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20.GEM GEM4 Summer School: Cell and Molecular Biomechanics in Medicine: Cancer
Summer 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 tissue
grows (post-operative period critical)
Image removed due to copyright restrictions.
Cementless & Cemented Stems (Smith & Nephew)
Loosening at bone-implant interface
Caused by:
• poor interfacial adhesion
• stress shielding
(inhibits straining of the bone)
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
• Porous metals have often been proposed
for prostheses
• Pores ~ 100-300 µm & biocompatible
surface - bone tissue in-growth does occur
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)
• 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 Fibre
Networks: A New Approach to Bone Growth Stimulation
Outline
Prosthetic Implants
-
Magaeto-Mechanical Actrcatfon ofFibre
Network Materials: Deflections crnd Straims
Elastic Properties of Fibre Network Materials
Design of an Integrated Magneto-Active
Prosthesis
Fibre Compatibility and Topography
Moment acting on a Single Ferromagnetic Fibre in an Applied Magnetic Field
∆r
−δ cos θ
=
x sin θ
r
2
2
−8Ms B cosθ ⎡ ⎛ x ⎞ ⎛ x ⎞ ⎤ ⎛ L ⎞
=
⎢3⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠ ⎥ ⎜⎝ ⎟⎠
3 Ef
L ⎦ D
⎣ L
∆z
δ sin θ
=
x cosθ
z
2
2
8Ms B sin θ tanθ ⎡ ⎛ x ⎞ ⎛ x ⎞ ⎤ ⎛ L ⎞
=
⎢3⎜⎝ L ⎟⎠ − ⎜⎝ L ⎟⎠ ⎥ ⎜⎝ D ⎟⎠
3 Ef
⎣
⎦
Relative deflection transverse to field, ∆r / r (%)
Measured and Predicted Deflections of a Single Ferromagnetic Fibre
-15
Experiment (ramping up)
Experiment (ramping down)
Theory
-10
-5
L = 50 mm, x = 45 mm
D = 375 µm, θ = 29°
6
-1
M = 1.6 10 A m
s
E = 210 GPa
f
0
0
0.05
0.1
Applied field, B (Tesla)
0.15
0.2
Magnetically-induced Deflection of a Welded Parallelogram
Experimental Set-Up
∆r
=
r
−4M s Bcos θ ⎛ L ⎞ 2
⎜ ⎟
⎝ D⎠
3 Ef
∆z
4M s Bsin θ tanθ
=
z
3 Ef
⎛ L⎞
⎜ ⎟
⎝ D⎠
2
Relative deflection transverse to field, ∆r / r (%)
Measured and Predicted Deflections of a Welded Parallelogram
-0.6
Experiment (ramping up)
Experiment (ramping down)
Theory
-0.5
-0.4
-0.3
-0.2
L = 19 mm, D = 375 µm,
6
-1
θ = 65°, M = 1.6 10 A m
-0.1
s
E = 210 GPa
f
0
0
0.05
0.1
0.15
0.2
0.25
Applied field, B (Tesla)
0.3
0.35
0.4
Magneto-Mechanical Induction of an Isotropic Fibre
Network Material
Relative dimensional change (%)
100
Predicted ∆R (-ive)
Experiment ∆R (-ive)
Predicted ∆Z (+ive)
Experiment ∆Z (+ive)
10
1
Ms = 1.6 106 A m-1
0.1
0.01
Ef = 210 GPa
B = 1 Tesla
0
20
40
60
80
Fibre segment aspect ratio, L/D (-)
Axial:
Transverse:
π 2
π2
∆Z
=
Z
∫
∆z sin θdθ
0
π2
∫
0
z sin θdθ
⎛ 16 Ms B⎞ ⎛ L ⎞
=⎜
⎟ ⎜ ⎟
⎝ 9Ef ⎠ ⎝ D ⎠
2
∆R
=
R
∫
∆r sin θdθ
0
π2
∫
0
r sin θdθ
⎛ −16M s B⎞ ⎛ L ⎞ 2
= ⎜
⎟ ⎜⎝ ⎟⎠
9πE
⎝
⎠ D
f
100
Magneto-Mechanical Induction of a Transversely Isotropic Fibre Network Material using X-ray Tomography
3-D tomographic reconstruction
10
Relative dimensional change (%)
Predicted ∆R (-ive)
Predicted ∆Z (+ive)
Experiment ∆Z (+ive)
1
0.1
Ms = 1.6 106 A m-1
Ef = 210 GPa
B = 1 Tesla
0.01
0
5
10
15
20
25
30
35
40
Fibre segment aspect ratio, L/D (-)
500 µm
n
∆Z ⎛ 4M s B ⎞ ⎛ L ⎞
=
⎜ ⎟
Z ⎜⎝ 3Ef ⎟⎠ ⎝ D ⎠
2
∑ Nθ sin
i
2
θi
i
n
∑ Nθ cosθ
i
i
i
n
∆R ⎛ 4M s B ⎞ ⎛ L ⎞
= −
⎜ ⎟
R ⎜⎝ 3Ef ⎟⎠ ⎝ D ⎠
2
∑ Nθ sinθ cosθ
i
i
i
n
∑ Nθ sinθ
i
i
i
i
Effect of the presence of an Environment (Compliant Matrix) on Network Straining
Predicted Peak Strains in a Surrounding Environment, as a function of its Stiffness
Peak induced strain, εmax (millistrain)
100
Ee = 0.001 GPa
Ee = 0.01 GPa
Ee = 0.1 GPa
Ee = 1 GPa
10
B = 1.5 Tesla
Ms = 1.6 106 A m-1
θ = 30°
Ef = 210 GPa
1
Range for effective
magnetic induction
0.1
0.01
0
10
20
30
40
Fibre segment aspect ratio, L/D (-)
50
• Beneficial strains (>1 millistrain) at L/D > 10
L⎞2
⎛
12πMs Bsin θ⎜ ⎟
⎝ D⎠
=
3
⎛
L⎞ ⎞
⎛
⎜ 9πEf tan θ + 28Ee ⎜⎝ ⎟⎠ ⎟
D ⎠
⎝
ε max
Measured and Predicted Magnetic Straining with Surrounding Environments (Matrices)
Relative deflection parallel to field, ∆Z / Z (%)
0.3
Experiment (rubber matrix)
Predicted (rubber matrix), L/D=6
Predicted (rubber matrix), L/D=10
Experiment (resin matrix)
Predicted (resin matrix), L/D=6
0.25
0.2
0.15
0.1
0.05
0
0
0.2
0.4
0.6
0.8
Applied field, B (Tesla)
1
1.2
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
Predicted and Measured Stiffness for an Isotropic Fibre Network
Stiffness of fibre network, Ea (GPa)
10
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)
1
Range for effective
magnetic induction
Ea
=
Ef
0.1
0.01
0
5
10
15
20
9f
2
⎛ L⎞
32
⎝ D⎠
25
Fibre segment aspect ratio, L/D
30
Prosthetic Implants
Magneto-Mechanical Actuation of Fibre
Network Materials: Deflections and Strains
Elastic Properties of Fibre Network Materials
.nesign of an Integrated Magneto-Active
rosthesis
Fibre Compatibility and Topography
Concept of an Integrated Prosthetic Design
•
•
•
•
Treatment by Exposure to Applied Field during Post-operative Period
Period
Only Magneto-Active Layer will respond to Applied Field
Magneto-Active Layer could be Graded, Anisotropic etc
All Materials could be Biocompatible
Outline
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
Fibre Biocompatibility and Topography
chondrocytes
ECM
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& Validatedfor 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*