Viscoelastic properties of articular cartilage at high frequencies
Geoffrey R FulcherDavid WL Hukins
Duncan ET Shepherd
School of Mechanical EngineeringUniversity of Birmingham
Articular cartilage Low friction & wear
Transmitting forces
Deformable: larger areas - lower stress
Articular cartilage Viscoelastic
Behaviour under the full range of physiological loading frequencies?
Rise time of heel strike force
Generally– 100-150 ms
Some people– 5-25 ms
– implicated in the onset of osteoarthritis
1 Hz– rise time 500 ms
90 Hz– rise time 5.6 ms
0
5
10
15
20
25
30
35
40
0 2 4 6 8 10 12 14 16 18 20
Time (ms)
Fo
rce
(N)
0
5
10
15
20
25
30
35
40
0 200 400 600 800 1000 1200 1400 1600 1800
Time (ms)
Fo
rce
(N)
Objective
To measure the viscoelastic properties of bovine articular cartilage at loading frequencies of up to 90 Hz
Viscoelasticity
Viscoelasticity phase angle of 0°
– material is purely elastic
phase angle of 90°– material is purely viscous
Viscoelastic material Storage modulus, E´
– elastic part of the response (where energy is stored and used for elastic recoil of the specimen when a stress is removed)
Loss modulus, E´´ – the viscous response (where energy is dissipated and
the material flows)
E'
E''δ 1tan
Materials & methods Bovine
Tibial plateau
Fluid bath
Indenter
Materials & methods Bose ElectroForce 3200
testing machine
WinTest
DMA (Dynamic Mechanical Analysis)
Materials & methods sinusoidally varying compressive force of between 16 N
and 36 N
1.7 MPa
1 to 90 Hz
Calculated:– E´– E´´
Results
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Frequency (Hz)
Mo
du
lus
(MP
a) Point 2 storage
Point 3 storage
Point 6 storage
Point 7 storage
Point 2 loss
Point 3 loss
Results
Storage modulus Curve fit
Slope
B)f(logAE e '
f
A
df
dE
'
Phase angle > 0 for all frequencies 1 to 90 Hz
– 3.4 to 5.7° (mean = 4.9°, SD = 0.6°)
Viscoelastic
Implications for osteoarthritis? More energy is stored by the tissue than is
dissipated
Effect is greater at higher frequencies.
Main mechanism for this excess energy to be dissipated is by the formation of cracks
Implications for osteoarthritis?
1 Hz
10 Hz
100 Hz
Conclusions Articular cartilage is viscoelastic 1 to 90 Hz
High frequency loading, seen in some of the population, may be implicated in osteoarthritis
Acknowledgements
Arthritis Research Campaign
Duncan ET Shepherd BEng, PhD, CEng, FIMechE
School of Mechanical EngineeringUniversity of Birmingham
[email protected] www.bioeng.bham.ac.uk