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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
http:
//up
load
.wik
imed
ia.o
rg/w
ikip
edia
/com
mon
s/f/
f2/O
penS
im_(
Leg)
.jpg
Pictures
http://nmbl.stanford.edu/research/models/upperextremity.htm
http://handsonhealingpt.com
http:
//w
ww
.max
shou
se.c
om/m
uscl
es_o
f_th
e_le
g_an
d_pa
w.h
tm