TNBiomechBW6up

7/30/2019 TNBiomechBW6up

1/23

Basic Biomechanics &

Biomaterials forOrtho aedic Sur eons

Tariq Nayfeh, M.D./Ph.D.

Outline

Introduction

Basic Definitions

Mechanics of Materials

Bending Theory

Biomaterials

Why Study Biomechanicsand Biomaterials

To Pass Exams? This area is actually a low yield area for time spent

studying and the number of questions asked

So Why Study It?

The basis of all implants and devices we use

The basis for most trauma we see

The basis for most of our interventions

Basic Definitions

Biomechanics is the science of theaction of forces, internal or externalon the living body.

tat cs s t e stu y o orces onbodies at rest

Dynamics is the study of the motionof bodies and the forces thatproduce the motion

Basic Definitions

Kinematics is the study of motion interms of displacement, velocity, andacceleration with reference to the causeof the motion

Kinesiology is the the study of humanmovement and motion

Principle Quantities

Basic Quantities Length

Time Mass

Derived Quantities Velocity (length/time)

Acceleration (length/time2)

Force (mass length/time2)


2/23

Scalars and Vectors

Scalar quantities have magnitudebut no direction.

Time, speed (not velocity), mass, volume

Vector quantities have magnitudeand direction.

Velocity, Force, Acceleration

Vectors

A vector can be resolvedinto its individualcomponents

FFy

Vectors can be added toform a new vector byadding their componentsor graphically by theparallelogram method

x

Moments

A moment (torque) is the rotationaleffect of a force about a point.

=

F

d

M

M = F x d

Free Body Diagrams

The forces acting

on a body may beidentified byisolating that bodypart as a free bodydiagram

Beer and Johnston, Mechanics of Materials

Example Free BodyDiagrams

Basic Laws of MechanicsNewtons Laws

First Law:

An object at rest will remain at rest andan object in motion will continue in

motion with a constant velocity unless itexperiences a net external force

Inertia is the tendency of an object toeither remain at rest or to maintain uniformmotion in a straight line

The weight of a body is a vector quantitythat is equal to the force of gravity actingon it


3/23

By combining the first and secondlaws: For equilibrium to occur thesum of the forces and moments


0F


Third Law:

For every actionthere is an equal andopposite reaction.

Joint Mechanics

How do jointsmaintain stability?

What produces

Joint Mechanics

Joints are stabilized by the

action of the muscles,ligaments and bonystructures.

The muscles are located at adistance from the joint

Muscle action producemoments about the jointcenter

Joint Mechanics

Joint reactionforces occur at the

joint center

These reaction forces can be greater than theweight of the body segment or the entire body

Joint Mechanics

When the muscle and joint reactionforces are balanced equilibriumoccurs and the body segments do

When there is an imbalance offorces acceleration (or deceleration)of the body segment occurs


4/23

Illustrative Problem

W=20 N

G= 15 N

0 xF 0yF

0 WGRB

35

2015

BR

BR

0M

N2753

15153020

030153

B

WGB

N240R


Hip Reaction forces in single legstance

Buckwalter, et al. Orthopaedic Basic Science


This person is trying to lift a 20 kgobject.

The force from the upper extremities

is 450 N The estimated moment arm of the

upper extremities is Lw = 2cm

The estimated moment arm of theweight is Lp= 30 cm.

Mspine = 450x0.02 + 200 x0.30

Mspine = 69 Nm


If the person bends

forward Lw = 25 cm

=

Mspine = 450x0.25+200x0.4

Mspine =192.5 Nm

Nordin and Frankel, Basic Biomechanics of theMusculoskeletal System

Forces across the hip andknee

Hip joint contact forces Single leg stance 2 to 3 x BW

Walking - 3 x BW

-,

Knee Tibiofemoral forces Rising from a chair 4 x BW

Walking 3 x BW

Stairs Ascent 6 to 7 x BW

Stair Descent 7 to 8 x BW

Mechanics of Materials

In order to understand how materialsbehave we need to define somebasic quantities.


5/23

Stress

Stress is the intensity

of internal force. Normal stress are

perpendicular to thesurface

Shear stress areparallel

F


AO/ASIF

Depending on how youslice the material you canget combinations of stressand sheer


In pure tension or compression

The plane of maximum shear is at 45 degrees to theaxis of loading!!

Strain

Strain (Engineering):

Relative measure of thedeformation (sixcomponents) of a body as aresult of loading.

Can be normal or shear

**A relative quantity withno units. Often expressedas a percent

L

L


AO/ASIF


6/23

Shear strain

Usually expressed as an angle radians


Hoop stress

r

Hoop stress is the stress in adirection perpendicular to theaxis of an item

***

t

pr

t

22

1

thickness of theitem decreasesthe hoop stressincreases***

Why is thisimportant?


Hoop Stress

As humans age, thediameter of theirbones increase, but

decreases

We will see later that thischange is not bad for ordinaryhuman activity. It mattersmost when we as surgeonsintervene.

Material Testing

In order to characterize how materialsbehave we have to create standardizemethods to test them and document

.

In the US the ASTM standards are themost widely used

In Europe the most widely used is theISO standards

Materials Testing

Materials of standardized sizes and shapes areplaced in testing machines and loadedfollowing standardized protocols


7/23

Stress-Strain CurvesStandardized curves used to help quantifyhow a material will respond to a given load.

AO/ASIF

Quantities Derived fromStress-Strain Curves

Yield Strength: The stress level at whicha material begins to deform plastically

Ultimate Strength: The stress level atwhich a material fails

Modulus of Elasticity: The linear slopeof the materials elastic stress-strainbehavior.

Ductility: The deformation to failure

Toughness: Energy to failure (the area

under the stress strain curve)

Elastic vs. Plastic Behavior

AO/ASIF

AO/ASIF

Types of failure

Ductile

Brittle

Elasticity vs. ductility andstrength

All of these materials

have the same

But they have different

toughness, ductility

and strength.



8/23

Force-deformation curves for materialshaving various combinations of structural

properties


Unloaded:A=cross section area

E=Youn smodulusof elasticit

Stiffness

uF

Longitudinal stiffness Sax =EAL

F =Saxu =SaxuEAL

Force-Displacement Curves

Similar to stress-strain

curves Not a material property,

instead a measure of howthe entire structurebehaves

Depends on

Material

Geometry

Force-Displacement Curves


Question

The linear relationship between an applied stress and the resultant

deformation defines a material's

1- modulus of elasticity.

2- brittleness.

3- yield strength.4- ultimate strength.

5- toughness.

If the question was changed to applied force, insteadof applied stress. The answer would change tostiffness.


9/23

Bending of Beams

Most bones and orthopaedicimplants are subjected to axial,bending, and torsion loading

ost a ures occur secon ary tobending and torsion

M

Linear bending theory

Bending Theory Definitions

Neutral Axis: The location where a beamexperiences zero stress (this is atheoretical axis and can actually be

located outside of the structure) Moment of Inertia: The geometric

property of a beam/s cross section thatdetermines the beams stiffness

There is a bending and a torsion moment of inertia(we will limit our discussion to bending)

n

tension

n

tension

n

tension

centricload

eccentricload

eccentricload

compressi

compressi

compressi

L o w s t r e s sL o w s t r e s s

HighstressHighstress


10/23

The resistance of a beam to bendingis directly proportional to itsmoment of inertia

Bending Resistance

The moment of inertia depends onits cross sectional area and shape

Bending resistancesolid cylinder= / 64 diam4

Bending resistance of a hollow cylinder= / 64 (outer diam4 inner diam4)or for thin shells= / 8 diam3 shell thickness

The bending stiffness of a half pin isproportional to one half the radius ofthe pin to what power?

3

4

One third

One fourth

Relative bendingresistance

Solid rod 1

Flat beam 3.5

Identical size

I beam edge on 6

I beam flat 0.6

Hollow cylinder 5.3

Gozna et al. 1982

ofcross sectional

area

When the diameter of a spinal instrumentation rod is increased from

4 mm to 5 mm, the rod's ability to resist a bend ing moment is

increased by approximately what percent?

1- 10%

2- 25%

3- 50%

4- 100%

5- 300%

%10044.1256256625

4

45

56464

46464

4

44

1

12

44

22

44

11

R

RR

dR

dR

850Kg. 800Kg. 60Kg. 20Kg.

Bone-implant composite AO/ASIF


11/23

Tension band principle

A properly donetension band shiftsthe neutral axis tothe surface of thebeam so thatcompressionoccurs across theentire crosssection

Example of tension bands

Example of tension bands

torque

shear

Mechanical Properties ofMaterials

Isotropy Material properties

do not depend ondirection

Anisotropy Material properties

depend on thedirection of loading

Aluminum Tendons

Ligaments

Cement


12/23

Anisotropy

Bone is an

anisotropicmaterial

depends on loaddirection andloading type


Bone MechanicsCortical bone isweakest in directionsthat cause tensilestresses.

In the transverse

direction the bone is

acting as a brittle

material

1. a compression crack begins at the fulcrum.

2. bone is weaker in tension than in compression.

3. bone is weaker in compression than in tension.

Three-point bending produces apredominantly transverse fracture because

.

compression.

5. the forces are resolved into pure tension.

Bending forces in the long bones most commonly result in what type of fracture

pattern?

1- Short oblique

2- Transverse with butterfly

3- Linear shear of 45

4- Spiral5- Segmental

What type of loading is most likely to cause a pure spiral fracture?

1- Crush

2- Bending

3- Tensile

4- Compression

5- Torsion

AO/ASIF

Bending forces in the long bones most commonly result in what type of fracture

pattern?

1- Short oblique

2- Transverse with butterfly

3- Linear shear of 45

4- Spiral

5- Segmental

What type of loading is most likely to cause a pure spiral fracture?

1- Crush

2- Bending

3- Tensile

4- Compression

5- Torsion


13/23

A 27-year-old patient sustains the

closed femoral fracture shown. Thisfracture pattern is most likely theresult of which of the followingorces

1. Pure torsion

2. Pure bending

3. Pure compression

4. Four-point bending

5. Torsion plus bending

Why are Long BonesHollow?

For the same total cross sectional area a hollowtube has higher bending and torsional resistancethan a solid tube

Most bones are loaded in bending and torsion

Bone responds to Wolfes law and tries to maximizethe bone density where stress is highest andminimize it where stress is lowest

The thinner a bone is the easier it is for nutrients toreach the osteocytes

Less energy is required to maintain the bone

Clinical QuestionCase 1: A 75 year old female

with osteoporosis falls andsustains a supracondylarfemur fracture. The patientundergoes ORIF with a

.She is allowed to increaseher weight bearing to fullweight bearing at 6 weeks.Two weeks later shepresents with increasingpain, swelling and can notbear weight.

Clinical Example

Case 2: A 75 year old female withosteoporosis falls and sustains anintertrochanteric hip fracture. She

intramedulary device and is allowedto weight bear as tolerated the nextday. Her fracture goes on to healwithout complications.

Clinical Example

Case 3: An 83 year old malewith multiple medicalproblems presents withsevere right hip pain andt e na ty to earweight. He had undergonea revision of his right totalhip 10 years ago to acementless stem.

Clinical Case

Why did the patient in Case 2 do wellwhile the patients in Case 1 andCase 3 have their implants fail?


14/23

Fatigue

Fatigue testing is done using the same type

of samples and machines that are used tocreate stress-strain curves. However, thesam les are loaded c clicall to failure.The goal of testing is to determine howmany loading cycles at a given load amaterial can withstand before failing.

**The failure stress levels are not thesame as the yield stress and ultimatestress.**

Fatigue

Fatigue testing generated fatiguelife curves.

Fatigue Endurance Limit The

does not fail (usually must lastgreater than 10 million cycles)

Fatigue life The number of cyclesthat a material can withstand at agiven stress level

Fatigue Life

EnduranceLimit

Fatigue LifeIn a fatigue test, the maximum stress

under which the material will not fail,

regardless of how many loading cycles are

applied, is defined as1- endurance limit.

2- failure stress.

- .

4- yield stress.

5- elastic limit.

Bone Fatigue

Bone has no in vitro endurancelimit!

In vivo bone heals

If bone fails to heal when subjectedto cyclic loads we get stressfractures

Clinical Examples

In Case 1 above the patient wasallowed to weight bear before herfracture healed. In this case the

resulted in rapid failure withrelatively few cycles.


15/23

Case 3

The applied stressto the smalldiameter implant

fatigue failure ofthe stem

Stress Concentration

When a structural member contains adiscontinuity, such as a hole or a suddenchange in cross section, high localizedstresses may occur near the discontinuity.


Stress Concentration

The highest stressconcentration occursnear a sharp point

p

any 21max

At higher rates of loading, bone absorbsmore energy prior to failure because

1. the modulus of elasticitydecreases.

2. bone is anisotropic.

3. bone is viscoelastic.

4. bone deforms plastically.

5. bone is stronger in compressionthan in tension.

Viscoelasticity

Viscoelasticty is a term used to describematerials that demonstrate time-dependantbehavior to loading.

Visco is derived from viscocity (fluid like)

Elastic come from elasticity (solid like)

Most normal temperature metals are elastic

Most biologic materials (bone, tendon,ligaments), glass, polymers, and metals athigh temperature exhibit viscoelastic behavior

A simple model for an elasticmaterial is a simple spring in whichinstantaneous displacement occurs

Viscoelasticity

.

The energy ofdisplacement is stored aspotential energy andrecovered when the loadis removed.



16/23

Viscous behavior can be modeled asa dashpot (shock absorber).Deflection occurs in response to the

Viscoelasticity

In this case theenergy producedfrom loading isdissipated as heat.


Viscoelastic Behavior is modeled asa combination of elastic and viscousmaterials.

Viscoelasticity

The energy fromloading ispartially storedand partiallydissipated


The biomechanical properties of ligamentsand bone demonstate

1. a time-dependent behavior.

2. a ra e- n epen en e av o r.

3. a straight-line load-deformation behavior.

4. modeling with linear elastic-springelements.

5. similar stress-stretch curves.

At higher rates of loading, bone absorbs more energy prior to failure

because

1- the modulus of elasticity decreases.

2- bone is anisotropic.

3- bone is viscoelastic.

4- bone deforms plastically.

5- bone is stronger in compression than in tension.

The change in strain of a material under a constant load that occurs

with time is defined as

1- creep.

2- relaxation.

3- energy dissipation.

4- plastic deformation.

5- elastic deformation.

Time

Stress Relaxation

Stress relaxation is the decrease ofstress with time under constant

strain.

Time


17/23

Stress Shielding

Wolffs law

If you dont use it, you lose it!

implant carries most of the stressand effectively unloads the bone

Examples are the proximal femurwith an ingrown implant and loss ofbone under a plate.

StressShielding

Assume the plate is stainless steel withE=190 GPa

Assume the bone is all cortical bone withE=17 GPa

Both the bone and the plate must deformthe same

P P

E AF

b

b

b

p

ssp

EE

bb

b

p

pE

E 10

17

190

)10(10

)10(

)10(

bp

p

bp

b

bbpbbpp

bp

AAP

AA

P

AAAAP

FFP

In a 77-year-old woman whounderwent total hip arthroplasty 10years ago. What is the predominant

cause of the proximal femoral bone

1. Stress shielding

2. Polyethylene debris-inducedosteolysis

3. Senile osteoporosis

4. Modulus of elasticity of the femoralstem

5. Diffuse osteopenia

Examples of Materials Usedfor Implants

Which of the following properties is most commonly associated with titanium

alloy implants when compared with cobalt-chromium alloys?

1- Lower elastic modulus

2- Lower corrosive resistance

3- Better wear characteristics

4- Lower notch sensitivity

5- Greater hardness

Elastic modulus and ultimate tensile strength of themost common orthopedic biomaterials, listed in order

of increasing modulus or strength:

ELASTIC MODULUS

cancellous bone

polyethylenePMMA (bone cement)

cortical bone

titanium alloystainless steel

cobalt-chromium alloy

ULTIMATE TENSILE STRENGTH

cancellous bonepolyethylene

PMMA (bone cement)

cortical bonestainless steel

titanium alloycobalt-chromium alloy

Stainless Steel

Used for fracture fixation and spinalimplants

Most common is 316L

, ,

The chromium forms an oxide layer onthe out side of the implant that acts as acorrosion resistant layer and forms thestainless quality to it

Strong material but can get stress orcrevice corrosion with time

Caused by cracking the Cr-oxide layer with loading


18/23

Cobalt-Chromium Alloys

There are a number of different alloys used for

implants depending on what type ofmanufacturing is used

Consists mostly of cobalt with chromium addedfor corrosion resistance

Like stainless steel the chromium forms asurface oxide layer

Used for joint replacements, bearing surfacesand occasionally for fracture fixation devices

Not all Co-Cr is the same and the mechanicalproperties are a function of which alloy is usedand how the alloy is processed

Titanium One of the most biocompatible metals

Very good corrosion resistance Resistance is generated by a rapidly formed oxidized layer on its

surface and this layer makes the titanium implant more corrosionresistant that Stainless steel or CoCr implants

os common y use a oy s - - 6% aluminum and 4% vanadium

Initially developed as a high strength to weight ratio material foraircraft

Its modulus of elasticity is around half of that of stainlesssteel or CoCr, hence using titanium implants my reducethe stress sheilding

Very notch sensitive leads to crack formation anddecreased fatigue life

Not a good bearing surface in joint arthroplasty because itgets rough with time

Ceramics Ceramics are materials are inorganic materials formed

from metallic and nonmetallic materials held together byionic and covalent bonds

Examples include silica, alumina, zirconia

Mechanical properties are very process dependant and can

Ceramtec a few years ago changed a single step in their processof making femoral heads (they did not change the material)which resulted in fracture of the heads in vivo

Ceramics are very stiff, very hard, demonstrate very littlewear

Can be very brittle

Very biocompatible if manufactured to a high purity level

Polymers

Polymers are large molecules made from

combinations of smaller molecules Nylon, PMMA, Polyethylene

depends on their micro and macro-structure

A polymers molecular weight depends onthe number of molecules in its chains

Polymers


Polyethylene

Semi-crystalline polymer

Basic momer is CH2 with a molecularweight of 28

Its mec an ca an wear propert esdepend on its molecular weight,structure, oxidation, cross linking,processing method, and sterilization

**Not all polyethylene is the same**


19/23

Highly cross-linked ultra-high molecular weight

polyethylene has what effect on tensile and fatiguestrength when compared with ultra-high molecularweigth polyethylene?

1. Increase tens e an atgue strengt

2. Increased tensile strength and decreased fatiguestrength

3. Decreased tensile and fatigue strength

4. Decreased tensile strength and no change infatigue strength

5. No change in tensile or fatigue strength

Crosslinking

Crosslinking is done to create largermolecular polyethylene moleculesthat can theoretically be more wear

There are two common methods forcrosslinking

Irradiation

Free radical generating chemical

Crosslinking

Lewis, Biomaterials 22 (2001) 371-401

Crosslinking

The major problem with crosslinking is thatusually higher doses of radiation which producethe greatest amount of crosslinking also maycause a degradation in the materials mechanicalproperties. Specifically a decrease in fracturetoug ness an at gue strengt an e.

Newer versions of highly crosslinkedpolyethylene are being released that are beingtreated by a combination of lower dose radiationand post irradiation melting and or annealing.These processes are showing promise for lowwear rates and small changes to the mechanicalproperties of the polyethylene

Tribology

The study of Friction, Lubrication,and Wear.


20/23

The natural joint

Elements that influence thetribological function of a joint are: The articular cartilage

The synovial fluid

And to a lesser extent the subcondralbone, capsule, soft tissues andligaments.

Frictionis the resistance to motion that isexperienced whenever one solid bodySlides over another

LOAD

DIRECTION OF

MOTIONFRICTION FORCE

LOAD

DIRECTION OF

MOTIONFRICTION FORCE

Lubrication.materials appliedto the interfacereducing friction andwear.

Lubrication.

Lubrication reduces Frictionreduces Wear

Ability of a bearing to support a fluidfilm will inevitably influence thefriction and wear of the bearingsurfaces during articulation

Lubrication modesBoundary Lubrication

HydrodynamicLubrication

Hydrostatic Lubrication

STRIBECK CURVE

Coefficientof Friction

()

Sommerfeld Number

(viscosity x sliding speed x radius / load)

BL

ML FFL


21/23

Boundary Lubrication

High Friction and Wear

Boundary Lubrication

No pressure build up in thelubricant.

Loading is 100% carried by theasperities in t e contact area.

The contact area is protected byabsorbed molecules of the lubricantand / or a thin oxide layer.

The characteristics for boundary

lubrication is the absence ofHydrodynamic pressure.

Fluid Film Lubrication

No Friction or Wear

Hydrodynamic Lubrication

Bearings are supported by a thinlayer of fluid which is pulled into thebearing through viscous

, ,sufficient hydrodynamic pressure tosupport load.

HD h >0.25m

EHD h ~0.025m

- 2.5 m

h HD h >0.25m

EHD h ~0.025m

- 2.5 m

h

Generation of fluid filmAs the ball rotates, fluid is drawn

into the converging wedge andbuilds up a pressure which carries

the load

Hydrodynamic Lubrication Pressure builds asspeed increases.

The surface

asperities areby a lubricant film.

The load andHydrodynamicpressures are inequilibrium.


22/23

Hydrostatic Lubrication

Bearings are supported on a thickfilm of fluid supplied from anexternal pressure source.

hP P

hP P

Artificial joint surfaces

Metal / Ceramic bearing on UHMWPE donot benefit from fluid film lubricationthey operate in a mixed fluid film regime.

approximately 200m of linearpenetration per year giving a lifeexpectancy of a 4mm thick cup about 20years.

M-on-M and Ceramic on Ceramic performin a fluid film regime therefore theresultant wear rate is significantlyreduced.

Which of the following features improvedfluid film lubrication in a metal-on-metaltotal hip arthroplasty?

1. Smaller diameter femoral head, a completelycongruent fit between the socket and thehead, and sufficient roughness to allow forsome microseparation between the head and

socket2. Smaller diameter femoral head, a slight

clearance between the socket and the head,and no surface roughness

3. Larger diameter femoral head, a completelycongruent fit between the socket and thehead, and minimal surface roughness

4. Larger diameter femoral head, a slightclearance between the socket and the head,and minimal surface roughness

5. Larger diameter femoral head, a slight

Clearance

a s a a earance

Radius CupRadius CupR2R2

----Head R1Head R1

--= Radial= RadialClearanceClearance

--ClearanceClearanceallows a fluidallows a fluid

Is there an optimalclearance?

No one clearance, itis a ratio to headdiameter

gets, the bigger theclearance gets

We must considermanufacturingcapabilities Nominaland Ranges etc

The lubricant fluid inVivo


23/23

Effect of clearance with bovineserum all tests to date

Too tightToo tightand too highand too high

clearancesclearances

0

may end upmay end up

in high wearin high wear

rates due torates due to

an increase inan increase in

frictionfriction

Does reduced clearancemake a difference?

BOA Manchester 2004McMinn presented earlyresults of 20 controlledclearance casesim lanted in 2004.

Radiolucenciesobserved in superioracetabulum in 10% ofthe cases to date.

Reduced Clearance

bearings need furtherassessment.

24 hour Cobalt output inRegular and low clearance BHR

Regular BHR vs Controlled Clearance BHR

Urine Cobalt Output

70

80

90 Regular BHR

Low Clearance BHR

0

10

20

30

40

50

60

UrineOutputg/24hr

Pre Op 5 day 2 month 6 month 1 year 4 year

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