Abstract

In the present literature on ektacytometry, small angle light scattering by ellipsoidal red blood cells is commonly approximated by Fraunhofer diffraction. Calculations on a sphere with the size and relative refractive index of a red cell, however, show that Fraunhofer diffraction deviates significantly from exact Mie theory. Anomalous diffraction is found to be a much better approximation. The anomalous diffraction theory is used to calculate the intensity distribution of the light scattered by an ellipsoidally deformed red blood cell. The derived expression shows that the ellipticity of isointensity curves in forward scattered light are equal to the ellipticity of the red blood cell. The theoretical expression is fitted to the intensity patterns measured with an ektacytometer. For the small observation angles used in ektacytometry, the experimental results confirm the validity of the anomalous diffraction approach.

© 1993 Optical Society of America

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References

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  1. S. Chien, J. Dormandy, E. Ernst, A. Matrai, Clinical Hemorheology (Nijhoff, Boston, Mass., 1987), Chap. 5, p. 129.
  2. J. H. F. I. van Breugel, “Hemorheology and its role in blood platelet adhesion under flow conditions,” Ph.D. dissertation (State University of Utrecht, Utrecht, The Netherlands, 1989).
  3. P. F. Mullaney, P. N. Dean, “The small angle light scattering of biological cells,” Biophys. J. 10, 764–772 (1970).
    [CrossRef] [PubMed]
  4. W. Groner, N. Mohandas, M. Bessis, “New optical technique for measuring erythrocyte deformability with the ektacytometer,” Clin. Chem. 26, 1435–1442 (1980).
    [PubMed]
  5. P. Latimer, “Light scattering by ellipsoids,” J. Colloid Interface Sci. 53, 102–109 (1975).
    [CrossRef]
  6. P. Latimer, P. Barber, “Scattering by ellipsoids of revolution,” J. Colloid Interface Sci. 63, 310–316 (1978).
    [CrossRef]
  7. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 11, p. 183.
  8. S. R. Keller, R. Skalak, “Motion of a tank-treading ellipsoidal particle in a shear flow,” J. Fluid Mech. 120, 27–47 (1982).
    [CrossRef]
  9. M. Bessis, N. Mohandas, “A diffractometric method for the measurement of cellular deformability,” Blood Cells 1, 307–313 (1975).
  10. N. Mohandas, M. R. Clark, M. S. Jacobs, S. B. Shohet, “Analysis of factors regulating erythrocyte deformability,” J. Clin. Invest. 66, 563–573 (1980).
    [CrossRef] [PubMed]
  11. M. R. Hardeman, P. Goedhart, D. Breederveld, “Laser diffraction ellipsometry of erythrocytes under controlled shear stress using a rotational viscosimeter,” Clin. Chim. Acta 165, 227–234 (1987).
    [CrossRef] [PubMed]
  12. T. Fischer, H. Schmidt-Schönbein, “Tank tread motion of red cell membranes in viscometric flow: behavior of intracellular and extracellular markers (with film),” Blood Cells 3, 351–365 (1977).
  13. P. M. A. Sloot, A. G. Hoekstra, H. v. d. Liet, C. G. Figdor, “Scattering matrix elements of biological particles measured in a flow through system: theory and practice,” Appl. Opt. 28, 1752–1762 (1989).
    [CrossRef] [PubMed]
  14. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1957), App. A, p. 479.
  15. Y. C. Fung, Biomechanics, 2nd ed. (Springer-Verlag, New York, 1984), Chap. 4, p. 106.
  16. L. Reynolds, C. Johnson, A. Ishimaru, “Diffuse reflectance from a finite blood medium: applications to the modeling of fiber optic catheters,” Appl. Opt. 15, 2059–2067 (1976).
    [CrossRef] [PubMed]
  17. G. R. Cokelet, H. J. Meiselman, “Rheological comparison of hemoglobin solutions and erythrocyte suspensions,” Science 162, 275–277 (1968).
    [CrossRef] [PubMed]
  18. J. Plazek, T. Marik, “Determination of undeformable erythrocytes in blood samples using laser light scattering,” Appl. Opt. 21, 4335–4338 (1982).
    [CrossRef]
  19. F. Storzicky, V. Blazek, J. Muzik, “An improved diffractometric method for measurement of cellular deformability,” J. Biomech. 13, 417–421 (1980).
    [CrossRef]
  20. P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  21. R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46, 65–72 (1984).
    [CrossRef] [PubMed]
  22. R. Tran-Son-Tay, S. P. Sutera, G. I. Zahalak, P. R. Rao, “Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow,” Biophys. J. 51, 915–924 (1987).
    [CrossRef] [PubMed]
  23. S. P. Sutera, P. R. Pierre, G. I. Zahalak, “Deduction of intrinsic mechanical properties of the erythrocyte membrane from observations of tank-treading in the rheoscope,” Biorheology 26, 177–197 (1989).
    [PubMed]
  24. C. Allard, N. Mohandas, M. Bessis, “Red cell deformability changes in hemolytic anemias estimated by diffractometric methods (ektacytometry),” Blood Cells 3, 209–221 (1977).
  25. M. Bessis, N. Mohandas, “Laser diffraction patterns of sickle cells in fluid shear fields,” Blood Cells 3, 229–239 (1977).
  26. G. J. Streekstra, E.-J. Nijhof, R. M. Heethaar, “A bi-plane rheoscope: a new approach in optical determination of red blood cell orientation and deformation in a Couette flow,” in Proceedings of the North Sea Conference on Biomedical Engineering, J. Cornelis, S. Peters, eds. (International Federation for Medical and Biological Engineering, Antwerp, 1990).

1989 (2)

P. M. A. Sloot, A. G. Hoekstra, H. v. d. Liet, C. G. Figdor, “Scattering matrix elements of biological particles measured in a flow through system: theory and practice,” Appl. Opt. 28, 1752–1762 (1989).
[CrossRef] [PubMed]

S. P. Sutera, P. R. Pierre, G. I. Zahalak, “Deduction of intrinsic mechanical properties of the erythrocyte membrane from observations of tank-treading in the rheoscope,” Biorheology 26, 177–197 (1989).
[PubMed]

1987 (2)

M. R. Hardeman, P. Goedhart, D. Breederveld, “Laser diffraction ellipsometry of erythrocytes under controlled shear stress using a rotational viscosimeter,” Clin. Chim. Acta 165, 227–234 (1987).
[CrossRef] [PubMed]

R. Tran-Son-Tay, S. P. Sutera, G. I. Zahalak, P. R. Rao, “Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow,” Biophys. J. 51, 915–924 (1987).
[CrossRef] [PubMed]

1984 (1)

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46, 65–72 (1984).
[CrossRef] [PubMed]

1982 (2)

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

S. R. Keller, R. Skalak, “Motion of a tank-treading ellipsoidal particle in a shear flow,” J. Fluid Mech. 120, 27–47 (1982).
[CrossRef]

1980 (3)

W. Groner, N. Mohandas, M. Bessis, “New optical technique for measuring erythrocyte deformability with the ektacytometer,” Clin. Chem. 26, 1435–1442 (1980).
[PubMed]

F. Storzicky, V. Blazek, J. Muzik, “An improved diffractometric method for measurement of cellular deformability,” J. Biomech. 13, 417–421 (1980).
[CrossRef]

N. Mohandas, M. R. Clark, M. S. Jacobs, S. B. Shohet, “Analysis of factors regulating erythrocyte deformability,” J. Clin. Invest. 66, 563–573 (1980).
[CrossRef] [PubMed]

1978 (1)

P. Latimer, P. Barber, “Scattering by ellipsoids of revolution,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

1977 (3)

T. Fischer, H. Schmidt-Schönbein, “Tank tread motion of red cell membranes in viscometric flow: behavior of intracellular and extracellular markers (with film),” Blood Cells 3, 351–365 (1977).

C. Allard, N. Mohandas, M. Bessis, “Red cell deformability changes in hemolytic anemias estimated by diffractometric methods (ektacytometry),” Blood Cells 3, 209–221 (1977).

M. Bessis, N. Mohandas, “Laser diffraction patterns of sickle cells in fluid shear fields,” Blood Cells 3, 229–239 (1977).

1976 (1)

1975 (3)

P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

M. Bessis, N. Mohandas, “A diffractometric method for the measurement of cellular deformability,” Blood Cells 1, 307–313 (1975).

P. Latimer, “Light scattering by ellipsoids,” J. Colloid Interface Sci. 53, 102–109 (1975).
[CrossRef]

1970 (1)

P. F. Mullaney, P. N. Dean, “The small angle light scattering of biological cells,” Biophys. J. 10, 764–772 (1970).
[CrossRef] [PubMed]

1968 (1)

G. R. Cokelet, H. J. Meiselman, “Rheological comparison of hemoglobin solutions and erythrocyte suspensions,” Science 162, 275–277 (1968).
[CrossRef] [PubMed]

Allard, C.

C. Allard, N. Mohandas, M. Bessis, “Red cell deformability changes in hemolytic anemias estimated by diffractometric methods (ektacytometry),” Blood Cells 3, 209–221 (1977).

Barber, P.

P. Latimer, P. Barber, “Scattering by ellipsoids of revolution,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

Bessis, M.

W. Groner, N. Mohandas, M. Bessis, “New optical technique for measuring erythrocyte deformability with the ektacytometer,” Clin. Chem. 26, 1435–1442 (1980).
[PubMed]

C. Allard, N. Mohandas, M. Bessis, “Red cell deformability changes in hemolytic anemias estimated by diffractometric methods (ektacytometry),” Blood Cells 3, 209–221 (1977).

M. Bessis, N. Mohandas, “Laser diffraction patterns of sickle cells in fluid shear fields,” Blood Cells 3, 229–239 (1977).

M. Bessis, N. Mohandas, “A diffractometric method for the measurement of cellular deformability,” Blood Cells 1, 307–313 (1975).

Blazek, V.

F. Storzicky, V. Blazek, J. Muzik, “An improved diffractometric method for measurement of cellular deformability,” J. Biomech. 13, 417–421 (1980).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1957), App. A, p. 479.

Breederveld, D.

M. R. Hardeman, P. Goedhart, D. Breederveld, “Laser diffraction ellipsometry of erythrocytes under controlled shear stress using a rotational viscosimeter,” Clin. Chim. Acta 165, 227–234 (1987).
[CrossRef] [PubMed]

Chien, S.

S. Chien, J. Dormandy, E. Ernst, A. Matrai, Clinical Hemorheology (Nijhoff, Boston, Mass., 1987), Chap. 5, p. 129.

Clark, M. R.

N. Mohandas, M. R. Clark, M. S. Jacobs, S. B. Shohet, “Analysis of factors regulating erythrocyte deformability,” J. Clin. Invest. 66, 563–573 (1980).
[CrossRef] [PubMed]

Cokelet, G. R.

G. R. Cokelet, H. J. Meiselman, “Rheological comparison of hemoglobin solutions and erythrocyte suspensions,” Science 162, 275–277 (1968).
[CrossRef] [PubMed]

Dean, P. N.

P. F. Mullaney, P. N. Dean, “The small angle light scattering of biological cells,” Biophys. J. 10, 764–772 (1970).
[CrossRef] [PubMed]

Dormandy, J.

S. Chien, J. Dormandy, E. Ernst, A. Matrai, Clinical Hemorheology (Nijhoff, Boston, Mass., 1987), Chap. 5, p. 129.

Ernst, E.

S. Chien, J. Dormandy, E. Ernst, A. Matrai, Clinical Hemorheology (Nijhoff, Boston, Mass., 1987), Chap. 5, p. 129.

Figdor, C. G.

Fischer, T.

T. Fischer, H. Schmidt-Schönbein, “Tank tread motion of red cell membranes in viscometric flow: behavior of intracellular and extracellular markers (with film),” Blood Cells 3, 351–365 (1977).

Fung, Y. C.

Y. C. Fung, Biomechanics, 2nd ed. (Springer-Verlag, New York, 1984), Chap. 4, p. 106.

Goedhart, P.

M. R. Hardeman, P. Goedhart, D. Breederveld, “Laser diffraction ellipsometry of erythrocytes under controlled shear stress using a rotational viscosimeter,” Clin. Chim. Acta 165, 227–234 (1987).
[CrossRef] [PubMed]

Groner, W.

W. Groner, N. Mohandas, M. Bessis, “New optical technique for measuring erythrocyte deformability with the ektacytometer,” Clin. Chem. 26, 1435–1442 (1980).
[PubMed]

Hardeman, M. R.

M. R. Hardeman, P. Goedhart, D. Breederveld, “Laser diffraction ellipsometry of erythrocytes under controlled shear stress using a rotational viscosimeter,” Clin. Chim. Acta 165, 227–234 (1987).
[CrossRef] [PubMed]

Heethaar, R. M.

G. J. Streekstra, E.-J. Nijhof, R. M. Heethaar, “A bi-plane rheoscope: a new approach in optical determination of red blood cell orientation and deformation in a Couette flow,” in Proceedings of the North Sea Conference on Biomedical Engineering, J. Cornelis, S. Peters, eds. (International Federation for Medical and Biological Engineering, Antwerp, 1990).

Hoekstra, A. G.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1957), App. A, p. 479.

Ishimaru, A.

Jacobs, M. S.

N. Mohandas, M. R. Clark, M. S. Jacobs, S. B. Shohet, “Analysis of factors regulating erythrocyte deformability,” J. Clin. Invest. 66, 563–573 (1980).
[CrossRef] [PubMed]

Johnson, C.

Keller, S. R.

S. R. Keller, R. Skalak, “Motion of a tank-treading ellipsoidal particle in a shear flow,” J. Fluid Mech. 120, 27–47 (1982).
[CrossRef]

Latimer, P.

P. Latimer, P. Barber, “Scattering by ellipsoids of revolution,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

P. Latimer, “Light scattering by ellipsoids,” J. Colloid Interface Sci. 53, 102–109 (1975).
[CrossRef]

Liet, H. v. d.

Marik, T.

Matrai, A.

S. Chien, J. Dormandy, E. Ernst, A. Matrai, Clinical Hemorheology (Nijhoff, Boston, Mass., 1987), Chap. 5, p. 129.

Meiselman, H. J.

G. R. Cokelet, H. J. Meiselman, “Rheological comparison of hemoglobin solutions and erythrocyte suspensions,” Science 162, 275–277 (1968).
[CrossRef] [PubMed]

Mohandas, N.

W. Groner, N. Mohandas, M. Bessis, “New optical technique for measuring erythrocyte deformability with the ektacytometer,” Clin. Chem. 26, 1435–1442 (1980).
[PubMed]

N. Mohandas, M. R. Clark, M. S. Jacobs, S. B. Shohet, “Analysis of factors regulating erythrocyte deformability,” J. Clin. Invest. 66, 563–573 (1980).
[CrossRef] [PubMed]

C. Allard, N. Mohandas, M. Bessis, “Red cell deformability changes in hemolytic anemias estimated by diffractometric methods (ektacytometry),” Blood Cells 3, 209–221 (1977).

M. Bessis, N. Mohandas, “Laser diffraction patterns of sickle cells in fluid shear fields,” Blood Cells 3, 229–239 (1977).

M. Bessis, N. Mohandas, “A diffractometric method for the measurement of cellular deformability,” Blood Cells 1, 307–313 (1975).

Mullaney, P. F.

P. F. Mullaney, P. N. Dean, “The small angle light scattering of biological cells,” Biophys. J. 10, 764–772 (1970).
[CrossRef] [PubMed]

Muzik, J.

F. Storzicky, V. Blazek, J. Muzik, “An improved diffractometric method for measurement of cellular deformability,” J. Biomech. 13, 417–421 (1980).
[CrossRef]

Nijhof, E.-J.

G. J. Streekstra, E.-J. Nijhof, R. M. Heethaar, “A bi-plane rheoscope: a new approach in optical determination of red blood cell orientation and deformation in a Couette flow,” in Proceedings of the North Sea Conference on Biomedical Engineering, J. Cornelis, S. Peters, eds. (International Federation for Medical and Biological Engineering, Antwerp, 1990).

Pierre, P. R.

S. P. Sutera, P. R. Pierre, G. I. Zahalak, “Deduction of intrinsic mechanical properties of the erythrocyte membrane from observations of tank-treading in the rheoscope,” Biorheology 26, 177–197 (1989).
[PubMed]

Plazek, J.

Rao, P. R.

R. Tran-Son-Tay, S. P. Sutera, G. I. Zahalak, P. R. Rao, “Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow,” Biophys. J. 51, 915–924 (1987).
[CrossRef] [PubMed]

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46, 65–72 (1984).
[CrossRef] [PubMed]

Reynolds, L.

Schmidt-Schönbein, H.

T. Fischer, H. Schmidt-Schönbein, “Tank tread motion of red cell membranes in viscometric flow: behavior of intracellular and extracellular markers (with film),” Blood Cells 3, 351–365 (1977).

Shohet, S. B.

N. Mohandas, M. R. Clark, M. S. Jacobs, S. B. Shohet, “Analysis of factors regulating erythrocyte deformability,” J. Clin. Invest. 66, 563–573 (1980).
[CrossRef] [PubMed]

Skalak, R.

S. R. Keller, R. Skalak, “Motion of a tank-treading ellipsoidal particle in a shear flow,” J. Fluid Mech. 120, 27–47 (1982).
[CrossRef]

Sloot, P. M. A.

Storzicky, F.

F. Storzicky, V. Blazek, J. Muzik, “An improved diffractometric method for measurement of cellular deformability,” J. Biomech. 13, 417–421 (1980).
[CrossRef]

Streekstra, G. J.

G. J. Streekstra, E.-J. Nijhof, R. M. Heethaar, “A bi-plane rheoscope: a new approach in optical determination of red blood cell orientation and deformation in a Couette flow,” in Proceedings of the North Sea Conference on Biomedical Engineering, J. Cornelis, S. Peters, eds. (International Federation for Medical and Biological Engineering, Antwerp, 1990).

Sutera, S. P.

S. P. Sutera, P. R. Pierre, G. I. Zahalak, “Deduction of intrinsic mechanical properties of the erythrocyte membrane from observations of tank-treading in the rheoscope,” Biorheology 26, 177–197 (1989).
[PubMed]

R. Tran-Son-Tay, S. P. Sutera, G. I. Zahalak, P. R. Rao, “Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow,” Biophys. J. 51, 915–924 (1987).
[CrossRef] [PubMed]

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46, 65–72 (1984).
[CrossRef] [PubMed]

Tran-Son-Tay, R.

R. Tran-Son-Tay, S. P. Sutera, G. I. Zahalak, P. R. Rao, “Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow,” Biophys. J. 51, 915–924 (1987).
[CrossRef] [PubMed]

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46, 65–72 (1984).
[CrossRef] [PubMed]

van Breugel, J. H. F. I.

J. H. F. I. van Breugel, “Hemorheology and its role in blood platelet adhesion under flow conditions,” Ph.D. dissertation (State University of Utrecht, Utrecht, The Netherlands, 1989).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 11, p. 183.

Yeh, C.

Zahalak, G. I.

S. P. Sutera, P. R. Pierre, G. I. Zahalak, “Deduction of intrinsic mechanical properties of the erythrocyte membrane from observations of tank-treading in the rheoscope,” Biorheology 26, 177–197 (1989).
[PubMed]

R. Tran-Son-Tay, S. P. Sutera, G. I. Zahalak, P. R. Rao, “Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow,” Biophys. J. 51, 915–924 (1987).
[CrossRef] [PubMed]

Appl. Opt. (4)

Biophys. J. (3)

P. F. Mullaney, P. N. Dean, “The small angle light scattering of biological cells,” Biophys. J. 10, 764–772 (1970).
[CrossRef] [PubMed]

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46, 65–72 (1984).
[CrossRef] [PubMed]

R. Tran-Son-Tay, S. P. Sutera, G. I. Zahalak, P. R. Rao, “Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow,” Biophys. J. 51, 915–924 (1987).
[CrossRef] [PubMed]

Biorheology (1)

S. P. Sutera, P. R. Pierre, G. I. Zahalak, “Deduction of intrinsic mechanical properties of the erythrocyte membrane from observations of tank-treading in the rheoscope,” Biorheology 26, 177–197 (1989).
[PubMed]

Blood Cells (4)

C. Allard, N. Mohandas, M. Bessis, “Red cell deformability changes in hemolytic anemias estimated by diffractometric methods (ektacytometry),” Blood Cells 3, 209–221 (1977).

M. Bessis, N. Mohandas, “Laser diffraction patterns of sickle cells in fluid shear fields,” Blood Cells 3, 229–239 (1977).

T. Fischer, H. Schmidt-Schönbein, “Tank tread motion of red cell membranes in viscometric flow: behavior of intracellular and extracellular markers (with film),” Blood Cells 3, 351–365 (1977).

M. Bessis, N. Mohandas, “A diffractometric method for the measurement of cellular deformability,” Blood Cells 1, 307–313 (1975).

Clin. Chem. (1)

W. Groner, N. Mohandas, M. Bessis, “New optical technique for measuring erythrocyte deformability with the ektacytometer,” Clin. Chem. 26, 1435–1442 (1980).
[PubMed]

Clin. Chim. Acta (1)

M. R. Hardeman, P. Goedhart, D. Breederveld, “Laser diffraction ellipsometry of erythrocytes under controlled shear stress using a rotational viscosimeter,” Clin. Chim. Acta 165, 227–234 (1987).
[CrossRef] [PubMed]

J. Biomech. (1)

F. Storzicky, V. Blazek, J. Muzik, “An improved diffractometric method for measurement of cellular deformability,” J. Biomech. 13, 417–421 (1980).
[CrossRef]

J. Clin. Invest. (1)

N. Mohandas, M. R. Clark, M. S. Jacobs, S. B. Shohet, “Analysis of factors regulating erythrocyte deformability,” J. Clin. Invest. 66, 563–573 (1980).
[CrossRef] [PubMed]

J. Colloid Interface Sci. (2)

P. Latimer, “Light scattering by ellipsoids,” J. Colloid Interface Sci. 53, 102–109 (1975).
[CrossRef]

P. Latimer, P. Barber, “Scattering by ellipsoids of revolution,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

J. Fluid Mech. (1)

S. R. Keller, R. Skalak, “Motion of a tank-treading ellipsoidal particle in a shear flow,” J. Fluid Mech. 120, 27–47 (1982).
[CrossRef]

Science (1)

G. R. Cokelet, H. J. Meiselman, “Rheological comparison of hemoglobin solutions and erythrocyte suspensions,” Science 162, 275–277 (1968).
[CrossRef] [PubMed]

Other (6)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1957), App. A, p. 479.

Y. C. Fung, Biomechanics, 2nd ed. (Springer-Verlag, New York, 1984), Chap. 4, p. 106.

G. J. Streekstra, E.-J. Nijhof, R. M. Heethaar, “A bi-plane rheoscope: a new approach in optical determination of red blood cell orientation and deformation in a Couette flow,” in Proceedings of the North Sea Conference on Biomedical Engineering, J. Cornelis, S. Peters, eds. (International Federation for Medical and Biological Engineering, Antwerp, 1990).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 11, p. 183.

S. Chien, J. Dormandy, E. Ernst, A. Matrai, Clinical Hemorheology (Nijhoff, Boston, Mass., 1987), Chap. 5, p. 129.

J. H. F. I. van Breugel, “Hemorheology and its role in blood platelet adhesion under flow conditions,” Ph.D. dissertation (State University of Utrecht, Utrecht, The Netherlands, 1989).

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Figures (4)

Fig. 1
Fig. 1

Measuring configuration of the ektacytometer.

Fig. 2
Fig. 2

Coordinate system used in the calculations of the light scattering by red blood cells in a Couette flow. The ellipsoidal red cell is situated in origin O with the longest axis directed along the ɛ axis. The intensity pattern is calculated in point P(x, y, z).

Fig. 3
Fig. 3

Comparison of anomalous diffraction, Fraunhofer diffraction, and the Mie theory for a spherical model of the red blood cell (R = 3.9 μm, α = 52).

Fig. 4
Fig. 4

Normalized intensity patterns and the isointensity curves (insets) at shear stresses of 0.18 N/m2 (left panel) and 2.1 N/m2 (right panel). The solid curves represent the measurements and the dashed curves represent the theoretical curves (– – – – – anomalous diffraction;–––– –––––, Fraunhofer diffraction). The theoretical curves were normalized by setting the scattering intensity at zero degrees to unity. The experimental curves were shifted to obtain optimal agreement with the theoretical curves.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

DI = ( l s ) / ( l + s ) ,
I F = I 0 ( 1 / k 2 r 2 ) | S ( ν ) | 2 ,
S ( ν ) = α 2 [ J 1 ( α ν ) / α ν ] , r = ( x 2 + y 2 + z 2 ) 1 / 2 , ν = 1 r [ ( x 2 / q ) + q y 2 ] 1 / 2 , α = k A = ( 2 π n med / λ 0 ) A .
I A = I 0 ( 1 / k 2 r 2 ) | S ( ν ) | 2 ,
S ( ν ) = α 2 0 π / 2 [ 1 exp ( i ϕ max sin τ ) ] × J 0 ( α ν cos τ ) sin τ cos τ d τ , ϕ max = 2 kc | m 1 | .
x 2 / ( q z 2 ν 2 ) + y 2 / ( z 2 ν 2 / q ) = 1 .
n int = 1.335 + 0.001823 Hb + 8.6526 × 10 6 Hb 2 .
I = I 0 | S ( β , γ ) | 2 k 2 r 2 ,
r = ( x 2 + y 2 + z 2 ) 1 / 2 ,
β = x / r , γ = y / r .
S ( β , γ ) = ( k 2 / 2 π ) A s c exp [ i k ( ɛ β + η γ ) ] d ɛ d η .
ɛ = ( ρ / q ) cos δ , β = ( ν q ) cos φ , η = ( ρ q ) sin δ , γ = ( ν q ) sin φ ,
S ( ν , φ ) = ( k 2 / 2 π ) 0 A { 0 2 π exp [ ik ρ ν cos ( φ δ ) ] d δ } ρ d ρ ,
J 0 ( μ ) = ( 1 / 2 π ) 0 2 π exp [ i μ cos ( δ ) ] d δ ,
S ( ν ) = k 2 0 A J 0 ( k ν ρ ) ρ d ρ .
S ( ν ) = α 2 [ J 1 ( α ν ) / α ν ] ,
S ( β , γ ) = ( k 2 / 2 π ) A s c { 1 exp [ i ϕ ( ɛ , η ) ] } exp [ i k ( ɛ α + η γ ) ] d ɛ d η .
ϕ ( ɛ , η ) = 2 k c | m 1 | [ 1 ( ɛ 2 / a 2 ) ( η 2 / b 2 ) ] 1 / 2 .
S ( ν ) = k 2 0 A { 1 exp [ i ϕ ( ρ ) ] } J 0 ( k ν ρ ) ρ d ρ ,
S ( ν ) = α 2 0 π / 2 { 1 exp [ i ϕ max sin ( τ ) ] } × J 0 ( α ν cos τ ) sin τ cos τ d τ .

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