Abstract

We propose a method for characterization of mature red blood cells (RBCs) morphology, based on measurement of light-scattering patterns (LSPs) of individual RBCs with the scanning flow cytometer and on solution of the inverse light-scattering (ILS) problem for each LSP. We considered a RBC shape model, corresponding to the minimal bending energy of the membrane with isotropic elasticity, and constructed an analytical approximation, which allows rapid simulation of the shape, given the diameter and minimal and maximal thicknesses. The ILS problem was solved by the nearest-neighbor interpolation using a preliminary calculated database of 250,000 theoretical LSPs. For each RBC in blood sample we determined three abovementioned shape characteristics and refractive index, which also allows us to calculate volume, surface area, sphericity index, spontaneous curvature, hemoglobin concentration and content.

© 2016 Optical Society of America

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References

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  1. 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] [PubMed]
  2. 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] [PubMed]
  3. T. Arnfred, S. D. Kristensen, and V. Munck, “Coulter 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(8), 717–721 (1981).
    [Crossref]
  4. D. H. Tycko, M. H. Metz, E. A. Epstein, and A. Grinbaum, “Flow-cytometric light scattering measurement of red blood cell volume and hemoglobin concentration,” Appl. Opt. 24(9), 1355–1365 (1985).
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  5. K. A. Sem’yanov, 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] [PubMed]
  6. 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]
  7. B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
    [Crossref] [PubMed]
  8. Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
    [Crossref] [PubMed]
  9. V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71(1), 243–255 (2000).
    [Crossref]
  10. 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]
  11. D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
    [Crossref] [PubMed]
  12. V. P. Maltsev, A. V. Chernyshev, and D. I. Strokotov, “Light-Scattering Flow Cytometry: Advanced Characterization of Individual Particle Morphology,” in Flow Cytometry: Principles, Methodology and Applications, S. Papandreou, ed. (Nova Science Publishers, 2013), pp. 79–103.
  13. A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
    [Crossref]
  14. A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  16. J. Hellmers, E. Eremina, and T. Wriedt, “Simulation of light scattering by biconcave Cassini ovals using the nullfield method with discrete sources,” J. Opt. A., Pure Appl. Opt. 8(1), 1–9 (2006).
    [Crossref]
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  19. H. J. Deuling and W. Helfrich, “The curvature elasticity of fluid membranes : A catalogue of vesicle shapes,” J. Phys. 37(11), 1335–1345 (1976).
    [Crossref]
  20. K. Khairy and J. Howard, “Spherical harmonics-based parametric deconvolution of 3D surface images using bending energy minimization,” Med. Image Anal. 12(2), 217–227 (2008).
    [Crossref] [PubMed]
  21. K. A. Brakke, “The Surface Evolver,” Exp. Math. 1(2), 141–165 (1992).
    [Crossref]
  22. 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]
  23. M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2234–2247 (2011).
    [Crossref]
  24. K. V. Gilev, E. Eremina, M. A. Yurkin, and V. P. Maltsev, “Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells,” Opt. Express 18(6), 5681–5690 (2010).
    [Crossref] [PubMed]
  25. S. Prahl, “Optical Absorption of Hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/index.html .

2014 (2)

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

2013 (1)

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

2011 (1)

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

2010 (2)

K. V. Gilev, E. Eremina, M. A. Yurkin, and V. P. Maltsev, “Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells,” Opt. Express 18(6), 5681–5690 (2010).
[Crossref] [PubMed]

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] [PubMed]

2009 (1)

D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
[Crossref] [PubMed]

2008 (2)

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

K. Khairy and J. Howard, “Spherical harmonics-based parametric deconvolution of 3D surface images using bending energy minimization,” Med. Image Anal. 12(2), 217–227 (2008).
[Crossref] [PubMed]

2006 (1)

J. Hellmers, E. Eremina, and T. Wriedt, “Simulation of light scattering by biconcave Cassini ovals using the nullfield method with discrete sources,” J. Opt. A., Pure Appl. Opt. 8(1), 1–9 (2006).
[Crossref]

2005 (1)

2000 (2)

1998 (1)

A. G. Borovoi, E. I. Naats, and U. G. Oppel, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3(3), 364–372 (1998).
[Crossref] [PubMed]

1992 (1)

K. A. Brakke, “The Surface Evolver,” Exp. Math. 1(2), 141–165 (1992).
[Crossref]

1985 (1)

1981 (2)

T. Arnfred, S. D. Kristensen, and V. Munck, “Coulter 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(8), 717–721 (1981).
[Crossref]

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]

1976 (1)

H. J. Deuling and W. Helfrich, “The curvature elasticity of fluid membranes : A catalogue of vesicle shapes,” J. Phys. 37(11), 1335–1345 (1976).
[Crossref]

1973 (1)

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]

1970 (1)

P. B. Canham, “The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell,” J. Theor. Biol. 26, 61–76 (1970).

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] [PubMed]

Arnfred, T.

T. Arnfred, S. D. Kristensen, and V. Munck, “Coulter 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(8), 717–721 (1981).
[Crossref]

Barbul, A.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Borovoi, A. G.

A. G. Borovoi, E. I. Naats, and U. G. Oppel, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3(3), 364–372 (1998).
[Crossref] [PubMed]

Brakke, K. A.

K. A. Brakke, “The Surface Evolver,” Exp. Math. 1(2), 141–165 (1992).
[Crossref]

Burton, A. C.

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] [PubMed]

Canham, P. B.

P. B. Canham, “The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell,” J. Theor. Biol. 26, 61–76 (1970).

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] [PubMed]

Chernyshev, A. V.

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[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]

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]

Chikova, E. D.

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

Dao, M.

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] [PubMed]

Depeursinge, C.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Deuling, H. J.

H. J. Deuling and W. Helfrich, “The curvature elasticity of fluid membranes : A catalogue of vesicle shapes,” J. Phys. 37(11), 1335–1345 (1976).
[Crossref]

Diez-Silva, M.

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] [PubMed]

Emery, Y.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Epstein, E. A.

Eremina, E.

K. V. Gilev, E. Eremina, M. A. Yurkin, and V. P. Maltsev, “Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells,” Opt. Express 18(6), 5681–5690 (2010).
[Crossref] [PubMed]

J. Hellmers, E. Eremina, and T. Wriedt, “Simulation of light scattering by biconcave Cassini ovals using the nullfield method with discrete sources,” J. Opt. A., Pure Appl. Opt. 8(1), 1–9 (2006).
[Crossref]

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]

Gilev, K. V.

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

K. V. Gilev, E. Eremina, M. A. Yurkin, and V. P. Maltsev, “Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells,” Opt. Express 18(6), 5681–5690 (2010).
[Crossref] [PubMed]

D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
[Crossref] [PubMed]

Grinbaum, A.

Han, J.

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] [PubMed]

Helfrich, W.

H. J. Deuling and W. Helfrich, “The curvature elasticity of fluid membranes : A catalogue of vesicle shapes,” J. Phys. 37(11), 1335–1345 (1976).
[Crossref]

Hellmers, J.

J. Hellmers, E. Eremina, and T. Wriedt, “Simulation of light scattering by biconcave Cassini ovals using the nullfield method with discrete sources,” J. Opt. A., Pure Appl. Opt. 8(1), 1–9 (2006).
[Crossref]

Hoekstra, A. G.

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

D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
[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]

Howard, J.

K. Khairy and J. Howard, “Spherical harmonics-based parametric deconvolution of 3D surface images using bending energy minimization,” Med. Image Anal. 12(2), 217–227 (2008).
[Crossref] [PubMed]

Jang, S.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

Khairy, K.

K. Khairy and J. Howard, “Spherical harmonics-based parametric deconvolution of 3D surface images using bending energy minimization,” Med. Image Anal. 12(2), 217–227 (2008).
[Crossref] [PubMed]

Kim, K.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

Kim, Y.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

Konokhova, A. I.

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

Korenstein, R.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Kristensen, S. D.

T. Arnfred, S. D. Kristensen, and V. Munck, “Coulter 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(8), 717–721 (1981).
[Crossref]

Lim, C.-T.

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] [PubMed]

Magistretti, P. J.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Maltsev, V. P.

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

K. V. Gilev, E. Eremina, M. A. Yurkin, and V. P. Maltsev, “Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells,” Opt. Express 18(6), 5681–5690 (2010).
[Crossref] [PubMed]

D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
[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]

K. A. Sem’yanov, 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] [PubMed]

V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71(1), 243–255 (2000).
[Crossref]

Marquet, P.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Metz, M. H.

Mikhaelis, I. M.

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

Moskalensky, A. E.

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

Munck, V.

T. Arnfred, S. D. Kristensen, and V. Munck, “Coulter 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(8), 717–721 (1981).
[Crossref]

Naats, E. I.

A. G. Borovoi, E. I. Naats, and U. G. Oppel, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3(3), 364–372 (1998).
[Crossref] [PubMed]

Nekrasov, V. M.

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

Oppel, U. G.

A. G. Borovoi, E. I. Naats, and U. G. Oppel, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3(3), 364–372 (1998).
[Crossref] [PubMed]

Park, H.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

Park, Y.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

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.

Rappaz, B.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Rodionov, A. A.

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

Rubtsov, N. B.

D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
[Crossref] [PubMed]

Sem’yanov, K. A.

Semyanov, K. A.

Shim, H.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

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, J. T.

Strokotov, D. I.

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
[Crossref] [PubMed]

Suresh, S.

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] [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]

Tsvetovskaya, G. A.

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

Tycko, D. H.

van Bockstaele, D. R.

D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
[Crossref] [PubMed]

Wriedt, T.

J. Hellmers, E. Eremina, and T. Wriedt, “Simulation of light scattering by biconcave Cassini ovals using the nullfield method with discrete sources,” J. Opt. A., Pure Appl. Opt. 8(1), 1–9 (2006).
[Crossref]

Yurkin, M. A.

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

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

K. V. Gilev, E. Eremina, M. A. Yurkin, and V. P. Maltsev, “Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells,” Opt. Express 18(6), 5681–5690 (2010).
[Crossref] [PubMed]

D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
[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]

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. (3)

Biophys. J. (1)

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 (1)

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]

Circ. Res. (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] [PubMed]

Cytometry A (1)

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Exp. Math. (1)

K. A. Brakke, “The Surface Evolver,” Exp. Math. 1(2), 141–165 (1992).
[Crossref]

Int. Dairy J. (1)

A. I. Konokhova, A. A. Rodionov, K. V. Gilev, I. M. Mikhaelis, D. I. Strokotov, A. E. Moskalensky, M. A. Yurkin, A. V. Chernyshev, and V. P. Maltsev, “Enhanced characterisation of milk fat globules by their size, shape and refractive index with scanning flow cytometry,” Int. Dairy J. 39(2), 316–323 (2014).
[Crossref]

J. Biomed. Opt. (3)

A. E. Moskalensky, M. A. Yurkin, A. I. Konokhova, D. I. Strokotov, V. M. Nekrasov, A. V. Chernyshev, G. A. Tsvetovskaya, E. D. Chikova, and V. P. Maltsev, “Accurate measurement of volume and shape of resting and activated blood platelets from light scattering,” J. Biomed. Opt. 18(1), 017001 (2013).
[Crossref] [PubMed]

A. G. Borovoi, E. I. Naats, and U. G. Oppel, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3(3), 364–372 (1998).
[Crossref] [PubMed]

D. I. Strokotov, M. A. Yurkin, K. V. Gilev, D. R. van Bockstaele, A. G. Hoekstra, N. B. Rubtsov, and V. P. Maltsev, “Is there a difference between T- and B-lymphocyte morphology?” J. Biomed. Opt. 14(6), 064036 (2009).
[Crossref] [PubMed]

J. Opt. A., Pure Appl. Opt. (1)

J. Hellmers, E. Eremina, and T. Wriedt, “Simulation of light scattering by biconcave Cassini ovals using the nullfield method with discrete sources,” J. Opt. A., Pure Appl. Opt. 8(1), 1–9 (2006).
[Crossref]

J. Phys. (1)

H. J. Deuling and W. Helfrich, “The curvature elasticity of fluid membranes : A catalogue of vesicle shapes,” J. Phys. 37(11), 1335–1345 (1976).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (1)

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

J. Theor. Biol. (1)

P. B. Canham, “The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell,” J. Theor. Biol. 26, 61–76 (1970).

Med. Image Anal. (1)

K. Khairy and J. Howard, “Spherical harmonics-based parametric deconvolution of 3D surface images using bending energy minimization,” Med. Image Anal. 12(2), 217–227 (2008).
[Crossref] [PubMed]

MRS Bull. (1)

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] [PubMed]

Opt. Express (1)

Rev. Sci. Instrum. (1)

V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71(1), 243–255 (2000).
[Crossref]

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

T. Arnfred, S. D. Kristensen, and V. Munck, “Coulter 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(8), 717–721 (1981).
[Crossref]

Sci. Rep. (1)

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

Other (3)

V. P. Maltsev, A. V. Chernyshev, and D. I. Strokotov, “Light-Scattering Flow Cytometry: Advanced Characterization of Individual Particle Morphology,” in Flow Cytometry: Principles, Methodology and Applications, S. Papandreou, ed. (Nova Science Publishers, 2013), pp. 79–103.

Y. Kim, K. Kim, and Y. Park, “Measurement Techniques for Red Blood Cell Deformability: Recent Advances,” in Blood Cell - An Overview of Studies in Hematology, T. Moschandreou, ed. (InTech, 2012).

S. Prahl, “Optical Absorption of Hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/index.html .

Supplementary Material (1)

NameDescription
» Data File 1: CSV (2 KB)      Coefficients of polynomial approximation

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Figures (3)

Fig. 1
Fig. 1

Examples of RBC shape profiles computed by Deuling’s approach (differential equations). a) SI = 0.7, c0 = 0 μm−1, and various V; b) V = 90 fl, c0 = 0 μm−1, and various SI; c) V = 90 fl, SI = 0.7, and various c0; d) ambiguous solution for V = 90 fl, SI = 0.8, c0 = −1.5 μm−1.

Fig. 2
Fig. 2

Alternative characteristics of RBC, resulting in unique shape definition.

Fig. 3
Fig. 3

Typical experimental LSP (points), best-fit theoretical LSP (solid gray line), best-fit (BF) values and confidence intervals (ME ± SD) for primary and derivative characteristics.

Tables (1)

Tables Icon

Table 1 Ranges of characteristics (components of Q) for construction of LSP database.

Equations (4)

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E(A, c 0 )=( k c /2 ) A ( c p + c m c 0 ) 2 dS
z=±(d/2 ) 1 ( 2x /d ) 2 n=0 N1 C n ( 2x /d ) 2n ,
C k ( h 1 /d , h 2 /d )= i,j=0 4 p i,j k ( h 1 /d ) i ( h 2 /d ) j ,
Φ( Q )= I exp I th (Q) 2 = j=1 k [ w( θ j )( I exp ( θ j ) I th ( θ j ,Q)) ] 2 ,

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