Abstract

We describe a method to obtain the fraction of poorly deformable red blood cells in a blood sample from the intensity pattern in an ektacytometer. In an ektacytometer red blood cells are transformed into ellipsoids by a shear flow between two transparent cylinders. The intensity pattern, due to a laser beam that is sent through the suspension, is projected on a screen. When measuring a healthy red blood cell population iso-intensity curves are ellipses with an axial ratio equal to that of the average red blood cell. In contrast poorly deformable cells result in circular iso-intensity curves. In this study we show that for mixtures of deformable and poorly deformable red blood cells, iso-intensity curves in the composite intensity pattern are neither elliptical nor circular but obtain cross-like shapes. We propose a method to obtain the fraction of poorly deformable red blood cells from those intensity patterns. Experiments with mixtures of poorly deformable and deformable red blood cells validate the method and demonstrate its accuracy. In a clinical setting our approach is potentially of great value for the detection of the fraction of sickle cells in blood samples of patients with sickle cell disease or to find a measure for the parasitemia in patients infected with malaria.

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References

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  1. M. Bessis and N. Mohandas, “Laser Diffraction Patterns of Sickle Cells in Fluid Shear Fields,” Blood Cells 3, 229–239 (1977).
  2. J. G. G. Dobbe, M. R. Hardeman, G. J. Streekstra, J. Strackee, C. Ince, and C. A. Grimbergen, “Analyzing red blood cell-deformability distributions,” Blood Cells Mol. Dis. 28(3), 373–384 (2002).
    [CrossRef] [PubMed]
  3. Y. C. Fung, Biomechanics, (Springer Verlag, New York, 1984).
  4. R. M. Johnson, C. J. Féo, M. Nossal, and I. Dobo, “Evaluation of covalent antisickling compounds by PO2 scan ektacytometry,” Blood 66(2), 432–438 (1985).
    [PubMed]
  5. S. Chien, J. Dormandy, E. Ernst, and A. Matrai, Clinical Hemorheology (Martinus Nijhoff publishers, Boston, 1987), p. 238.
    [PubMed]
  6. T. Fischer and 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).
  7. M. Bessis and N. Mohandas, “A Diffractometric Method for the Measurement of Cellular Deformability,” Blood Cells 1, 307–313 (1975).
  8. M. R. Hardeman, P. T. Goedhart, J. G. G. Dobbe, and K. P. Lettinga, “Laser-assisted Optical Rotational Analyser (LORCA); A new instrument for measurement of various structural hemorheological parameters,” Clin. Hemorheol. 14(4), 605–619 (1994).
  9. J. G. G. Dobbe, G. J. Streekstra, M. R. Hardeman, C. Ince, and C. A. Grimbergen, “Measurement of the distribution of red blood cell deformability using an automated rheoscope,” Cytometry 50(6), 313–325 (2002).
    [CrossRef] [PubMed]
  10. G. J. Streekstra, A. G. Hoekstra, and R. M. Heethaar, “Anomalous diffraction by arbitrarily oriented ellipsoids: applications in ektacytometry,” Appl. Opt. 33(31), 7288–7296 (1994).
    [CrossRef] [PubMed]
  11. C. Allard, N. Mohandas, and M. Bessis, “Red Cell Deformability Changes in Hemolytic Anemias Estimated by Diffractometric Methods (Ektacytometry),” Blood Cells 3, 209–221 (1977).
  12. M. Bessis, N. Mohandas, and C. Feo, “Automated ektacytometry: a new method of measuring red cell deformability and red cell indices,” Blood Cells 6(3), 315–327 (1980).
    [PubMed]
  13. J. Plasek and T. Marik, “Determination of undeformable erythrocytes in blood samples using laser light scattering,” Appl. Opt. 21(23), 4335–4338 (1982).
    [CrossRef] [PubMed]
  14. M. Bessis, C. Feo, and E. Jones, “Quantitation of red cell deformability during progressive deoxygenation and oxygenation in sickling disorders (the use of an automated Ektacytometer),” Blood Cells 8(1), 17–28 (1982).
    [PubMed]
  15. D. J. Abraham, A. S. Mehanna, F. C. Wireko, J. Whitney, R. P. Thomas, and E. P. Orringer, “Vanillin, a potential agent for the treatment of sickle cell anemia,” Blood 77(6), 1334–1341 (1991).
    [PubMed]
  16. L. Lawson, and J. Hanson, Solving Least Squares Problems, (Prentice-Hall, Englewood Cliffs, N.J., 1974), pp. 18.
  17. S. Twomey, Introduction to the mathematics of inversion in remote sensing and indirect measurements, (Elsevier Scientific Publishing Company, Amsterdam, 1977), pp. 115.
  18. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, (Cambridge University Press, Cambridge, 1988), pp. 528.
  19. G. J. Streekstra, A. G. Hoekstra, E. J. Nijhof, and R. M. Heethaar, “Light scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction,” Appl. Opt. 32, 2266–2272 (1993).
    [CrossRef] [PubMed]
  20. H. C. van de Hulst, Light Scattering by Small Particles, (Wiley, New York, 1957), pp. 3.
  21. M. R. Hardeman, R. M. Bauersachs, and H. J. Meiselman, “RBC Laser diffractometry and RBC Aggregometry with a rotational viscometer: comparison with rheoscope and Myrenne Aggregometer,” Clin. Hemorheol. 8, 581–593 (1988).

2002 (2)

J. G. G. Dobbe, M. R. Hardeman, G. J. Streekstra, J. Strackee, C. Ince, and C. A. Grimbergen, “Analyzing red blood cell-deformability distributions,” Blood Cells Mol. Dis. 28(3), 373–384 (2002).
[CrossRef] [PubMed]

J. G. G. Dobbe, G. J. Streekstra, M. R. Hardeman, C. Ince, and C. A. Grimbergen, “Measurement of the distribution of red blood cell deformability using an automated rheoscope,” Cytometry 50(6), 313–325 (2002).
[CrossRef] [PubMed]

1994 (2)

G. J. Streekstra, A. G. Hoekstra, and R. M. Heethaar, “Anomalous diffraction by arbitrarily oriented ellipsoids: applications in ektacytometry,” Appl. Opt. 33(31), 7288–7296 (1994).
[CrossRef] [PubMed]

M. R. Hardeman, P. T. Goedhart, J. G. G. Dobbe, and K. P. Lettinga, “Laser-assisted Optical Rotational Analyser (LORCA); A new instrument for measurement of various structural hemorheological parameters,” Clin. Hemorheol. 14(4), 605–619 (1994).

1993 (1)

1991 (1)

D. J. Abraham, A. S. Mehanna, F. C. Wireko, J. Whitney, R. P. Thomas, and E. P. Orringer, “Vanillin, a potential agent for the treatment of sickle cell anemia,” Blood 77(6), 1334–1341 (1991).
[PubMed]

1988 (1)

M. R. Hardeman, R. M. Bauersachs, and H. J. Meiselman, “RBC Laser diffractometry and RBC Aggregometry with a rotational viscometer: comparison with rheoscope and Myrenne Aggregometer,” Clin. Hemorheol. 8, 581–593 (1988).

1985 (1)

R. M. Johnson, C. J. Féo, M. Nossal, and I. Dobo, “Evaluation of covalent antisickling compounds by PO2 scan ektacytometry,” Blood 66(2), 432–438 (1985).
[PubMed]

1982 (2)

J. Plasek and T. Marik, “Determination of undeformable erythrocytes in blood samples using laser light scattering,” Appl. Opt. 21(23), 4335–4338 (1982).
[CrossRef] [PubMed]

M. Bessis, C. Feo, and E. Jones, “Quantitation of red cell deformability during progressive deoxygenation and oxygenation in sickling disorders (the use of an automated Ektacytometer),” Blood Cells 8(1), 17–28 (1982).
[PubMed]

1980 (1)

M. Bessis, N. Mohandas, and C. Feo, “Automated ektacytometry: a new method of measuring red cell deformability and red cell indices,” Blood Cells 6(3), 315–327 (1980).
[PubMed]

1977 (3)

T. Fischer and 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 and N. Mohandas, “Laser Diffraction Patterns of Sickle Cells in Fluid Shear Fields,” Blood Cells 3, 229–239 (1977).

C. Allard, N. Mohandas, and M. Bessis, “Red Cell Deformability Changes in Hemolytic Anemias Estimated by Diffractometric Methods (Ektacytometry),” Blood Cells 3, 209–221 (1977).

1975 (1)

M. Bessis and N. Mohandas, “A Diffractometric Method for the Measurement of Cellular Deformability,” Blood Cells 1, 307–313 (1975).

Abraham, D. J.

D. J. Abraham, A. S. Mehanna, F. C. Wireko, J. Whitney, R. P. Thomas, and E. P. Orringer, “Vanillin, a potential agent for the treatment of sickle cell anemia,” Blood 77(6), 1334–1341 (1991).
[PubMed]

Allard, C.

C. Allard, N. Mohandas, and M. Bessis, “Red Cell Deformability Changes in Hemolytic Anemias Estimated by Diffractometric Methods (Ektacytometry),” Blood Cells 3, 209–221 (1977).

Bauersachs, R. M.

M. R. Hardeman, R. M. Bauersachs, and H. J. Meiselman, “RBC Laser diffractometry and RBC Aggregometry with a rotational viscometer: comparison with rheoscope and Myrenne Aggregometer,” Clin. Hemorheol. 8, 581–593 (1988).

Bessis, M.

M. Bessis, C. Feo, and E. Jones, “Quantitation of red cell deformability during progressive deoxygenation and oxygenation in sickling disorders (the use of an automated Ektacytometer),” Blood Cells 8(1), 17–28 (1982).
[PubMed]

M. Bessis, N. Mohandas, and C. Feo, “Automated ektacytometry: a new method of measuring red cell deformability and red cell indices,” Blood Cells 6(3), 315–327 (1980).
[PubMed]

C. Allard, N. Mohandas, and M. Bessis, “Red Cell Deformability Changes in Hemolytic Anemias Estimated by Diffractometric Methods (Ektacytometry),” Blood Cells 3, 209–221 (1977).

M. Bessis and N. Mohandas, “Laser Diffraction Patterns of Sickle Cells in Fluid Shear Fields,” Blood Cells 3, 229–239 (1977).

M. Bessis and N. Mohandas, “A Diffractometric Method for the Measurement of Cellular Deformability,” Blood Cells 1, 307–313 (1975).

Dobbe, J. G. G.

J. G. G. Dobbe, M. R. Hardeman, G. J. Streekstra, J. Strackee, C. Ince, and C. A. Grimbergen, “Analyzing red blood cell-deformability distributions,” Blood Cells Mol. Dis. 28(3), 373–384 (2002).
[CrossRef] [PubMed]

J. G. G. Dobbe, G. J. Streekstra, M. R. Hardeman, C. Ince, and C. A. Grimbergen, “Measurement of the distribution of red blood cell deformability using an automated rheoscope,” Cytometry 50(6), 313–325 (2002).
[CrossRef] [PubMed]

M. R. Hardeman, P. T. Goedhart, J. G. G. Dobbe, and K. P. Lettinga, “Laser-assisted Optical Rotational Analyser (LORCA); A new instrument for measurement of various structural hemorheological parameters,” Clin. Hemorheol. 14(4), 605–619 (1994).

Dobo, I.

R. M. Johnson, C. J. Féo, M. Nossal, and I. Dobo, “Evaluation of covalent antisickling compounds by PO2 scan ektacytometry,” Blood 66(2), 432–438 (1985).
[PubMed]

Feo, C.

M. Bessis, C. Feo, and E. Jones, “Quantitation of red cell deformability during progressive deoxygenation and oxygenation in sickling disorders (the use of an automated Ektacytometer),” Blood Cells 8(1), 17–28 (1982).
[PubMed]

M. Bessis, N. Mohandas, and C. Feo, “Automated ektacytometry: a new method of measuring red cell deformability and red cell indices,” Blood Cells 6(3), 315–327 (1980).
[PubMed]

Féo, C. J.

R. M. Johnson, C. J. Féo, M. Nossal, and I. Dobo, “Evaluation of covalent antisickling compounds by PO2 scan ektacytometry,” Blood 66(2), 432–438 (1985).
[PubMed]

Fischer, T.

T. Fischer and 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).

Goedhart, P. T.

M. R. Hardeman, P. T. Goedhart, J. G. G. Dobbe, and K. P. Lettinga, “Laser-assisted Optical Rotational Analyser (LORCA); A new instrument for measurement of various structural hemorheological parameters,” Clin. Hemorheol. 14(4), 605–619 (1994).

Grimbergen, C. A.

J. G. G. Dobbe, M. R. Hardeman, G. J. Streekstra, J. Strackee, C. Ince, and C. A. Grimbergen, “Analyzing red blood cell-deformability distributions,” Blood Cells Mol. Dis. 28(3), 373–384 (2002).
[CrossRef] [PubMed]

J. G. G. Dobbe, G. J. Streekstra, M. R. Hardeman, C. Ince, and C. A. Grimbergen, “Measurement of the distribution of red blood cell deformability using an automated rheoscope,” Cytometry 50(6), 313–325 (2002).
[CrossRef] [PubMed]

Hardeman, M. R.

J. G. G. Dobbe, G. J. Streekstra, M. R. Hardeman, C. Ince, and C. A. Grimbergen, “Measurement of the distribution of red blood cell deformability using an automated rheoscope,” Cytometry 50(6), 313–325 (2002).
[CrossRef] [PubMed]

J. G. G. Dobbe, M. R. Hardeman, G. J. Streekstra, J. Strackee, C. Ince, and C. A. Grimbergen, “Analyzing red blood cell-deformability distributions,” Blood Cells Mol. Dis. 28(3), 373–384 (2002).
[CrossRef] [PubMed]

M. R. Hardeman, P. T. Goedhart, J. G. G. Dobbe, and K. P. Lettinga, “Laser-assisted Optical Rotational Analyser (LORCA); A new instrument for measurement of various structural hemorheological parameters,” Clin. Hemorheol. 14(4), 605–619 (1994).

M. R. Hardeman, R. M. Bauersachs, and H. J. Meiselman, “RBC Laser diffractometry and RBC Aggregometry with a rotational viscometer: comparison with rheoscope and Myrenne Aggregometer,” Clin. Hemorheol. 8, 581–593 (1988).

Heethaar, R. M.

Hoekstra, A. G.

Ince, C.

J. G. G. Dobbe, M. R. Hardeman, G. J. Streekstra, J. Strackee, C. Ince, and C. A. Grimbergen, “Analyzing red blood cell-deformability distributions,” Blood Cells Mol. Dis. 28(3), 373–384 (2002).
[CrossRef] [PubMed]

J. G. G. Dobbe, G. J. Streekstra, M. R. Hardeman, C. Ince, and C. A. Grimbergen, “Measurement of the distribution of red blood cell deformability using an automated rheoscope,” Cytometry 50(6), 313–325 (2002).
[CrossRef] [PubMed]

Johnson, R. M.

R. M. Johnson, C. J. Féo, M. Nossal, and I. Dobo, “Evaluation of covalent antisickling compounds by PO2 scan ektacytometry,” Blood 66(2), 432–438 (1985).
[PubMed]

Jones, E.

M. Bessis, C. Feo, and E. Jones, “Quantitation of red cell deformability during progressive deoxygenation and oxygenation in sickling disorders (the use of an automated Ektacytometer),” Blood Cells 8(1), 17–28 (1982).
[PubMed]

Lettinga, K. P.

M. R. Hardeman, P. T. Goedhart, J. G. G. Dobbe, and K. P. Lettinga, “Laser-assisted Optical Rotational Analyser (LORCA); A new instrument for measurement of various structural hemorheological parameters,” Clin. Hemorheol. 14(4), 605–619 (1994).

Marik, T.

Mehanna, A. S.

D. J. Abraham, A. S. Mehanna, F. C. Wireko, J. Whitney, R. P. Thomas, and E. P. Orringer, “Vanillin, a potential agent for the treatment of sickle cell anemia,” Blood 77(6), 1334–1341 (1991).
[PubMed]

Meiselman, H. J.

M. R. Hardeman, R. M. Bauersachs, and H. J. Meiselman, “RBC Laser diffractometry and RBC Aggregometry with a rotational viscometer: comparison with rheoscope and Myrenne Aggregometer,” Clin. Hemorheol. 8, 581–593 (1988).

Mohandas, N.

M. Bessis, N. Mohandas, and C. Feo, “Automated ektacytometry: a new method of measuring red cell deformability and red cell indices,” Blood Cells 6(3), 315–327 (1980).
[PubMed]

C. Allard, N. Mohandas, and M. Bessis, “Red Cell Deformability Changes in Hemolytic Anemias Estimated by Diffractometric Methods (Ektacytometry),” Blood Cells 3, 209–221 (1977).

M. Bessis and N. Mohandas, “Laser Diffraction Patterns of Sickle Cells in Fluid Shear Fields,” Blood Cells 3, 229–239 (1977).

M. Bessis and N. Mohandas, “A Diffractometric Method for the Measurement of Cellular Deformability,” Blood Cells 1, 307–313 (1975).

Nijhof, E. J.

Nossal, M.

R. M. Johnson, C. J. Féo, M. Nossal, and I. Dobo, “Evaluation of covalent antisickling compounds by PO2 scan ektacytometry,” Blood 66(2), 432–438 (1985).
[PubMed]

Orringer, E. P.

D. J. Abraham, A. S. Mehanna, F. C. Wireko, J. Whitney, R. P. Thomas, and E. P. Orringer, “Vanillin, a potential agent for the treatment of sickle cell anemia,” Blood 77(6), 1334–1341 (1991).
[PubMed]

Plasek, J.

Schmidt Schönbein, H.

T. Fischer and 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).

Strackee, J.

J. G. G. Dobbe, M. R. Hardeman, G. J. Streekstra, J. Strackee, C. Ince, and C. A. Grimbergen, “Analyzing red blood cell-deformability distributions,” Blood Cells Mol. Dis. 28(3), 373–384 (2002).
[CrossRef] [PubMed]

Streekstra, G. J.

J. G. G. Dobbe, M. R. Hardeman, G. J. Streekstra, J. Strackee, C. Ince, and C. A. Grimbergen, “Analyzing red blood cell-deformability distributions,” Blood Cells Mol. Dis. 28(3), 373–384 (2002).
[CrossRef] [PubMed]

J. G. G. Dobbe, G. J. Streekstra, M. R. Hardeman, C. Ince, and C. A. Grimbergen, “Measurement of the distribution of red blood cell deformability using an automated rheoscope,” Cytometry 50(6), 313–325 (2002).
[CrossRef] [PubMed]

G. J. Streekstra, A. G. Hoekstra, and R. M. Heethaar, “Anomalous diffraction by arbitrarily oriented ellipsoids: applications in ektacytometry,” Appl. Opt. 33(31), 7288–7296 (1994).
[CrossRef] [PubMed]

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

Thomas, R. P.

D. J. Abraham, A. S. Mehanna, F. C. Wireko, J. Whitney, R. P. Thomas, and E. P. Orringer, “Vanillin, a potential agent for the treatment of sickle cell anemia,” Blood 77(6), 1334–1341 (1991).
[PubMed]

Whitney, J.

D. J. Abraham, A. S. Mehanna, F. C. Wireko, J. Whitney, R. P. Thomas, and E. P. Orringer, “Vanillin, a potential agent for the treatment of sickle cell anemia,” Blood 77(6), 1334–1341 (1991).
[PubMed]

Wireko, F. C.

D. J. Abraham, A. S. Mehanna, F. C. Wireko, J. Whitney, R. P. Thomas, and E. P. Orringer, “Vanillin, a potential agent for the treatment of sickle cell anemia,” Blood 77(6), 1334–1341 (1991).
[PubMed]

Appl. Opt. (3)

Blood (2)

D. J. Abraham, A. S. Mehanna, F. C. Wireko, J. Whitney, R. P. Thomas, and E. P. Orringer, “Vanillin, a potential agent for the treatment of sickle cell anemia,” Blood 77(6), 1334–1341 (1991).
[PubMed]

R. M. Johnson, C. J. Féo, M. Nossal, and I. Dobo, “Evaluation of covalent antisickling compounds by PO2 scan ektacytometry,” Blood 66(2), 432–438 (1985).
[PubMed]

Blood Cells (6)

M. Bessis and N. Mohandas, “Laser Diffraction Patterns of Sickle Cells in Fluid Shear Fields,” Blood Cells 3, 229–239 (1977).

T. Fischer and 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 and N. Mohandas, “A Diffractometric Method for the Measurement of Cellular Deformability,” Blood Cells 1, 307–313 (1975).

M. Bessis, C. Feo, and E. Jones, “Quantitation of red cell deformability during progressive deoxygenation and oxygenation in sickling disorders (the use of an automated Ektacytometer),” Blood Cells 8(1), 17–28 (1982).
[PubMed]

C. Allard, N. Mohandas, and M. Bessis, “Red Cell Deformability Changes in Hemolytic Anemias Estimated by Diffractometric Methods (Ektacytometry),” Blood Cells 3, 209–221 (1977).

M. Bessis, N. Mohandas, and C. Feo, “Automated ektacytometry: a new method of measuring red cell deformability and red cell indices,” Blood Cells 6(3), 315–327 (1980).
[PubMed]

Blood Cells Mol. Dis. (1)

J. G. G. Dobbe, M. R. Hardeman, G. J. Streekstra, J. Strackee, C. Ince, and C. A. Grimbergen, “Analyzing red blood cell-deformability distributions,” Blood Cells Mol. Dis. 28(3), 373–384 (2002).
[CrossRef] [PubMed]

Clin. Hemorheol. (2)

M. R. Hardeman, P. T. Goedhart, J. G. G. Dobbe, and K. P. Lettinga, “Laser-assisted Optical Rotational Analyser (LORCA); A new instrument for measurement of various structural hemorheological parameters,” Clin. Hemorheol. 14(4), 605–619 (1994).

M. R. Hardeman, R. M. Bauersachs, and H. J. Meiselman, “RBC Laser diffractometry and RBC Aggregometry with a rotational viscometer: comparison with rheoscope and Myrenne Aggregometer,” Clin. Hemorheol. 8, 581–593 (1988).

Cytometry (1)

J. G. G. Dobbe, G. J. Streekstra, M. R. Hardeman, C. Ince, and C. A. Grimbergen, “Measurement of the distribution of red blood cell deformability using an automated rheoscope,” Cytometry 50(6), 313–325 (2002).
[CrossRef] [PubMed]

Other (6)

Y. C. Fung, Biomechanics, (Springer Verlag, New York, 1984).

S. Chien, J. Dormandy, E. Ernst, and A. Matrai, Clinical Hemorheology (Martinus Nijhoff publishers, Boston, 1987), p. 238.
[PubMed]

L. Lawson, and J. Hanson, Solving Least Squares Problems, (Prentice-Hall, Englewood Cliffs, N.J., 1974), pp. 18.

S. Twomey, Introduction to the mathematics of inversion in remote sensing and indirect measurements, (Elsevier Scientific Publishing Company, Amsterdam, 1977), pp. 115.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, (Cambridge University Press, Cambridge, 1988), pp. 528.

H. C. van de Hulst, Light Scattering by Small Particles, (Wiley, New York, 1957), pp. 3.

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Figures (5)

Fig. 1
Fig. 1

Ellipsoidal particle with semi-axes a, b and c illuminated by a laser beam. The b-axis is in the y-direction perpendicular to the x-z plane.

Fig. 2
Fig. 2

Isointensity curves of a 1:1 mixture of oblate (q = 1, α = 56.9) and prolate (q = 4.7, α = 48.5) spheroids. The volumes of the particles are 95 fl. The isointensity curves 1, 2 and 3 represent intensities I(0)/2, I(0)/4, and I(0)/10 respectively (I(0) is the intensity at the center of the screen).

Fig. 3
Fig. 3

Isointensity curves in the intensity patterns of suspensions with different fractions nu of poorly deformable cells (top row: left nu = 1.0, right nu = 0.0; bottom row: left nu = 0.75, right nu = 0.25).

Fig. 4
Fig. 4

Isointensity curves in the intensity pattern of a 1:1 mixture (nu = 0.50) of poorly deformable (1) and deformable (3) red blood cells.

Fig. 5
Fig. 5

The measured fractions of poorly deformable red blood cells nu(measured) versus the fractions of poorly deformable cells in the prepared samples nu(sample).

Equations (6)

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

I A = I o ( 1 / k 2 r 2 ) | S ( ν ) | 2 ,
S ( ν ) = α 2 0 π / 2 [ 1 - exp ( - i ϕ max sin τ ) ] J o ( α ν cos τ ) sin τ cos τ d τ , α = k a b , ϕ max = 2 k c ( m - 1 ) , q = a / b , ν = 1 r [ ( x 2 / q ) + q y 2 ] 1 / 2 , r = ( x 2 + y 2 + z 2 ) 1 / 2 .
I s c ( x , y ) = n 1 I ( x , y , q 1 ) + n 2 I ( x , y , q 2 ) .
I m e a s = I m a t n .
n = I m a t - 1 I m e a s .
n u = n 1 / ( n 1 + n 2 ) .,

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