20.310J Molecular, Cellular, and Tissue Biomechanics ......Source: Nia, Hadi Tavakoli, et al....
Transcript of 20.310J Molecular, Cellular, and Tissue Biomechanics ......Source: Nia, Hadi Tavakoli, et al....
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
(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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
(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
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
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
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
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
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
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
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