Abstract

A light scattering technique for simultaneously determining the volume (V) and hemoglobin concentration (HC) of individual sphered red blood cells (RBCs) is described. Light scattered into two angular intervals yields measurements S1 and S2, respectively. Since a sphered RBC is essentially a homogeneous dielectric sphere having a complex refractive index that is linear in HC, with a proper choice of detector acceptance angles, tables relating V and HC to S1 and S2 can be computed via Mie theory. Absolute calibration is possible using droplets of water-immisible oils of accurately known refractive index. Results of experimental tests of the method are compared with those obtained from hematological reference measurements.

© 1985 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. For concise reviews of the subject and extensive bibliographies, see T. M. Jovin et al., “Automatic Sizing and Separation of Particles by Ratios of Light Scattering Intensities,” J. Histochem. Cytochem. 24, 269 (1976);G. C. Salzman, “Flow Cytometry: The Use of Lasers for Rapid Analysis and Separation of Single Biological Cells,” in The Biomedical Laser, L. Goldman, Ed. (Springer, New York, 1981), Chap. 5.
    [CrossRef] [PubMed]
  2. L. P. Bayvel, A. R. Jones, Electromagnetic Scattering and Its Applications (Applied Science, London, 1981), pp. 22–47.
  3. M. M. Wintrobe et al., Clinical Hematology (Lea & Febiger, Philadelphia, 1981), p. 18.
  4. J. D. Bessman, R. K. Johnson, “Erythrocyte Volume Distribution in Normal and Abnormal Subjects,” Blood 46, 369 (1975).
    [PubMed]
  5. H. E. Kubitschek, “Electronic Measurement of Particle Size,” Res. Appl. Ind. 13, 128 (1960).
  6. N. Mohandas et al., “Inaccuracies Associated with the Automated Measurement of MCHC in Dehydrated Cells,” Blood 56, 125 (1980).
    [PubMed]
  7. T. Arnfred, S. D. Kristensen, V. Munck, “Colter Counter Model S and Model S-Plus Measurements of Mean Erythrocyte Volume (MCV) are Influenced by the Mean Erythrocyte Haemoglobin Concentration (MCHC),” Scand. J. Clin. Lab. Invest. 41, 717 (1981).
    [CrossRef]
  8. Y. R. Kim, L. Ornstein, “Isovolumetric Sphering of Erythrocyte for More Accurate and Precise Cell Volume Measurement by Flow Cytometry,” Cytometry 3, 419 (1983).
    [CrossRef] [PubMed]
  9. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Chap. 3.
  10. Ref. 3, Chap. 4.
  11. R. Barer, S. Joseph, “Refractometry of Living Cells,” Q. J. Microsc. Sci. 95, 399 (1954).
  12. Ref. 9, chap. 8.
  13. R. B. Pennell, “Composition of Normal Human Red Cells,” in The Red Blood Cell, C. Bishop, D. M. Surgenor, Eds. (Academic, New York, 1964), Chap. 2.
  14. R. S. Longhurst, Geometrical and Physical Optics (Longman, London, 1967), pp. 446–448.
  15. O. W. van Assendelft, Spectrophotometry of Haemoglobin Derivatives (van Gorcum, Assen, The Netherlands, 1970, pp. 23–25 and Chap. 3 and Chap. 3.
  16. H. P. Mansberg, A. M. Saunders, W. Groner, “The Hemalog D White Cell Differential System,” J. Histochem. Cytochem. 22, 711 (1974).
    [CrossRef] [PubMed]
  17. National Committee for Clinical Laboratory Standards (NCCLS), Publication H7-T (1981).
  18. International Committee for Standardization in Haematology, J. Clin. Pathol. 31, 139 (1978).
    [PubMed]
  19. M. R. Clark et al., “Study on the Dehydrating Effect of the Red Cell Na+/K+-Pump in Nystatin-Treated Cells with Varying Na+ and Water Contents,” Biochim. Biophys. Acta 646, 422 (1981).
    [CrossRef] [PubMed]
  20. L. M. Corash et al., “Separation of Erythrocytes According to Age on a Simplified Density Gradient,” J. Lab. Clin. Med. 84, 147 (1974).
    [PubMed]
  21. M. R. Clark, A. C. Greenquist, S. B. Shohet, “Stabilization of the Shape of Sickled Cells by Calcium and A23187,” Blood 48, 899 (1976).
    [PubMed]
  22. L. Ornstein, Mt. Sinai School of Medicine; private communication.

1983 (1)

Y. R. Kim, L. Ornstein, “Isovolumetric Sphering of Erythrocyte for More Accurate and Precise Cell Volume Measurement by Flow Cytometry,” Cytometry 3, 419 (1983).
[CrossRef] [PubMed]

1981 (2)

T. Arnfred, S. D. Kristensen, V. Munck, “Colter Counter Model S and Model S-Plus Measurements of Mean Erythrocyte Volume (MCV) are Influenced by the Mean Erythrocyte Haemoglobin Concentration (MCHC),” Scand. J. Clin. Lab. Invest. 41, 717 (1981).
[CrossRef]

M. R. Clark et al., “Study on the Dehydrating Effect of the Red Cell Na+/K+-Pump in Nystatin-Treated Cells with Varying Na+ and Water Contents,” Biochim. Biophys. Acta 646, 422 (1981).
[CrossRef] [PubMed]

1980 (1)

N. Mohandas et al., “Inaccuracies Associated with the Automated Measurement of MCHC in Dehydrated Cells,” Blood 56, 125 (1980).
[PubMed]

1978 (1)

International Committee for Standardization in Haematology, J. Clin. Pathol. 31, 139 (1978).
[PubMed]

1976 (2)

For concise reviews of the subject and extensive bibliographies, see T. M. Jovin et al., “Automatic Sizing and Separation of Particles by Ratios of Light Scattering Intensities,” J. Histochem. Cytochem. 24, 269 (1976);G. C. Salzman, “Flow Cytometry: The Use of Lasers for Rapid Analysis and Separation of Single Biological Cells,” in The Biomedical Laser, L. Goldman, Ed. (Springer, New York, 1981), Chap. 5.
[CrossRef] [PubMed]

M. R. Clark, A. C. Greenquist, S. B. Shohet, “Stabilization of the Shape of Sickled Cells by Calcium and A23187,” Blood 48, 899 (1976).
[PubMed]

1975 (1)

J. D. Bessman, R. K. Johnson, “Erythrocyte Volume Distribution in Normal and Abnormal Subjects,” Blood 46, 369 (1975).
[PubMed]

1974 (2)

H. P. Mansberg, A. M. Saunders, W. Groner, “The Hemalog D White Cell Differential System,” J. Histochem. Cytochem. 22, 711 (1974).
[CrossRef] [PubMed]

L. M. Corash et al., “Separation of Erythrocytes According to Age on a Simplified Density Gradient,” J. Lab. Clin. Med. 84, 147 (1974).
[PubMed]

1960 (1)

H. E. Kubitschek, “Electronic Measurement of Particle Size,” Res. Appl. Ind. 13, 128 (1960).

1954 (1)

R. Barer, S. Joseph, “Refractometry of Living Cells,” Q. J. Microsc. Sci. 95, 399 (1954).

Arnfred, T.

T. Arnfred, S. D. Kristensen, V. Munck, “Colter Counter Model S and Model S-Plus Measurements of Mean Erythrocyte Volume (MCV) are Influenced by the Mean Erythrocyte Haemoglobin Concentration (MCHC),” Scand. J. Clin. Lab. Invest. 41, 717 (1981).
[CrossRef]

Barer, R.

R. Barer, S. Joseph, “Refractometry of Living Cells,” Q. J. Microsc. Sci. 95, 399 (1954).

Bayvel, L. P.

L. P. Bayvel, A. R. Jones, Electromagnetic Scattering and Its Applications (Applied Science, London, 1981), pp. 22–47.

Bessman, J. D.

J. D. Bessman, R. K. Johnson, “Erythrocyte Volume Distribution in Normal and Abnormal Subjects,” Blood 46, 369 (1975).
[PubMed]

Clark, M. R.

M. R. Clark et al., “Study on the Dehydrating Effect of the Red Cell Na+/K+-Pump in Nystatin-Treated Cells with Varying Na+ and Water Contents,” Biochim. Biophys. Acta 646, 422 (1981).
[CrossRef] [PubMed]

M. R. Clark, A. C. Greenquist, S. B. Shohet, “Stabilization of the Shape of Sickled Cells by Calcium and A23187,” Blood 48, 899 (1976).
[PubMed]

Corash, L. M.

L. M. Corash et al., “Separation of Erythrocytes According to Age on a Simplified Density Gradient,” J. Lab. Clin. Med. 84, 147 (1974).
[PubMed]

Greenquist, A. C.

M. R. Clark, A. C. Greenquist, S. B. Shohet, “Stabilization of the Shape of Sickled Cells by Calcium and A23187,” Blood 48, 899 (1976).
[PubMed]

Groner, W.

H. P. Mansberg, A. M. Saunders, W. Groner, “The Hemalog D White Cell Differential System,” J. Histochem. Cytochem. 22, 711 (1974).
[CrossRef] [PubMed]

Johnson, R. K.

J. D. Bessman, R. K. Johnson, “Erythrocyte Volume Distribution in Normal and Abnormal Subjects,” Blood 46, 369 (1975).
[PubMed]

Jones, A. R.

L. P. Bayvel, A. R. Jones, Electromagnetic Scattering and Its Applications (Applied Science, London, 1981), pp. 22–47.

Joseph, S.

R. Barer, S. Joseph, “Refractometry of Living Cells,” Q. J. Microsc. Sci. 95, 399 (1954).

Jovin, T. M.

For concise reviews of the subject and extensive bibliographies, see T. M. Jovin et al., “Automatic Sizing and Separation of Particles by Ratios of Light Scattering Intensities,” J. Histochem. Cytochem. 24, 269 (1976);G. C. Salzman, “Flow Cytometry: The Use of Lasers for Rapid Analysis and Separation of Single Biological Cells,” in The Biomedical Laser, L. Goldman, Ed. (Springer, New York, 1981), Chap. 5.
[CrossRef] [PubMed]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Chap. 3.

Kim, Y. R.

Y. R. Kim, L. Ornstein, “Isovolumetric Sphering of Erythrocyte for More Accurate and Precise Cell Volume Measurement by Flow Cytometry,” Cytometry 3, 419 (1983).
[CrossRef] [PubMed]

Kristensen, S. D.

T. Arnfred, S. D. Kristensen, V. Munck, “Colter Counter Model S and Model S-Plus Measurements of Mean Erythrocyte Volume (MCV) are Influenced by the Mean Erythrocyte Haemoglobin Concentration (MCHC),” Scand. J. Clin. Lab. Invest. 41, 717 (1981).
[CrossRef]

Kubitschek, H. E.

H. E. Kubitschek, “Electronic Measurement of Particle Size,” Res. Appl. Ind. 13, 128 (1960).

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics (Longman, London, 1967), pp. 446–448.

Mansberg, H. P.

H. P. Mansberg, A. M. Saunders, W. Groner, “The Hemalog D White Cell Differential System,” J. Histochem. Cytochem. 22, 711 (1974).
[CrossRef] [PubMed]

Mohandas, N.

N. Mohandas et al., “Inaccuracies Associated with the Automated Measurement of MCHC in Dehydrated Cells,” Blood 56, 125 (1980).
[PubMed]

Munck, V.

T. Arnfred, S. D. Kristensen, V. Munck, “Colter Counter Model S and Model S-Plus Measurements of Mean Erythrocyte Volume (MCV) are Influenced by the Mean Erythrocyte Haemoglobin Concentration (MCHC),” Scand. J. Clin. Lab. Invest. 41, 717 (1981).
[CrossRef]

Ornstein, L.

Y. R. Kim, L. Ornstein, “Isovolumetric Sphering of Erythrocyte for More Accurate and Precise Cell Volume Measurement by Flow Cytometry,” Cytometry 3, 419 (1983).
[CrossRef] [PubMed]

L. Ornstein, Mt. Sinai School of Medicine; private communication.

Pennell, R. B.

R. B. Pennell, “Composition of Normal Human Red Cells,” in The Red Blood Cell, C. Bishop, D. M. Surgenor, Eds. (Academic, New York, 1964), Chap. 2.

Saunders, A. M.

H. P. Mansberg, A. M. Saunders, W. Groner, “The Hemalog D White Cell Differential System,” J. Histochem. Cytochem. 22, 711 (1974).
[CrossRef] [PubMed]

Shohet, S. B.

M. R. Clark, A. C. Greenquist, S. B. Shohet, “Stabilization of the Shape of Sickled Cells by Calcium and A23187,” Blood 48, 899 (1976).
[PubMed]

van Assendelft, O. W.

O. W. van Assendelft, Spectrophotometry of Haemoglobin Derivatives (van Gorcum, Assen, The Netherlands, 1970, pp. 23–25 and Chap. 3 and Chap. 3.

Wintrobe, M. M.

M. M. Wintrobe et al., Clinical Hematology (Lea & Febiger, Philadelphia, 1981), p. 18.

Biochim. Biophys. Acta (1)

M. R. Clark et al., “Study on the Dehydrating Effect of the Red Cell Na+/K+-Pump in Nystatin-Treated Cells with Varying Na+ and Water Contents,” Biochim. Biophys. Acta 646, 422 (1981).
[CrossRef] [PubMed]

Blood (3)

J. D. Bessman, R. K. Johnson, “Erythrocyte Volume Distribution in Normal and Abnormal Subjects,” Blood 46, 369 (1975).
[PubMed]

N. Mohandas et al., “Inaccuracies Associated with the Automated Measurement of MCHC in Dehydrated Cells,” Blood 56, 125 (1980).
[PubMed]

M. R. Clark, A. C. Greenquist, S. B. Shohet, “Stabilization of the Shape of Sickled Cells by Calcium and A23187,” Blood 48, 899 (1976).
[PubMed]

Cytometry (1)

Y. R. Kim, L. Ornstein, “Isovolumetric Sphering of Erythrocyte for More Accurate and Precise Cell Volume Measurement by Flow Cytometry,” Cytometry 3, 419 (1983).
[CrossRef] [PubMed]

J. Clin. Pathol. (1)

International Committee for Standardization in Haematology, J. Clin. Pathol. 31, 139 (1978).
[PubMed]

J. Histochem. Cytochem. (2)

For concise reviews of the subject and extensive bibliographies, see T. M. Jovin et al., “Automatic Sizing and Separation of Particles by Ratios of Light Scattering Intensities,” J. Histochem. Cytochem. 24, 269 (1976);G. C. Salzman, “Flow Cytometry: The Use of Lasers for Rapid Analysis and Separation of Single Biological Cells,” in The Biomedical Laser, L. Goldman, Ed. (Springer, New York, 1981), Chap. 5.
[CrossRef] [PubMed]

H. P. Mansberg, A. M. Saunders, W. Groner, “The Hemalog D White Cell Differential System,” J. Histochem. Cytochem. 22, 711 (1974).
[CrossRef] [PubMed]

J. Lab. Clin. Med. (1)

L. M. Corash et al., “Separation of Erythrocytes According to Age on a Simplified Density Gradient,” J. Lab. Clin. Med. 84, 147 (1974).
[PubMed]

Q. J. Microsc. Sci. (1)

R. Barer, S. Joseph, “Refractometry of Living Cells,” Q. J. Microsc. Sci. 95, 399 (1954).

Res. Appl. Ind. (1)

H. E. Kubitschek, “Electronic Measurement of Particle Size,” Res. Appl. Ind. 13, 128 (1960).

Scand. J. Clin. Lab. Invest. (1)

T. Arnfred, S. D. Kristensen, V. Munck, “Colter Counter Model S and Model S-Plus Measurements of Mean Erythrocyte Volume (MCV) are Influenced by the Mean Erythrocyte Haemoglobin Concentration (MCHC),” Scand. J. Clin. Lab. Invest. 41, 717 (1981).
[CrossRef]

Other (10)

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Chap. 3.

Ref. 3, Chap. 4.

L. P. Bayvel, A. R. Jones, Electromagnetic Scattering and Its Applications (Applied Science, London, 1981), pp. 22–47.

M. M. Wintrobe et al., Clinical Hematology (Lea & Febiger, Philadelphia, 1981), p. 18.

Ref. 9, chap. 8.

R. B. Pennell, “Composition of Normal Human Red Cells,” in The Red Blood Cell, C. Bishop, D. M. Surgenor, Eds. (Academic, New York, 1964), Chap. 2.

R. S. Longhurst, Geometrical and Physical Optics (Longman, London, 1967), pp. 446–448.

O. W. van Assendelft, Spectrophotometry of Haemoglobin Derivatives (van Gorcum, Assen, The Netherlands, 1970, pp. 23–25 and Chap. 3 and Chap. 3.

National Committee for Clinical Laboratory Standards (NCCLS), Publication H7-T (1981).

L. Ornstein, Mt. Sinai School of Medicine; private communication.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (17)

Fig. 1
Fig. 1

Mie theory differential cross sections for scattering into a conical shell of half-angle θ about the incident beam direction. Dashed curves, HC = 31 g/dliter; solid curve, HC = 34 g/dliter; dotted curves, HC = 37 g/dliter. λ = 0.842 μm, ns = 1.330, n0 = 1.335, α = 0.001942 dliter/g, μM = 0.2520 cm2/μM.

Fig. 2
Fig. 2

Schematic diagrams of dark-field systems for measuring the light scattered by a sphered red blood cell characterized by volume V and hemoglobin concentration HC, flowing in a fluid having refractive index ns. (A) Single-angular interval detection; (B) double-angular interval detection.

Fig. 3
Fig. 3

Cross sections for scattering into finite angular intervals as functions of V and HC. Wavelength and refractive-index parameters as given in Fig. 1. (A) S1 is the cross section for θ = 5.5°, Δθ = 5.0°. (B) S2 is the cross section for θ = 3.0°, Δθ = 2.5°.

Fig. 4
Fig. 4

Mapping of (S1,S2) pairs into (V,HC) pairs for a solvable system. Solid curves are constant-V contours; dashed curves are constant-HC contours. System parameters are those of Figs. 1 and 3.

Fig. 5
Fig. 5

The (S1,S2) to (V,HC) mapping for an unsolvable system. Wavelength and refractive index parameters as given in Fig. 1. θ1 = 3.5°, Δθ1 = 2.5°, θ2 = 2.0°, Δθ2 = 1.5°.

Fig. 6
Fig. 6

Schematic diagram of the experimental optical system.

Fig. 7
Fig. 7

The (S1,S2) to (V,HC) mapping for the experimental system of Fig. 6. Wavelength and refractive-index parameters as given in Fig. 1. θ1 = 5.5°, Δθ1 = 3.5°, θ2 = 3.0°, Δθ2 = 2.5°. Only that region of the S1-S2 plane used in the data analysis is shown.

Fig. 8
Fig. 8

Block diagram of the experimental data acquisition and analysis system.

Fig. 9
Fig. 9

Example of the output produced by the PDP 11 data analysis program. The abscissa (X) and ordinate (Y) axes of the 2-D pulse height distribution (cytogram) on the left have units of channel number (0–60). The top histogram on the right gives the HC distribution, the bottom histogram gives the V distribution. Means and standard deviations of these distributions are printed below the histograms. System parameters and cell counts are listed at the top. Kx and Ky are conversion factors between pulse height channel numbers and cross sections in μm2 (S1 = 2πKxX, S2 = 2πKyY). Physical cells, the number of events falling within the (V,HC) grid; RBC total cells, the total event count.

Fig. 10
Fig. 10

Comparison of MCV measurements from the experimental system with reference values for randomly selected hospital samples. Solid line represents identity. Linear regression results (y =ax + b): number of samples N = 72; mean MCVREF = 92.4; s.d. MCVREF = 7.3; mean MCVSYS = 90.4; s.d. MCVSYS = 7.3; slope a = 0.87; intercept b = 10.10; s.d. of regression Syx = 2.50; correlation coefficient r = 0.94.

Fig. 11
Fig. 11

Comparison of MCHC measurements from the experimental system with reference values for randomly selected hospital samples. N = 72; mean MCHCREF = 33.1; s.d. MCHCREF = 1.4; mean MCHCSYS = 33.4; s.d. MCHCSYS = 1.4; a = 0.85; b = 5.30; Syx = 0.68; r = 0.87.

Fig. 12
Fig. 12

Comparison of MCH values from the experimental system with reference values for randomly selected hospital samples (MCHSYS = MCVSYS · MCHCSYS/100). N = 72; mean MCHREF = 30.6; s.d. MCHREF = 2.8; mean MCHSYS = 30.3; s.d. MCHSYS = 2.9; a = 0.98; b = 2.5; Syx = 0.80; r = 0.96.

Fig. 13
Fig. 13

Comparisons of system measurements of MCV and MCHC with reference values for samples consisting of red cells in altered hydration states. MCV results (top): N = 11, mean MCVREF = 83.6; s.d. MCVREF = 16.2; mean MCVSYS = 83.5; s.d. MCVSYS = 16.2; a = 1.00; b = 0.26; Syx = 1.67, r = 0.99. MCHC results (bottom): N = 10 (outlier excluded); mean MCHCREF = 35.7; s.d. MCHCREF = 5.6; mean MCHCSYS = 36.0; s.d. MCHCREF = 5.4; a = 0.96; b = 1.71; Syx = 0.82; r = 0.99.

Fig. 14
Fig. 14

Cytograms and histograms associated with the top (Fl), middle (F3), and bottom (F5) fractions of a whole blood sample separated into red cell density fractions on a Stractan column having a discontinuous density gradient.

Fig. 15
Fig. 15

Cytogram and histograms obtained from a blood sample prepared by mixing equal parts of the lowest and highest density fractions.

Fig. 16
Fig. 16

The (S1,S2) to (V,HC) mapping for the optical system used to test the oil droplet calibration method. System parameters: λ = 0.6328 μm, ns = 1.3339, n0 = 1.345, α = 0.001942 dliter/g, μM = 0.1616 cm2/μM, θ1 = 2.0°, Δθ1 = 1.0°, θ2 = 5.0°, Δθ2 = 10.0°.

Fig. 17
Fig. 17

Cytograms and histograms from measurements on oil droplet samples using the He–Ne laser system (Fig. 16).

Tables (3)

Tables Icon

Table I System Measurement Results for Five Fractions of a Normal Blood Sample Separated on a Discontinuous Stractan Density Gradient; for Comparison, the Reference MCHC Values for Each Fraction are Also Tabulated

Tables Icon

Table II System Measurement Results for Samples Consisting of Various Mixtures of the Density-Separated Fractions Defined in Table I

Tables Icon

Table III Refractive Indices of the Oils Used In the Oil Droplet Samples and the Results of System Measurements on the Samples

Equations (7)

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

n R = n 0 + α · HC ,
n I = ln 10 π M λ μ M · HC ,
d σ d θ = sin θ k 2 0 2 π ( i 1 sin 2 ϕ + i 2 cos 2 ϕ ) d ϕ = π k 2 ( i 1 + i 2 ) sin θ ,
S = θ θ + Δ θ ( d σ / d θ ) d θ = f ( λ , n s , θ , Δ θ ; V , HC ) .
S 1 = θ 1 θ 1 + Δ θ 1 ( d σ / d θ ) d θ = f ( λ , n s , θ 1 , Δ θ 1 ; V , HC ) ,
S 2 = θ 2 θ 2 + Δ θ 2 ( d σ / d θ ) d θ = f ( λ , n s , θ 2 , Δ θ 2 ; V , HC ) ,
J = | S 1 V S 2 HC S 1 HC S 2 V | 0 .

Metrics