Biomechanics of Solids

Devendra BajajGraduate Student, LAMP

Department of Mechanical EngineeringUMBC

ENCH 484/693: Biomedical Engineering. (April 18, 2007)

Historical Facts

Anatomical studies of the ShoulderDrawings of the torsoand the arms

Leonardo da

Vinci1452-1519

Studies of the human skull

www.davinciandthebrain.org

Historical Facts

Illustration of skull from the 1918 editionAn illustration from 1918 edition

Henry Grey1827-1860

www.wikipedia.org

List of bones of Human Skeleton1. Frontal bone 2. Parietal bone 3. Temporal bone 4. Occipital bone 5. Zygomatic

bone 6. Superior and inferior maxilla 7. Mandible 8. Cervical vertebrae incl. atlas & axis thoracic vertebrae9. Nasal bone 10. Sternum11. Humerus12. Ilna13. Radius14. Lumbar vertebrae 15. Pelvis

16. Sacrum 17. Hip joint18. Femur19. Patella20. Tibia21. Fibula22. Greater trochanter

of femur 23. Condyles

of femur25. Clavicle or collarbone 26. Condyles

of humerus27. Head of radius28. Ribs29. Scapula or shoulder blade

www.wikipedia.org

Loads Transmitted

Bone: Femur

www.wikipedia.org

Major Concerns

Bone health issues, such as osteoporosis, are expected to affect 50% of Americans by the year 2010*

*Bone Health and Osteoporosis: A Report of the Surgeon General, HHS 2004

Fracture and Treatment of Hip Joints

Statistics show that about 80 % of all failures that lead to the revision operation of a total hip are caused by aseptic loosening of the total hip.

http://www.doereport.com/imagescooked/12945W.jpg

Human Tooth

http://www.nlm.nih.gov

Restorative Dentistry

Demineralization

ExcavationRestoration

Failure of Restored Teeth

100 µm

500 µm

Arola et al., J. Mat Sci.:Materials in Medicine, 1998

The story so far…..

Hard Tissues: Historical perspectiveTypes of bonesLoad distributionAge related problemsFailure and treatment of Hip jointRestorative dentistryFracture of restored toothMicrostructure of BONE AND HUMAN TOOTHInfluence of AGING?

Microstructure of Bone

Nalla et al., Materials Science and Engineering, 2006

Bone: Influence of Aging

Young 34 years

Aged 85 years

Nalla et al., Materials Science and Engineering, 2006

Bone becomes more porous with age

Microstructure of Dentin

peritubular dentin

intertubular dentin

5 µm

Ten Cate, Oral Histology 1998Porter et al., Biomaterials 2005

67 nm

~10-12 nm

Collagen Debanding

Mineral Crystal

Dentinal Tubule

Molar

OcclusalSurface

Dentin: Influence of Aging

Bajaj

et al., Biomaterials 2006

Young 17 years

Aged 50 years

Dentin becomes less porous with age

Dentin v/s

Bone

Which one has reparative properties ?BONE or DENTIN

“Teeth are exquisitely sensitive to local stress and trauma and we are conscious of our teeth in a way quite unlike our sense of what our bones are up to.” -

John D. Curry

Why study the MECHANICAL properties of hard tissues???

“It is unfortunate that we have so little idea of the mechanical properties of many of the interesting bio materials. This is because of the small size and conventional shape of many of the structures in which they are found. Their histological structure shows that they are often very well designed mechanically, but, unfortunately, we usually cannot quantify them well.” John D. Curry

Structure Tubule orientation

Aging

Applications to other engineering materials (MEMS/NEMS)

10 nm

Rouland, 2002

Ritchie et al., 2002

Testing of Hard Tissues

Tensile

0

20

40

60

80

100

120

0.000 0.005 0.010 0.015 0.020 0.025

Stre

ss (M

Pa)

Strain

Sano et al., J Dent Mat. 1984

σut

Testing of Hard Tissues

Flexure

P(t)/2P(t)/2

P(t)

0

50

100

150

200

0.000 0.005 0.010 0.015 0.020

Ben

d S

tress

(MP

a)

Strain (m/m)

Elastic Modulus

Strength

Energy to

Fracture

Arola and Reprogel, Biomaterials 2006

Tubule Orientation

θ=0° θ=90°

0

20

40

60

80

100

120

140

160

0.000 0.005 0.010 0.015 0.020

θ=0o

θ=90o

Stre

ss (M

Pa)

StrainArola and Reprogel, Biomaterials 2006

θ=0°

θ=90°

Tubule Orientation

θ=0° θ=90°

Arola and Reprogel, Biomaterials 2006

θ=0°

θ=90°

0

10

20

30

40

50

60

70

80

102 103 104 105 106 107

θ = 0ο

θ = 90ο

Stre

ss a

mpl

itude

, σa (M

Pa)

Cycles, N

Dentin: Influence of Aging

Arola and Reprogel, Biomaterials 2005

Young 18 years

Old 66 years

0

20

40

60

80

100

120

140

0.000 0.005 0.010 0.015 0.020

OldYoung

Stre

ss (M

Pa)

Strain (m/m)

Dentin: Influence of Aging

Arola and Reprogel, Biomaterials 2005

Young 18 years

Old 66 years

0

10

20

30

40

50

60

70

80

102 103 104 105 106 107

YoungOld

Stre

ss a

mpl

itude

, σa (M

Pa)

Cycles, N

10-7

10-6

10-5

10-4

0.8 0.9 1.0

da/d

N (m

m/c

ycle

)

ΔK (MPa∗m0.5)ΔK

th

mC

Testing of Hard TissuesFatigue

4.0

2.01.0

a

6.0

1.0

2.0High Crack Growth

Resistance

Low Crack Growth ResistanceI II III

Bajaj

et al., Biomaterials 2006

Primary section

Possible specimen

Fatigue Crack Growth

10-7

10-6

10-5

10-4

10-3

0.5 0.6 0.7 0.8 0.9 1.0 2.0

OldYoungda

/dN

(mm

/cyc

le)

ΔK (MPa∗m0.5)

Dentin

Bajaj

et al., Biomaterials 2006

Mechanisms of Crack Growth

Bajaj

et al., J Biomed Mat Res, 2007b (submitted)

Fatigue Crack Growth

Bone

Nalla

et al., Biomaterials, 2005

The story so far…..

Microstructure of BONE and DENTINInfluence of AGE on structureTesting of hard tissuesTensile Flexure Fatigue

Fatigue in DENTINFatigue in BONE

Why do we see differences in properties with AGING ?STRUCTURECHEMISTRY

Changes in Structure & Chemistry

Specimen Surface

Depth of the source of secondaryelectron information (~5nm)

Depth of the source of Backscatteredelectron information (~1/3 total depth)

Depth of the source of X-Rayinformation (~3µm)

SEX-Rays

Incidence Electron Beam

BSE

Binary

1.0 μmThreshold

Energy Dispersive x-ray Analysis

Bajaj, Masters Thesis, 2006

Influence of Structure

0.00

0.05

0.10

0.15

0.20

0.25

10 20 30 40 50 60 70 80 90Are

a of

Lum

en /

Are

a of

Tub

ule

Age (years)

0

5

10

15

20

25

30

0.00 0.05 0.10 0.15 0.20

Cra

ck G

row

th E

xpon

ent (

m)

Area of Lumen/Area of Tubule

r = 0.799P = 0.0028

OcclusionofDegreeTubuleofAreaLumenofArea

=

Dentin

Bajaj, Masters Thesis, 2006

Influence of Chemistry

2.0

2.1

2.2

2.3

2.4

2.5

2.6

10 20 30 40 50 60 70 80 90

Ca

/ P

Age (years)

10

15

20

25

30

2.0 2.1 2.2 2.3 2.4 2.5 2.6

Cra

ck G

row

th E

xpon

ent (

m)

Ca/P

r = 0.878P = 0.0056

Dentin

Bajaj, Masters Thesis, 2006

Influence of Structure

Nalla

et al., Materials Science and Engineering, 2006

Bone

Influence of Chemistry

Ager

et al., J Biomed Optics, 2005

Bone

Conclusions

Aging results in changes in properties of hard tissues

Changes in structure and chemistry are responsible for changes in properties

Enamel (E)

Dentin (D)

PulpDEJ

2 mm

250 µm

D

E

What is the biological seed to aging?How does the mineral and non-mineral component contribute

to strength?How much damage accumulates in these tissues per day?Can we arrest these cracks mechanically or chemically?