Tuesday, February 15, 2005 Mechanical Testing (continued)
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Types of mechanical analysis Kinematics - just the connections
Statics- forces without motion Dynamics- forces with motion Rigid
versus deformable body FBDs F EL F BL F BR F ER
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Mechanics of rigid versus deformable body Rigid body: Sum of
forces in all directions Deformable body: Sum of differential
stresses in all directions Continuum mechanics describes
equilibrium
Cell Deformation Most cells are constantly deformed in vivo by
both internal and external forces. Experimental deformations can be
done by poking, squishing, osmotic swelling, electrical/magnetic
fields, drugs, etc. Comparative strain tolerance Unit : microstrain
(
Slide 8
Elasticity (Stiffness) ut tensio sic vis Youngs Modulus: Stress
over strain Shear Modulus: Related to Poisson Cells have both area
and shear stiffness, mostly due to the cytoskeleton, although
lipids contribute some. Comparative Stiffnesses Related to polymer
cross-linking
Slide 9
Material Parameters Moduli: Youngs (E, K V ) area (K A ) shear
(G), bending ( f, flexural, energy*length) (also p) Stiff versus
compliant (E versus Y) Strength (UTS); Failure point Brittle versus
ductile (Area under stress/strain) Incompressible/Compressible
(Poisson, Hardness: Mohs scale: Talc= 1; Diamond = 10. To
characterize cells- how do they respond to forces in their
environment?
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Comparative Mechanical Properties Strain Steel Wood Bone Stress
Cells Steel Wood Bone Cells Cellular pre-stress
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Elastic Behaviours < 1 < 0 E = K A = P/ A/A Unixaxial
stress Pressure 1 2
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Poissons Effect swelling Incompressible Means no volume
change
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Tension a.Uniaxial tension, b. Flexure Both with orthogonal
strain. Cells Are in nutrient broth and attached To substrate. b.
Radial and biaxial tensions
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Cell testing methods
Slide 19
Stretching Out-of-plane distension of circular substrates: A
and B are kinematically driven, I.e. surface strain of culture ~
friction between platen & substrate. C and D are kinetically
driven: surface strain ~ fluid interaction with substrate.
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Compressing Hydrostatic Porous High pO 2 Anisotropic strain
Friction: Nutrient block Hydrostatic loading (a) and platen
abutment (b), with a 3D Cell arrangement, can be either Confined or
without side support
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Shear Shear Strain = tan( ) G tan F/A
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Shear due to fluid flow i.e., for water = 0.01 Poise
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Shear stress from flow in a pipe P 1 P 2 Shear rate
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Shear stimuli to cells A cone-plate flow chamber, where
kinematically controls shear rate (dU/dl). Fully developed viscous
flows exist (thin) atop the culture surface: homogeneous shear
stress.
Slide 26
Shear Stimuli Parallel plate flow chamber, Kinetically
controlling shear Rate by P.
Slide 27
DI distribution in a single cell grouped by height for
consecutive 3 min intervals with no flow, and immediately after
flow onset. DI in individual 3D subimages increased in magnitude
and variability just after flow onset; values correlated with
height in the cell. Decreased variation was computed with continued
flow.
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Magnetic tweezers Wang et al, Science
Slide 30
Force produced is proportional to deflection of a stiff beam
Tends to sink into cell. AFM best for pure elastic materials.
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Ferromagnetic Bead - Integrin/matrix Beads can be
functionalized by coating with RGD or de-functionalized by coating
with AcLDL. Then beads can be put in with cells, allowed to attach.
Cells are then fixed, then decorated with stained Abs for CSK
proteins. Then compare stain intensity on cells Area of contact is
uncontrolled
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Proteins binding to RGD beads
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Optical Tweezer
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Large strains to RBCs with Optical Tweezers High resolution
Refractivity of bead Trapping in the beam Limited force
Slide 37
Dao, Lim & Suresh. J. of Mech. & Physics of solids
Slide 38
Ordinary versus phase-contrast microscopy Light density Phase
Interference
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Fluid shear and pressure: Blood flow forces
Slide 43
Microspheres DIC overlaid with Fluorescence Images from
confocal laser-scanning microscope optical cross-sectioning of 15 m
microspheres with dark red-fluorescent ring stain with a
green-fluorescent stain throughout the bead. Left panel provides
represents poor instrument alignment. Correct image registration
has been achieved in the right panel, where the dark red ring is
aligned with the green disk.
Slide 44
Microspheres in cells
Slide 45
Particle Tracking Heidemann: Trends in Cell Biology 14:160,
2004 Test both structure and function 5 nM, 33 ms resolution Like a
flock Of birds
Slide 46
Stiffness from particle tracking Network stiffness by particle
tracking Metamorph Software from Universal Imaging
Slide 47
In an ideal elastic material, the K.E. imparted by KT, moves
the sphere, that is then subject to restoring force back to its
original position. MSD = C, therefore D = C/ For a VE material, D
not constant.
Slide 48
Nuclear lamin For a 1 micron sphere in lamin-poor regions, D ~
0.21 m 2 /s, corresponding to = 2 X 10 -3 Pa-s.. In water, D ~ 0.44
m 2 /s, corresponding to = 1 X 10 -3 Pa-s
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Actin red, microtubules green Heterogeneous distribution: the
polymer solution is main determinant of mechanics.
Slide 51
Stiffness from thermal motion (a)-(c) Serial images of a 23 mm
long relatively stiff fiber. There is little visible bending,
consistent with a long persistence length, = 12.0 mm. (d)-(f)
Serial images of a 20 mm long flexible fiber. There is marked
bending and a short persistence length, =0.28 mm. The fibers
undergo diffusional motion and are not adhering to a glass surface,
rather are free in solution, a necessary condition for using
statistical mechanics to obtain persistence lengths. The width of
each frame is 25 mm. 0 22 42 Seconds 0 52 62 S
Slide 52
Video Tracking
Slide 53
Necturus erythrocytes loaded with fluo-4 (10 M) and exposed to
UV light emitted from a mercury vapor bulb and filtered through a
FITC cube (400 x). (A) Cells display little fluorescence under
isosmotic conditions (n=6). (B) Addition of A23187 (0.5 M) to the
extracellular medium increased fluorescence under isosmotic
conditions (n=6). (C) Exposure to a hypotonic (0.5x) Ringer
solution increased fluorescence compared to basal conditions (n=6).
(D) A low Ca 2+ hypotonic Ringer solution (5 mM EGTA) did not
display the level of fluorescence normally observed following
hypotonic swelling (n=6). Light et al. Swelling RBCs control Ca ++
pore Hypo Hypo+ EGTA
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Stimulation Protocols
Slide 56
Harmonic motion (undamped) Gel motion follows simple rules
Model will predict dynamic and Static equilibrium. Natural
Frequency
Slide 57
Damped Spring
Slide 58
Viscosity & Elasticity A complex material can be modeled as
a purely viscous material combined with a purely elastic material,
thus mathematically separating the viscosity of a material from its
elasticity. A purely viscous component is a Newtonian fluid- it has
no memory and no elasticity; it cannot deform as a solid. Cells
generally behave as solid-liquid composites. V-E tools can quantify
their behaviour, since the models separate viscosity from
elasticity in a kind of finite element model.
Slide 59
Maxwell Model: Differential method For step input: d /dt=0
Slide 60
Maxwell model: Laplace Method Viscosity: Pascal-sec For a step
input Mechanical Impedance. Compliance + Slipperiness = /E
Gel/cell Model Make a complete model and label all parameters
Describe the output, relating what happens and why. What is the
time constant? State the assumptions and simplifications
Slide 64
Classwork/Homework Add damping to your model of cytogel
Describe how you can model thermal fluctuations in cell diameter,
and list all the elements. List assumptions. Write the model
equation for the above. Complete a simulink model of the above, and
do all labelling, including all parameter values.
