMed]

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

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Figures (6)

Fig. 1
Fig. 1

Model of a red blood cell. The shape of the red blood cell is described in Eq. (1).

Fig. 2
Fig. 2

Schematic layout of the SFC: HFH, hydrofocusing head; PMT, photomultiplier tube.

Fig. 3
Fig. 3

Rotation angle of a spheroid particle as a function of time. Angle 0° corresponds to the particle orientation at which the symmetry axes are coincident with the direction of the flow line. The parameter s is the characteristic of the Poiseuille flow profile, y 0 is the distance of the spheroid center from the center of the flow, and ∊ is the ratio between the spheroid axes.

Fig. 4
Fig. 4

Indicatrices of a sphered erythrocyte calculated from Mie theory, RGD, WKB, and 2wWKB approximations. Calculation parameters: diameter, d = 6.3 µm; refractive index, m = 1.41; wavelength, λ = 0.6328 µm; medium refractive index, m 0 = 1.333. The indicatrices were normalized at 1 in the forward direction, polar scattering angle θ = 0, and were shifted relative to one another.

Fig. 5
Fig. 5

Indicatrices of the erythrocyte calculated from the WKB for different orientations relative to the direction of the incident beam. The indicatrices are normalized at 1 in the forward direction, polar scattering angle θ = 0, and are shifted relative to one another.

Fig. 6
Fig. 6

Experimental flying light-scattering indicatrices of the erythrocyte measured with the SFC. We shifted the indicatrices relative to one another to observe the differences in the indicatrix shape easily.

Equations (8)

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z2=0.86d/221-2x/d20.01384083+0.28429172x/d2+0.013069322x/d4.
ESr=foˆ, ıˆexpikrr, foˆ, ıˆ=k24π-oˆ×oˆ×EirVFoˆ, ıˆ, Foˆ, ıˆ=1VVm2-1expikıˆ-oˆrdV,
foˆ, ıˆ=k24π-oˆ×oˆ×eiVFoˆ, ıˆ, Foˆ, ıˆ=1VVm2-1expikSr×expik Z1Zm-1dzdV,
Er=ei2m+1exp-im-1kr1expimkr+R expiχ1-mkr,
T=μ2sy01+2-1cosβ,
2+1dβdt=2sy01+2-1cosβ.
βt=arctan tan2sy02+1 t.
V15=Imax-Imin/Imax+Imin,

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