Transcript Single Joint System - Michigan State University

What do you think when you
hear the word biomechanics?
What are some subdisciplines of
bionechanics?
Advanced Biomechanics of
Physical Activity (KIN 831)
Lecture 1
Biomechanics of Bone
Single Joint
System*
Dr. Eugene W. Brown
Department of Kinesiology
Michigan State University
* Material included in this presentation is derived primarily from two sources:
Enoka, R. M. (1994). Neuromechanical basis of kinesiology. (2nd ed.). Champaign, Il: Human Kinetics.
Nordin, M. & Frankel, V. H. (1989). Basic Biomechanics of the Musculoskeletal System. (2nd ed.). Philadelphia: Lea
& Febiger.
Components of a Single Joint
System
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Rigid Link (Bone, Tendon, Ligament)
Joint
Muscle
Neuron
Sensory Receptor
Purpose of Bone?
Some Purposes of Bone
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•
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Provides mechanical support
Produces red blood cells
Protects internal organs
Provides rigid mechanical links and muscle
attachment sites
• Facilitates muscle action and body
movement
• Serves as active ion reservoir for calcium
and phosphorus
Wolff’s Law
“Every change in the form and function of a
bone or of their function alone is followed
by certain definitive secondary alteration in
their external conformation, in accordance
with mathematical laws”.
Composition and Structure of Bone
•
Consists of cells and an organic extracellular matrix
of fibers and ground substance
•
High content of inorganic materials (mineral salts
combined with organic matrix)
– Organic component  flexible and resiliant
– Inorganic component  hard and rigid
•
Mineral portion of bone primarily calcium and
phosphate (minerals 65-70% of dry weight)
•
Bone is reservoir for essential minerals (e.g., calcium)
Composition and Structure of Bone
• Collagen
– Mineral salts embedded in variously oriented protein
collagen (strength in various directions) in
extracellular matrix
– Tough and pliable, resists stretching
– 95% of extracellular matrix (25-30%) of dry weight
of bone
Schematic illustration of section of the shaft of long
bone without inner marrow
Concentric layers of mineralized matrix that surround
a central canal containing blood vessels and nerves
•Haversian canal – small
canal at center of each osteon
containing blood vessels and
nerve cells
•Lamellae - concentric layers
of mineralized matrix
surrounding haversian canal
•Lacunae – small cavities at
boundaries of each lamella
containing one bone cell or
osteocyte
•Canaliculi – small channels
that radiate from lacuna
connecting lacunae of
adjacent lamellae and
reaching havesrian canal
•Cement line
-limit of canaliculi
-collagen fibers in bone
matrix do not cross cement
line
-weakest portion of bone’s
microstructure
Microscopic-macroscopic structure of bone. Data form Rho et al., 1998.
What are the types of bone?
Two Types of Bone
• compact (or cortical) bone – outer shell,
dense structure, surrounds cancellous bone
• Cancellous (or trabicular) bone
– Does not contain haversion canals
– contains red bone marrow in spaces
-------------------------------------------------------• Biomechanical properties are similar; differ
in porosity and density (see figure)
• Quantity of compact and cancellous tissue
in bone differs by function
Two Types of Bone
Two Types of Bone
Periosteum
• Dense fibrous membrane that surrounds
bone; outer layer permeated by blood
vessels and nerve fibers that pass into cortex
via Volkmann’s canals
• Inner osteogenic layer contains osteocytes
(generate new bone) and osteoblasts (bone
repair)
Endosteum
• Lines medullary cavityof long bones, filled
with yellow fatty marrow
• Contains osteoblasts and osteoclasts
(resorption of bone)
Biphasic Behavior of Bone
• Minerals  hard and rigid
• Collagen and ground substance  resilient
-------------------------------------------------------Combination  stronger than either alone
Load Deformation Testing
Load Deformation Curve
• B – max. load
before
deformation
• D’ – deformation
before structural
change
• Area under curve
is force x
distance =
work= energy
Load Deformation Curve
• Slope of elastic region defines stiffness
• Area under curve defines energy that can be
stored
• Elastic region – return to original
configuration once load is removed
• Plastic region – deformation of material
• Load deformation curve is usefull when
determining comparative characteristics of
whole structures (e.g., bone, tendon,
cartilage, ligaments)
What is the function of
normalization?
What is the function of normalization?
• Independent of geometry of material
• Permits comparison of different materials
(e.g., bone, tendons, cartilage, ligaments)
What are some examples of
normalization?
Normalizing Load
• Stress – force/area
• Strain – length change/initial length
(unitless value)
– Two types of strain
• Linear – causes change in length
• Shear – causes change in angular relations (radians)
Stress-Strain Relationships
• Similar to load deformation curve
Stress-Strain Relationships
Elastic modulus (Young’s
modulus) – slope of the stressstrain curve in the elastic
region (measure of stiffness)
Plastic modulus – slope of the
stress-strain curve in the plastic
region
Area under stress strain curve
is measure of energy absorbed
Relationships of Age to Stress-Strain
Characteristics of Bone
indirect relation between age and energy absorption
Cortical vs. Cancellous Bone
• Cortical bone stiffer, withstand greater
stress but less strain before failure
• Cancellous bone fractures when strain
exceeds 75%
• Cortical bone fractures when strain exceeds
2%
• Cancellous bone has larger capacity to store
energy
Properties of Stiffness and Brittle/Ductile
Interpretation?
Properties of Stiffness and Brittle/Ductile
•Metal – large plastic
region
•Virtually no plastic
region in glass
•Stress-strain curve
of bone not linear
•Yielding of bone
tested in tension
caused by debonding
of osteons at cement
lines and
microfractures
Ductile and Brittle Fracture
•Young bone more ductile
•Bone more brittle at higher loading rates
Load-deformation Relationships
Typical Response of Long Bone
to Loads
• greatest resistance to compression
• weakest response to shear loads
• intermediate strength for tension
Typical Response of Long Bone
to Loads
Safety Factor
• Safety factor - bones are 2 to 5 times
stronger than forces they commonly
encounter in activities of daily living; bone
strength and stiffness are greatest in the
direction in which loads are most
commonly imposed (see figure)
Physiologic Area
What is Wolff’s Law?
Remodeling of Bone
• Wolff’s Law
• Remodeling – balance between bone
absorption of osteoclasts and bone
formation by osteoblasts
– osteoporosis –increase porosity of bone,
decrease in density and strength, increase in
vulnerability to fractures
– piezoelectric effect – electric potential created
when collagen fibers in bone slip relative to one
another, facilitates bone growth
– use of electric and magnetic stimulation to
facilitate bone healing
Factors Influencing the Dynamic
Response of Bone
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Mechanical properties of bone
Geometry
Loading mode
Rate of loading
Frequency of loading
Factors Influencing the Dynamic Response of Bone
• Result of loading of bone in transverse and longitudinal directions
dissimilar (anisotrophy)
• Bone tends to be strongest in directions most commonly loaded
Behavior of bone under tension,
compression, bending, shear,
torsion, and combined loading
Behavior of Bone Under Tension
• under tensile loading structure lengthens and
narrows
• equal and opposite loads applied outward
• maximum tensile stress occurs on a plane
perpendicular to the applied load (see figure)
Tensile Loading
Behavior of Bone Under Tension
• failure mechanism is mainly debonding of
cement lines and pulling out of the osteons
(see figure)
Failure Under Tensile Loading
Behavior of Bone Under Tension
• clinically tensile fractures produced in
bones with a large portion of cancellous
bone
• example: contraction of the triceps surae on
the calcaneous (see figure)
Tensile Fracture of Calcaneous
Behavior of Bone Under Compression
• under compression structure shortens and
widens
• maximum compression stress occurs on
plane perpendicular to applied load (see
figure)
• equal and opposite forces applies inward
Compression Loading
Behavior of Bone Under Compression
• failure mechanism is mainly oblique cracking of
osteons (see figure)
Failure Under Compression Loading
Behavior of Bone Under Compression
• example: fractures of vertebrae weakened by age
• example: fracture of femoral neck (see figure)
Failure Under Compression Loading
Behavior of Bone Under Shear
• deformation occurs internally in an angular
manner (see figures)
• load applied parallel to surface of structure
Shear Loading
Shear Loading
Behavior of Bone Under Shear
• note that tensile and compressive loads also
produce shear stress (see figure)
Shear Loading
Behavior of Bone Under Shear
• shear modulus – stiffness of material under shear
loading
• clinically shear fractures are most often seen in
cancellous bone
• examples: femoral condyles and tibial plateau
Behavior of Bone Under Bending
• bending subjects bone to a combination of
tension and compression (tension on one
side of neutral axis, compression on the
other side, and no stress or strain along the
neutral axis)
• magnitude of stresses is proportional to the
distance from the neutral axis (see figure)
• long bone subject to increased risk of
bending fractures
Bending Loading
Three Point Bending Load
(figure A)
What examples of three point
bending can you provide?
Three Point Bending
• two equal and opposite moments (see figure A)
• failure usually occurs in the middle
• since weaker in tension, failure usually initiated in
location of tension; immature bone may fail first
in compression
• example: footballer’s fracture in soccer
• example: boot top fracture in skiing (see figure)
Failure Under Three Point Loading
Four Point Bending
• two force couples (see figure B)
• magnitude of four point bending is same
throughout area between force couples
• structure breaks at weakest point
• example:
Four Point Bending Load
(figure B)
Failure Under Four Point Loading
Behavior of Bone Under Torsion
• load applied to cause twist about an axis
• magnitude of stress proportional to distance
from neutral axis (see figure)
• shear stresses distributed over entire structure
Torsion Loading
Behavior of Bone Under Torsion
• maximal shear stresses act on planes
parallel and perpendicular to neutral axis
Bone Load Under Torsion
Behavior of Bone Under Torsion
• clinically bone fails first in shear with initial
crack parallel to neutral axis; second crack
along plane of maximum tension
• Example (see slide)
Failure Under Torsion
Behavior of Bone Under
Combined Loading
• typical loading pattern
– bone subjected to multiple interdependent loads
– irregular geometric pattern
• example: walking and jogging
Combined Loading of Bone
Influence of Muscle Activity on
Stress Distribution in Bone
• contraction of muscles alter the stress distribution
in bone
• contraction may decrease or eliminate tensile
stress by producing compressive stress
• contraction may increase compressive stress
• example: three point bending of the tibia in skier
falling forward (contraction of the triceps surae
reduces tensile stress on posterior side of tibia but
increasing compressive stress) (see figure)
Muscle Activity Changing Stress
Distribution
Rate Dependency in Bone
• bone is viscoelastic – biomechanical
behavior varies with the rate at which bone
is loaded (rate of applied and removed load)
• high rate of load application - bone stiffer
and can store more energy before failure
(loads must be within physiologic range)
(see figure)
• example: paired tibia
Rate Dependency Example
• What interpretation can
you derive from this
slide?
Rate Dependency Example
• amount of energy
stored before failure
approximately doubled
at higher rate
• load to failure almost
doubled
• deformation to failure
did not change
significantly
• approximately 50%
stiffer at higher loading
rate
Rate Dependency of Bone
• high rate loading results in greater energy
storage before failure
• Failure after high rate loading results in
rapid release of energy and resulting
communition of bone and extensive soft
tissue damage
Fatigue of Bone Under Repetitive Load
• fatigue fracture – fracture caused by
repeated application of load
– Few repetitions at high load
– Many repetitions at low load
• pattern of relationship between load and
repetitions (see figure)
• Possible for fatigue curve of some materials
to be asymptotic (material will not fail
under load and frequency being applies)
Fatigue Fracture Curve
Comparison of Bone
In Vitro and In Vivo
In Vitro
• fatigue fracture curve not asymptotic
• bone fatigues rapidly when loaded or
deformation approaches yield strength
(small number of repetitions needed to
produce fracture)
In Vivo
• fatigue process mitigated by self-repairing
process
• fatigue fractures result when remodeling
process outpaced by fatigue process
• exercise may fatigue muscles and reduce
their potential to attenuate load on bone
Influence of Bone Geometry on
Biomechanical Behavior
• tension and compression load to failure
proportional to cross-sectional area of bone
• stiffness of bone proportional to crosssectional area
• area moment of inertia
– cross-sectional area
– distribution of bone tissue around neutral axis
Influence of Bone Geometry on Biomechanical Behavior
• In bending beam 3 is stiffest
• Beam 3 can withstand highest load because greatest amount of
material distributed at t distance from neutral axis
Influence of Bone Geometry on
Biomechanical Behavior
• Length of bone influences strength and
stiffness in bending
• Long bones subject to high bending
moments
• Tubular shape  increased moment of
inertia because tissue is farther from neutral
axis
Influence of Bone Geometry on Biomechanical Behavior
• Torsion strength and
stiffness directly
related to crosssectional area and
distribution of bone
Influence of Bone Geometry on
Biomechanical Behavior
• Remodeling – altering size, shape, and
structure of bones to meet mechanical
demands placed on it (Wolff’s Law)
Influence of Bone Geometry on
Biomechanical Behavior
• Positive correlation between bone mass and
body weight
• Weightlessness (space travel) – results in
decreased bone mass