August 16, 2012

Elise H. E. Walker1,3

Thomas G. Sandercock2 Eric J. Perreault1,3

Influence of scaling assumptions on tendon stiffness

estimation

1BME @ Northwestern University 2Physio @ Northwestern University 3SMPP @ Rehabilitation Institute of Chicago

2

Why are tendon models so important?

MusculoskeletalModel

Muscle-TendonModel

TendonModel

stiffn

ess

3

0

1.0

3.5

0.0 0.033 0.10

(m/m)

=

1

37.5

Model 1: generic tendon curve

FE Zajac (1989). Crit Rev Biomed Eng 17(4).Figure 9B

𝑭 𝒐

𝑳𝑻

𝟑𝟕 .𝟓 ∙ 𝑭𝒐

𝑳𝑻⟹𝑲 𝑻

𝑳𝑻

𝑨𝑻

Model 2: architectural calculation of stiffness

4

Cui et al (2008). J Biomechanics 41.Equation 5

𝑬 ∙ 𝑨𝑻

𝑳𝑻⟹𝑲𝑻

5

Key model assumptions

How well does this assumption hold for diverse muscle-tendon units?

0

1.0

3.5

0.0 0.033 0.10

(m/m)

~𝝈 𝐓=~𝑭 𝐓

137.5

𝑬𝝈𝒐 ZAJAC

1200 MPa𝑬𝝈𝒐 32 MPa

𝑬 /𝝈𝒐 37.5

CUI

522 MPa

𝐅𝐨 /𝐀𝐓?

6

Methods: estimating stiffness

TendonStiffness

Muscle TendonUnit Stiffness

JointStiffness

1) Compile

3) Compare

2) Calculate

7

Predicting model performance

𝑬𝝈𝒐

0

1.0

3.5

0.0 0.033 0.10

(m/m)

~𝝈 𝐓=~𝑭 𝐓

137.5

SOL

66.6

PLA

44.2

FHL

29.2 𝟑𝟕 .𝟓𝑬𝝈𝒐

=¿

Zajac

¿𝑬

𝑭𝒐 /𝑨𝑻

8

Tendon stiffnessSOLPLAFHL Z

-40

0

FHL

% E

rror

PLA SOL

20

-20

40

60

-60

Tendon Stiffness Error

Cui Model

Zajac Model

Cui et al (2008). J Biomechanics 41. & Cui et al (2009). J Biomechanics 42.

9

Muscle-tendon stiffnessSOLPLAFHL Z

Cui et al (2008). J Biomechanics 41.

15

Mus

cle-

Tend

on S

tiffne

ss (N

/mm

)

Force (N)

10

5

20

00 20 40 5010 30

FHLSOLPLA

Cui Model

Zajac Model

Experimental Data

10

Joint stiffness

Cui Model

Zajac Model

Experimental Data300

Join

t Stiff

ness

(Nm

/rad

)

Knee Torque (Nm)

200

100

400

0

Knee Stiffness

0 20 40 60-20-40

Pfeifer et al (2012). IEEE Trans Biomed Eng.

11

𝑳𝑻

𝑨𝑻

Tendon models influence the results of biomechanical simulations.

Zajac model is useful if geometric parameters are not available.

With geometric parameters, we can predict Zajac error with E/stress.

Improved accuracy with Cui’s model when architecture is available.

Take Home Message

SOL

PLA

FHL

Z

12

Co-authors: Eric Perreault Tom Sandercock

A big THANK YOU to…

Former lab members: Lei Cui Xiao Hu Serge Pfeifer

13

Questions?

14

http://handsonhealingpt.com http://www.eorthopod.com/content/hamstring-tendon-graft-reconstruction-acl

http://www.total-physio.com

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Pictures

http://nmbl.stanford.edu/research/models/upperextremity.htm

http://handsonhealingpt.com

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