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

d.e.shepherd@bham.ac.uk www.bioeng.bham.ac.uk