AEM GEM4 seminar - MIT OpenCourseWare

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20.GEM GEM4 Summer School: Cell and Molecular Biomechanics in Medicine: CancerSummer 2007

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Magneto-Mechanical Stimulation ofEarb Bone Growth into Sudaee Lqers on implants

Athina MwkaIci (Dept. of Engineering) H.J. GriEths & T.W. C1pe (Dept. of Materids Science &

Metd1wgy)

Courtesy ofthina Markaki. Used with permission.

University of Cmb~dge

Prosthetic Implants -

Magneto-Mechanical Actuation of Fibre Network Materials: Deflections and Strains

Elastic Properties of Fibre Network Materials

Design of an Integrated Magneto-Active Prosthesis

Fibre Compatibility and Topography

Bone-Implant Adhesion in Implants

• Bonding via: a) bone cement (durability often poor)b) rough/porous surface, into which bone tissuegrows (post-operative period critical)

oosening at bone-implant interface Caused by: • poor interfacial adhesion • stress shielding

(inhibits straining of the bone)

Cementless & Cemented Stems (Smith & Nephew)

Image removed due to copyright restrictions. L

Strain Regulated Bone Modelling (Formation) and Remodelling (Resorption) (H.M. Frost 1987)

Healthy bone growth is stimulated by mechanical strain. Physiologically benefits start at ~ 1 millistrain.

Use of Porous Metals for Prosthesis

Image removed due to copyright restrictions.

Canine femur after incorporation of a Ti mesh (Oka et al, J. Bone & Joint Surgery, 1997;79:1003-1007)

•• Porous metals have often been proposedPorous metals have often been proposed for prosthesesfor prostheses

•• Pores ~ 100Pores ~ 100--300300 µµm & biocompatiblem & biocompatible surfacesurface -- bone tissue inbone tissue in--growth does occurgrowth does occur

• Fibre Network Materials Good Potential for Control over: (a) Material (fibre diameter, section shape) (b) Architecture (porosity, fibre orientation

distribution, inter-joint spacing)

Image removed due to copyright restrictions.

Magneto-Mechanical Actuation of Bonded FibreNetworks: A New Approach to Bone Growth Stimulation

Outline


Magaeto-Mechanical Actrcatfon ofFibre Network Materials: Deflections crnd Straims




Moment acting on a Single Ferromagnetic Fibre in an Applied Magnetic Field

∆r r

= −δcos θ x sin θ

= −8Ms B cosθ 3 E f

3 x L

⎛ ⎝⎜ ⎞

⎠⎟ − x

L ⎛ ⎝⎜ ⎞

⎠⎟

2⎡

⎣⎢

⎤

⎦⎥

L D

⎛ ⎝⎜ ⎞

⎠⎟

2

∆z δsin θ =

z x cosθ

= 8Ms B3 sin

Eθ

f

tanθ ⎢⎣

⎡3⎜⎝ ⎛

Lx ⎟ −

⎠ ⎞ ⎜

⎝ ⎛

Lx ⎟

⎠ ⎞ 2

⎥⎦

⎤ ⎜⎝ ⎛

DL ⎟

⎠ ⎞ 2

Measured and Predicted Deflections of a Single Ferromagnetic Fibre

L = 50 mm, x = 45 mm D = 375 µm, θ = 29°

M s = 1.6 106 A m-1

Ef = 210 GPa

-15

-10

-5

0

Experiment (ramping up) Experiment (ramping down) Theory

Rel

ativ

e de

flect

ion

trans

vers

e to

fiel

d,∆r

/ r (

%)

0 0.05 0.1 0.15 0.2Applied field, B (Tesla)

Magnetically-induced Deflection of a Welded Parallelogram

Experimental Set-Up

∆r r

= −4MsBcos θ

3 Ef

L D

⎛ ⎝⎜ ⎞

⎠⎟

2

∆z z

= 4Ms Bsin θ tanθ

3 Ef

L D

⎛ ⎝⎜ ⎞

⎠⎟

2

Measured and Predicted Deflections of a Welded Parallelogram

Rel

ativ

e de

flect

ion

trans

vers

e to

fiel

d,∆r

/ r (

%) -0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Experiment (ramping up) Experiment (ramping down) Theory

L = 19 mm, D = 375 µm,

θ = 65°, M = 1.6 10 6 A m-1 s

Ef = 210 GPa

Applied field, B (Tesla)

Magneto-Mechanical Induction of an Isotropic FibreNetwork Material

100

10

1

0.1

0.01 0 20 40 60 80 100

Fibre segment aspect ratio, L/D (-)

Axial: Transverse:

Rel

ativ

e di

men

sion

al c

hang

e (%

) Predicted ∆R (-ive)

Predicted ∆Z (+ive) Experiment ∆Z (+ive)

Experiment ∆R (-ive)

M s = 1.6 106 A m-1

Ef = 210 GPa B = 1 Tesla

π 2 π 2

∫ ∆zsin θdθ ∫ ∆r sin θdθ ∆Z

= 0 π 2 =

⎛ ⎜ 16MsB⎞

⎟ ⎛⎜ L ⎞⎟

2 ∆R = 0

π 2 = ⎛ ⎜

−16MsB⎞ ⎟

⎛⎜ L ⎞⎟ 2

Z ⎝ 9πE f ⎠ ⎝ D⎠⎝ 9Ef ⎠ ⎝ D⎠ R∫ zsin θdθ ∫ r sin θdθ 0 0

Magneto-Mechanical Induction of a Transversely Isotropic Fibre Network Material using X-ray Tomography

3-D tomographic reconstruction

0.01

0.1

1

10

0 5 10 15 20 25 30 35 40

Predicted ∆R (-ive) Predicted ∆Z (+ive) Experiment ∆Z (+ive)

Rel

ativ

e di

men

sion

al c

hang

e (%

)

Fibre segment aspect ratio, L/D (-)

M s = 1.6 106 A m-1

Ef = 210 GPa B = 1 Tesla

n n

i i i i500 µm∆Z ⎛ 4M s B⎞ ⎛ L ⎞

2 ∑ i

Nθ sin2 θ∆R ⎛ 4M s B⎞ ⎛ L ⎞

2 ∑ i

Nθ sinθi cosθ

Z =

⎝⎜ 3Ef ⎠⎟ ⎝⎜ D ⎠⎟ ∑

n

Nθ cosθiR

= ⎝⎜

− 3Ef ⎠⎟ ⎝⎜ D ⎠⎟

∑ n

Nθ sinθii ii i

Effect of the presence of an Environment (Compliant Matrix) on Network Straining

100

Predicted Peak Strains in a Surrounding Environment, as a function of its Stiffness

Peak

indu

ced

stra

in, ε

max

(mill

istra

in)

10

1

0.1

E e = 0.001 GPa E e = 0.01 GPa E e = 0.1 GPa E e = 1 GPa

B = 1.5 Tesla M s = 1.6 106 A m-1

θ = 30° Ef = 210 GPa

Range for effectivemagnetic induction

0 10 20 30 40 50 Fibre segment aspect ratio, L/D (-) εmax =

12πMsBsin θ L D

⎛ ⎝⎜ ⎞

⎠⎟

2

9πEf tan θ + 28Ee L D

⎛ ⎝⎜ ⎞

⎠⎟

3⎛

⎝⎜

⎞

⎠⎟

• Beneficial strains (>1 millistrain) at L/D > 10

0.01

Measured and Predicted Magnetic Straining with Surrounding Environments (Matrices)

Rel

ativ

e de

flect

ion

para

llel t

o fie

ld, ∆

Z / Z

(%)

0.3

0.25

0.2

0.15

0.1

0.05

0

Experiment (rubber matrix) Predicted (rubber matrix), L/D=6 Predicted (rubber matrix), L/D=10 Experiment (resin matrix) Predicted (resin matrix), L/D=6

0 0.2 0.4 0.6 0.8 1 1.2 Applied field, B (Tesla)

Prosthetic Implants





Predicted and Measured Stiffness for an Isotropic Fibre Network

Stiff

ness

of f

ibre

net

wor

k, E

a (G

Pa)

10

1

0.1

0.01 0 5 10 15 20 25 30

Gibson & Ashby Cubic Array Predicted (f=10%) Predicted (f=15%) Predicted (f=25%)Experiment (f=0.10) Experiment (f=0.15) Experiment (f=0.25)

E 9 fa

Ef

= 32 L

D ⎠ ⎛ ⎝

⎞ 2

Range for effectivemagnetic induction

Fibre segment aspect ratio, L/D




.nesign of an Integrated Magneto-Active rosth esis


Concept of an Integrated Prosthetic Design

•• Treatment by Exposure to Applied Field during PostTreatment by Exposure to Applied Field during Post--operative Periodoperative Period•• Only MagnetoOnly Magneto--Active Layer will respond to Applied FieldActive Layer will respond to Applied Field•• MagnetoMagneto--Active Layer could be Graded, Anisotropic etcActive Layer could be Graded, Anisotropic etc•• All Materials could be BiocompatibleAll Materials could be Biocompatible

Outline






Fibre Biocompatibility and Topography

ECM

chondrocytes

Freeze dried Critically point dried Cartilage Cells (chondrocytes) cultured on a 446 (ferritic) stainless steel

fibre network

Network ofFerromagnetic Fibres Deforms Elastically in Magnetic Field, inducing Strain in any Matrix present

An Analytical Model has been Developed describirg this Process and has been Eqerimental& Validated for Simple Fibre configurations

Model Predictions suggest that Physiologically Beneficial Strains could be induced in in-Growing Bone Tissue using Magnetic Fields already employed for Diagnostic Purposes

In Wtro Experirnentationc is needed to explore the Wabitiv Of the cone*

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AEM GEM4 seminar - MIT OpenCourseWare