Abstract

Current methods for predicting stress distribution on a cell surface due to optical trapping forces are based on a traditional ray optics scheme for fixed geometries. Cells are typically modeled as solid spheres as this facilitates optical force calculation. Under such applied forces however, real and non-rigid cells can deform, so assumptions inherent in traditional ray optics methods begin to break down. In this work, we implement a dynamic ray tracing technique to calculate the stress distribution on a deformable cell induced by optical trapping. Here, cells are modeled as three-dimensional elastic capsules with a discretized surface with associated hydrodynamic forces calculated using the Immersed Boundary Method. We use this approach to simulate the transient deformation of spherical, ellipsoidal and biconcave capsules due to external optical forces induced by a single diode bar optical trap for a range of optical powers.

© 2010 OSA

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

2008 (3)

R. W. Applegate, J. Squier, T. Vestad, J. Oakey, and D. W. M. Marr, “Fiber-focused diode bar optical trapping for microfluidic flow manipulation,” Appl. Phys. Lett. 92(1), 013904 (2008).
[CrossRef]

P. Parag, S. Jadhav, C. D. Eggleton, and K. Konstantopoulos, “Roles of cell and microvillus deformation and receptor-ligand binding kinetics in cell rolling,” Am. J. Physiol. Heart Circ. Physiol. 295(4), H1439–H1450 (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]

2007 (2)

G. Y. H. Lee and C. T. Lim, “Biomechanics approaches to studying human diseases,” Trends Biotechnol. 25(3), 111–118 (2007).
[CrossRef] [PubMed]

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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)

2005 (5)

P. Bagchi, P. C. Johnson, and A. S. Popel, “Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow,” J. Biomech. Eng. 127(7), 1070–1080 (2005).
[CrossRef]

F. Wottawah, S. Schinkinger, B. Lincoln, R. Ananthakrishnan, M. Romeyke, J. Guck, and J. Käs, “Optical rheology of biological cells,” Phys. Rev. Lett. 94(9), 098103 (2005).
[CrossRef] [PubMed]

M. Lofsted and T. Moller, “An evaluation framework for ray-triangle intersection algorithms,” J. Graphics, GPU, Games Tools 10(2) 13–26 (2005).
[CrossRef]

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

2001 (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[CrossRef] [PubMed]

2000 (3)

R. M. Hochmuth, “Micropipette aspiration of living cells,” J. Biomech. 33(1), 15–22 (2000).
[CrossRef]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[CrossRef] [PubMed]

A. Diaz, N. Pelekasis, and D. Barthes-Biesel, “Transient response of a capsule subjected to varying flow conditions: Effect of internal fluid viscosity and membrane elasticity,” Phys. Fluids 12(5), 948–957 (2000).
[CrossRef]

1999 (2)

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76(2), 1145–1151 (1999).
[CrossRef] [PubMed]

E. Lac, D. Barthes-Biesel, N. A. Pelekasis, and J. Tsamopoulos, “Spherical capsules in three-dimensional unbounded Stokes flows: Effect of the membrane constitutive law and onset of buckling,” J. Fluid Mech. 516, 303–334 (1999).
[CrossRef]

1998 (2)

C. D. Eggleton and A. S. Popel, “Large deformation of red blood cell ghosts in a simple shear flow,” Phys. Fluids 10(8), 1834–1845 (1998).
[CrossRef]

R. R. Huruta, M. L. Barjas-Castro, S. T. O. Saad, F. F. Costa, A. Fontes, L. C. Barbosa, and C. L. Cesar, “Mechanical properties of stored red blood cells using optical tweezers,” Blood 92(8), 2975–2977 (1998).
[PubMed]

1997 (1)

T. Moller and B. Trumbore, “Fast, minimum storage ray-triangle intersection,” J. Graphics, GPU, Games Tools 2(1) 21–28 (1997).

1995 (1)

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, and G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69(5), 1666–1673 (1995).
[CrossRef] [PubMed]

1993 (1)

A. L. Weisenhorn, M. Khorsandi, S. Kasas, V. Gotzos, and H.-J. Butt, “Deformation and height anomaly of soft surfaces studied with an AFM,” Nanotechnology 4(2), 106–113 (1993).
[CrossRef]

1992 (2)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[CrossRef] [PubMed]

J. Y. Walz and D. C. Prieve, “Prediction and measurement of the optical trapping forces on a microscopic dielectric sphere,” Langmuir 8(12), 3073–3082 (1992).
[CrossRef]

1989 (1)

C. Peskin and D. McQueen, “A three dimensional computational method for blood flow in the heart I. Immersed elastic fibers in a viscous incompressible fluid,” J. Comput. Phys. 81(2), 372–405 (1989).
[CrossRef]

1972 (1)

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

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Ananthakrishnan, R.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

F. Wottawah, S. Schinkinger, B. Lincoln, R. Ananthakrishnan, M. Romeyke, J. Guck, and J. Käs, “Optical rheology of biological cells,” Phys. Rev. Lett. 94(9), 098103 (2005).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[CrossRef] [PubMed]

Applegate, R. W.

R. W. Applegate, J. Squier, T. Vestad, J. Oakey, and D. W. M. Marr, “Fiber-focused diode bar optical trapping for microfluidic flow manipulation,” Appl. Phys. Lett. 92(1), 013904 (2008).
[CrossRef]

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Bagchi, P.

P. Bagchi, P. C. Johnson, and A. S. Popel, “Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow,” J. Biomech. Eng. 127(7), 1070–1080 (2005).
[CrossRef]

Barbosa, L. C.

R. R. Huruta, M. L. Barjas-Castro, S. T. O. Saad, F. F. Costa, A. Fontes, L. C. Barbosa, and C. L. Cesar, “Mechanical properties of stored red blood cells using optical tweezers,” Blood 92(8), 2975–2977 (1998).
[PubMed]

Bareil, P. B

Bareil, P. B.

Barjas-Castro, M. L.

R. R. Huruta, M. L. Barjas-Castro, S. T. O. Saad, F. F. Costa, A. Fontes, L. C. Barbosa, and C. L. Cesar, “Mechanical properties of stored red blood cells using optical tweezers,” Blood 92(8), 2975–2977 (1998).
[PubMed]

Barthes-Biesel, D.

A. Diaz, N. Pelekasis, and D. Barthes-Biesel, “Transient response of a capsule subjected to varying flow conditions: Effect of internal fluid viscosity and membrane elasticity,” Phys. Fluids 12(5), 948–957 (2000).
[CrossRef]

E. Lac, D. Barthes-Biesel, N. A. Pelekasis, and J. Tsamopoulos, “Spherical capsules in three-dimensional unbounded Stokes flows: Effect of the membrane constitutive law and onset of buckling,” J. Fluid Mech. 516, 303–334 (1999).
[CrossRef]

Beil, M.

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

Bilby, C.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Bonnefoy, S.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

Brakenhoff, G. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, and G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69(5), 1666–1673 (1995).
[CrossRef] [PubMed]

Bronkhorst, P. J. H.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, and G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69(5), 1666–1673 (1995).
[CrossRef] [PubMed]

Butt, H.-J.

A. L. Weisenhorn, M. Khorsandi, S. Kasas, V. Gotzos, and H.-J. Butt, “Deformation and height anomaly of soft surfaces studied with an AFM,” Nanotechnology 4(2), 106–113 (1993).
[CrossRef]

Cesar, C. L.

R. R. Huruta, M. L. Barjas-Castro, S. T. O. Saad, F. F. Costa, A. Fontes, L. C. Barbosa, and C. L. Cesar, “Mechanical properties of stored red blood cells using optical tweezers,” Blood 92(8), 2975–2977 (1998).
[PubMed]

Chichester, J.

I. Sraj, J. Chichester, E. Hoover, R. Jimenez, J. Squier, C. D. Eggleton, and D. W. M. Marr, “Cell deformation cytometry using diode-bar optical stretchers,” J. Biomed. Opt. in press.
[PubMed]

Chiou, A

Chiou, A.

Costa, F. F.

R. R. Huruta, M. L. Barjas-Castro, S. T. O. Saad, F. F. Costa, A. Fontes, L. C. Barbosa, and C. L. Cesar, “Mechanical properties of stored red blood cells using optical tweezers,” Blood 92(8), 2975–2977 (1998).
[PubMed]

Cunningham, C. C.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[CrossRef] [PubMed]

Dao, M.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

David, P. H.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

Diaz, A.

A. Diaz, N. Pelekasis, and D. Barthes-Biesel, “Transient response of a capsule subjected to varying flow conditions: Effect of internal fluid viscosity and membrane elasticity,” Phys. Fluids 12(5), 948–957 (2000).
[CrossRef]

Diez-Silva, M.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

Ebert, S.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Eggleton, C. D.

P. Parag, S. Jadhav, C. D. Eggleton, and K. Konstantopoulos, “Roles of cell and microvillus deformation and receptor-ligand binding kinetics in cell rolling,” Am. J. Physiol. Heart Circ. Physiol. 295(4), H1439–H1450 (2008).
[CrossRef]

C. D. Eggleton and A. S. Popel, “Large deformation of red blood cell ghosts in a simple shear flow,” Phys. Fluids 10(8), 1834–1845 (1998).
[CrossRef]

I. Sraj, J. Chichester, E. Hoover, R. Jimenez, J. Squier, C. D. Eggleton, and D. W. M. Marr, “Cell deformation cytometry using diode-bar optical stretchers,” J. Biomed. Opt. in press.
[PubMed]

Erickson, H. M.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Evans, E.

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

Fontes, A.

R. R. Huruta, M. L. Barjas-Castro, S. T. O. Saad, F. F. Costa, A. Fontes, L. C. Barbosa, and C. L. Cesar, “Mechanical properties of stored red blood cells using optical tweezers,” Blood 92(8), 2975–2977 (1998).
[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]

Gallet, F.

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76(2), 1145–1151 (1999).
[CrossRef] [PubMed]

Gotzos, V.

A. L. Weisenhorn, M. Khorsandi, S. Kasas, V. Gotzos, and H.-J. Butt, “Deformation and height anomaly of soft surfaces studied with an AFM,” Nanotechnology 4(2), 106–113 (1993).
[CrossRef]

Grimbergen, J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, and G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69(5), 1666–1673 (1995).
[CrossRef] [PubMed]

Guck, J.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

F. Wottawah, S. Schinkinger, B. Lincoln, R. Ananthakrishnan, M. Romeyke, J. Guck, and J. Käs, “Optical rheology of biological cells,” Phys. Rev. Lett. 94(9), 098103 (2005).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[CrossRef] [PubMed]

Hénon, S.

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76(2), 1145–1151 (1999).
[CrossRef] [PubMed]

Hochmuth, R. M.

R. M. Hochmuth, “Micropipette aspiration of living cells,” J. Biomech. 33(1), 15–22 (2000).
[CrossRef]

Hoover, E.

I. Sraj, J. Chichester, E. Hoover, R. Jimenez, J. Squier, C. D. Eggleton, and D. W. M. Marr, “Cell deformation cytometry using diode-bar optical stretchers,” J. Biomed. Opt. in press.
[PubMed]

Huruta, R. R.

R. R. Huruta, M. L. Barjas-Castro, S. T. O. Saad, F. F. Costa, A. Fontes, L. C. Barbosa, and C. L. Cesar, “Mechanical properties of stored red blood cells using optical tweezers,” Blood 92(8), 2975–2977 (1998).
[PubMed]

Jadhav, S.

P. Parag, S. Jadhav, C. D. Eggleton, and K. Konstantopoulos, “Roles of cell and microvillus deformation and receptor-ligand binding kinetics in cell rolling,” Am. J. Physiol. Heart Circ. Physiol. 295(4), H1439–H1450 (2008).
[CrossRef]

Jimenez, R.

I. Sraj, J. Chichester, E. Hoover, R. Jimenez, J. Squier, C. D. Eggleton, and D. W. M. Marr, “Cell deformation cytometry using diode-bar optical stretchers,” J. Biomed. Opt. in press.
[PubMed]

Johnson, P. C.

P. Bagchi, P. C. Johnson, and A. S. Popel, “Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow,” J. Biomech. Eng. 127(7), 1070–1080 (2005).
[CrossRef]

Käs, J.

F. Wottawah, S. Schinkinger, B. Lincoln, R. Ananthakrishnan, M. Romeyke, J. Guck, and J. Käs, “Optical rheology of biological cells,” Phys. Rev. Lett. 94(9), 098103 (2005).
[CrossRef] [PubMed]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[CrossRef] [PubMed]

Kasas, S.

A. L. Weisenhorn, M. Khorsandi, S. Kasas, V. Gotzos, and H.-J. Butt, “Deformation and height anomaly of soft surfaces studied with an AFM,” Nanotechnology 4(2), 106–113 (1993).
[CrossRef]

Khorsandi, M.

A. L. Weisenhorn, M. Khorsandi, S. Kasas, V. Gotzos, and H.-J. Butt, “Deformation and height anomaly of soft surfaces studied with an AFM,” Nanotechnology 4(2), 106–113 (1993).
[CrossRef]

Konstantopoulos, K.

P. Parag, S. Jadhav, C. D. Eggleton, and K. Konstantopoulos, “Roles of cell and microvillus deformation and receptor-ligand binding kinetics in cell rolling,” Am. J. Physiol. Heart Circ. Physiol. 295(4), H1439–H1450 (2008).
[CrossRef]

Lac, E.

E. Lac, D. Barthes-Biesel, N. A. Pelekasis, and J. Tsamopoulos, “Spherical capsules in three-dimensional unbounded Stokes flows: Effect of the membrane constitutive law and onset of buckling,” J. Fluid Mech. 516, 303–334 (1999).
[CrossRef]

Lang, M. J.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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, G. Y. H.

G. Y. H. Lee and C. T. Lim, “Biomechanics approaches to studying human diseases,” Trends Biotechnol. 25(3), 111–118 (2007).
[CrossRef] [PubMed]

Lenormand, G.

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76(2), 1145–1151 (1999).
[CrossRef] [PubMed]

Lenz, D.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Liao, G. B.

Lim, C. T.

G. Y. H. Lee and C. T. Lim, “Biomechanics approaches to studying human diseases,” Trends Biotechnol. 25(3), 111–118 (2007).
[CrossRef] [PubMed]

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

Lincoln, B.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

F. Wottawah, S. Schinkinger, B. Lincoln, R. Ananthakrishnan, M. Romeyke, J. Guck, and J. Käs, “Optical rheology of biological cells,” Phys. Rev. Lett. 94(9), 098103 (2005).
[CrossRef] [PubMed]

Lofsted, M.

M. Lofsted and T. Moller, “An evaluation framework for ray-triangle intersection algorithms,” J. Graphics, GPU, Games Tools 10(2) 13–26 (2005).
[CrossRef]

Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[CrossRef] [PubMed]

Marr, D. W. M.

R. W. Applegate, J. Squier, T. Vestad, J. Oakey, and D. W. M. Marr, “Fiber-focused diode bar optical trapping for microfluidic flow manipulation,” Appl. Phys. Lett. 92(1), 013904 (2008).
[CrossRef]

I. Sraj, J. Chichester, E. Hoover, R. Jimenez, J. Squier, C. D. Eggleton, and D. W. M. Marr, “Cell deformation cytometry using diode-bar optical stretchers,” J. Biomed. Opt. in press.
[PubMed]

McQueen, D.

C. Peskin and D. McQueen, “A three dimensional computational method for blood flow in the heart I. Immersed elastic fibers in a viscous incompressible fluid,” J. Comput. Phys. 81(2), 372–405 (1989).
[CrossRef]

Mercereau-Puijalon, O.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

Micoulet, A.

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

Mills, J. P.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

Milon, G.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

Mitchell, D.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Moller, T.

M. Lofsted and T. Moller, “An evaluation framework for ray-triangle intersection algorithms,” J. Graphics, GPU, Games Tools 10(2) 13–26 (2005).
[CrossRef]

T. Moller and B. Trumbore, “Fast, minimum storage ray-triangle intersection,” J. Graphics, GPU, Games Tools 2(1) 21–28 (1997).

Moon, T. J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[CrossRef] [PubMed]

Nijhof, E. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, and G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69(5), 1666–1673 (1995).
[CrossRef] [PubMed]

Oakey, J.

R. W. Applegate, J. Squier, T. Vestad, J. Oakey, and D. W. M. Marr, “Fiber-focused diode bar optical trapping for microfluidic flow manipulation,” Appl. Phys. Lett. 92(1), 013904 (2008).
[CrossRef]

Parag, P.

P. Parag, S. Jadhav, C. D. Eggleton, and K. Konstantopoulos, “Roles of cell and microvillus deformation and receptor-ligand binding kinetics in cell rolling,” Am. J. Physiol. Heart Circ. Physiol. 295(4), H1439–H1450 (2008).
[CrossRef]

Pelekasis, N.

A. Diaz, N. Pelekasis, and D. Barthes-Biesel, “Transient response of a capsule subjected to varying flow conditions: Effect of internal fluid viscosity and membrane elasticity,” Phys. Fluids 12(5), 948–957 (2000).
[CrossRef]

Pelekasis, N. A.

E. Lac, D. Barthes-Biesel, N. A. Pelekasis, and J. Tsamopoulos, “Spherical capsules in three-dimensional unbounded Stokes flows: Effect of the membrane constitutive law and onset of buckling,” J. Fluid Mech. 516, 303–334 (1999).
[CrossRef]

Peskin, C.

C. Peskin and D. McQueen, “A three dimensional computational method for blood flow in the heart I. Immersed elastic fibers in a viscous incompressible fluid,” J. Comput. Phys. 81(2), 372–405 (1989).
[CrossRef]

Popel, A. S.

P. Bagchi, P. C. Johnson, and A. S. Popel, “Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow,” J. Biomech. Eng. 127(7), 1070–1080 (2005).
[CrossRef]

C. D. Eggleton and A. S. Popel, “Large deformation of red blood cell ghosts in a simple shear flow,” Phys. Fluids 10(8), 1834–1845 (1998).
[CrossRef]

Prieve, D. C.

J. Y. Walz and D. C. Prieve, “Prediction and measurement of the optical trapping forces on a microscopic dielectric sphere,” Langmuir 8(12), 3073–3082 (1992).
[CrossRef]

Quinn, D. J.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

Richert, A.

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76(2), 1145–1151 (1999).
[CrossRef] [PubMed]

Romeyke, M.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

F. Wottawah, S. Schinkinger, B. Lincoln, R. Ananthakrishnan, M. Romeyke, J. Guck, and J. Käs, “Optical rheology of biological cells,” Phys. Rev. Lett. 94(9), 098103 (2005).
[CrossRef] [PubMed]

Saad, S. T. O.

R. R. Huruta, M. L. Barjas-Castro, S. T. O. Saad, F. F. Costa, A. Fontes, L. C. Barbosa, and C. L. Cesar, “Mechanical properties of stored red blood cells using optical tweezers,” Blood 92(8), 2975–2977 (1998).
[PubMed]

Schinkinger, S.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

F. Wottawah, S. Schinkinger, B. Lincoln, R. Ananthakrishnan, M. Romeyke, J. Guck, and J. Käs, “Optical rheology of biological cells,” Phys. Rev. Lett. 94(9), 098103 (2005).
[CrossRef] [PubMed]

Seufferlein, T.

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

Sheng, Y

Sheng, Y.

Sixma, J. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, and G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69(5), 1666–1673 (1995).
[CrossRef] [PubMed]

Spatz, J.

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

Squier, J.

R. W. Applegate, J. Squier, T. Vestad, J. Oakey, and D. W. M. Marr, “Fiber-focused diode bar optical trapping for microfluidic flow manipulation,” Appl. Phys. Lett. 92(1), 013904 (2008).
[CrossRef]

I. Sraj, J. Chichester, E. Hoover, R. Jimenez, J. Squier, C. D. Eggleton, and D. W. M. Marr, “Cell deformation cytometry using diode-bar optical stretchers,” J. Biomed. Opt. in press.
[PubMed]

Sraj, I.

I. Sraj, J. Chichester, E. Hoover, R. Jimenez, J. Squier, C. D. Eggleton, and D. W. M. Marr, “Cell deformation cytometry using diode-bar optical stretchers,” J. Biomed. Opt. in press.
[PubMed]

Streekstra, G. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, and G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69(5), 1666–1673 (1995).
[CrossRef] [PubMed]

Suresh, S.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

Tan, K. S.

J. P. Mills, M. Diez-Silva, D. J. Quinn, M. Dao, M. J. Lang, K. S. 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]

Trumbore, B.

T. Moller and B. Trumbore, “Fast, minimum storage ray-triangle intersection,” J. Graphics, GPU, Games Tools 2(1) 21–28 (1997).

Tsamopoulos, J.

E. Lac, D. Barthes-Biesel, N. A. Pelekasis, and J. Tsamopoulos, “Spherical capsules in three-dimensional unbounded Stokes flows: Effect of the membrane constitutive law and onset of buckling,” J. Fluid Mech. 516, 303–334 (1999).
[CrossRef]

Ulvick, S.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Vestad, T.

R. W. Applegate, J. Squier, T. Vestad, J. Oakey, and D. W. M. Marr, “Fiber-focused diode bar optical trapping for microfluidic flow manipulation,” Appl. Phys. Lett. 92(1), 013904 (2008).
[CrossRef]

Walz, J. Y.

J. Y. Walz and D. C. Prieve, “Prediction and measurement of the optical trapping forces on a microscopic dielectric sphere,” Langmuir 8(12), 3073–3082 (1992).
[CrossRef]

Weisenhorn, A. L.

A. L. Weisenhorn, M. Khorsandi, S. Kasas, V. Gotzos, and H.-J. Butt, “Deformation and height anomaly of soft surfaces studied with an AFM,” Nanotechnology 4(2), 106–113 (1993).
[CrossRef]

Wottawah, F.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

F. Wottawah, S. Schinkinger, B. Lincoln, R. Ananthakrishnan, M. Romeyke, J. Guck, and J. Käs, “Optical rheology of biological cells,” Phys. Rev. Lett. 94(9), 098103 (2005).
[CrossRef] [PubMed]

J. Graphics, GPU, Games Tools (1)

T. Moller and B. Trumbore, “Fast, minimum storage ray-triangle intersection,” J. Graphics, GPU, Games Tools 2(1) 21–28 (1997).

Acta Biomater. (1)

S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Beil, and T. Seufferlein, “Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria,” Acta Biomater. 1(1), 15–30 (2005).
[CrossRef]

Am. J. Physiol. Heart Circ. Physiol. (1)

P. Parag, S. Jadhav, C. D. Eggleton, and K. Konstantopoulos, “Roles of cell and microvillus deformation and receptor-ligand binding kinetics in cell rolling,” Am. J. Physiol. Heart Circ. Physiol. 295(4), H1439–H1450 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

R. W. Applegate, J. Squier, T. Vestad, J. Oakey, and D. W. M. Marr, “Fiber-focused diode bar optical trapping for microfluidic flow manipulation,” Appl. Phys. Lett. 92(1), 013904 (2008).
[CrossRef]

Biophys. J. (5)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[CrossRef] [PubMed]

P. J. H. Bronkhorst, G. J. Streekstra, J. Grimbergen, E. J. Nijhof, J. J. Sixma, and G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69(5), 1666–1673 (1995).
[CrossRef] [PubMed]

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76(2), 1145–1151 (1999).
[CrossRef] [PubMed]

Blood (1)

R. R. Huruta, M. L. Barjas-Castro, S. T. O. Saad, F. F. Costa, A. Fontes, L. C. Barbosa, and C. L. Cesar, “Mechanical properties of stored red blood cells using optical tweezers,” Blood 92(8), 2975–2977 (1998).
[PubMed]

J. Biomech. (1)

R. M. Hochmuth, “Micropipette aspiration of living cells,” J. Biomech. 33(1), 15–22 (2000).
[CrossRef]

J. Biomech. Eng. (1)

P. Bagchi, P. C. Johnson, and A. S. Popel, “Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow,” J. Biomech. Eng. 127(7), 1070–1080 (2005).
[CrossRef]

J. Biomed. Opt. (1)

I. Sraj, J. Chichester, E. Hoover, R. Jimenez, J. Squier, C. D. Eggleton, and D. W. M. Marr, “Cell deformation cytometry using diode-bar optical stretchers,” J. Biomed. Opt. in press.
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Supplementary Material (3)

» Media 1: AVI (4364 KB)     
» Media 2: AVI (3442 KB)     
» Media 3: AVI (4350 KB)     

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Figures (9)

Fig. 1
Fig. 1

Angles at the front and back surface of a sphere used in TRO. The angles that incident and refracted rays at the back surface make with the laser axis are α - β and 2α - 2β respectively.

Fig. 2
Fig. 2

Dynamic ray-tracing on a spherical cell exposed to a laser sheet from a 1x200 μm long diode bar. The surface of a cell is discretized using a triangular mesh. The inset shows the ray-tracing of a single ray intersecting a triangle of nodes: A, B and C are coordinates of the triangle. P is the point of ray-triangle intersection. N is the surface normal, I the incident ray, T the refracted ray and R the reflected ray. α and β are the angles of incident and refracted rays with the surface normal; i, r, and t are the angles with the laser axis Z.

Fig. 3
Fig. 3

Trapping efficiency Q on the front and back surface of a spherical cell from both the TRO and DRT.

Fig. 4
Fig. 4

Transient forces determined using DRT for a laser power of 12 mW/µm. Note, the initial forces at time t* = 0 are the forces that remain constant using TRO on a sphere.

Fig. 5
Fig. 5

Side view of the deformed spherical cell when reaching a steady-state shape from a fully 3D simulation colored by the dimensionless elastic energy, Eng/Eh (Media 1). The initial radius is 3.3 μm and the diode power is 42 mW/μm. The red square represents the diode bar (not drawn to scale) where the diode long axis is in and out of the figure.

Fig. 6
Fig. 6

Fnet and steady-state deformation as laser power is increased from 12 mW/µm to 72 mW/µm.

Fig. 7
Fig. 7

2D slice of an RBC with the y-axis as the axis of symmetry. A ray can intersect up to four surfaces.

Fig. 8
Fig. 8

Comparing deformation at steady state for different RBC shapes.

Fig. 9
Fig. 9

Side view of the deformed RBC when reaching a steady-state shape from a fully 3-D simulation colored by the dimensionless elastic energy, Eng, normalized by Eh on (a) oblate sphere of major to minor axis ratio 1.28:1 (Media 2) and (b) biconcave disc of radius 4 μm (Media 3). Diode power is 42 mW/μm.

Tables (1)

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Table 1 Net optical forces on different RBC shapes of same surface area using 12 mW/ μm.

Equations (9)

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F o p t i c a l = n m Q P c ,
n m sin α = n p sin β .
Q f r o n t ( α ) = 1 + R ( α ) cos ( 2 α ) n ( 1 R ( α ) ) cos ( α β ) Q f r o n t ( α ) = R ( α ) sin ( 2 α ) n ( 1 R ( α ) ) sin ( α β )
Q b a c k ( α ) = ( 1 R ( α ) ) [ n cos ( α β ) + n R ( β ) cos ( 3 β α ) ( 1 R ( β ) ) cos ( 2 α 2 β ) ] Q b a c k ( α ) = ( 1 R ( α ) ) [ n sin ( α β ) + n R ( β ) sin ( 3 β α ) ( 1 R ( β ) ) sin ( 2 α 2 β ) ] ,
Q = cos ( i ) R ( α ) cos ( r ) n ( 1 R ( α ) ) cos ( t ) Q = sin ( i ) R ( α ) sin ( r ) n ( 1 R ( α ) ) sin ( t ) ,
Q x , y = ( 1 R ( α ' ) ) [ n x n m cos ( i ) n x n m R ( α ) cos ( r ) n y n m ( 1 R ( α ) ) cos ( t ) ] , Q x , y = ( 1 R ( α ' ) ) [ n x n m sin ( i ) n x n m R ( α ) sin ( r ) n y n m ( 1 R ( α ) ) sin ( t ) ] ,
R = I + ( 2 cos α ) N T = n x n y I + ( cos β + n x n y cos α ) N
D F = L B L + B ,
y = 0.5 a [ 1 ( z / a ) 2 ] 1 / 2 [ C 0 + C 1 ( z / a ) 2 + C 2 ( z / a ) 4 ] ,

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