Abstract

At present, hemoglobin concentration and the volume of an erythrocyte can be determined from the intensities of light scattered by an individual cell at fixed angular intervals. This method is used in modern hemoglobin analyzers, but it requires calibration of optical and electronic units by certified particles of known size and refractive index. We describe a method that is based on the parametric solution of an inverse light-scattering problem and does not require a calibration procedure. The method is based on the use of parameters of the entire angular light-scattering pattern, called an indicatrix here. These parameters do not depend on the absolute intensity of light scattering. The indicatrix parameters form approximating equations that relate these parameters to the size and the phase-shift parameters of the particle. The applicability of the method is demonstrated by measurement of the indicatrices of individual sphered erythrocytes. The indicatrices of the individual erythrocytes were measured with a scanning flow cytometer at an angular range of from 15 to 55 deg. The volume and the hemoglobin concentration have been calculated by use of the developed method and by fitting of the experimental indicatrices to the indicatrices calculated from the Mie theory.

© 2000 Optical Society of America

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References

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  1. C. K. Lin, J. S. Lin, S. Y. Chen, M. L. Jiang, C. F. Chiu, “Comparison of hemoglobin and red blood cell distribution width in the differential diagnosis of microcytic anemia,” Arch. Pathol. Lab. Med. 116, 1030–1032 (1992).
    [PubMed]
  2. D. H. Tycko, M. H. Metz, E. A. Epstein, A. Grinbaum, “Flow-cytometric light scattering measurement of red blood cell volume and hemoglobin concentration,” Appl. Opt. 24, 1355–1365 (1985).
    [CrossRef] [PubMed]
  3. V. P. Maltsev, “Estimation of morphological characteristics of single particles from light scattering data in flow cytometry,” Russian Chem. Bull. 43, 1115–1124 (1994).
    [CrossRef]
  4. N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
    [PubMed]
  5. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Appendix A, p. 609.
  6. A. Bunyaratvej, S. Buthachat, S. Ratanasritong, S. Chitagatgone, “Thalassemic red cells determined by different technology of blood cell analyzers,” J. Med. Assoc. Thailand 75, 223–227 (1992).
  7. A. V. Chernyshev, V. I. Prots, A. A. Doroshkin, V. P. Maltsev, “Measurement of scattering properties of individual particles with a scanning flow cytometer,” Appl. Opt. 34, 6301–6305 (1995).
    [CrossRef] [PubMed]
  8. V. P. Maltsev, A. V. Chernyshev, K. A. Sem’yanov, 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]
  9. V. P. Maltsev, V. N. Lopatin, “A parametric solution of the inverse light-scattering problem for individual spherical particles,” Appl. Opt. 36, 6102–6108 (1997).
    [CrossRef] [PubMed]
  10. URL: http://bioeng.seas.upenn.edu/courses/BE210/Hgbextdata.txt .
  11. M. Hammer, D. Schweitzer, B. Michel, E. Thamm, A. Kolb, “Single scattering by red blood cells,” Appl. Opt. 37, 7410–7418 (1998).
    [CrossRef]
  12. 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]
  13. J. T. Saari, J. S. Beck, “Hypotonic hemolysis of human red blood cells: a two-phase process,” J. Membr. Biol. 23, 213–226 (1975).
    [CrossRef] [PubMed]
  14. 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]
  15. A. Porath Furedi, “The mutual effect of hydrogen ion concentration and osmotic pressure on the shape of the human erythrocyte as determined by light scattering and by electronic cell volume measurement,” Cytometry 4, 263–267 (1983).
    [CrossRef] [PubMed]
  16. Y. R. Kim, L. Ornstein, “Isovolumetric sphering of erytrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3, 419–427 (1983).
    [CrossRef] [PubMed]

1999 (1)

1998 (2)

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

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]

1997 (1)

1996 (1)

1995 (1)

1994 (1)

V. P. Maltsev, “Estimation of morphological characteristics of single particles from light scattering data in flow cytometry,” Russian Chem. Bull. 43, 1115–1124 (1994).
[CrossRef]

1992 (2)

C. K. Lin, J. S. Lin, S. Y. Chen, M. L. Jiang, C. F. Chiu, “Comparison of hemoglobin and red blood cell distribution width in the differential diagnosis of microcytic anemia,” Arch. Pathol. Lab. Med. 116, 1030–1032 (1992).
[PubMed]

A. Bunyaratvej, S. Buthachat, S. Ratanasritong, S. Chitagatgone, “Thalassemic red cells determined by different technology of blood cell analyzers,” J. Med. Assoc. Thailand 75, 223–227 (1992).

1986 (1)

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

1985 (1)

1983 (2)

A. Porath Furedi, “The mutual effect of hydrogen ion concentration and osmotic pressure on the shape of the human erythrocyte as determined by light scattering and by electronic cell volume measurement,” Cytometry 4, 263–267 (1983).
[CrossRef] [PubMed]

Y. R. Kim, L. Ornstein, “Isovolumetric sphering of erytrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3, 419–427 (1983).
[CrossRef] [PubMed]

1975 (1)

J. T. Saari, J. S. Beck, “Hypotonic hemolysis of human red blood cells: a two-phase process,” J. Membr. Biol. 23, 213–226 (1975).
[CrossRef] [PubMed]

Beck, J. S.

J. T. Saari, J. S. Beck, “Hypotonic hemolysis of human red blood cells: a two-phase process,” J. Membr. Biol. 23, 213–226 (1975).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Appendix A, p. 609.

Bunyaratvej, A.

A. Bunyaratvej, S. Buthachat, S. Ratanasritong, S. Chitagatgone, “Thalassemic red cells determined by different technology of blood cell analyzers,” J. Med. Assoc. Thailand 75, 223–227 (1992).

Buthachat, S.

A. Bunyaratvej, S. Buthachat, S. Ratanasritong, S. Chitagatgone, “Thalassemic red cells determined by different technology of blood cell analyzers,” J. Med. Assoc. Thailand 75, 223–227 (1992).

Chen, S. Y.

C. K. Lin, J. S. Lin, S. Y. Chen, M. L. Jiang, C. F. Chiu, “Comparison of hemoglobin and red blood cell distribution width in the differential diagnosis of microcytic anemia,” Arch. Pathol. Lab. Med. 116, 1030–1032 (1992).
[PubMed]

Chernyshev, A. V.

Chitagatgone, S.

A. Bunyaratvej, S. Buthachat, S. Ratanasritong, S. Chitagatgone, “Thalassemic red cells determined by different technology of blood cell analyzers,” J. Med. Assoc. Thailand 75, 223–227 (1992).

Chiu, C. F.

C. K. Lin, J. S. Lin, S. Y. Chen, M. L. Jiang, C. F. Chiu, “Comparison of hemoglobin and red blood cell distribution width in the differential diagnosis of microcytic anemia,” Arch. Pathol. Lab. Med. 116, 1030–1032 (1992).
[PubMed]

Doroshkin, A. A.

Epstein, E. A.

Grinbaum, A.

Groner, W.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Hammer, M.

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]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Appendix A, p. 609.

Jiang, M. L.

C. K. Lin, J. S. Lin, S. Y. Chen, M. L. Jiang, C. F. Chiu, “Comparison of hemoglobin and red blood cell distribution width in the differential diagnosis of microcytic anemia,” Arch. Pathol. Lab. Med. 116, 1030–1032 (1992).
[PubMed]

Kim, Y. R.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Y. R. Kim, L. Ornstein, “Isovolumetric sphering of erytrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3, 419–427 (1983).
[CrossRef] [PubMed]

Kolb, A.

Lin, C. K.

C. K. Lin, J. S. Lin, S. Y. Chen, M. L. Jiang, C. F. Chiu, “Comparison of hemoglobin and red blood cell distribution width in the differential diagnosis of microcytic anemia,” Arch. Pathol. Lab. Med. 116, 1030–1032 (1992).
[PubMed]

Lin, J. S.

C. K. Lin, J. S. Lin, S. Y. Chen, M. L. Jiang, C. F. Chiu, “Comparison of hemoglobin and red blood cell distribution width in the differential diagnosis of microcytic anemia,” Arch. Pathol. Lab. Med. 116, 1030–1032 (1992).
[PubMed]

Lopatin, V. N.

Maltsev, V. P.

Metz, M. H.

Michel, B.

Mohandas, N.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Orlik, J.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Ornstein, L.

Y. R. Kim, L. Ornstein, “Isovolumetric sphering of erytrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3, 419–427 (1983).
[CrossRef] [PubMed]

Porath Furedi, A.

A. Porath Furedi, “The mutual effect of hydrogen ion concentration and osmotic pressure on the shape of the human erythrocyte as determined by light scattering and by electronic cell volume measurement,” Cytometry 4, 263–267 (1983).
[CrossRef] [PubMed]

Prots, V. I.

Ratanasritong, S.

A. Bunyaratvej, S. Buthachat, S. Ratanasritong, S. Chitagatgone, “Thalassemic red cells determined by different technology of blood cell analyzers,” J. Med. Assoc. Thailand 75, 223–227 (1992).

Saari, J. T.

J. T. Saari, J. S. Beck, “Hypotonic hemolysis of human red blood cells: a two-phase process,” J. Membr. Biol. 23, 213–226 (1975).
[CrossRef] [PubMed]

Schweitzer, D.

Sem’yanov, K. A.

Shvalov, A. N.

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, 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]

Tarasov, P. A.

Thamm, E.

Tycko, D. H.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

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

Wyatt, J.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Appl. Opt. (6)

Arch. Pathol. Lab. Med. (1)

C. K. Lin, J. S. Lin, S. Y. Chen, M. L. Jiang, C. F. Chiu, “Comparison of hemoglobin and red blood cell distribution width in the differential diagnosis of microcytic anemia,” Arch. Pathol. Lab. Med. 116, 1030–1032 (1992).
[PubMed]

Blood (1)

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Cytometry (3)

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. Porath Furedi, “The mutual effect of hydrogen ion concentration and osmotic pressure on the shape of the human erythrocyte as determined by light scattering and by electronic cell volume measurement,” Cytometry 4, 263–267 (1983).
[CrossRef] [PubMed]

Y. R. Kim, L. Ornstein, “Isovolumetric sphering of erytrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3, 419–427 (1983).
[CrossRef] [PubMed]

J. Med. Assoc. Thailand (1)

A. Bunyaratvej, S. Buthachat, S. Ratanasritong, S. Chitagatgone, “Thalassemic red cells determined by different technology of blood cell analyzers,” J. Med. Assoc. Thailand 75, 223–227 (1992).

J. Membr. Biol. (1)

J. T. Saari, J. S. Beck, “Hypotonic hemolysis of human red blood cells: a two-phase process,” J. Membr. Biol. 23, 213–226 (1975).
[CrossRef] [PubMed]

Russian Chem. Bull. (1)

V. P. Maltsev, “Estimation of morphological characteristics of single particles from light scattering data in flow cytometry,” Russian Chem. Bull. 43, 1115–1124 (1994).
[CrossRef]

Other (2)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Appendix A, p. 609.

URL: http://bioeng.seas.upenn.edu/courses/BE210/Hgbextdata.txt .

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Figures (6)

Fig. 1
Fig. 1

Indicatrix of an individual homogeneous sphere calculated from Mie theory. The refractive index of the surrounding medium is 1.333, water.

Fig. 2
Fig. 2

Parametric plot. The indicatrix parameters Δ2(15) and L(15) were evaluated from indicatrices that were calculated within such a size and refractive-index region that corresponds to the characteristics of a typical erythrocyte. The plot region is divided into three subregions by lines, and the corresponding equations are shown on the plot.

Fig. 3
Fig. 3

Size parameter as a function of the indicatrix fringe pitch Δ2(15). The points marked by 1, 2, and 3 correspond to the subregions in Fig. 2.

Fig. 4
Fig. 4

Phase-shift parameter as a function of the indicatrix forward visibility V f (15).

Fig. 5
Fig. 5

Experimental indicatrices of (a) individual nonspherical and spherical erythrocytes and (b) a spherical erythrocyte processed with a flying light-scattering indicatrix method and with a fit of Mie theory.

Fig. 6
Fig. 6

Analysis of a blood sample containing sphered erythrocytes. The results of the analysis are shown as (a) the erythrocyte hemoglobin content versus the volume map, histograms of the distribution of (b) the erythrocyte volume, and (c) the hemoglobin content.

Tables (1)

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Table 1 Approximating Equations for Calculation of Size and Phase-Shift Parameters

Equations (4)

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nR-n0=β×HbC,
nI=14π λσ×HbC NAM,
α=p11+p2Vf15Δ215+p3Vf154,
ρ=q11+q2Δ2151-q3Vf15cos-1Vf15-q41-q41/2,

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