Abstract

For studying the elastic properties of a biconcave red blood cell using the dual-trap optical tweezers without attaching microbeads to the cell, we implemented a three-dimensional finite element simulation of the light scattering and cell’s deformation using the coupled electromagnetic and continuum mechanics modules. We built the vector field of the trapping beams, the cell structure layout, the hyperelastic and viscoelastic cell materials, and we reinforced the constraints on the cell constant volume in the simulation. This computation model can be useful for studying the scattering and the other mechanical properties of the biological cells.

©2013 Optical Society of America

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  1. M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  27. E. A. Evans, “A new material concept for the red cell membrane,” Biophys. J. 13(9), 926–940 (1973).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2013 (1)

2012 (2)

J. H. Zhou, M. C. Zhong, Z. Q. Wang, and Y. M. Li, “Calculation of optical forces on an ellipsoid using vectorial ray tracing method,” Opt. Express 20(14), 14928–14937 (2012).
[Crossref] [PubMed]

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, and A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (2)

2009 (1)

M. Khan, H. Soni, and A. K. Sood, “Optical tweezers for probing erythrocyte membrane deformability,” Appl. Phys. Lett. 95(23), 233703 (2009).
[Crossref]

2008 (4)

Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. S. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008).
[Crossref] [PubMed]

C. Y. Chee, H. P. Lee, and C. Lu, “Using 3D fluid-structure interaction model to analyze the biomechanical properties of erythrocyte,” Phys. Lett. A 372(9), 1357–1362 (2008).
[Crossref]

G. B. Liao, P. B. Bareil, Y. Sheng, and A. Chiou, “One-dimensional jumping optical tweezers for optical stretching of bi-concave human red blood cells,” Opt. Express 16(3), 1996–2004 (2008).
[Crossref] [PubMed]

A. C. De Luca, G. Rusciano, R. Ciancia, V. Martinelli, G. Pesce, B. Rotoli, L. Selvaggi, and A. Sasso, “Spectroscopical and mechanical characterization of normal and thalassemic red blood cells by Raman Tweezers,” Opt. Express 16(11), 7943–7957 (2008).
[Crossref] [PubMed]

2007 (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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

2006 (1)

T. Wriedta, J. Hellmers, E. Ereminab, and R. Schuh, “Light scattering by single erythrocyte: Comparison of different Methods,” J. Quant. Spectrosc. Ra. 100(1-3), 444–456 (2006).
[Crossref]

2005 (4)

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. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10(6), 064013 (2005).
[Crossref] [PubMed]

A. Karlsson, J. 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]

M. Friebel and M. Meinke, “Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements,” J. Biomed. Opt. 10(6), 064019 (2005).
[Crossref] [PubMed]

2004 (1)

G. J. C. G. M. Bosman, “Erythrocyte aging in sickle cell disease,” Cell. Mol. Biol. (Noisy-le-grand) 50(1), 81–86 (2004).
[PubMed]

2003 (1)

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[Crossref]

1999 (1)

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999).
[Crossref]

1997 (1)

A. Krantz, “Red cell-mediated therapy: Opportunities and challenges,” Blood Cells Mol. Dis. 23(1), 58–68 (1997).
[Crossref] [PubMed]

1987 (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

1973 (2)

E. A. Evans, “A new material concept for the red cell membrane,” Biophys. J. 13(9), 926–940 (1973).
[Crossref] [PubMed]

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]

1972 (1)

E. Evans and Y. C. Fung, “Improved measurements of the erythrocyte geometry,” Microvasc. Res. 4(4), 335–347 (1972).
[Crossref] [PubMed]

Andersson-Engels, S.

A. Karlsson, J. 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]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

Bai, J. J.

Bareil, P. B.

Bareil, P. P.

Bonnefoy, S.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

Bosman, G. J. C. G. M.

G. J. C. G. M. Bosman, “Erythrocyte aging in sickle cell disease,” Cell. Mol. Biol. (Noisy-le-grand) 50(1), 81–86 (2004).
[PubMed]

Brown, A. T.

Y. Z. Yoon, J. Kotar, A. T. Brown, and P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[Crossref]

Chee, C. Y.

C. Y. Chee, H. P. Lee, and C. Lu, “Using 3D fluid-structure interaction model to analyze the biomechanical properties of erythrocyte,” Phys. Lett. A 372(9), 1357–1362 (2008).
[Crossref]

Chen, J. Y.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10(6), 064013 (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]

Chiou, A.

Choi, W. S.

Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. S. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008).
[Crossref] [PubMed]

Ciancia, R.

Cicuta, P.

Y. Z. Yoon, J. Kotar, A. T. Brown, and P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[Crossref]

Dao, M.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[Crossref]

David, P. H.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

De Luca, A. C.

Diez-Silva, M.

Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. S. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008).
[Crossref] [PubMed]

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

Ding, H.

Duval, P. L.

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

Eggleton, C. D.

Ereminab, E.

T. Wriedta, J. Hellmers, E. Ereminab, and R. Schuh, “Light scattering by single erythrocyte: Comparison of different Methods,” J. Quant. Spectrosc. Ra. 100(1-3), 444–456 (2006).
[Crossref]

Evans, E.

E. Evans and Y. C. Fung, “Improved measurements of the erythrocyte geometry,” Microvasc. Res. 4(4), 335–347 (1972).
[Crossref] [PubMed]

Evans, E. A.

E. A. Evans, “A new material concept for the red cell membrane,” Biophys. J. 13(9), 926–940 (1973).
[Crossref] [PubMed]

Fedyanin, A. A.

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, and A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[Crossref] [PubMed]

Feld, M. S.

Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. S. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008).
[Crossref] [PubMed]

Friebel, M.

M. Friebel and M. Meinke, “Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements,” J. Biomed. Opt. 10(6), 064019 (2005).
[Crossref] [PubMed]

Fung, Y. C.

E. Evans and Y. C. Fung, “Improved measurements of the erythrocyte geometry,” Microvasc. Res. 4(4), 335–347 (1972).
[Crossref] [PubMed]

Gu, M.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10(6), 064013 (2005).
[Crossref] [PubMed]

He, J.

A. Karlsson, J. 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. Wriedta, J. Hellmers, E. Ereminab, and R. Schuh, “Light scattering by single erythrocyte: Comparison of different Methods,” J. Quant. Spectrosc. Ra. 100(1-3), 444–456 (2006).
[Crossref]

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. 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]

Karmenyan, A.

Kauppila, A.

Kawata, S.

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999).
[Crossref]

Khan, M.

M. Khan, H. Soni, and A. K. Sood, “Optical tweezers for probing erythrocyte membrane deformability,” Appl. Phys. Lett. 95(23), 233703 (2009).
[Crossref]

Khokhlova, M. D.

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, and A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[Crossref] [PubMed]

Kinnunen, M.

Kotar, J.

Y. Z. Yoon, J. Kotar, A. T. Brown, and P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[Crossref]

Krantz, A.

A. Krantz, “Red cell-mediated therapy: Opportunities and challenges,” Blood Cells Mol. Dis. 23(1), 58–68 (1997).
[Crossref] [PubMed]

Lang, M. J.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

Lee, H. P.

C. Y. Chee, H. P. Lee, and C. Lu, “Using 3D fluid-structure interaction model to analyze the biomechanical properties of erythrocyte,” Phys. Lett. A 372(9), 1357–1362 (2008).
[Crossref]

Li, Y. M.

Liao, G. B.

Lim, C. T.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[Crossref]

Lim, J.

Lin, Z. F.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10(6), 064013 (2005).
[Crossref] [PubMed]

Lu, C.

C. Y. Chee, H. P. Lee, and C. Lu, “Using 3D fluid-structure interaction model to analyze the biomechanical properties of erythrocyte,” Phys. Lett. A 372(9), 1357–1362 (2008).
[Crossref]

Lu, J. Q.

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]

Lykotrafitis, G.

Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. S. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008).
[Crossref] [PubMed]

Lyubin, E. V.

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, and A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[Crossref] [PubMed]

Marr, D. W. M.

Martinelli, V.

Meinke, M.

M. Friebel and M. Meinke, “Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements,” J. Biomed. Opt. 10(6), 064019 (2005).
[Crossref] [PubMed]

Mercereau-Puijalon, O.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

Mills, J. P.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

Milon, G.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

Mir, M.

Myllylä, R.

Okamoto, K.

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999).
[Crossref]

Park, Y. K.

Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. S. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008).
[Crossref] [PubMed]

Pesce, G.

Popescu, G.

J. Lim, H. Ding, M. Mir, R. Zhu, K. Tangella, and G. Popescu, “Born approximation model for light scattering by red blood cells,” Biomed. Opt. Express 2(10), 2784–2791 (2011).
[Crossref] [PubMed]

Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. S. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008).
[Crossref] [PubMed]

Quinn, D. J.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

Rancourt-Grenier, S.

Rotoli, B.

Rusciano, G.

Sasso, A.

Schuh, R.

T. Wriedta, J. Hellmers, E. Ereminab, and R. Schuh, “Light scattering by single erythrocyte: Comparison of different Methods,” J. Quant. Spectrosc. Ra. 100(1-3), 444–456 (2006).
[Crossref]

Selvaggi, L.

Sheng, Y.

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]

Skryabina, M. N.

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, and A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[Crossref] [PubMed]

Soni, H.

M. Khan, H. Soni, and A. K. Sood, “Optical tweezers for probing erythrocyte membrane deformability,” Appl. Phys. Lett. 95(23), 233703 (2009).
[Crossref]

Sood, A. K.

M. Khan, H. Soni, and A. K. Sood, “Optical tweezers for probing erythrocyte membrane deformability,” Appl. Phys. Lett. 95(23), 233703 (2009).
[Crossref]

Sraj, I.

Suresh, S.

Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. S. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008).
[Crossref] [PubMed]

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[Crossref]

Swartling, J.

A. Karlsson, J. 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]

Szatmary, A. C.

Tan, K. S. W.

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

Tangella, K.

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]

Wang, P. N.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10(6), 064013 (2005).
[Crossref] [PubMed]

Wang, Z. Q.

Wei, M. T.

Wriedta, T.

T. Wriedta, J. Hellmers, E. Ereminab, and R. Schuh, “Light scattering by single erythrocyte: Comparison of different Methods,” J. Quant. Spectrosc. Ra. 100(1-3), 444–456 (2006).
[Crossref]

Xu, L.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10(6), 064013 (2005).
[Crossref] [PubMed]

Yamane, T.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

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]

Yoon, Y. Z.

Y. Z. Yoon, J. Kotar, A. T. Brown, and P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[Crossref]

Yu, J. T.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10(6), 064013 (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]

Zhong, M. C.

Zhou, J. H.

Zhu, R.

Appl. Phys. Lett. (1)

M. Khan, H. Soni, and A. K. Sood, “Optical tweezers for probing erythrocyte membrane deformability,” Appl. Phys. Lett. 95(23), 233703 (2009).
[Crossref]

Biomed. Opt. Express (2)

Biophys. J. (2)

E. A. Evans, “A new material concept for the red cell membrane,” Biophys. J. 13(9), 926–940 (1973).
[Crossref] [PubMed]

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]

Blood Cells Mol. Dis. (1)

A. Krantz, “Red cell-mediated therapy: Opportunities and challenges,” Blood Cells Mol. Dis. 23(1), 58–68 (1997).
[Crossref] [PubMed]

Cell. Mol. Biol. (Noisy-le-grand) (1)

G. J. C. G. M. Bosman, “Erythrocyte aging in sickle cell disease,” Cell. Mol. Biol. (Noisy-le-grand) 50(1), 81–86 (2004).
[PubMed]

IEEE Trans. Biomed. Eng. (1)

A. Karlsson, J. 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. (4)

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, and A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[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]

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10(6), 064013 (2005).
[Crossref] [PubMed]

M. Friebel and M. Meinke, “Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements,” J. Biomed. Opt. 10(6), 064019 (2005).
[Crossref] [PubMed]

J. Mech. Phys. Solids (1)

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[Crossref]

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

J. Quant. Spectrosc. Ra. (1)

T. Wriedta, J. Hellmers, E. Ereminab, and R. Schuh, “Light scattering by single erythrocyte: Comparison of different Methods,” J. Quant. Spectrosc. Ra. 100(1-3), 444–456 (2006).
[Crossref]

Microvasc. Res. (1)

E. Evans and Y. C. Fung, “Improved measurements of the erythrocyte geometry,” Microvasc. Res. 4(4), 335–347 (1972).
[Crossref] [PubMed]

Nature (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

Opt. Express (5)

Phys. Lett. A (1)

C. Y. Chee, H. P. Lee, and C. Lu, “Using 3D fluid-structure interaction model to analyze the biomechanical properties of erythrocyte,” Phys. Lett. A 372(9), 1357–1362 (2008).
[Crossref]

Phys. Rev. Lett. (1)

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (2)

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. U.S.A. 104(22), 9213–9217 (2007).
[Crossref] [PubMed]

Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. S. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A. 105(37), 13730–13735 (2008).
[Crossref] [PubMed]

Soft Matter (1)

Y. Z. Yoon, J. Kotar, A. T. Brown, and P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[Crossref]

Other (2)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

X. C. Fung, Biomechanics: Mechanical Properties of Living Tissue, 2nd ed. (Springer, 1993).

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Figures (6)

Fig. 1
Fig. 1 (a): Biconcave RBC in a dual-trap optical tweezers; (b) A quarter of the model used to compute light-scattering by the RBC.

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Fig. 2
Fig. 2 (a) Background electrical field; (b) Total electrical field on an RBC of diameter 7.8 μm with two trapping beams separated by 6.6 μm.

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Fig. 3
Fig. 3 Background field in the cross section of an RBC in the x-y plane (a) and in the x-z plane (c); Total field in the cross section of RBC in the x-y plane (b) and in the x-z plane (d). The RBC diameter = 7.8 μm, and the focal points of the two trapping beams were separated by 6.6 μm.

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Fig. 4
Fig. 4 Stress distributions on a biconcave RBC trapped in the dual-trap optical tweezers. Beam separation S (in μm) is given under each figure. Value of the stress is referred to the color bar. Value of the stress was halved for S = 7.3 μm.

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Fig. 5
Fig. 5 Flow chart to compute RBC deformation in the equilibrium state with coupled RF and Continuum Mechanics ComsolTM modules.

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Fig. 6
Fig. 6 3D deformation of an RBC in dual-trap tweezers. First row: beam separation: S = 7.3 µm; Second row: S = 3.8 µm. Color bar: displacement positive (outward) or negative (inward).

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Equations (13)

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E 1,2 (x,y,z)={ 480P n 1 W(z) exp[ − (x±S/2 ) 2 + y 2 W (z) 2 ]exp{ j 2π λ [ (x ±S /2 ) 2 + y 2 + z 2 ] 1/2 }   (z>0) 480P n 1 W(z) exp[ − (x±S/2 ) 2 + y 2 W (z) 2 ]exp{ −j 2π λ [ (x ±S /2 ) 2 + y 2 + z 2 ] 1/2 }  (z≤0)
E x1,2 = E 1,2 cos ϕ 1,2 sin θ 1,2 E y1,2 = E 1,2 cos ϕ 1,2 cos θ 1,2 E z1,2 = E 1,2 sin ϕ 1,2
y=±0.5 R 0 1− ( x 2 + z 2 ) R 0 2 [ c 0 + c 1 x 2 + z 2 R 0 2 + c 2 ( x 2 + z 2 ) 2 R 0 4 ]
σ → =( T ↔ 2 − T ↔ 1 )⋅ n →
T ij =ε[ E i E j + 1 ε μ 0 B i B j − 1 2 ( E 2 + 1 ε μ 0 B 2 ) δ ij ]
( T ↔ ⋅ n → ) i =ε ∑ j E i E j n j −(1/2)ε E 2 n i
σ → =( T ↔ 2 − T ↔ 1 )⋅ n → =( ε 2 E 2n E → 2 − ε 1 E 1n E → 1 )−(1/2 )( ε 2 E 2 2 − ε 1 E 1 2 ) n →
( ε 2 E 2n E → 2 − ε 1 E 1n E → 1 )= ε 2 E 2n 2 n → − ε 1 E 1n 2 n → + ε 2 E 2n E → 2t − ε 1 E 1n E → 1t =( ε 2 E 2n 2 − ε 1 E 1n 2 ) n →
σ → =[( ε 2 E 2n 2 − ε 1 E 1n 2 )−(1/2 )( ε 2 E 2 2 − ε 1 E 1 2 )] n →    =(1/2 )[( ε 2 E 2n 2 − ε 1 E 1n 2 )−( ε 2 E 2t 2 − ε 1 E 1t 2 )] n →    =(1/2 )( ε 1 − ε 2 )[( ε 1 ε 2 ) E 1n 2 + E 1t 2 ] n →
W= C 10 ( I ¯ 1 −3 )+ C 01 ( I ¯ 2 −3 )+ 1 2 κ ( J−1 ) 2
I 1 =trace(B)= λ 1 2 + λ 2 2 + λ 3 2
I 2 = 1 2 [ I 1 2 −trace( B 2 ) ]= λ 1 2 λ 2 2 + λ 2 2 λ 3 2 + λ 3 2 λ 1 2
J 2 =det(B)= λ 1 2 λ 2 2 λ 3 2

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