Transcript Bone Form and Function

Bone Form and Function
Forces
Constrained by Newton’s Laws of Motion
1. “Law of inertia” – Body in motion (or at rest)
tends to stay that way.
2. “F = Ma” – a force gives a body acceleration in
the direction of the force (Bemis et al. 2004).
That acceleration increases with the force and
decreases with the Mass of the object.
3. “Equal and opposite” – an object receiving a
force from another object, in turn, delivers an
equal and opposite force.
Center of Mass
• CoM = “center of gravity” – point about
which a solid body is evenly balanced.
• To find the Center of Mass:
Vectors and components of force
• Scalar quantities – values with magnitude
and no direction
– Examples: length, mass, temperature
• Vector quantities* - magnitude and
direction
– Examples: moving objects.
Leg supporting the body
Fb = downward and backward force
Ground reaction force pushing back
Fg = upward and forward force
Fv = Fg sine(theta)
Fh = Fg cosine(theta)
Properties of the arrow drawings:
direction and magnitude
pelvis
a
femur
Angles:
a. hip
b. knee
c. ankle
d. toe
b
tibiotarsus
phalanges
c
tarsometatarsus
•
•
“off bird” landmark
d
Corbin and Reilly, 1998
Reilly, 2000
Amount of time foot on the ground
decreases with increasing speed
Coturnix
500
470ms
600
500
400
Numida
583ms
77%
436ms
75%
300
275ms
200ms
64%
200
Time (ms)
400
66%
300
315ms
200
50%
55%
100
100
0
1
2
0
3
Relative Speed
1
Foot Down
Foot Up
2
3
Relative Speed
• Bone juxtapositions constantly changing
260
240
220
200
180
160
140
120
100
80
60
40
20
0
Hip (mean)
Angle (degrees)
0
260
240
220
200
180
160
140
120
100
80
60
40
20
0
1
Knee
0
260
240
220
200
180
160
140
120
100
80
60
40
20
0
1
Ankle
0
260
240
220
200
180
160
140
120
100
80
60
40
20
0
SPEED (m/sec)
0.066
0.135
0.178
1
Toe
0
1
Stride Time
• Hence, bones (and other materials) have
to be able to respond to changing forces
Stress and Strain
• Gravity acting on center of mass
– Strong downward force:
• Feet
• Supporting skeletal elements
• Joint surfaces
• Contraction of muscles
– Strong forces on attachment sites
• Biting or chewing
– Muscular attachment sites
• Bones (jaws and skull)
– Teeth (surrounding flesh and bone)
Stress and Strain
• Stress – measured as pressure over
cross-sectional area
• Strain – deformation in material caused by
stress
• Compare elastic rubber band and rigid bone
• Stress-strain curve:
fracture
Yield point
Stress
(force/c.s. area)
Plastic region
Strain
(deformation)
Connective tissues (revisited)
• Extracellular matrix / producing cells = High
• ECM
– HOH, Proteins, Carbs.
– Ex. “loose fibrous CT”, dense CT, Tendon, Ligament,
Bone, etc.
• Morphology of CT:
– Collagen/Elastin ratio
– Arrangement of fibers
• dependent upon forces acting on the material.
A – major components of Loose, fibrous CT
B – Molecular structure of the material
Arrangement of collagen fibers in dense CT
A – dense irregular CT (dermis of skin)
B – layers of a ligament
C – cable-like arrangement of a tendon