Abstract

We present a theoretical analysis of the behaviour of erythrocytes in an optical trapping system. We modeled erythrocyte behaviour in an optical trap by an algorithm which divided the cell surface into a large number of elements and recursively summed the force and torque on each element. We present a relationship between the torque and angle of orientation of the cell, showing that stable equilibrium orientations are at angles of 0°, 180° and 360° and unstable equilibrium orientations are at 90° and 270° relative to the axis of beam propagation. This is consistent with our experimental observations and with results described in the literature. We also model behaviour of the erythrocyte during micromanipulation by calculating the net force on it. Such theoretical analysis is practical as it allows for the optimization of the optical parameters of a trapping system prior to performing a specific optical micromanipulation application, such as cell sorting or construction of a cell pattern for lab-on-a-chip applications.

© 2000 Optical Society of America

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References

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  1. M Zahn and S. Seeger, “Optical tweezers in pharmacology,” Cell. Mol. Biol. 44, 747–761 (1998).
    [PubMed]
  2. M. Zahn, J. Renken, and S. Seeger, “Fluorimetric multiparameter cell assay at the single cell level fabricated by optical tweezers,” FEBS Letters 443, 337–340 (1999).
    [CrossRef] [PubMed]
  3. K. Schutze, H. Posl, and G. Lahr, “Laser micromanipulation systems as universal tools in cellular and molecular biology and in medicine,” Cellular and Molecular Biology 44, 735–746 (1998).
    [PubMed]
  4. H. Liang, W. H. Wright, S. Cheng, W. He, and M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
    [CrossRef] [PubMed]
  5. A. Clement-Sengewald, K. Schutze, A. Ashkin, G. A. Palma, G. Kerlen, and G. Brem, “Fertilization of bovine oocytes induced solely with combined laser microbeam and optical tweezers,” J Assisted Reproduction and Genetics 13, 259–265 (1996).
    [CrossRef]
  6. W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Optics. 33: 1735–1748 (1994).
    [CrossRef]
  7. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Optics Lett. 11, 288–290 (1986).
    [CrossRef]
  8. R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B. 14, 3323–3333 (1997).
    [CrossRef]
  9. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
    [CrossRef] [PubMed]
  10. S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher order mode Nd:YAG laser beams,” Electr. Lett. 27, 1831–1832 (1991).
    [CrossRef]
  11. A. Elgsaeter, B. T. Stokke, A. Mikkelsen, and D. Branton, “The molecular basis of erythrocyte shape,” Science 234, 1217–1223 (1986).
    [CrossRef] [PubMed]
  12. P. Zachee, J. Snauwaert, P. Vandenberghe, L. Hellemans, and M. Boogaerts, “Imaging of red blood cells with the atomic force microscope,” British Journal of Haemotology 95, 472–481 (1996).
    [CrossRef]
  13. A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,”, J. of Biomedical Optics,  4, 36–46 (1999).
    [CrossRef]
  14. W. R. Platt, “Color atlas and textbook of hematology,” Pitman Medical Publishing Co., London (1969).
  15. W. Wang, A. E. Chiou, G. J. Sonek, and M. W. Berns, “Self-aligned dual-beam optical laser trap using photorefractive phase conjugation.J. Opt. Soc. Am. B. 14, 697–705 (1997).
    [CrossRef]
  16. N. Curle and H. J. Davies, “Modern fluid dynamics”, Van Nostrand, Princeton, New Jersey (1968).
  17. G. K. Batchelor, “An introduction to fluid dynamics,” Cambridge University Press, Cambridge (1967).
  18. T. C. Bakker Schut, E. F. Schipper, B. G. de Groot, and J. Greve, “Optical-trapping micromanipulation using 780 nm diode lasers”, Opt. Lett. 18, 447–449, (1993).
    [CrossRef]
  19. A. Krantz, “Red-cell mediated therapy: opportunities and challenges,” Blood Cells, Molecules and Diseases 23, 58–68 (1997).
    [CrossRef]

1999

M. Zahn, J. Renken, and S. Seeger, “Fluorimetric multiparameter cell assay at the single cell level fabricated by optical tweezers,” FEBS Letters 443, 337–340 (1999).
[CrossRef] [PubMed]

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,”, J. of Biomedical Optics,  4, 36–46 (1999).
[CrossRef]

1998

M Zahn and S. Seeger, “Optical tweezers in pharmacology,” Cell. Mol. Biol. 44, 747–761 (1998).
[PubMed]

K. Schutze, H. Posl, and G. Lahr, “Laser micromanipulation systems as universal tools in cellular and molecular biology and in medicine,” Cellular and Molecular Biology 44, 735–746 (1998).
[PubMed]

1997

R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B. 14, 3323–3333 (1997).
[CrossRef]

W. Wang, A. E. Chiou, G. J. Sonek, and M. W. Berns, “Self-aligned dual-beam optical laser trap using photorefractive phase conjugation.J. Opt. Soc. Am. B. 14, 697–705 (1997).
[CrossRef]

A. Krantz, “Red-cell mediated therapy: opportunities and challenges,” Blood Cells, Molecules and Diseases 23, 58–68 (1997).
[CrossRef]

1996

P. Zachee, J. Snauwaert, P. Vandenberghe, L. Hellemans, and M. Boogaerts, “Imaging of red blood cells with the atomic force microscope,” British Journal of Haemotology 95, 472–481 (1996).
[CrossRef]

A. Clement-Sengewald, K. Schutze, A. Ashkin, G. A. Palma, G. Kerlen, and G. Brem, “Fertilization of bovine oocytes induced solely with combined laser microbeam and optical tweezers,” J Assisted Reproduction and Genetics 13, 259–265 (1996).
[CrossRef]

1994

W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Optics. 33: 1735–1748 (1994).
[CrossRef]

1993

H. Liang, W. H. Wright, S. Cheng, W. He, and M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

T. C. Bakker Schut, E. F. Schipper, B. G. de Groot, and J. Greve, “Optical-trapping micromanipulation using 780 nm diode lasers”, Opt. Lett. 18, 447–449, (1993).
[CrossRef]

1992

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

1991

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher order mode Nd:YAG laser beams,” Electr. Lett. 27, 1831–1832 (1991).
[CrossRef]

1986

A. Elgsaeter, B. T. Stokke, A. Mikkelsen, and D. Branton, “The molecular basis of erythrocyte shape,” Science 234, 1217–1223 (1986).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Optics Lett. 11, 288–290 (1986).
[CrossRef]

Ashkin, A.

A. Clement-Sengewald, K. Schutze, A. Ashkin, G. A. Palma, G. Kerlen, and G. Brem, “Fertilization of bovine oocytes induced solely with combined laser microbeam and optical tweezers,” J Assisted Reproduction and Genetics 13, 259–265 (1996).
[CrossRef]

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Optics Lett. 11, 288–290 (1986).
[CrossRef]

Bakker Schut, T. C.

Batchelor, G. K.

G. K. Batchelor, “An introduction to fluid dynamics,” Cambridge University Press, Cambridge (1967).

Berns, M. W.

W. Wang, A. E. Chiou, G. J. Sonek, and M. W. Berns, “Self-aligned dual-beam optical laser trap using photorefractive phase conjugation.J. Opt. Soc. Am. B. 14, 697–705 (1997).
[CrossRef]

W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Optics. 33: 1735–1748 (1994).
[CrossRef]

H. Liang, W. H. Wright, S. Cheng, W. He, and M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

Bjorkholm, J. E.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Optics Lett. 11, 288–290 (1986).
[CrossRef]

Boogaerts, M.

P. Zachee, J. Snauwaert, P. Vandenberghe, L. Hellemans, and M. Boogaerts, “Imaging of red blood cells with the atomic force microscope,” British Journal of Haemotology 95, 472–481 (1996).
[CrossRef]

Branton, D.

A. Elgsaeter, B. T. Stokke, A. Mikkelsen, and D. Branton, “The molecular basis of erythrocyte shape,” Science 234, 1217–1223 (1986).
[CrossRef] [PubMed]

Brem, G.

A. Clement-Sengewald, K. Schutze, A. Ashkin, G. A. Palma, G. Kerlen, and G. Brem, “Fertilization of bovine oocytes induced solely with combined laser microbeam and optical tweezers,” J Assisted Reproduction and Genetics 13, 259–265 (1996).
[CrossRef]

Cheng, S.

H. Liang, W. H. Wright, S. Cheng, W. He, and M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

Chiou, A. E.

W. Wang, A. E. Chiou, G. J. Sonek, and M. W. Berns, “Self-aligned dual-beam optical laser trap using photorefractive phase conjugation.J. Opt. Soc. Am. B. 14, 697–705 (1997).
[CrossRef]

Chu, S.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Optics Lett. 11, 288–290 (1986).
[CrossRef]

Clement-Sengewald, A.

A. Clement-Sengewald, K. Schutze, A. Ashkin, G. A. Palma, G. Kerlen, and G. Brem, “Fertilization of bovine oocytes induced solely with combined laser microbeam and optical tweezers,” J Assisted Reproduction and Genetics 13, 259–265 (1996).
[CrossRef]

Curle, N.

N. Curle and H. J. Davies, “Modern fluid dynamics”, Van Nostrand, Princeton, New Jersey (1968).

Davies, H. J.

N. Curle and H. J. Davies, “Modern fluid dynamics”, Van Nostrand, Princeton, New Jersey (1968).

de Groot, B. G.

Dorschel, K.

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,”, J. of Biomedical Optics,  4, 36–46 (1999).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Optics Lett. 11, 288–290 (1986).
[CrossRef]

Elgsaeter, A.

A. Elgsaeter, B. T. Stokke, A. Mikkelsen, and D. Branton, “The molecular basis of erythrocyte shape,” Science 234, 1217–1223 (1986).
[CrossRef] [PubMed]

Friebel, M.

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,”, J. of Biomedical Optics,  4, 36–46 (1999).
[CrossRef]

Gauthier, R. C.

R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B. 14, 3323–3333 (1997).
[CrossRef]

Greve, J.

Hahn, A.

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,”, J. of Biomedical Optics,  4, 36–46 (1999).
[CrossRef]

He, W.

H. Liang, W. H. Wright, S. Cheng, W. He, and M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

Hellemans, L.

P. Zachee, J. Snauwaert, P. Vandenberghe, L. Hellemans, and M. Boogaerts, “Imaging of red blood cells with the atomic force microscope,” British Journal of Haemotology 95, 472–481 (1996).
[CrossRef]

Inaba, H.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher order mode Nd:YAG laser beams,” Electr. Lett. 27, 1831–1832 (1991).
[CrossRef]

Ishigure, M.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher order mode Nd:YAG laser beams,” Electr. Lett. 27, 1831–1832 (1991).
[CrossRef]

Kerlen, G.

A. Clement-Sengewald, K. Schutze, A. Ashkin, G. A. Palma, G. Kerlen, and G. Brem, “Fertilization of bovine oocytes induced solely with combined laser microbeam and optical tweezers,” J Assisted Reproduction and Genetics 13, 259–265 (1996).
[CrossRef]

Krantz, A.

A. Krantz, “Red-cell mediated therapy: opportunities and challenges,” Blood Cells, Molecules and Diseases 23, 58–68 (1997).
[CrossRef]

Lahr, G.

K. Schutze, H. Posl, and G. Lahr, “Laser micromanipulation systems as universal tools in cellular and molecular biology and in medicine,” Cellular and Molecular Biology 44, 735–746 (1998).
[PubMed]

Liang, H.

H. Liang, W. H. Wright, S. Cheng, W. He, and M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

Mikkelsen, A.

A. Elgsaeter, B. T. Stokke, A. Mikkelsen, and D. Branton, “The molecular basis of erythrocyte shape,” Science 234, 1217–1223 (1986).
[CrossRef] [PubMed]

Muller, G.

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,”, J. of Biomedical Optics,  4, 36–46 (1999).
[CrossRef]

Palma, G. A.

A. Clement-Sengewald, K. Schutze, A. Ashkin, G. A. Palma, G. Kerlen, and G. Brem, “Fertilization of bovine oocytes induced solely with combined laser microbeam and optical tweezers,” J Assisted Reproduction and Genetics 13, 259–265 (1996).
[CrossRef]

Platt, W. R.

W. R. Platt, “Color atlas and textbook of hematology,” Pitman Medical Publishing Co., London (1969).

Posl, H.

K. Schutze, H. Posl, and G. Lahr, “Laser micromanipulation systems as universal tools in cellular and molecular biology and in medicine,” Cellular and Molecular Biology 44, 735–746 (1998).
[PubMed]

Renken, J.

M. Zahn, J. Renken, and S. Seeger, “Fluorimetric multiparameter cell assay at the single cell level fabricated by optical tweezers,” FEBS Letters 443, 337–340 (1999).
[CrossRef] [PubMed]

Roggan, A.

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,”, J. of Biomedical Optics,  4, 36–46 (1999).
[CrossRef]

Sato, S.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher order mode Nd:YAG laser beams,” Electr. Lett. 27, 1831–1832 (1991).
[CrossRef]

Schipper, E. F.

Schutze, K.

K. Schutze, H. Posl, and G. Lahr, “Laser micromanipulation systems as universal tools in cellular and molecular biology and in medicine,” Cellular and Molecular Biology 44, 735–746 (1998).
[PubMed]

A. Clement-Sengewald, K. Schutze, A. Ashkin, G. A. Palma, G. Kerlen, and G. Brem, “Fertilization of bovine oocytes induced solely with combined laser microbeam and optical tweezers,” J Assisted Reproduction and Genetics 13, 259–265 (1996).
[CrossRef]

Seeger, S.

M. Zahn, J. Renken, and S. Seeger, “Fluorimetric multiparameter cell assay at the single cell level fabricated by optical tweezers,” FEBS Letters 443, 337–340 (1999).
[CrossRef] [PubMed]

M Zahn and S. Seeger, “Optical tweezers in pharmacology,” Cell. Mol. Biol. 44, 747–761 (1998).
[PubMed]

Snauwaert, J.

P. Zachee, J. Snauwaert, P. Vandenberghe, L. Hellemans, and M. Boogaerts, “Imaging of red blood cells with the atomic force microscope,” British Journal of Haemotology 95, 472–481 (1996).
[CrossRef]

Sonek, G. J.

W. Wang, A. E. Chiou, G. J. Sonek, and M. W. Berns, “Self-aligned dual-beam optical laser trap using photorefractive phase conjugation.J. Opt. Soc. Am. B. 14, 697–705 (1997).
[CrossRef]

W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Optics. 33: 1735–1748 (1994).
[CrossRef]

Stokke, B. T.

A. Elgsaeter, B. T. Stokke, A. Mikkelsen, and D. Branton, “The molecular basis of erythrocyte shape,” Science 234, 1217–1223 (1986).
[CrossRef] [PubMed]

Vandenberghe, P.

P. Zachee, J. Snauwaert, P. Vandenberghe, L. Hellemans, and M. Boogaerts, “Imaging of red blood cells with the atomic force microscope,” British Journal of Haemotology 95, 472–481 (1996).
[CrossRef]

Wang, W.

W. Wang, A. E. Chiou, G. J. Sonek, and M. W. Berns, “Self-aligned dual-beam optical laser trap using photorefractive phase conjugation.J. Opt. Soc. Am. B. 14, 697–705 (1997).
[CrossRef]

Wright, W. H.

W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Optics. 33: 1735–1748 (1994).
[CrossRef]

H. Liang, W. H. Wright, S. Cheng, W. He, and M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

Zachee, P.

P. Zachee, J. Snauwaert, P. Vandenberghe, L. Hellemans, and M. Boogaerts, “Imaging of red blood cells with the atomic force microscope,” British Journal of Haemotology 95, 472–481 (1996).
[CrossRef]

Zahn, M

M Zahn and S. Seeger, “Optical tweezers in pharmacology,” Cell. Mol. Biol. 44, 747–761 (1998).
[PubMed]

Zahn, M.

M. Zahn, J. Renken, and S. Seeger, “Fluorimetric multiparameter cell assay at the single cell level fabricated by optical tweezers,” FEBS Letters 443, 337–340 (1999).
[CrossRef] [PubMed]

Appl. Optics.

W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Optics. 33: 1735–1748 (1994).
[CrossRef]

Biophys. J.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

Blood Cells, Molecules and Diseases

A. Krantz, “Red-cell mediated therapy: opportunities and challenges,” Blood Cells, Molecules and Diseases 23, 58–68 (1997).
[CrossRef]

British Journal of Haemotology

P. Zachee, J. Snauwaert, P. Vandenberghe, L. Hellemans, and M. Boogaerts, “Imaging of red blood cells with the atomic force microscope,” British Journal of Haemotology 95, 472–481 (1996).
[CrossRef]

Cell. Mol. Biol.

M Zahn and S. Seeger, “Optical tweezers in pharmacology,” Cell. Mol. Biol. 44, 747–761 (1998).
[PubMed]

Cellular and Molecular Biology

K. Schutze, H. Posl, and G. Lahr, “Laser micromanipulation systems as universal tools in cellular and molecular biology and in medicine,” Cellular and Molecular Biology 44, 735–746 (1998).
[PubMed]

Electr. Lett.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher order mode Nd:YAG laser beams,” Electr. Lett. 27, 1831–1832 (1991).
[CrossRef]

Exp. Cell Res.

H. Liang, W. H. Wright, S. Cheng, W. He, and M. W. Berns, “Micromanipulation of chromosomes in PTK2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical forces (optical tweezers),” Exp. Cell Res. 204, 110–120 (1993).
[CrossRef] [PubMed]

FEBS Letters

M. Zahn, J. Renken, and S. Seeger, “Fluorimetric multiparameter cell assay at the single cell level fabricated by optical tweezers,” FEBS Letters 443, 337–340 (1999).
[CrossRef] [PubMed]

J Assisted Reproduction and Genetics

A. Clement-Sengewald, K. Schutze, A. Ashkin, G. A. Palma, G. Kerlen, and G. Brem, “Fertilization of bovine oocytes induced solely with combined laser microbeam and optical tweezers,” J Assisted Reproduction and Genetics 13, 259–265 (1996).
[CrossRef]

J. of Biomedical Optics

A. Roggan, M. Friebel, K. Dorschel, A. Hahn, and G. Muller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,”, J. of Biomedical Optics,  4, 36–46 (1999).
[CrossRef]

J. Opt. Soc. Am. B.

W. Wang, A. E. Chiou, G. J. Sonek, and M. W. Berns, “Self-aligned dual-beam optical laser trap using photorefractive phase conjugation.J. Opt. Soc. Am. B. 14, 697–705 (1997).
[CrossRef]

R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B. 14, 3323–3333 (1997).
[CrossRef]

Opt. Lett.

Optics Lett.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Optics Lett. 11, 288–290 (1986).
[CrossRef]

Science

A. Elgsaeter, B. T. Stokke, A. Mikkelsen, and D. Branton, “The molecular basis of erythrocyte shape,” Science 234, 1217–1223 (1986).
[CrossRef] [PubMed]

Other

N. Curle and H. J. Davies, “Modern fluid dynamics”, Van Nostrand, Princeton, New Jersey (1968).

G. K. Batchelor, “An introduction to fluid dynamics,” Cambridge University Press, Cambridge (1967).

W. R. Platt, “Color atlas and textbook of hematology,” Pitman Medical Publishing Co., London (1969).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of erythrocyte showing angle of incidence (θ) and angles α and β, as defined for modeling studies. This schematic shows minimal cross section of erythrocyte.

Fig. 2.
Fig. 2.

Torque exerted on an erythrocyte versus the angle of the cell in a dual beam trapping system. Unstable and stable equilibrium positions as shown. The inset defines the angle, ϕ with respect to the bottom beam.

Fig. 3.
Fig. 3.

Results of theoretical modelling (top row) and experimental results (bottom row) showing an erythrocyte before trapping (a,d), during reorientation in a dual beam optical trap (b,e), and after the stable trapping is achieved (c,f). Figures in the top row demonstrate triangular elements used in the algorithm for theoretical determination of behaviour.

Fig. 4.
Fig. 4.

Movie clip showing rotation of erythrocyte in our experimental optical trapping system (2.7 MB version).

Fig. 5.
Fig. 5.

The force of the optical trapping system versus the offset of the cell center in the Z-direction, for an erythrocyte in a dual beam trapping system. A maximum in the displacement defines the equilibrium location of the cell.

Fig. 6.
Fig. 6.

Movie clip showing micromanipulation of a single erythrocyte with its smallest cross section in the direction of translation (4.7 MB version).

Equations (5)

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

d F SC = n M I c dA { 1 + R cos ( 2 ϑ ( r i ) ) + ( 1 + m n = 0 T 2 n ) T 2 n = 0 R n ( cos ( α ( r i ) + n β ( r i ) ) }
d F GR = n M I c dA { R sin ( 2 ϑ ( r i ) ) + ( 1 + m n = 0 T 2 n ) T 2 n = 0 R n ( sin ( α ( r i ) + n β ( r i ) ) }
T = surface elements r i × dF
m a = F γ v
γ = 3 π η D

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