Abstract

The discrete sources method (DSM) and the discrete dipole approximation (DDA) were compared for simulation of light scattering by a red blood cell (RBC) model. We considered RBCs with diameters up to 8 μm (size parameter up to 38), relative refractive indices 1.03 and 1.06, and two different orientations. The agreement in the angle-resolved S 11 element of the Mueller matrix obtained by these methods is generally good, but it deteriorates with increasing scattering angle, diameter and refractive index of a RBC. Based on the DDA simulations with very fine discretization (up to 93 dipoles per wavelength) for a single RBC, we attributed most of the disagreement to the DSM, which results contain high-frequency ripples. For a single orientation of a RBC the DDA is comparable to or faster than the DSM. However, the relation is reversed when a set of particle orientations need to be simulated at once. Moreover, the DSM requires about an order of magnitude less computer memory. At present, application of the DSM for massive calculation of light scattering patterns of RBCs is hampered by its limitations in size parameter of a RBC due to the high number of harmonics used for calculations.

© 2010 OSA

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  5. M. A. Yurkin, K. A. Semyanov, P. A. Tarasov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Experimental and theoretical study of light scattering by individual mature red blood cells by use of scanning flow cytometry and a discrete dipole approximation,” Appl. Opt. 44(25), 5249–5256 (2005).
    [CrossRef] [PubMed]
  6. A. Karlsson, J. P. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. 52(1), 13–18 (2005).
    [CrossRef] [PubMed]
  7. T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh, “Light scattering by single erythrocyte: comparison of different methods,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 444–456 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. E. Eremina, “Light scattering by an erythrocyte based on Discrete Sources Method: shape and refractive index influence,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1526–1534 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [PubMed]
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    [CrossRef]
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  26. M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. I. Theoretical analysis,” J. Opt. Soc. Am. A 23(10), 2578–2591 (2006).
    [CrossRef]
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    [CrossRef]
  29. M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15(26), 17902–17911 (2007).
    [CrossRef] [PubMed]
  30. Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109(8), 1461–1473 (2008).
    [CrossRef]

2009

E. Eremina, “Light scattering by an erythrocyte based on Discrete Sources Method: shape and refractive index influence,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1526–1534 (2009).
[CrossRef]

2008

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109(8), 1461–1473 (2008).
[CrossRef]

2007

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15(26), 17902–17911 (2007).
[CrossRef] [PubMed]

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: An overview and recent developments,” JQSRT 106, 558–589 (2007).

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transf. 106(1-3), 546–557 (2007).
[CrossRef]

2006

E. Eremina, J. Hellmers, Y. Eremin, and T. Wriedt, “Different shape models for erythrocyte: Light scattering analysis based on the discrete sources method,” J. Quant. Spectrosc. Radiat. Transf. 102(1), 3–10 (2006).
[CrossRef]

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh, “Light scattering by single erythrocyte: comparison of different methods,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 444–456 (2006).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. I. Theoretical analysis,” J. Opt. Soc. Am. A 23(10), 2578–2591 (2006).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy,” J. Opt. Soc. Am. A 23(10), 2592–2601 (2006).
[CrossRef]

2005

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244(1-6), 15–23 (2005).
[CrossRef]

J. Q. Lu, P. Yang, and X. H. Hu, “Simulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. 10(2), 024022 (2005).
[CrossRef] [PubMed]

M. A. Yurkin, K. A. Semyanov, P. A. Tarasov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Experimental and theoretical study of light scattering by individual mature red blood cells by use of scanning flow cytometry and a discrete dipole approximation,” Appl. Opt. 44(25), 5249–5256 (2005).
[CrossRef] [PubMed]

A. Karlsson, J. P. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. 52(1), 13–18 (2005).
[CrossRef] [PubMed]

2000

Yu. Eremin, “The method of discrete sources in electromagnetic scattering by axially symmetric structures,” J. Commun. Technol. Electron. 45(Suppl.2), 269–280 (2000).

K. A. Semyanov, P. A. Tarasov, J. T. Soini, A. K. Petrov, and V. P. Maltsev, “Calibration-free method to determine the size and hemoglobin concentration of individual red blood cells from light scattering,” Appl. Opt. 39(31), 5884–5889 (2000).
[CrossRef]

1999

1998

1997

P. Mazeron, S. Muller, and H. El Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34(2), 99–110 (1997).
[CrossRef] [PubMed]

1994

1985

1981

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

1973

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

Alsholm, P.

Andersson-Engels, S.

A. Karlsson, J. P. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. 52(1), 13–18 (2005).
[CrossRef] [PubMed]

A. M. K. Nilsson, P. Alsholm, A. Karlsson, and S. Andersson-Engels, “T-Matrix Computations of Light Scattering by Red Blood Cells,” Appl. Opt. 37(13), 2735–2748 (1998).
[CrossRef]

Brock, R. S.

Chernyshev, A. V.

Chien, S.

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

Draine, B. T.

El Azouzi, H.

P. Mazeron, S. Muller, and H. El Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34(2), 99–110 (1997).
[CrossRef] [PubMed]

Epstein, E. A.

Eremin, Y.

E. Eremina, J. Hellmers, Y. Eremin, and T. Wriedt, “Different shape models for erythrocyte: Light scattering analysis based on the discrete sources method,” J. Quant. Spectrosc. Radiat. Transf. 102(1), 3–10 (2006).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244(1-6), 15–23 (2005).
[CrossRef]

Eremin, Yu.

Yu. Eremin, “The method of discrete sources in electromagnetic scattering by axially symmetric structures,” J. Commun. Technol. Electron. 45(Suppl.2), 269–280 (2000).

Eremina, E.

E. Eremina, “Light scattering by an erythrocyte based on Discrete Sources Method: shape and refractive index influence,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1526–1534 (2009).
[CrossRef]

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh, “Light scattering by single erythrocyte: comparison of different methods,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 444–456 (2006).
[CrossRef]

E. Eremina, J. Hellmers, Y. Eremin, and T. Wriedt, “Different shape models for erythrocyte: Light scattering analysis based on the discrete sources method,” J. Quant. Spectrosc. Radiat. Transf. 102(1), 3–10 (2006).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244(1-6), 15–23 (2005).
[CrossRef]

Flatau, P. J.

Fung, Y. C.

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

Grinbaum, A.

He, J. P.

A. Karlsson, J. P. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. 52(1), 13–18 (2005).
[CrossRef] [PubMed]

Hellmers, J.

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh, “Light scattering by single erythrocyte: comparison of different methods,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 444–456 (2006).
[CrossRef]

E. Eremina, J. Hellmers, Y. Eremin, and T. Wriedt, “Different shape models for erythrocyte: Light scattering analysis based on the discrete sources method,” J. Quant. Spectrosc. Radiat. Transf. 102(1), 3–10 (2006).
[CrossRef]

Hoekstra, A. G.

Hu, X. H.

J. Q. Lu, P. Yang, and X. H. Hu, “Simulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. 10(2), 024022 (2005).
[CrossRef] [PubMed]

Karlsson, A.

A. Karlsson, J. P. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. 52(1), 13–18 (2005).
[CrossRef] [PubMed]

A. M. K. Nilsson, P. Alsholm, A. Karlsson, and S. Andersson-Engels, “T-Matrix Computations of Light Scattering by Red Blood Cells,” Appl. Opt. 37(13), 2735–2748 (1998).
[CrossRef]

Lu, J. Q.

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15(26), 17902–17911 (2007).
[CrossRef] [PubMed]

J. Q. Lu, P. Yang, and X. H. Hu, “Simulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. 10(2), 024022 (2005).
[CrossRef] [PubMed]

Maltsev, V. P.

Mann, I.

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109(8), 1461–1473 (2008).
[CrossRef]

Mazeron, P.

P. Mazeron, S. Muller, and H. El Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34(2), 99–110 (1997).
[CrossRef] [PubMed]

Metz, M. H.

Mukai, S.

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109(8), 1461–1473 (2008).
[CrossRef]

Muller, S.

P. Mazeron, S. Muller, and H. El Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34(2), 99–110 (1997).
[CrossRef] [PubMed]

Nilsson, A. M. K.

Okada, Y.

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109(8), 1461–1473 (2008).
[CrossRef]

Patitucci, P.

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

Petrov, A. K.

Polyzos, D.

Sano, I.

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109(8), 1461–1473 (2008).
[CrossRef]

Schuh, R.

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh, “Light scattering by single erythrocyte: comparison of different methods,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 444–456 (2006).
[CrossRef]

Semyanov, K. A.

Shvalov, A. N.

Skalak, R.

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

Soini, E.

Soini, J. T.

Swartling, J.

A. Karlsson, J. P. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. 52(1), 13–18 (2005).
[CrossRef] [PubMed]

Tarasov, P. A.

Tozeren, A.

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

Tsang, W. C.

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

Tsinopoulos, S. V.

Tycko, D. H.

Wriedt, T.

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh, “Light scattering by single erythrocyte: comparison of different methods,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 444–456 (2006).
[CrossRef]

E. Eremina, J. Hellmers, Y. Eremin, and T. Wriedt, “Different shape models for erythrocyte: Light scattering analysis based on the discrete sources method,” J. Quant. Spectrosc. Radiat. Transf. 102(1), 3–10 (2006).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244(1-6), 15–23 (2005).
[CrossRef]

Yang, P.

J. Q. Lu, P. Yang, and X. H. Hu, “Simulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. 10(2), 024022 (2005).
[CrossRef] [PubMed]

Yurkin, M. A.

Zarda, R. P.

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

Appl. Opt.

Biophys. J.

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

Biorheology

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

P. Mazeron, S. Muller, and H. El Azouzi, “Deformation of erythrocytes under shear: a small-angle light scattering study,” Biorheology 34(2), 99–110 (1997).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng.

A. Karlsson, J. P. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. 52(1), 13–18 (2005).
[CrossRef] [PubMed]

J. Biomed. Opt.

J. Q. Lu, P. Yang, and X. H. Hu, “Simulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. 10(2), 024022 (2005).
[CrossRef] [PubMed]

J. Commun. Technol. Electron.

Yu. Eremin, “The method of discrete sources in electromagnetic scattering by axially symmetric structures,” J. Commun. Technol. Electron. 45(Suppl.2), 269–280 (2000).

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transf.

Y. Okada, I. Mann, I. Sano, and S. Mukai, “Acceleration of the iterative solver in the discrete dipole approximation: Application to the orientation variation of irregularly shaped particles,” J. Quant. Spectrosc. Radiat. Transf. 109(8), 1461–1473 (2008).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transf. 106(1-3), 546–557 (2007).
[CrossRef]

E. Eremina, J. Hellmers, Y. Eremin, and T. Wriedt, “Different shape models for erythrocyte: Light scattering analysis based on the discrete sources method,” J. Quant. Spectrosc. Radiat. Transf. 102(1), 3–10 (2006).
[CrossRef]

E. Eremina, “Light scattering by an erythrocyte based on Discrete Sources Method: shape and refractive index influence,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1526–1534 (2009).
[CrossRef]

T. Wriedt, J. Hellmers, E. Eremina, and R. Schuh, “Light scattering by single erythrocyte: comparison of different methods,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 444–456 (2006).
[CrossRef]

JQSRT

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: An overview and recent developments,” JQSRT 106, 558–589 (2007).

Opt. Commun.

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of light scattering by erythrocyte based on discrete sources method,” Opt. Commun. 244(1-6), 15–23 (2005).
[CrossRef]

Opt. Express

Other

M. A. Yurkin, “Discrete dipole simulations of light scattering by blood cells” PhD thesis, (University of Amsterdam, 2007).

“Description of the national compute cluster Lisa,” https://subtrac.sara.nl/userdoc/wiki/lisa/description (2009).

M. A. Yurkin, and A. G. Hoekstra, “User manual for the discrete dipole approximation code ADDA v.0.79,” http://a-dda.googlecode.com/svn/tags/rel_0_79/doc/manual.pdf (2009).

J. P. Greer, J. Foerster, and J. N. Lukens, eds., Wintrobe's Clinical Hematology, (Lippincott Williams & Wilkins Publishers, Baltimore, USA, 2003).

V. P. Maltsev, and K. A. Semyanov, Characterisation of Bio-Particles from Light Scattering, Inverse and Ill-Posed Problems Series (VSP, Utrecht, 2004).

“ADDA - light scattering simulator using the discrete dipole approximation”, http://code.google.com/p/a-dda/ (2009).

Y. Eremin, N. Orlov, and A. Sveshnikov, “Models of electromagnetic scattering problems based on discrete sources method” in: Generalizes Multipole Techniques for Electromagnetic and Light Scattering, T. Wriedt, ed. (Elsevier, Amsterdam, 1999), Chapter 4.

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Figures (7)

Fig. 1
Fig. 1

Profile of the RBC model with diameter 6 μm.

Fig. 2
Fig. 2

S 11(θ) in logarithmic scale for RBCs with D = 6 mm, m = 1.03 (a,c) and 1.06 (b,d), β = 0° (a,b) and 90° (c,d) simulated with the DSM and the DDA.

Fig. 5
Fig. 5

Same as Fig. 2, but for D = 8 mm.

Fig. 6
Fig. 6

Convergence of the DDA results for S 11(120°) with refining discretization for a RBC with D = 7.5 mm, m = 1.03, β = 0° (a) and β = 90° (b). Confidence intervals determined from these data (see text) are shown by hatched bands.

Fig. 3
Fig. 3

Same as Fig. 2, but for D = 7 mm.

Fig. 7
Fig. 7

Same as Fig. 4 (a,c), but with addition of confidence bounds obtained by DDA simulations with dipole sizes from λ/17 to λ/93 (see text).

Fig. 4
Fig. 4

Same as Fig. 2, but for D = 7.5 mm.

Tables (1)

Tables Icon

Table 1 Time and memory requirements for DSM and DDA methods.a

Equations (1)

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

z ( ρ ) = R 1 ( ρ R ) 2 ( C 0 + C 1 ( ρ R ) 2 + C 2 ( ρ R ) 4 ) , C 0 = 0.187 , C 1 = 1.035 , C 2 = 0.774 ,

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