Abstract

We studied the influence of shape and secondary, or intercellular, organization on the absorption and scattering properties of red blood cells to determine whether these properties are of any practical significance for optical evaluation of whole blood and its constituents. A series of measurements of transmittance and reflectance of light from bovine blood in a flow cuvette was conducted with a 650–900-nm integrating sphere at shear rates of 0–1600 s-1, from which the influence of cell orientation, elongation, and aggregate formation on the absorption (μa) and the reduced scattering (μs′) coefficients could be quantified. Aggregation was accompanied by a decrease of 4% in μs′ compared with the value in randomly oriented single cells. Increasing the degree of cell alignment and elongation as a result of increasing shear rate reduced μs′ by 6% and μa by 3%, evaluated at a shear rate of 1600 s-1. Comparison with T-matrix computations for oblate- and prolate-shaped cells with corresponding elongation and orientation indicates that the optical properties of whole blood are determined by those of its individual cells, though influenced by a collective scattering factor that depends on the cell-to-cell organization. We demonstrate that cell morphological changes must be taken into consideration when one is conducting whole blood spectroscopy.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
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2002 (1)

2001 (4)

M. R. Hardeman, J. G. G. Dobbe, C. Ince, “The laser-assisted optical rotational cell analyzer (LORCA) as red blood cell aggregometer,” Clin. Hemorheol. Microcirc. 25, 1–11 (2001).

H. Bäumler, B. Neu, R. Mitlöhner, R. Georgieva, H. J. Meiselman, H. Kiesewetter, “Electrophoretic and aggregation behavior of bovine, horse and human red blood cells in plasma and in polymer solutions,” Biorheology 38, 39–51 (2001).
[PubMed]

M. Hammer, A. N. Yaroslavsky, D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. 47, N65–N69 (2001).
[CrossRef]

N. V. Shepelevich, I. V. Prostakova, V. N. Lopatin, “Light-scattering by optically soft randomly oriented spheroids,” J. Quant. Spectrosc. Radiat. Transfer 70, 375–381 (2001).
[CrossRef]

1999 (3)

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4, 47–53 (1999).
[CrossRef] [PubMed]

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. 4, 36–46 (1999).
[CrossRef] [PubMed]

W. Steenbergen, R. Kolkman, F. F. M. de Mul, “Light-scattering properties of undiluted human blood subjected to simple shear,” J. Opt. Soc. Am. A 16, 2959–2967 (1999).
[CrossRef]

1998 (2)

1995 (2)

A. M. K. Nilsson, R. Berg, S. Andersson-Engels, “Measurements of the optical properties of tissue in conjunction with photodynamic therapy,” Appl. Opt. 34, 4609–4619 (1995).
[CrossRef] [PubMed]

L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Computer Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

1993 (1)

L.-G. Lindberg, P. Å. Öberg, “Optical properties of blood in motion,” Opt. Eng. 32, 253–257 (1993).
[CrossRef]

1985 (1)

1980 (1)

M. F. Perutz, K. Imai, “Regulation of oxygen affinity of mammalian haemoglobins,” J. Mol. Biol. 136, 183–191 (1980).
[CrossRef] [PubMed]

1979 (2)

K. Sakamoto, H. Kanai, “Electrical characteristics of flowing blood,” IEEE Trans. Biomed. Eng. BME-26, 686–695 (1979).
[CrossRef]

H. L. Goldsmith, J. C. Marlow, “Flow behavior of erythrocytes. II. Particle motions in concentrated suspensions of ghost cells,” J. Colloid Interface Sci. 71, 383–407 (1979).
[CrossRef]

1977 (2)

R. A. Meyer, “Light scattering from red blood cell ghosts: sensitivity of angular dependent structure to membrane thickness and refractive index,” Appl. Opt. 16, 2036–2038 (1977).
[CrossRef] [PubMed]

T. Karino, H. L. Goldsmith, “Flow behaviour of blood cells and rigid spheres in an annular vortex,” Philos. Trans. R. Soc. London Ser. B 279, 413–445 (1977).
[CrossRef]

1975 (1)

H. Schmid-Schönbein, K. A. Kline, L. Heinrich, E. Volger, T. Fischer, “Microrheology and light transmission of blood. III. The velocity of red cell aggregate formation,” Pflügers Arch. 354, 299–317 (1975).
[CrossRef] [PubMed]

1972 (2)

H. Schmid-Schönbein, E. Volger, H. J. Klose, “Microrheology and light transmission of blood. II. The photometric quantification of red cell aggregate formation and dispersion in flow,” Pflügers Arch. 333, 140–155 (1972).
[CrossRef] [PubMed]

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, H. Schmid-Schönbein, “Microrheology and light transmission of blood. I. The photometric effects of red cell aggregation and red cell orientation,” Pflügers Arch. 333, 126–139 (1972).
[CrossRef] [PubMed]

1970 (1)

J. Goldstone, H. Schmid-Schönbein, R. Wells, “The rheology of red blood cell aggregates,” Microvasc. Res. 2, 273–286 (1970).
[CrossRef] [PubMed]

1969 (1)

H. Schmid-Schönbein, R. Wells, “Fluid drop-like transition of erythrocytes under shear,” Science 165, 288–291 (1969).
[CrossRef]

1968 (1)

H. L. Goldsmith, “The microrheology of red blood cell suspensions,” J. Gen. Physiol. 52, 5s–28s (1968).
[CrossRef]

Alsholm, P.

Andersson-Engels, S.

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Bäumler, H.

H. Bäumler, B. Neu, R. Mitlöhner, R. Georgieva, H. J. Meiselman, H. Kiesewetter, “Electrophoretic and aggregation behavior of bovine, horse and human red blood cells in plasma and in polymer solutions,” Biorheology 38, 39–51 (2001).
[PubMed]

Berg, R.

Brechtelsbauer, H.

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, H. Schmid-Schönbein, “Microrheology and light transmission of blood. I. The photometric effects of red cell aggregation and red cell orientation,” Pflügers Arch. 333, 126–139 (1972).
[CrossRef] [PubMed]

de Mul, F. F. M.

Dobbe, J. G. G.

M. R. Hardeman, J. G. G. Dobbe, C. Ince, “The laser-assisted optical rotational cell analyzer (LORCA) as red blood cell aggregometer,” Clin. Hemorheol. Microcirc. 25, 1–11 (2001).

Dörschel, K.

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. 4, 36–46 (1999).
[CrossRef] [PubMed]

Epstein, E. A.

Fischer, T.

H. Schmid-Schönbein, K. A. Kline, L. Heinrich, E. Volger, T. Fischer, “Microrheology and light transmission of blood. III. The velocity of red cell aggregate formation,” Pflügers Arch. 354, 299–317 (1975).
[CrossRef] [PubMed]

Friebel, M.

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. 4, 36–46 (1999).
[CrossRef] [PubMed]

Georgieva, R.

H. Bäumler, B. Neu, R. Mitlöhner, R. Georgieva, H. J. Meiselman, H. Kiesewetter, “Electrophoretic and aggregation behavior of bovine, horse and human red blood cells in plasma and in polymer solutions,” Biorheology 38, 39–51 (2001).
[PubMed]

Goldbach, T.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4, 47–53 (1999).
[CrossRef] [PubMed]

Goldsmith, H. L.

H. L. Goldsmith, J. C. Marlow, “Flow behavior of erythrocytes. II. Particle motions in concentrated suspensions of ghost cells,” J. Colloid Interface Sci. 71, 383–407 (1979).
[CrossRef]

T. Karino, H. L. Goldsmith, “Flow behaviour of blood cells and rigid spheres in an annular vortex,” Philos. Trans. R. Soc. London Ser. B 279, 413–445 (1977).
[CrossRef]

H. L. Goldsmith, “The microrheology of red blood cell suspensions,” J. Gen. Physiol. 52, 5s–28s (1968).
[CrossRef]

Goldstone, J.

J. Goldstone, H. Schmid-Schönbein, R. Wells, “The rheology of red blood cell aggregates,” Microvasc. Res. 2, 273–286 (1970).
[CrossRef] [PubMed]

Grinbaum, A.

Hahn, A.

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. 4, 36–46 (1999).
[CrossRef] [PubMed]

Hammer, M.

M. Hammer, A. N. Yaroslavsky, D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. 47, N65–N69 (2001).
[CrossRef]

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

Hardeman, M. R.

M. R. Hardeman, J. G. G. Dobbe, C. Ince, “The laser-assisted optical rotational cell analyzer (LORCA) as red blood cell aggregometer,” Clin. Hemorheol. Microcirc. 25, 1–11 (2001).

Heinich, L.

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, H. Schmid-Schönbein, “Microrheology and light transmission of blood. I. The photometric effects of red cell aggregation and red cell orientation,” Pflügers Arch. 333, 126–139 (1972).
[CrossRef] [PubMed]

Heinrich, L.

H. Schmid-Schönbein, K. A. Kline, L. Heinrich, E. Volger, T. Fischer, “Microrheology and light transmission of blood. III. The velocity of red cell aggregate formation,” Pflügers Arch. 354, 299–317 (1975).
[CrossRef] [PubMed]

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Imai, K.

M. F. Perutz, K. Imai, “Regulation of oxygen affinity of mammalian haemoglobins,” J. Mol. Biol. 136, 183–191 (1980).
[CrossRef] [PubMed]

Ince, C.

M. R. Hardeman, J. G. G. Dobbe, C. Ince, “The laser-assisted optical rotational cell analyzer (LORCA) as red blood cell aggregometer,” Clin. Hemorheol. Microcirc. 25, 1–11 (2001).

Jacques, S. L.

L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Computer Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Kanai, H.

K. Sakamoto, H. Kanai, “Electrical characteristics of flowing blood,” IEEE Trans. Biomed. Eng. BME-26, 686–695 (1979).
[CrossRef]

Karino, T.

T. Karino, H. L. Goldsmith, “Flow behaviour of blood cells and rigid spheres in an annular vortex,” Philos. Trans. R. Soc. London Ser. B 279, 413–445 (1977).
[CrossRef]

Karlsson, A.

Kiesewetter, H.

H. Bäumler, B. Neu, R. Mitlöhner, R. Georgieva, H. J. Meiselman, H. Kiesewetter, “Electrophoretic and aggregation behavior of bovine, horse and human red blood cells in plasma and in polymer solutions,” Biorheology 38, 39–51 (2001).
[PubMed]

Kline, K. A.

H. Schmid-Schönbein, K. A. Kline, L. Heinrich, E. Volger, T. Fischer, “Microrheology and light transmission of blood. III. The velocity of red cell aggregate formation,” Pflügers Arch. 354, 299–317 (1975).
[CrossRef] [PubMed]

Klose, H. J.

H. Schmid-Schönbein, E. Volger, H. J. Klose, “Microrheology and light transmission of blood. II. The photometric quantification of red cell aggregate formation and dispersion in flow,” Pflügers Arch. 333, 140–155 (1972).
[CrossRef] [PubMed]

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, H. Schmid-Schönbein, “Microrheology and light transmission of blood. I. The photometric effects of red cell aggregation and red cell orientation,” Pflügers Arch. 333, 126–139 (1972).
[CrossRef] [PubMed]

Kolb, A.

Kolkman, R.

Lindberg, L.-G.

L.-G. Lindberg, P. Å. Öberg, “Optical properties of blood in motion,” Opt. Eng. 32, 253–257 (1993).
[CrossRef]

Lopatin, V. N.

N. V. Shepelevich, I. V. Prostakova, V. N. Lopatin, “Light-scattering by optically soft randomly oriented spheroids,” J. Quant. Spectrosc. Radiat. Transfer 70, 375–381 (2001).
[CrossRef]

Marlow, J. C.

H. L. Goldsmith, J. C. Marlow, “Flow behavior of erythrocytes. II. Particle motions in concentrated suspensions of ghost cells,” J. Colloid Interface Sci. 71, 383–407 (1979).
[CrossRef]

Meiselman, H. J.

H. Bäumler, B. Neu, R. Mitlöhner, R. Georgieva, H. J. Meiselman, H. Kiesewetter, “Electrophoretic and aggregation behavior of bovine, horse and human red blood cells in plasma and in polymer solutions,” Biorheology 38, 39–51 (2001).
[PubMed]

Metz, M. H.

Meyer, R. A.

Michel, B.

Mitlöhner, R.

H. Bäumler, B. Neu, R. Mitlöhner, R. Georgieva, H. J. Meiselman, H. Kiesewetter, “Electrophoretic and aggregation behavior of bovine, horse and human red blood cells in plasma and in polymer solutions,” Biorheology 38, 39–51 (2001).
[PubMed]

Müller, G.

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. 4, 36–46 (1999).
[CrossRef] [PubMed]

Neu, B.

H. Bäumler, B. Neu, R. Mitlöhner, R. Georgieva, H. J. Meiselman, H. Kiesewetter, “Electrophoretic and aggregation behavior of bovine, horse and human red blood cells in plasma and in polymer solutions,” Biorheology 38, 39–51 (2001).
[PubMed]

Nilsson, A. M. K.

Öberg, P. Å.

L.-G. Lindberg, P. Å. Öberg, “Optical properties of blood in motion,” Opt. Eng. 32, 253–257 (1993).
[CrossRef]

Perutz, M. F.

M. F. Perutz, K. Imai, “Regulation of oxygen affinity of mammalian haemoglobins,” J. Mol. Biol. 136, 183–191 (1980).
[CrossRef] [PubMed]

Polyzos, D.

Prostakova, I. V.

N. V. Shepelevich, I. V. Prostakova, V. N. Lopatin, “Light-scattering by optically soft randomly oriented spheroids,” J. Quant. Spectrosc. Radiat. Transfer 70, 375–381 (2001).
[CrossRef]

Roggan, A.

A. Roggan, M. Friebel, K. Dörschel, A. Hahn, G. Müller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. 4, 36–46 (1999).
[CrossRef] [PubMed]

Sakamoto, K.

K. Sakamoto, H. Kanai, “Electrical characteristics of flowing blood,” IEEE Trans. Biomed. Eng. BME-26, 686–695 (1979).
[CrossRef]

Schlichting, H.

H. Schlichting, Boundary-Layer Theory (McGraw-Hill, New York, 1968).

Schmid-Schönbein, H.

H. Schmid-Schönbein, K. A. Kline, L. Heinrich, E. Volger, T. Fischer, “Microrheology and light transmission of blood. III. The velocity of red cell aggregate formation,” Pflügers Arch. 354, 299–317 (1975).
[CrossRef] [PubMed]

H. Schmid-Schönbein, E. Volger, H. J. Klose, “Microrheology and light transmission of blood. II. The photometric quantification of red cell aggregate formation and dispersion in flow,” Pflügers Arch. 333, 140–155 (1972).
[CrossRef] [PubMed]

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, H. Schmid-Schönbein, “Microrheology and light transmission of blood. I. The photometric effects of red cell aggregation and red cell orientation,” Pflügers Arch. 333, 126–139 (1972).
[CrossRef] [PubMed]

J. Goldstone, H. Schmid-Schönbein, R. Wells, “The rheology of red blood cell aggregates,” Microvasc. Res. 2, 273–286 (1970).
[CrossRef] [PubMed]

H. Schmid-Schönbein, R. Wells, “Fluid drop-like transition of erythrocytes under shear,” Science 165, 288–291 (1969).
[CrossRef]

Schwarzmaier, H.-J.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4, 47–53 (1999).
[CrossRef] [PubMed]

Schweitzer, D.

M. Hammer, A. N. Yaroslavsky, D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. 47, N65–N69 (2001).
[CrossRef]

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

Sellountos, E. J.

Shepelevich, N. V.

N. V. Shepelevich, I. V. Prostakova, V. N. Lopatin, “Light-scattering by optically soft randomly oriented spheroids,” J. Quant. Spectrosc. Radiat. Transfer 70, 375–381 (2001).
[CrossRef]

Steenbergen, W.

Thamm, E.

Tsinopoulos, S. V.

Tycko, D. H.

van de Hulst, H. C.

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

Volger, E.

H. Schmid-Schönbein, K. A. Kline, L. Heinrich, E. Volger, T. Fischer, “Microrheology and light transmission of blood. III. The velocity of red cell aggregate formation,” Pflügers Arch. 354, 299–317 (1975).
[CrossRef] [PubMed]

H. Schmid-Schönbein, E. Volger, H. J. Klose, “Microrheology and light transmission of blood. II. The photometric quantification of red cell aggregate formation and dispersion in flow,” Pflügers Arch. 333, 140–155 (1972).
[CrossRef] [PubMed]

H. J. Klose, E. Volger, H. Brechtelsbauer, L. Heinich, H. Schmid-Schönbein, “Microrheology and light transmission of blood. I. The photometric effects of red cell aggregation and red cell orientation,” Pflügers Arch. 333, 126–139 (1972).
[CrossRef] [PubMed]

Wang, L.

L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Computer Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Wells, R.

J. Goldstone, H. Schmid-Schönbein, R. Wells, “The rheology of red blood cell aggregates,” Microvasc. Res. 2, 273–286 (1970).
[CrossRef] [PubMed]

H. Schmid-Schönbein, R. Wells, “Fluid drop-like transition of erythrocytes under shear,” Science 165, 288–291 (1969).
[CrossRef]

Yaroslavsky, A. N.

M. Hammer, A. N. Yaroslavsky, D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. 47, N65–N69 (2001).
[CrossRef]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4, 47–53 (1999).
[CrossRef] [PubMed]

Yaroslavsky, I. V.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4, 47–53 (1999).
[CrossRef] [PubMed]

Zheng, L.

L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Computer Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Appl. Opt. (6)

Biorheology (1)

H. Bäumler, B. Neu, R. Mitlöhner, R. Georgieva, H. J. Meiselman, H. Kiesewetter, “Electrophoretic and aggregation behavior of bovine, horse and human red blood cells in plasma and in polymer solutions,” Biorheology 38, 39–51 (2001).
[PubMed]

Clin. Hemorheol. Microcirc. (1)

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Figures (9)

Fig. 1
Fig. 1

Schematic of the flow setup in which the blood was circulating: a flask and a cuvette, connected by PVC tubing. A detailed drawing of the cuvette is also shown.

Fig. 2
Fig. 2

Optical setup with the integrating sphere and the two detection systems: the spectrometer-CCD camera for spectral measurements and the photodiode-lock-in amplifier for faster data sampling. The transmitted and reflected light was measured with the cuvette placed in position T and R, respectively.

Fig. 3
Fig. 3

Bovine RBC spheroid equivalents for the T-matrix computations, representing the different morphological conditions studied experimentally. We modeled the effect of cell alignment by varying the orientation of the symmetry axis of the RBC spheroid relative to the incident beam (arrows) from (a) 0° (oblate, a/ b = 0.617, x = 16.36) to (b) 90° (oblate, a/ b = 0.617, x = 16.36). (c) Model of cell-elongation influence (prolate, a = 2.625, a/ b = 1.369, x = 27.83).

Fig. 4
Fig. 4

Processed CCD image of the relative difference in transmittance (633 nm) of flowing (400 ml/min) and nonflowing blood. Bright areas correspond to higher transmittance under flowing conditions compared with nonflowing; dark areas to weaker transmittance; and medium gray to no significant difference. The blood was flowing from left to right. The circle shows the optical probe position, and the traces show the intensity along the two vertical lines indicated.

Fig. 5
Fig. 5

(a) Transmittance T and reflectance R spectra for three blood samples with Hb contents of 112, 125 and 143 g/l. The blood was flowing at 200 ml/min, corresponding to a shear rate of 800 s-1. (b) Reduced scattering and absorption coefficients were obtained from the data in (a) by means of an inverse Monte Carlo method.

Fig. 6
Fig. 6

(a) Transmittance, (b) reflectance, (c) scattering, and (d) absorption at 800 nm versus applied shear rate. The average values and standard deviations of seven samples with values of Hb ranging from 112 to 145 g/l are shown. The optical signals were normalized at a shear rate of 800 s-1. Data represented by the solid curves were collected with increasing shear rates at the discrete points shown. The dashed curves were interpolated from the results shown in Fig. 7; i.e., data continuously collected after flow stop.

Fig. 7
Fig. 7

(a) Light transmittance and reflectance as well as (b) reduced scattering and absorption coefficients measured by means of lock-in detection, with a sample rate of 1 sample/s. During the first 20 s the blood was flowing at 200 ml/min (800 s-1), after which the pump was turned off. The recording on nonflowing blood continued for another 10 min, after which the flow at 200 ml/min was resumed. The signals are normalized with respect to the average value of data collected during the first 20 s. Average values and standard deviations for four blood samples are shown.

Fig. 8
Fig. 8

Reduced scattering and absorption cross sections per cell with increasing aggregate size. The data were obtained from scattering computations of prolate-shaped aggregates, represented by a power-law distribution of spheres.

Fig. 9
Fig. 9

Reduced scattering and absorption cross sections of the oblate-shaped RBC spheroid [Figs. 3(a) and 3(b)] with increasing angle between the symmetry axis and the incident beam. Note the different scales on the vertical axes.

Tables (2)

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Table 1 Average Values and Standard Deviations of the Relative Change in Experimentally Measured Optical Properties of Whole Blood

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Table 2 Optical Properties Obtained from T-Matrix Computations of Spheroids, Modeling the Listed Morphological Conditions of RBCsa

Equations (5)

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

Grecty= dUydy= 12Qyht3 h  t
T=IT/Iref,
R=RBSIR/Iref,
g=N  Pθ, ϕcosθsinθdθdϕ,
fx= ε4xspheroid5ε2-1x5ε2-1xspheroid2ε2-x1/2,

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