Dynamic Mechanical Response of

Brain Tissues

2nd Symposium on TBI, University of Maryland, 19 May 2011

Weinong Wayne Chen

Schools of Aeronautics/Astronautics and Materials Engr.

Purdue University, West Lafayette, IN

(765) 494-1788, wchen@purdue.edu

Tusit Weerasooriya

Steve Son

Eric Nauman

Riyi Shi

Collaborators:Farhana Pervin

Xu Nie

Brett Sanborn

Yun Ge

Kolsky Bar

Lindholm, 1964

Some of the Kolsky Bars at Purdue

Non-Uniform Loading on Soft Specimens

After Gray, 2000

Note: Lead is harder than most

soft tissues.

Non-homogeneous Deformation

– Uniform deformation along specimen thickness

– Related to dynamic stress equilibrium in most cases

Two-dimensional Effects in the Specimen

– Friction effect

– Radial inertia in specimen

Dynamic Characterization of Soft Materials

Modified Kolsky Bar for Soft Materials

Some Tissues Dynamically Characterized

Livers

Lungs

SkinKidneys

Tendon

Reticular membrane

Specimen

cross-sections

Tendons under tension

Muscles under

compression and tension

White Matter

Gray matter

MTS

SHPB

Dynamic Properties of Gray and White Matters

Scatter in Response of Bovine Gray Matter

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30 35 40 45

Strain (%)

Str

ess

(KP

a)

Strain Rate: 400/s

Strain Rate: 1200/s

Strain Rate: 1800/s

Error Bar

0

2

4

6

8

10

12

14

0 10 20 30 40 50 60

Strain (%)

Str

ess

(KP

a)

Strain Rate : 0.01/s

Strain Rate: 0.1/s

Error Bar

High-rate Results

Low rates

Brain Tissues from Different Animals

0 10 20 30 40 50 60 70

0

100

200

300

400

En

gin

ee

rin

g S

tre

ss (

KP

a)

Engineering Strain (%)

Male Hog Gray Matter

Female Hog Gray Matter

Strain Rate :1000/s

0 10 20 30 40 50 60 70

0

100

200

300

400

En

gin

ee

ring

Str

ess (

KP

a)

Engineering Strain (%)

Hog

Steer

Lamb

Gray Matter @ 1000/s

0 10 20 30 40 50 60 70

0

400

800

1200

1600

En

gin

ee

rin

g S

ters

s (

KP

a)

Engineering Strain (%)

Yorkshire Gilt

Cross-bred Hog

Gray Matter @ 3000/s

Male/Female

Pig/Cow/Lamb

Purebred/Crossbred

Specimen dimension:

ϕ10 mm outer diameter

ϕ5 mm inner diameter

1.7 mm thickness

Camera frame rate: 50,000 fps

STRIKER

PULSE SHAPER

FLANGE

MOMENTUM TRAP

STRAIN GAGE

SPECIMEN

PLEXIGLAS

HIGH SPEED CAMERA

PRESET GAP

WHEATSTONE

BRIDGEPRE AMPLIFIER

OSCILLOSCOPE

Brain Tissue Lateral Deformation

A Washer-shaped Gel Specimen under Compression

66% Peak Axial Strain

Strain Rate ~2,000/s

G ~ 200 kPa

Strain Rate ~2,000/s

G ~ 5 MPa

Disturbances in Measured Axial Stresses

x

p

p

x

x

o

x

x

o aap

2

22

3

2

18116

3

pE

E

x

zyxx

1

1

pzy

5.0

pE xx

xE p

Aluminum 3.5 GPa ~7 MPa 0.002

Plexiglass 0.2 GPa ~3 MPa 0.015

Soft Tissue 1.1 kPa ~2 MPa 1800

xEp

Measured axial stress

dominated by pressure from

inertia, friction, etc.

Inertia pressure (Forrestal and Warren, 2010)

Ideally, p ~ 0

05.0%5 x

When

Impact rod (TW, 0.375” Dia.)

Impact pin

Impact sleeveIncident tube

Specimen sleeve

SpecimenStrain gage

Specimen adapter

Impact rod

Impact sleeve

Impact pin

Cushion (fixed to rigid wall)

Kolsky Torsion Bar for Dynamic Shear Response

Kolsky Torsion Bar for Dynamic Shear Response

Dynamic shear response under torsional loading

No radial-inertia effect.

No stress concentrations at the edges.

Pure shear properties of the material at high rates.

• “Desk-top” Kolsky torsion bar setup

Camera model: Cordin 550

Frame rate=50,000 fps

Outer adapter, fixed to torque

sensor.

Inner adapter, connected to

torsion bar.

Gel sample

No slippage or debonding at the

specimen-adapter interface.

High-speed Imaging of Deformation

Shear stress-strain curves

(Note the small stress amplitude)

Shear strain rate history

0 50 100 150 200 250 3000

400

800

1200

1600

2000

0

400

800

1200

1600

2000

Sh

ea

r S

tre

ss (

Pa

)

Sh

ea

r S

tra

in R

ate

(1

/s)

Time (microsecond)

Strain rate history

Stress history

0.00 0.04 0.08 0.12 0.16 0.200

600

1200

1800

2400

3000

Sh

ea

r S

tre

ss (

Pa

)

Shear Strain

Dynamic Shear Stress-Strain Responses

Ring-shaped Specimen

O.D.=19 mm

I.D.=14.3 mm

Thickness=2 mm

Dynamic Shear Strain Rate and Strain

0 100 200 300 400 500 6000

100

200

300

400

500

600

700

800

900

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Sh

ea

r str

ain

Sh

ea

r str

ain

ra

te (

1/s

)

Time (microseconds)

Shear strain rate history

Shear strain history

Dynamic Stress-Strain Curves

0.0 0.1 0.2 0.3 0.4 0.5 0.60

1

2

3

4

5

E

qu

iva

len

t str

ess (

KP

a)

Equivalent strain

Sample #1

Sample #2

Sample #3

Sample #4

Sample #5

A Comparison of Axial/Shear Responses

0.0 0.1 0.2 0.3 0.4 0.5 0.60

1

2

3

4

5

Equiv

ale

nt str

ess (

KP

a)

Equivalent strain

Sample #1

Sample #2

Sample #3

Sample #4

Sample #5

Shear strain rate=700/s

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

300

600

900

1200

1500

1800

Equiv

ale

nt S

tress (

KP

a)

Equivalent Strain

Strain rate=2000/s

Summary

• Uniaxial brain tissue compression experiments

too sensitive to disturbances.

• Necessary to separate volumetric and shear

responses.

• Novel dynamic shear experimental methods

developed, calibrated, and used for brain

tissue characterization.