Investigating Cartilage Stress Dennis Cody November 22, 2004.

Investigating Cartilage StressInvestigating Cartilage Stress

Dennis Cody

November 22, 2004

OutlineOutline

History PTC & Pro/Engineer Stanford

VA – Investigation of Stress in Cartilage Description of Patellofemoral Pain. Determine when bone can be assumed rigid. Understand apparent discrepancies in literature.

PTC Stanford VA

Parametric Technology Parametric Technology CorporationCorporation

5 years in Quality Assurance – Senior QAE

Software: Pro/Engineer, Pro/Mechanica, Pro/Intralink

Transition to new defect tracking database

Desire to enhance people’s lives and health

PTC

Stanford – Design and Prototype Stanford – Design and Prototype Tools for Surgical ProcedureTools for Surgical Procedure

Implant pegs: placement, depth, diameter, angle

Method of creating peg holes

Tools: Cutting Block Depth Resection Gauge Drilling Template Template Impactor

Posterior Peg Impactor Tibial Trial Tibial Spacer

PTC Stanford

OutlineOutline

History PTC & Pro/Engineer Stanford

VA – Investigation of Stress in Cartilage Description of Patellofemoral Pain. Determine when bone can be assumed rigid. Understand apparent discrepancies in literature.

PTC Stanford VA

OutlineOutline

Determine when bone can be assumed rigid.Understand apparent discrepancies in

literature.

When looking at stresses in cartilage:

PTC Stanford VA

Motivation - PFPSMotivation - PFPS

What is PF Pain Syndrome?Anterior knee painAssociated with repetitive

exerciseCause difficult to determine

Muscle imbalanceAttachmentBone shape, alignment…

http://www.medicalmultimediagroup.com

Background Methods Results

ObjectiveObjective

Obtain PF joint data in young adult volunteers using non-invasive techniques. Kinematics Kinetics Contact areas Stresses

Focus: From static MR Images, create a finite element model that can be used for analyses

Background Methods Results

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HypothesisHypothesis

Subjects with PF pain will have elevated cartilage stresses (compared to age and activity matched subjects without PF Pain), either because of increased PF forces and/or decreased PF contact areas.

Assumption to test: When looking at patellar and femoral cartilage stresses due to physiological loads, the underlying bone can be treated as a rigid material.

Background Methods Results

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BackgroundBackground

Modeling and solving models with bone elements is expensive.Some studies consider bone as a rigid material. (Li et al., 2001, Zhang et al., 1999)

Others consider the bone elements.(Beaupré et al., 2000, Brown et al., 1984)

Background Methods Results

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Background – Previous WorkBackground – Previous Work

3D Model of tibio-femoral joint (Donahue et al., 2002)

Model with bone Model with rigid backing No difference of more than 2%

Background Methods Results

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Background – Previous WorkBackground – Previous Work

Ideal model with plug and indentor (Brown et al., 1984)

Cancellous bone modulus value impacts effect of rigid implant in bone

Impactor has small radius smaller than in PF joint?

Background Methods Results

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Background – Previous WorkBackground – Previous Work

Author Section Thickness (mm) Modulus (MPa)Beaupré Cartilage 3 6

Subchondral 1 2000

Cancellous 16 200

Brown Cartilage ~ 1.25 3.45-20.7

Subchondral ~ 2.85 2070 - 13800

Cancellous ~ 13 34.5 - 690

Donahue Cartilage 3D model of 30 yr old specimen,

varying thickness

15

Subchondral 6900 - 20000

Cancellous 400

Background Methods Results

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MethodsMethods

Contact formulation

Plane Strain

Cancellous modulus

Subchondral bone thickness

Cartilage bone interface radius

Background Methods Results

Figure modified from Beaupré et al., 2000.

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ModelModel

Model hemisphere contacting a plate (axisymmetric)Allows curved and flat surfaceTwo models: Cartilage and bone

elements

Background Methods Results

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ModelModel

Model hemisphere contacting a plate (axisymmetric)Allows curved and flat surfaceTwo models: Cartilage and bone

elements Cartilage with rigid

backing

Background Methods Results

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Methods – Plane StrainMethods – Plane Strain

Master-Slave surface

Background Methods Results

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Methods – Plane StrainMethods – Plane Strain

Master-Slave surface

Hertz contact

Background Methods Results

Remove ABAQUS Series

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Master-Slave surface

Hertz contact

Compare with results from Beaupré’s PE model

Methods – Plane StrainMethods – Plane Strain

Background Methods Results

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Methods – Plane StrainMethods – Plane Strain

Master-Slave surface

Hertz contact

Comparison with results from Beaupré’s PE model.

PE vs.

Background Methods Results

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Methods – AxisymmetricMethods – Axisymmetric

Master-Slave surface

Hertz contact

Comparison with results from Beaupré’s PE model.

PE vs. Axisymmetric

Background Methods Results

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Stress With Stress With RadiusRadius

σ1-max = 432 kPa

σ 2-max = 396 kPa

σ 3-max = 401 kPa

σ 4-max = 407 kPa

σ 7-max = 414 kPa

σ 8-max = 420 kPa

r

2r

2r

r

FF

FF

1-max 5-max 3.8%

2-max 6-max 4.4%

3-max 7-max 3.2%

4-max 8-max 3.2%

1-max

3-max= 1.08

5-max

7-max= 1.08 0%

2-max

4-max= .97

6-max

8-max= 0.98 1%

=?

=?

r = 20.5 mm2r = 40.5mmF = 230NCart thk = 3.5 mmSubch bone = 0.5 mmCanc modulus = 600 MPa

Background Methods Results

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σ5-max = 449 kPa

σ6-max = 413 kPa

Stress With Stress With LoadLoad

σ5-max = 300 kPa

σ6-max = 294 kPa

σ7-max = 414 kPa

σ8-max = 420 kPa

σ3-max = 401 kPa

σ4-max = 407 kPa

F

σ1-max = 292 kPa

σ2-max = 286 kPa

F 2F

2F

1-max 5-max 2.8%

2-max 6-max 2.6%

3-max 7-max 3.2%

4-max 8-max 3.2%

1-max

3-max= 0.73

5-max

7-max= 0.72 1%

2-max

4-max= 0.70

6-max

8-max= 0.70 0%

=?

=?

r = 40.5 mmF = 115N2F = 230NCart thk = 3.5 mmSubch bone = 0.5 mmCanc modulus = 600 MPa

Background Methods Results

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Stress PatternsStress Patterns

Background Methods Results

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Trends in ResultsTrends in Results

Background Methods Results

Modulus (MPa)

Thickness (mm)

Octahedral Shear Hydrostatic OI

600 3 1.72% 0.68% 0.53%

600 1 1.37% 1.32% 0.87%

200 3 3.77% 1.36% 0.30%

200 1 6.99% 3.36% 1.12%

34.5 3 10.1% 3.47% 0.34%

34.5 1 40.1% 15.8% 4.21%

OI : Osteogenic Index = k * σOctahedral Shear + σHydrostatic (k = 0.35)

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SummarySummary

Contact model ran successfully in Abaqus

Rigid assumption valid for healthy young subjects, probably not for osteoporotic subjects

Model differences explain difference in results

Thank YouThank You