Abstract

Light scattering by single cells is widely applied for flow cytometric differentiation of cells. However, even for human red blood cells (RBCs), which can be modeled as homogeneous dielectric particles, the potential of light scattering is not yet fully exploited. We developed a dedicated flow cytometer to simultaneously observe the forward scattering cross section (FSC) of RBCs for orthogonal laser beams with incident wave vectors $\vec {k}_1$ and $\vec {k}_2$. At a wavelength $\lambda = 632.8\;\textrm{nm}$, bimodal distributions are observed in two-dimensional dot plots of FSC($\vec {k}_1$) vs. FSC($\vec {k}_2$), which result from the RBCs’ random orientation around the direction of flow, as well as from the distributions of their size and their optical properties. Typically, signals of $7.5\times 10^4$ RBCs were analyzed. We actively oriented the cells in the cytometer to prove that orientation is the main cause of bimodality. In addition, we studied the wavelength dependence of FSC($\vec {k}_1$) using $\lambda = 413.1\;\textrm{nm},\;457.9\;\textrm{nm},\;488\;\textrm{nm}$ and 632.8 nm, covering both weak and strong light absorption by the RBCs. Simulations of the light scattering by single RBCs were performed using the discrete dipole approximation (DDA) for a range of sizes, orientations and optical properties to obtain FSC distributions from RBC ensembles. Using the axisymmetric biconcave equilibrium shape of native RBCs, the experimentally observed distributions cannot be reproduced. If, however, an elongated shape model is employed that accounts for the stretching of the cell by hydrodynamic forces in the cytometer, the features of the strongly bimodal measured frequency distributions are reproduced by the simulation. Elongation ratios significantly greater than 1 in the range of 1.5 to 2.5 yield the best agreement between experiments and simulated data.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2018 (2)

M. Mugnano, P. Memmolo, L. Miccio, F. Merola, V. Bianco, A. Bramanti, A. Gambale, R. Russo, I. Andolfo, A. Iolascon, and P. Ferraro, “Label-free optical marker for red-blood-cell phenotyping of inherited anemias,” Anal. Chem. 90(12), 7495–7501 (2018).
[Crossref]

N. Toepfner, C. Herold, O. Otto, P. Rosendahl, A. Jacobi, M. Kräter, J. Stächele, L. Menschner, M. Herbig, L. Ciuffreda, L. Ranford-Cartwright, M. Grzybek, Ü. Coskun, E. Reithuber, G. Garriss, P. Mellroth, B. Henriques-Normark, N. Tregay, M. Suttorp, M. Bornhauser, E. R. Chilvers, R. Berner, and J. Guck, “Detection of human disease conditions by single-cell morpho-rheological phenotyping of blood,” eLife 7, e29213 (2018).
[Crossref]

2017 (4)

J. E. Mancuso and W. D. Ristenpart, “Stretching of red blood cells at high strain rates,” Phys. Rev. Fluids 2(10), 101101 (2017).
[Crossref]

K. Gilev, E. Yastrebova, D. Strokotov, M. Yurkin, N. Karmadonova, A. Chernyshev, V. Lomivorotov, and V. Maltsev, “Advanced consumable-free morphological analysis of intact red blood cells by a compact scanning flow cytometer,” Cytometry 91(9), 867–873 (2017).
[Crossref]

A. von Meyer, J. Cadamuro, T. Streichert, E. Gurr, G. M. Fiedler, A. Leichtle, A. Petersmann, K.-H. Pick, M. Orth, L. Risch, O. Sonntag, Y. Schmitt, B. Wiegel, T. Gottfried, and W. G. Guder, “Standard operating procedure for peripheral venous blood sampling,” Laboratoriumsmedizin 41(6), 333–340 (2017).
[Crossref]

J. Mauer, M. Peltomäki, S. Poblete, G. Gompper, and D. A. Fedosov, “Static and dynamic light scattering by red blood cells: A numerical study,” PLoS One 12(5), e0176799–19 (2017).
[Crossref]

2016 (2)

2015 (1)

D. Dannhauser, D. Rossi, F. Causa, P. Memmolo, A. Finizio, T. Wriedt, J. Hellmers, Y. Eremin, P. Ferraro, and P. A. Netti, “Optical signature of erythrocytes by light scattering in microfluidic flows,” Lab Chip 15(16), 3278–3285 (2015).
[Crossref]

2014 (1)

J. B. Freund, “Numerical simulation of flowing blood cells,” Annu. Rev. Fluid Mech. 46(1), 67–95 (2014).
[Crossref]

2013 (2)

C. Ahlgrim, T. Pottgiesser, T. Sander, Y. O. Schumacher, and M. W. Baumstark, “Flow cytometric assessment of erythrocyte shape through analysis of FSC histograms: Use of kurtosis and implications for longitudinal evaluation,” PLoS One 8(3), e59862 (2013).
[Crossref]

T. Yaginuma, M. S. N. Oliveira, R. Lima, T. Ishikawa, and T. Yamaguchi, “Human red blood cell behavior under homogeneous extensional flow in a hyperbolic-shaped microchannel,” Biomicrofluidics 7(5), 054110 (2013).
[Crossref]

2012 (1)

C. Misbah, “Vesicles, capsules and red blood cells under flow,” J. Phys.: Conf. Ser. 392, 012005 (2012).
[Crossref]

2011 (1)

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: Capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transfer 112(13), 2234–2247 (2011).
[Crossref]

2010 (2)

M. Diez-Silva, M. Dao, J. Han, C.-T. Lim, and S. Suresh, “Shape and biomechanical characteristics of human red blood cells in health and disease,” MRS Bull. 35(5), 382–388 (2010).
[Crossref]

Ö. Ergül, A. Arslan-Ergül, and L. Gürel, “Computational study of scattering from healthy and diseased red blood cells,” J. Biomed. Opt. 15(4), 045004 (2010).
[Crossref]

2009 (2)

S. S. Lee, Y. Yim, K. H. Ahn, and S. J. Lee, “Extensional flow-based assessment of red blood cell deformability using hyperbolic converging microchannel,” Biomed. Microdevices 11(5), 1021–1027 (2009).
[Crossref]

G. Tomaiuolo, M. Simeone, V. Martinelli, B. Rotoli, and S. Guido, “Red blood cell deformation in microconfined flow,” Soft Matter 5(19), 3736–3740 (2009).
[Crossref]

2007 (4)

S. Suresh, “Biomechanics and biophysics of cancer cells,” Acta Mater. 55(12), 3989–4014 (2007).
[Crossref]

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. W. Tan, C. T. Lim, G. Milon, P. H. David, O. Mercereau-Puijalon, S. Bonnefoy, and S. Suresh, “Effect of plasmodial RESA protein on deformability of human red blood cells harboring Plasmodium falciparum,” Proc. Natl. Acad. Sci. 104(22), 9213–9217 (2007).
[Crossref]

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106(1-3), 558–589 (2007).
[Crossref]

M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt. 46(18), 3811–3820 (2007).
[Crossref]

2006 (2)

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh, “Light scattering by single erythrocyte: Comparison of different methods,” J. Quant. Spectrosc. Radiat. Transfer 100(1-3), 444–456 (2006), VIII Conference on Electromagnetic and Light Scattering by Nonspherical Particles.
[Crossref]

M. Piagnerelli, K. Zouaoui Boudjeltia, D. Brohee, A. Vereerstraeten, P. Piro, J.-L. Vincent, and M. Vanhaeverbeek, “Assessment of erythrocyte shape by flow cytometry techniques,” J. Clin. Pathol. 60(5), 549–554 (2006).
[Crossref]

2005 (2)

2004 (2)

J. P. Mills, L. Qie, M. Dao, C. T. Lim, and S. Suresh, “Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers,” Mech. & chemistry biosystems : MCB 1(3), 169–180 (2004).

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry 59A(2), 203–209 (2004).
[Crossref]

1998 (1)

V. Ost, J. Neukammer, and H. Rinneberg, “Flow cytometric differentiation of erythrocytes and leukocytes in dilute whole blood by light scattering,” Cytometry 32(3), 191–197 (1998).
[Crossref]

1986 (1)

T. W. Secomb, R. Skalak, N. Özkaya, and J. F. Gross, “Flow of axisymmetric red blood cells in narrow capillaries,” J. Fluid Mech. 163, 405–423 (1986).
[Crossref]

1985 (1)

1984 (1)

H. A. Cranston, C. W. Boylan, G. L. Carroll, S. P. Sutera, J. R. Williamson, I. Y. Gluzman, and D. J. Krogstad, “Plasmodium falciparum maturation abolishes physiologic red cell deformability,” Science 223(4634), 400–403 (1984).
[Crossref]

1983 (1)

Y. R. Kim and L. Ornstein, “Isovolumetric sphering of erythrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3(6), 419–427 (1983).
[Crossref]

1981 (1)

Y. Fung, W. C. Tsang, and P. Patitucci, “High-resolution data on the geometry of red blood cells,” Biorheology 18(3-6), 369–385 (1981).
[Crossref]

1979 (1)

R. M. Hochmuth, P. R. Worthy, and E. A. Evans, “Red cell extensional recovery and the determination of membrane viscosity,” Biophys. J. 26(1), 101–114 (1979).
[Crossref]

1976 (1)

H. Reid, J. Dormandy, A. Barnes, P. Lock, and T. Dormandy, “Impaired red cell deformability in peripheral vascular disease,” Lancet 307(7961), 666–668 (1976). Originally published as Volume 1, Issue 7961.
[Crossref]

1973 (2)

H. Schmid-Schönbein, J. Weiss, and H. Ludwig, “A simple method for measuring red cell deformability in models of the microcirculation,” Blut 26(6), 369–379 (1973).
[Crossref]

R. Skalak, A. Tozeren, R. Zarda, and S. Chien, “Strain energy function of red blood cell membranes,” Biophys. J. 13(3), 245–264 (1973).
[Crossref]

1972 (1)

1968 (1)

P. B. Canham and A. C. Burton, “Distribution of size and shape in populations of normal human red cells,” Circ. Res. 22(3), 405–422 (1968).
[Crossref]

1957 (1)

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–445 (1908).
[Crossref]

Ahlgrim, C.

C. Ahlgrim, T. Pottgiesser, T. Sander, Y. O. Schumacher, and M. W. Baumstark, “Flow cytometric assessment of erythrocyte shape through analysis of FSC histograms: Use of kurtosis and implications for longitudinal evaluation,” PLoS One 8(3), e59862 (2013).
[Crossref]

Ahn, K. H.

S. S. Lee, Y. Yim, K. H. Ahn, and S. J. Lee, “Extensional flow-based assessment of red blood cell deformability using hyperbolic converging microchannel,” Biomed. Microdevices 11(5), 1021–1027 (2009).
[Crossref]

Andolfo, I.

M. Mugnano, P. Memmolo, L. Miccio, F. Merola, V. Bianco, A. Bramanti, A. Gambale, R. Russo, I. Andolfo, A. Iolascon, and P. Ferraro, “Label-free optical marker for red-blood-cell phenotyping of inherited anemias,” Anal. Chem. 90(12), 7495–7501 (2018).
[Crossref]

Arslan-Ergül, A.

Ö. Ergül, A. Arslan-Ergül, and L. Gürel, “Computational study of scattering from healthy and diseased red blood cells,” J. Biomed. Opt. 15(4), 045004 (2010).
[Crossref]

Bär, M.

Barer, R.

Barnes, A.

H. Reid, J. Dormandy, A. Barnes, P. Lock, and T. Dormandy, “Impaired red cell deformability in peripheral vascular disease,” Lancet 307(7961), 666–668 (1976). Originally published as Volume 1, Issue 7961.
[Crossref]

Baumstark, M. W.

C. Ahlgrim, T. Pottgiesser, T. Sander, Y. O. Schumacher, and M. W. Baumstark, “Flow cytometric assessment of erythrocyte shape through analysis of FSC histograms: Use of kurtosis and implications for longitudinal evaluation,” PLoS One 8(3), e59862 (2013).
[Crossref]

Berner, R.

N. Toepfner, C. Herold, O. Otto, P. Rosendahl, A. Jacobi, M. Kräter, J. Stächele, L. Menschner, M. Herbig, L. Ciuffreda, L. Ranford-Cartwright, M. Grzybek, Ü. Coskun, E. Reithuber, G. Garriss, P. Mellroth, B. Henriques-Normark, N. Tregay, M. Suttorp, M. Bornhauser, E. R. Chilvers, R. Berner, and J. Guck, “Detection of human disease conditions by single-cell morpho-rheological phenotyping of blood,” eLife 7, e29213 (2018).
[Crossref]

Bianco, V.

M. Mugnano, P. Memmolo, L. Miccio, F. Merola, V. Bianco, A. Bramanti, A. Gambale, R. Russo, I. Andolfo, A. Iolascon, and P. Ferraro, “Label-free optical marker for red-blood-cell phenotyping of inherited anemias,” Anal. Chem. 90(12), 7495–7501 (2018).
[Crossref]

Bilby, C.

B. Lincoln, H. M. Erickson, S. Schinkinger, F. Wottawah, D. Mitchell, S. Ulvick, C. Bilby, and J. Guck, “Deformability-based flow cytometry,” Cytometry 59A(2), 203–209 (2004).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bonnefoy, S.

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[Crossref]

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[Crossref]

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Proc. Natl. Acad. Sci. (1)

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. W. Tan, C. T. Lim, G. Milon, P. H. David, O. Mercereau-Puijalon, S. Bonnefoy, and S. Suresh, “Effect of plasmodial RESA protein on deformability of human red blood cells harboring Plasmodium falciparum,” Proc. Natl. Acad. Sci. 104(22), 9213–9217 (2007).
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Science (1)

H. A. Cranston, C. W. Boylan, G. L. Carroll, S. P. Sutera, J. R. Williamson, I. Y. Gluzman, and D. J. Krogstad, “Plasmodium falciparum maturation abolishes physiologic red cell deformability,” Science 223(4634), 400–403 (1984).
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G. Tomaiuolo, M. Simeone, V. Martinelli, B. Rotoli, and S. Guido, “Red blood cell deformation in microconfined flow,” Soft Matter 5(19), 3736–3740 (2009).
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Figures (7)

Fig. 1.
Fig. 1. Experimental setup to measure integrated scattering cross sections of forward scatter of RBCs at different wavelengths and solid angles of observation. (a) Setup for the detection of 2D FSC. The HeNe laser beam is divided by a polarizing beam splitter to allow simultaneous observation of forward scatter in two directions, characterized by orthogonal wavevectors $\vec {k}_1$ and $\vec {k}_2$. Two identical microscope objectives $7\times$ / N.A. = 0.19 to collimate scattered light were mounted. (b) Longitudinal section of the mounted flow cell with some characteristic measurements (in mm). Sheath fluid is indicated in blue, sample fluid in red. (c) For the 1D FSC($\vec {k}_1$) measurements at 4 laser wavelengths, an objective $20\times$ / N.A. = 0.4 was used. BS: beam splitter, IF: interference filter, PMT: photomultiplier tube, $\lambda /2$ and $\lambda /4$: retardation plates.
Fig. 2.
Fig. 2. (a) Cross section through the center of the undeformed shape model defined by Eq. (5). Surface triangulations of (b) the undeformed axisymmetric shape model and (c) the stretched model. Arrows indicate the orientation of the RBC relative to the flow axis and the two incident lasers with wavevectors $\vec {k}_1$ and $\vec {k}_2$. “Figure axis” denotes the symmetry axis before stretching.
Fig. 3.
Fig. 3. Measurement data (left) and simulation (right) of the 2-direction orthogonal FSC for native RBCs. Each isolated dark blue dot in the 2D plot corresponds to a single cell. Color codes the density of the dots (bright=high density). The histograms on the top and side are projections of the dot plot to a single axis. The simulation was performed using the stretched shape model and the hematological parameters from the CBC (Tab. 1) and 1×105 random samples. Top row: RBCs injected through a circular injection capillary (7.5×104 events) and simulation with uniformly distributed orientation angle $\beta \in \mathcal {U}(-90^{\circ }, 90^{\circ })$. Bottom row: Flattened capillary (9.7×104 events) resulting in preferential orientation “face-on to $\vec {k}_1$” and simulation with normally distributed orientation $\beta \in \mathcal {N}(0, 36^{\circ })$.
Fig. 4.
Fig. 4. Simulation of the 2D FSC in using the undeformed, axisymmetric shape model and the hematological parameters from the CBC. The bimodal distribution shown in Fig. 3 cannot be reproduced when neglecting the deformation of RBCs in flow.
Fig. 5.
Fig. 5. Dependence of the simulated FSC on orientation angle $\beta$ and elongation factor $f_x$ for fixed volume and Hb concentration.
Fig. 6.
Fig. 6. Comparison between measurements and simulations of the cross section for forward scatter FSC $(3.3^{\circ }\le \vartheta \le 17.4^{\circ })$ at four different laser vacuum wavelengths $\lambda$ with 2.9×105, 2.6×105, 2.1×105 and 2.8×105 measured events, respectively, from top to bottom. The $y$-axes show the probability density function. The simulated histograms (1×105 events) were smoothed using the 0.5 µm2 Gaussian noise that was also applied to the 2D histograms.
Fig. 7.
Fig. 7. Simulated dependence of the FSC of the stretched shape model on the waist diameter $2w_0$ of a (circular) Gaussian beam for an average-volume RBC and three different orientations $\beta$ at fixed Hb concentration. Dashed lines indicate the short ($2\,w_{0\parallel } = 10\;{\mu\textrm{m}}$) and long ($2\,w_{0\perp } = 42\;{\mu\textrm{m}}$) axis, respectively, of the elliptical focus employed in the experiment. A plane wave corresponds to $w_0\to \infty$.

Tables (3)

Tables Icon

Table 1. Hematological parameters of the concentration distribution (normal) and size distribution (log-normal) of the RBC sample. $\mathrm {MCHC} = \mathbb {E}(c_\textrm {Hb})$, $\mathrm {MCV} = \mathbb {E}(V)$ and $\mathrm {RDW} = \mathrm {CV}(V)$ were obtained from the complete blood count (CBC). Here $\mathbb {E}$ denotes the expectation value (or mean) and $\mathrm {CV}$ denotes the coefficient of variation, i. e., the relative standard deviation. Since the hemoglobin concentration distribution width $\mathrm {HDW} = \mathrm {CV}(c_\textrm {Hb})$ is not a routinely measured parameter in impedance-based analyzers, we set it to a typical value that best fits the measurements of sphered RBCs.

Tables Icon

Table 2. Parameters of the shape models used. The volume $V$ was varied by changing the diameter $D$ only. Parameters $D$, $c$, $h$ and $b$ refer to the axisymmetric shape before deformation. Values marked with an asterisk ($^*$) correspond to an average RBC with $V = 92.7\;{fL} = \mathrm {MCV}$. $S$ is the surface area and the sphericity index (SI) is defined as $\mathrm {SI} = {\sqrt [3]{36\pi \,V^2}}/{S}$.

Tables Icon

Table 3. RI of water and RBCs [30] (at ${c_{\textrm {Hb}}} = 344\;\textrm{g L}^{-1} = {\textrm {MCHC}}$) assumed for simulation. $\mathfrak {m} = \mathfrak {n}/n_{\textrm {H}_2\textrm{O}}$ is the relative RI of the RBCs.

Equations (18)

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ε ˙ max = 2 π V ˙ tan ( ψ / 2 ) R min 3 = 11.2 × 10 3 s 1 .
Δ E + n 2 k 2 E = 0 ,
n = n + i κ = ε r μ r
E = E i + E s .
ρ 4 + 2 R 4 ρ 2 z 2 + z 4 + R 1 ρ 2 + R 2 z 2 + R 3 = 0.
( x , y , z ) ( f x x , f y y , f z z ) .
n ( λ ; c Hb ) = n H 2 O ( λ ) + c Hb [ B ( λ ) + i α ( λ ) ] .
( I s , Q s , U s , V s ) T = 1 k m 2 r 2 S ( ϑ , φ ) ( I i , Q i , U i , V i ) T .
( I i , Q i , U i , V i ) T = I i ( 1 , cos 2 φ , sin 2 φ , 0 ) .
I s ( ϑ , φ ) = 1 k m 2 r 2 I i ( S 11 + S 12 cos 2 φ + S 13 sin 2 φ ) ,
FSC = 1 k m 2 Ω ( S 11 + S 12 cos 2 φ + S 13 sin 2 φ ) sin ϑ d ϑ d φ ,
Ω circle = { ϑ [ ϑ 1 , ϑ 2 ] , φ [ 0 , 2 π ] }
Ω stripe = { ϑ [ ϑ 3 , ϑ 4 ] , | sin φ | [ ϑ 3 / ϑ , 1 ] } .
β = 0 : 5 : 90 , c Hb = ( 290 : 15 : 395 ) g L 1 , D = ( 5.4 : 0.4 : 10.2 ) μ m .
FSC ( k 1 ) = g ( V , β , c Hb ) and FSC ( k 2 ) = g ( V , 90 β , c Hb )
v z ( ρ ) = v max [ 1 ρ 2 R eff 2 ] ,
γ ˙ typ = v z ( 0 ) v z ( Δ ρ ) Δ ρ = v max Δ ρ R eff 2 = 880 s 1 .
DI = f x 1 / f x f x + 1 / f x .