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

• Rigid Link (Bone, Tendon, Ligament)

• Joint

• Muscle

• Neuron

• Sensory Receptor

Purpose of Bone?

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

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 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

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

• 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 cross-sectional 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 cross-sectional 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