Joint Loading

Joint (organ)

MechanicsBiology Organ Tissue Cell amp Molecular Levels

copy ADAM Inc All rights reserved This content is excluded from our Creative Commonslicense For more information see httpocwmiteduhelpfaq-fair-use

Tissue Cells

Extracellular Matrix

Molecular Mechanics

HA

copy source unknown All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-use

1

p = 0

p = 0

p is ldquohighrdquo

Dgel = Hmiddotk

PSet 5 1 (Prob 710ab)

X1

L

0

u1(x1t)

U1(x1t)

uo

2

Questions bull What distinguishes solid-phase viscoelasticity

Time Onlyhellip

hellipfrom poroelasticity Space and Time

copy source unknown All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-use

bull Does poroelasticity operate at cellular and molecular scales as well as tissue scale

3

Questions bull What distinguishes solid-phase viscoelasticity

Time Onlyhellip

hellipfrom poroelasticity Space and Time

copy source unknown All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-use

bull Does poroelasticity operate at cellular and molecular scales as well as tissue scale

3

Cells Synthesize 100s of Extracellular Matrix Macromolecules

collagens

proteoglycans

glycoproteins

(Dick Heinegaringrd Nature Revs Rheumatology 2010)

Source Heinegaringrd Dick and Tore Saxne The Role of the Cartilage Matrixin Osteoarthritis Nature Reviews Rheumatology 7 no 1 (2011) 50-56

4

copy Wiley All rights reserved This content is excluded from our Creative Commonslicense For more information see httpocwmiteduhelpfaq-fair-use

Hk = f(pH Ionic strength) [PSet 4 Prob 1]

GAGs

aggrecan

collagen

G

n~30

TITRATION

Qnet = 0

Qnet

copy source unknown All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-use

5

Biochem J

copy The Biochemical Society All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-useSource Bowes Joane H and R H Kenten The Amino-acid Composition and Titration Curveof Collagen LRFKHPLFDO-RXUQDO 43 no 3 (1948) 358

6

CELL

bull Aggrecan density in tissues subjected to compression (cartilage disc tendon) is 10 ndash 40 X higher than this image (ldquoHrdquo)

bull GAGs also resist fluid flow (ldquokrdquo)

400 nm

(Fetal bovine aggrecan Laurel Ng) Courtesy Elsevier Inc httpwwwsciencedirectcom Used with permissionSource Ng Laurel et al Individual Cartilage Aggrecan Macromolecules and theirConstituent Glycosaminoglycans Visualized via Atomic Force Microscopy Journal ofStructural Biology 143 (2003) 242-57

7

Swelling (ldquoHrdquo) amp Fluid Flow (ldquokrdquo) in Bio-Porous Mediardquo Molecular Networks amp Gels

Polyelectrolyte Gels Swell Network resists Electrostatic Forces (ldquoHrdquo) fluid flow (ldquokrdquo)

Neutral

Charged copy source unknown All rights reserved This content is excludedfrom our Creative Commons license For more informationsee httpocwmiteduhelpfaq-fair-use

Courtesy of Macmillan Publishers Limited Used with permissionSource Ono Toshikazu et al Lipophilic Polyelectrolyte Gels as Super-absorbentPolymers for Nonpolar Organic Solvents Nature Materials 6 no 6 (2007) 429-33

8

Problem 711 and Figure 734 removed due to copyright restrictions See the problem in the textbookSource Grodzinsky Alan Field Forces and Flows in Biological Systems Garland Science 2011

9

Problem 711 and Figure 734 removed due to copyright restrictions See the problem in the textbooke Grodzinsky Alan Field Forces and Flows in Biological Systems Garland Science 2011Sourc

10

Problem 711 and Figure 734 removed due to copyright restrictions See the problem in the textbooke Grodzinsky Alan Field Forces and Flows in Biological Systems Garland Science 2011Sourc

10

Two-Layer Poroelastic Model

Problem 711 and Figure 734 removed due to copyright restrictions See the problem in the textbookSource Grodzinsky Alan Field Forces and Flows in Biological Systems Garland Science 2011

11

Motivated by Malaviya

J Orthop Res 2000

PSet 5Prob 3

(d)

(Connective Tiss Res 1979)

bull bull bull

Chondroitin sulfate = Aggrecan

Dermatan sulfate = decorin (ldquoSLRPsrdquo)

copy Taylor amp Francis Group All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-useSource Gillard Gerald C et al The Influence of Mechanical Forces on the GlycosaminoglycanContent of the Rabbit Flexor Digitorum Profundus Tendon Connective Tissue Research 7no 1 (1979) 37-46

12

(Connective Tiss Res 1979)

bull bull bull

Chondroitin sulfate = Aggrecan

Dermatan sulfate = decorin (ldquoSLRPsrdquo)

copy Taylor amp Francis Group All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-useSource Gillard Gerald C et al The Influence of Mechanical Forces on the GlycosaminoglycanContent of the Rabbit Flexor Digitorum Profundus Tendon Connective Tissue Research 7no 1 (1979) 37-46

12

PROTEOGLYCAN SUPERFAMILY bull ECM molecules with (1) Core protein and

(2) Glycosaminoglycan (GAG) chains

bull ldquoSub-familiesrdquo of extracellular PGs bull Large Aggregating (Aggrecan)

bull Small Leucine-Rich PG (SLRPs)

13

(Decorin)

Example of Small-Leucine-Rich

Proteoglycans copy Annual Reviews All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-useSource Iozzo Renato V DMatrix Proteoglycans From Molecular esign to CellularFunction $QQXDO5HYLHZRILRFKHPLVWU 67 no 1 (1998) 609-52

(Iozzo + Normal and decorin null mice J Biol Chem 1999)

SKIN decorin

KO

Normal (WT)

decorin KO

Decorin amp Tendon Collagen Fibrillogenesis

Courtesy of The Journal of Biological Chemistry Used with permissionSource Iozzo Renato V The Biology of the Small Leucine-rich ProteoglycansFunctional Network of Interactive Proteins -RXUQDORILRORJLFDOampKHPLVWU 274no 27 (1999) 18843-6

14

Example of Small-Leucine-Rich

Proteoglycans copy Annual Reviews All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-useSource Iozzo Renato V DMatrix Proteoglycans From Molecular esign to CellularFunction $QQXDO5HYLHZRILRFKHPLVWU 67 no 1 (1998) 609-52

(Iozzo + Normal and decorin null mice J Biol Chem 1999)

SKIN decorin

KO

Normal (WT)

decorin KO

Decorin amp Tendon Collagen Fibrillogenesis

Courtesy of The Journal of Biological Chemistry Used with permissionSource Iozzo Renato V The Biology of the Small Leucine-rich ProteoglycansFunctional Network of Interactive Proteins -RXUQDORILRORJLFDOampKHPLVWU 274no 27 (1999) 18843-6

14

Dynamic Torsional Shear

(Static Offset Compression)

Culture Medium

TISSUE

copy American Chemical Society All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-useSource Jin Moonsoo and Alan J Grodzinsky Effect of Electrostatic Interactions betweenGlycosaminoglycans on the Shear Stiffness of Cartilage A Molecular Model and ExperimentsMacromolecules 34 no 23 (2001) 8330-39

15

ldquoDynamic Torsional Shearrdquo Apply sinusoidal shear strain (08 amplitude at 05 Hz)

and measure sinusoidal stress amplitude amp phase

copy American Chemical Society All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-useSource Jin Moonsoo and Alan J Grodzinsky Effect of Electrostatic Interactions betweenGlycosaminoglycans on the Shear Stiffness of Cartilage A Molecular Model and ExperimentsMacromolecules 34 no 23 (2001) 8330-39

Is Phase Delay due to iscoelastic -OR- Poroelastic behavior V

16

Non-zero phase angle Viscoelastic Poroelastic oth Dynamic Behavior in Pure Shear

Phase Angle

copy American Chemical Society All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-useSource Jin Moonsoo and Alan J Grodzinsky Effect of Electrostatic Interactions betweenGlycosaminoglycans on the Shear Stiffness of Cartilage A Molecular Model and ExperimentsMacromolecules 34 no 23 (2001) 8330-39

17

Non-zero phase angle Isolates Viscoelasticity of ECM (or gel or molecular network) Dynamic Behavior in Pure Shear

Phase Angle

copy American Chemical Society All rights reserved This content is excluded from our CreativeCommons license For more information see httpocwmiteduhelpfaq-fair-useSource Jin Moonsoo and Alan J Grodzinsky Effect of Electrostatic Interactions betweenGlycosaminoglycans on the Shear Stiffness of Cartilage A Molecular Model and ExperimentsMacromolecules 34 no 23 (2001) 8330-39

18

Compression

Rat Monkey Rhinoceros

cartilage

bone

200 m 400 m 1 mm Courtesy of the authors Used with permissionSource Malda Jos et al Of Mice Men and Elephants The Relation betweenArticular Cartilage Thickness and Body Mass 3OR6RQH 8 no 2 (2013) e57683

Safranin-O (red) stains Glycosaminoglycans (of Proteoglycans)

19

(Kopesky+Matrix Biol 10)

Hadi Tavakoli Nia Tissue-Level Nanomechanics Biophysical J 2011 2013

Courtesy of Elsevier Inc httpwwwsciencedirectcom Used with permissionSource Nia Hadi Tavakoli et al Poroelasticity of Cartilage at the NanoscaleBiophysical Journal 101 no 9 (2011) 2304-13

100 nm

80 nm

Aggrecan

Collagen Network

200 nm

Courtesy of Elsevier Inc httpwwwsciencedirectcom Used with permissionSource Nia Hadi Tavakoli et al High-bandwidth AFM-based Rheology Revealsthat Cartilage is Most Sensitive to High Loading Rates at Early Stages of ImpairmentBiophysical Journal 104 no 7 (2013) 1529-37

20

15 nm

Tissue-Level Nanomechanics dominated by poroelasticity

tan lt = Ersquo (O)

Courtesy of Elsevier Inc httpwwwsciencedirectcom Used with permissionSource Nia Hadi Tavakoli et al Poroelasticity of Cartilage at the NanoscaleBiophysical Journal 101 no 9 (2011) 2304-13

High-Frequency Asymptote

Low-Frequency Asymptote

fpeak

2peakf d Ek

Ersquorsquo (O)

21

Problem removed due to copyright restrictions See the problem in the textbookSource Grodzinsky Alan Field Forces and Flows in Biological Systems Garland Science 2011

22

Is this tissue Poroelastic Test fpeak vs d2

fpeak [Ek d 2]

YES

3 cows

d2Ekporo ][

Nia Biophysical J 2011 Courtesy of Elsevier Inc httpwwwsciencedirectcom Used with permissionSource Nia Hadi Tavakoli et al Poroelasticity of Cartilage at the NanoscaleBiophysical Journal 101 no 9 (2011) 2304-13

23

Is this tissue Poroelastic Test fpeak vs d2

fpeak [Ek d 2]

YES

3 cows

d2Ekporo ][

Nia Biophysical J 2011 Courtesy of Elsevier Inc httpwwwsciencedirectcom Used with permissionSource Nia Hadi Tavakoli et al Poroelasticity of Cartilage at the NanoscaleBiophysical Journal 101 no 9 (2011) 2304-13

23

MIT OpenCourseWarehttpocwmitedu

20310J 3053J 6024J 2797J Molecular Cellular and Tissue Biomechanics Spring 2015

For information about citing these materials or our Terms of Use visit httpocwmiteduterms