what do you think when you hear the word biomechanics?
TRANSCRIPT
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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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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”.
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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 bone’s 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 Volkmann’s 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 (Young’s 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 Wolff’s Law?
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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
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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: footballer’s 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 (Wolff’s 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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