Abstract

Two important optical properties of red blood cells (RBCs), their microscopic scattering cross sections σs, and the mean cosine of their scattering angles μ¯, contribute to the optical behavior of whole blood. Therefore, the ability of Mie theory to predict values of σs and μ¯ was tested by experiment. In addition, the effect of red blood cell size on σs and μ¯ was investigated in two ways: (1) by studying erythrocytes from the dog, goat, and human, three species known to have different RBC sizes and (2) by allowing the RBCs from each species to shrink or swell osmotically. Values of σs obtained by measuring the collimated transmittance of dilute RBC suspensions illuminated with a He–Ne laser agreed with those predicted by Mie theory. Moreover, measured σs values were directly proportional to RBC volume. By contrast, values of μ¯ from Mie theory were consistently greater than those obtained experimentally by making angular scattering measurements in a goniometer. Thus Mie theory appears to yield adequate values for the RBC’s microscopic scattering cross section, but by treating the RBC as a sphere with an equal volume, Mie theory fails to take the RBC’s anisotropy into account and thus yields spuriously high values for μ¯.

© 1988 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  9. J. M. Schmitt, “Optical Measurement of Blood Oxygen by Implantable Telemetry,” Ph.D. Dissertation, Stanford U. (1986).
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    [CrossRef]
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    [PubMed]
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    [CrossRef]
  13. A. P. Shepherd, C. G. Burgar, “A Solid State Arteriovenous Oxygen Difference Analyzer for Flowing Whole Blood,” Am. J. Physiol. 232, H437 (1977).
    [PubMed]
  14. G. D. Pedersen, N. J. McCormick, L. O. Reynolds, “Transport Calculations for Light Scattering in Blood,” Biophys. J. 16, 199 (1976).
    [CrossRef] [PubMed]
  15. R. Pierce, “An Experimental Determination of the Average Scattering and Absorption Cross Sections of Human Red Blood Cells for Near Infrared Light,” M.S. Thesis, Electrical Engineering Department, U. Washington (1972).
  16. R. Barer, “Spectrophotometry of Clarified Cell Suspensions,” Science 21, 709 (1955).
    [CrossRef]
  17. L. O. Reynolds, N. J. McCormick, “Approximate Two-Parameter Phase Function for Light Scattering,” J. Opt. Soc. Am. 70, 1206 (1980).
    [CrossRef]
  18. L. Henyey, J. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93, 70 (1941).
    [CrossRef]
  19. P. L. Altman, D. S. Dittmer, Biology Data Book (Federation of American Societies of Experimental Biology1964), pp. 267–268.
  20. E. Ponder, Hemolysis and Related Phenomena (Grune and Statton, New York, 1948).
  21. B. Barer, S. Joseph, “Refractometry of Living Cells,” Q. J. Microsc. Sci. 95, 399 (1954).

1988 (1)

1987 (2)

J. M. Steinke, A. P. Shepherd, “Diffuse Reflectance of Whole Blood: Model for a Diverging Light Beam,” IEEE Trans. Biomed. Eng. BME-34, 826 (1987).
[CrossRef]

J. M. Steinke, A. P. Shepherd, “Reflectance Measurements of Hematocrit and Oxyhemoglobin Saturation,” Am. J. Physiol. 253, H147 (1987).
[PubMed]

1986 (2)

J. M. Steinke, A. P. Shepherd, “Role of Light Scattering in Spectrophotometric Measurements of Arteriovenous Oxygen Difference,” IEEE Trans. Biomed. Eng. BME-33, 729 (1986).
[CrossRef]

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for in vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98 (1986).
[CrossRef]

1980 (1)

1977 (1)

A. P. Shepherd, C. G. Burgar, “A Solid State Arteriovenous Oxygen Difference Analyzer for Flowing Whole Blood,” Am. J. Physiol. 232, H437 (1977).
[PubMed]

1976 (1)

G. D. Pedersen, N. J. McCormick, L. O. Reynolds, “Transport Calculations for Light Scattering in Blood,” Biophys. J. 16, 199 (1976).
[CrossRef] [PubMed]

1970 (3)

1955 (1)

R. Barer, “Spectrophotometry of Clarified Cell Suspensions,” Science 21, 709 (1955).
[CrossRef]

1954 (1)

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

1948 (1)

1941 (1)

L. Henyey, J. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93, 70 (1941).
[CrossRef]

Altman, P. L.

P. L. Altman, D. S. Dittmer, Biology Data Book (Federation of American Societies of Experimental Biology1964), pp. 267–268.

Barer, B.

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

Barer, R.

R. Barer, “Spectrophotometry of Clarified Cell Suspensions,” Science 21, 709 (1955).
[CrossRef]

Burgar, C. G.

A. P. Shepherd, C. G. Burgar, “A Solid State Arteriovenous Oxygen Difference Analyzer for Flowing Whole Blood,” Am. J. Physiol. 232, H437 (1977).
[PubMed]

Dittmer, D. S.

P. L. Altman, D. S. Dittmer, Biology Data Book (Federation of American Societies of Experimental Biology1964), pp. 267–268.

Greenstein, J.

L. Henyey, J. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93, 70 (1941).
[CrossRef]

Henyey, L.

L. Henyey, J. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93, 70 (1941).
[CrossRef]

Joseph, S.

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

Kubelka, P.

McCormick, N. J.

L. O. Reynolds, N. J. McCormick, “Approximate Two-Parameter Phase Function for Light Scattering,” J. Opt. Soc. Am. 70, 1206 (1980).
[CrossRef]

G. D. Pedersen, N. J. McCormick, L. O. Reynolds, “Transport Calculations for Light Scattering in Blood,” Biophys. J. 16, 199 (1976).
[CrossRef] [PubMed]

Meindl, J. D.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for in vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98 (1986).
[CrossRef]

Mihm, F. G.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for in vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98 (1986).
[CrossRef]

Moaveni, M. K.

M. K. Moaveni, “A Multiple Scattering Field Theory Applied to Whole Blood,” Ph.D. Dissertation, U. Washington (1970).

Pedersen, G. D.

G. D. Pedersen, N. J. McCormick, L. O. Reynolds, “Transport Calculations for Light Scattering in Blood,” Biophys. J. 16, 199 (1976).
[CrossRef] [PubMed]

Pierce, R.

R. Pierce, “An Experimental Determination of the Average Scattering and Absorption Cross Sections of Human Red Blood Cells for Near Infrared Light,” M.S. Thesis, Electrical Engineering Department, U. Washington (1972).

Pisharoty, N. R.

R. J. Zdrojkowski, N. R. Pisharoty, “Optical Transmission and Reflection by Blood,” IEEE Trans. Biomed. Eng. BME-17, 122 (1970).
[CrossRef]

Ponder, E.

E. Ponder, Hemolysis and Related Phenomena (Grune and Statton, New York, 1948).

Reynolds, L. O.

L. O. Reynolds, N. J. McCormick, “Approximate Two-Parameter Phase Function for Light Scattering,” J. Opt. Soc. Am. 70, 1206 (1980).
[CrossRef]

G. D. Pedersen, N. J. McCormick, L. O. Reynolds, “Transport Calculations for Light Scattering in Blood,” Biophys. J. 16, 199 (1976).
[CrossRef] [PubMed]

L. O. Reynolds, “Optical Diffuse Reflectance and Transmittance from an Anisotropically Scattering Finite Blood Medium,” Ph.D. Dissertation, U. Washington (1975).

Schmitt, J. M.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for in vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98 (1986).
[CrossRef]

J. M. Schmitt, “Optical Measurement of Blood Oxygen by Implantable Telemetry,” Ph.D. Dissertation, Stanford U. (1986).

Shepherd, A. P.

J. M. Steinke, A. P. Shepherd, “Diffusion Model of the Optical Absorbance of Whole Blood,” J. Opt. Soc. Am. A 5, 813 (1988).
[CrossRef] [PubMed]

J. M. Steinke, A. P. Shepherd, “Diffuse Reflectance of Whole Blood: Model for a Diverging Light Beam,” IEEE Trans. Biomed. Eng. BME-34, 826 (1987).
[CrossRef]

J. M. Steinke, A. P. Shepherd, “Reflectance Measurements of Hematocrit and Oxyhemoglobin Saturation,” Am. J. Physiol. 253, H147 (1987).
[PubMed]

J. M. Steinke, A. P. Shepherd, “Role of Light Scattering in Spectrophotometric Measurements of Arteriovenous Oxygen Difference,” IEEE Trans. Biomed. Eng. BME-33, 729 (1986).
[CrossRef]

A. P. Shepherd, C. G. Burgar, “A Solid State Arteriovenous Oxygen Difference Analyzer for Flowing Whole Blood,” Am. J. Physiol. 232, H437 (1977).
[PubMed]

Steinke, J. M.

J. M. Steinke, A. P. Shepherd, “Diffusion Model of the Optical Absorbance of Whole Blood,” J. Opt. Soc. Am. A 5, 813 (1988).
[CrossRef] [PubMed]

J. M. Steinke, A. P. Shepherd, “Diffuse Reflectance of Whole Blood: Model for a Diverging Light Beam,” IEEE Trans. Biomed. Eng. BME-34, 826 (1987).
[CrossRef]

J. M. Steinke, A. P. Shepherd, “Reflectance Measurements of Hematocrit and Oxyhemoglobin Saturation,” Am. J. Physiol. 253, H147 (1987).
[PubMed]

J. M. Steinke, A. P. Shepherd, “Role of Light Scattering in Spectrophotometric Measurements of Arteriovenous Oxygen Difference,” IEEE Trans. Biomed. Eng. BME-33, 729 (1986).
[CrossRef]

Twersky, V.

Zdrojkowski, R. J.

R. J. Zdrojkowski, N. R. Pisharoty, “Optical Transmission and Reflection by Blood,” IEEE Trans. Biomed. Eng. BME-17, 122 (1970).
[CrossRef]

Am. J. Physiol. (2)

J. M. Steinke, A. P. Shepherd, “Reflectance Measurements of Hematocrit and Oxyhemoglobin Saturation,” Am. J. Physiol. 253, H147 (1987).
[PubMed]

A. P. Shepherd, C. G. Burgar, “A Solid State Arteriovenous Oxygen Difference Analyzer for Flowing Whole Blood,” Am. J. Physiol. 232, H437 (1977).
[PubMed]

Astrophys. J. (1)

L. Henyey, J. Greenstein, “Diffuse Radiation in the Galaxy,” Astrophys. J. 93, 70 (1941).
[CrossRef]

Biophys. J. (1)

G. D. Pedersen, N. J. McCormick, L. O. Reynolds, “Transport Calculations for Light Scattering in Blood,” Biophys. J. 16, 199 (1976).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng. (4)

J. M. Steinke, A. P. Shepherd, “Role of Light Scattering in Spectrophotometric Measurements of Arteriovenous Oxygen Difference,” IEEE Trans. Biomed. Eng. BME-33, 729 (1986).
[CrossRef]

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An Integrated Circuit-Based Optical Sensor for in vivo Measurement of Blood Oxygenation,” IEEE Trans. Biomed. Eng. BME-33, 98 (1986).
[CrossRef]

R. J. Zdrojkowski, N. R. Pisharoty, “Optical Transmission and Reflection by Blood,” IEEE Trans. Biomed. Eng. BME-17, 122 (1970).
[CrossRef]

J. M. Steinke, A. P. Shepherd, “Diffuse Reflectance of Whole Blood: Model for a Diverging Light Beam,” IEEE Trans. Biomed. Eng. BME-34, 826 (1987).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (1)

Q. J. Microsc. Sci. (1)

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

Science (1)

R. Barer, “Spectrophotometry of Clarified Cell Suspensions,” Science 21, 709 (1955).
[CrossRef]

Other (6)

R. Pierce, “An Experimental Determination of the Average Scattering and Absorption Cross Sections of Human Red Blood Cells for Near Infrared Light,” M.S. Thesis, Electrical Engineering Department, U. Washington (1972).

P. L. Altman, D. S. Dittmer, Biology Data Book (Federation of American Societies of Experimental Biology1964), pp. 267–268.

E. Ponder, Hemolysis and Related Phenomena (Grune and Statton, New York, 1948).

J. M. Schmitt, “Optical Measurement of Blood Oxygen by Implantable Telemetry,” Ph.D. Dissertation, Stanford U. (1986).

M. K. Moaveni, “A Multiple Scattering Field Theory Applied to Whole Blood,” Ph.D. Dissertation, U. Washington (1970).

L. O. Reynolds, “Optical Diffuse Reflectance and Transmittance from an Anisotropically Scattering Finite Blood Medium,” Ph.D. Dissertation, U. Washington (1975).

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Figures (5)

Fig. 1
Fig. 1

Logarithm of collimated transmittance (O.D.col = −log10Tc) vs the hematocrit-to-cell volume ratio (H/V). Data from canine RBCs have been fit to a line through the origin. The slopes of these lines were used to determine the values of σs. Note that slopes (and thus σs) increased as RBCs swelled osmotically. The slopes of the curves for suspensions in saline are steeper than the plasma curve. This difference in slopes illustrates the role that the index of refraction of the suspending medium plays in determining the apparent scattering characteristics of the erythrocyte.

Fig. 2
Fig. 2

Microscopic scattering cross sections from three species vs their respective cell volumes. The scattering cross sections σs are directly proportional to cell volume, and light scattering would be lost if cell volume could fall to zero.

Fig. 3
Fig. 3

Effect of osmotically induced changes in red cell volume on microscopic scattering cross sections σs. Data shown are from all three species in the various salt concentrations.

Fig. 4
Fig. 4

Macroscopic scattering cross sections ∑s from three species vs hematocrit. In spite of the marked differences in microscopic scattering cross sections shown in Fig. 2, the macroscopic light-scattering properties are not appreciably different among the three species. Symbols denote species of RBCs and the medium in which they were suspended.

Fig. 5
Fig. 5

Angular light scattering data for human red blood cells. Logarithm of scattered intensity is plotted vs scattering angle. Osmotically induced increases in cell volume reduced large-angle scattering. Curves represent the two-parameter Reynolds-McCormick phase function. Mean cosine of scattering angles μ ¯ was calculated from Eq. (7) after parameters of best fit were obtained.

Tables (2)

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Table I Scattering Cross Sections σs and μ ¯ from Experiment

Tables Icon

Table II Scattering Cross Sections(σs and μ ¯ from Mie Theory

Equations (7)

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T c = exp [ - ( s + a ) d ] ,
s = H σ s ( 1 - H ) / V ,
a = H σ a / V ,
T c = exp - ( s d ) .
θ med = sin - 1 [ sin ( θ air ) / η med ] .
f ( μ ) = K ( 1 + g 2 - 2 g μ ) - ( α + 1 ) ,
μ ¯ = [ 2 α g L - ( 1 + g 2 ) ] / [ 2 g ( α - 1 ) ] ,

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