quantifying fatigue cracking damage in polyethylene tibial

Quantifying fatigue crack damage in

polyethylene tibial inserts of

prosthetic knee joints

MS Candidate

Dept. of Mechanical Engineering

University of Utah

November 17, 2014

Carly Lockard

Introduction

• Total knee arthroplasty (TKA): gold-standard treatment for

degenerative and arthritic knee diseases

• Replaces damaged articular surfaces with metal and polyethylene

articular surfaces – prosthetic knee joint

2

Femoral

component

Tibial insert

Metal tibial

plateau and stem

Condyles of

tibia

Femur

Condyles of

femur

Tibia

Articular

cartilage

Introduction (2)

3

• Problem: failure of prosthetic knee joints• Statistical survivorship decreases after 10 – 15 years of use• Main causes of failure [1]

• Polyethylene wear, and aseptic loosening and instability due to osteolysis (bone death) cause more than 40% of all failures

Aseptic

loosening

31%

Instability

19%Infection

16%

Polyethylene

wear

10%

Arthrofibrosis

7%

Malalignment

7%

Other

10%

[1] Schroer, W. C., Berend, K. R., Lombardi, A. V., Barnes, C. L., Bolognesi, M. P., Berend, M. E., Ritter, M. A., and Nunley, R. M., 2013,

“Why are total knee failing today? Etiology of total knee revision in 2010 and 2011.,” J. Arthroplasty, 28(Suppl. 1), pp. 116–119.

Introduction (3)

4

• Failure results in revision surgery to replace components

• Current revision rate up to 10% (65,000 revisions per year in U.S.)1

• Revision rate expected to increase

due to growing number of younger,

more active patients2

• Average age for primary TKA is 60 years

• 10 – 15 year implant lifetime3 means

patients outlive their prosthetic knee joints

• Reduced wear increases longevity and reduces revision surgeries

18 to 44

years

2%

45 to

64

years

41%65+

years

57%

Patient ages at time of primary TKA4

[1] Pabinger, C., Berghold, A., Boehler, N., and Labek, G., 2013, “Revision rates after knee replacement: Cumulative results from worldwide clinical studies versus joint registers.,” Osteoarthritis Cartilage, 21, pp. 263–268.[2] Kurtz, S. M., Lau, E., Ong, K., Zhao, K., Kelly, M., and Bozic, K., 2009, “Future young patient demand for primary and revision joint replacement: National projections from 2010 to 2030,” Clincal Orthop. Relat. Res., 467(10), pp. 2606–2612.[3] Heyse, T. J., Ries, M. D., Bellemans, J., Goodman, S. B., Scott, R. D., Wright, T. M., Lipman, J. D., Schwarzkopf, R., and Figgie, M. P., 2014, “Total knee arthroplasty in patients with juvenile idiopathic arthritis.,” Clin. Orthop., 472(1), pp. 147–154.[4] Losina, E., Thronhill, T. S., Rome, B. N., Wrights, J., and Katz, J. N., 2012, “The dramatic increase in total knee replacement utilization rates in the United States cannot be fully explained by growth in population size and the obesity epidemic,” J. Bone Joint Surg. Am., 94(3), pp. 201–207.

Introduction (3)

5

• Why is the prosthetic knee joint prone to polyethylene wear?

- Low congruency between femoral component and tibial insert allows

knee mobility but contributes to small contact area1

- Up to 7 x body-weight force2 is applied over the small contact area

results in high local contact stress

- This high contact stress in the prosthetic knee joint means yield stress

of polyethylene may be exceeded1

- Cyclic loading, as experienced in the knee during gait, under high

stress causes fatigue wear3

[1] D’Lima, D. D., Steklov, N., Fregly, B. J., Banks, S. A., and Colwell Jr., C. W., 2008, “In vivo contact stresses during activities of daily living after knee

arthroplasty,” J. Orthop. Res., 26, pp. 1549–1555.

[2] Blunn, G. W., Walker, P. S., Joshi, A., and Hardinge, K., 1991, “The dominance of cyclic sliding in producing wear in total knee replacements,” Clin. Orthop.,

(274), pp. 253–260.

[3] Simis, K. S., Bistolfi, A., Bellare, A., and Pruitt, L. A., 2006, “The combined effects of crosslinking and high crystallinity on the microstructural and

mechanical properties of ultra high molecular weight polyethylene,” Biomaterials, 27, pp. 1688–1694.

Introduction (4)

6

• Wear modes:

1. Adhesive – material from tibial insert surface transfers to the

surface of femoral component1

2. Abrasive – asperities on hard femoral component ‘plough’

through soft tibial insert surface, removing surface material1

3. Oxidative – free radicals break polyethylene bonds1

4. Fatigue wear (fatigue crack damage) – alternating loading and

unloading causes subsurface crack initiation and growth1

• Our focus: fatigue crack damage, which causes severe wear through

delamination, or separation of entire surface from bulk of implant

resulting in catastrophic failure

[1] Hallab, N. J., Jacobs, J. J., and Katz, J. L., 2004, “Orthopaedic Applications,” Biomaterials Science: An Introduction to Materials in Medicine, Ratner, B. D.,

Hoffman, A. S., Schoen, F. J., and Lemons, J. E., eds., Elsevier Academic Press, San Diego, CA, pp. 527–555.

Objectives

7

1. Develop a non-destructive method to measure fatigue crack

damage

2. Develop a finite element model of contact stress occurring in

tibial insert during knee simulator testing

3. Evaluate how well modeled local stress predicts fatigue crack

damage

Overview

1. Knee simulator wear testing- Tibial insert wear testing using a gait-mimicking knee simulator

2. Subsurface fatigue crack damage measurement- Novel trans-illumination method tested on two tibial inserts

3. Finite element modeling of knee simulator testing- Two applicable polyethylene material models

4. Comparison between experimentally determined fatigue crack damage and high stress locations in finite element model

5. Conclusions

8

Overview





5. Conclusions

9

Knee simulator testing

10

Femoral

component

(posterior view)

Tibial insert

(posterior view)

Container

for bovine

calf serum

Pivot point for

varus-valgus rotation

Anterior-posterior buffer load

cells

Attachment for

femoral

component

Attachment

for tibial

insert (metal

tibial plateau)

Tibial insert

enclosure

• Knee simulator mimics in-vivo

conditions during normal

walking gait1

• Induces adhesive-abrasive wear

and fatigue crack damage

• Amount of adhesive-abrasive

wear is measured (gravimetric)1

• Fatigue crack damage just

noted as binary (yes or no)1Knee simulator with tibial insert and femoral

component configured for testing, located at

University of Nebraska

[1] International Organization for Standardization, 2009, “Implants for surgery - Wear of total knee-joint prostheses- Part 1: Loading and displacement

parameters for wear-testing machines with load control and corresponding environmental conditions for test.”

Knee simulator testing (2)

11

Internal-external rotation torques

(pneumatic actuators) and load cells

Axial force (actuator) and load cell,

universal joint at base allows rotation

Left and right anterior-

posterior forces

(pneumatic actuators)

and load cells

Left and right anterior-

posterior buffer forces

(springs) and

load cells

Flexion-extension

actuation

Femoral component

Tibial insert attachment

(metal tibial plateau)

Internal-external

rotation buffer

torques (springs) and

load cells

Attachment

for femoral

componentTibial insert

Posterior pivot

point for varus-

valgus rotation

Tibial insert enclosure

Anterior pivot point for

varus-valgus rotation

(obscured)

• Knee simulator applies and

records axial (along tibia)

force, anterior-posterior

force, and internal-external

torque using actuators

• Knee simulator also

provides buffer forces and

torques in the anterior-

posterior and internal-

external directions using

springs

• Buffer forces and torques

mimic the action of knee

ligaments

Knee simulator testing (3)

• Apply simulated gait cycles at 1 Hz (normal gait stride frequency)1

• Test until damage is noted or to the required minimum lifetime of 6

million cycles1

• Average the input and measured forces/torques and displacements over

19 cycles to obtain average load and displacement data

- These data are later used as input for finite element model

• Results:

- Fatigue crack damage occurred at less than 6 million cycles

- This indicates that the yield stress of polyethylene was exceeded

12

[1] International Organization for Standardization, 2009, “Implants for surgery - Wear of total knee-joint prostheses- Part 1: Loading and displacement

parameters for wear-testing machines with load control and corresponding environmental conditions for test.”

Overview





5. Conclusions

1

3

Fatigue crack damage measurement

• Existing subsurface fatigue crack damage measurement techniques:

1. Thin slice microscopy1:

- Commonly used

- Destructive

- Risk of artifacts

2. Scanning acoustic

tomography2:

- Non-destructive

- Poor resolution

14

Thin slice

Side view of removed slice,

dark-field microscopy view

Crack section

Cutting plane

Subsurface

crack

Thin slice microscopy

Specimen

Water bath

Transducer Receiver

Processed image on monitor screen

Crack image

Crack

Specimen image

monitor screen

Scanning acoustic tomography

[1] Petzow, G., ed., 1999, Metallographic Etching: Techniques for Metallography, Cermaography, Plastography, ASM International, USA.[2] Shibata, N., and Tomita, N., 2005, “The anti-oxidative properties of α-tocopherol in γ- irradiated UHMWPE with respect to fatigue and oxidation resistance,” Biomaterials, 26(29), pp. 5755–5762.

Fatigue crack damage measurement (2)

3. Microscopic computed tomography (micro-CT)1:

- High resolution

- Non-destructive

- Expensive

15

Specimen

X-ray

source

Beam

Detector

Thin slice images produced by

each beam are assembled into

3D image of specimen

Thin slice

images

3D image

Microscopic computed tomography (micro-CT)

[22] Teeter, M. G., Yuan, X., Naudie, D. D. R., and Holdsworth, D. W., 2010, “Technique to quantify subsurface cracks in retrieved polyethylene components

using micro-CT,” J. Long. Term Eff. Med. Implants, 20(1), pp. 27–34.


16

Anterior

Fatigue crack

damage

Anterior Fatigue crack

damage

• Measured fatigue crack damage in two tibial inserts:

1. Tibial insert 1: knee simulator wear tested, cruciate sacrificing

2. Tibial insert 2: retrieved implant, cruciate retaining

• Both GUR 1050 ultra-high molecular weight polyethylene

(UHMWPE), gamma irradiation sterilized, nitrogen flush packaged

Tibial insert 1 Tibial insert 2

• Use diffused light from a fiber optic illuminator to uniformly trans-

illuminate tibial inserts

• Trans-illumination reveals fatigue crack damage

• Images are processed to quantify fatigue crack damage


17

Fiber optic illuminator Opaque plastic sheeting

Diffusing screen Camera

Tibial insertVise

Tripod

Anterior

Fatigue crack

damage

Damaged Pristine


18

• Quantifying fatigue crack damage

– Step 1: Wiener filter is applied to

remove noise from gray-scale image

– Step 2: Edges are mapped using Canny

algorithm, resulting in a black and white

edge image

– Step 3: All but outer edge pixels are

suppressed

– Step 4: Piecewise cubic spline is fitted

to outer edge pixels to enclose fatigue

crack damage

– Step 5: Damage area is quantified

19

C

D

B

A


• Illustration of fatigue crack damage image processing steps

applied to Tibial Insert 2

A: Wiener filtered image of fatigue crack damage

B: Edges mapped using the Canny edge detection

algorithm

C: Non-damage edge pixels have been removed

D: All but outer edge pixels removed

20


E: Outer pixels are superimposed on fatigue

crack damage image for illustration

F: Piecewise cubic spline is fit to outer edge pixels

G: Cubic spline is superimposed on fatigue crack

damage image for illustration

H: Superimposed image on the tibial insert

to show scale

E Outer edge pixels

(dark grey)

Fatigue crack

damage regionNon-

damage region

F Outer edge pixels

(red)Cubic

spline

(blue)

G

Fatigue crack

damage regionNon-

damage region

Outer edge pixels

and spline (dark grey)

H

6

mm

• Fitting a piecewise cubic

spline to the outer fatigue

crack damage pixels allows

the fatigue crack damage

area to be approximated by

area enclosed within cubic

spline

• This allows quantitative

comparison between

different fatigue crack

damage regions

• Results for tested inserts:

1. Tibial insert 1: 22 mm2

2. Tibial insert 2: 38 mm2

21


0 2 4 6 80

2

4

6

8

10

12

14

x [mm]

y [m

m] Representative jagged

spline regions

Image noise

Irregularity

caused by

indistinct

edges

0 2 4 6 80

2

4

6

8

10

12

14

x [mm]

y [m

m]

02

46

810

12

0 1 2 3 4 5 6

x [mm

]

y [mm]

0 2 4 6 8 10 120

1

2

3

4

5

6

x [mm]

y [m

m]

0 2 4 6 8 10 120

1

2

3

4

5

6

x [mm]

y [m

m]

Representative

jagged spline

regions

0 1 2 3 4 5 6

12

10

8

6

4

2

00 2 4 6 8 10 12

0

1

2

3

4

5

6

x [mm]

y [m

m]


22


• Results:

- Qualitative comparison between piecewise cubic spline and fatigue crack damage shows good agreement

- Area is successfully approximated via cubic spline fitting

• Possible sources of error:

- Deep fatigue crack damage

- Weak crack edges

- Noise

A B C

Cubic

spline

Fatigue

crack

damage

Jagged

spline

regions

57

Figure 2.23: Cubic spline superimposed on the fatigue crack damage image for tibial insert 2. (A)

The fatigue crack damage area (enclosed in black rectangle) relative to the tibial insert. (B) A

magnified view of the fatigue crack damage region. (C) The cubic spline superimposed on the

fatigue crack damage image.

2.4 Discussion

This new method to quantify fatigue crack damage overcomes the reliance on subjective

identification of fatigue crack damage edges [13,18] and manual tracing techniques [13]. In

addition, the fatigue crack area is measured, which has not been done for existing techniques such

as SAT [21] and trans-illumination for qualitative evaluation [12]. The measured fatigue crack

damage area represents a quantitative result for comparing fatigue crack damage severity between

tibial insert specimens.

The measurement accuracy when using this technique is dependent on three primary

factors. First, if the fatigue crack damage plane is not parallel to the viewing plane during fatigue

crack damage image capture, the resulting area projection will underestimate the actual fatigue

crack damage area. The orientation of the fatigue crack damage plane relative to the viewing

plane in the two tibial inserts that we tested is unknown and warrants further investigation.

[1] Bartel, D. L., Bicknell, V. L., and Wright, T. M., 1986, “The effect of conformity, thickness, and material on stresses in ultra-high molecular weight

components for a total joint replacement,” J. Bone Joint Surg. Am., 68, pp. 1041–1051.


Overview





5. Conclusions

2

3

Finite element model

• Difficult to measure local stress in tibial insert during knee simulator

testing, so there is a need for simulation

• Apply loading and displacement conditions identical to knee

simulator to allow comparison to experimentally induced fatigue

crack damage

• Limit simulation to stance phase, during which axial force is

significantly higher (2 x body-weight) than during swing phase (~0 x

body-weight)

24

Stance Swing

0% 60% 100%

Finite element model (2)

• Many material models to describe constitutive UHMWPE behavior:

Linear elastic, J2-plasticity, viscoelastic, Hybrid model, etc.1

• We selected two models that used material parameters that could be

calculated from measured data from our specific UHMWPE or a

similar UHMWPE formulation:

1. Linear elastic (LE)

1. Linear viscoelastic (LVE)

where

25

s = Ee

G = ¢G + i ¢¢G

¢¢G =s

esind¢¢G =

s

ecosd and

[1] Kurtz, S. M., ed., 2009, UHMWPE Biomaterial Handbook: Ultra High Molecular Weight Polyethylene in Total Joint Replacement and Medical Devices,

Elsevier Academic Press, New York, New York.

• Initial course mesh:

- Rigid-body shell elements are used for femoral component since no stress

is calculated

- Solid quadratic tetrahedral elements are used for tibial insert – allow

deformation and stress calculation

- Mesh refinement is needed to obtain a converged stress solution


26

Quadrilateral

shell element

Triangular

shell element Tetrahedral solid element

Femoral component Tibial insert


• Convergence study using abbreviated trial, with convergence criteria:

1. Change in maximum von Mises stress magnitude: < 3% change for

doubled number of elements in contact region

2. Qualitative: are stress contours continuous?

3. Hertz approximation: ellipsoids approximate contacting condyles,

loaded with axial force that corresponds to maximum stress in FE model

under two contact conditions

27

Contact conditionHertz contact stress

[MPa]

Maximum von Mises stress

from finite element model

[MPa]

Single-condyle 53.5979.61

Double-condyle 42.54


28

Von Mises stress

[Pa]

+7.961e+07

+7.299e+07

+6.636e+07

+5.973e+07

+5.310e+07

+4.647e+07

+3.985e+07

+3.322e+07

+2.659e+07

+1.996e+07

+1.333e+07

+6.706e+06

+7.814e+04Tibial insert

Femoral component

Converged solution for abbreviated trial Converged solution mesh

n

n x

xSection n-n

x

y

z

y

z

• Once qualitative and quantitative criteria are met, the converged

solution tibial mesh is applied to the full length stance phase model

• Results of full-length, stance phase simulation:

- phase simulation


29

0 0.1 0.2 0.3 0.4 0.5 0.60

10

20

30

40

50

60

70

80

Time [seconds]

Vo

n M

ises

str

ess

[M

Pa]

Linear elastic model (LE)

Linear viscoelastic model (VE)

0 0.1 0.2 0.3 0.4 0.5 0.60

10

20

30

40

50

60

70

80

Time [seconds]

Von

Mis

es s

tres

s [

MP

a]



0 0.1 0.2 0.3 0.4 0.5 0.60

10

20

30

40

50

60

70

80

Time [seconds]

Vo

n M

ises

str

ess

[M

Pa]



0 0.1 0.2 0.3 0.4 0.5 0.60

10

20

30

40

50

60

70

80

Time [seconds]

Von

Mis

es s

tres

s [

MP

a]



LE: 79.82

VE: 79.75

LE: 51.38VE: 48.17

σy

σy

Linear elastic

Linear viscoelastic

- Stress in medial condyle

exceeds stress in lateral

condyle

- Yield stress is exceeded

during majority of stance

phase simulation

- Material model results for von

Mises stress maxima differ

throughout stance


30

• Difference in maximum von Mises stress magnitude between

simulations using linear elastic and linear viscoelastic models:

*Normalized to lateral condyle maximum

** Normalized to overall (both condyles) maximum

Medial condyle Lateral condyle

Maximum difference in maximum von Mises stress between linear elastic and linear viscoelastic material models[MPa]

4.38 10.12

Average difference in maximum von Mises stress over 0.61 s stance phase simulation between the two material models[MPa]

-0.17 0.96

Root mean square (RMS) difference in maximum von Mises stress over 0.61 s stance phase simulation between the two material models[MPa]

2.01 4.09

RMS difference as percentage of overall maximum subsurface von Mises stress [%]

2.52 % 7.96 % *

5.12 % **

• The locations of the maximum von Mises stress magnitude for each

of the 20 output frames are slightly different for simulations using

linear elastic versus linear viscoelastic model

• Lowest, highest maxima occur in similar locations for each

UHMWPE material model (within <1 mm) and follow a similar path

during the simulation (indicated by arrows in figure)


31

+79.90e+06

+75.40e+06

+70.92e+06

+66.43e+06

+61.94e+06

+57.46e+06

+52.97e+06

+48.45e+06

+43.99e+06

+39.50e+06

Maximum von

Mises stress

locations

Von Mises stress

[Pa]

LE model

+79.75e+06

+75.34e+06

+70.94e+06

+66.53e+06

+62.12e+06

+57.72e+06

+53.31e+06

+48.90e+06

+44.50e+06

+40.09e+06

Von Mises stress

[Pa]

LVE model

Linear elastic Linear viscoelastic


32

Number of occurrences of von Mises stress ≥ the yield stress in

single location

LE model LVE model

1 2 3 4 5 6 7 8+ 1 2 3 4 5 6 7 8+

Locations where the Von Mises stress exceeds the

UHWMPE yield stress for the linear elastic model (top

left), linear viscoelastic model (top right), and for both

models superimposed for comparison (bottom)

• The locations at which the von

Mises stress exceeds the yield

stress for each of the 20 output

frames overlaps by 81% between

simulations using linear elastic

and linear viscoelastic models

• LE versus LVE, overall: similar

magnitudes and locations for

maximum von Mises stress, but

differences demonstrate that

material model has a substantial

effect on UHMWPE response to

conditions imposed by the knee

simulator

Overview





5. Conclusions

3

3

34

Finite element model versus experimental results

+79.75e+06+75.34e+06+70.94e+06+66.53e+06+62.12e+06+57.72e+06+53.31e+06+48.90e+06+44.50e+06+40.09e+06

Experimentally measured fatigue

crack damage contour

Von Mises stress

[Pa]

Maximum von

Mises stress

locations

• How do the locations of maximum stress compare to the location of

fatigue crack damage?*

• Highest von Mises stress maxima are located away from (> 5mm

lateral to) fatigue crack damage

Linear viscoelastic

35

Medial

condyle

Experimentally measured

fatigue crack damage

contour

Number of occurrences of von Mises stress exceeds the yield stress in a single location

1 2 3 4 5 6 7 8+

LVE material

model

Finite element model versus experimental results (2)

• Fatigue crack damage occurs in locations where the von Mises

stress exceeds the yield stress, but does not occur in all locations

where the yield stress is exceeded

• There is a greater number of occurrences of von Mises stress that

exceeds the yield stress in locations with no fatigue crack damage

Linear viscoelastic

• High (tensile) principal stress maxima are located near fatigue crack

• Compressive principal stress:

• Tensile principal σ:


36

Compressive principal stress

[Pa]-1.65e+08-1.55e+08-1.45e+08-1.34e+08-1.24e+08-1.14e+08-1.04e+08-9.35e+07-8.33e+07-7.31e+07


fatigue crack damage contour

+1.40e+08+1.25e+08+1.10e+08+9.48e+07+7.97e+07+6.46e+07+4.96e+07+3.45e+07+1.94e+07+4.34e+06

Tensile principal stress

[Pa]

– Maxima located 6 – 10 mm

lateral to fatigue crack

damage

- Maxima clustered near (3 mm lateral, 2

mm anterior) posterior edge of fatigue

crack damage

- Substantially higher than maxima

elsewhere in condyle (80-140 MPa

versus 4-35 MPa)


37

Shear stress, x-z[Pa]

+2.06e+07+1.89e+07+1.73e+07+1.56e+07+1.40e+07+1.23e+07+1.06e+07+0.90e+06+0.73e+06+0.56e+06

Shear stress, y-z[Pa]

+2.65e+07+2.47e+07+2.30e+07+2.12e+07+1.95e+07+1.77e+07+1.60e+07+1.42e+07+1.25e+07+1.07e+07

Shear stress, x-y[Pa]

+4.98e+07+3.86e+07+3.60e+07+3.33e+07+3.07e+07+2.82e+07+2.54e+07+2.27e+07+2.01e+07+1.74e+07+1.48e+07


fatigue crack damage

contour

• High x-y and x-z shear stress

maxima are located near fatigue

crack damage

• x-y and x-z shear stress: - Maxima are clustered within ≤ 5

mm from the fatigue crack damage

• y-z shear stress: - Maxima are spread over the

posterior portion of medial condyle

Shear stress maxima for each output frame of the stance

phase simulation for the linear viscoelastic material model

with fatigue crack damage superimposed.

Overview





5. Conclusions

3

8

Conclusions

• Experimental (fatigue crack damage measurement):

1. Trans-illumination technique allows precise (1 mm2 resolution),

measurement of fatigue crack damage

2. Reduces subjectivity present compared to using other methods

(e.g. hand tracing)

3. Accuracy evaluated qualitatively only – would be beneficial to confirm

via other methods (micro-CT, thin-slice microscopy)

39

Conclusions (2)

• Finite element model:

1. Linear elastic, Linear viscoelastic material models result in different

von Mises stress results

• RMS difference of only ~3%, but maximum difference up to 21% (lateral

condyle)

• Material model is important for conditions seen in knee simulator testing

2. Von Mises stress maxima are insufficient for predicting fatigue crack

damage location

3. Maximum tensile stress, shear stress locations are predictive of the

location of fatigue crack damage

• Located < 3 mm and ≤ 5 mm respectively from experimentally

determined fatigue crack damage contour

40

quantifying fatigue cracking damage in polyethylene tibial

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