musculoskeletal [including mcmaster health sciences ... · musculoskeletal biomechanics ... and...

8/28/2012

1

Greg Wohl Ph.D., P.Eng.

Department of Mechanical Engineering

McMaster School of Biomedical Engineering

Musculoskeletal

Biomechanics

Suggested Reading [including McMaster Health Sciences Library call numbers]

• Einhorn TA, O’Keefe RJ, Buckwalter JA, eds. Orthopaedic Basic Science:

Foundations of Clinical Practice, 3rd Edtion. AAOS. 2007 [WE 102 .O77 2007]

• Buckwalter JA, Einhorn TA, Simon SR, eds. Orthopaedic Basic Science: Biology

and Biomechanics of the Musculoskeletal System, 2nd Edtion. AAOS. 2000.

[WE 102 .O77 2000]

• Bartel DL, Davy DT, Keaveny TM. Orthopaedic Biomechanics: Mechanics and

Design in Musculoskeletal Systems. Pearson Prentice Hall Bioengineering. 2006.

[WE 102 .B283O 2006]

• Nordin M, Frankel VH, eds. Basic Biomechanics of the Musculoskeletal System.

Lippincott Williams & Wilkins. 2001. [WE 103 .B311 2001]

• Mow VC, Huiskes R, eds. Basic Orthopaedic Biomechanics & Mechano-biology,

3rd Edition. Lippincott Williams & Wilkins. 2005. [WE 103 .B3125 2005]

Musculoskeletal Biomechanics

I. Joint Mechanics

II. Material Properties and Behaviours• stress, strain, elastic modulus

• wear and fatigue

• directional properties (anisotropy)

• viscoelasticity

III. Examples of Bone Adaptation in Aging and Repair• Aging – bone geometry and structural properties

• Repair – the effect of implant modulus on bone adaptation

I. Joint Mechanics

• Mechanical “advantage” (levers, moments)

• Joint structures and dynamics

• Determination of joint loading

• Example of novel measurement techniques

Mechanical AdvantageLevers — Moments (Torque)

F F

2F

M1

M1 = F • L

M2

M2 = F • L

L L

M1 = 2F • L M2 = F • L

M1 = 2F • L/2 M2 = F • L

L/2

=

≠

=

3.3 cm

30 cm

Diarthrodial Joint MomentsMuscle – Joint Loads

a

b

Mw

Mw = Fw • 30 cm

Mm

Mm = Fm • 3.3 cm

Mw = MmEquilibrium:

b ≈ 9 • aGeometry:

Fw

Fm

FJ

Loads: Fm ≈ 9 • Fw

FJ = 8 • Fw

Load

Equilibrium:Fm = Fw + FJ

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Limbs and Diarthrodial Jointsa compromise

A

B

d D

Kinematic Advantage

a

b

Mechanical Disadvantage

joint loads > body weight

Example: Hip Joint ForcesLim et al., J Am Acad Orthop Surg 2007

JRF = 500 N + 1500 N

JRF = 2000 N

What if a patient

has hip OA?

JRF = ?

Example: Hip Joint ForcesLim et al., J Am Acad Orthop Surg 2007

JRF = 500 N + 1500 N

JRF = 2000 N

JRF = ?

JRF = 500 N + 1000 N

JRF = 1500 N

Joint Structures and Dynamics

• Kinematics constrained by:

• bone geometry, ligaments, tendon/muscles

• Load transfer:

• Compressive:

– cartilage, meniscus, bone

• Tensile:

– ligament, tendon/muscle

Knee Kinematics cruciate ligaments

CC

DD

BB

AA

femur

tibia

anterior posterior

Cruciate 4-Bar Linkage

DA

C

B

A

D

BC

A

D

C

B

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http://nyic.stemlegal.com/wp-content/uploads/2009/01/normal-knee-anatomy.jpg

Knee Kinematics Cartilage and Meniscus

ExtensionFlexion

Divergence of femoral condyles

Cartilage and Meniscus

Nordin 2001

- meniscus damage and knee mechanics

Knee Kinematics Cartilage and Meniscus Joint Structures

• Kinematics constrained by:

• bone geometry, ligaments, tendon/muscles

• Load transfer:

• Compressive:

– cartilage, meniscus, bone

• Tensile:

– ligament, tendon/muscle

Knee Walking Curves

Ethier and Simmons

Determination of Joint Loading

• Significant number of variables

• Timing of load application

e.g. muscle activation

• Indeterminate system

(too many unknowns)

• Difficulties measuring tissue

loads in situ or in vivo

• Compression (bone / cartilage)

• Tension (muscle / tendon)

• Tension (ligament)

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Why is it important to measure /

determine joint loads?

• Natural loading environment of joint tissues.

• Effect of altered mechanics, injury or disease

on joint loading.

• Predict need for repair / replacement

• Understand effect of repair / replacement

• Engineer suitable implants or biological

alternatives.

Radius

Axis of

Symmetry

A

CC

B

Annulus

"Radial" components of

applied pressure

Fr

Fc Tangential

component

Radial

component

Tangentialcomponent

Radial

component

cF

Annulus, C

Verticalcomponent

Radial

component

Applied pressure

direction

Vertical

reaction

Force transmission

Shrive NG

Meniscus Loading in the Knee

Meniscus

ArticularCartilage

Articular Cartilage

Unloaded Femur

Meniscus Intact Meniscus Deficient

Small deformation

of cartilage

Articular CartilageArticular Car

tilage

Large deformation

of cartilage

Relatively high average pressure

and high pressure gradients

Relatively low average pressure

and low pressure gradients

Effect of Meniscus Deficiency

Shrive NG

Experimental Measurements of Joint Loads

Experimental Measurements of Joint Loads Experimental Measurements of Joint Loads

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Experimental Measurements of Joint Loads


I. Joint Mechanics




• viscoelasticity



II. Material Properties & Behaviour

1. Material properties (e.g., stress, strain)

2. Wear and Fatigue

3. Directional properties (anisotropy)

4. ViscoelasticityENERGY

Mechanical Tests: Tensile Test — Bone

LO

AD

[N

]

DEFORMATION [mm]

AA

BB CCDD

D1D1

ULTIMATE

FAILURE

POINT

ELASTIC

REGION

(stiffness)

PLASTIC REGION

YIELD

POINT

1) Material Properties

and energy (toughness)

LO

AD

[N

]

DEFORMATION [mm]

ceramic

aluminum

Brittle: PMMA

ceramic

bone

Ductile: aluminum

stainless steel

cobalt-chromium

bone

Ductile vs. Brittle Properties

Intermediate:

titanium

Structural (Architectural) Effects

LO

AD

[N

]

DEFORMATION [mm]


Load and Deformation are Structural Properties

- they depend on both geometric and material properties

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Stress (σ) – Normalization of Load

F

F

σ = F / A

MPa = N / mm2

F

A


Strain (ε) – Normalization of Deformation

F

F

L

∆L ε = ∆L / L

ε = mm / mm

(dimensionless)


Stress–Strain Curve- independent of the size of the sample

LOAD

DEFORMATION

AA

BB CC

ULTIMATE

STRESS

YIELD

STRESS

Stress

(F/A)

[MPa]

Strain

(∆L/L)

[mm/mm = ε]

SLOPE = ELASTIC MODULUS

≅


Elastic Modulus (“Young’s” Modulus)

(normalized stiffness)

Stress

[MPa]

Strain

[mm/mm]

∆ε

∆σE

E = ∆σ / ∆ε

MPa = [MPa] / [mm/mm]


Representative stress-strain curves

of common materials*


Str

ess [M

Pa]

Strain

[mm/mm]

cobalt chromium 210

titanium 110

stainless steel 190

bone 17

E [GPa]

2000

1600

0

1200

800

400

* values from Wright and Maher,

in Einhorn et al. 2007

1) Material Properties – Examples

Examples of Geometric and Material Changes (Bone)

Osteoporosis ⎯ loss of bone mass (geometric)

⎯ also altered material properties?

Charles Turner

www.engr.iupui.edu

8/28/2012

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Kondo et al. AJSM 2004

Normal

ligament

Healing

ligament

Comparison of Healing Ligament Properties

Inoue et al. CTR 1990

-20%

-50%

Structural vs. Material II. Material Properties & Behaviour


2. Wear and Fatigue


4. Viscoelasticity

• Wear Failure

• A structure loaded repetitively in shear

will sustain cumulative damage resulting

in attrition and loss of the surface.

http://www.iti.northwestern.edu/research

/a_projects/bridges/hoan.html

2) Wear and Fatigue

Failure Mechanisms

http://www.azom.com/article.aspx?ArticleID=909

• Fatigue (Cyclic) Failure

• A structure loaded repetitively below its

monotonic failure force, will accumulate

microscopic damage leading to crack

formation, loss of strength and eventual

fracture

2) Wear and Fatigue

In bone, cracks are repaired by osteonal remodeling

2) Wear and Fatigue

In implants, fatigue and wear are the

most common failure mechanisms

E.g., UHMWPE implant wear rapidly

compared to metal-on-metal (MoM)

implants

UHMWPE

MoM



2. Wear and Fatigue


4. Viscoelasticity

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Poisson’s Effect – lateral deflection due to axial load

2) Directional Properties

E.g., elastic band E.g., balloon

2) Poisson’s Effect

– Loading of the Intervertebral Disc

• Nucleus pulposus is always under

compression and carries the majority

of compressive load

• Annulus fibrosis carries load through

hoop stress

Whiting and Zernicke, 1998

Bartel et al., 2006


• Isotropic:Material properties are the same regardless of direction (do not depend on direction of load)

• e.g., metals, glass, plastics

• Anisotropic:Material properties depend on loading direction

• e.g., wood, bone, ligament, meniscus, cartilage

• anisotropy governed by microstructure (e.g., fibril structures, lamellar growth)

Anisotropic Behaviourtensile loading — cortical bone

Str

ess

Strain

L

T


Anisotropy of Cortical Bone




2. Wear and Fatigue


4. Viscoelasticity

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• Mechanical properties sensitive to:

• strain rate

• load duration

• Time dependent behaviours:

• creep

• stress-relaxation

4) Viscoelasticity

Str

ess

Strain

1500/sec

300/sec

0.1/sec

(running)

0.001/sec

(slow walk)

strain rate dependence — (e.g., cortical bone)

4) Viscoelasticity

creep, stress relaxation — (e.g., cartilage, ligaments, tendons)

Me

asu

red

De

form

atio

nA

pp

lied

Lo

ad

CREEP

Me

asu

red

Lo

ad

Ap

plie

d

De

form

atio

n

STRESS-RELAXATION

4) Viscoelasticity

High strain rate

(ligament failure)

Low strain rate

(bone avulsion)

Strain-Rate Dependence – Bone

4) Viscoelasticity


I. Joint Mechanics




• viscoelasticity



Effect of Bone Geometry on Bone

Mechanics in Aging

Age (Years)

Bon

e m

ass

0 10 20

exercise

cessation

no exercise

30 40 50 60

��

x

Adapted from Modlesky and Lewis 2002

Exercise, Aging and Bone Mass

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Effect of Bone Geometry on Bone

Mechanics in Aging

Seeman, NEJM 2003

Effect of Geometry and Structural Properties

Bending:

tension

compression

M

M

neutral

axis c

c = max radius of section

I = moment of inertia

Icircle =π c4

4

σmax = �4 M 1

π c3

σmax =M c

I

y = distance from n.a.

y

σ =M y

I

c1

c2

Moment of Inertia (second moment of area):- a measure of the distribution of material in a section

c1

L L

A1 = π c12 A2 = π (c2

2- c12)

d

I1 =π c1

4

4 I2 = (c24- c1

4)π

4 3 I1 = I2

A1 = A2

∆A I = Σ d2 ∆A


c2

c [mm] A [mm2] I [mm4] σ [MPa]

~ c2 ~ c4 ~ 1/c3

c1 A1 I1 σ1

c1

2

A1

2

I1

42.8 σ1

c1

2

A1

2

3 I1

41.3 σ1

1

2

3c2

c1

c1

c1 ,

same amount of material same amount of material

better load resistancebetter load resistance

Bone distribution (hollow tubes)

optimization of Strength:Weight ratio


1) Material Properties - Examples

• 1982 – Rubin and Lanyon

Animal Activity Peak strain [µε]

Horse radius Trotting -2800 (-0.28% ε) Dog radius Trotting -2400 Goose humerus Flying -2800 Sheep femur Trotting -2200 Pig radius Trotting -2400 Fish hypural Swimming -3000 Monkey mandible Biting -2200

Peak bone strains are similar across species

(and bone sizes) for various physiological activities

from Martin et al., 1998

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Stress

[MPa]

Strain [mm/mm]


At a given stress (σ), a material with a greater

modulus of elasticity (E) will experience less strain (ε)

E1 E2

E3

E1 > E2 > E3

ε1

σ

ε2 ε3

ε1 < ε2 < ε3

Selected Material Properties - tensile tests

E σσσσu σσσσy

Material: [GPa] [MPa] [MPa]

Stainless Steel 190 930 790

Cobalt Chromium 210 1896 1606

Titanium 110 965 896

PMMA 2.1 30

Cortical Bone 17.0 130

Trabecular Bone 0.1 50


Selected Material Properties - tensile tests

E σσσσu σσσσy

Material: [GPa] [MPa] [MPa]

Stainless Steel 190 930 790

Cobalt Chromium 210 1896 1606

Titanium 110 965 896

PMMA 2.1 30

Cortical Bone 17.0 130

Trabecular Bone 0.1 50


stress shielding

unloaded

(unstrained)

region

unloaded

(unstrained)

region

Stress Shielding Examples


stress shielding

unloaded

(unstrained)

region

unloaded

(unstrained)

region

Nordin 2001

QUESTIONS?

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