biological frameworks for engineers · •tiny workhorse project –reports due wed, nov 26...
TRANSCRIPT
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ME 411 / ME 511
Biological Frameworks
for Engineers
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Class Organization
• Lab 3 report due Mon
• Tiny Workhorse Project
– Reports due Wed, Nov 26
– Presentations
• 10 min with 1-2 min Q&A
• Mon, Nov 24: Kevin/Ye, Nathan/Kateri,
Scott/Spencer, Brian/Wai
• Wed, Nov 26: Jarrod/Mark, Tadbhagya/Amit,
Tzu-Jin/Jiayang, James/Kevin
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ME 411 / ME 511
Bone System
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Bones
Living concrete:
Type 1 collagen
hydroxyapatite
[Ca3(PO4)2]3· Ca(OH)2)
Functions:
Structural
Motion
Protection
Mineral Storage
(Cell Factory)
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Extracellular Matrix
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Types of Bone
Trabecular
Cortical
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Cortical Bone
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Trabecular Bone
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Biomechanics of Cortical
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Biomechanics of Trabecular
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Biomechanics of Trabecular
Compressive stress–strain curves for trabecular bone of different relative densities.
Relative density is the ratio of the apparent density (r* in this figure) to the density
of solid cortical bone (rs).
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Bone Remodeling
• Maintenance of mineral homeostasis
• Reconstruct in the face of mechanical stimulation
• Maintain structural integrity in the face of accumulated microdamage
• Enhance healed bone
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Remodeling
• Osteoclasts
– Recruited to
dissolve bone
• Osteoblasts
– Recruited to
synthesize bone
• Lining Cells
– Reside on surface
of bone tissue
• Osteocytes
– Reside permanently inside bone tissue
– Long branches sense pressures or cracks and direct osteclasts
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Mechanobiology
Wolff’s Law:“Every change in the form and the
function of a bone or of their function
alone is followed b certain definite
changes in their internal architecture,
and equally definite secondary
alterations in their external confirmation”
…bone will adapt its
internal architecture in
response to external
constraints and loads.
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Histology
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Normal Bone– Calcium is green.
– Fat cells in bone marrow are white
– Dark Red are other bone marrow cells
– Osteoid is new collagen
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• Osteoporosis
– Loss of bone
mass per unit
volume
– Ratio of mineral
to organic
phase
maintained
Bone Pathologies
– Decreased strength, density, and stiffness
– True osteoporosis is accompanied by fracture
– Bone loss without fracture is osteopenia
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Bone Pathologies
• Rickets (Osteomalacia)
– Mineralization
of the matrix of
the skeleton is
defective
– Cannot
metabolize
Calcium or Vitamin D
– Lack of calcium collagen does not stain “green”
– Decreased strength, density, and stiffness
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Forearm Biomechanics
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Forearm Biomechanics
1. Biceps
2. Brachialis
3. Brachioradialis
4. Extensor Carpi
Radialis Longus
(wrist)
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A (cm2)
Simplifications:
1. PCSA = Amuscle = Vmuscle / Lmuscle
2. Muscle force areal density:
w = 20 N/cm2 [McMahon, 1984]
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Bending Moment
ˆ ˆ
cos
sin
i xi yi
xi i i
yi i i
T T i T j
T wA
T wA
Simplifications:
1. Neglect arm mass
2. Ignore moment at elbow joint
Knowns:
1. Ltot = 31 cm
2. W = 12.2 kg = 119.7 N
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CalculationsA
(cm2)
w
(N/cm2)
Lh
(cm)
Lf
(cm)
Theta
(rad)
Fx
(N)
Fy
(N)
M
(N cm)
2. Brachialis 13 20 10 5 1.107 116.3 232.6 1163
1. Bicep 12.3 20 31 8 1.318 61.5 238.2 1906
3. Brachioradialis 2.9 20 8 24 0.322 55.0 18.3 440
4. ECRL 3.6 20 3 25 0.119 71.5 8.6 214
W. 12.2 kg weight -119.7
JRFx
(N)
JRFy
(N)
304 378
Notes
1. The Moment is highest at the Bicep connection
2. The reaction forces are much larger than the weight held
3. "Mechanical Disadvantage" = muscle often act with short lever arm
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Simplified Bending Stress
2
( )( )( )
bone
x
z bone
z bone
A
F xM x yx
I A
I y dA
Simplifications:
1. Consider radius bone only
2. Hollow circular beam
Knowns:
1. Medullary canal Di = 0.7 cm
2. Outer diameter Do = 1.4 cm
E
Stress-Strain Assumptions:
1. Linear elasticity
Knowns:
1. E = 17 GPa
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Bone Stress
0
500
1000
1500
2000
0 5 10 15 20 25
Mom
ent
(N c
m)
Distance (cm)
Notes:
1. Iz = pi/64 * (Do^4 - Di^4)
2. A = pi/4 * (Do^2 - Di^2)
J
(cm4)
Do
(cm)
Di
(cm)
Iz
(cm4)
Abone
(cm2)
0.35 1.40 0.70 0.175 1.15
Max M
(N cm)
Max y
(cm)
Iz
(cm4)
Stress M
(N/cm2)
1906 0.7 0.175 7603
Fx
(N)
A
(cm2)
Stress F
(N/cm2)
304 1.15 265
Stress M + F (N/cm2) 7868
Cortical Stiffness, E (GPa) 17
Strain (microstrain) 4628
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The Human Knee
“Bulbs” or condyles
Femur
- lateral condyle
- medial condyle
Patella
Tibia
- lateral condyle
- medial condyle
Tibial condyles are concave
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Cruciate Ligaments
Named because “cross” over one another
Anterior cruciate ligament (ACL):
- connect tibia to lateral femoral condyle
- knee stabilizer
Posterior cruciate ligament (PCL):
- connect tibia to meidal femoral condyle
- knee stabilizer
Tearing of ACL:
- Sudden direction change
- Deceleration force crosses the knee
- Popping sensation, rapid onset of
swelling, and buckling sensation
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Meniscus• Cartilage layer between
femur and tibia
• Entire knee enclosed in
fluid-filled capsule
– Reduced friction &
wear
Compressive modulus (MPa)
Cartilage thickness (mm)
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Knee Forces
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Questions?