What do you think when you hear the word biomechanics?

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What do you think when you hear the word
biomechanics?
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What are some subdisciplines of bionechanics?
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Advanced Biomechanics of Physical Activity (KIN
831)

• Lecture 1
• Biomechanics of Bone

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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.

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Components of a Single Joint System

• Rigid Link (Bone, Tendon, Ligament)
• Joint
• Muscle
• Neuron
• Sensory Receptor

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Purpose of Bone?
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Some Purposes of Bone

• 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

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Wolffs 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.

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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)

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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

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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

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• 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

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• Cement line
• -limit of canaliculi
• -collagen fibers in bone matrix do not cross
  cement line
• -weakest portion of bones microstructure

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Microscopic-macroscopic structure of bone. Data
form Rho et al., 1998.
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What are the types of bone?
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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

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Two Types of Bone
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Two Types of Bone
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Periosteum

• Dense fibrous membrane that surrounds bone outer
  layer permeated by blood vessels and nerve fibers
  that pass into cortex via Volkmanns canals
• Inner osteogenic layer contains osteocytes
  (generate new bone) and osteoblasts (bone repair)

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Endosteum

• Lines medullary cavityof long bones, filled with
  yellow fatty marrow
• Contains osteoblasts and osteoclasts (resorption
  of bone)

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Biphasic Behavior of Bone

• Minerals ? hard and rigid
• Collagen and ground substance ? resilient
• --------------------------------------------------
  ------
• Combination ? stronger than either alone

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Load Deformation Testing
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Load Deformation Curve

• B max. load before deformation
• D deformation before structural change
• Area under curve is force x distance work
  energy

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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)

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What is the function of normalization?
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What is the function of normalization?

• Independent of geometry of material
• Permits comparison of different materials (e.g.,
  bone, tendons, cartilage, ligaments)

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What are some examples of normalization?
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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)

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Stress-Strain Relationships

• Similar to load deformation curve

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Stress-Strain Relationships
Elastic modulus (Youngs modulus) slope of the
stress-strain 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
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Relationships of Age to Stress-Strain
Characteristics of Bone
indirect relation between age and energy
absorption
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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

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Properties of Stiffness and Brittle/Ductile
Interpretation?
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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

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Ductile and Brittle Fracture

• Young bone more ductile
• Bone more brittle at higher loading rates

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Load-deformation Relationships
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Typical Response of Long Bone to Loads

• greatest resistance to compression
• weakest response to shear loads
• intermediate strength for tension

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Typical Response of Long Bone to Loads
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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)

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Physiologic Area
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What is Wolffs Law?
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Remodeling of Bone

• Wolffs 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

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Factors Influencing the Dynamic Response of Bone

• Mechanical properties of bone
• Geometry
• Loading mode
• Rate of loading
• Frequency of loading

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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

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  Behavior of bone under tension, compression,
bending, shear,torsion, and combined loading
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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)

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Tensile Loading
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Behavior of Bone Under Tension

• failure mechanism is mainly debonding of cement
  lines and pulling out of the osteons (see figure)

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Failure Under Tensile Loading
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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)

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Tensile Fracture of Calcaneous
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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

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Compression Loading
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Behavior of Bone Under Compression

• failure mechanism is mainly oblique cracking of
  osteons (see figure)

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Failure Under Compression Loading
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Behavior of Bone Under Compression

• example fractures of vertebrae weakened by age
• example fracture of femoral neck (see figure)

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Failure Under Compression Loading
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Behavior of Bone Under Shear

• deformation occurs internally in an angular
  manner (see figures)
• load applied parallel to surface of structure

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Shear Loading
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Shear Loading
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Behavior of Bone Under Shear

• note that tensile and compressive loads also
  produce shear stress (see figure)

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Shear Loading
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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

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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

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Bending Loading
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Three Point Bending Load(figure A)
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What examples of three point bending can you
provide?
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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 footballers fracture in soccer
• example boot top fracture in skiing (see figure)

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Failure Under Three Point Loading
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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

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Four Point Bending Load(figure B)
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Failure Under Four Point Loading
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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

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Torsion Loading
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Behavior of Bone Under Torsion

• maximal shear stresses act on planes parallel and
  perpendicular to neutral axis

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Bone Load Under Torsion
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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)

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Failure Under Torsion
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Behavior of Bone Under Combined Loading

• typical loading pattern
• bone subjected to multiple interdependent loads
• irregular geometric pattern
• example walking and jogging

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Combined Loading of Bone
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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)

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Muscle Activity Changing Stress Distribution
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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

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Rate Dependency Example

• What interpretation can you derive from this
  slide?

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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

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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

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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)

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Fatigue Fracture Curve
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Comparison of Bone In Vitro and In Vivo
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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)

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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

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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 cross-sectional
  area
• area moment of inertia
• cross-sectional area
• distribution of bone tissue around neutral axis

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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

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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

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Influence of Bone Geometry on Biomechanical
Behavior

• Torsion strength and stiffness directly related
  to cross-sectional area and distribution of bone

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Influence of Bone Geometry on Biomechanical
Behavior

• Remodeling altering size, shape, and structure
  of bones to meet mechanical demands placed on it
  (Wolffs Law)

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Influence of Bone Geometry on Biomechanical
Behavior

• Positive correlation between bone mass and body
  weight
• Weightlessness (space travel) results in
  decreased bone mass

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