Tuesday, February 15, 2005

1. Tuesday, February 15, 2005 • Mechanical Testing (continued)

2. Types of mechanical analysis • Kinematics - just the connections • Statics- forces without motion • Dynamics- forces with motion • Rigid versus deformable body • FBDs FELFBL FBR FER

3. 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

4. Loading Types • Tension- compression • Uniaxial/bi-axial • Bending • Torsion • Shear • Reaction • Traction • Friction

5. Cytomechanical forces: • Gravitational: • Muscle contraction: • Contact: • Buoyant: • Hydraulic: (Static or dynamic) • Pneumatic • Fluid shear

6. 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 (me)

7. Elasticity (Stiffness) • “ut tensio sic vis” • Young’s 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

8. Material Parameters • Moduli: Young’s (E, KV) area (KA ) shear (G), bending (kf, flexural, energy*length) (also lp) • Stiff versus compliant (E versus Y) • Strength (UTS); Failure point • Brittle versus ductile (Area under stress/strain) • Incompressible/Compressible (Poisson, n) • Hardness: Moh’s scale: Talc= 1; Diamond = 10. To characterize cells- how do they respond to forces in their environment?

11. Steel Wood Bone Stress s Cells Comparative Mechanical Properties Steel Wood Bone Cells Strain e Cellular ‘pre-stress’

13. Elastic Behaviours Unixaxial stress Pressure n < 1 n< 0 E = s/e KA = P/DA/A 1 2

14. Poisson’s Effect Incompressible Means no volume change swelling

16. Tension b. Radial and biaxial tensions • Uniaxial tension, b. Flexure • Both with orthogonal strain. Cells • Are in nutrient broth and attached • To substrate.

17. Cell testing methods

18. 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.

19. Compressing Hydrostatic loading (a) and ‘platen abutment’ (b), with a 3D Cell arrangement, can be either Confined or without side support Anisotropic strain Friction: Nutrient block Hydrostatic Porous High pO2

20. F/A Shear a Shear Strain = tan(a) t = G tan(a)

21. Shear due to fluid flow i.e., h for water = 0.01 Poise

22. Shear stress from flow in a pipe Shear rate P1 P2

24. 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.

25. Shear Stimuli Parallel plate flow chamber, Kinetically controlling shear Rate by D P.

26. 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.

28. Magnetic tweezers Wang et al, Science

29. Force produced is proportional to deflection of a stiff beam • Tends to sink into cell. • AFM best for pure elastic materials.

30. 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 Ab’s for CSK proteins. • Then compare stain intensity on cells • Area of contact is uncontrolled

31. Proteins binding to RGD beads

32. Optical Tweezer

35. Large strains to RBCs with Optical Tweezers • High resolution • Refractivity of bead • Trapping in the beam • Limited force

36. Dao, Lim & Suresh. J. of Mech. & Physics of solids

37. Ordinary versus phase-contrast microscopy Light density Phase Interference

41. Fluid shear and pressure: Blood flow forces

42. Microspheres • Images from confocal laser-scanning microscope optical cross-sectioning of 15 µm • 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. DIC overlaid with Fluorescence

43. Microspheres in cells

44. Particle Tracking Test both structure and function 5 nM, 33 ms resolution Like a flock Of birds Heidemann: Trends in Cell Biology 14:160, 2004

45. Stiffness from particle tracking • Network stiffness by particle tracking • Metamorph Software from Universal Imaging

46. In an ideal elastic material, the K.E. imparted by KT, moves the msphere , that is then subject to restoring force back to its original position. MSD = C, therefore D = C/t. • For a VE material, D not constant.

47. Nuclear lamin • For a 1 micron sphere in lamin-poor regions, D ~ 0.21 mm2/s, corresponding to h = 2 X 10-3 Pa-s.. In water, D ~ 0.44mm2/s, corresponding to h = 1 X 10-3 Pa-s

49. Actin red, microtubules green • Heterogeneous distribution: the polymer solution is main determinant of mechanics.

50. Stiffness from thermal motion 0 22 42 Seconds (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 52 62 S