dynamic deformation of a soft particle in dual-trap ...dynamic deformation of a soft particle in...
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Dynamic deformation of a soft
particle in dual-trap optical tweezers
Sebastien Rancourt-Grenier*, Steven Wei, Jar-Jin Bai, Arthur Chiou, Paul Bareil*, Pierre-Luc Duval*
and Yunlong Sheng*
Center for Optics Photonics and Lasers, Université Laval
Inst. Biophotonics Eng. Nat Yang-Ming University
COMSOL Conference 2010 Boston Presented at the
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Cell elasticity measurement
• Suspended cells: (Micro-Rheology)
– Spherical RBC (swollen)
– Biconcave RBC
• Adhered cells (Tensegrity)
Suresh, 2003
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Free RBC squeezed through hole
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Guck, Biophys. J. 2001
Bareil, et al Opt. Express 14,
12503 (2006).
Optical fiber dual counter-
propagating beam stretcher Trapped stretched cell
Laser Light
Deformation < 5-10%
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Outline • Dual-trap tweezers experiments • 3D stress distributions
– Geometric Optics, Matlab – Generalized Mie Scattering theory – Comsol RF module, FDTD,
• 3D static deformation, Deformation 5-10% – analytical solution, – Comsol structural mechanics
• 3D Dynamic deformation – Comsol Multiphysics
• Fitting
z
x
Deformation 20 %
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Experimental setup
• Two laser beams with a controlled separation between their optical axes
• (a) Normal RBC; (b) RBC immersed in solution de 1mM de N-ethylmaleimide (NEM) solution for 30 minutes
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3D stress distribution Single beam centered
NA=0.16
Dual Beams
D=20um
FDTD
T-Matrix, Point Matching Method
Ray Tracing
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3D stress, Dual-beam tweezers
x
z
Geometrical approach
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Multi-Physics Solutions
• 3D field distribution – Geometric optics ray
tracing – FDTD – Generalized Mie-scattering – T-Matrix – Comsol RF module
– Approximate – Modeling high NA
Gaussian beam – More accurate
– Modeling high NA
beam
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Static deformation of membrane • Compute to membrane internal stress for a spherical RBC
• Compute the strain from the stress by Hook’s law
• Compute the displacements of the membrane from the strains
sin( ) 2 cos( ) sin( ) 0N N
N R
sin( ) ( )cos( ) sin( ) 0NN
N N R
0RN N R
1 1( cot( ) )
sin( )
uv w
R R
1( )
vw
R
1 1 cot( )
sin( )
v u uw
R R R
2( )
1
EhN
2( )
1
EhN
2(1 )
EhwN
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Static deformation analytical solution
D=0,00µm D=0,63µm D=1,27µm D=1,90µm D=2,54µm D=3,17µm
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Multi-Physics Solutions
• Static deformation of cell
– Analytical solution
– Comsol Structural Mechanics module
– Only for Spherical cells – Validation of numerical
calculation – Deformed non-spherical
cells
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Stress redistribution as RBC is gradually deformed
ComsolTM Structured Mechanics + Embadded Geometrical optics Matlab code
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Computing stress and deformation for any shape of the cell membrane
• FE Comsol MultiphysicsTM – RF module; – Structural Mechanics module
• Embedded Matlab codes of geometrical optics
• Deformable mesh • Linear Solver of a huge system of
linear equations by iterations • Minimize the errors
0 1f'(U ) = -f(U )E1/ 2
2
1
1( / )
N
i i
i
C E WN
N = numbre of degree of feedom
W = mean deformations
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Comsol MultiphysicsTM
• 3D Dynamic deformation: • Iterating
– Stress redistribution on defomred cell
– Deformation of the deformed cell
• Computing – RF module; – Structural Mechanics module – Embedded Matlab code of ray
tracing
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3D deformation of spherical RBC as the stress re-distribution on the deformed cell is considered
D=0,00µm D=0,63µm D=1,27µm D=1,90µm D=2,54µm D=3,17µm
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Equilibrium deformation
Rancourt, Opt. Exp. 10462-72 (2010)
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Theory fits to experimental data
T= 24oC (sans NEM) T= 37oC (sans NEM) T= 42oC (sans NEM) T= 24oC (avec NEM) T= 37oC (avec NEM) T= 42oC (avec NEM)
6
6,5
7
7,5
8
8,5
9
9,5
10
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00
Distance entre les deux laser 2D (µm)
Ax
e l
on
g (
µm
)
Données expérimentalesSimulation analytiqueSimulation numérique
6
6,5
7
7,5
8
8,5
9
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00Distance entre les deux laser 2D (µm)
Ax
e l
on
g (
µm
)
Données expérimentalesSimulation numériqueSimulation analytique
6
6,5
7
7,5
8
8,5
9
9,5
10
10,5
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00Distance entre les deux laser 2D (µm)
Axe l
on
g (
µm
)
Données expérimentalesSimulation numériqueSimulation analytique
6
6,5
7
7,5
8
8,5
9
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00Distance entre les deux laser 2D (µm)
Axe l
on
g (
µm
)
Données expérimentalesSimulation numériqueSimulation analytique
6
6,5
7
7,5
8
8,5
9
9,5
10
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00Distance entre les deux laser 2D (µm)
Axe l
on
g (
µm
)
Données expérimentalesSimulation numériqueSimulation analytique
6
6,5
7
7,5
8
8,5
9
9,5
10
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00Distance entre les deux laser 2D (µm)
Axe l
on
g (
µm
)
Données expérimentalesSimulation numériqueSimulation analytique
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Conclusion
1) Computed 3D radiation stress distribution by GO, FDTD and T-matrix on a sphere in dual-trip tweezers
2) Compute static 3D deformation of the spherical membrane with asymmetrical external load
3) Computed the stress redistribution and membrane re-deformation with finite element method
4) Theory is fit to experimental results for membrane’s deformation > 20 %
5) Differentiate normal and NEM treated RBCs, by their elasticity
(Normal RBC) (NEM treated )
(5,07 1,11) /Gh N m (8,59 1,14) /Gh N m
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Future Work
• Biconcave shape of RBC – Comsol CAD module
• High NA Gaussian beam as background field • Trapped particle floats • Nanoparticle Scattering
– RF module solver of EM field
• Other deformable particles • Other type of tweezers
• Cell mechanics