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.

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References

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  1. M Zahn, S. Seeger, "Optical tweezers in pharmacology," Cell. Mol. Biol. 44, 747-761 (1998).
    [PubMed]
  2. M. Zahn, J. Renken, 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, 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. Opt. 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," Opt. 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, D. Branton, "The molecular basis of erythrocyte shape," Science 234, 1217-1223 (1986).
    [CrossRef] [PubMed]
  12. P. Zachee, J. Snauwaert, P. Vandenberghe, L. Hellemans, 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, 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
    [CrossRef]

Other

M Zahn, S. Seeger, "Optical tweezers in pharmacology," Cell. Mol. Biol. 44, 747-761 (1998).
[PubMed]

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

K. Schutze, H. Posl, 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]

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]

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]

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

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

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]

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]

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

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

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]

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

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]

N. Curle, 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).

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]

A. Krantz, "Red-cell mediated therapy: opportunities and challenges," Blood Cells, Molecules and Diseases
[CrossRef]

Supplementary Material (2)

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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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