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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)
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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
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By combining the first and secondlaws: For equilibrium to occur thesum of the forces and moments
Basic Laws of MechanicsNewtons Laws
0F
Basic Laws of MechanicsNewtons Laws
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
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Illustrative Problem
W=20 N
G= 15 N
0 xF 0yF
0 WGRB
35
2015
BR
BR
0M
N2753
15153020
030153
B
WGB
N240R
Illustrative Problem
Hip Reaction forces in single legstance
Buckwalter, et al. Orthopaedic Basic Science
Illustrative Problem
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
Illustrative Problem
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.
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Stress
Stress is the intensity
of internal force. Normal stress are
perpendicular to thesurface
Shear stress areparallel
F
Beer and Johnston, Mechanics of Materials
AO/ASIF
Depending on how youslice the material you canget combinations of stressand sheer
Beer and Johnston, Mechanics of Materials
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
Beer and Johnston, Mechanics of Materials
AO/ASIF
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Shear strain
Usually expressed as an angle radians
Beer and Johnston, Mechanics of Materials
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?
Beer and Johnston, Mechanics of Materials
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
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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.
Beer and Johnston, Mechanics of Materials
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Force-deformation curves for materialshaving various combinations of structural
properties
Beer and Johnston, Mechanics of Materials
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
Buckwalter, et al. Orthopaedic Basic Science
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.
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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
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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
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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
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Anisotropy
Bone is an
anisotropicmaterial
depends on loaddirection andloading type
Buckwalter, et al. Orthopaedic Basic Science
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
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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?
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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.
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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.
Beer and Johnston, Mechanics of Materials
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.
Buckwalter, et al. Orthopaedic Basic Science
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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.
Buckwalter, et al. Orthopaedic Basic Science
Viscoelastic Behavior is modeled asa combination of elastic and viscousmaterials.
Viscoelasticity
The energy fromloading ispartially storedand partiallydissipated
Buckwalter, et al. Orthopaedic Basic Science
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
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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
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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
Buckwalter, et al. Orthopaedic Basic Science
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**
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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.
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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
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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.
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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
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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