Isotropic: same in all directions

1
Isotropic same in all directions
Neurofilaments Cross-linked In frog axon
2
Linker proteins for actin
3
Particle Tracking in fibroblastsLecture 5
4
Tracking particles Regional stiffness
5

• 3- Think of a balloon with stiff meridional
  bands- networks can stretch more easily along the
  axis with less stiff ropes.
• 4 hoop stress versus axial stress

6
Cylindrical Stresses
7
(No Transcript)
8
Buckling Bending
20 cm
10 cm
9
Tension Field Theory
Membrane
10
Coupling Mechano-/Biochemical-/Cellular-
11
Inside a Blood Vessel
Endothelial cells with Nucleus bulging out
Blood flow
10 microns
12
Cells- fluid or solid?

• Micropipet aspiration comparison between ECs and
  chondrocytes
• Comparison between EC cell nucleus
• Stiffness following spreading or adapting to
  flow.
• ECs in flow will minimize force on nucleus
• Enucleus 9 Ecytoplasm

13
Applying global strains to Nucleus1
Round
Spread
Compression relaxation done quickly to measure
passive props while avoiding adaptation. No
hysteresis or plastic behaviour seen in spread
cells and nuclei. 1. Caille, N J. Biomech, 2002
Nucleus
14

• Material properties, not inhomogeneity, explains
• The non-linear behaviour

15
(No Transcript)
16
Slow cell squishing
17
FEM of compression
18
Bone Adaptation

• Most bones experience 1000s of loads daily
• Bone cells must detect mech signals in situ and
  adjust bone architecture appropriately.
• Sensor cells Osteocytes Effector cells
  Osteoblasts, osteoclasts
• Signalling molecules PGs, NO
• Responses bone formation/resorption

19

• Bending forces not only cause deformation of
  osteocytes, but generate pressure gradients that
  drive fluid flow through the canalicular spaces.
  Bending causes compressive stress on one side of
  the bone and tensile stresses on the other. This
  leads to a pressure gradient in the interstitial
  fluids that drives fluid flow from regions of
  compression to tension. Fluid flows through the
  canaliculae and across the osteocytes, providing
  nutrients and causing flow-related shear stresses
  on the cell membranes. The fluid flow also
  creates an electric potential called a streaming
  potential

20

• Strain detected by mechanoreceptors or by CAMs. G
  protein in membrane causes Ca and other 2nd
  messengers.

21

• osteocytes (Oc) and bone lining cells (BLC)
  detect mechanical signals and communicate those
  signals to the bone surface. Soluble mediators,
  which include
• prostaglandins (PGs) and nitric oxide (NO), are
  released and cause the recruitment and/or
  differentiation of osteoblasts (Ob) from
  proliferating and nonproliferating
  osteoprogenitor cells.

22

• The error function, i.e., the daily loading
  stimulus (S)
• minus the normal loading pattern (F So), drives
  bone adaptation. Abnormally low values of the
  error function cause increased osteoclast
  activity on bone remodeling surfaces, while
  abnormally high values cause increased osteoblast
  activity on bone modeling surfaces

23

• Rats jumping various of numbers of times per day
  showed that five jumps per day were sufficient
  to increase bone mass, but increasing numbers of
  jumps gave diminishing returns with respect to
  bone mass. These data very closely fit the
  mathematical relationship proposed in Eq. 1

24

• G proteind mechanochemical signal transducer

25

• Focal adhesions by Integrin and associated
  proteins.

26
Load type affects adaptation

• Long bones are loaded mostly in bending
• Strain _at_ neutral axis is small, and increases
  away from axis
• Loading that changes the neutral axis, changes
  bone formation 1
• 1. Turner, CH J. Orthop. Sci, 1998.

27

• MC3T3-E1 osteoblasts subjected to fluid shear
  (12dynes/cm2) for 60min undergo dramatic
  reorganization of the actin
• cytoskeleton. A Control cells not subjected to
  flow have poorly organized stress fibers labeled
  with Texas red-phalloidin.
• B Cells subjected to fluid flow for 60 min
  develop prominent stress fibers labeled with
  Texas red-phalloidin that are aligned roughly
  parallel to each other. C and D Control cells not
  subjected to fluid shear which have poorly
  organized stress fibers

28
Adaptation Cascade

• Transduction Biochemical transmission.effecto
  r cell..tissue
• Ion channels.Ca,NOS, COX, PGs, G protein.Obs,
  Ocs..trabeculae
• It is an error driven feedback system
• Driven more by infrequent abnormal strains than
  by normal strains encountered during predominant
  activity1
• 1. Layton, LE The success and failure of the
  adaptive response to functional loading-bearing
  in averting bone fracture Bone131992

29
Quantifying bone adaptation
30
Bone Loading Waveforms
31
Resonant Stimuli for Bone

• Loading frequencies near 20 Hz
• Vibration 1
• Error Driven
• 1. Rubin, C.

32
(No Transcript)
33
Mechano - regulation

• Growth, proliferation, protein synthesis, gene
  expression, homeostasis.
• Transduction process- how?
• Single cells do not provide enough material.
• MTC can perturb 30,000 cells and is limited.
• MTS is more versatile- more cells, longer
  periods, varied waveforms..

34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
Markov Chains

• A dynamic model describing random movement over
  time of some activity
• Future state can be predicted based on current
  probability and the transition matrix

39
Sliding filamentds
40
Dynamic equilibrium
41
Sliding Filament Model
Ratchet
For A-M, vo 0.5 um/s
42
Harmonic motion (undamped)
Gel motion follows simple rules Model will
predict dynamic and Static equilibrium.
Natural Frequency
43
(No Transcript)
44
Transition Probabilities
Todays Game Outcome
Win Lose
Win 3/4 1/2
Lose 1/4 1/2
Sum 1 1
Need a P for Todays game
Tomorrows Game Outcome
45
Grades Transition Matrix
This Semester
Grade Tendencies
To predict future Start with now What are the
grade probabilities for this semester?
Next Semester
46
Markov Chain
Intial Probability Set independently
47
Computing Markov Chains
A is the transition probability A .75 .5
.25 .5 P is starting Probability P.1
.9 for i 120 P(,i1)AP(,i) end
48
Control System, I.e. climate control
49
Finding G
50
Temperature Control
51
Example Control System
-
3
u
52
Homework

• 1. Assuming the buckling force calculated in 6,
  compare the energy required to bend the
  microtubule as in 5. (State assumptions).
• 2. Find evidence (for or against) that the
  tension field theory applies to endothelial cell
  regulation.
• 3. Make a model of bone adaptation. What kind of
  function fits the data?
• 4. Make a model of A-M sliding filaments.
• 5. Based on bending forces of microtubules,
  calculate how many would be present in the EC, in
  the experiments shown (make simplifying
  assumptions).

53
Bibliography

• 1.      Hamill OP, Martinac B. Molecular basis of
  mechanotransduction in living cells. Physiol Rev
  81 2001 (2)685-740.
• 2.      Lang F, Busch, GL, Ritter M, Volkl H,
  Waldegger S, Gulbins E, Haussinger D. Functional
  significance of cell volume regulatory
  mechanisms. Physiol. Rev 1998 78247-273.
• 3.      Zhu C, Bao G, Wang N. Cell mechanics
  Mechanical response, cell adhesion, and molecular
  deformation. Annu Rev Biomed Eng 2000
  2189-226.
• 4.      Turner CH. Mechanical transduction
  mechanisms in bone. J Bone Miner Res 2000 15
  (4)105.
• Tavi P, Laine M, Weckstrom M, Ruskoaho H. Cardiac
  mechanotransduction from sensing to disease and
  treatment. Trends in Pharmacological Sciences
  2001 22 (5)254-260.

54
Bibliography

• 6.      Craelius W. Stretch activation of rat
  cardiac myocytes. Experimental Physiology 1993
  78 (3)411-423.
• 7.      Ingber DE and Folkman J. How does
  extracellular matrix control capillary
  morphogenesis? Cell 1989 58803-805.
• 8.      Craelius, W, Huang, CJ, Palant, CE,
  Guber H Mechanotransduction of swelling by rat
  mesangial cells, Mechanotransduction 2000,
  Engineering and Biological Materials and
  Structures, ENPC, France, 13-20, 2000.
• 9.      Craelius, W, Huang, CJ, Guber, H,
  Palant, CE Rheological behaviour of rat
  mesangial cells during swelling in vitro,
  Biorheology 35397-405, 1998.
• 10.  Pedersen SF, Hoffmann EK, Mills JW. The
  cytoskeleton and cell volume regulation. Comp
  Biochem Phys A 2001 130 (3)385-399, Sp Iss SI.
• 11.  Lange K. Regulation of cell volume via
  microvillar ion channels. J Cell Phys 2000 185
  (1) 21-35.